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5. Fatigue of steel structuresFatigue loading, Whlers approach and fracture mechanics, fatigue strength,influence of notches, damage accumulation, Eurocode approach.

Damage due to fatigue occurs when loading is markedly varying in time.

Resistance R decreases due to:- initiation of cracks,- cracks growth.

Fatigue limit state (in general): )Tmin()Tmax( RF (valid for given time T)for required probabilities p

S0

T0

STR decreases with time

MSFmax = Rmin

loadingF,resistanceR

reliabilityS [ % ]

timeT

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Fatigue tests (see mechanical tests of material, bachelor course)

low-cycle fatigue (< about 50 000 cycles, plastic behaviour)

multi-cycle fatigue (elastic behaviour)

design fatigue strength curve e.g. for surviving

with probability of p = 95 %

(hyperbola)

time strength"(for Ni cycles)

cut-off limit(permanent

fatigue strength) Ni [ N ] number of cycles up to damage

Whlers curve

1 cycle

stress range

N cycles (time)

regimes:

pulsating tension

alternating loading

pulsating compression

+

+-

-

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Whlers curve in log coordinates (S-N curves, stress-number of cycles curves):

Usually expressed in the form:

i.e.m

a

N= logloglog maN

log

log N

N=210

6

N=510

6

N=110

8

bilinear

trilinear

designationof category

C

Fatigue is predominantly investigated experimentally.Cardinal difference is in behaviour of:

Machined specimen (e.g. as in tensile test):- decisive is initiation of cracks (due to pores, defects): important for

mechanical elements.

Real steel structure (e.g. various welded pieces):- time to initiation of cracks is very short,- fatigue strength (R) is given especially by time of crack propagation

up to critical length (fatigue fracture).

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Determination of loading effects

Actual loading has stochastic distribution.

Dynamic effects are taken into account:- by dynamic calculations,- approximately with help of dynamic coefficient fat (given in standards).

T

In fatigue design may be used:

1. Constant amplitude of stress range

N

and N are approximately estimated.In Eurocodes is determined equivalent stress range

E,2, which corresponds to fatigue damage of N = 2106:E,2 = 1 2 3 ... kproduct of equivalent damage factors

(for bridges and cranes given in Eurocodes)

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2. Stress range spectrum

Actual stress distribution is evaluated by some of the cycle counting methods, e.g.:

- reservoir method:

- rainflow method:

1

2 3 4

1 1

2

3

4

5

2

3

4

5

1

23

454'3'

history after

filtration

idea of "pagoda"

(turned of 90)

The stress ranges are arranged into several degree spectrum (for several ):

N

n1 (for stress range 1)n

2 n3 histogram:

12 3 4

Nn1 n2 n3 n4

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Determination of fatigue strength

Influence of stress range . is substantial. The fatigue strength in compression is higher:

ATTENTION: welded elements have always tensionresidual stresses in weld location !!! always tension.

Influence of stress concentration is essential:

Influence of yield point fy is negligible(steel S235 and S460 have roughly the same fatigue strength).

Influence of environment: fatigue strength is lowered by aggressiveenvironment, corrosion, low and high temperatures.

;

+

-

( in compression may be taken 60% of6 only)

NOTCHES are concentrators of stresses cracks,

they are especially at weld locations (see detail categories).

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Solution of fatigue problems

1. Whlers approach (for design of new structures standards, Eurocode).

2. Fracture mechanics:Investigates development of a crack enables to determine residual life".

Fatigue design according to Eurocode (EN 1993-1-9)

Loading: design values of stress range for: Ff= 1,00

Fatigue resistance:according to assessment method- damage tolerant method (requires inspections, maintenance): Mf= 1,15- safe life method (without inspections): Mf= 1,35(the coefficients may be lowered for elements with lower consequences)

The design may be performed for:

constant amplitude of nominal (equivalent) stress range E,2, stress range spectrum.

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Modifications of the assessment:

- compressive portion of the stress range may be reduced to 60 %,

- due to size effect (usually t > 25 mm) the fatigue strength is reduced by coefficient ks.

Design for stress range spectrum"For several degree spectrum ( i, n i, see e.g. fori = 4) the Palmgren-Miner lineardamage accumulation hypothesis may be used:

1n

i Ri

EidNnD

number of cycles with amplitudeFfi

number of cycles with the sameamplitude up to collapse, determinedfrom curve corresponding tocategory of given detaillog NNRi

log

nEiFfi

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Recommendations for fatigue design:1. Selection of suitable details (to minimize notches).2. Restriction of tension residual stresses ( welds of necessary size only,

multilayer welds are better).3. Correct determination of fatigue loading (, N).

Fabrication:

1. Without notches (possibly grinding, TIG remelting, trimming by mechanical way- by hammering, shot peening; in progress ultrasonic +mechanical treatment).

2. Low residual stresses (MAG, TIG welding).

Example of crane girder:

t

max.

100

manual weld: KD 100

MAG, SAW: KD 112

KD 80

KD 80

older opinions,today frequently welded

KD 80

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Complementary notes:

Fracture mechanicsUnlike as in Whlers approach the development of given crack is investigated.

Enables to determine residual life of the structure.

1. Linear fracture mechanics - investigates the crack within multi-cyclefatigue (most of the body is elastic).1. Nonlinear fracture mechanics - investigates the crack within low-cycle

fatigue (crack vicinity is plastic).

Linear fracture mechanics

r 02a

b

r

K

I2

max=coefficient of stress intensity (after Irwin).

Solution consists of:

b)(a,faK Ia) Stress in crack face:b) Velocity of crack spread (Paris law): m

d

dKC

N

a N number of cycles

C, m material constants

K amplitude KI

i.e. (KI ,max- KI, min)/2

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For given KI = KIC (fracture toughness material constant)

a critical length of the crack acrmay be determined:

and by integration of Paris law also the residual life

(i.e. the number of cycles up to fatigue damage):

2

b),cr(a

ccr

1

=

f

Ka

I

cr

0 K

da

a f

aN

log

log Napprox. 10 000 cycles

quasi-static fracture

low-cycle fatigue

multi-cycle fatiguecut-off limit

Nonlinear fracture mechanics (low-cycle fatigue)

Region of plastic deformations use of pl necessary

pl el

tot

Manson-Coffin relation:

Manson relation:

C, N2pl = 2N number of half-cyclesC constant (-0,5 up - 0,8)

' 0,5 up 0,7yfy' coeff. of fatigue strength fy

Cbpleltot )2()2)(( N'NE/f

'y