Analysis of Stress-Strain Relationship in Materials Containing Voids by Means of Plastic Finite Element Method.

Abstract

Applying the finite element method in two dimensions, an analysis is performed to derive the stress-strain relationship of material containing voids in matrix, and which is subjected to large deformation. The conditions assumed for the analysis are applicability of continuum body mechanics, Mises yield criterion, J2 flow theory, power work-hardening, plane stress in two-dimensional system and uniform cyclically recurring void distribution. Taking as example a case of material presenting 0.3 work-hardening, it is indicated from the analysis that:- —With voids arrayed in square lattice, total elongation would be little affected by change in void size; —With a void spacing in lattice of 10 fim, a uniform elongation 12–14% should be obtained in a wide range of void sizes from 0.01 to 8.0 μm; —Tensile strength should start to lower at a void areal fraction of around 1%; —A sharply lowered uniform elongation of a level far below 1% should be presented by material of low work-hardening exponent. The severe decline of ductility seen with 316 stainless steel upon neutron irradiation at temperatures around 600 K is interpreted as resulting from a combination of low work-hardening and the presence of voids in matrix.