ME 322 - Mechanical Design 1 Partial notes Part 4...

1

ME 322 - Mechanical Design 1

Partial notes ndash Part 4 (Fatigue)

2

Ni =

Np =

NT =

Metal Fatigue is a process which causes premature irreversible damage or

failure of a component subjected to repeated loading

FATIGUE - What is it

3

Metallic Fatigue

bull A sequence of several very complex phenomena encompassing several disciplines

ndash motion of dislocations

ndash surface phenomena

ndash fracture mechanics

ndash stress analysis

ndash probability and statistics

bull Begins as an consequence of reversed plastic deformation within a single crystallite but ultimately may cause the destruction of the entire component

bull Influenced by a componentrsquos environment

bull Takes many forms

ndash fatigue at notches

ndash rolling contact fatigue

ndash fretting fatigue

ndash corrosion fatigue

ndash creep-fatigue

Fatigue is not cause of failure per se but leads to the final fracture event

4

The Broad Field of Fracture Mechanics

5

Intrusions and Extrusions The Early Stages of Fatigue Crack Formation

6

Locally the crack grows in shear

macroscopically it grows in tension

Δσ

Δσ

c

Schematic of Fatigue Crack Initiation Subsequent Growth

Corresponding and Transition From Mode II to Mode I

7

The Process of Fatigue

The Materials Science Perspective bull Cyclic slip

bull Fatigue crack initiation

bull Stage I fatigue crack growth

bull Stage II fatigue crack growth

bull Brittle fracture or ductile rupture

8

Features of the Fatigue Fracture Surface of a Typical

Ductile Metal Subjected to Variable Amplitude Cyclic

Loading

(Collins ref 22 )

A ndash fatigue crack area

B ndash area of the final static

failure

9

Appearance of Failure Surfaces Caused by

Various Modes of Loading (SAE Handbook)

10

Factors Influencing Fatigue Life

Applied Stresses

bull Stress range ndash The basic cause of plastic deformation and consequently the accumulation of damage

bull Mean stress ndash Tensile mean and residual stresses aid to the formation and growth of fatigue cracks

bull Stress gradients ndash Bending is a more favorable loading mode than axial loading because in bending fatigue cracks propagate into the region of lower stresses

Materials

bull Tensile and yield strength ndash Higher strength materials resist plastic deformation and hence have a higher fatigue strength at long lives Most ductile materials perform better at short lives

bull Quality of material ndash Metallurgical defects such as inclusions seams internal tears and segregated elements can initiate fatigue cracks

bull Temperature ndash Temperature usually changes the yield and tensile strength resulting in the change of fatigue resistance (high temperature decreases fatigue resistance)

bull Frequency (rate of straining) ndash At high frequencies the metal component may be self-heated

11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis

Allowable Load - Fatigue Life

Material

Properties

Information path in strength and fatigue life prediction

procedures

Strength-Fatigue Analysis Procedure

12

Stress Parameters Used in Static Strength and

Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13

Constant and Variable Amplitude Stress Histories

Definition of a Stress Cycle amp Stress Reversal

One

cycle

m

max

min

Str

es

s

Time 0

Constant amplitude stress history a)

Str

es

s

Time

0

Variable amplitude stress history

One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R

In the case of the peak stress history

the important parameters are

14

Str

ess

Time

Stress history Rainflow counted cycles

i-1

i-2

i+1

i

i+2

Stress History and the ldquoRainflowrdquo Counted Cycles

1 1i i i iABS ABS

A rainflow counted cycle is identified when any two adjacent reversals in thee

stress history satisfy the following relation

15



1 1i i i iABS ABS

The stress amplitude of such a cycle is

1

2

i i

a

ABS

The stress range of such a cycle is

1i iABS

The mean stress of such a cycle is

1

2

i im

The Mathematics of the Cycle Rainflow Counting Method

for Fatigue Analysis of StressLoad Histories

16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting

Procedure (N Dowling ref 2)

