On the penny-shaped crack in a non-homogeneous interlayer under torsion

Abstract

This paper presents a theoretical treatment of a penny-shaped crack in an interfacial zone, along the thickness of which the elastic modulus is assumed as μ₂(z) = (α +bz)^k, wherek represents the distribution parameter independent of material properties and interlayer thicknessh. The theoretical formulations governing the torsion deformation behavior of the material are based on the use of a dislocation density function and integral transform technique. The stress intensity factor is obtained by solving a singular integral equation. Numerical examples are given to show the effects of material properties, interlayer thickness, and especially the distribution parameterk on the stress intensity factor. In the numerical procedure, modified Bessel functions are used, and the rate of convergence depends greatly on the ratio ofh/c, wherec is the crack radius.