A theoretical study of branched cracks in piezoelectrics

The plane problem of a brittle piezoceramic with an arbitrarily oriented br anched crack is theoretically investigated in this study. Lekhnitskii's com plex potentials and a distributed dislocation model are employed to formula te the problem. The crack closure is taken into consideration. The branched crack problem is reduced to solving three singular integral equations. The accuracy of the present scheme is confirmed by comparison with the existin g results in the literature. The results obtained in this study present cri tical information about the electroelastic fields and fracture parameters a ssociated with a branched crack in piezoceramics. Numerical results show th at applied electric loading has a significant effect on branched cracks. Th e criterion of a modified hoop stress intensity factor, which accounts for fracture toughness anisotropy, is applied to predict potential branching di rections. Numerical examples indicate that a crack may branch off from a st raight path even under symmetric loading and geometry. The present scheme c omplemented with an experimentally validated fracture criterion can be used to simulate crack branching in piezoelectrics. (C) 2000 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.