notches in fatigue - illinoisfcp.mechse.illinois.edu/files/2014/07/1-notches.pdf · notches in...

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

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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

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Stress Concentration Factor

Applied stress

Local stress

a21appliedlocal

Inglis Solution 1910

2a

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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

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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

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K and K

Str

ess (

MP

a)

Strain

KtS

Kte

SK

eK

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Stress and Strain Concentration

Kt

Nominal Stress

Str

ess/S

train

Concentr

ation

1K

2

tKK

First yielding

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Neuber’s Rule S

tress (

MP

a)

Strain

KtS

Kte

eKSK tt

Stress calculated with

elastic assumptions

Actual stress

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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

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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

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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

Fatigue Life, Reversals

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1 106 107 105 10 102 103 104

Fatigue Life, Reversals

1

10

102

105

104

103

2

2

E

K t

or

2 S

2 2 E

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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

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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 ?

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Similitude

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Fatigue of Notches

From Dowling, Mechanical Behavior of Materials, 1999

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Notch Size

Kt Kf

Kt

Kf

Large Notch Small Notch

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Microstructure Size

Kt Kf

Kt Kf

Low Strength High Strength

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Stress Gradient

Kt Kf

Kt

Kf

Low Kt High Kt

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Kt vs Kf

0

2

4

6

8

10

0 2 4 6 8 10

Kt

Kf

Kf = Kt

Experiments

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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 >>

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Pererson’s Constant

1000 500 2000 1500

0.1

0.03

0.7

0.3

Ultimate Strength, MPa

, m

m

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Static Strength

hole

Kt = 2.5

slot

Kt = 5

diamond

Kt = 20

edge

Kt = 20

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1018 Steel Test Data

0

20

40

60

80

100

0 2 4 6 8 10

load, kN

displacement, mm

edge

diamond

slot

hole

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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

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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

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Cracks at Notches

D

a a D + a

KtS S S

a << D a >> D

aSKK t aDSK

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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

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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

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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

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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

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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

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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 !

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Specimens with Similar Geometry

Kt = 2.4 Kt = 10.7

Ultimate Strength 780 MPa

Yield Strength 660 MPa

25 25

2.5 2.5

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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

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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

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Small Crack Growth

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Threshold

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Normalized Thresholds

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Growth from Notches

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Cracks at Notches

D a crack tip plastic zone

notch plastic zone

notch stress field

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Crack Growth

K or a

Cra

ck g

row

th r

ate

Long cracks

Crack tip plasticity controls

Short cracks

Notch plasticity

controls

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Closure Observations

a b

d c c 1st subcycle

d 500th subcycle

a

b

1026 steel

1/2 = 0.005

2/2 = 0.001

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Closure Correlation

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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

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area

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Small Notches

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Threshold Stress Intensity

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Hardness Corelation

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Flaw Sensitivity

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Fatigue Limit

Notches in Fatigue