Evaluation by the stress intensity factor of two coplanar cracks in a piezoelectric strip under mechanical and transient thermal loadings

Abstract

In this paper, the fracture problem of a piezoelectric material strip containing two coplanar cracks perpendicular to its boundaries is considered. The problem is solved for a strip that is suddenly heated from both the top and the bottom surfaces under static mechanical loading. In spite of many studies in the thermo-electro-mechanical fracture problem of a piezoelectric material strip with a crack, not much work has been done in the context of the crack contact problem. The main object of this paper is also to study the crack contact problem. By using the Fourier transform, the thermoelectromechanical fracture problem is reduced to a system of singular integral equations, which are solved numerically. The numerical results for the stress and thermal stress intensity factors are computed as a function of the normalized time and geometric parameters. For the cases of two embedded cracks and an embedded crack and an edge crack, the effect of the upper crack geometry on the fracture behavior of the lower crack are considered under the pure mechanical load and the pure thermal load, respectively. The following facts can be found from the numerical results. First, the stress intensity factor of lower edge crack under pure mechanical load monotonically decreases with increasing the upper embedded crack length. Second, absolute value of the stress intensity factor of inner crack tip under the pure thermal load increases with increasing the heating temperature. Finally, taking the crack contact into consideration, it is found that the edge crack in the strip under the heating process would be fully closed at some time after the thermal shock.