Effect of stresses and strains on impurity redistribution in a plate under uniaxial loading

Abstract

A model for the saturation of the surface layer of a thin metal plate with an impurity from the environment under uniaxial mechanical loading is proposed and investigated. The effect of stresses and strains on the diffusion process is analyzed. It is shown that, first, due to the deformation of the crystal lattice of the base, stresses that occur in local volumes lead to a change in the diffusion activation energy; second, stresses influence impurity transfer (this effect is similar to mass transfer by pressure diffusion in liquids). The joint effect of the two types of influences of stresses and strains on the behavior of the system at various geometrical and physical sample parameters is numerically investigated.Introduction. As is known, stresses and strains occurring in the zone where diffusion takes place (diffusion zone) have an impact on diffusion processes. Many studies have been devoted to the investigation of this phenomenon (for instance, see [1][2][3]).The appearance of concentration stresses in the case of a binary system is due, first, to the difference between the atomic sizes of the diffusing substance and the base, and, second, to the inequality of the partial diffusion coefficients of the impurity and base, which leads to inequality of the opposite partial fluxes and the appearance of redundant vacancies causing stresses [4]. The stresses caused by the appearance of atoms of another substance in the lattice of the base are called concentration stresses, and the stresses due to the difference in diffusion mobility between the atoms of the base and the impurity atoms are called diffusion stresses. It is difficult to separate one type of stresses from the other. Stresses and strains in the diffusion zone eventually occur due to heterogeneity of concentration fields. From now on, concentration stresses and strains will be considered from this perspective.The dependence of diffusion processes on stresses has motivated the Development of methods for controlling impurity redistribution. One of these methods is the use of an additional external load. To investigate the role of external loading in the presence of internal stresses, it is necessary to solve the problem of mechanical equilibrium of the sample taking into account the possible feedback between diffusion and mechanical processes. In the case where inertia forces may be neglected (due to the low rate of diffusion processes) under quasistatic loading, the problem is divided into two parts: the problem of mechanical equilibrium and the nonlinear diffusion problem. The purpose of this work is to investigate the impact of various physical factors on the parameters of the diffusion zone under quasistatic uniaxial loading.Problem of Mechanical Equilibrium. Let us consider a plate of length L, width h, and depth δ (L h δ) which is subjected to uniaxial mechanical loading. The magnitude of the external load p is specified. Impurity from the environment or impurity from a previously applied layer containing an excess of the diffusing element can penetr...

Application of micropolar theory to the description of the skin effect due to hydrogen saturation

“…where J D is a flux due to the concentration gradient, and J f is a flux due to the additional driving force changing the mobility of impurity in a stress field [20, 21, 25, 47].…”

“…To account for an additional driving force, one can consider a phenomenon similar to barodiffusion in liquids, which means that the interaction of the impurity with the stress field is only through the hydrostatic stress [20, 21, 47. In this case, the flux J f is as follows:…”

“…According to the Arrhenius law, the diffusion coefficient depends on the activation energy for the reaction [16]. Following [47], one can correlate the activation energy with a potential energy of a deformable material, Π , to investigate the influence of mechanical stresses on the diffusion process, so that…”

“…A stress-induced diffusion is considered to model the skin effect due to hydrogen saturation. The influence of inner stresses is due to the dependence of the diffusion coefficient on the local elastic energy and due to the driving force in the diffusion equation [20,[45][46][47][48][49][50]. The model accounts for the mutual influence of the inner stresses and strains and dissolved hydrogen [51].…”

On modeling of stress‐induced diffusion within micropolar and classical approaches

“…Influence of the inner stresses and strains on the mass transport process can be due to the additional driving force in the diffusion equation [31][32][33][34][35][36][37] or due to the dependence of the diffusion coefficient on the local energy [38][39][40][41], which can be correlated with the activation energy for the reaction appearing in the Arrhenius law [42]. According to the classical Fick's first law, matter flows from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient.…”