Complex Function Method Of Thermoelectric Materials With Complex Defects

Thermoelectric materials,as a new type of environment-friendly materials,can better realize the conversion between electric energy and heat energy.Thermoelectric materials are widely used for thermoelectric power generation and thermoelectric refrigeration in human society.However,due to the brittleness of thermoelectric materials,defects will occur in production or work.In this paper,the fracture problem of thermoelectric materials with complex defects is studied by using complex function method.The main work is as follows:1.In the first chapter,the development and research status of thermoelectric materials and fracture mechanics are introduced.In the second chapter,the equilibrium equation and constitutive equation of thermoelectric materials can be obtained from Gauss' s law,Ohm's law and Fourier's law.On this basis,the governing equation of thermoelectric materials is obtained.2.In chapter 3,the fracture mechanics of thermoelectric materials with square holes is analyzed by means of conformal mapping,and the fracture mechanics of thermoelectric materials under the action of current and energy flow at infinite distance is studied.The complex expressions of potential function,temperature function and stress function are obtained according to the boundary conditions of electrical insulation and thermal permeability and the boundary conditions of stress and displacement.On this basis,the real analytical expressions of energy flow and circumferential stress components are given.3.In chapter 4,the fracture mechanics of thermoelectric materials with pentacle holes is studied.Based on the theory of complex function,the expressions of the electric potential function,temperature function and stress function are obtained by using the basic equations of thermoelectric materials and various boundary conditions,and the real expressions of the circumferential energy flow and circumferential stress component at the edge of the hole are obtained.On this basis,the effects of air thermal conductivity and orifice size on the temperature field and stress field at the boundary are discussed.4.In chapter 5,the electric field potential function of thermoelectric material with lip crack is obtained by using the complex function method under the electrical insulation boundary condition.Based on this,the expression of electric field intensity factor is obtained,and the effect of crack length on the electric field at crack tip is analyzed.