Numerical study of the grain-size dependent Young’s modulus and Poisson’s ratio of bulk nanocrystalline materials

Abstract

We present a numerical study of the elastic properties of bulk nanocrystalline materials based on a continuum theory, introduced by Fried and Gurtin (2009), for nanoscale polycrystalline elasticity that captures length-scale effects and accounts for interactions across grain boundaries via interface and junction conditions. The theory involves a balance equation containing fourth-order gradients of the displacement field. A relatively inexpensive, non-conforming finite-element method based on C0-continuous basis functions is presented. We develop the variational form of the method and establish consistency. The formulation weakly enforces continuity of derivatives of the displacement field across interelement boundaries and stabilization is achieved via Nitsche’s method. Based on this approach, numerical studies are performed for a polycrystal subject to an uniaxial deformation. Results indicate that the theory predicts lower Young’s modulus for bulk nanocrystalline materials than for conventional coarsely-grained polycrystals. Moreover, as the grain size decreases below a certain threshold, the effective elastic modulus decreases and the effective Poisson’s ratio increases. The distribution of the effective stress shows that the theory captures high strain gradients in the vicinity of the grain boundaries and triple junctions.