Dynamic stress intensity factors at the tip of a uniformly loaded semi-infinite crack in an orthotropic material

Abstract

A method for analyzing the elastodynamic response of an infinite orthotropic material with a semi-infinite crack under impact loads is presented. Uniform loading for three loading modes is considered, i.e. opening, in-plane shear and antiplane shear, and solution for the stress intensity factor history around the crack tip is found. Laplace and Fourier transforms along with the Wiener–Hopf technique are employed to solve the displacement formulation of the equations of motion. The asymptotic expression for the stress near the crack tip is analyzed which leads to a closed-form solution of the dynamic stress intensity factor for each loading mode. It is found that the stress intensity factors are proportional to the square root of time as expected. Results for orthotropic materials are shown to converge to known solutions for isotropic materials derived independently.