Nonlinear microstructural constitutive equation of nanocrystalline metals

Abstract

Based on experimental observations, nanocrystalline materials are modeled as composite systems in which the amorphous interfacial phase is treated as the matrix, whereas the nano-scale single crystals are modeled as inclusions. Generally speaking, the elastic moduli of nanoscale crystals are higher than those of the amorphous matrix phase, and the deformation mechanism of nanocrystalline materials depends heavily on the size of the crystals. For conventional macro size crystal materials, such as coarse-grained polycrystalline materials, the deformation mechanism due to dislocation movement is dominant. When the crystal size is reduced to a certain critical value, plastic deformation is caused by shear banding in the amorphous matrix. In order to model such a deformation mechanism in nanocrystalline materials, constitutive equations are established based on internal variable theory. The proposed model reveals the relation between the yield strength and the grain size of the material.