Fatiga

Fatigue
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
May 1, 2001

Introduction
The concept of “fatigue” arose several times in the Module on Fracture (Module 23), as in the
growth of cracks in the Comet aircraft that led to disaster when they became large enough
to propagate catastrophically as predicted by theGriffith criterion. Fatigue, as understood
by materials technologists, is a process in which damage accumulates due to the repetitive
application of loads that may be well below the yield point. The process is dangerous because a
single application of the load would not produce any ill effects, and a conventional stress analysis
might lead to a assumption of safety that does not exist.
In onepopular view of fatigue in metals, the fatigue process is thought to begin at an
internal or surface flaw where the stresses are concentrated, and consists initially of shear flow
along slip planes. Over a number of cycles, this slip generates intrusions and extrusions that
begin to resemble a crack. A true crack running inward from an intrusion region may propagate
initially along one of theoriginal slip planes, but eventually turns to propagate transversely to
the principal normal stress as seen in Fig. 1.

Figure 1: Intrusion-extrusion model of fatigue crack initiation.
When the failure surface of a fatigued specimen is examined, a region of slow crack growth
is usually evident in the form of a “clamshell” concentric around the location of the initial flaw.
(See Fig. 2.) Theclamshell region often contains concentric “beach marks” at which the crack
was arrested for some number of cycles before resuming its growth. Eventually, the crack may
become large enough to satisfy the energy or stress intensity criteria for rapid propagation,
following the previous expressions for fracture mechanics. This final phase produces the rough
surface typical of fast fracture. Inpostmortem examination of failed parts, it is often possible to
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correlate the beach marks with specific instances of overstress, and to estimate the applied stress
at failure from the size of the crack just before rapid propagation and the fracture toughness of
the material.

Figure 2: Typical fatigue-failure surfaces. From B. Chalmers, Physical Metallurgy, Wiley, p. 212,
1959.
The modernstudy of fatigue is generally dated from the work of A. W¨hler, a technologist in
o
the German railroad system in the mid-nineteenth century. Wohler was concerned by the failure
of axles after various times in service, at loads considerably less than expected. A railcar axle
is essentially a round beam in four-point bending, which produces a compressive stress along
the top surface and a tensilestress along the bottom (see Fig. 3). After the axle has rotated a
half turn, the bottom becomes the top and vice versa, so the stresses on a particular region of
material at the surface varies sinusoidally from tension to compression and back again. This is
now known as fully reversed fatigue loading.

Figure 3: Fatigue in a railcar axle.

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S-N curves
Well before a microstructuralunderstanding of fatigue processes was developed, engineers had
developed empirical means of quantifying the fatigue process and designing against it. Perhaps
the most important concept is the S-N diagram, such as those shown in Fig. 41 , in which a
constant cyclic stress amplitude S is applied to a specimen and the number of loading cycles N
until the specimen fails is determined. Millions ofcycles might be required to cause failure at
lower loading levels, so the abscissa in usually plotted logarithmically.

Figure 4: S − N curves for aluminum and low-carbon steel.
In some materials, notably ferrous alloys, the S − N curve flattens out eventually, so that
below a certain endurance limit σe failure does not occur no matter how long the loads are
cycled. Obviously, the designer...