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The influence of external action on the dynamics of elastic, thermal and concentration waves propagation

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2025年 238卷

作者： Parfenova, Elena S. Knyazeva, Anna G. Russian Acad Sci Siberian Branch Inst Strength Phys & Mat Sci Tomsk Russia

This paper presents the nonlinear coupled mathematical model allowing investigating the interrelation between the mechanical, thermal and diffusion processes in solid body. The model takes into account the finiteness of relaxation times of mass and heat fluxes. This is of interest for dynamical processes with characteristic times comparable to relaxation times, when the changes in the temperature and impurity concentration are described by hyperbolic thermal conductivity and diffusion equations. Additionally, the model takes into account the temperature and concentration dependencies of the diffusion coefficients;it gives rise to additional nonlinearity. The model is thermodynamically consistent and follows from the nonlinear equations of the thermoelastic diffusion theory. The implicit difference scheme of second approximation order in time and spatial steps, linearization relatively to known time moment and double-sweep method are used for the numerical implementation of the equation system. Examples of interrelating wave propagating under external actions are considered. The results show that distortions in the strain/stress and temperature distributions appear due to the interaction between the phenomena of different physical nature. The specific rates of different physical processes are different. Although diffusion is the slowest of them all, the influence of the diffusion wave is reflected in stress and strain waves far beyond the diffusion wave front. It is shown that regardless of the external action character and impulse form, the influence of the considered processes on each other does not change, but the wave picture becomes much more complicated with increasing number of actions.

关键词： Nonlinear coupled mathematical model thermoelastic diffusion theory Heat and mass fluxes Relaxation time

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Surface treatment of metal by combined particle beam

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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 2024年 205卷

作者： Parfenova, Elena S. Knyazeva, Anna G. Russian Acad Sci Siberian Branch Inst Strength Phys & Mat Sci 2-4 Pr Akad Skii Tomsk 634055 Russia

This work is related to modeling of metal surface modification process by combined particles beam. On the basis of thermodynamics of irreversible processes, including equations of state in differential form, a nonlinear model is formulated. The model takes into account the interaction of thermal, diffusion and mechanical waves and finiteness of relaxation times of thermal and diffusion processes. For the combined particle flow such model is proposed for the first time. The numerical algorithm is based on implicit difference schemes. The study of the interaction of waves of different nature is carried out on the example of a copper target treated with nickel and gold particles. It is shown that deformations take the maximal value at the left boundary, which is directly related to the presence of impurity concentration gradients. Depending on the pulse duration, the difference between the extrema on the elastic wave becomes less significant. With increasing temperature, obviously, the diffusion process accelerates. The propagation velocities of the interacting waves are different. The character of distributions of concentrations of introduced particles directly depends on the value of parameters proportional to relaxation times.

关键词： diffusion Stress wave Heat/mass flux relaxation time Coupled model Numerical algorithm thermoelastic diffusion theory

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