Three-dimensional evolution of mechanical percolation in nanocomposites with random microstructures.

摘要

One mechanism that is expected to play a large role in the enhanced, and sometimes novel, mechanical properties of nanocomposites is the probabilistic formation of percolated or connected microstructures. The majority of the models used to describe mechanical percolation have the functional form of a power law and depend on prior knowledge of a percolation threshold or critical volume fraction. While these models have been fairly accurate predictors of electrical conductivity in composites, they do not take any microstructural mechanisms, other than connectivity, into consideration. Classic mean-field micromechanics models, however, do not capture the variability in effective properties due to a random microstructure. In this work, aspects of both modeling approaches, i.e. probabilistic events and micromechanics, are adopted. A computational unit cell model is used to calculate the effective composite properties of random microstructures based on principles of micromechanics. The influence of the spatial randomness is incorporated using Monte Carlo techniques to simulate microstructural realizations. In this way, the modeling paradigm is reversed. Instead of using a percolation threshold to predict mechanical properties, mechanical properties are used to demonstrate the location of apparent percolation thresholds. By observing the distributions and variations of the predicted effective properties, the evolution of microstructural events can be tracked.;Microstructures were simulated for a model material system consisting of metallic particles in a polymer matrix. Effects of a matrix-particle interface, interfacial thickness and interfacial stiffness, were also considered. The influence of particle aspect ratio on the apparent percolation threshold was also explored.