Statistical simulation of small fatigue crack nucleation and coalescence in a lamellar TiAl alloy
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I. INTRODUCTION
THE fatigue crack growth curves of TiAl alloys generally exhibit a very steep slope.[1–7] This characteristic poses a potential problem for the design and application of TiAl components because of inadequate fatigue resistance. Two possible approaches can be taken to ensure a sufficient fatigue life in TiAl alloy components.[3,8] One approach is a design based on the fatigue threshold, DKth, of large cracks. Any existing cracks at or below the inspection detection level may be designed not to propagate under the operating stress levels, which means the operating stress intensity levels must be kept below the growth threshold of large fatigue cracks. Alternatively, the operating stress level may be designed not to exceed the fatigue limit in order to prevent crack initiation. In both cases, the presence of small cracks might render the approaches nonconservative if the small cracks propagate at stress intensity levels below the large crack threshold. The size dependence of the growth response of fatigue cracks is often presented in terms of the Kitagawa diagram,[9] which is a double logarithmic plot of stress range vs crack length. In such a plot, the large crack fatigue threshold is represented by a straight line with a slope of 21/2, as shown in Figure 1, which is constructed for a lamellar TiAl alloy based on previous data.[6,7] In contrast, the fatigue limit is typically represented by a horizontal line since it is independent of the crack size. The fatigue limit (300 MPa) shown in Figure 1 was estimated based on the elastic limit (280 MPa) and the assumption that fatigue crack nucleation would not occur without at least a small amount of microplasticity. This value of the fatigue limit, which is not precise, is intended for illustration only. It should be replaced with an actual experimental value when one becomes available. For stresses above the crack growth threshold, fatigue cracks KWAI S. CHAN, Institute Scientist, is with Southwest Research Institute, San Antonio, TX 78238. BETTINA WITTKOWSKY, Scientist, formerly with the GKSS Research Center, is with Proctor & Gamble European Service GmbH, D-53881 Euskirchen, Germany, MICHAEL PFUFF, Scientist, is with the GKSS Research Center, D-21502 Geesthacht, Germany. Manuscript submitted August 25, 1998.
METALLURGICAL AND MATERIALS TRANSACTIONS A
would propagate until failure at the critical stress intensity factor, Kc. For stresses above the fatigue limit but below the large crack DKth, large fatigue cracks would not propagate but some small fatigue cracks could propagate to failure even though most of the small cracks nucleated may arrest.[7] Thus, it is evident that the stress states above the fatigue limit and DKth lines in Figure 1 are regions where fatigue crack growth and failure would occur. On the other hand, both large and small fatigue cracks are expected not to grow at stresses below the fatigue limit and DKth boundaries. This region may be used as the basis for design of damage tolerant components. Unfortunately, it is uncertain that
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