Construction of stress analysis system for nano-scaled structures and its verification

从宏观角度出发，从微观角度提出了一种新的材料强度力学，并构建了该领域的应力分析体系。在本研究中，考虑由表面能通过Herring关系导出的表面应力，重建了力平衡的边界条件。该公式涉及到曲面或界面的自由能，是一个包含曲面曲率的非线性方程，除数值解外不能精确求解。虽然，我们假设即使非线性方程线性化，表面应力对纳米尺度结构的应力和位移分布的影响也可以近似估计。因此，采用线性化边界条件进行应力分析。本文计算了弹性压头在涂有纳米厚度非晶膜的弹性半空间上的压痕实验。在分析中，定义了一个由表面应力、分析模型的代表性长度和弹性模量组成的相关无量纲参数。通过确定两个结构的参数，我们可以使一个结构的应力分布与另一个结构的应力分布一致。当参数值减小时，表面应力的影响也减小，体应力的分布与有序边界条件下的分布一致。当参数值增大时，由于表面应力的作用，位移和体应力增大。基于边界元法，建立了考虑表面应力的纳米结构应力分析系统。研究了分散在纳米尺度颗粒中的复合材料的力学性能和颗粒内的应力分布，为该系统的分析提供了理论依据。分析结果发现，在颗粒尺寸小于10nm的情况下，表观复合模量与常规复合模量规则的预测结果存在显著差异。此外，即使复合材料施加拉伸载荷，由于表面应力，颗粒中的应力状态也是压缩的。可以说，在纳米尺度的颗粒中很难出现位错等缺陷，材料的整体变形是由滑移作为界面进行的。少

A new mechanics for strength of materials was devised in a microscopic view approaching from a macroscopic one, and a stress analysis system in such a field was newly constructed. In this study, a boundary condition for equilibrium of force was rebuilt by considering a surface stress derived from surface energy through Herring's relationship. The formulation involves free energy of surface or interface, it is a nonlinear equation containing curvature of surface, and cannot solve exactly except numerically. Although, we supposed that an influence of surface stresses upon the distribution of stress and displacement for nano-scaled structures could be approximately estimated even if the nonlinear equation was linearized. Thus, a stress analysis was performed by using the linearized boundary condition. Here, nano indentation test that an elastic indenter is pressed to an elastic half space coated a nano-thickness amorphous film was calculated. In the analysis, a relevant dimensionless para … More meter consisted of surface stresses, a representative length of model for analysis and elastic modulus was denfined. We can make coincidence of a stress distribution for a structure with that for another one by agreed the parameters for both structures. Furthermore, when the value of parameter decreases, the influence of surface stresses also reduces, and the distribution of bulk stresses agrees with that for ordinal boundary condition. When the value of parameter increases, the displacement and bulk stresses increase owing to the surface stresses.A stress analysis system for nano-scaled structure was developed on the basic of the boundary element method taking into consideration surface stresses. As an demonstration for analysis using the system, mechanical properties of composite materials dispersed nano-scaled particle and the stress distribution in the particle were investigated. As a result for analysis, it was found that apparent composite modulus is significantly different from a prediction using conventional composite modulus rule below 10nm of the size of particle. Furthermore, stress state in the particle is compressive due to surface stresses even if tensile load is applied to the composite materials. We can say that any defect such as dislocation is hard to occur in the nano-scaled particles and global deformation of materials proceeds by a slip as the interface. Less