Stochastic micromechanical modelling of unidirectional carbon and flax fibre composites

Unidirectional (UD) fibre-reinforced polymer composites are made from a polymer matrix and a non-woven fibre reinforcement, leading to high strength and stiffness along the direction of the fibres. The longitudinal tensile strength of a UD composite is governed by localized microstructural features such as porosity, fibre spacing, fibre-property scatter, and fibre-matrix bonding. Micromechanical modelling with representative volume elements (RVEs) can be implemented to predict the orthotropic material properties of a UD composite, offering an alternative to extensive mechanical testing once a model is validated. The thesis develops a stochastic modelling workflow that features randomized fibre positions and properties within the RVEs, and validates the predicted longitudinal tensile properties against the experimental properties of UD synthetic (carbon) and UD natural (flax) fibre composites. A generation algorithm was developed to construct high fibre volume fraction RVEs on Abaqus with statistically random fibre properties and positions, the latter of which were verified against micrographs using Ripley’s K function and nearest-neighbour statistics. The epoxy matrix and fibre-matrix interfaces were modelled using Drucker-Prager plasticity and cohesive zone modelling respectively, and the extended finite element method (XFEM) was implemented to model fibre and matrix cracking. UD carbon and UD flax composites were manufactured with vacuum bagging and compression moulding, and tested in longitudinal tension for model validation at two fibre volume fractions. The models were calibrated to the vacuum-bagged datasets through a sensitivity analysis, and validated against the compression-moulded datasets. Randomized fibre properties and positions proved to be necessary for strength prediction, the fibre volume fraction was the most significant parameter, while randomized fibre radii were not as significant. The predicted properties of the carbon composites were within 1.44% of the experimental results, while the properties of the flax composite were within 8.25% and 2.53% at the lower and higher fibre volume fractions respectively. The results demonstrate that an identical modelling workflow can be applied to both synthetic and natural UD composites, and that microstructural variability with randomized fibre properties is critical for longitudinal strength prediction.