Finite Element Study Of Three-dimensional Thermal-Mechanical Coupling Problem Considering Thermal Relaxation Effect

The progress of science and technology and the popularization of microelectronic devices have promoted rapid development of ultra-short pulse laser technology,which makes the thermo-mechanical coupling problem under the condition of very short time(femtosecond magnitude)gradually attracted the attention of scholars.For solving thermo-mechanical coupling problems,the numerical inversion in the integral transformation method usually leads to the reduction of calculation accuracy.In order to solve this important problem,In this paper,COMSOL finite element software is used to solve the governing equation of thermo-mechanical coupling problem directly in time domain.Compared with the conventional sequential coupling method,the full coupling method is adopted in this paper.Although the total stiffness matrix of a single physical field in the conventional sequential coupling method is much smaller than that of a multi-physical field in the fully coupled method,the sequential decoupling method requires repeated iterations between physical fields,resulting in loss of accuracy.Therefore,considering the superiority of the fully coupled method in dealing with the non-linear multi-physical field coupling problem,the fully coupled method is adopted in this paper.Many related studies have shown that the propagation speed of thermal signals is limited when the applied time of thermal load is equal to the thermal relaxation time of the medium and the characteristic size of the medium is smaller than or equal to the average free path of the hot carrier.This is not consistent with the results predicted by the Fourier heat transfer model.To solve this problem,researchers consider the finite propagation of thermal signals by introducing the concept of relaxation time.In order to accurately describe the thermo-mechanical coupling phenomena in very short time and improve the shortcomings of classical thermoelastic theory,scholars have established a variety of non-Fourier heat conduction models which can describe the heat propagation at finite speed,including thermal wave model(C-V model),single-phase lag model,dual-phase lag model,three-phase lag model,thermal-mass model,etc.thus further improving the corresponding model.A system of generalized thermoelasticity theory.The main research contents are as follows:(1)Firstly,based on the L-S generalized thermoelastic model,the validity and reliability of the fully coupled solution are verified by comparing the literature.(2)Based on L-S generalized thermoelasticity theory,the three-dimensional thermo-mechanical coupling transient response of nickel thin films under thermal shock is solved.Firstly,the thermo-mechanical coupling governing equations in cylindrical coordinates are derived,and the corresponding finite element governing equations are established according to the variational principle expressions of the derived L-S generalized thermoelasticity theory.Finally,the dimensionless thermo-mechanical coupling governing equations are established.The PDE coefficient matrix was determined and the distribution of temperature,displacement and stress in nickel film was obtained.The effect of thermal relaxation time on the thermoelastic response of nickel film was discussed.The effect of laser pulse width on the thermoelastic response of nickel film was also studied.(3)Aiming at the three-dimensional thermo-mechanical coupling transient response of nickel thin films under thermal shock,based on the dual-phase-lag heat conduction model,the variational principle of DPL generalized thermoelasticity theory is deduced,the corresponding finite element governing equation in cylindrical coordinate system is established,the corresponding PDE coefficient matrix is determined,the distribution law of temperature,displacement and stress in nickel thin films is obtained,and the short-pulse stress is studied.The relationship between the non-Fourier heat conduction behavior and the thermal wave in the light-shock nickel film is discussed.The effect of relaxation time parameters on the heat transfer characteristics in the nickel film is also discussed.(4)Based on the three-phase-lag heat conduction model,the variational principle of TPL generalized thermoelasticity theory is deduced for the three-dimensional thermo-mechanical coupling problem considering thermal relaxation effect.The corresponding finite element coupling governing equation in cylindrical coordinates is established and the corresponding PDE coefficient matrix is determined.The effects of three thermal relaxation time parameters,i.e.thermal flow lag phase,temperature gradient lag phase and thermal displacement gradient lag phase,on thermal displacement,temperature distribution,displacement and stress variation in nickel films subjected to thermal shock are discussed respectively.(5)By comparing and analyzing the results of seven generalized thermoelastic theories for three-dimensional transient thermo-mechanical coupling of nickel thin films impacted by short-pulse laser,the differences of seven generalized thermoelastic theories are obtained.It is found that the propagation velocities of temperature waves obtained from the classical thermoelastic theory,L-S theory,G-L theory,type II G-N theory,DPL theory and TPL theory are limited,while those predicted by type III G-N theory are diffusive.The results also show that TPL theory and L-S theory have little influence on the displacement u_r calculation results of nickel films,but have great influence on temperature,displacement u_z and stress.