A microscopic model for the void growth behavior

A model for void growth behavior is developed on the basis of a dislocation theory. In order to model many uniformly distributed voids, a spherical unit cell with a growing void is considered to be subjected to a hydrostatic tensile stress under the condition of a constant applied strain rate. In the spherical unit cell, the relationships between several deformation parameters characterizing the void growth behavior are determined. It is assumed that as a void grows, it maintains the spherical shape and a constant average density of mobile dislocations in the intervoid matrix. A microscopic constitutive equation related to the void growth is established by correlating the mobility of dislocations to the thermally activated shear stress. Taking into account a mechanical condition that the applied energy rate is dissipated by the plastic work rate expended for the motion of dislocations, an equation controlling the void growth is developed. The relationship of the void growth rate to the hydrostatic tensile stress and the void fraction is derived as a function of the product of the thermally activated shear stress and the activation volume for dislocation motion for two limiting cases of the mobile dislocation distribution. The effect of localized deformation behavior on the void growth is discussed compared with a continuum plasticity theory.