Multi-scale Modelling of Spatial Variability in Textile Composites: Uncertainty Quantification based on Experimental Data of Internal Geometry

The advantages of using composites for design, manufacturing and during operation are well known. Besides a lower weight for the same or an enhanced performance, this new type of material further reduces maintenance costs and enables a full integration of individual parts for aeronautical components. In automotive, composite materials are even crucial to realise the upcoming regulations in further reducing the CO2 exhaust gases. Though, the introduction of composites is hampered by the relatively high cost of raw material and the uncertain quality of high-performance composite structures. In order to assure the design requirements, high safety factors and strict manufacturing tolerances are enforced that hinder composites to be a competitive material for design. An improved assessment of the quality of any composite part is achieved by identifying the irregularity in the tow reinforcement. The variability in macroscopic performance is dominated by the randomness in the geometrical characteristics at the lower scale, especially for textile products. However, no evident step in this direction has been made over the past decades. Sources of variability remain poorly understood and computational methods are lacking for building representative numerical models. The majority of the state-of-the-art restricts to local features, without regarding the spatial dependency of tow path parameters at different locations. In addition, due to the lack of measured data, researchers content themselves with assumptions on the input distribution and correlation functions, which lead to incorrect estimates of the actual limits of material properties. The next step in this development should consist in a modelling approach that introduces scatter at the different levels and is calibrated with experimental work. This dissertation provides a multi-scale framework for generating realistic virtual textile specimens. A roadmap is provided to characterise the spatial scatter in the internal structure of any textile composite and simulate random models possessing the measured statistical information on average. Therefore, it is a first step towards a systematic modelling approach for textile composites where powerful simulation procedures are applied in combination with experimental data. This contribution complies with the industrial interest of virtual testing towards first time right. High-fidelity simulations are gaining ever more importance and decisions are increasingly pursued based on simulation results, demonstrating the need for instruments such as realistic models. Virtual textile specimens with random reinforcement are acquired in three main steps. First, an experimental methodology is presented to characterise the geometrical variability in terms of the centroid coordinates and cross-sectional parameters on the short-range (meso-scale) and long-range (macro-scale). Non-destructive state-of-the-art inspection techniques such as X-ray micro-computed tomography, optical imaging or digital image correlation are applied to measure the fabric architecture in a reliable and efficient way across the composite volume. The inherent scatter of each tow path parameter in each tow direction is quantified in terms of an average trend, standard deviation and correlation length by applying the reference period collation method. Secondly, a stochastic multi-scale modelling approach is developed to reproduce the measured variation in the tow reinforcement within the unit cell and between neighbouring unit cells. Random instances of tow paths are acquired by combining the deduced average trends with generated zero-mean fluctuations possessing the experimental standard deviation and correlation lengths on average. Zero-mean deviations which are only correlated along the tow path are produced by the Monte Carlo Markov Chain for textile structures, while uncertain quantities that are dependent along and between tow paths are generated using the cross-correlated Series Expansion method. In the last step, virtual composite specimens with random fibre architecture are created in the WiseTex format by an intrusive approach. Nominal tow path descriptions are overwritten with realistic tow representations obtained from the previous step, while preserving the original fibre mechanics and matrix properties. This framework is demonstrated for a carbon-epoxy 2/2 twill woven composite produced by resin transfer moulding. Substantial differences in tow path information are observed for warp and weft direction attributed to the manufacturing process of the weave. A good correspondence is obtained for the experimental and simulated deviations trends in terms of wavelengths of the centrelines and extreme values for all tow properties.status: publishe