The effect of the ratio of the radius of the hole and crack length on the multi‐field behaviors of thermoelectric materials under oblique loads

Abstract

AbstractThis paper establishes a defect model of thermoelectric materials that the oblique multi‐field loads are applied along an arbitrary direction with the crack initiated from a circular hole, and gives both analytical solutions and finite element method (FEM) simulation. On the one hand, in virtue of the conformal mapping function and the Cauchy integral formula, the analytical solutions of electric current density, energy flux, and stress are obtained. Furthermore, the thermoelectric field intensity factors (TEIFs) and the stress intensity factors are also attained. Most notably, we apply the extreme value theorem of multivariate function to explore the effect of the ratio of the radius of the hole, R, and crack length, L, on the fields’ intensity factors of thermoelectric materials under oblique multi‐field loads. Importantly, the maximum value of the mode‐II stress intensity factor (SIF) is obtained when . On the other hand, the finite element simulation is used to explore the fracture behaviors of thermoelectric materials. The analytical solutions and the finite element simulation results are consistent. The effects of the oblique multi‐field loads on the thermoelectric field and the stress field at the crack tip are detailed. The concentration phenomenon of the thermoelectric field and the stress field at the crack tip are influenced by the radius of the circular hole, the crack length, and the directions of the loads.