fatigue

1

Sequence Effects in Fatigue

Professor Darrell F. SocieUniversity of Illinois at Urbana-Champaign

© 2002-2005 Darrell Socie, All Rights Reserved

2

Fatigue Seminar © 2002-2005 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50

Outline

1. Mean Stress2. Nonlinear Damage Models3. Crack Growth Interactions4. Crack Tip Plasticity Models5. Crack Closure Models

3


Mean Stresses

mean stress

stress range

stre

ss

2SS

S minmaxmean

+=

Smax

Smin

max

min

SS

R =

4


General Observations

n Tensile mean stresses reduce the fatigue life or decrease the allowable stress rangenCompressive mean stresses increase the

fatigue life or increase the allowable stress range

5


Mechanism

Fatigue damage is a shear process

∆S

Tensile mean stresses open microcracks and make sliding easier

2Smean

6


Goodman 1890

Mechanics Applied to EngineeringJohn Goodman, 1890

“.. whether the assumptions of the theory are justifiable or not …. We adopt it simply because it is the easiest to use, and for all practical purposes, represents Wöhlers data.

Sultimate = Smin + 2 ∆S

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Goodman Diagram

Mean stress

Alte

rnat

ing

stre

ss

Su0

Se

107 cycles

105 cycles

−

∆

=∆

−= ultimate

mean

1R SS

12S

2S

R = -1 R = 1

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Test Data ( 1941 )

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.2

0.4

0.6

0.8

1.0

1.2

0

Mean StressUltimate Strength

Alte

rnat

ing

Str

ess

Fat

igue

Lim

it

J.O. Smith, The Effect of Range of Stress on the Fatigue Strength of Metals,Engineering Experiment Station Bulletin 334, University of Illinois, 1941

9


Compression

Se

Su0R = -1 R = 1

-Su

R = -∞

no influence

detrimental

beneficial

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Modified Goodman ( no yielding )

Se

Su0R = -1 R = 1

-SuR = -∞

Sys

Sys

-Sys

ysmean SS2S

<+∆

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Mean Stress Influence on Life

0.1

1

10

100

1000

-0.6 -0.4 -0.2 0 0.2 0.4 0.6Mean Stress

Ultimate Strength

Rel

ativ

e F

atig

ue L

ife

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Stress Concentrations

PlasticZone

∆ε

∆ε The elastic material surroundingthe plastic zone around a stressconcentration forces the material to deform in strain control

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Mean Stresses at Notches

σ

ε

σ

ε

σ

ε

elastic plastic

NominalNotch

NotchNominal

Nominal mean stress is less than notch mean stress

Nominal mean stress is greater than notch mean stress

Nominal Notch

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Morrow Mean Stress Correction

cf

'f

bf

mean'f )N2()N2(

E2ε+

σ−σ=

ε∆

10-5

10-4

0.001

0.01

0.1

1

Reversals, 2Nf

Str

ain

Am

plitu

de

100 101 102 103 104 105 106 107

Emeanσ

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Smith Watson Topper

σ

ε

∆ε

σmaxcb

f'f

'f

b2f

2'f

max )N2()N2(E2

+εσ+σ

=ε∆

σ

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Mean Stress Relaxation

Stadnick and Morrow, “Techniques for Smooth Specimen Simulation of Fatigue Behavior of Notched Members”ASTM STP 515, 1972, 229 -252

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Loading Histories

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Test Results

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Sources of Mean/Residual Stress

n Loading Historyn Fabricationn Shot PeeningnHeat Treating

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Loading History

Tension overloads produce favorable compressive residual stress

Compressive overloads produce unfavorable tensile residual stress

σ

ε

σ

ε

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Fabrication

22


Cold Expansion

1965 Basic Cx process conceptualized (Boeing)The split sleeve is slipped onto the mandrel, which is attached to the hydraulic puller unit.

The mandrel and sleeve are inserted into the hole with the nosecap held firmly against the workpiece.

When the puller is activated, the mandrel is drawn through the sleeve radially expanding the hole.

Courtesy of Fatigue Technology Inc.

