Scaling of Metal Plasticity on Approach to Nanoscale: Asymptotic Analysis

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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.