Scaling of Metal Plasticity on Approach to Nanoscale: Asymptotic Analysis

在纳米尺度上，与纳米复合材料中的颗粒或纤维间距、微型电子元件中的薄膜厚度和MEMS元件的尺寸相比，金属晶粒晶格中的位错间距、控制微电子器件中薄膜边界层厚度和织构渐变的晶粒尺寸以及引发断裂的微孔尺寸不再是可以忽略的。这可能会或可能不会导致主要的有益尺寸效应，例如强度增加一个数量级，必须了解这一点，以确保可靠性和优化性能。最近提出了几种微米范围的应变梯度理论，但它们在纳米尺度上的渐近特性似乎是不现实的。因此，提出了一种改进的应变梯度理论。由于小尺寸渐近解比实际值域的解简单得多，因此采用渐近匹配技术来获得该值域的简单解析解。应变梯度理论，通过结合不同性质的边界层和连续的晶体尺寸或织构梯度来增强，然后用于模拟颗粒尺寸对金属基纳米复合材料刚度和强度的影响。将Hashin的复合球模型和Dvorak的变换场分析等宏观尺度的方法扩展到微观尺度，用特征应变代替应变梯度效应。最近在微米厚度的拉伸自由薄膜中观察到的尺寸对强度和峰后软化的影响也得到澄清。最后，分析了应变梯度在微孔隙形成过程中引发断裂的作用。

On approach to nano-scale, the spacing of dislocations in crystal lattice of metal grains, the crystal grain sizes governing the thickness of boundary layers and texture gradation in thin films in micro-electronic devices, and the size of fracture triggering micro-voids, cease being negligible compared to the spacing of particles or fibers in nanocomposites, to thickness of thin films in miniature electronic components, and to size of MEMS components. This may or might not cause major beneficial size effects such as strength increase by an order of magnitude, which must be understood to ensure reliability and optimize performance. Several strain gradient theories were recently proposed for the micrometer range but their asymptotic properties on approach to nanoscale appear to be unrealistic. An improved strain-gradient theory is, therefore, developed. Since the small-size asymptotic solutions are much simpler than the solutions for the practical range, the technique of asymptotic matching is used to obtain simple analytical solutions for that range. The strain gradient theory,enhanced through incorporation of boundary layers of different properties and continuous crystal size or texture gradation, is then used to model the effect of particle size on the stiffness and strength of metal-matrix nanocomposites. The macro-scale methods for composites, such as Hashin's composite spheres model and Dvorak's transformation field analysis, are extended to micro-scale by replacing the strain gradient effect with eigenstrains. The size effects on strength and postpeak softening, recently observed in tensioned free thin films of micrometerthicknesses are also clarified. Finally, the role of strain gradients in micro-void formation that triggers fracture is also analyzed.