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Chapter 6: Fatigue Failure���Resulting from Variable Loading

All machines and structural designs are problems in fatigue because the forces of Nature are always at work and each object must respond in some fashion. Carl Osgood, Fatigue Design

6.1 Introduction

Cross-section of a fatigued section, showing fatigue striations or beachmarks originating from a fatigue crack at A.

Typical fatigue fracture surfaces of smooth and notched cross-sections under different loading conditions and stress levels.

Beach marks

A

C

A

Fatigue failure of a bolt – The failure started at A (Stage I) propagated in B (Stage II) leading to catastrophic failure at C (Stage III)

root of thread (crack initiation)

beachmarks (crack propagation)

fast fracture

Fatigue Fracture Surfaces

[Taken from Elements of the Mechanical Behavior of Solids, by N. P. Suh and Arthur P. L. Turner, McGraw-Hill, 1975, p. 462]

root of thread (crack initiation)

beachmarks (crack propagation)

fast fracture

Region B: Beachmarks Caused by Fatigue Crack Propagation

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1. By minimizing initial flaws, especially surface flaws. Great care is taken to produce fatigue-insusceptible surfaces through processes, such as grinding or polishing, that leave exceptionally smooth surfaces. These surfaces are then carefully protected before being placed into service.

2. By maximizing crack initiation time. Surface residual stresses are imparted (or at least tensile residual stresses are relieved) through manufacturing processes, such as shot peening or burnishing, or by a number of surface treatments.

3. By maximizing crack propagation time. Substrate properties, especially those that retard crack growth, are also important. For example, fatigue cracks propagate more quickly along grain boundaries than through grains (because grains have much more efficient atomic packing). Thus, using a material that does not present elongated grains in the direction of fatigue crack growth can extend fatigue life (e.g., by using cold-worked components instead of castings).

4. By maximizing the critical crack length. Fracture toughness is an essential ingredient. (The material properties that allow for larger internal flaws are discussed in Chapter 6.)

To Maximize Design Life 6.3 Fatigue-Life Methods

•  Stress-life method – Low loads – Typically used for High-cycle fatigue

•  Strain-life method – Good for low-cycle fatigue

•  Linear-Fracture mechanics

6-5 Strain-Life Method •  Bauschinger’s theory •  R.W. Landgraf

– The strength decreases with stress repetitions during the controlled cyclic strain test.

Fatigue ductility coefficient: Fatigue strength coefficient:

Fatigue ductility exponent: Fatigue strength exponent: b

cF

F'

'

σ

ε

Mason-Coffin Relationship: ( ) ( )cFbF

pe

NNE

222

222'

'

εσε

εεε

+=Δ

Δ+

Δ=

Δ

N=number of cycle before failure

A log-log plot for true strain amplitude of SAE 1020 steel

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b c

(See Table A-23) Cyclic Properties of Metals