Transient analysis of fracture initiation in a coupled thermoelastic solid

An isotropic, thermoelastic solid is initially at rest at uniform (absolute) temperature, and contains a semi-infinite, plane crack. Application of in-plane and normal point forces to each face of the crack causes transient 3D growth. The related problem of discontinuities in temperature and displacement that exist on regions that exhibit dynamic similarity is first considered. Asymptotic expressions, whose inverses are valid near the crack edges for short times, are obtained in integral transform space. These lead to equations of the Wiener–Hopf type for the fracture problem. Analytical solutions are obtained and, upon inversion, subjected to a dynamic energy release rate criterion that accounts for kinetic energy. A particular form of rapid growth in time of the forces is found to cause crack initiation growth rates that indeed vary with position, but not with time. The influence of particular types of mixed-mode loading upon crack edge contour and thermal response near the edge is also examined.