Effect of elastic stress on two-phase binary diffusion couples
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I.
INTRODUCTION
INTERFACE reactions occur readily during the fabrication of composite materials. Such systems are rarely in equilibrium and there often exist significant thermodynamic driving forces for interdiffusion between the reinforcement and matrix phases and for the formation of new phases at the interface.[1,2] Interdiffusion leads to compositional stresses when the partial molar volumes of the diffusing species are different. The formation of a new phase induces misfit strains owing to a difference in crystal structure or lattice parameter between the newly formed phase and existing phases. These stresses are in addition to thermal stresses that arise during temperature changes when the coefficients of thermal expansion are different between phases. Although the integrity of a reinforcement-matrix interface depends critically on the elastic state of the interface and the presence of other phases formed by interface reaction, relatively little work exists examining the effect of stress on the kinetics of intermediate phase growth. An analysis of quasi-stationary trajectories of phase growth rates has shown that misfit strains might lead to the initial dissolution of the equilibrium phase and its subsequent growth,[3] work that is in agreement with studies of phase equilibria in stressed systems.[4] Analysis of phase changes in a thin film using a gradient energy approach also indicates the importance of the stress field in altering the form of the diffusion equations.[5] More recently, the effect of compositional strain in a ternary alloy has been examined for a set of displacement boundary conditions for which the local state of strain depends only on the local state of strain depends only on the local composition.[6] W.C. JOHNSON, Professor, is with the Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903-2442. Manuscript submitted May 31, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
The intent of the present work is to examine the effect of misfit strain and applied stress on interdiffusion and interfacial velocity in a binary, planar diffusion couple. Unfortunately, analytical solutions for the time dependence of either the composition field or interfacial velocity in reaction couples are usually difficult to obtain unless the diffusion couple can be considered as infinite in extent.[7,8] This is especially true for elastically stressed systems for which the elastic field depends on the system geometry and the elastic and composition fields are coupled, either through the diffusion equations or boundary conditions for diffusion. Therefore, in order to investigate the effects of elastic stress on interdiffusion and interfacial reaction, a numerical technique based on a front-tracking, finite-difference approximation is developed. The interface is assumed to remain planar, although this may not always be a valid assumption.[9,10] The governing equations and boundary conditions for the stress and diffusion fields are presented in Section II. The numerica
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