Effective moduli of particle-filled composite with inhomogeneous interphase: Part II – mapping method and evaluation

Abstract In this part of the two-part paper, a method that maps a particle together with the inhomogeneous interphase into an effective homogeneous particle is used to predict the effective moduli of particle-filled composites with an inhomogeneous interphase. The effective bulk modulus of the equivalent particle can be obtained in closed-form expressions for a wide variety of variations of the elastic properties of the interphase. The effective shear modulus is obtained by two different models: a differential scheme based on the Hashin–Shtrikman lower bound and an average approximation using the average value of the elastic properties of the interphase. This mapping method can be used along with many micromechanics approaches to evaluate the effective moduli of particle-filled composites with an inhomogeneous interphase. In this part, the effective moduli of a composite obtained using the generalized self-consistent method (GSCM) and the third-order approximation (TOA) of Torquato are compared with the bounds presented in Part I. It is found that the effective bulk and shear moduli are within the bounds for the considered case.