Research On Thermal Elasto-plastic Constitutive Theory Of Isotropic And Transversely Isotropic Materials

In recent years, material science has been developed quickly. High temperature resistant materials have been used widely in the fields of aviation,aerospace and power generation unit. It is a hot issue in the research of mechanics and material science to establish the thermal elasto-plastic constitutive theory considering temperature influence.The study of the thermal elasto-plastic constitutive equation which is not universal is mostly on the basis of phenomenological theory with special material. It has important theoretical significance and application value to establish the uniform thermal elastic plastic constitutive equation of the double variable with the consideration of both the external force and temperature. It is important especially for the application of high temperature alloy materials in large equipment manufacturing industry in China. Based on the tensor function representation theorem, the constitutive equation which plays a unique role in the current study of the deformation mechanics is established for describing the mechanical behavior of materials. The concrete form of the constitutive relation of the material tensor is determined by the symmetry of the material. Its complete and irreducible properties explicitly specify the numbers and types of scalar invariants in the nonlinear constitutive equations. The numbers and the specific forms of the independent elastic tensor and the elasto-plastic tensor are defined, too. The constitutive equations are general applicable to a wide class of materials and the constitutive equations are universal applicability.In the finite deformation range, the numbers of isotropic and transversely isotropic 2n order elastic and elasto-plastic constants are studied on the basis of tensor representation theorem. Two categories of isotropic and transversely isotropic materials' nonlinear elasto-plastic constitutive equations are derived.Based on elasto-plastic constitutive equations, two kinds of isotropic,transversely isotropic materials' thermal elasto-plastic constructive equations by considering the temperature change are derived under thermal loading stage. The equations are expressed by using invariant representations.The equations are simplified under quasi-static condition and compared with the experiment data. For isotropic materials, tensile tests of the AZ31 casting magnesium alloy and 45 steel under the conditions of room temperature are used for isotropic elastic plastic constitutive equation fitting analysis while high temperature experiments of HCP polycrystalline magnesium are used for isotropic thermal elasto-plastic constitutive equation. For the transversely isotropic material, the DZ125 material is selected as the normal and high temperature tensile test material to analyze the elasto-plastic and the thermal elasto- plastic constitutive equations. The following results could be obtained.The isotropic and transversely isotropic constitutive equations under the quasi static uniaxial load are obtained. The elastic constants and elasto-plastic constants are obtained at different temperature ranges. It is showed that the nonlinear thermal elasto-plastic constitutive equations on the basis of tensor function can describe the tensile hardening and softening of these selected test materials effectively.