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Multi-scale modelling of fibre assemblies
[Thesis]. Manchester, UK: The University of Manchester; 2014.
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Abstract
Manufacturing of textile preforms involve preform compaction which influences the fibre volume fraction and level of crimp in the final laminates affecting the laminate properties. The preform compaction behaviour is highly non-linear and depends on a number of tow-level factors which in turn is guided by filament-level interactions. Hence experimentally predicting the compaction behaviour of a preform, made of large fibre bundles, remains as an obstacle to the understanding of the compaction mechanics due to the stochastic effects of filament-level interactions. This thesis proposes a novel multi-scale modelling technique which predicts the compaction behaviour of large fibre bundles or tows. The model considers real inter-fibre frictional interactions; the friction coefficients are obtained by carrying out friction tests on carbon fibres. Since the inter-fibre friction varies with the inter-fibre orientation, experiments are done to study the effects of fibre orientation on friction. The tests have shown a significant increase in coefficient of friction (from 0.2 to 0.45) for parallel tows due to bedding and entanglement of fibres in comparison to the friction between perpendicular tows. Modelling of the filament-level compaction behaviour requires inter filament friction coefficient which is not equal to the tow friction. In addition, the filaments within a tow can slip relative to each other. Therefore, inter filament friction can influence tow friction. Hence filament friction is determined from tow friction and used in the compaction models. Numerical models of compaction of large fibre bundles are developed which use this experimentally-obtained fibre friction coefficient as input. The solid model requires extensive computational effort. A two-dimensional (2D) model has been developed where the bending and torsional behaviour are incorporated with the help of springs. This 2D model has resulted in improved computational efficiency compared to the solid model (that is, a 99% improvement in CPU time for a 37 filament assembly). The model is then extended to tow- and fabric-levels. The tow-scale results are in close agreement (~5%) with validation tests. A further 3D modelling technique using beam elements has been presented as a further scope which is able to use the level of compaction obtained from the 2D model and also overcomes the limitations of the 2D model. This 3D modelling technique has shown 88% reduction in CPU time compared to that of solid model of same fibre bundle.