Fracture mechanical assessment of interface cracks with contact zones in piezoelectric bimaterials under thermoelectromechanical loadings: I. Electrically permeable interface cracks

An electrically permeable interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric spaces under the action of a remote electromechanical loading and a temperature flux is considered. Assuming that all fields are independent on the coordinate x₂ co-directed with the crack front, the stresses, the electrical and the temperature fluxes as well as the derivatives of the jumps of the displacements, the electrical potential and the temperature at the interface are presented via a set of analytic functions in the (x₁,x₃)-plane with a cut along the crack. Due to this representation firstly an auxiliary problem concerning the direction of the heat flux permitting a transition from a perfect thermal contact to a separation has been solved for a piezoelectric bimaterial. Besides, an inhomogeneous combined Dirichlet–Riemann boundary value problem has been formulated and solved exactly for the above mentioned interface crack. Stress and electrical displacements intensity factors are found in a clear analytical form which is especially easier for a small contact zone length. A simple equation and a closed form analytical formula for the determination of the real contact zone length have been derived and compared with the associated equation of the classical (oscillating) interface crack model defining the zone of crack faces interpenetration. For a numerical illustration of the obtained results a bimaterial cadmium selenium/glass has been used, and the influence of the heat flux upon the contact zone length and the associated stress intensity factor has been shown.