Boundary layers in fibrous composite materials

Abstract

Many studies in the theory of composite materials are based on the homogenization approach, which consists of the substitution of the original heterogeneous medium by a homogeneous one with certain effective properties. Though this procedure works well for the entire composite solid, it cannot be applied in the vicinity of the outer boundary. The transmission of an external load applied at the boundary to the inner domain of the material occurs by a redistribution of stresses between the constitutive components (inclusions and matrix) and involves strong singularities in the local stress field, which may result in microscopic failure of the composite structure. In the present paper, we propose an approximate analytical procedure, allowing determination of the stress–strain field in the vicinity of the outer boundaries of fibre-reinforced composite materials. It is also shown that controlled decrease in bonding between the components leads to a more uniform redistribution of local stresses, which can essentially reduce the risk of failure.