1

Chapter 6. Fatigue Failure

2

3

We will emphasize topics from the following sections:

6-1 to 6-3 Introduction to fatigue failure and failure theories

6-7 Stress- life method

6-8 S-N diagram

6-9 Endurance limit modifying factors

6-10 Stress concentration and notch sensitivity

6-11 to 13 Fluctuating stresses

4

Introduction to Fatigue Failure

A – crack initiates at thread root

B – crack propagation (beach marks)

C – final fast fracture

Fatigue failure of a bolt subjected

to repeated unidirectional loads

5

Methods for Predicting Fatigue Failure

1. Strain-Life Method– Analyzes localized plastic deformation

– Accurate for low-cycle fatigue problems

2. Fracture Mechanics Method– Predicts incremental crack growth rates

3. Stress-Life Method– Traditional method

– Based on stress levels only

– Easiest method to implement

We will consider only

the stress-life method

6

Fatigue Testing

Uniaxial Fatigue Test Rotating Beam Test

7

Fatigue Testing Procedure

− Perform test at many different stress levels

− Determine number of cycles to failure

− Plot number of cycles to failure vs. applied stress

− This plot (called the S-N diagram) can be used to estimate the number of cycles to failure for a given stress level

8

Typical S-N Curve

Sut – failure at

first load cycle

– endurance limit

(can withstand unlimited

load cycles)

eS

9

Endurance Limit

Endurance limit – the stress level below which

failure will not occur, regardless of how many

cycles (also known as the fatigue limit)

- endurance limit under ideal test conditions

- endurance limit under service conditionseS

eS

10

Relation between Endurance Limit and

Tensile Strength

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Relation between Endurance Limit and

Tensile Strength (cont.)

ksi200ksi,100

ksi200,5.0

ut

utute

S

SSS

MPaSMPa

MPaSSS

ut

utute

1400,700

1400,5.0

in SI units

12

Endurance Limit Modifying Factors

f

e

d

c

b

a

efedcbae

k

k

k

k

k

k

SkkkkkkS

- Surface condition modifying factor

- Size modification factor

- Load modification factor

- Temperature modification factor

- Reliability factor

- Miscellaneous effects modification factor

These are

called “Marin”

factors

13

Surface Factor, ka

buta Sak

14

Size Factor, kb

For bending and torsion

For axial loads

kb = 1

mm2545151.1

mm5179.224.1

in10291.0

in211.0879.0

157.0

107.0

157.0

107.0

dd

dd

dd

dd

kb

15

Loading Factor, kc

torsion59.0

axial85.0

bending1

ck

16

Temperature Factor, kd

RT

Td

S

Sk

17

Reliability Factor, ke

Accounts for scatter in fatigue data and desired reliability

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Miscellaneous Effects Factor, kf

Corrosion

Electrolytic plating

Metal spraying

Cyclic frequency

Frettage corrosion

(corrosion at contact surfaces)

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Example 6-6

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Example 6-6 - Endurance Limit

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Example 6-6 - Fatigue Strength at 70,000 cycles

Section 6-8, for 103 < N < 106

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Example 6-6 - Fatigue Strength at 70,000 cycles

(cont.)

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Stress Concentration and Notch Sensitivity

Static loading (chapter 3) => Kt and Kts

Fatigue loading – some materials are less sensitive to stress

concentrations => reduced stress concentration

Fatigue stress concentration factors

ofs

of

K

K

max

max

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Notch Sensitivity

1

1

1

1

shear

ts

fs

t

f

K

Kq

K

Kq

where 0 ≤ q, qshear ≤ 1

Note:

q=0 => Kf = 1 (no sensitivity to notches)

q=1 => Kf = Kt (no reduction due to fatigue)

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Notch Sensitivity – Axial and Bending Loading

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Neuber Equation

(basis for Fig. 6-26 - steels)

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Notch Sensitivity – Torsion Loading

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Fatigue Stress Concentration Factors

)1(1

)1(1

1

1

1

1

shear

tsshearfs

tf

ts

fs

t

f

KqK

KqK

K

Kq

K

Kq

Solving for Kf and Kfs gives

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Example 6-7

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Example 6-7 (cont.)

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Characterization of Fluctuating Stress

rangestress

amplitudestress

0stressmean

r

a

m

Zero Mean Stress (ex. Rotating beam experiment)

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Characterization of Fluctuating Stress (cont.)

Non-zero mean stress (shafts under combined loading)

rangestress

stressminimum

stressmaximum

amplitudestress

stressmean

min

max

r

a

m

33

Fluctuating Stress (cont.)

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Fatigue Failure Criteria for

Non-zero Mean Stress

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Yield Line (Langer Line)

Yielding occurs if

Factor of safety associated with yielding

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Goodman Failure Criteria

See text for other failure criteria (Gerber, ASME elliptic, etc.)

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Example 6-9 (cont.)