Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

A closed-form solution is constructed for a bi-material consisting of two piezoelectric (or piezoelectric and dielectric) half-planes, which are periodically bonded along the interface and can partially contact along the initially unbonded parts. Under compressive loading, the size of the frictionless contact zone is usually quite large; in some cases the interface is completely closed. Such a situation is frequently observed in industrial applications. Since the periodic bonding of two different materials is extremely widespread, it is very important to study the influence of the mutual material properties of the composite and the applied loading on the size and shape of the opened regions, as well as the stress intensity factor at the bonding points. To formulate the problem, the electromechanical factors are presented through piecewise analytic functions, so that the problem in question is reduced to the combined periodic Dirichlet–Riemann problem, which is solved exactly. The obtained solution provides explicit formulas for the mechanical stresses and displacements along the interface and allows one to find the dependence of the contact zones and the stress intensity factor on the ratio of the bonded parts of the interface to the period for the different values of applied loading and materials.