Stress–strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the `average stress in the matrixʹ concept of Mori and Tanaka (Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with mis®tting inclusion. Acta Metall. 21, 571±580) a micromechanical model is presented for the prediction of the elastic ®elds in coated inclusion composites with imperfect interfaces. The solutions of the e€ective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and ®bers, respectively, the interface imperfections are taken to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting e€ective shear modulus for each material and the stress ®elds in the composite are presented under a transverse shear loading situation