Power series like relation of power law and coupled creep constrained grain boundary cavitation under strain gradient plasticity analysis

Abstract

The continuum damage theory of Kachanov and Rabotnov has limitations since the mechanical properties of a material (especially plastic deformation and fracture) are determined by its microstructure. When a solid deforms at high temperature its microstructure may in some sense be altered- holes and cracks may nucleate and grow inside the solid by various mechanism controlled by diffusion and by power law creep or by a combination of these mechanisms. Considering a coupled diffusion power law creep mechanism using a mechanistic model approximate analytical equations for the growth rate under multi-axial stress states are developed. These results are related to the power law mechanistic results in a power series like form, which are used to analyze the crack, tip fields for the coupled mechanism using a strain gradient plasticity analysis. The Kachanov-Rabotnov results and the HRR results are shown to be special cases of these results. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 25-34