30079_18b - Fig 18.12 Surface flaw shape parameter(From Ref...

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Fig. 18.12 Surface flaw shape parameter. (From Ref. 22. Adapted by permission of Prentice-Hall, Inc., Englewood Cliffs, New Jersey.) To approximate the effects of strain hardening, a flow stress cr 0 , taken to be an average of the yield and ultimate strengths, is often used when computing the plastic collapse stress. The plastic collapse stress a c is that applied stress which produces cr 0 across the remaining uncracked ligament, and is the maximum applied stress that a perfectly plastic material can sustain. This stress may be determined using a limit load analysis. In general, the plastic collapse stress is a function of geometry, type of loading, type of support (boundary conditions), and through-thickness constraint (plane stress or plane strain). 6 ' 25 For a single through-thickness crack of length a in a strip with width b loaded in tension (see Fig. 18.9), if end rotations are restrained, the plastic collapse stress under plane stress conditions may be approximated by 25 a c = a 0 (\ - alb} (18.39) 18.5 FATIGUE AND STRESS CONCENTRATION Static or quasistatic loading is rarely observed in modern engineering practice, making it essential for the designer to address himself or herself to the implications of repeated loads, fluctuating loads, and rapidly applied loads. By far, the majority of engineering design projects involve machine parts Fig. 18.13 Failure assessment diagram.
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subjected to fluctuating or cyclic loads. Such loading induces fluctuating or cyclic stresses that often result in failure by fatigue. Fatigue failure investigations over the years have led to the observation that the fatigue process actually embraces two domains of cyclic stressing or straining that are significantly different in character, and in each of which failure is probably produced by different physical mechanisms. One domain of cyclic loading is that for which significant plastic strain occurs during each cycle. This domain is associated with high loads and short lives, or low numbers of cycles to produce fatigue failure, and is commonly referred to as low-cycle fatigue. The other domain of cyclic loading is that for which the strain cycles are largely confined to the elastic range. This domain is associated with lower loads and long lives, or high numbers of cycles to produce fatigue failure, and is commonly referred to as high-cycle fatigue. Low-cycle fatigue is typically associated with cycle lives from 1 up to about 10 4 or 10 5 cycles. Fatigue may be characterized as a progressive failure phenomenon that proceeds by the initiation and propagation of cracks to an unstable size. Although there is not complete agreement on the microscopic details of the initiation and propagation of the cracks, pro- cesses of reversed slip and dislocation interaction appear to produce fatigue nuclei from which cracks may grow. Finally, the crack length reaches a critical dimension and one additional cycle then causes complete failure. The final failure region will typically show evidence of plastic deformation produced just prior to final separation. For
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