Two collinear cracks under combined quadratic thermo-electro-elastic loading

Abstract

The fracture problem of piezoelectric materials in multi-field coupling is a very attractive research topic in engineering. There is important theoretical value and practical significance. This paper focuses on solving the fracture problem of two collinear cracks subjected to the combined quadratic thermo-electro-elastic loads. Under the assumptions of permeable cracks, by using Fourier transform and its inverse transform, the mixed boundary value problem of cracks is transformed into two pairs of double integral equations. By introducing auxiliary functions that satisfy the boundary conditions, the singular integral equations are further obtained. Combined with the superposition theorem, the analytical solution of the intensity factors is finally obtained explicitly. A numerical example is used to demonstrate the method presented in this paper. The analysis results reveal that the dimensionless quantities (i.e., $w_{c}$ and $\epsilon_{r}$) have significant effect on some physical quantities around the tips of two collinear cracks (i.e., $Q_{c} ,$ $D_{c}$ and $K_{\Delta \phi }^{Inn} /K_{\Delta \phi }^{0}$ or $K_{\Delta \phi }^{Out} /K_{\Delta \phi }^{0}$).