Dynamic fracture analysis of a finite crack subjected to an incident horizontally polarized shear wave

Abstract

The transient response for diffraction of an incident horizontally polarized shear wave by a finite crack in an unbounded elastic solid is investigated in this study. In analyzing this problem, an infinite number of diffracted waves generated by two crack tips must be taken into account that will make the analysis extremely difficult. An alternative methodology different from the conventional superposition method is used to construct the reflected and diffracted fields. The complete solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are the problems for applying exponentially distributed (in the Laplace transform domain) traction and screw dislocation on the crack faces and along the crack tip line, respectively. The exact transient closed form solutions of dynamic stress intensity factor for two crack tips are obtained and expressed in very simple and compact formulations. Each term in the formulations has its own physical meaning. The solutions are valid for an infinite length of time and have accounted for the contributions of an infinite number of diffracted waves. Numerical results of both tips for different incident angles are evaluated which indicate that the dynamic stress intensity factors will oscillate near the correspondent static values after the first three waves have passed the specified crack tip. Some discrepancies of the numerical results compared with available solutions are discussed in detail.