Several cracks in a rectangular bar reinforced by a piezoelectric layer subjected to torsion

Abstract

This paper provides the torsional solution of multiple arbitrarily shaped cracks in an isotropic rectangular cross-section coated by a piezoelectric layer. A uniform electric displacement is applied on the left and right edges of the piezoelectric layer. First, the stress components and the warping function of the rectangular cross-section bar with the piezoelectric coating containing a Volterra-type screw dislocation are found in terms of the screw dislocation density function using Fourier integral transform. The dislocation solution is then reduced to a set of integral equations with a singularity of the Cauchy-type to examine multiple arbitrarily shaped cracks situated in the coated rectangular bar subjected to combining torsion and the forced electric displacement by making use of the distributed dislocation technique (DDT). The numerical solution of the integral equations is presented to calculate stress intensity factors (SIFs) and torsional stiffness. Next, several examples are presented to evaluate the effects of significant parameters on the fracture behavior of the problem. Furthermore, a novel idea is presented to reduce stress intensity factors to a minimum through suitable values of the uniform electric displacement on the left and right edges of the piezoelectric coating.