DYNAMIC CRACK-PROPAGATION IN PIEZOELECTRIC MATERIALS .1. ELECTRODE SOLUTION

An analysis is performed for the transient response of a semi-infinite , anti-plane crack propagating in a hexagonal piezoelectric medium. Th e mixed boundary value problem is solved by transform methods together with the Wiener-Hopf and Cagniard-de Hoop techniques. As a special ca se, a closed form solution is obtained for constant speed crack propag ation under external anti-plane shear loading with the conducting elec trode type of electric boundary condition imposed on the crack surface (a second type of boundary condition is considered in Part II of this work). In purely elastic, transversely isotropic elastic solids, ther e is no antiplane mode surface wave. However, for certain orientations of piezoelectric materials, a surface wave will occur-the Bleustein-G ulyaev wave. Since surface wave speeds strongly influence crack propag ation, the nature of antiplane dynamic fracture in piezoelectric mater ials is fundamentally different from that in purely elastic solids, ex hibiting many features only associated with the in-plane modes in the elastic case. For a general distribution of crack face tractions, the dynamic stress intensity factor and the dynamic electric displacement intensity factor are derived and discussed in detail for the electrode case. As for inplane elastodynamic fracture, the stress intensity fac tor and energy release rate go to zero as the crack propagation veloci ty approaches the surface wave speed. However, the electric displaceme nt intensity does not vanish. Copyright (C) 1996 Elsevier Science Ltd