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Theory of Cold Expansion


24


Fatigue Life Improvement


100

200

300

0108107106105104103

Nom

inal

Str

ess

Fatigue Life

Cold Expanded

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Shot Peening

-600

-400

-200

0

200

0 0.2 0.4 0.6 0.8

Depth (mm)

Res

idua

l Str

ess

(MP

a)

Residual stress in a shot peened leaf spring

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Shot Peening Results

www.metalimprovement.com

500

1000

1500

5000

0 1000 1500 2000 2500Fat

igue

str

engt

h at

2x1

06cy

cles

, M

Pa

Ultimate Tensile Strength, MPa

2S

S uFL =

Smooth

Notched

Shot PeenedSmooth & Notched

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Heat Treating

200

600

400

00 5 10 15

Brin

ellH

ardn

ess

Depth, mm

0 5 10 15-1500

-1000

-500

0

500

1000

Depth, mm

Res

idua

l Str

ess,

MP

a

Radial

Circumferential

Axial

50 mm diameter induction hardened 1045 steel shaft

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Outline


29


Cumulative Damage

….….

…. ….

High - Low

Low - High

nH nL

nL nH

∆SL

∆SH

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Linear Damage

∆SH

∆SL

Nf H Nf L

Lf

L

Hf

H

F Nn

Nn

Nn

Damage +==∑Miners Rule:

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Nonlinear Damage

0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1.0

00

Cycle ratio,

Dam

age

frac

tion

nNf

0040 .=ε∆

0200.=ε∆

ΣD = 0.7

ΣD = 1.3

ΣD ~ 1

32


Periodic Overload Results

10 100 103 104 105 106 107 108 109

10-3

10-4

0.01

0.1

Str

ain

Am

plitu

de

Fatigue Life

….

….

The fatigue limit is reduced by a factor of 3 when a few large cycles are applied

Bonnen and Topper, “The Effects of Periodic Overloads on Biaxial Fatigue of Normalized SAE 1045 Steel”ASTM STP 1387, 2000, 213-231

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Relative Miner’s Rule

3.0Nn

Df

==∑ ∑

Set Miner’s damage sum to a number less than 1

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Outline


35


Crack Growth Physics

σ

σMaximum load

Minimum load

σ

ε

Mean stresses in plastic zone are small

36


Mean Stress Effects

From Dowling, Mechanical Behavior of Materials, 1999

( )γ−∆

=R1KC

dNda m

0 < γ < 0.5

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Sequences

time

+

-

Load

time

+

-

Load

time

+

-

Load

time

+

-

Load

a

d

b

c

Stephens, R.I., Chen, D.K., and B.W.Hom,”Fatigue Crack Growth with Negative Stress Ratios Following SingleOverloads in 2024-T3 and 7075-T6 Aluminum Alloys, ASTM STP 595, 1976, 27 - 35

38


Crack Growth

10 20 30 40 50 60 70

Cycles x 103

25

30

35

40

45

50

Cra

ck le

ngth

, mm

dc

ba

No overload

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Crack Growth Rate

10-4

10-3

10-5

0 1 2 3 4

Distance from peak load, mm

Gro

wth

rat

e, m

m/c

ycle

40


Outline


41


Stress Fields After Overload

monotonic plastic zone

cyclic plastic zone

overload compressive plastic zone

overload monotonic plastic zone

Before

After

42


Crack Growth Retardation

10-4

10-3

10-5

0 1 2 3 4Distance from peak load, mm

Gro

wth

rat

e, m

m/c

ycle

43


Wheeler Model

CAip

yi

dNda

aa

r

dNda

−=

γ

ap

ai ryi

44


Outline


45


Compression

Crack open

Crack closed

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Compressive Stresses

Compressive stresses are not very damaging in crack growth

Str

ess

Crack opening level

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Crack Closure - Elber

( )meffKCdNda

∆=

( ) KR4.05.0Keff ∆+=∆

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Maximum Stress Dependence

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Newman Model

1AA2A

AAA1A

S)071.0415.0(A

2S

cos)05.034.0825.0(A

RARARAASS

KR1

SS

1K

103

3102

0

max1

1

0

max20

33

2210

max

o

max

o

eff

−+=

−−−=

σα−=

σ

πα+α−=

+++=

∆

−

−

=∆

α

Newman

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Closure Observations

a b

dcc 1st subcycle

d 500th subcycle

σ

ε

a

b

1026 steel

∆ε1/2 = 0.005

∆ε2/2 = 0.001

51


Spectrum Loading

-1000

1000

Str

ain

(µε)

Non Damaging Cycles

52

Sequence Effects in Fatigue

fatigue

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