The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Pressure and thermal effects on elastic properties of single crystal alpha-Al2O3 from Monte-Carlo simulation

A rectangular structural unit cell of a-Al2O3 is generated from its hexagonal one. For the rectangular structural crystal with a simple interatomic potential [Matsui, Mineral Mag. 58A, 571 (1994)], the relations of lattice constants to homogeneous pressure and temperature are calculated by using Monte-Carlo method at temperature 298K and 0 GPa, respectively. Both numerical results agree with experimental ones fairly well. By comparing pair distribution function, the crystal structure of a-Al2O3 has no phase transition in the range of systematic parameters. Based on the potential model, pressure dependence of isothermal bulk moduli is predicted. Under variation of general strains, which include of external and internal strains, elastic constants of a-Al2O3 in the different homogeneous load are determined. Along with increase of pressure, axial elastic constants increase appreciably, but nonaxial elastic constants are slowly changed.

Size-Dependent Elastic Properties Of Ni Nanofilms By Molecular Dynamics Simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

A nanoindentation analysis of the effects of microstructure on elastic properties of Al2O3/SiC composites

Nanoindentation tests were carried out to investigate certain elastic properties of Al2O3/SiCp composites at microscopic scales (nm up to mu m) and under ultra-low loads from 3 mN to 250 mN, with special attention paid to effects caused by SiC particles and pores. The measured Young's modulus depends on the volume fraction of SiC particles and on the composite porosity and it can compare with that of alumina. The Young's modulus exhibits large scatters at small penetrations, but it tends to be constant with lesser dispersion as the indentation depth increases. Further analysis indicated that the scatter results from specific microstructural heterogeneities. The measured Young's moduli are in agreement with predictions, provided the actual role of the microstructure is taken into account. (C) 2007 Elsevier Ltd. All rights reserved.

The size-dependent bending elastic properties of nanobeams with surface effects

A theoretical model is presented to investigate the size-dependent bending elastic properties of a nanobeam with the influence of the surface relaxation and the surface tension taken into consideration. The surface layer and its thickness of a nanostructure are defined unambiguously. A three-dimensional (3D) crystal model for a nanofilm with n layers of relaxed atoms is investigated. The four nonzero elastic constants of the nanofilm are derived, and then the Young's modulus for simple tension is obtained. Using the relation of energy equilibrium, the size-dependent effective elastic modulus and effective flexural rigidity of a nanobeam with two kinds of cross sections are derived, and their dependence on the surface relaxation and the surface tension is analysed.

Size-dependent elastic properties of Ni nanofilms by molecular dynamics simulation

Size-dependent elastic properties of Ni nanofilms are investigated by molecular dynamics ( MD) simulations with embedded atom method (EAM). The surface effects are considered by calculating the surface relaxation, surface energy, and surface stress. The Young's modulus and yield stress are obtained as functions of thickness and crystallographic orientation. It is shown that the surface relaxation has important effects on the the elastic properties at nanoscale. When the surface relaxation is outward, the Young's modulus decreases with the film thickness decreasing, and vice versa. The results also show that the yield stresses of the films increase with the films becoming thinner. With the thickness of the nanofilms decreasing, the surface effects on the elastic properties become dominant.

The effects of surface tension on the elastic properties of nano structures

In the absence of external loading, surface tension will induce a residual stress field in the bulk of nano structures. However, in the prediction of mechanical properties of nano structures, the elastic response of the bulk is usually described by classical Hooke’s law, in which the aforementioned residual stress was neglected in the existing literatures. The present paper investigates the influences of surface tension and the residual stress in the bulk induced by the surface tension on the elastic properties of nano structures. We firstly present the surface elasticity in the Lagrangian and the Eulerian descriptions and point out that even in the case of infinitesimal deformations the reference and the current configurations should be discriminated; otherwise the out-plane terms of surface displacement gradient, associated with the surface tension, may sometimes be overlooked in the Eulerian descriptions, particularly for curved and rotated surfaces. Then, the residual stress in the bulk is studied through the non-classical boundary conditions and used to construct the linear elastic constitutive relations for the bulk material. Finally, these relations are adopted to analyze the size-dependent properties of pure bending of Al nanowires. The present results show that surface tension will considerably affect the effective Young’s modulus of Al nanowires, which decrease with either the decrease of nanowires thickness or the increase of the aspect ratio.