Shape change of a pore in a stressed solid via surface diffusion motivated by surface and elastic energy variation

When a solid is stressed at a high temperature, atoms may move along various paths, causing a pore pre-existing in the solid to change shape. This paper assumes that atoms only diffuse on the pore surface and the solid is elastic. Both surface energy and elastic energy vary as the pore changes shape. When the surface energy variation dominates, the pore evolves to an equilibrium shape close to an ellipse. When the elastic energy variation dominates, the pore never reaches equilibrium ; noses emerge and sharpen into crack tips. We describe the pore shape with a conformal mapping of many terms, determine the elastic field by a complex variable method, and evolve the mapping coefficients (and thereby the pore shape) by a set of ordinary differential equations. The numerical simulation gives the threshold for the shape instability, the time for a supercritical pore to grow crack tips, and the crack size when it just forms. Also explored are the effects of the applied stress state and surface tension anisotropy. We discuss the implications of the results for the lifetime of crystals stressed at elevated temperatures.