A novel semi-empirical analytical method for stiffness prediction of unidirectional discontinuous-fiber composites

A simple and efficient micromechanical model of unidirectional discontinuous-fiber composites (UDC) is critical for predicting the mechanical properties of injection molded fiber-reinforced thermoplastics (IMFT). A new explicit expression of longitudinal modulus E₁₁ is constructed by introducing a fiber aspect ratio weight function considering to the advantages of Cox shear lag model and Halpin-Tsai model. The Halpin-Tsai model is modified by introducing an equivalent fiber aspect ratio to study the variation of transverse modulus E₂₂ with fiber aspect ratio l/a. Based on the stress distribution of Hsueh model in RVE, a simple explicit expression of Poisson's ratio v₁₂ is derived by using average approximation method and mixing principle, which can reduce the Halpin-Tsai equation. Poisson's ratio v₂₃ is deduced by assuming that the Poisson's ratio properties are isotropic, and then the underestimation of shear modulus G₂₃ is corrected by the modified Halpin-Tsai model for v₂₃ based on reverse engineering. The Halpin-Tsai model is modified by introducing an equivalent fiber aspect ratio to study the variation of shear modulus G₁₂ with l/a. The validity of the novel semi-empirical analytical model is verified by compared with the prediction results of other famous models (including finite element method) and experimental results. In addition, the elastic moduli of IMFT were predicted well, which indirectly demonstrates the superiority of the novel modified model.