INFLUENCE OF POROSITY ON PLANE-STRAIN TENSILE CRACK-TIP STRESS-FIELDSIN ELASTIC-PLASTIC MATERIALS .2.

This paper continues the investigation of Drugan and Miao (1992). Ther e we studied analytically the influence of a uniform porosity distribu tion on the stress field near a plane strain tensile crack tip in duct ile (elastic-ideally plastic) material, assuming that material very ne ar the tip is at yield at all angles about the tip. Our solutions exhi bited completely continuous stress fields for porosity f less-than-or- equal-to 0. 02979, but for higher porosities they involved radial surf aces of radial normal stress jumps. Here we investigate whether, for t his higher range of porosity, relaxing our assumption of yield at all angles about the tip will facilitate solutions exhibiting fully contin uous stress fields. The answer to this is shown to be yes, with a sing le near-tip sector assembly providing such solutions for this entire h igher porosity range. On either side of the crack symmetry plane, this solution configuration consists of a leading plastic sector possessin g radial stress characteristics (''generalized centered fan''), follow ed by a plastic sector of constant Cartesian components of stress, fol lowed finally by a sector of purely elastic material adjacent to the c rack flank, The angular extents of these sectors vary substantially wi th porosity level. In regions of purely elastic response, we have acco unted for the influence of porosity on the overall, or effective, elas tic moduli. Among the interesting features of these new solutions are a significantly enlarged generalized centered fan sector as compared t o that of the fully plastic Part I solutions for the same f values, an d 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 th e fully plastic solutions, the radial normal component of stress becom es negative near the crack flank.