Simulation of grain boundary diffusion creep: analysis of some new numerical techniques

We consider the simulation of deformation of polycrystalline materials by grain-boundary diffusion creep. For a given network of grain boundaries intersecting at nodes, with appropriate boundary conditions, we can calculate the rate at which material will be dissolved or deposited along each grain boundary and hence predict the rate at which each grain will move to accommodate this dissolution/deposition. We discuss two numerical methods for simulating the network changes over a finite time-interval, based on using the movement of adjacent grain boundaries over a small time-interval to estimate the velocities of the nodes. (The second of these methods has enabled us to speed up solution by 100 times in typical experiments compared with a naive forward-Euler approach.) We show that the accuracy with which the node velocities can be estimated is dependent only on the precision of the machine with which they are computed and deduce that, for all practical purposes, the lack of precise node velocity values does not detract from the quality of our solution. Finally, we consider the underlying stability of the problem under various different boundary conditions and conclude that our methods have the potential for providing useful insight into the effect of grain size and shape on deformation in polycrystalline materials