Page 298 - Materials Science and Engineering An Introduction

270 • Chapter 8 / Failure

Fatigue

fatigue Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating
stresses (e.g., bridges, aircraft, machine components). Under these circumstances, it is
possible for failure to occur at a stress level considerably lower than the tensile or yield
strength for a static load. The term fatigue is used because this type of failure normally
occurs after a lengthy period of repeated stress or strain cycling. Fatigue is important
inasmuch as it is the single largest cause of failure in metals, estimated to be involved in
approximately 90% of all metallic failures; polymers and ceramics (except for glasses)
are also susceptible to this type of failure. Furthermore, fatigue is catastrophic and
insidious, occurring very suddenly and without warning.
Fatigue failure is brittle-like in nature even in normally ductile metals in that there
is very little, if any, gross plastic deformation associated with failure. The process occurs
by the initiation and propagation of cracks, and typically the fracture surface is perpendicular
to the direction of an applied tensile stress.

8.7 CYCLIC STRESSES
The applied stress may be axial (tension–compression), flexural (bending), or
torsional (twisting) in nature. In general, three different fluctuating stress–time
modes are possible. One is represented schematically by a regular and sinusoidal
time dependence in Figure 8.17a, where the amplitude is symmetrical about a mean
Tutorial Video: zero stress level, for example, alternating from a maximum tensile stress (s max ) to
Cyclical Fatigue a minimum compressive stress (s min ) of equal magnitude; this is referred to as a
Failure reversed stress cycle. Another type, termed a repeated stress cycle, is illustrated in
What is the Mechanism Figure 8.17b; the maxima and minima are asymmetrical relative to the zero stress
of Cyclical Fatigue level. Finally, the stress level may vary randomly in amplitude and frequency, as
Failure? exemplified in Figure 8.17c.
Also indicated in Figure 8.17b are several parameters used to characterize the fluc-
tuating stress cycle. The stress amplitude alternates about a mean stress s m , defined as
the average of the maximum and minimum stresses in the cycle, or
Mean stress for cyclic
loading—dependence
on maximum and s max + s min (8.14)
minimum stress levels s m = 2

The range of stress s r is the difference between s max and s min , namely,
Computation of
range of stress for (8.15)
cyclic loading s r = s max - s min

Stress amplitude s a is one-half of this range of stress, or
Computation of
stress amplitude for s a = s r = s max - s min (8.16)
cyclic loading 2 2

Finally, the stress ratio R is the ratio of minimum and maximum stress amplitudes:

s min
Computation of R = (8.17)
stress ratio s max