The significance of effective modulus theory (homogenization) in composite laminate mechanics

In this work, we consider the issues regarding the homogenization of fiber-reinforced layers in a laminate in the presence of macroscopic (ply-level) stress gradients. This is accomplished by considering a series of (free edge) boundary value problems similar to those treated by Pagano and Rybicki in 1974. Despite our inability to provide such a homogenization theory, if one truly exists, we can devise approaches to predict the fiber/matrix interfacial stresses in an arbitrary cell by applying certain displacements and/or tractions on the cell boundaries. These boundary conditions are those derived by representing each layer in the laminate by conventional effective modulus theory. It is shown that these approximations can lead to reasonably accurate interfacial stresses and offer great promise as a means of solving practical laminate problems reinforced by fibers of moderate diameter.