Design and Effective Properties of a Functionally Graded Unidirectional Fiber-Reinforced Composite

The present work deals with the design of a fiber-reinforced composite lamina with varying fiber-volume fraction (FVF) along its thickness direction. In the available elastic analyses of this kind of composite, the elastic properties are evaluated based on the assumptions like continuous variation of FVF and existence of decoupled representative volume element (RVE) at every point along the thickness direction. In order to predict the graded material properties without any of these assumptions at present, first a micro-structure of similar graded composite is designed for the variation of FVF according to a sigmoid function of thickness coordinate. Next, a continuum micro-mechanics finite element model of the corresponding representative volume (RV) is derived. The RV is basically composed of several micro-volumes of different FVFs and the classical homogenization treatment is implemented over these micro-volumes without decoupling them from the overall volume of RV. The importance of this coupled analysis is verified through a parallel decoupled analysis. The effect of the total number of micro-volumes within a specified thickness of lamina on its graded elastic properties is presented. The characteristics of graded elastic properties according to the sigmoid function are also discussed.