Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

Abstract

A two-dimensional steady-state analysis of semi-infinite brittle crack growth at a constant subcritical rate in an unbounded fully-coupled thermoelastic solid under mixed-mode thermomechanical loading is made. The loading consists of normal and shear tractions and heat fluxes applied as point sources (line loads in the out-of-plane direction). A related problem is solved exactly in an integral transform space, and robust asymptotic forms used to reduce the original problem to a set of integral equations. The equations are partially coupled and exhibit operators of both Cauchy and Abel types, yet can be solved analytically. The temperature change field at a distance from the moving crack edge is then constructed, and its dominant term is found to be controlled by the imposed heat fluxes. The role of this term is, indeed, enhanced if the heat fluxes serve to render the crack as a net heat source/sink for the solid, as opposed to being a transmitter of heat across its plane. More generally, the influence of thermoelastic coupling on this field, as well as other functions, is found to increase with crack speed.