Elastic moduli of filled polymers: The effect of particle shape

Abstract

Eshelby’s theory is known for its simplicity in the treatment of the elastic moduli of a composite filled with spheres. His approach is utilized in this paper to estimate the five elastic constants of a filled polymer containing aligned ellipsoids. The anisotropy‐particle‐shape effect is characterized by the aspect ratios (ρ) of an ellipsoid. Because Eshelby’s theory is limited to dilute dispersions, we have to confine the present derivation to the intrinsic moduli. The basic definition and method are outlined in the discussion of shear moduli which have the form analogous to that of spherical filler and have also been investigated by several authors relating explicitly to disk‐ and needle‐shaped particles. Equations on the bulk, longitudinal, and transverse Young’s moduli are the new results which are valid for all values of ρ. Orienting fibers (ρ≳1) parallel or disks (ρ<1) perpendicular to the stretch direction has the similar reinforcing effect and is illustrated with data on glass and boron in epoxy resins.