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模型，并建立了该领域的应力分析系统。在本研究中，通过考虑由表面能产生的表面应力，通过Herring关系，重新建立了力平衡的边界条件。该格式涉及表面或界面的自由能，是一个含有曲面曲率的非线性方程，除了数值求解外，不能精确求解。然而，我们假设，即使将非线性方程线性化，表面应力对纳米结构的应力和位移分布的影响也可以近似估计。因此，利用线性化边界条件进行了应力分析。计算了弹性压头压在涂覆纳米厚度非晶薄膜的弹性半空间上的纳米压痕实验。在分析中，提出了一个相关的无量纲Para…更多地由表面应力组成，定义了具有代表性的分析模型长度和弹性模数。我们可以通过约定两个结构的参数来使两个结构的应力分布一致。此外，随着参数取值的减小，表面应力的影响也减小，体应力的分布与顺序边界条件下的分布一致。在考虑表面应力的边界元方法的基础上，建立了纳米尺度结构的应力分析系统。作为应用该系统进行分析的演示，研究了分散纳米颗粒的复合材料的力学性能和颗粒内的应力分布。结果表明，在颗粒尺寸小于10 nm的情况下，复合材料的表观弹性模数与常规复合材料弹性模数的预测值相差很大。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。我们可以说，在纳米颗粒中很难出现位错等缺陷，材料的整体变形是通过滑移作为界面进行的。较少

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