Fatigue

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 the Griffithcriterion. 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 one popular viewof 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 the original slipplanes, 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.) The clamshell region oftencontains 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. In postmortem examination offailed parts, it is often possible to 1

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 modern study of fatigue is generallydated 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 tensile stress along the bottom (seeFig. 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 microstructural understanding of fatigue processeswas 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 of cycles might be required to causefailure 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 will size the structure to keep the stresses...