22

The Fatigue S-N method (Nominal Stress Approach)

bull The principles of the S-N approach (the nominal stress method)

bull Fatigue damage accumulation

bull Significance of geometry (notches) and stress analysis in fatigue

evaluations of engineering structures

bull

bull Fatigue life prediction in the design process

23

A B

Note In the case of smooth

components such as the

railway axle the nominal stress

and the local peak stress are

the same

peakS

Smin

Smax

Woumlhlerrsquos Fatigue Test

24

Characteristic parameters of the S - N curve are

Se - fatigue limit corresponding to N = 1 or 2106 cycles for

steels and N = 108 cycles for aluminum alloys

S103 - fully reversed stress amplitude corresponding to N = 103

cycles

m - slope of the high cycle regime curve (Part 2)

Fully reversed axial S-N curve for AISI 4130 steel Note the break at the LCFHCF transition and

the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se

Part 1 Part 2 Part 3

Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25

Most of available S - N fatigue data has been obtained from fully reversed rotational bending tests

However material behavior and the resultant S - N curves are different for different types of loading

It concerns in particular the fatigue limit Se

The stress endurance limit Se of steels (at 106 cycles) and the fatigue strength S103 corresponding

to 103 cycles for three types of loading can be approximated as (ref 1 23 24)

S103 = 090Su and Se = S106 = 05 Su - bending

S103 = 075Su and Se = S106 = 035 - 045Su - axial

S103 = 072Su and Se = S106 = 029 Su - torsion

103 104

105 106 107

01

03

05

10

S103

Se

Number of cycles Log(N)

Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26

Approximate endurance limit for various materials

Magnesium alloys (at 108 cycles) Se = 035Su

Copper alloys (at 108 cycles) 025Sult Se lt050Su

Nickel alloys (at 108 cycles) 035Su ltSe lt 050Su

Titanium alloys (at 107 cycles) 045Su ltSelt 065Su

Al alloys (at 5x108 cycles) Se = 045Su (if Su le 48 ksi) or Se = 19 ksi (if Sugt 48 ksi)

Steels (at 106 cycles) Se = 05Su (if Su le 200 ksi) or Se = 100 ksi (if Sugt200 ksi)

Irons (at 106 cycles) Se = 04Su (if Su le 60 ksi) or Se = 24 ksi (if Sugt 60 ksi)

S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A

a aS C N or N C S C S

SSm and A

S S

N

27

Fatigue Limit ndash Modifying Factors

For many years the emphasis of most fatigue testing was to gain

an empirical understanding of the effects of various factors on

the base-line S-N curves for ferrous alloys in the intermediate

to long life ranges The variables investigated include

- Rotational bending fatigue limit Sersquo

- Surface conditions ka

- Size kb

- Mode of loading kc Se = ka kb kc kd ke kfmiddotSersquo

- Temperature kd

- Reliability factor ke

- Miscellaneous effects (notch) kf

Fatigue limit of a machine

part Se

28

Ca

Effect of various surface finishes

on the fatigue limit of steel

Shown are values of the ka the

ratio of the fatigue limit to that

for polished specimens

Below a generalized empirical graph

is shown which can be used to

estimate the effect of surface finish

in comparison with mirror-polished

specimens [Shigley (23) Juvinal

(24) Bannantine (1) and other

textbooks]

Surface Finish Effects on Fatigue Endurance Limit

The scratches pits and machining marks on the surface of a material add stress concentrations to the

ones already present due to component geometry The correction factor for surface finish is sometimes

presented on graphs that use a qualitative description of surface finish such as ldquopolishedrdquo or ldquomachinedrdquo

(from J Bannantine ref1)

ka

29

Size Effects on Endurance Limit Fatigue is controlled by the weakest link of the material with the probability of existence (or density) of a

weak link increasing with material volume The size effect has been correlated with the thin layer of

surface material subjected to 95 or more of the maximum surface stress

There are many empirical fits to the size effect data A fairly conservative one is

bull The size effect is seen mainly at very long lives

bull The effect is small in diameters up to 20 in (even in bending and torsion)

