Macrocrack-microcrack interaction in piezoelectric materials, Part I: Basic formulations and J-analysis

The macrocrack-microcrack interaction problem in transversely isotropic pie zoelectric materials is studied. The microcracks near a macrocrack tip in t he 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 config urations and under different loading conditions are given, from which the i nteraction 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 mod e II stress intensity factors and the electric displacement intensity facto r are evaluated. In order to confirm the proposed method as well as the num erical results, a consistency check is proposed which is based on the J-int egral analysis and provides a powerful tool to examine the numerical result s. Thus, any mistakes are avoided since they would certainly lead to unsati sfied numerical results contrary to the check. It is concluded also that th e disturbance of the near-tip electric field provides another source of shi elding.