Closed form expressions for CTEs of composite materials by the thermo-elastic micromechanics approach

Abstract An analytical thermo-elastic micromechanics model is developed to estimate the homogenized Coefficients of Thermal Expansion (CTEs) properties of a composite material. This model is based on the Concentric Cylinder Model (CCM), using Variational Asymptotic Method (VAM). Closed form expressions for both axial and transverse CTEs of composite materials are derived, satisfying the displacement continuity and the transverse stress equilibria conditions at the interface between the reinforcement and the matrix material. The resulting expressions are functions of fiber material properties, matrix material properties and their volume fractions. The results obtained through these derived closed form expressions of CTEs are compared with those available in literature and the experimentally measured CTEs. Further, closed form expressions for the calculation of 3D displacement, strains and stresses of both the reinforcement and matrix are derived. The results obtained by the use of the developed expressions are validated with the results obtained through 3D Finite Element analysis of a composite beam like structure for a given temperature load.