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

With the development of material science,more and more alloy materials have been applied to high temperature conditions.Good material properties make transversely isotropic materials widely used in mechanical manufacturing,biotechnology,aerospace and other fields.Many studies are based on phenomenological theory to establish empirical formulas or consider the influence of temperature on constitutive equation by weighting,Establishing the thermal constitutive equation with temperature as the direct variable of the constitutive equation has important theoretical significance and practical engineering value.At present,the descriptions of mechanical behavior of alloy materials at different temperatures are mostly based on the establishment of approximate exponential and hyperbolic functions and the combination of classical constitutive models.At the same temperature,the stress-strain curves of different alloy materials vary greatly due to their different properties.Even for a specific alloy material,the stress-strain curves at low,medium and high temperatures are quite different.Therefore,the practicability and accuracy of this constitutive model can not meet people's needs.The polynomial constitutive equation based on tensor function representation theorem plays an important role in the study of deformation body mechanics.Because of the symmetry of isotropic,transversely isotropic and orthotropic materials,the constitutive equation expressed by tensors has a special form.The coefficients of the constitutive equation expressed by polynomials require completeness and irreducibility,so it is necessary to study the nonlinear constitutive equation of materials with symmetrical characteristics.In this paper,the elastoplastic constitutive equation of transversely isotropic materials expressed by tensor function polynomials is applied to the study of high temperature elastoplastic deformation of transversely isotropic alloys.A non-linear transversely isotropic thermoelastic plastic constitutive equation with temperature as a direct variable is established and applied to theanalysis of high temperature tensile elastic-plastic deformation of transversely isotropic materials.Three kinds of transversely isotropic materials with different high temperature mechanical behavior are selected in this paper:GH5188Co-based Alloy ? GH706 Ni-Fe-Co Based Alloy ? DZ125 Nickel-based Directional Solidification Cast Alloy,The non-linearity of stress-strain curves obtained by three kinds of alloys in uniaxial tension tests at high temperature increases in turn,and the dispersion of the curves also shows an enlarged trend.By fitting the experimental data,the values of elastic-plastic coefficients and temperature coefficients which are not zero in the constitutive equation for transverse and longitudinal samples of three alloys under uniaxial tension at elevated temperature are determined.The mechanical behavior of GH5188Co-based alloy,GH706 Ni-Fe-Co-based alloy and DZ125 Ni-based directionally solidified casting alloy at unknown temperature was deduced by using constitutive equation.The predicted stress-strain curves were compared with the experimental stress-strain curves.The predicted curves were compared with the experimental data.The comparison and analysis show that the predicted curve images are satisfactory,which verifies the practical ability of the non-linear transversely isotropic thermoelastic plastic constitutive equation.