Influence of interface energy and grain boundary on the elastic modulus of nanocrystalline materials

With reducing the grain size into nanometer scale for polycrystalline materials, the influence of nonlocal interactions in grain boundaries on the mechanical properties of the material is reinforced as well as the interface energy stemming from the surfaces of grains is increased, resulting in that the mechanical properties of the polycrystalline represent size-dependence significantly. In this work, the influence of the interface energy and grain boundaries on the elastic properties of nanocrystalline materials is investigated in the framework of continuum mechanics. An analytical expression of the elastic modulus is addressed to describe the grain size effects on the Young's modulus of nanocrystalline materials. The numerical results illustrate that the elastic modulus of nanocrystalline materials decreases with the reduction of the grain size to nanometer scale. The grain size effects become remarkable when the grain size lowers down to several tens nanometers, and the influence of the interface energy and grain boundary must be taken into account. The contribution of the density on the mechanical properties in nanocrystalline materials is analyzed by discussing the influence of the grain boundary thickness on the elastic modulus. The comparison between the proposed theoretical results and the present measurement shows that the proposed model can predict the experiments quite well.