Effect of the mechanical boundary condition at the crack surfaces on the stress distribution at the crack tip in piezoelectric materials

A finite element technique is used to study the stress distributions at the crack tip of a piezoelectric ceramic because of the combined mechanical and electrical loads. For high electrical to mechanical load ratios, the assumption of crack surfaces to be free of surface traction as the mechanical boundary condition is not valid for two cases of combined electrical and mechanical loadings—(i) applied stress and negative applied electric field (electric field opposite to the direction of poling) and (ii) applied strain and positive applied electric field. The stress distributions at the crack tip for these loading conditions under the assumption of closed crack mechanical boundary condition are found to be different from those under the assumption of crack surfaces to be free of surface traction.