Influence of the grain size and structural state of grain boundaries on the parameter of low-temperature and high-rate superplasticity of nanocrystalline and microcrystalline alloys

A model has been proposed for calculating the grain size optimum for the deformation of nanocrystalline and microcrystalline materials under superplasticity conditions. The model is based on the concepts of the theory of nonequilibrium grain boundaries in metals. It has been demonstrated that the optimum grain size $d_{\mathrm{opt}}$ can be calculated as the size at which a high level of nonequilibrium of grain boundaries is combined with a high intensity of the accommodation of grain boundary sliding. The dependences of the quantity $d_{\mathrm{opt}}$ on the rate and temperature of the strain and the thermodynamic parameters of the material have been derived. The results obtained have been compared with the experimental data on the superplasticity of nanocrystalline and microcrystalline aluminum and magnesium alloys.