Stress effects in non-circular cross section members

In the case of non-circular members the approach is based on so called effective diameter de

The effective diameter de for non-circular cross sections is obtained by equating the volume of material

stressed at and above 95 of the maximum stress to the same volume in the rotating-bending

specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2

The material volume subjected to stresses

095max is concentrated in the ring of

005d2 thick

The surface area of such a ring is

max

22 2

095 095 007664

A d d d

The effective diameter de for members

with non-circular cross sections

rectangular cross section under bending

F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31

Loading Effects on Endurance Limit

The ratio of endurance limits for a material found using axial and rotating

bending tests ranges from 06 to 09

The ratio of endurance limits found using torsion and rotating bending tests

ranges from 05 to 06 A theoretical value obtained from von Mises-Huber-

Hencky failure criterion is been used as the most popular estimate

( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S

suggested by Shigl y kek

( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S

suggested by Shigl kek y

32

From Shigley and Mischke Mechanical Engineering Design 2001

u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33

Reliability factor ke

The reliability factor accounts for the scatter of reference data such

as the rotational bending fatigue limit Sersquo

The estimation of the reliability factor is based on the assumption that

the scatter can be approximated by the normal statistical probability

density distribution

1 008ae

zk

The values of parameter za associated with various levels of

reliability can be found in Table 7-7 in the textbook by Shigley etal

34

(source S Nishijima ref 39)

S-N curves for assigned probability of failure P - S - N curves

35

Stress concentration factor Kt and the

notch factor effect kf

Fatigue notch factor effect kf depends on the stress

concentration factor Kt (geometry) scale and material

properties and it is expressed in terms of the Fatigue Notch

Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D

Stresses in axisymmetric

notched body

n

peak

t n

FS

A

and

K

37

Stresses in prismatic notched body

n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38

Stress concentration factors used in fatigue

analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39

Stress concentration

factors Kt in shafts

Bending load

Axial load

S =

S =

40

S =

41

Similarities and differences between the stress field near the notch

and in a smooth specimen

x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42

The Notch Effect in Terms of the Nominal Stress

np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf

K Fatigue notch factor

43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK

Definition of the fatigue notch factor Kf

1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant

r ndash notch tip radius

11

1

tf

KK

rr

NEUBERrsquos approach

ρ ndash constant


18

330010

u

u

a inS

for S in in

45

The Neuber constant lsquoρrsquo for steels and aluminium alloys

46

Curves of notch sensitivity index lsquoqrsquo versus notch radius

(McGraw Hill Book Co from ref 1)

47

Plate 1 W1 = 50 in d1 = 05 in Su = 100 ksi Kt = 27 q = 097 Kf1 = 265

Illustration of the notchscale effect

Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48

Procedures for construction of approximate fully reversed

S-N curves for smooth and notched components

Nf (logartmic)

JuvinalShigley method

Nf (logartmic)

Collins method

Sar ar ndash nominallocal

stress amplitude at zero

mean stress m=0 (fully

reversed cycle)

frsquo

49



Sar ar ndash nominallocal stress amplitude at zero mean stress m=0

(fully reversed cycle)

Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE

bull The empirical relationships concerning the S ndashN curve data are

only estimates Depending on the acceptable level of uncertainty

in the fatigue design actual test data may be necessary

bull The most useful concept of the S - N method is the endurance

limit which is used in ldquoinfinite-liferdquo or ldquosafe stressrdquo design

philosophy

bull In general the S ndash N approach should not be used to estimate

lives below 1000 cycles (N lt 1000)

