Void Growth and Collapse in Viscous Solids

Deformation of an isolated void in an infinite block of linearly or nonlinearly viscous material is studied for remote axisymmetric stressing. The material is isotropic and incompressible with a power-law dependence of strain-rate on stress. Included in the family of materials are a linearly viscous solid and a rigid–perfectly plastic solid at the extreme limit of nonlinearity. Evolution of the void shape and size is analyzed in detail for voids starting as spheres in the linearly viscous material under all possible combinations of remote axisymmetric stressing. Asymptotic, or self-similar, shapes towards which the voids evolve are exhibited as are the associated rates of growth or collapse. Under conditions of high remote triaxial stressing the growth-rate of the asymptotic void is found to be identical to that of a spherical void with the same volume. The influence of nonlinearity on the growth-rate and deformation of a spherical void is investigated. Under high triaxiality conditions the behavior of a void in the nonlinearly viscous or rigid–perfectly plastic material is qualitatively different from that of a void in a linearly viscous material. In particular, a void in a nonlinear block undergoing tensile straining with sufficiently large superimposed remote hydrostatic tension grows more rapidly in directions perpendicular to the straining direction than along it and becomes significantly oblate. Asymptotic growth-rates are estimated numerically for the nonlinear materials. The results for the isolated void are used in a simple, approximate way to investigate the roles of material nonlinearity and stressing conditions on the strain required for ductile failure by void growth and coalescence.