Notches in Fatigue - Illinoisfcp.mechse.illinois.edu/files/2014/07/1-Notches.pdf · Notches in Fatigue Professor Stephen Downing Department of Mechanical Science and Engineering University

Notches in Fatigue

Professor Stephen Downing

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign

© 2002-2012 Darrell Socie, All Rights Reserved

Fatigue Seminar © 2002-2012 Darrell Socie, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 50

Outline

1. Notch Rules

2. Fatigue Notch Factor

3. Stress Intensity Factors for Notches

4. Frost Data and Kf

5. Small Crack Growth

6. Small Notches


Stress Concentration Factor

Applied stress

Local stress

a21appliedlocal

Inglis Solution 1910

2a


Notch Rules

Neuber

Glinka

Seeger

n

1

2

tKE

eSK

n

1

2

tKn1

1

EdeSK

SK

K*S

KSK

KEeSK

p

t

y

tLimitp

n

1

**2

p


Define K and K after Yielding

S , e

,

Define: nominal stress, S

nominal strain, e

notch stress,

notch strain,

Stress concentration

Strain concentration

SK

eK


K and K

Str

ess (

MP

a)

Strain

KtS

Kte

SK

eK


Stress and Strain Concentration

Kt

Nominal Stress

Str

ess/S

train

Concentr

ation

1K

2

tKK

First yielding


Neuber’s Rule S

tress (

MP

a)

Strain

KtS

Kte

eKSK tt

Stress calculated with

elastic assumptions

Actual stress


Neuber’s Rule for Fatigue

2222

eKSK tt

Stress and strain amplitudes

Elastic nominal stress

E2

S

2

e

Substitute and rearrange

22E

2

SK t

The product of stress times strain controls fatigue life


SN Materials Data

10 1 10 102 103 106 107 105 104

Fatigue Life, Reversals

100

1000

10000

Str

ess A

mplit

ude, M

Pa

93 steels

17 aluminums


N Materials Data

93 steels

17 aluminums

10-4

10-2

10-3

0.1

10

1

Str

ain

Am

plit

ure

1 10 102 103 106 107 105 104



1 106 107 105 10 102 103 104


1

10

102

105

104

103

2

2

E

K t

or

2 S

2 2 E


Outline

1. Notch Rules





6. Small Notches


A Dilemma

Stress analysis and stress concentration factors are

independent of size and are related only to the ratio

of the geometric dimensions to the loads

Fatigue is a size dependant phenomena

How do you put the two together ?


Similitude


Fatigue of Notches

From Dowling, Mechanical Behavior of Materials, 1999


Notch Size

Kt Kf

Kt

Kf

Large Notch Small Notch


Microstructure Size

Kt Kf

Kt Kf

Low Strength High Strength


Stress Gradient

Kt Kf

Kt

Kf

Low Kt High Kt


Kt vs Kf

0

2

4

6

8

10

0 2 4 6 8 10

Kt

Kf

Kf = Kt

Experiments


Peterson’s Equation

1

1K1K t

f

mmMPa2070

025.0

8.1

u

0

1

2

3

4

10-4 10-3 10-2 0.1 1 10 102 103

Kf

No effect when <<

Full effect when >>


Pererson’s Constant

1000 500 2000 1500

0.1

0.03

0.7

0.3

Ultimate Strength, MPa

, m

m


Static Strength

hole

Kt = 2.5

slot

Kt = 5

diamond

Kt = 20

edge

Kt = 20


1018 Steel Test Data

0

20

40

60

80

100

0 2 4 6 8 10

load, kN

displacement, mm

edge

diamond

slot

hole


Notched SN Curve

100

1000

10000

100

Cycles

Str

ess A

mplit

ude,

MP

a

101 102 103 104 105 106 107

Smooth specimen data

Notched specimen Kf

Stress concentrations are not very important at short lives


Outline

1. Notch Rules





6. Small Notches


Cracks at Notches

D

a a D + a

KtS S S

a << D a >> D

aSKK t aDSK


Stress Intensity Factors

0 0.1 0.2 0.3 0.4 0.5 0.6

1.0

0

3.0

2.0

D

a

DS

K

aSKK t

aDSK


Cracks at Holes

10 1 1 12

Once a crack reaches 10% of the hole radius,

it behaves as if the hole was part of the crack


Outline

1. Notch Rules





6. Small Notches


Crack Growth Data

10-12

10-11

10-10

10-9

10-8

10-7

10-6

1 10 100

Cra

ck G

row

th R

ate

, m

/cycle

mMPa,K

mKCdN

da

KTH

Kc

a2

12.1KTH

Nonpropagating cracks


Frost Data

nucleation fracture

Rotating bending

Notched bar

Notched plate

1 3 5 7 9 11 13 15

1.0

0.8

0.6

0.4

0.2

0

Kt

Snom

inal

Sfa

tigue lim

it

tK

1 nonpropagating cracks

Frost, “A Relation Between the Critical Alternating Propagation Stress and Crack Length for Mild Steel”

Proceedings of the Institute for Mechanical Engineers, Vol. 173, No. 35, 1959, 811-836


Significance

D

KS th

fl

For Kt > 4, the notch acts like a crack with a depth D

Kt does not play a role for sharp notches !


Specimens with Similar Geometry

Kt = 2.4 Kt = 10.7

Ultimate Strength 780 MPa

Yield Strength 660 MPa

25 25

2.5 2.5


Test Results

1

100

1000

Nom

inal S

tress A

mplit

ude

1 10 100 103 104 105 106 107

Total Fatigue Life, Cycles

Strength Limited

Crack Growth Dominated

Fatigue Strength Dominated

Threshold Stress Intensity Dominated

Kt = 2.4

Kt = 10.7


Outline

1. Notch Rules





6. Small Notches


Small Crack Growth


Threshold


Normalized Thresholds


Growth from Notches


Cracks at Notches

D a crack tip plastic zone

notch plastic zone

notch stress field


Crack Growth

K or a

Cra

ck g

row

th r

ate

Long cracks

Crack tip plasticity controls

Short cracks

Notch plasticity

controls


Closure Observations

a b

d c c 1st subcycle

d 500th subcycle

a

b

1026 steel

1/2 = 0.005

2/2 = 0.001


Closure Correlation


Outline

1. Notch Rules





6. Small Notches


area


Small Notches


Threshold Stress Intensity


Hardness Corelation


Flaw Sensitivity


Fatigue Limit

Notches in Fatigue

Documents

Notches in Fatigue - Illinoisfcp.mechse.illinois.edu/files/2014/07/1-Notches.pdf · Notches in Fatigue Professor Stephen Downing Department of Mechanical Science and Engineering University