A contact zone approach for an arc crack at the interface between two electrostrictive materials

Solution of the contact problem for an electrostrictive plane with circular electrostrictive inclusion having an arc crack at the materials interface under the influence of general mechanical and electrical loadings at infinity is obtained. It is assumed that both materials are isotropic and linear elastic and crack faces are smooth and permeable to an electric field. The problem is considered as an uncoupled problem of electroelasticity. Solution of electrostatics problem is obtained by complex potentials method. Boundary problem of electroelasticity for four complex potentials that are analogues of Kolosov–Muskhelishvili potentials is reduced to the singular integral equation of the second kind which is solved under the condition of displacements uniqueness and vanishing of the crack opening within the contact zone. Singular integral equation is resolved approximately by developed new algorithm which takes into account simultaneously a possible complex singularity at the “open” crack tips and a contact zone of unknown length. Crack opening, normal and shear stresses at materials interface and the stress intensity factors at the crack tips are found.