Transient elastodynamic analysis of a penny-shaped crack

Abstract

Transient elastodynamic analysis of a stationary penny-shaped crack in an infinite elastic solid is presented. The analysis is based on a non-hypersingular time-domain boundary integral equation method and is fully three-dimensional. An incident, transient and planar displacement pulse of longitudinal or transverse wave-type is taken as applied loading. A collocation method is used for solving the time-domain boundary integral equations. Constant elements are applied away from the crack front, while special elements called “crack front elements” are adopted near the crack front to describe the local behavior of the unknown quantities properly. By using a linear shape function in time and by invoking the causality and the time-translation properties of Green's functions, an explicit time-stepping scheme is obtained for computing the discrete crack opening displacements at the collocation points, from which the transient dynamic stress intensity factors are subsequently extracted. Numerical results are presented for several cases, to analyze the dynamic overshoot phenomena and the effects of the type and direction of incident transient elastic waves on the time history and the spatial variation of the dynamic stress intensity factors.