Role of crack length, crack spacing and layer thickness ratio in the electric potential and temperature of thermoelectric bi-materials systems

The influence of dual collinear interface cracks on the electric potential and temperature of thermoelectric bi-materials system under the electric load and thermal load is reported. The nonlinear governing equations of thermoelectric materials are transformed into the Laplace equations with the help of the driving force of the electric current density and the energy flux introduced. Firstly, based on the boundary conditions about the electric potential and the temperature, the interface electric current density and the interface energy flux the boundary of crack-free system are obtained. Then, the problem of the dual interface cracks is transformed into a Riemann-Hilbert problem, and analytical solutions of the electric current density and the energy flux are achieved. Furthermore, we provide the intensity factors of electric current density and energy flux around the crack tip. Finally, we unveil the crucial role of crack length, crack spacing and layer thickness ratio in the electric potential and temperature of thermoelectric bi-materials by numerical experiments.