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Strain-Based Fatigue Analysis

Dr. Nuri Ersoy

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Material Models

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Material Models

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Material Models

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Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,by Norman E. Dowling. ISBN 0-13-186312-6.

2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,

or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),

write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 07458.

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oA

B

Cy

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Testing the Materials for Strain Life Approach

a

Nf

af

f/Eplastic

elastic

Nf3Nf2Nf1

p

E1

c1

b

1

aa

(d)

cyclic

monotonic

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Ramberg-Osgood equation

The cyclic stress strain curve isrepresented by Ramberg-Osgoodequation:

nn

aaa

HEHE

/1/1

222

where

a is the strain amplitudea is the stress amplitudeH is the Cyclic Strength Coefficientn is the Strain Hardening Exponent.

(c)

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Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,by Norman E. Dowling. ISBN 0-13-186312-6.

2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,

or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),

write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 07458.

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Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,by Norman E. Dowling. ISBN 0-13-186312-6.

2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,

or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),

write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 07458.

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Cycle Dependent Material Response

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Cycle Dependent Material Response

Strain ControlStress Control

Cyclic

Hardening

Cyclic

Softening

Drive

Response

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0 100 200 300 400

-5E-3

0

5E-3

strain(mm/mm)

Secs.

0 100 200 300 400

-400

-200

0

200

400

600

stress(MPa)

Secs.

-0.01 -5E-3 0 5E-3 0.01-600

-400

-200

0

200

400

600

800

strain (mm/mm)

Time range : 0 secs to 435 secs

1

3

579

24

68

Cyclic Softenening

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Stable Hysteresis Loops

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Stable Hysteresis Loops

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Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,by Norman E. Dowling. ISBN 0-13-186312-6.

2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,

or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),

write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 07458.

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Stable Hysteresis Loops

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Effect of Notches

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Effect of Notches-Neubers rule

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Notched Components: Neubers Rule

se

s

e

kk

sk

ek

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constant2

2

E

skE

sk

E

E

esesk

kkk

tt

t

t

Stress and Strain Concentration Factors: Neubers

Rule

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1

2

3Kf

e

s

Cyclic Curve

Neuber Equation

Solution point

Graphical Solution for Local and

constant

n

HE

/1

222

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constantaa

Construction of the Local Hysteresis Loop

Using Neubers Rule

naaa

HE

/1

2

constant

n

HE

/1

222

Strain Life Results from a Series of LCF Tests

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Strain Life Results from a Series of LCF Tests

1E0 1E1 1E2 1E3 1E4 1E5 1E6 1E7 1E8

1E-4

1E-3

1E-2

1E-1

1E0

Life Curve Display

LogStrain

Log Life (Reversals)

Total strain curve fit

Elastic strain curve fit

Plastic strain curve fit

Total strain data

Elastic strain data

Plastic strain data

Sf': 670 MPa

b : -0.0582

(X/Y)

Ef': 0.374c : -0.54

E : 2.05E5 MPa

(X/Y)

: Run-out pts

Strain Life Results from a Series of LCF Tests

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f

f/E

plastic

elastic

Nf3Nf2Nf1

c

1

b 1

cNbNE ffff

a 22

LogStrain

Log Life

Strain Life Results from a Series of LCF Tests

Coffin-Manson Strain-Life Equation

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exponentductilityfatigue

tcoefficienductilityfatigue

cycle1reversals2

failuretoreversalsofnumber2

exponentstrengthfatigue

tcoefficienstrengthfatigue

amplitudestrain

22

c

N

b

cNbN

E

f

f

f

a

fff

f

a

Coffin Manson Strain Life Equation

Coffin-Manson Strain-Life Equation

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exponentductilityfatigue

tcoefficienductilityfatigue

cycle1reversals2

failuretoreversalsofnumber2

exponentstrengthfatigue

stressmean

tcoefficienstrengthfatigue

amplitudestrain

22)(

c

N

b

cNbNE

f

f

m

f

a

fff

mf

a

q

Modified for Mean Stress Effect

Effect of Mean Stress

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Generalized Strain-Life Equation:

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strengthultimate

failurestrain toultimate

cycle1reversals2

failuretoreversalsofnumber2

amplitudestrain

225.3

u

6.06.012.0

S

N

NNES

f

f

a

fffu

a

q

Method of Universal Slopes

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Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Third Edition,by Norman E. Dowling. ISBN 0-13-186312-6.

2007 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved.

This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system,

or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s),

write to: Rights and Permissions Department, Pearson Education Inc., Upper Saddle river, NJ 07458.

General Procedure

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for calculating life for

constant amplitudestrain histories

Rainflow Counting and Stress/Strain Space

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Rainflow Counting and Stress/Strain Space

Damage and Life

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Fatigue is

the process where repeated variations in

loading cause failure even when the nominal

stresses are below the material yield strength;

Damage is

The inverse of life for a given strain amplitude

and is cumulative until failure

g

Miners Rule

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Nf3Nf1

LogStrain

Log Life

1

i

i

N

n