Evaluation of the stress and strain during transition layer formation between a particle and a matrix

When manufacturing composites, a transition layer is formed between a particle and a matrix. The composition and width of the layer both depend on technological parameters of the process. Application of the appropriate model of transition layer formation makes it possible to study in dynamics the evolution of transition zone size and the properties of obtained materials depending on the synthesis conditions. In addition, a new phase formation and boundary movement are accompanied by diffusion resulting in the redistribution of concentrations. These processes cause diffusion (concentration) stresses due to a difference in the phases' properties and a difference in the diffusant mobility in the phases.
The paper presents a model for estimating the stresses and strains during the transition layer formation between a spherical particle and a matrix. The model includes the problem of the reaction diffusion with the boundaries moving due to a new phase growth. In a quasi-steady-state approximation, the diffusion problem involves finding the concentration distribution in the regions of given sizes and the determining of the phase boundaries' position. The latter subproblem is solved numerically. It is followed by finding the concentration distribution. The problem of mechanical equilibrium is solved analytically. The resulting data depend on the position of the boundaries and distribution of the concentrations.