Abstract

A coupled mathematical model of the initial stage of particle penetration into a metal surface in the nonisothermal approximation is presented. It is assumed that at the moment of collision with the target the implanted particles have enough energy to generate elastic mechanical disturbances that affect the redistribution of the implanted material. In the general case, the model includes the equation of continuity, the heat conduction equation, the balance equations for implanted component balance, and the equation of motion. The governing relationships correspond to the theory of generalized thermoelastic diffusion. The model takes the finiteness of relaxation times of heat and mass fluxes and the interaction of waves of different physical nature (waves of impurity concentration, stresses (strain), and temperature) into account. The simplifying approximations, nondimensionalization of the equation system, and the method of their solution are described in detail. The problem was implemented numerically using the double sweep method. Examples of coupled problem solving for the system of Mo(Ni) materials are presented. The processes of penetration and redistribution of the impurity in the surface layer of the target are considered in detail at times before and after the relative relaxation times of heat and mass fluxes. It is shown that the interaction of waves of different physical natures leads to temperature and concentration distributions that do not comply with the classical ideas following from models with the Fourier and Fick laws. The results demonstrate distortions in deformation and temperature waves, which is indicative of the interaction between the processes. It is revealed that wave profiles change more noticeably as the current time is closer to the relative relaxation time of the mass flux and the time of the external pulse action.

中文翻译：

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粒子束穿透到目标表面初期的非等温机械扩散模型。

摘要

提出了在非等温近似中颗粒渗透到金属表面的初始阶段的耦合数学模型。假设在与目标碰撞的瞬间，植入的粒子具有足够的能量以产生弹性机械干扰，从而影响植入材料的重新分布。在一般情况下，模型包括连续性方程，导热方程，用于植入部件平衡的平衡方程和运动方程。控制关系对应于广义热弹性扩散理论。该模型考虑了热通量和质量通量的弛豫时间的有限性以及不同物理性质的波（杂质浓度，应力（应变）和温度波）之间的相互作用。详细描述方程组的简化近似，无量纲化及其求解方法。该问题是使用双重扫描方法以数字方式实现的。给出了Mo（Ni）材料系统耦合问题求解的示例。在热和质量通量的相对弛豫时间之前和之后，将详细考虑目标表面层中杂质的渗透和再分布过程。结果表明，具有不同物理性质的波的相互作用导致温度和浓度分布不符合遵循傅立叶和菲克定律的模型所遵循的经典思想。结果证明了变形和温度波的畸变，这表明了过程之间的相互作用。