Modelling interface diffusion creep in two-phase materials

We propose a 2D model for deformation of a two-phase material where interface diffusion is the only creep mechanism. We assume there is no chemical interaction between the phases though both are soluble, no voids are allowed to develop, and there is a quasi-steady state. Local equilibrium is assumed between the phases at all interfaces, in the same way as is done in many single-phase diffusion creep models. Our model shows that the behaviour of the two-phase composite is completely different from that of a single-phase aggregate. Specifically, the system of equations cannot be solved if the model is closed with respect to gain or loss of the two chemical species involved (mathematically the system is overdetermined). Therefore a two-phase material under stress is predicted to change its bulk chemistry as it deforms, by exchange with its surroundings. The behaviour of our model is very dependent on interface topology. Even for chemically open systems, some topologies provide too many chemical constraints to allow any diffusion. Our model is a preliminary attempt at simulating multi-phase diffusion creep, but is sufficient to show that this process will exhibit remarkable features, or that the assumptions which have been successful in modelling single-phase creep must be modified for the multi-phase case.