ANALYTICAL SOLUTIONS OF GENERALIZED T-STRESS IN LINEAR PIEZOELECTRIC MEDIA UNDER VARIOUS CRACK-FACE CONDITIONS

Abstract

This thesis presents the closed-form solution of the generalized T-stress components of a penny-shaped crack in a transversely isotropic, linear piezoelectric, infinite medium under different crack-face conditions including electrically permeable, impermeable, semi-permeable and energetically consistent conditions. The solution for the case of uniform remote and crack-face mechanical/electrical loadings are derived for all four crack-face conditions whereas that for a crack under a pair of self-equilibrated, crack-face concentrated loads is obtained for permeable and impermeable cases. In the derivation, existing analytical solutions of the generalized stress field are employed together with an explicit expression resulting from the asymptotic expansion of the near-front field. All involved differentiations and limits are carried out in a careful manner following standard procedures and the final solution of the generalized T-stress components involves only elementary functions. In addition, the established Green’s function for the generalized T-stress is utilized to form an integral formula capable of computing the generalized T-stress for impermeable and permeable cracks under general crack-face loading. The analytical/semi-analytical feature of the derived solutions play a key role in the investigation of the influence of various parameters such as the crack-face conditions, electrical/mechanical far field, and the crack-face loading on the value of the generalized T-stress components along the crack front. A selected set of results is reported and significant and useful findings are concluded.