Generalized T-stress solutions for penny-shaped cracks in transversely isotropic piezoelectric media

Abstract

A novel set of analytical and semi-analytical solutions is obtained for the generalized T-stress for both electrically impermeable and permeable penny-shaped cracks embedded in a transversely isotropic, linear piezoelectric, infinite medium under uniform far-field loading and general mechanical and electrical crack-face loading. The generalized stress field of the crack for two basic loading cases, viz. uniformly distributed self-equilibrated crack-face loading and a pair of crack-face self-equilibrated unit normal point forces and unit point electrical charges, are employed together with the asymptotic near-front expansion to establish fundamental solutions for the generalized T-stress. Such fundamental solutions are explicit and involve only elementary functions, and are then utilized to form an explicit integral formula for computing the generalized T-stress of a penny-shaped crack under general crack-face loading. The exact integration of the integral formula is also established for specific loading conditions, whereas its evaluation via an efficient quadrature for general loading conditions is also addressed. A selected set of numerical results is presented to verify the proposed quadrature and significant and useful findings are also reported.