Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites

Abstract

This paper addresses a micromechanics based strength theory to estimate the ultimate strength of unidirectionally fiber reinforced composites. The fibers used can be transversely isotropic in an elastic region but become isotropically hardening in a plastic one. The matrix material is considered as isotropically elastic–plastic. The stress state generated in each constituent material is explicitly expressed as a function of overall applied loads by making use of a bridging matrix that correlates the stress state in the fibers with that in the matrix. In this way, the composite strength is treated in terms of those of the constituent materials. Whenever one of the constituent materials attains its failure stress state, the corresponding overall applied stress is defined as the ultimate strength of the composite. This is because in most cases either the fiber fracture or the matrix breaking is the source that initiates the composite failure. The well-developed maximum normal stress theory of isotropic materials is applied to govern the constituent failure. One of the best advantages of the present theory is that the composite strength can be well estimated using minimum number of input data, which are the constituent properties and the fiber volume fraction only. Another advantage is that the failure mode and the stress level in each constituent material are automatically indicated when the composite fails. Such information is important for composite design. The present theory has been used to predict the off-axial strengths or strength envelop of a number of unidirectional composites. Good correlation between the predicted strengths and available experimental data has been found. Application to laminate strength analysis has been shown. The simulated strength envelope of an angle-plied laminate using original constituent properties agrees well with experimental data. Comparison of this strength theory with another well-known phenomenological theory, the Tsai–Wu theory, shows that the present theory is grossly much more accurate for the considered laminate, which indicates that understanding of the matrix inelastic deformation is critical for laminate strength analysis.