Thermal-mechanical Coupled Field Analysis Of Cylindrical Structure With Temperature And Stress-dependent Thermal Conductivity

For the discussion of engineering structure strength and fatigue under variable temperature load,the influence of temperature load should be considered.The steps of traditional method of analyzing the influence of temperature on stress includes considering the thermal conductivity as a constant,calculating the thermal strain caused by temperature changes,and analyzing its influence on the stress field.In this method,we only consider the influence of temperature on stress field but ignore the influence of stress field on temperature.However,some research have reported that the thermal conductivity of materials exhibits obvious temperature dependence and stress dependence.In this paper,the analytical method is carried out on investigating the thermal-mechanical coupling problem of axisymmetric structure plane,analyzing the influence of the coupling of material parameters on the temperature field and stress field,and using the COMSOL software to numerically simulate the space problem.The main research work includes the following parts.First,considering three types of thermal conductivity,including constant,temperature-dependent,and temperature-stress dependent,three kinds of structures,such as axisymmetric plane strain,plane stress and generalized plane strain models,we derive the governing equations based on equilibrium equations,geometric equations,constitutive equations,and the steady-state heat conduction equation.These equations are with respect to temperature and displacement functions.The temperature boundary conditions and the stress boundary conditions are also expressed based these functions.Second,for the three types of thermal conductivity.analytical methods are used to solve the temperature and stress coupling fields.When the thermal conductivity is constant,accurate analytical solutions of temperature field,displacement field and stress field are obtained.When the thermal conductivity is temperature-dependent,the analytical solution of the temperature field is directly obtained;and the asymptotic analytical solution of the displacement field is obtained by the power series method.We also demonstrate the accuracy and convergence of the power series.When the thermal conductivity depends on both temperature and stress,the field governing differential equations are nonlinear equations.The power series iteration method is employed for solving the temperature field and stress field.Furthermore,its convergence is also discussed.The research results show that for the internally heated and externally cooled structure,when the thermal conductivity is positively correlated with temperature,neglecting the correlation will underestimate the Von Mises stress in the plane strain and generalized plane strain models.For the plane stress model,the Von Mises stress at the inner and outer walls will be underestimated.The effect should enlarge when the thermal conductivity is negatively correlated with temperature;it is opposite to the positive correlation result.When the thermal conductivity is positively correlated with the hydrostatic stress,the correlation is ignored.For the plane strain,plane stress,and generalized plane strain models,the Von Mises stress will be underestimated.Final,the COMSOL software was used to simulate the axisymmetric plane strain and three-dimensional axisymmetric problems when the thermal conductivity has temperature and stress dependence.The numerical simulation results of the former are consistent with the results obtained by the analytical method.The source of the latter model is the structure that undergo temperature load and gradual internal pressure in the engineering field.The calculation results show that the maximum Von Mises stress occurs at the bottom of the structure,and the Von Mises stress gradually increases along the depth.The method proposed in this paper is of guiding significance for the analysis of thermal and mechanical coupling problems in engineering.Related conclusions can provide a theoretical basis for the strength and fatigue analysis of structures under multiple loads of temperature and stress.