Sf. Li et Pa. Mataga, DYNAMIC CRACK-PROPAGATION IN PIEZOELECTRIC MATERIALS .1. ELECTRODE SOLUTION, Journal of the mechanics and physics of solids, 44(11), 1996, pp. 1799-1830
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