Rational analysis methods are presented to cover, separately, possible brittle fracture and ductile yield failures of the matrix in fibre/polymer composite materials subjected to purely in-plane loads. The models cover both carbon fibres, which customarily fail before the matrix, and glass-fibre composites in which the matrix usually fails first Delaminations, both at edges and from damage, are excluded, because they need quite different analyses. Customary progressive-failure and ply-discounting analyses are shown to be erroneous, because one cannot characterize a fracture-mechanics problem with strength-of-material analyses. An explanation is provided for why, unlike fibre failures and matrix yielding, matrix cracking cannot be assessed on a ply-by-ply basis. There is an interaction with adjacent plies which can act as crack stoppers. In other words, not even the classical laminate theory is valid when the matrix really cracks. Gaps in the understanding of the subject, in regard to residual thermal stresses, are identified. A distinction is drawn between conventional carbon-fibre/polymer composites, for which even a crude analysis of matrix failures can suffice because only structurally insignificant matrix microcracking precedes the fibre failures in properly designed laminates and in glass-fibre-reinforced plastics in which the matrix really can fail first. In metal-matrix composites, a far more accurate model will be needed because the matrix then carries most of the load. The knowledge of this subject 30 years ago is shown to be far superior to what is commonly used to analyse composite materials today and it is suggested that the introduction of the many abstract mathematical interactive failure criteria, valid only for truly homogeneous anisotropic materials, was largely responsible for this.