51

Constant amplitude cyclic stress histories

Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0

No of cycles logN 2106

Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53

The tensile mean stress is in general detrimental while the compressive mean stress is beneficial or

has negligible effect on the fatigue durability

Because most of the S ndash N data used in analyses was produced under zero mean stress (R = -1)

therefore it is necessary to translate cycles with non- zero mean stress into equivalent cycles with

zero mean stress producing the same fatigue life

There are several empirical methods used in practice

The Hiagh diagram was one of the first concepts where the mean stress effect could be accounted

for The procedure is based on a family of Sa ndash Sm curves obtained for various fatigue lives

Steel AISI 4340

Sy = 147 ksi (Collins)

54

Mean Stress Correction for Endurance Limit

Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1

Sa ndash stress amplitude

applied at the mean

stress Smne 0 and fatigue

life N = 1-2x106cycles

Sm- mean stress

Se- fatigue limit at Sm=0

Su- ultimate strength

frsquo- true stress at fracture

55

Mean stress correction for arbitrary stress

amplitude applied at non-zero mean stress

Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S

Soderberg (1930) 1a m

ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and

resulting in fatigue life of

N cycles

Sm- mean stress

Sar- fully reversed stress

amplitude applied at

mean stress Sm=0 and

resulting in the same

fatigue life of N cycles



56

Comparison of various

methods of accounting

for the mean stress effect

Most of the experimental data lies between the Goodman and the yield line

57

Approximate Goodmanrsquos diagrams for ductile

and brittle materials

Kf

Kf

Kf

58

The following generalisations can be made when discussing

mean stress effects

1 The Soumlderberg method is very conservative and seldom used

3 Actual test data tend to fall between the Goodman and Gerber curves

3 For hard steels (ie brittle) where the ultimate strength approaches the

true fracture stress the Morrow and Goodman lines are essentially the

same For ductile steels (of gt S) the Morrow line predicts less

sensitivity to mean stress

4 For most fatigue design situations R lt 1 (ie small mean stress in

relation to alternating stress) there is little difference in the theories

5 In the range where the theories show a large difference (ie R values

approaching 1) there is little experimental data In this region the yield

criterion may set design limits

6 The mean stress correction methods have been developed mainly for the

cases of tensile mean stress

For finite-life calculations the endurance limit in any of the equations can be

replaced with a fully reversed alternating stress level corresponding to that

finite-life value

59

Procedure for Fatigue Damage Calculation

NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i

n cycles applied atn cycles applied at n cycles applied atD

N cycles to failure at N cycles to failure at N cycles to failure at

n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60

n1 - number of cycles of stress range 1


ni - number of cycles of stress range i

1

1

1D

N - damage induced by one cycle of stress range 1

11

1

n

nD

N - damage induced by n1 cycles of stress range 1

2

2

1D


22

2

n

nD


1i

i

DN

- damage induced by one cycle of stress range i

ini

i

nD

N - damage induced by ni cycles of stress range i

61

Total Damage Induced by the Stress History

1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i

n cyclesapplied atn cyclesapplied at n cyclesapplied atD


n nn nD D D D

N N N N

It is usually assumed that fatigue failure occurs when the cumulative damage

exceeds some critical value such as D =1

ie if D gt 1 - fatigue failure occurs

For D lt 1 we can determine the remaining fatigue life

1 1 2 2

1 1

R

i i

LD n N n N n N

LR - number of repetitions of

the stress history to failure

1 2 3

R iN L n n n n N - total number of cycles to failure

62

jN = a

m

j

if j gt e

It is assumed that stress cycles lower than the fatigue limit j lt e produce no damage (Nj=) in

the case of constant amplitude loading however in the case of variable amplitude loading the extension of the S-N curve with the slope lsquom+2rdquo is recommended The total damage produced by the entire stress spectrum is equal to

1

j

jj

D D

It is assumed that the component fails if the damage is equal to or exceeds unity ie when D 1

This may happen after a certain number of repetitions BL (blocks) of the stress spectrum which can be calculated as

BL = 1D

Hence the fatigue life of a component in cycles can be calculated as

N = BLNT where NT is the spectrum volume or the number of cycles extracted from given stress history

NT = (NOP - 1)2

If the record time of the stress history or the stress spectrum is equal to Tr the fatigue life can be expressed in working hours as

