Journal of the Nigerian Association of Mathematical Physics

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

M O Oyesanya


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
AJOL African Journals Online