Analysis of the effect of interfacial slippage on the elastic moduli of a particle‐filled polymer

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Abstract
An attempt was made to study the effect of interfacial slippage on the filler reinforcement based on the boundary condition that the constituents of a particle‐filled composite can slip relative to each other, but no cavities are formed at the interfaces. The elastic field satisfying these conditions is derived using the linear theory of elasticity and the effective elastic moduli of the composite are calculated. The following assumptions are made: (1) Filler particles are spherical, (2) fillers are completely dispersed, and (3) the volume fraction of fillers is sufficiently small that the interaction among fillers may be neglected. The expression for the shear modulus of the composite μ**, which is derived here, is consistent with the viscosity of a suspension which has been derived by Oldroyd. Experiments who that the increase of Young's modulus by glass beads (GB) is lower in polystyrene (PS) than in epoxy resin (Ep). The reinforcement in Ep‐GB systems can be estimated by the well known formula derived assuming perfect adhesion. However, the reinforcement in PS‐GB systems is in rather good agreement with the formula derived here assuming interfacial slippage.

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