Conservation laws of the J(k)-vector for microcrack damage in piezoelectric materials

This paper focuses on characterizing damaged anisotropic piezoelectric mate rials by using the principles of fracture mechanics. The interpretation and evaluation of the two components of the J(k)-vector along contours enclosi ng strongly interacting microcracks in two-dimensional piezoelectric materi als are presented. The conservation laws of the J(k)-vector established by Budiansky and Rice (ASME J. Appl. Mech. 40 (1973) 201) for traditional non- piezoelectric materials and extended by Chen and Hasebe (Int. J. Fract. 89 (1998) 333) and Chen (Int. J. Solids Struct. 38 (2000a) 3193 and 38 (2000b) 3213) for interacting multiple cracks are reexamined for anisotropic piezo electric materials containing interacting multiple cracks. The interaction problem for arrays of arbitrarily orientated and distributed microcracks su bjected to mechanical and electrical loading is studied in detail. The cont ribution of the second component of the J(k)-vector, evaluated in the local coordinate system that is attached to each microcrack, to the J(k)-vector evaluated in the global coordinate system is calculated. It is found that t he conservation laws of the J(k)-vector are still valid in damaged piezoele ctric materials, although in the present problem the elastic and electric f ields are coupled which add complications to the original formulations by B udiansky and Rice. In other words, the total contributions from the microcr acks to both components of the J(k)-vector evaluated in the global system v anish, provided that the selected closed contour encloses all microcracks a nd/or discontinuities. (C) 2001 Published by Elsevier Science Ltd.