A theoretical study of branched cracks in piezoelectrics

Abstract The plane problem of a brittle piezoceramic with an arbitrarily oriented branched crack is theoretically investigated in this study. Lekhnitskii’s complex potentials and a distributed dislocation model are employed to formulate 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 existing results in the literature. The results obtained in this study present critical information about the electroelastic fields and fracture parameters associated with a branched crack in piezoceramics. Numerical results show that applied electric loading has a significant effect on branched cracks. The criterion of a modified hoop stress intensity factor, which accounts for fracture toughness anisotropy, is applied to predict potential branching directions. Numerical examples indicate that a crack may branch off from a straight path even under symmetric loading and geometry. The present scheme complemented with an experimentally validated fracture criterion can be used to simulate crack branching in piezoelectrics.