Conservation Laws for Microcrack Damage in Piezoelectric Materials

Abstract

This chapter focuses on characterizing damaged anisotropic piezoelectric materials by using the principles of fracture mechanics, i.e., the conservation laws and energy release rates. The interpretation and evaluation of the two components of the J _k vector along contours enclosing strongly interacting microcracks in two-dimensional piezoelectric materials are presented. The conservation laws of the J _k vector established by Budiansky and Rice (1973) in single crack problems for traditional non-piezoelectric materials and extended in the above chapters to interacting multiple cracks [Chen and Hasebe (1998) and Chen (2001a, b)] are re-examined for anisotropic piezoelectric materials containing interacting multiple cracks. The interaction problem for arrays of arbitrarily orientated and distributed microcracks subjected to combined mechanical and electrical loading is studied in detail. The contribution of the second component of the J _k vector, evaluated in the local coordinate system which is attached to each microcrack, to the J _k vector evaluated in the global coordinate system is calculated. It is found that the conservation laws of the J _k vector are still valid in damaged piezoelectric materials, although in the present problem the elastic and electric fields are coupled which add complications to the original formulations by Budiansky and Rice (1973).