Dynamics steady crack propagation of antiplane shear in an elastic perfectly plastic material

Abstract

A theoretical analysis of steady‐state crack growth in an elastic ideally‐plastic material under small‐scale yielding conditions has been carried out for anti‐plane shear. Asymptotic expansion method is used to construct the solutions for the region near the crack line. Exact solutions for the distribution of strain on the crack line within the primary active plastic zone is obtained. It is shown that the solution reduces to the correct asymptotic form as the crack speed approaches zero (quasi‐static) for any point on the crack line. The results are used to discuss the applicability of quasi‐static solutions to moving steady‐state situations. It is found that if the crack propagation speed is less than 0.1 of the shear wave speed, the quasi‐static solutions can be accurately approximated for the steady state solutions.