Fracture of thermoelectric materials: An electrical and thermal strip saturation model

Cracking is a critical issue in the preparation and application of thermoelectric materials. Traditional models for thermoelectric fracture predict infinite electric current and heat flux at the crack tip. However, it is impossible since infinite electric current and heat cannot be sustained at the atomic level. To give a physically reasonable fracture prediction of thermoelectric materials, this paper proposes an analytical model of thermoelectric fracture based on the concept of electrical and thermal field saturation along a strip at the crack front, in which we assume the electric current and heat flux cannot exceed a saturation limit. Firstly, based on the complex variable method, we derive the thermoelectric field solutions with electrical and thermal field saturation at the crack tip. Then, the thermally induced stresses and the fracture criterions are given. The results show that the thermoelectric field predicted by the saturation model exhibits no singularity at the crack tip, which may give better agreement with the experimental observations and thus shows better application potential.