Influence of Porosity on Plane Strain Tensile Crack-Tip Stress Fields in Elastic-Plastic Materials: Part II

This paper continues the investigation of Drugan and Miao (1992). There we studied analytically the influence of a uniform porosity distribution on the stress field near a plane strain tensile crack tip in ductile (elastic-ideally plastic) material, assuming that material very near the tip is at yield at all angles about the tip. Our solutions exhibited completely continuous stress fields for porosity f ≤ 0.02979, but for higher porosities they involved radial surfaces of radial normal stress jumps. Here we investigate whether, for this higher range of porosity, relaxing our assumption of yield at all angles about the tip will facilitate solutions exhibiting fully continuous stress fields. The answer to this is shown to be yes, with a single near-tip sector assembly providing such solutions for this entire higher porosity range. On either side of the crack symmetry plane, this solution configuration consists of a leading plastic sector possessing radial stress characteristics (“generalized centered fan ”), followed by a plastic sector of constant Cartesian components of stress, followed finally by a sector of purely elastic material adjacent to the crack flank. The angular extents of these sectors vary substantially with porosity level. In regions of purely elastic response, we have accounted for the influence of porosity on the overall, or effective, elastic moduli. Among the interesting features of these new solutions are a significantly enlarged generalized centered fan sector as compared to that of the fully plastic Part I solutions for the same f values, and for f values just slightly above the 0.02979 level, a narrow elastic sector exists in which stresses vary so rapidly with angle that they appear to be nearly discontinuous. This rapid variation spreads out as the elastic sector enlarges with increasing f, and, in contrast to the fully plastic solutions, the radial normal component of stress becomes negative near the crack flank.