1.12 – Micromechanics of Linear Elastic Continuous Fiber Composites

Strength-of-materials approaches, which lead to rule-of-mixture models, and elasticity approaches, as well as finite-element analyses of idealized microstructures, are discussed as a means of estimating the various extensional and shear moduli, the major Poisson’s ratio, and coefficients of thermal expansion of fiber-reinforced composite materials. Numerical results for a medium modulus graphite-epoxy material are presented. Results from the various approaches are compared. It is shown that for the extensional modulus and thermal expansion coefficient in the fiber direction, E 1 and α 1 , respectively, as well as for the major Poisson’s ratio, (ν) 12 , the rule-of-mixtures results are quite accurate when compared to the more exacting finite-element results. For extension modulus E 2 , shear modulus G 12 , and coefficient of thermal expansion α 2 , properties normal to the fiber direction, the rule-of-mixtures results do not compare well with the finite-element results. However, so-called alternative and modified rule-of-mixture models for those properties are presented which lead to better agreement with finite-element results. Elasticity approaches, in the form of concentric cylinder models, lead to very good comparisons for E 1 and G 12 , and also provide a means for estimating the three-dimensional elastic properties necessary to characterize transversely isotropic composite materials.