Diffusive relaxation of stress concentrations at grain boundary cavities in elevated temperature creep

This work deals with certain aspects of elevated temperatures creep cavitation of grain boundaries under cyclic and rapidly applied loading. The response of partially damaged materials (where damage is represented as crack-like cavities on the grain boundaries) following load alterations at temperatures in the vicinity of 0.5 T_m or higher is analyzed. The interaction between grain boundary diffusion and elastic deformation is important in alleviating local stress concentrations under these conditions. The stress levels considered are assumed to be low enough that plastic deformation is significant. Diffusive processes contribute to high temperature creep rupture by material redistribution from the void surfaces to the grain boundaries, and any non-uniform matter accommodation along the grain boundaries is accomplished by elastic deformation under the conditions assumed. The same material redistribution mechanism dominates in the stress relaxation process. The analysis of the stress and displacement fields is based on consideration of the coupled elasticity-diffusion boundary value problem, which leads to an integral equation. On the basis of the solution obtained, the detailed analysis of the process under cyclic, step and ramp loadings is given. For suddenly applied loading the results demonstrate that the elastic stress concentration is effectively relaxed by diffusion after t = 0.05τ where $\text{τ ≈}\text{L}{}^3\text{DE}$, L is half of the distance between adjacent tips of neighboring cracks along the grain boundary, E is Young's modulus, and D is diffusion parameter relating volumetric flux along the grain boundary to the stress gradient. By t = 0.25τ the stress distribution becomes essentially identical to that calculated for rigid grains, i.e. diffusion has become the dominant process and elastic deformability of the adjoining grains is then irrelevant.