Void growth in power-law creeping solids: Effect of surface diffusion and surface energy

This paper addresses the growth of a void in a nonlinearly creeping material in the presence of the void-surface energy effect and void-surface diffusion driven by surface curvature gradients. Large strain finite element analysis of the coupled problem indicates that microstructural variables (porosity and void aspect ratio), as well as macroscopic deformation rates are strongly affected by the relative strength of the void-surface energy effect and the void-surface diffusion process vis-a-vis the rate of creep deformation in the bulk of the solid. The phenomenon is characterized by two-dimensionless groups, one measuring the strength of the surface diffusion process with respect to the nonlinear creep deformation in the interior of the solid, and the other the magnitude of the surface energy of the void in relation to the applied load and the size of the void. The computations reveal a rich variety of solutions that reflect a wide range of external load, material, and geometric parameters. Classical void growth studies that ignore both surface diffusion and surface energy effects are shown to recover only one case of this family of solutions. The computations also serve to quantitatively evaluate recent constitutive theories for porous nonlinear materials that account for continuously evolving microstructure, but do not include surface diffusion or surface energy effects.