On a plane crack in piezoelectric solids

A new analytical solution for a piezoelectric plane with an elliptical void is derived by removing the commonly held assumptions that the void boundary is impermeable and a void axis is perpendicular to the poling direction. The approach of Lekhnitskiiʹs complex potential functions is used in the derivation. Applicability of the common practice of reducing a void solution to a crack solution is examined. It is shown that a recently reported solution for exact electric boundary conditions is actually the well known solution for a permeable crack. A unified formulation for plane cracks containing air or vacuum is then developed to account for different electric boundary conditions. Crack closure is taken into consideration in the analysis. The influence of electric boundary conditions and crack orientation on fracture parameters is discussed.