Multi-scale modeling of complex fluids and deformable fibrou(...).pdf

Multi-scale modeling of complex fluids and deformable fibrous media for liquid composite molding

Bergamasco, Luca
Izquierdo Estallo, Salvador (dir.) ; Fueyo Díaz, Norberto (dir.)

Universidad de Zaragoza, 2014

Abstract: In the last few years, the interest of the aerial and terrestrial transport industry in the fabrication of textile-reinforced composite materials has sensibly grown. This is basically due to the remarkable properties of these materials, which combine high mechanical strength with reduced weight. The manufacturing techniques that provide better control on the final quality of the components rely on autoclave curing: heat and pressure are applied on vacuum bags to achieve high volume fractions of the reinforcement and low number of defects due to the presence of voids. Nevertheless, autoclave curing implies high costs for the acquisition of the vessel and the process is energy and time consuming. To reduce the production costs, the industry has increased its interest in out-of-autoclave processing technologies, that is, liquid composite molding (LCM) techniques. In its most basic version, the technique consists in the injection of a catalyzed resin into a closed cavity, where a pre-placed fiber stack lies. When the resin has completely permeated the preform, the mold is subject to high temperatures to induce the curing of the resin to obtain the composite. The current challenge for this technology is to achieve the same quality standards for the final component as those achievable with in-autoclave processing. In LCM processes, the final quality of the component depends on several factors, such as: the structure of the textile, the arrangement of the layers, the adaption to the mold, the compaction process, the operating conditions, the geometry of the component, the configuration of the injection points for the resin, the physical and chemical interactions between the resin and the textile. All these factors affect the correct saturation of the reinforcement, and therefore process parameters must be adequately controlled in order to guarantee the required quality standards for the composite. In this sense, mold filling simulation software is a valuable tool for the process optimization; however the permeability of the reinforcement is required as an input parameter. An accurate evaluation of the permeability of the reinforcement however, represents a challenging task. Fibrous preforms for LCM generally present a hierarchical structure: the fibers are bunched in yarns, which in turn are bundled in a fabric. This structure, undergoes complex deformations during the production process: 1) during the compaction in the mold and 2) during the injection of the resin. This issue remarkably complicates an accurate evaluation of the permeability of the reinforcement and may be at the origin of the scatter observed in the experimental measurements. From a modeling point of view, the different length scales to be taken into account (typically ranging between one and three orders of magnitude) hinders a proper simulation of the deformation of the textile. The typical diameter of the fibers ranges indeed in few micrometers, while the characteristic dimension of the yarns is in the order of the millimeter. This issue represents a constraint for standard numerical approaches due to computational limits. In order to account for the effect on the permeability of the deformation of the hierarchical structure of the preform, multi-scale modeling techniques must be adopted. The objective of the thesis is the development of novel theoretical and numerical frameworks to account for the effect on the permeability of the multi-scale deformations that the textile undergoes during the two aforementioned stages of the process. The development focuses on the fiber-yarn level in 2D, where the yarn is always modeled as suspension of fibers by analogy with a complex fluid. The numerical implementations use computational fluid dynamic (CFD) tools. In order to address the problem, the permeability of a textile preform for LCM is first analyzed by experimental means. A standard CFD approach is then adopted for the simulation of a representative elementary volume of the textile; it is shown that, by means of this approach, the experimental permeability cannot be recovered over the full range of porosities. An X-ray computed microtomography of the textile is then performed. The obtained data are used for the virtual reconstruction of the exact geometry of the textile after its use for LCM. The simulations with this latter geometry provide better results; however the uncertainties on permeability still hold, and the permeability is always overestimated. These uncertainties are discussed in detail and motivate the work described hereafter. The first modeling block of the thesis concerns the analysis of the deformation that the textiles undergo during the compaction in the mold. A continuum model is first developed and validated for the squeeze flow of epoxy-based materials, the rheology of which is given by a viscoplastic constitutive law. The model is then applied to the compaction of yarns, where a viscoplastic behavior for the fiber bundle is assumed in the quasi-static regime of compression and by an analogy with flowing granular media. The rheological parameters are obtained from experimental data by a simplified analytical model for the deformation of the yarns under compaction. The commercial CFD code ANSYS Fluent is adopted for the numerical solution. The model yields information about the evolution of the fiber volume fraction during the compaction and is found to correctly recover the experimental force for high compression ratios. The second modeling block of the thesis concerns the analysis of the deformation that the textiles undergo during the injection of the resin. A numerical framework is first developed and validated for the direct numerical simulation of dilute colloidal suspensions of polymeric molecules. The numerical method consists in a coupled finite-volume/lattice-Boltzmann solution: finite volume method for hydrodynamics and lattice Boltzmann method for the sub-grid-scale physics. For computational efficiency, the lattice Boltzmann solution is accelerated on a graphic processing unit (GPGPU) with a tailored implementation and efficiently coupled with the macroscopic solver (ANSYS Fluent). The numerical method is then exploited for the solution of a mesoscopic model for the flow-induced fiber dynamics during the injection. A statistical model for the fiber dynamics is derived, based on analogy of the yarn with a non-Brownian suspension of particles with confining potentials. The fiber topology during the injection is recovered by a topological invariant and yields information about the change in permeability due to the clustering of fibers in steady-state, fully-saturated conditions. The results are presented in the form of phase diagrams, which show that in the deformable case the permeability can be up to one order of magnitude lower than in the rigid case. On the basis of the results obtained, the following main conclusions can be drawn: 1. The model developed for the compaction in the mold showed to be appropriate for a phenomenological analysis of the deformation of the yarns under compression. The model allows to analyze quantitatively the evolution of the fiber volume fraction, which yields useful information for a better understanding of the distribution of the fibers before the injection. 2. The model developed for the fiber dynamics during the injection, allows to analyze their topology induced by the fluid flow. The clustering of fibers significantly reduces the permeability at the fiber level, which could explain the overestimation obtained with simplified numerical approaches. The phase diagrams obtained for the permeability, both at the yarn and fiber level, allow to identify the best operating conditions for the infiltration of the resin. The proposed models have been developed using fluid dynamic techniques, which opens the possibility for a unified framework for the analysis, and ultimately, for a more precise estimation of the permeability. This work aims to represent a first tentative in this direction.

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