Torsional analysis of four-sided cross-sections coated by an orthotropic layer weakened by multiple defects

Abstract

In this study, an analytical model for a four-sided cross-section bar reinforced by an orthotropic coating weakened by multiple cracks and cavities, under torsional loading, is presented. The main scope of the paper is to evaluate the effects of an orthotropic coating on stress intensity factors in a four-sided cross-section bar weakened by multiple arbitrarily oriented cracks and cavities. The four-sided bar and its orthotropic coating are under torsional loading governed by Saint-Venant torsional theory. The torsional stress field of the four-sided domain reinforced by the orthotropic coating containing a screw dislocation was first achieved in terms of the screw dislocation density function by using finite Fourier transform. Then, the stress field of the problem is reduced to a set of integral equations with a Cauchy singularity in the domain using the distribution dislocation method. The stress intensity factors, the torsional rigidity of the domain and the hoop stress around the cavities will be determined by the numerical solution of these singular integral equations. The stress components in the vicinity of the crack tips, and Von-Mises yield criterion are utilized to determine plastic zone size ahead of the crack tips. Finally, multiple numerical results are provided to illustrate the capability of the dislocation method in handling different cases of crack and cavity configurations and arrangements.