Dynamic mechanical properties of particulate‐filled composites

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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.