On the Integro‐Differential Equation Associated with Diffusive Crack Growth Theory

May 2003
Quarterly Journal of Mechanics & Applied Mathematics;May2003, Vol. 56 Issue 2, p289
Academic Journal
At high temperatures, polycrystalline materials often suffer creep fracture under prolonged loading conditions. Microstructural examinations reveal that nucleation, propagation and linkage of interfacial cracks normal to the principal stress directions are responsible for the premature failure. To simulate service conditions, a semi‐infinite crack is considered to grow, in steady state, along a grain boundary via a coupled process of surface and grain‐boundary diffusion within an elastic bi‐crystal subjected to a remote constant applied stress. Governing equations based on equilibrium and Hooke's law obeyed within the adjoining grains, and matter conservation and Fick's diffusion laws prevailing at both crack surfaces and the interface are employed to derive the singular integro‐differential equation for the normal stress distribution along the interface ahead of the moving crack tip.


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