In this study, the transient response of a surface crack in an elastic solid subjected to dynamic anti-plane concentrated loadings is investigated. The angles of the surface crack and the half-plane are 60° and 90°. In analyzing this problem, an infinite number of diffracted and reflected waves generated by the crack tip and edge boundaries must be taken into account and it will make the analysis extremely difficult. The solutions are determined by superposition of the proposed fundamental solution in the Laplace transform domain and by using the method of image. The fundamental solution to be used is the problem for applying exponentially distributed traction on the crack faces. The exact transient solutions of dynamic stress intensity factor are obtained and expressed in formulations of series form. The solutions are valid for an infinite length of time and have accounted for the contribution of an infinite number of diffracted waves. The explicit value of the dynamic overshot for the perpendicular surface crack is obtained from the analysis. Numerical results are evaluated which indicate that the dynamic stress intensity factors will oscillate near the correspondent static values after the first three or six waves have passed the crack tip.
International Journal of Fracture 109(3), pp.239-261