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

从宏观力学的角度出发，提出了一种新的材料强度力学，并建立了该领域的应力分析系统。在这项研究中，一个边界条件的平衡力被重建，通过考虑一个表面应力来自表面能通过Herring的关系。该公式涉及到表面或界面的自由能，是一个包含表面曲率的非线性方程，只能用数值方法求解。虽然，我们认为，表面应力的影响的应力和位移的纳米尺度结构的分布可以近似估计，即使非线性方程线性化。因此，通过使用线性化边界条件进行应力分析。这里，计算了将弹性压头压向涂覆有纳米厚度非晶膜的弹性半空间的纳米压痕测试。在分析中帕拉 关于我们 表组成的表面应力，一个代表性的长度的分析模型和弹性模量的定义。通过对两种结构的参数进行协调，可以使两种结构的应力分布趋于一致。此外，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。在边界元法的基础上，建立了考虑表面应力的纳米结构应力分析系统。作为该系统分析的示范，研究了分散纳米颗粒的复合材料的力学性能和颗粒中的应力分布。作为分析的结果，发现表观复合模量与使用常规复合模量规则预测的颗粒尺寸在10nm以下显著不同。此外，即使对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，任何缺陷如位错都很难发生，材料的整体变形是通过界面滑移来进行的。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