T = BL Tr

63

Main Steps in the S-N Fatigue Life Estimation Procedure

bull Analysis of external forces acting on the structure and the component in question

bull Analysis of internal loads in chosen cross section of a component

bull Selection of individual notched component in the structure

bull Selection (from ready made family of S-N curves) or construction of S-N curve adequate for given notched element (corrected for all effects)

bull Identification of the stress parameter used for the determination of the S-N curve (nominalreference stress)

bull Determination of analogous stress parameter for the actual element in the structure as described above

bull Identification of appropriate stress history

bull Extraction of stress cycles (rainflow counting) from the stress history

bull Calculation of fatigue damage

bull Fatigue damage summation (Miner- Palmgren hypothesis)

bull Determination of fatigue life in terms of number of stress history repetitions Nblck (No of blocks) or the number of cycles to failure N

bull The procedure has to be repeated several times if multiple stress concentrations or critical locations are found in a component or structure

64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2

An unnotched machine component undergoes a variable amplitude

stress history Si given below The component is made from a steel

with the ultimate strength Suts=150 ksi the endurance limit

Se=60 ksi and the fully reversed stress amplitude at N1000=1000

cycles given as S1000=110 ksi

Determine the expected fatigue life of the component

Data Kt=1 SY=100 ksi Suts=150 ksi Se=60 ksi S1000=110 ksi

The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts

S S Sfor fatigue endurance S S

S S S

S S Sfor any stress amplitude S

SS S

S

69

Calculations of Fatigue Damage

a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70

Results of rainflow counting D a m a g e

No S S m S a S ar (Sm=0) D i =1N i =1CS a -m

1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

2

Ni =

Np =

NT =

Metal Fatigue is a process which causes premature irreversible damage or

failure of a component subjected to repeated loading

FATIGUE - What is it

3

Metallic Fatigue














ndash creep-fatigue


4


5


6



Δσ

Δσ

c



7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

3

Metallic Fatigue














ndash creep-fatigue


4


5


6



Δσ

Δσ

c



7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

4


5


6



Δσ

Δσ

c



7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

5


6



Δσ

Δσ

c



7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

6



Δσ

Δσ

c



7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

7







8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

8



Loading

(Collins ref 22 )



failure

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

9



10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

10


Applied Stresses




Materials





11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

11

Component

Geometry

Loading

History

Stress-Strain

Analysis

Damage

Analysis


Material

Properties


procedures


12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

12


Fatigue Analyses

peak

t

n

peak

K

S

n

y

dn

0

T

r

peak

Str

ess

M

b) a)

n

y

dn

0

T

r

peak

Str

ess

S

S

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

13



One

cycle

m

max

min

Str

es

s

Time 0


Str

es

s

Time

0


One

reversal

b)

max min

max mi

max min

mi

max

n

n

2 2

2

peak peak peak

peak peak

peak peak

peak

m

peak

pe

peakpe

ak

ak

a

R



14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

14

Str

ess

Time


i-1

i-2

i+1

i

i+2


1 1i i i iABS ABS



15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

15



1 1i i i iABS ABS


1

2

i i

a

ABS


1i iABS


1

2

i im



16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

16

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

17

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

18

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

19

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

20

Stress History

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Str

es

s (

MP

a)x

10

2

-3

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Reversal point No

Str

es

s (

MP

a)x

10

2

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

21

Number of Cycles

According to the

Rainflow Counting


22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

22






bull


23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

23

A B





the same

peakS

Smin

Smax


24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

24





cycles



the endurance limit

Number of cycles N

Str

ess a

mp

litu

de

S

a (

ksi)

