Elastodynamic analysis of the Finite punch and finite crack problems in orthotropic materials

Abstract

The transient elastodynamic response of the finite punch and finite crack problems in orthotropic materials is examined. Solution for the stress intensity factor history around the punch corner and crack tip is found. Laplace and Fourier transforms together with the Wiener–Hopf technique are employed to solve the equations of motion in terms of displacements. A detailed analysis is made in the simplified case when a flat rigid punch indents an elastic orthotropic half-plane, the punch approaches with a constant velocity normally to the boundary of the half-plane. An asymptotic expression for the singular stress near the punch corner is analyzed leading to an explicit expression for the dynamic stress intensity factor which is valid for the time the dilatational wave takes to travel twice the punch width. In the crack problem, a finite crack is considered in an infinite orthotropic plane. The crack faces are loaded by impact uniform pressure in mode I. An expression for the dynamic stress intensity factor is found which is valid while the dilatational wave travels the crack length twice. Results for orthotropic materials are shown to converge to known solutions for isotropic materials derived independently.