Analytical solutions for multiple mode III cracks in a cylindrical bar with an orthotropic coating under dynamic loading

Abstract

This study presents an analytical formulation for a cylindrical bar, with an orthotropic layer, containing multiple mode III cracks under time-dependent torsion. The transient response to a dislocation cut with time-dependent Burgers vector is obtained in the cross-section of the cylindrical bar, with an orthotropic layer, with the help of the Fourier and Laplace transform. The dislocation solution is used to drive a group of singular integral equations for the study of circular domains with the orthotropic coating containing smooth radial cracks under transient torsional loading. The singular integral equations are evaluated numerically to calculate the torsional rigidity of the domain, and the dynamic stress intensity factors at the singular crack tips. Finally, there are several examples to illustrate the effect of the orthotropic coating on the dynamic stress intensity factors and torsional rigidity of the domain under consideration. K E Y W O R D Scylindrical bar, distributed dislocation method, dynamic stress intensity factor (DSIF), orthotropic coating, torsional transient loading