On a moving interface crack with a contact zone in a piezoelectric bimaterial

An inplane problem for a crack moving with constant subsonic speed along the interface of two piezoelectric materials is considered. A mechanically frictionless and electrically permeable contact zone is assumed at the right crack tip whilst for the open part of the crack both electrically permeable and electrically insulated conditions are considered. In the first case a moving concentrated loading is prescribed at the crack faces and in the second case an additional electrical charge at the crack faces is prescribed as well. The main attention is devoted to electrically permeable crack faces. Introducing a moving coordinate system at the leading crack tip the corresponding inhomogeneous combined Dirichlet–Riemann problem is formulated and solved exactly for this case. All electromechanical characteristics at the interface are presented in a closed form for arbitrary contact zone lengths, and further, the transcendental equation for the determination of the real contact zone length is derived. As a particular case of the obtained solution a semi-infinite crack with a contact zone is considered. The numerical analysis performed for a certain piezoelectric bimaterial showed an essential increase of the contact zone length and the associated stress intensity factor especially for the near-critical speed region. Similar investigations have been performed for an electrically insulated crack and the same behavior of the above mentioned parameters is observed.