Dynamics Fatigue Failure Due to Variable Loading

7/28/2019 Dynamics Fatigue Failure Due to Variable Loading

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Fatigue Failure Due toVariable Loading

Section V


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2

Variable Loading?

What have we been ignoring?

How rate the lifetime of fatigue or cyclic loadedparts?

Endurance Limit

Estimating Fatigue Life

Determining the Endurance Limit

Characterizing Fluctuating Stress

Fatigue Failure Criterion Graphically

Talking Points


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3

In many actual life applications, some machine members aresubjected to stresses fluctuating between levels.

Often, machine members are found to fail under the action ofthese repeated or fluctuated stresses.

Most careful analysis reveals that the actual maximumstresses were below the ultimate strength of the material, andquite frequently even below the yield strength.

The most distinguishing characteristic of these failures is thatthe stresses have been repeated a very large number oftimes.

This type of failure is called fatigue failure.

Variable Loading?


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What have we been ignoring?

Suppose the countershaftis rotating Static

Dynamic Is fatigue an issue?

What type of stresscondition do we now have

if the shaft is rotating andthe loads remain in a fixeddirection?


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Reversed Bending

As the shaft rotatesthe stress alternatesbetween Tension @ C

Compression @ D

Shaft rotates 180

degrees Tension @ D

Compression @ C

C

D

D

C


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Reversed Bending - Fatigue Common indications of

reverse bending

fatigue Beach Marks

Dark areas indicated inthis figure are

representative ofabrupt or fastfracture

STRESS PATTERNS FOR

REVERSE BENDING


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Unidirection Bending

What does each Beach markrepresent? Crackslowlypropagated and

then stops Illustrates how the crack front

propagates thru the cross-section

Failure in a threaded rod orbolt due to unidirectionalbending Rough area representing fast

fracture

Common Fatigue Patterns


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What type of loading caused

this failure? Fast fractureCrack grew from

the center outward

UNIAXIAL TENSILE LOADING


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How rate the lifetime of

fatigue or cyclic loaded parts? Strain Life

Ideal for low cycle fatigueapplications

1N10

3

, where N is the number ofloading cycles

Based on the plasticity at localizedregions of the part

Method is typically not practical fordesign use because it requires

knowledge of strain concentrationlevels, pages 316 to 317

Fracture Mechanics Approach Requires the assumption of a pre-

existing crack

Used to predict growth of the

crack with respect to a specifiedlevel of stress intensity

Pages 319 to 323

Stress Life High fatigue life calculations

10^3N106

Large amounts of data

Widely used

Covered in this course


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Endurance Limit Is a stress level in a material that can withstand an infinitenumber

of loading cycles.

In your text andthroughout literature on the subject, the endurancelimit is typically referenced by Se.

To determine the endurance limit we use a S-N curve Always plotted on Log-Log Scale

Se

S - Strength of the material

N - Number of cycles executed

N=1 - cycle represents a loadapplication in one direction,

removal, and then once again inthe opposite direction

Knee of the S-N Curve


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Estimating Fatigue Life Approximating fatigue

103N106

Just as we saw the linearbehavior of true stress-strainwhen plotted on log scale, thedata tends to follow apiecewise linear function.

We will use this same principalto develop a power-law for

estimating points in the highcycleregion on the S-Ndiagram.

Sf

aN

b

6

3

6

6

3

6

3

6

10

2

1010

10

10

10

10

6

10

1000

logloglog2

gives....)(intongSubstituti

log3

1log

3

1

gives....equationstwothesegSubtractin

)(610loglog

)(31000loglog

intercepttheisandslopetheiswhere

loglog

S

SS

S

SC

b

S

fS

S

Sb

CbCbS

CbCbS

Cb

CNbS

e

ut

f

e

ut

S

fS

S

S

a

2

10

2

10

6

3

C

log10(a)

Finally resulting in


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Determining the Endurance

Limit A rotary device serves as an excellent means of

acquiring such data in a timely manner. Several thousand cycles can be executed rather quickly

Below is a sketch of a simple apparatus that can beused to determine the value of the endurance limit.


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Much Endurance Data on record

isfor steels Mischke, one of the authors of the

text has actually done anextensive study in this area andhas determined that the

endurance limit of the material. Steels

It is important to note thatthese estimates are forclean, highlypolishedspecimens that are free ofsurface defects.

Se

0.504Sut, ksi or MPaSut 212 ksi (1460 MPa

107 ksi Sut 212 ksi

740 MPa Sut 1460 MPa

Your text emphasizesthis point bythe inclusion of a primemark

above the endurance limit symbol.


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Endurance Limit (EL) Modifying

Factors Factors that can reduce the

EL: Surface condition, (ka)

Size factor, (kb) Load factor, (kc)

Temperature, (kd)

Reliability factor, (ke)

Miscellaneous-effects factor,

(kf) These factors are used to adjust

the endurance limit obtained fromrotating beam specimens.

Se kakbkckdkekf SeModified EL - Marins Equation

Now we will discuss how toeffectively estimate these modification

factors.


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Surface Factor, ka Mischke performed a

regression analysis toapproximate the surface factor

The surface factor, ka, takesthe following form:

where Sut is the minimumtensile strength and a and bare found from the table

ka aSutb


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Size Factor, kb Once again Mischke has provided

a means for estimating the ELsize modification factor

The size factor arises because ofthe geometry of the specimenused to obtain the endurancelimit

Diameter 0.30 in.

Extruded or drawn bar stock Grain elongation in the direction

perpendicular to fatigue crackgrowth

Likelihood of surface flaws is low

kb

0.879d0.107 0.11 d 2 in.

0.91d0157 2< d 10 in.

1.24d0.107 2.79 d 51 mm

1.51d0.157 51< d 254 mm.

For larger parts are more likely tocontain flaws which can result in

premature material failure

For axially loaded specimens thesize factor is one.

Effective circular cross-section may becomputed for non-circular geometry (see

Table 7-5.)


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Loading Factor, kc Since the usual test used to obtain the EL is the reversed

bending load, modification factors are needed.

Some texts on this subject do not include this factor and

require the user to implement an estimation in the ELinstead.

kc

1 bendin

0.85 axial

0.59 torsion

Se

0.50Su bendin

0.45Su axial

0.29Su torsion


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Temperature, Reliability andMiscellaneous Factors

Temperature isrelatively simple tocompute and

understand

Reliability Factor

Will not be covered indetail in this course

Extensive, throughcoverage is given to thisfactor in the text Statistics background is

required

Miscellaneouseffects

Corrosion Manufacturing

process

Residual stresses

Coatings All of which can have

an adverse effect onthe EL

kd STSRT

where ST and SRT are the tensile strength

at the operating and room temperatures respectively.


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Characterizing FluctuatingStress

Fatigue loading is oftentimescaused by a variable loadingsource.

To develop failure criterion forfluctuating stresses, which causefatigue failures, we mustcharacterize how the stress levels

vary as time.

Sinusoidal stress oscillating

about a static stress

Repeated Stress

Completely reversed stress

a

max min2

m max min

2


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Fatigue Failure Criterion Gerber

Modified Goodman

Soderberga

Se

m

Sy

1

n

a

Se

m

Sut

1

n

na

Se

nm

Sut

2

1


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Fatigue Failure CriterionGraphically

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Dynamics Fatigue Failure Due to Variable Loading

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