Three-dimensional crack-tip fields in four-point-bending copper single-crystal specimens

Abstract

The three-dimensional near-tip fields in copper single crystals loaded in four-point bending are characterized numerically. For comparison purposes, the corresponding plane-strain fields are also computed numerically and their asymptotic behavior determined semi-analytically. On the basis of these analyses, we investigate: (i) the dependence of the fields on the hardening law; (ii) the degree of correlation between surface and interior fields in finite specimens; and (iii) the degree of correlation between plane-strain and three-dimensional fields. In particular, we endeavor to ascertain the extent to which surface observations of near-tip fields in single crystals, such as those obtained by Moire interferometry, are representative of interior fields, and the extent to which these are representative of plane-strain fields. Our calculations reveal marked differences in the pattern of slip activity in the interior and on the surface of the specimen. These discrepancies, in turn, result in significant variations in the state of stress and strain. These observations suggest that, for the test geometries under consideration, surface observations provide only an indirect measure of conditions in the interior, and point to a need for the development of experimental techniques enabling the direct observation of interior fields.