Void collapse and void growth in crystalline solids

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Abstract
The problem of large deformation and eventual collapse (or growth to a final shape, depending on the microstructure and loading) of voids in a crystalline solid which undergoes plastic flow by slip on crystallographic planes is considered and solved analytically for plane problems, using certain reasonable simplifying assumptions. It is shown that because of local anisotropic plastic flow, an initially circular (in two dimensions or spherical in three dimensions) void quickly deforms into a noncircular (or nonspherical) shape, even under all-around uniform far-field pressure or tension. Using an incremental solution, the shape of the void at each loading stage is approximated by an equivalent ellipse, and this procedure is continued until either the void collapses into a crack (which occurs always under compression and in special cases even under tension) or attains a constant aspect ratio (under tension only). The residual stresses in the vicinity of the collapsing void are calculated and used to establish whether or not the crack which is formed by the void collapse will continue to grow upon the release of the overall uniform compressive loads. It is shown that this depends on the initial void size, on the ductility of the material, as well as on the rate of the loading which affects the ductility. The mechanism of possible overall failure caused by void collapse under far-field compressive loads and possible subsequent crack growth upon unloading is studied, using power-law rate-dependent plastic slip and experimental results on flow stress under shock loading. Results are compared with experimental observations, arriving at good agreement. In particular, the important effect of the loading rate on void collapse and subsequent failure mode is illustrated. Furthermore, the void growth processes under simple shear and tensile loading are investigated, and it is shown that, depending on the far-field loading condition and the microstructure, a void may grow by self-similar expansion or it may collapse into a crack. The mechanisms of void deformation under various loading conditions are illustrated.

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