Constitutive modeling for nanocrystalline metals based on cooperative grain boundary mechanisms

In nanocrystalline metals, the plastic deformation is accommodated primarily at the grain boundaries. Yang and Wang (J. Mech. Phys. Solids, 2003) suggested a deformation model based on clusters consisting of nine grains and incorporating both the Ashby-Verrall mechanism and a 30° rotation of closely linked pairs of grains. In the present article, the insertion and rotation processes are considered together as a cooperative deformation mechanisms, and the degree to which each process contributes is determined by the application of the principle of maximum plastic work. Plane strain and three-dimensional constitutive relations based on this concept are derived for which a general stress state drives the orientation evolution of various grain clusters under the Reuss assumption. Detailed calculation shows that the strain rate depends linearly on the stress, with the values of the coefficients in this linear relationship dictated by the microscopic energy dissipation. The deformation contributed to the overall response by the grain boundary mechanism is discussed in the spirit of the Hashin-Shtrikman bounds.