Time-dependent power output and elastic/plastic fracture analyses of porous thermoelectric ceramics for generators

If made in porous foam, thermoelectric ceramics for power generation can enhance the power output by directly extracting thermal energy from heat sources. This paper discusses the time-dependent power output and elastic/plastic fracture of the porous thermoelectric generator (TEG) with a small oblique-through crack. Analytical solutions of temperature and thermal stress of the TEG are derived based on an effective model of porous foam. The finite element numerical model is created to validate the analytical solutions and to explore more thermomechanical properties and constitutive behaviors of the porous materials. Comparing to the traditional bulk TEG, porous TEG can greatly improve the power output however the thermal stress is enhanced therefore the strength is substantially reduced. The power output gradually increases to a peak value and then decreases with the length of the TEG. Based on the criterion of fracture mechanics, a simplified and useful expression of the critical heat flux for crack propagation is identified. The critical heat flux for crack growth is inversely proportional to the porosity and the crack length. A more rigid contact between the TEG and the elastic boundary results in a larger thermal stress and a smaller critical heat flux. The velocity of crack propagation is mostly determined by the porosity and the ratio of the initial crack length to the arbitrary crack length. Also observed is that the length of plastic zone at the crack tips increases with the increasing porosity.