Transient analysis of a propagating crack with finite length subjected to a horizontally polarized shear wave

In this study\ the transient response of a _nite crack subjected to an incident horizontally polarized shear wave and then propagated with a constant speed in an unbounded elastic solid is investigated[ Initially\ the _nite crack with crack length l is stress!free and at rest[ At time t 9\ an incident horizontally polarized shear wave strikes at one of the crack tips and will arrive at the other tip at a later time[ Then\ two crack tips propagate along the crack tip line with di}erent velocities as the corresponding stress intensity factors reach their fracture toughness[ The correspondent con_guration is shown in Fig[ 0[ In analyzing this problemdi}racted waves generated by two propagating crack tips must be taken into account and it makes the analysis extremely di.cult[ In order to solve this problem\ the transform formula in the Laplace transform domain between moving and stationary coordinates is _rst established[ Complete solutions are determined by superposition of proposed fundamental solutions in the Laplace transform domain[ The fundamental solutions to be used are from the problems of applying exponentially distributed traction and screw dislocation on crack faces and along the crack tip line\ respectively[ The exact transient solutions of dynamic stress intensity factor for the _rst few di}racted waves that arrive at two crack tips are obtained and expressed in compact formulations[ Numerical calculations of dynamic stress intensity factors for both tips are evaluated and the results are discussed in detail