Sy

Se


Infinite life

Su

S103

10m A m

aS C N N

Fatigue S-N curve

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

25









103 104

105 106 107

01

03

05

10

S103

Se


Re

lative

str

ess a

mp

litu

de

S

aS

u

Torsion

Axial Bending

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

26









S ndash N curve

33

1 1 1

2

10101log lo

0

g

1

3

A

m mm ma

m m

e e

A


SSm and A

S S

N

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

27








- Size kb


- Temperature kd




part Se

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

28

Ca












textbooks]






ka

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

29











specimen

0097

0097

1 03

0869 03 100

10 8

1189 8 250

b

b

e

e

e

e

if d inS

S d if in d in

or

if d mmS

S d if d mm

k

k

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

30

+

-

095max

max

005d2



005d2 thick


max

22 2

095 095 007664

A d d d




F

09

5t

t

Equivalent diameter

max095 095 005

A Ft

A Ft t Ft

200766 005

0808

e

e

d Ft

d Ft

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

31







( ) ( )(07 09)

07 09 ( 085)c

e axial e bendi

c

ngS S


( ) ( )0577

057( 059)

e torsion e bendi

c

ng

c

S


32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

32


u T u T

e RT e RT

u RT u R

d

T

e T dS

S SS S

Sk

Sk

Temperature Effect

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

33







1 008ae

zk



34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

34



35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

35






Factor Kf

1f

f

kK

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

36

1

peak

n

2

2

11

3

3

3

2

A D B

C

F

F

2

2

2

2

2

2

3

3

3

3

11

C

A B

D


notched body

n

peak

t n

FS

A

and

K

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

37


n

peak

t n

t

FS

A

and

K

K S

A

B C

2

2

2

2

2

2

3

3

D

E

11

peak

n

2

2

11

3

3 3

2

A D B

C

F

F

1

E

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

38


analysis

peak

t

n

peak

K

S

n S

x

dn

0

W

r

peak

Str

ess

S

n

x

dn

0

W

r

Str

ess

M

peak

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

39



Bending load

Axial load

S =

S =

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

40

S =

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

41



x

dn

0

W

r

peak S

tres

s

S

n=S peak= n=S

P

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

42


np

n1

S2

cycles N0 N2

Sesmooth

N (S)m = C

S

max

Str

ess r

an

ge

S

n2

n3

n4 notched

smooth

e

e

f

SS

K

S

f t

K Kf


43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

43

1

2

3

Nsm

ooth

22

peak

smooth

e

peak

Str

ess

1

2

Nnotched

notched

e

M

notched

f notched

smooth

smoo he

e

tfo NNrK


1

22= peak

Str

ess

2

Nnotched

notched

e

S

Se

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

44

1

1 1 11

tf t

KK q K

a r

1

1q

a r

PETERSONs approach

a ndash constant


11

1

tf

KK

rr


ρ ndash constant


18

330010

u

u

a inS

for S in in

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

45


46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

46



47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

47



Plate 2

W2= 05 in

d2 = 05 i

Su = 100 ksi

Kt = 27

q = 078

Kf1 = 232

pea

k

m1

r d1

W1

pea

k

r

d2

W2

m2

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

48



Nf (logartmic)


Nf (logartmic)

Collins method




reversed cycle)

frsquo

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

49





Sar (l

og

art

mic

)

Nf (logartmic)

Manson method 09Su

100 101 102 103 104 105 106 2106

Sersquokakckbkdke

Sersquokakckbkdkekf

Se

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

50

NOTE






philosophy



51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

51


Fully reversed

m = 0 R = -1

Pulsating

m = a R = 0

Cyclic

m gt 0 R gt 0

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

52

Mean Stress Effect

smlt 0

sm= 0

smgt 0


Str

ess a

mplit

ude lo

gS

a

time

smlt 0

sm= 0

smgt 0

Str

ess a

mplit

ude S

a

0

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

53









Steel AISI 4340


54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

54


Gereber (1874) S

S

S

S

a

e

m

u

2

1

Goodman (1899)

S

S

S

S

a

e

m

u

1

Soderberg (1930) S

S

S

S

a

e

m

y

1

Morrow (1960)

