Composites with fractal microstructure: The effect of long range correlations on elastic–plastic and damping behavior

Abstract

The effect of correlations of the spatial distribution of inclusions in a two-phase composite is studied numerically in this work. Microstructures with fractal distribution of inclusions, characterized by long-range power law correlations, are compared with random inclusion distributions of same volume fraction. The elastic–plastic response of composites with stiff elastic inclusions and elastic–plastic matrix is studied, and it is concluded that fractal microstructures always lead to stiffer composites, with higher strain hardening rates, compared with the equivalent composites with randomly distributed inclusions. Composites with filler distributions characterized by shorter range, exponential correlations exhibit behavior intermediate between that of random and power law-correlated microstructures. Larger variability from replica to replica is observed in the fractal case. The pressure in inclusions is larger in the case of fractal microstructures, indicating that these are expected to be advantageous in applications such as toughening of thermoset polymers which takes place via the cavitation mechanism. The effect of the spatial distribution of inclusions on the effective damping of the composite is also investigated. The matrix is considered elastic and non-dissipative, while inclusions dissipate energy. The composite with fractal microstructure provides more damping than the random microstructure of same filler volume fraction, and the effect increases with increasing fractal dimension. When damping is introduced only in the interfaces between matrix and inclusions, the spatial distribution of fillers becomes inconsequential for the overall composite behavior. These results are relevant for the design of composites with hierarchical multiscale structure.