Effects of Material Characteristics on Thermal Stress around an Equiangular Polygonal Hole in a Thermoelectric Material

In this study, we conducted a theoretical analysis of thermal stress around an arbitrarily-shaped hole in a thermoelectric material under electric current density and energy flux loading. Based on complex variable methods, conformal mapping, and analytical continuation theorem, the exact solutions of the thermal stress around a hole were obtained for the Seebeck coefficient and electric and heat conductivity. Based on the conversion efficiency equation of thermoelectric materials, higher electrical conductivity, and lower heat conductivity should be selected to achieve an optimal design. The theoretical results indicated that higher electrical conductivity could reduce the thermal stress around the hole. However, energy flux and thermal stress concentration might be generated around the adiabatic hole due to the presence of a matrix with lower heat conductivity. Hence, thermoelectric materials with lower thermal conductivity should be selected carefully to avoid premature failure around the hole caused by thermal stress concentration. Finally, we also obtained and discussed the stress intensity factors of a hypocycloid-type crack.