A mixtures-based model for the grain size dependent mechanical behavior of nanocrystalline materials

A mixtures-based constitutive model was developed on the basis of the analysis of the real mixtures status of nanocrystalline materials. The grain boundary phase was assumed to have two equivalent parts: parts I and II. The strain of part I is the same as that of the interior of the grain, the stress of part II is equal to the sum of the total stress on the interior of the grain and that of part I of the boundary. The model developed in this paper was used to calculate Youngʹs moduli for nanocrystalline materials. The predictions are in good agreement with the results in the literature. The model was then applied to evaluate the stress–strain relation in nanocrystalline materials. Overall, the model seems to have captured the effect of the size of the grains on the transitions of the yield strength, the strain-hardening features and the flow stress–strain relations for nanocrystalline materials.