A plane strain problem for an electrically conducting interface crack between linear
transversely isotropic piezoelectric and isotropic elastic conductor materials under
remote mechanical loading is considered. The attention is focused on a hybrid
complex variable method which combines the Stroh formalism for piezoelectric
materials with the Muskhelishvili formalism for conducting isotropic elastic materials.
This method is illustrated in detail for the open crack model and the contact zone
crack model. Using special presentations of mechanical quantities via sectionally
analytic functions, a combined Dirichlet–Riemann and Hilbert boundary value
problem is formulated and solved analytically. Stress intensity factors as well
as the crack tip energy release rate are found in a clear analytical form.
Furthermore, transcendental equations for the determination of the realistic contact
zone length and the location of the first interpenetration point have been
obtained. A significant influence of the external mechanical loading on the crack
opening and the stresses as well as the contact zone and interpenetration
region lengths is observed. The dependencies of the mentioned values on the
intensities of the mechanical loading are presented in tables and associated
diagrams.
