Theoretical justification of Tsai's modulus based on micromechanical analysis

This paper deals with the application of micromechanics for the determination of lamina effective properties. Micromechanical models can be considered as the first step of the composite material mechanical design and the traditional estimative of the effective elastic properties presents the drawback of uncertainties related to the fibers' properties and matrix curing effect. On this basis, Tsai's modulus was proposed based on average normalized properties for carbon fiber reinforced polymers (CFRP). On one hand, this approach has the advantage to be a simple procedure with good results; on the other hand, its generality needs to be confirmed because it is based on empirical approach. The present work develops a theoretical justification of the Tsai's modulus by comparing it with two micromechanical models: asymptotic homogenization, a rigorous analytical model; and VSPKc, a model based on mechanical principles of the traditional rule of mixture. Ranges of average properties for polymeric matrices and carbon fibers are selected, generating 65,536 data with the micromechanical models to be employed for each one of the five independent lamina's elastic properties. Results show that the difference between Tsai's modulus and the average normalized properties estimated by micromechanical models is smaller than 15% for all the properties. In this regard, the investigation provides a theoretical justification of Tsai's modulus approach. [Display omitted]