S

S

Sa

e

m

f

1


applied at the mean



Sm- mean stress




55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

55



Gereber (1874)

2

1a m

ar u

S S

S S

Goodman (1899) 1a m

ar u

S S

S S


ar y

S S

S S

Morrow (1960)

1a m

ar f

S S

S


applied at the mean

stress Smne 0 and


N cycles

Sm- mean stress








56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

56





57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

57



Kf

Kf

Kf

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

58


mean stress effects
















finite-life value

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

59


NT

n 1

n 2

n 3

n 4

c y c l e s

e

N o N 2

e

Ni(i)m = a

2

N1 N3

1

3

Str

ess r

an

ge

1 1 2 2

1 1 2 2

1 21 2

11 2

i i

i i

i

i in n ni

i i



n nn nD D D D

N N N N

1 1 2 2

1 1

R

i i

LD n N n N n N

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

60




1

1

1D


11

1

n

nD


2

2

1D


22

2

n

nD


1i

i

DN


ini

i

nD


61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

61


1 1 2 2

1 1 2 2

1 2

1 211 2

i i

i i

ii i

n n ni

i i



n nn nD D D D

N N N N





1 1 2 2

1 1

R

i i

LD n N n N n N



1 2 3


62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

62

jN = a

m

j

if j gt e



1

j

jj

D D



BL = 1D



NT = (NOP - 1)2


T = BL Tr

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

63














64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

64

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

65

Stress History

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 5 10 15 20 25 30 35

Reversal point No

Str

ess (

ksi)

Example 2








The stress history

Si = 0 20 -10 50 10 60 30 100 -70 -20 -60 -40 -80 70 -30

20 -10 90 -40 10 -30 -10 -70 -40 -90 80 -20 10 -20 10 0

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

66

411108861

log60log6

log110log3

log60log10log

log110log1000log

logloglog

26

6

mC

Cm

Cm

Cm

Cm

CSmN

CSN

a

m

a

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

67

S-N Curve

10

100

1000

1000 10000 100000 1000000 10000000

No of cycles

Str

es

s a

mp

litu

de

(k

si)

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

68

Goodman Diagram

0

10

20

30

40

50

60

70

80

90

100

-100 -50 0 50 100 150

Mean stress (ksi)

Str

es

s a

mp

litu

de

(k

si)

SY

Suts

1

0

0

1 1

1

1

m

m

a m maa r at S

e uts uts

a m a

a r at Sma r uts

uts


S S S


SS S

S

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

69


a) Cycle No11

Sar=8793 ksi

N11= C( SaN)-m= 186610268793-114=12805 cycles

D11=0000078093

b) Cycle No 14

Sar=750 ksi

N14= C( SaN)-m= 18661026750-114=78561 cycles

D14=0000012729

c) Cycle no 15

Sar=9828 ksi

N14= C( SaN)-m= 186610269828-114=3606 cycles

D14=000027732

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

70



1 30 5 15 1552 20155E-13 0

2 40 30 20 2500 46303E-11 0

3 30 45 15 2143 79875E-12 0

4 20 -50 10 1000 13461E-15 0

5 50 -45 25 2500 46303E-11 0

6 30 5 15 1552 20155E-13 0

7 100 20 50 5769 63949E-07 0

8 20 -20 10 1000 13461E-15 0

9 30 -25 15 1500 13694E-13 0

10 30 -55 15 1500 13694E-13 0

11 170 5 85 8793 78039E-05 780E-05

12 30 -5 15 1500 13694E-13 0

13 30 -5 15 1500 13694E-13 0

14 140 10 70 7500 12729E-05 127E-05

15 190 5 95 9828 000027732 0000277

n 0 =15 D = 000036873 3677E-04

D=0000370 D=3677E-04

L R = 1D =271203 L R = 1D =271961

N=n 0 L R =15271203=40680 N=n 0 L R =15271961=40794

Date post:	08-Aug-2020
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ME 322 - Mechanical Design 1 Partial notes Part 4...

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