Effective moduli for micropolar composite with interface effect

Size-dependence is well observed for metal matrix composites, however the classical micromechanical model fails to describe this phenomenon. There are two different ways to consider this size-dependency: the first approach is to include the nonlocal effect by idealizing the matrix material as a high order continuum (e.g., micropolar or strain gradient); the second is to take into account the interface effect. In this work, we combine these two approaches together by introducing the interface effect into a micropolar micromechanical model. The interface constitutive relations and the generalized Young-Laplace equation for micropolar material model are firstly presented. Then they are incorporated into the micropolar micromechanical model to predict the effective bulk and shear moduli of a fiber-reinforced composite. Two intrinsic length scales appear: one is related to the microstructure of the matrix material, the other comes from the interface effect. The size-dependent effective moduli due to the nonlocal effect and interface effect can be synchronized or desynchronized for nanosize fibers, depending on the nature of the interface. For the relatively large fiber size, the size-dependence is dominated by the nonlocal effect. As expected, when the fiber size tends to infinity, classical result can be recovered.