Beer

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CONFIRMING PAGES

6

Fatigue Failure Resulting
from Variable Loading

Chapter Outline

6–1

Introduction to Fatigue in Metals

6–2

Approach to Fatigue Failure in Analysis and Design

6–3

Fatigue-Life Methods

6–4

The Stress-Life Method

265

6–5

The Strain-Life Method

268

6–6

The Linear-ElasticFracture Mechanics Method

6–7

The Endurance Limit

6–8

Fatigue Strength

6–9

Endurance Limit Modifying Factors

258
264

265

270

274

275
278

6–10

Stress Concentration and Notch Sensitivity

6–11

Characterizing Fluctuating Stresses

6–12

Fatigue Failure Criteria for Fluctuating Stress

6–13

Torsional Fatigue Strength under Fluctuating Stresses

6–14Combinations of Loading Modes

6–15

Varying, Fluctuating Stresses; Cumulative Fatigue Damage

6–16

Surface Fatigue Strength

6–17

Stochastic Analysis

6–18

Road Maps and Important Design Equations for the Stress-Life Method

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CONFIRMING PAGESMechanical Engineering Design

In Chap. 5 we considered the analysis and design of parts subjected to static loading.
The behavior of machine parts is entirely different when they are subjected to timevarying loading. In this chapter we shall examine how parts fail under variable loading
and how to proportion them to successfully resist such conditions.

6–1

Introduction to Fatigue in Metals
Inmost testing of those properties of materials that relate to the stress-strain diagram,
the load is applied gradually, to give sufficient time for the strain to fully develop.
Furthermore, the specimen is tested to destruction, and so the stresses are applied only
once. Testing of this kind is applicable, to what are known as static conditions; such
conditions closely approximate the actualconditions to which many structural and
machine members are subjected.
The condition frequently arises, however, in which the stresses vary with time or
they fluctuate between different levels. For example, a particular fiber on the surface of
a rotating shaft subjected to the action of bending loads undergoes both tension and compression for each revolution of the shaft. If the shaft is part of anelectric motor rotating
at 1725 rev/min, the fiber is stressed in tension and compression 1725 times each minute.
If, in addition, the shaft is also axially loaded (as it would be, for example, by a helical
or worm gear), an axial component of stress is superposed upon the bending component.
In this case, some stress is always present in any one fiber, but now the level of stress isfluctuating. These and other kinds of loading occurring in machine members produce
stresses that are called variable, repeated, alternating, or fluctuating stresses.
Often, machine members are found to have failed under the action of repeated or
fluctuating stresses; yet the most careful analysis reveals that the actual maximum
stresses were well below the ultimate strength of the material, and quitefrequently even
below the yield strength. The most distinguishing characteristic of these failures is that
the stresses have been repeated a very large number of times. Hence the failure is called
a fatigue failure.
When machine parts fail statically, they usually develop a very large deflection,
because the stress has exceeded the yield strength, and the part is replaced before fracture
actuallyoccurs. Thus many static failures give visible warning in advance. But a fatigue
failure gives no warning! It is sudden and total, and hence dangerous. It is relatively simple to design against a static failure, because our knowledge is comprehensive. Fatigue is
a much more complicated phenomenon, only partially understood, and the engineer seeking competence must acquire as much knowledge of...