Effects of crack aspect ratio on the behavior of small surface cracks in fatigue: Part I. Simulation
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TRODUCTION
THE growth behavior of naturally initiating small fatigue cracks has generated a great deal of interest[1,2,3] in studies on the fatigue of materials. An understanding of the behavior of such cracks is important for many reasons. First, since small-crack growth regime links crack initiation to large-crack growth, a complete understanding of fatigue requires a knowledge of small-crack growth behavior. Second, extensive data[1–10] on a number of materials indicate that growth rates of small cracks (typically surface crack length, 2c , 500 mm) are significantly higher than those of large cracks under equivalent stress intensity factor ranges (DK). This characteristic has generally been termed as anomalous small crack growth behavior. In addition, small-crack growth data also exhibit a high degree of scatter compared to large-crack growth data, contributing to the anomaly. The anomalous growth characteristics have been suggested to be due to (1) the lack of a fully developed crack wake to cause crack closure,[2,11] (2) larger plastic zones at the tips of small cracks,[10,12] and (3) the crystallographic nature of crack growth induced by microstructure.[5,13] Crack closure levels, initially low at small crack sizes, were found[11,14,15] to develop with crack extension, reaching the level of closure for large cracks. Based on the premise that large plastic zones at small crack tips, relative to those of large cracks, result in higher driving forces, attempts[12,16] were made to correlate growth rates in terms of D J, to account for the effects of crack tip plastic deformation. The higher growth rates of small cracks subjected to fatigue under maximum stress levels close to or beyond yield stress were rationalized on this basis. The crystallographic nature of crack growth within a single or a few grains also seems[13,17] to provide a partial explanation of anomalous K.S. RAVICHANDRAN, Assistant Professor, is with the Department of Metallurgical Engineering, The University of Utah, Salt Lake City, UT 84112. Manuscript submitted March 20, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS A
behavior, especially in large-grained materials. Crack growth is significantly influenced by the crystallographic orientations of grains when the sizes of cracks are comparable to the grain size. It appears that these factors either singly or collectively explain the behavior of small cracks, depending on crack size, stress level, and microstructure. An important aspect of small cracks to which relatively little attention[18–22] has been paid is the effect of crack shape or aspect ratio (a/c; a is the crack depth and c is the halfsurface length) on crack growth behavior. It should be noted that, first of all, the loading (tension or bending) can affect the aspect ratio variation for large surface cracks.[23] However, since the present study is restricted to the nominally tensile loading condition only, we limit the discussion to this case where a/c is nearly constant (a/c ' 1) at a/t , 0.5, in which t is the specimen thickness.[24
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