Fracture Analysis Of Thermoelectric Materials With Defects

As a kind of new structure material,thermoelectric materials have excellent properties and broad applications prospects.Its appearance provides a direction for solving the energy shortage and environmental pollution.It has been widely used in the fields of national defense?aeronautics and various engineering structures.However,most thermoelectric materials are brittle and have low toughness,which can easily lead to material fracture and structural damage,and have a great impact on the safety performance of materials.In recent years,many experts have paid attention to the fracture problems in thermoelectric materials.In this paper,thermoelectric materials with defects are studied under the boundary conditions of thermal insulation and electrical insulation,which provides theoretical support for the application of materials in engineering practice.In view of the two-dimensional problem of thermoelectric materials with parabolic crack.Based on the basic equations and analytic function theory of thermoelectric materials,The analytical expressions of electric potential ?temperature and stress fields are derived by the conformal mapping technique and Cauchy integration formula.On this basis,the real expressions of hoop energy flux and hoop stress are presented.In view of the fracture mechanics of thermoelectric material with an equilateral triangle hole,the analytical expressions of the electric potential?temperature and stress fields extended to the infinite term are obtained,the real expressions of hoop energy flux ?hoop stress and hoop heat flux are also derived.Next,for the convenience of engineering application,the real expressions of hoop energy flux?hoop stress and hoop heat flux when the conformal mapping takes the finite term are derived.Finally,numerical examples are given to illustrate the influence of loads and the triangle size on hoop energy flux ?hoop stress and hoop heat flux.The problem of a straight crack emanating from an elliptic hole in an infinite plate thermoelectric material is discussed by using conformal mapping technique.The exact solutions of temperature and stress components are presented based on complex variable method and Cauchy integral formula.The expressions for field intensity factor and stress intensity factor at the crack tip are also obtained.Numerical results are carried out to illustrate the effects of the value of elliptical hole size and crack length on these intensity factor.