Fracture-mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models (Q1573739)

The authors consider an interface crack between two semi-infinite ceramic half-spaces under remote mixed-mode loading. By assuming that the displacements and electrical potential fields are independent of the coordinate \(x_2\), the stresses and electrical displacements as well as the derivatives of displacement and electrical potential jumps are presented via a sectionally holomorphic vector function analytically continued across mechanically and electrically bonded parts of material interface. By introducing an artificial frictionless contact zone at the right-hand side crack tip, and by assuming electrically permeable crack faces, the problem is reduced to a combined Dirichlet-Riemann boundary value problem. An exact analytical solution of this problem is found and stresses, electrical displacements and derivatives of displacement and electrical potential jumps along the correspondent parts of the material interface are written in a clear analytical form. The stress intensity factors (SIFs) and the energy release rates (ERRs) at the singular points are found, and the electrical intensity factor could be expressed via these values. The contact zone model (in Comninou's sense) is derived as a particular case of the obtained solution. The authors derive a simple transcendental equation and corresponding asymptotic formulas for the determination of real contact zone length. It is shown that only for a remote tension stress the real contact zone length is extremely small, while for an essential shear field it becomes longer and even comparable with the crack length. Another important case of the solution corresponding to zero artificial contact zone length is analyzed as well. This case coincides with a classical approach to interface crack investigation, and leads to a solution possessing oscillating singularities at the crack tip. Associated SIFs, ERRs and mechanical and electrical fields at the crack tip are found in an analytical form which is similar to the corresponding solution for a crack between two isotropic semi-infinite planes. Analytical relationships between fracture-mechanical parameters of various models are found, and recommendations are suggested concerning the application of numerical methods to the problem of interface crack in the discontinuity area of a piezoelectric bimaterial.