An analytical model for predicting the tension modulus and poisson'S ratio of satin weave composites

Predicting elastic properties of braided composites is useful in aerospace structures. Previous methods used to predict elastic parameters are usually based on experimental databases or finite element methods. In this paper an attempt is made to establish an analytical model by combining the energy method and composite micromechanics based on representative volume element (RVE) for 8-harness satin weave composites to predict the tension modulus and Poisson's ratio. The RVE of satin weave composites can be divided into three different sub unit cells: bending cells, semi-bending cells and straight cells. And the crimp of fiber yarns in these cells makes an influence on their tension properties. In this paper the minimum complementary energy principle (MCEP) is applied to calculate the tension modulus of bending yarns. With uniaxial external tension loading, interaction internal force and constraint moments being expressed as 0-order tensor Ti respectively (i is the number of force and moments), the total complementary energy of the RVE can be expressed by Ti. Then the MCEP gives the virtual displacement Δi of each virtual stress Ti. Thus the bending yarns tension modulus is obtained based on Δi and Ti. According to the constitutive relations, principles of the strain in one direction being the same and the sum of the internal stress being zero, equations can be got on the relationship of the stress and strain in the fiber and matrix. Thus, the effective tension modulus and Poisson's ratio of satin weave composites can be calculated using the stress and strain of the fiber and matrix. Errors of the tension modulus and Poisson's ratio between analytical prediction and numerical simulation are smaller than 2%.