Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part I: Basic Formulations and J-Analysis

The macrocrack-microcrack interaction problem in transversely isotropic piezoelectric materials is studied. The microcracks near a macrocrack tip in the process zone are assumed to be parallel to the latter, while the poling direction of the piezoelectric materials is assumed to be perpendicular to the cracks. Three kinds of elementary solutions with different crack configurations and under different loading conditions are given, from which the interaction problem is reduced to a system of Fredholm integral equations by using the pseudo-traction electric displacement method (abbreviated PTED). After the equations are solved numerically, the traditional mode I and mode II stress intensity factors and the electric displacement intensity factor are evaluated. In order to confirm the proposed method as well as the numerical results, a consistency check is proposed which is based on the J-integral analysis and provides a powerful tool to examine the numerical results. Thus, any mistakes are avoided since they would certainly lead to unsatisfied numerical results contrary to the check. It is concluded also that the disturbance of the near-tip electric field provides another source of shielding.