3-DIMENSIONAL CRACK-TIP FIELDS IN 4-POINT-BENDING COPPER SINGLE-CRYSTAL SPECIMENS

The three-dimensional near-tip fields in copper single crystals loaded in four-point bending are characterized numerically. For comparison p urposes, the corresponding plane-strain fields are also computed numer ically 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 s urface and interior fields in finite specimens; and (iii) the degree o f correlation between plane-strain and three-dimensional fields. In pa rticular, we endeavor to ascertain the extent to which surface observa tions 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 c alculations reveal marked differences in the pattern of slip activity in the interior and on the surface of the specimen. These discrepancie s, in turn, result in significant variations in the state of stress an d strain. These observations suggest that, for the test geometries und er consideration, surface observations provide only an indirect measur e of conditions in the interior, and point to a need for the developme nt of experimental techniques enabling the direct observation of inter ior fields. Copyright (C) 1996 Elsevier Science Ltd