Extrusion die swell of carbon black‐filled natural rubber

Extrusion die swell of natural rubber compounded with a wide variety of carbon blacks has been determined in a capillary rheometer using a long circular die. The range of variation of carbon black loading, surface area, and structure are, respectively, 10 to 60 phr, 44 to 124 m²/g, and 78 to 120 cc/100 g. The effective carbon black volume fraction φ_e not participating in the strain recovery leading to die swell is assumed to be the sum of the actual filler volume fraction and the fraction of unextractable rubber determined experimentally for each compound. Bagley and Duffey's analysis of extrusion die swell of unfilled polymers as unconstrained elastic recovery was adopted for a filled elastomeric system whose relative shear modulus (G/G₀) is assumed to vary as (1 − φ_e)^−N. The matrix shear modulus G₀, originally introduced by Nakazima and Shida on the basis of a linearized approximation, will depend on the shear stress level because of nonlinear deformation. The power N will vary with shear stress which changes the orientation of carbon black aggregates. Except for these features, die swell data for a wide range of carbon black compounds fall on a single curve when plotted in the manner of the predicted relation between the wall shear stress, die swell, and φ_e. Replacing φ_e by Medalia's φ′ based on an equivalent sphere concept introduces a larger scatter around the mean curve.