Complex Variable Method Of Collinear Cracks In Thermoelectric Materials

Thermoelectric material is a new structural material that can realize the mutual con-version between electrical energy and thermal energy.Because of its excellent physical properties and unique advantages,it is widely used in the fields of national defense and aero-nautics,and it also has broad application prospects in engineering materials.The defects in thermoelectric materials are the main reasons for the decrease of their strength.These defects can cause crack growth and even fracture.The cracks at the edges and the periodic collinear cracks are important mechanical models in fracture mechanics.This paper takes thermoelec-tric materials as an example.The two cases of collinear cracks are discussed.The problem of circular orifices and periodic collinear cracks are studied by complex function method,which provides a reference for the mathematical research of thermoelectric materials.The first part of the solution to the problem of circular orifice cracks:construct different conformal mappings,map the infinite plane in the physical plane to the inside of the unit circle in the mathematics plane,introduce a new analytical function,and find the circularity according to the Cauchy integral formula The analytical expression of the intensity factor of the orifice and analysis of the variation law of the intensity factor with the parameters.The solution to the second part of the periodic collinear crack problem is as follows:under different boundary conditions,a new analytical function is introduced,and the peri-odicity of the function is used to degrade the collinear crack problem into a single crack problem with additional conditions,and then use the analytical solution.The continuation method is used to find the expression of the electric intensity factor of the collinear crack.The influence of crack length and crack spacing on the generation of electric intensity fac-tor is discussed.The change of interference effect between collinear cracks is analyzed and discussed.The scale effect between two thermoelectric materials is given.