Scaling of Metal Plasticity on Approach to Nanoscale: Asymptotic Analysis

接近纳米尺度的金属塑性尺度：渐近分析

• 批准号: 0301445
• 负责人: Zdenek Bazant
• 金额: --
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-04-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0301445&HistoricalAwards=false
• 关键词: Scaling; Metal; Plasticity; Approach; Nanoscale

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.

在接近纳米尺度时，与纳米复合材料中的颗粒或纤维的间距相比，与微型电子部件中的薄膜厚度相比，金属晶粒的晶格中的位错的间距、控制微电子器件中的薄膜中的边界层厚度和纹理渐变的晶粒尺寸以及触发断裂的微空隙的尺寸不再是可忽略的，以及MEMS部件的尺寸。这可能会也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，必须理解这一点以确保可靠性和优化性能。最近提出了几个应变梯度理论的微米范围内，但他们的渐近性质的方法纳米似乎是不现实的。因此，一个改进的应变梯度理论。由于小尺寸渐进解比实际范围的解简单得多，因此使用渐进匹配技术来获得该范围的简单解析解。应变梯度理论，通过纳入不同的属性和连续的晶体尺寸或纹理渐变的边界层增强，然后被用来模拟金属基纳米复合材料的刚度和强度的颗粒尺寸的效果。将Hashin的复合材料球模型和Dvorak的变换场分析等宏观尺度方法推广到细观尺度，用本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强度和峰后软化的尺寸效应也得到了澄清。最后，还分析了应变梯度在微孔洞形成中的作用。