Computer simulation of superplastic deformation

In this paper, a numerical procedure is described to simulate the grain structure evolution of fine grain materials during superplastic deformation. The basic assumption is that the dominant mechanism for the deformation of the material under mechanical loading is grain-boundary sliding accomodated by grain-boundary diffusion. At each time step, the full set of equations which control the grain-boundary diffusion process are solved by the numerical technique suggested by Cocks [1–2] with a further extension to the situation of grains with arbitrary sizes and shapes. The grain boundary network is updated according to grain velocities obtained from the numerical analysis. Any four-rayed grain boundary junction is supposed to be unstable. Therefore a vanishing grain-boundary will lead to either a “neighbour-switching” [3] or “grain vanishing” event. It is demonstrated that the computer simulation based on these few assumptions is able to capture the main characteristics of microstructural evolution in fine grain materials during superplastic deformation. Most importantly, the grain size increases slightly and the grain shape is essentially preserved, remaining equiaxed after a hundred percent elongation.