Influence of Permittivity of a Medium inside the Crack Gap on Generalized T-stresses of Cracks in 3D Piezoelectric Media

Abstract

This paper investigates the influence of the permittivity of a medium inside the crack gap on generalized T-stresses of planar and non-planar cracks in a linear piezoelectric media under semi-permeable and energetically consistent boundary conditions by using the boundary element method. Penny-shaped planar crack and spherical cap non-planar crack are investigated in the present study. Numerical results indicate that the permittivity of a medium inside the crack gap plays an important role on the values of the generalized T-stresses. Solutions of generalized T-stresses of a penny-shaped crack with semi-permeable and energetically consistent boundary conditions lie between the permeable solution (upper bound) and the impermeable solution (lower bound) for the entire range of permittivity of a medium considered in the numerical study. It is evidently indicated from the numerical results that when the permittivity of a medium inside the crack gap increases, the energetically consistent solution approaches the permeable solution more quickly than the semi-permeable solution. In addition, the non-planar geometry of the crack surface of the spherical cap crack causes the upper and lower bounds of the generalized T-stresses to differ from those of the penny-shaped planar crack. More specifically, besides the permeable and impermeable solutions, the energetically consistent solution is the bound of the generalized T-stress for the spherical cap crack.