A nanocrystalline material can be regarded as a composite system in which the amorphous interfacial phase is treated as the matrix with the the nano-scale single crystals as the inclusions. In general, as the elastic moduli of the nanoscale crystals are higher than those of the amorphous matrix, the material's deformation mechanism depends greatly on the size of the crystals. For macro size crystal materials, the deformation is caused mainly by dislocation motions. When the crystal size is below a critical value, the plastic deformation is largely by shear banding in the amorphous matrix. Based on such deformation mechanism, this chapter develops a general constitutive model for nanocrystalline materials using an internal variable theory. The model reveals some special characteristics of the relationship between the yield strength and grain size and predicts the kinematic hardening behavior of nanocrystalline metals.
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