Theory and validation of the master ply concept for invariant-based stiffness of composites

Abstract

The objective of this paper is to unveil the background theory behind the universal master ply assumption, based on the invariant approach, to describe ply elastic properties. It was demonstrated that using ply-based constitutive relations, trace-normalized stiffness properties can be derived for different materials. Theoretical predictions for trace-normalized parameters were plotted as functions of the unidirectional ply longitudinal modulus (Ex), which defines the particular material system. Ply stiffness extensive empirical data were obtained from literature for four types of material systems (high modulus carbon/epoxy, standard modulus carbon/epoxy, aramid/epoxy, and glass/epoxy) and correlated quite well to theoretical predictions. Theoretical curves presented a nonlinear region for low Ex which gradually evolves to a plateau as Ex increases. It was verified that the master ply concept averaging the trace-normalized ply stiffness matrix elements can be applied for high modulus carbon/epoxy, standard modulus carbon/epoxy, and aramid/epoxy material systems. However, glass/epoxy systems can not be represented by this concept. The exposed theoretical background supports trace-based approach and enhances its effectiveness as a design tool, encompassing all the consequent advantages.