Dynamic mechanical properties of particulate‐filled composites

TLDR

In composites with glass spheres, the relative shear modulus follows the Mooney equation in rubbery matrices, but in rigid epoxy matrices it falls between the Mooney and Kerner predictions, with reductions attributed to limited filler modulus contrast, lower Poisson’s ratio, and thermal stresses that also introduce temperature dependence below the glass transition, while particle aggregation further raises the modulus. The authors refine the Kerner lower‑bound shear‑modulus model by incorporating the maximum packing fraction of filler particles, improving agreement with experimental data. Experimental tests show that the relative shear modulus of rigid‑matrix composites lies between the Mooney and Kerner bounds, that torsion/flexure measurements underestimate moduli because of a surface layer, that surface treatment can significantly alter damping without affecting modulus, and that accounting for maximum packing fraction in the Kerner model reconciles theory with observations.

Abstract

Abstract The relative shear moduli of composites containing glass spheres in a rubbery matrix obey the Mooney equation, analogous to the relative viscosity of similar suspensions in Newtonian liquids. However, when the matrix is a rigid epoxy, the relative shear moduli are less than what the Mooney equation predicts but greater than what the Kerner equation predicts. Relative moduli are less for rigid matrices than for rubbery matrices because (1) the modulus of the filler is not extremely greater compared to that of the rigid matrix; (2) Poisson's ratio is less than 0.5 for a rigid matrix; (3) thermal stresses in the matrix surrounding the particles reduce the apparent modulus of the polymer matrix because of the nonlinear stress—strain behavior of the matrix. This latter effect gives rise to a temperature dependence of the relative modulus below the glass transition temperature of the polymer matrix. Formation of strong aggregates increases the shear modulus the same as viscosity is increased by aggregation. Torsion or flexure tests on specimens made by casting or by molding give incorrect low values of moduli because of a surface layer containing an excess of matrix material; this gives rise to a fictitious increase in apparent modulus as particle size decreases. The mechanical damping can be markedly changed by surface treatment of the filler particles without noticeable changes in the modulus. The Kerner equation, which is a lower bound to the shear modulus, is modified and brought into closer aggrement with the experimental data by taking into account the maximum packing fraction of the filler particles.