Transient Analysis of a Semi-infinite Crack Subjected to Dynamic Concentrated Forces

Abstract

An exact transient closed-form solution for a semi-infinite crack subjected to a timedependent concentrated force is obtained in this study. The total wave field is due to the effect of this point source and the scattering of the incident waves by the crack tip. An alternative methodology for constructing the reflected and diffracted field is proposed, which proves both powerful and efficient in solving complicated dynamic crack problems. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem. The waves reflected by the traction-free crack surface and diffracted from the crack tip can be constructed by superimposing this fundamental solution. The superposition is performed in the Laplace transform domain. Numerical results for the time history of stresses and stress intensity factors during the transient process are obtained and compared with the corresponding static values. It is shown that the field solution will approach the static value after the last diffracted wave has passed.