The Wiener-Hopf technique in elastodynamic crack problems with characteristic lengths in loading

Abstract

This paper describes a solution procedure for analyzing the elastodynamic fields of a semi-infinite crack in an otherwise unbounded solid. The deformations are caused by a pair of concentrated normal impact forces which are symmetric with respect to the crack plane and attain certain fixed characteristic lengths. The crucial steps in the analysis are based on integral transforms and the direct application of the Wiener-Hopf technique as if there were no fixed characteristic length. Exact expressions, which are the sum of a number of finite range integrations, are obtained for the resulting mode I transient stress intensity factors as functions of time. For comparison to previous works we also consider the particular situation when the pair of concentrated forces located a distance away from the crack tip are acting on the crack faces. The formulation departs significantly from the superposition argument used in previous works. The present formulation allows the solution to be presented in a more straightforward manner, and has potential with regard to other elastodynamic crack problems. The numerical results are presented for various characteristic lengths. It is shown that the behaviors of stress intensity factors, for the cases where the concentrated forces are not acting on the crack faces, experience finite discontinuities when direct longitudinal and transverse waves emitted from the loading position arrive at the crack tip. These are quite different from those where the concentrated forces are acting on the crack faces.