Surface effect on the self-equilibrium state and size-dependent elasticity of FCC thin films

Abstract

On the {1 1 0} solid surface, surface stresses of two perpendicular directions, such as ⟨1 0 0⟩ and ⟨1 1 0⟩, will differ. These different surface stresses cause different equilibrium strains in the ⟨1 0 0⟩ and ⟨1 1 0⟩ directions on a {1 1 0} thin film. In this paper, an analytical formulation is presented to predict the equilibrium strains of orthotropic thin films with {1 0 0}, {1 1 1} or {1 1 0} surfaces. This formulation is composed of the elastic constants of bulk materials and surface parameters such as surface stresses and surface elastic tensors. Transition metals with FCC structures (Cu, Ag, Au, Ni, Pd and Pt) are used in this study, along with a surface relaxation model that calculates surface parameters using atomistic calculations. Molecular dynamics simulations are performed and compared with the results of this suggested method, and both results show good agreement. In addition, size-dependent elastic constants are calculated analytically from the predicted equilibrium state.

Stress and displacement configurations in the vicinity of a void in a nanometer copper strip

“…The size effects on Young's modulus observed in experiments have also been seen in computer simulations which also have reported size effects on Poisson's ratio [21][22][23]. Furthermore, computer simulations have also observed that strain rate influences the elastic response [24][25][26].…”

Molecular dynamics-based continuum models for the linear elasticity of nanofilms and nanowires with anisotropic surface effects

“…[2009] proposed a continuum-based bridging model for a nanofilm using the surface elasticity model by Gurtin and Murdoch [1975;1978]. Cho et al [2009] suggested a sequential multiscale method in order to determine initial surface stress and surface Lamé constants using a matching method based on a molecular dynamics (MD) simulation.…”

“…It is well known that the mechanical properties of a nanosized structure significantly differ from those of bulk materials because of the surface effect. Therefore, although the surface effect is negligible in macroscale studies, it is crucial for a nanosized structure analysis to account for the influence of the surface effect [Miller and Shenoy 2000;Zhou and Huang 2004;Diao et al 2004;Liang et al 2005;Guo and Zhao 2005;Sun and Zhang 2005;Dingreville et al 2005;Wang et al 2008;He and Lilley 2008;Zhang et al 2008;Dingreville et al 2008;Park 2009;.…”

“…As one of the continuum approaches, Gurtin and Murdoch [1975;1978] introduced a surface elasticity model for isotropic surfaces using initial surface stress and surface Lamé constants. A plate theory based on Kirchhoff and Mindlin plate theories, which included the surface effect by using Gurtin and Keywords: surface effects, sequential multiscale model, finite element method, nanofilm, nanowire, size-dependent elasticity, molecular dynamics simulation.…”

Untitled

“…It is well known that the mechanical properties of a nanosized structure significantly differ from those of bulk materials because of the surface effect. Therefore, although the surface effect is negligible in macroscale studies, it is crucial for a nanosized structure analysis to account for the influence of the surface effect [Miller and Shenoy 2000;Zhou and Huang 2004;Diao et al 2004;Liang et al 2005;Guo and Zhao 2005;Sun and Zhang 2005;Dingreville et al 2005;Wang et al 2008;He and Lilley 2008;Zhang et al 2008;Dingreville et al 2008;Park 2009;.…”