Axisymmetric Problem of Energetically Consistent Interacting Annular and Penny-Shaped Cracks in Piezoelectric Materials

Abstract

The axisymmetric problem of a concentric set of energetically consistent annular and penny-shaped cracks in an infinite piezoelectric body subjected to uniform far-field electromechanical loading is addressed. With the aid of a robust innovated technique, the pertinent four-part mixed boundary value problem (MBVP) is reduced to a decoupled Fredholm integral equation of the second kind. The results of two limiting cases of a single penny-shaped crack and a single annular crack are recovered. The contour plots of dimensionless intensity factors (IFs) at each crack front provide the stress and electric displacement intensity factors (SIFs and EDIFs, respectively) for all combination of crack sizes. The impermeable, permeable, and semipermeable models are also examined as limiting cases.