Micromechanical prediction of Elastic properties of unidirectional glass and carbon fiber-reinforced epoxy composites using the halpin–tsai model

Abstract

This study presents a calibrated analytical micromechanical framework for predicting the linear elastic behavior of unidirectional glass fiber/epoxy and carbon fiber/epoxy composites over a wide range of fiber volume fractions. The approach combines the classical rule of mixtures for the longitudinal Young’s modulus with the semi empirical Halpin–Tsai equations to estimate the transverse Young’s modulus and the in-plane shear modulus. The framework is specifically formulated to support durability-oriented composite design through rapid and physically consistent estimation of elastic properties governing load transfer and stress distribution. Material parameters, including fiber and matrix Young’s moduli (Ef, Em), shear moduli (Gf, Gm), Poisson’s ratios (νf, νm), and fiber volume fraction (Vf up to 0.80), are taken from established material property databases and implemented within a literature-informed modeling scheme. To preserve physical realism at high fiber contents, a shear correction factor is introduced for Vf > 0.50 to account for microstructural interaction and fiber clustering effects. The predicted effective elastic constants (E1, E2, G12, ν12) exhibit consistent and physically meaningful trends across the full fiber volume fraction range. The model predictions were evaluated against trends widely reported in the composite micromechanics literature, and the results showed overall agreement in the nonlinear reduction in stiffness gains at elevated fiber volume fractions. Comparative results indicate that carbon fiber/epoxy composites achieve up to approximately 30% higher stiffness than glass fiber/epoxy systems at equivalent fiber contents, reflecting the influence of stiffness contrast on composite response. The analysis further indicates that stiffness saturation begins approximately in the Vf = 0.60–0.70 range, where the incremental gains in E2 and G12 become noticeably smaller for both composite systems. This behavior provides design-relevant guidance by showing that, beyond this range, further increases in fiber content may offer limited stiffness improvement relative to the associated manufacturing complexity. Overall, the calibrated Halpin–Tsai methodology offers a practical and computationally efficient tool for preliminary evaluation and design-stage optimization of the elastic performance of high-performance composite structures.