Modelling the variability and reliability of high-performance composite materials

Abstract

Carbon-fibre reinforced polymers (CFRPs) are the material of choice for light-weight structural applications. The microstructure of CFRPs ranges from simple to more complex architectures, allowing them to be tailored for specific applications. However, composite material systems present intrinsic variability which leads to a stochastic mechanical response. The behaviour of composite materials under different loading conditions (ranging from static to complex cyclic loads) is still to be fully understood. This study aims to develop models to predict the variability and reliability of different composite architectures, leading to safer and more reliable composite structure designs.

Tow-Based Discontinuous Composites (TBDCs) are an up-and-coming class of high-performance discontinuous composites, which combine high manufacturability and good mechanical properties. Their architecture, composed by randomly oriented carbon fibre tows, results in a microstructure with the most extreme levels of variability. The spatial variability of TBDC strain fields was quantitatively characterised with a new proposed method, which enabled the identification of a relationship between the characteristic length-scales of the strain fields and the material's microstructural features. The intrinsic variability of these materials leads to a notch insensitive behaviour, that was experimentally characterised not only for circular notches of different diameters but also for non-circular notch geometries.

A stochastic Finite Element (FE) framework able to replicate the intrinsic variability of TBDC materials was proposed. The framework considers an implicit representation of the material's microstructure, by using a Stochastic Equivalent Laminate analogy, and predicts the elastic response, damage initiation and final failure of TBDCs under static loading. The FE framework was validated against experimental results for different TBDC material systems, with both random and preferential fibre orientations.

Numerical models were used to explore the design space of discontinuous composites, in order to identify optimal microstructure designs that maximise their stiffness and strength. Ultra-thin tapes (20 $\upmu$m) of high modulus (425-760 GPa) carbon-fibres were used to manufacture and test TBDC under static loading. The experimental results showed increases of strength up to 100\%, when compared with commercially available TBDC systems, and resulted in a discontinuous composite with mechanical properties that match the strength and overcome the stiffness of aerospace-graded continuous-fibre quasi-isotropic laminates.

Composites are often subjected to cyclic loading, presenting further challenges in predicting their reliability. An analytical model to predict the fatigue response of unidirectional composites was also proposed. Due to its analytical formulation, the model was able to predict, for the first time in the literature, the evolution of the micromechanical fatigue damage in composites with any number of fibres. Strength reductions throughout fatigue life (up to 10 million cycles) are computed in less than sixty seconds. The model generates stochastic S-N curves and was successfully validated against experiments from the literature.

This work shows the potential of TBDCs to match the mechanical properties of continuous-fibre quasi-isotropic laminates while still having high manufacturability. The models developed throughout this work can be used to support material design, to identify optimal TBDC microstructures for enhanced mechanical performance.