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266 Mechanical 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 time-
varying 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

In most 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 actual conditions 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 com-
pression for each revolution of the shaft. If the shaft is part of an electric 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 is
fluctuating. 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 quite frequently 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
actually occurs. 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 sim-
ple to design against a static failure, because our knowledge is comprehensive. Fatigue is
a much more complicated phenomenon, only partially understood, and the engineer seek-
ing competence must acquire as much knowledge of the subject as possible.
A fatigue failure has an appearance similar to a brittle fracture, as the fracture sur-
faces are flat and perpendicular to the stress axis with the absence of necking. The frac-
ture features of a fatigue failure, however, are quite different from a static brittle fracture
arising from three stages of development. Stage I is the initiation of one or more micro-
cracks due to cyclic plastic deformation followed by crystallographic propagation
extending from two to five grains about the origin. Stage I cracks are not normally dis-
cernible to the naked eye. Stage II progresses from microcracks to macrocracks forming
parallel plateau-like fracture surfaces separated by longitudinal ridges. The plateaus are
generally smooth and normal to the direction of maximum tensile stress. These surfaces
can be wavy dark and light bands referred to as beach marks or clamshell marks, as seen
in Fig. 6–1. During cyclic loading, these cracked surfaces open and close, rubbing
together, and the beach mark appearance depends on the changes in the level or fre-
quency of loading and the corrosive nature of the environment. Stage III occurs during
the final stress cycle when the remaining material cannot support the loads, resulting in