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This paper presents an analytical model for size effects on the longitudinal tensile strength of composite fibre bundles. The strength of individual fibres is modelled by a Weibull distribution, while the matrix (or fibre-matrix interface) is represented through a perfectly-plastic shear-lag model. A probabilistic analysis of the failure process in hierarchical bundles (bundles of bundles) is performed, so that a scaling law relating the strength distributions and characteristic lengths of consecutive bundle levels is derived. An efficient numerical scheme (based on asymptotic limits) is proposed, hence couponsized bundle strength distributions are obtained almost instantaneously. Parametric studies show that both fibre and matrix properties are critical for bundle strength; model predictions at different scales are validated against experimental results available in the literature.

The initiation and propagation of kink-bands are investigated through an experimental study and numerical modelling. Based on the results achieved, the sequence of events and key features for kink-band formation are identified; particularly, matrix yielding is found to play a crucial role in the process, and fibres are found to fail in the compressive side first. The findings from both the experimental and numerical programmes show a remarkable agreement, and are further applied to the development of an analytical model (Part II of this paper) for kink-band formation.

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An analytical micromechanical model for kink-band formation in an unidirectional fibre-reinforced composite is developed. This is supported by the conclusions of experimental and numerical programmes (presented in Part I of this paper) and is based on the equilibrium of an imperfect fibre laterally supported by an elasto-plastic matrix. The model predicts the longitudinal compressive strength of the composite (in closed form), the deflection and main stress fields in fibres and matrix at different stages of kink-band formation, the kink-band width, and the orientation of the fibres at the onset of fibre failure.

In-mould flow during manufacturing of Sheet Moulding Compounds (SMCs) heavily affects the material microstructure and its mechanical properties. This influence is studied here for carbon SMCs on panels compression moulded with limited charge coverage. The high in-mould flow caused severe in-plane tow distortions, while their planarity was preserved. Flow induced fibre orientation plays a paramount role in the material failure, whereas local manufacturing defects had no discernible influence. The properties difference between specimens with preferential orientation of 0° and 90° was 150% for tensile stiffness, 260% for tensile strength, 120% for compressive stiffness and 32% for compressive strength. The compressive strength and failure strain for 45° and 90° specimens were higher than those for tension, and comparable for 0° specimens. Compressive and tensile moduli were similar for specimens with the same orientation. A clear link between SMCs manufacturing and mechanical performance is highlighted, together with its implications on structural design.

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