Soft interphase volume fraction of composites containing arbitrarily shaped mono−/poly-disperse fillers: Theoretical and numerical investigations

Interphase, a crucial structural component in composite materials connecting the fillers and matrix, typically possesses unique physical properties and plays a crucial role in determining the overall transport and mechanical behaviors of the material system. In this work, we propose a generic theoretical framework to precisely determine the volume fraction f_si of soft interphase around arbitrarily shaped hard fillers, including both convex and concave shapes with arbitrary size dispersity, in three−/two-dimensional (3D/2D) heterogeneous material systems. Specifically, a composite material is regarded as a three-phase structure composed of a homogeneous matrix, hard anisotropic fillers, and their surrounding interpenetrable interphase layers with a constant “thickness” for each filler volume fraction. The seminal hard -core soft-shell (i.e., cherry-pit) model and statistical geometry theories are employed to derive explicit analytical formalism of f_si which is subsequently verified via a series of numerical experiments using Monte Carlo sampling. We systematically investigate the dependence of f_si on the filler characteristics, including filler volume fraction, geometric size factor, fineness, and filler shape and size distributions. Interestingly, we find that filler sphericity can be used as the sole shape descriptor to control the interphase volume fraction for all filler shapes, including those with irregular non-convex morphologies. Our framework provides an efficient and accurate tool for composite design that complements expansive numerical simulations, which is also readily applicable to understanding the effect of f_si on physical properties of composites.