Fracture initiation in a thermoelastic solid with relaxation: Transient three-dimensional analysis

Abstract

ABSTRACTTransient, 3D growth of a plane, brittle crack in an isotropic, thermoelastic solid is considered. The solid is initially at rest at uniform (absolute) temperature and contains a semi-infinite, plane crack. Growth is caused by the application of in-plane and normal point forces to each face of the crack. The related problem of displacement discontinuities that exist on regions that exhibit dynamic similarity is first considered. An exact solution in integral transform space leads to asymptotic forms, valid for short times. These are used to generate equations of the Wiener–Hopf type for the fracture problem. Analytic solution expressions are obtained and, upon inversion, subjected to a dynamic energy release rate criterion that includes kinetic energy. Results show that a particular form of rapid growth in time of the forces can, in the crack initiation phase, cause crack growth rates that vary with position, but not with time.