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On the modulus of particulate‐filled composites: Application of van der Poel's equation

1976; Wiley; Volume: 14; Issue: 11 Linguagem: Inglês

10.1002/pol.1976.180141112

1542-9385

Ray A. Dickie,

Material Dynamics and Properties

Abstract Application of the van der Poel equation (as recently corrected and simplified by Smith) to modulus‐composition data on polymer composites is discussed. The van der Poel equation is in good agreement with experimental results on systems for which the ratio of filler to matrix modulus is either much less than or, if the filler particles are large enough, much greater than unity. For these systems, it is shown that the van der Poel equation is essentially equivalent to an empirically modified form of the Kerner equation. Discrepancies between the van der Poel equation and experimental modulus values for the remaining systems are analyzed in terms of an effective volume fraction v eff . A functional form for v eff found to be in agreement with experimental results on several systems is: v eff = v f + k ′( v f / d ) 2/3 where v f is filler volume fraction, d is filler particle size, and k ′ is an empirical parameter. For the systems studied, k ′ ranges between 0.28 and 1 μm 2/3 .