Transient Analysis of a Propagating In-Plane Crack in a Finite Geometry Body Subjected to Static Loadings

Abstract

In this study, a cracked body with finite boundaries subjected to static loading and the crack propagating with a constant speed are analyzed. The interaction of the propagating crack with reflected waves generated from traction-free boundaries is investigated in detail. The methodology for constructing the scattered field by superimposing the fundamental solution in the Laplace transform domain is proposed. The fundamental solutions represent the responses of applying exponentially distributed loadings in the Laplace transform domain on the surface of a half-plane or a crack. The dynamic stress intensity factors of a propagating crack induced from the interaction with the first few reflected waves generated from the traction-free boundary are obtained in an explicit closed form. The analytical solutions of dynamic stress intensity factors are compared with available numerical and experimental results and the agreement is quite good. We find one thing very interesting: the dynamic stress intensity factor for a long time period is a universal function of the instantaneous extending rate of a crack tip times the static stress intensity factor for an equivalent stationary crack for the finite strip problem. It was also found that the reflected waves generated from free boundaries always increase the stress intensity factor, and the influence from reflected waves generated from the boundary, which is perpendicular to the crack, are weaker than those generated from the boundary, which is parallel to the crack.