Atomistic and mean-field estimates of effective stiffness tensor of nanocrystalline copper
This work provides a computationally efficient mean-field model for predicting elastic properties of nanocrystalline copper, relevant for materials science and engineering of nanostructured metals.
The study derives the full elasticity tensor for nanocrystalline copper via molecular simulations, finding that shear modulus decreases with grain size while bulk modulus remains nearly constant. A closed-form mean-field model based on single-crystal data and average grain size predicts effective elastic properties with good agreement to atomistic simulations.
The full elasticity tensor for nano-crystalline copper is derived in molecular simulations by performing numerical tests for a set of generated samples of the polycrystalline material. The results are analysed with respect to the anisotropy degree of the overall stiffness tensor resulting from the limited number of grain orientations and their spatial distribution. The dependence of the overall bulk and shear moduli of an isotropized polycrystal on the average grain diameter is analysed. It is found that while the shear modulus decreases with grain size, the bulk modulus shows negligible dependence on the grain diameter and is close to the bulk modulus of a single crystal. A closed-form mean-field model of effective elastic properties for a bulk nano-grained polycrystal with cubic grains, i.e. made of a material with cubic symmetry, is formulated. In the model all parameters are based on the data for a single crystal and on the averaged grain size without any need for additional fitting. It is shown that the proposed model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations.