In the collaborative effort towards standardisation of out-of-plane permeability measurement, an international benchmarking exercise was carried out whereby 19 participants worldwide were instructed to measure the out-of-plane permeability following a number of strict guidelines, informed by the outcomes of the first international benchmarking exercise completed in 2021. This paper presents the results of the exercise and an assessment of the reproducibility of the data and the suitability of the proposed test method. The data returned were subjected to a number of statistical analysis methods, which showed that adherence to the test guidelines resulted in a high likelihood of a participant not being an outlier and therefore providing evidence that the test method proposed in this paper is a suitable way forward for a standardised test method.

This article presents an innovative approach to modeling particle bed growth through suspension dead-end filtration, a process of paramount importance in various industrial and environmental contexts. More precisely, it focuses on the numerical formulation of a continuous approach based on a Stokes-Darcy coupling. In a Level-Set/FEM frame, this model effectively captures the dynamic evolution of particle beds (cake), taking into account the interaction between suspended particles and porous media. Model validation is also a key focus of this paper. Numerical tests are carried out under various conditions, and their results are compared with analytical solutions and experimental data drawn from the literature. This permits corroboration of the predictive capabilities of the model, confirming the robustness and accuracy of the proposed approach. Firstly, Stokes-Darcy coupled flows are investigated in simplified cases such as rectangular geometries and coaxial cylinders. These scenarios serve as benchmarks to assess the model performance under simple and varied conditions. Additionally, the more challenging case of a three-dimensional anisotropic flow between two ellipsoids is addressed, where the evolution of the cake takes place in three dimensions. Through rigorous analysis and comparison with analytical solutions, the model is proved efficient in capturing the inherent complexities of such scenarios. Finally, richer two-dimensional Stokes-Darcy flows are considered, in the presence of both impermeable and permeable obstacles, representing a crucial step towards modeling real industrial processes. This last study highlights not only the formation of particle-free zones but also the practical relevance of this work.

Transient two-phase flows within fibrous media are considered at local scale. Upscaling these flows constitute a key procedure towards a tractable description in an industrial context. However, the task remains challenging as a time-dependent behaviour is observed within a geometrically complex structure with interplay of various physical phenomena (capillary effects, viscous dissipation, etc.). The usual upscaling strategies encountered in both soil sciences and composite materials communities are reviewed, compared, and finally adapted to reach a method that is relevant to describe fibrous media imbibition. Using finite element flow simulations on statistical representative volume elements, the proposed approach first considers several definitions for saturation in order to characterise the flow dynamics as well as the characteristic length associated with the transient behaviour. Next, two methods are proposed to assess a resulting capillary pressure, demonstrating the importance to properly define the capillary pressure acting on the interface. The first one considers the mean pressure jump at the interface, while the second one uses a machine-learning technique, namely Gaussian process regression, to retrieve the mean curvature of the interface. Those methods are found to be both consistent and in agreement with the results from the literature. Finally, a novel approach that stochastically describes the position of the flow front through a presence distribution is detailed. The spread of the front can be compared to the saturation length, and its value has been found to be small enough to be neglected at upper scale, justifying the use of sharp interface models for similar porous media and flow settings.

Permeability measurements of engineering textiles exhibit large variability as no standardization method currently exists; numerical permeability prediction is thus an attractive alternative. It has all advantages of virtual material characterization, including the possibility to study the impact of material variability and small-scale parameters. This paper presents the results of an international virtual permeability benchmark, which is a first contribution to permeability predictions for fibrous reinforcements based on real images. In this first stage, the focus was on the microscale computation of fiber bundle permeability. In total 16 participants provided 50 results using different numerical methods, boundary conditions, permeability identification techniques. The scatter of the predicted axial permeability after the elimination of inconsistent results was found to be smaller (14%) than that of the transverse permeability (∼24%). Dominant effects on the permeability were found to be the boundary conditions in tangential direction, number of sub-domains used in the renormalization approach, and the permeability identification technique.

Liquid Composite Moulding processes are considered as promising and effective to manufacture structure composite parts reinforced with synthetic and natural fabrics. The main novelty of this work is the estimation of capillary pressure (Pcap) for both fabrics at different fibre volume fractions (Vf) and with different liquids. From the previous works, the Pcap was defined as the equivalence between Washburn’s equation and Darcy’s law while our novel model for the capillary wicking could predict very well the swelling behaviour of natural fabrics. The combination of our Pcap definition and our novel model was explored in this study. Linear trends, thresholds and extremums of Pcap at different conditions were found for the first time. These results are relevant to estimate the importance of capillary effects during Liquid Composite Moulding processes and extremely valuable for numerical models at the fibrous scale to predict voids formation.

This work describes a computational strategy, based on a stabilised finite element method, to simulate bifluid flow with capillary effects in a fibrous microstructure. In this framework, triple junction equilibrium is imposed as a natural condition in the weak formulation of the Stokes problem. Two types of 2D microstructures are then considered, hexagonal and random, and studied in terms of numerical permeability and capillary pressure.

Recent years have seen the development and democratization of continuous fibre composite materials for the manufacture of primary aeronautical structures. Composite materials exhibit excellent specific properties compared to aluminium alloys historically used for these applications. The need in cadence improvement leads the aeronautic industry to consider new processes for primary aeronautical structures manufacturing. Therefore, new dry reinforcements are developed, such as the HiTape® reinforcement designed by Hexcel Reinforcements. HiTape® plies are designed for automated laying in order to build dry stacks that can be formed and infused/injected by a liquid resin afterwards to greatly increase the production rates. To understand and predict results from the forming stage, numerical models are considered as a useful tool. In this work, we propose a new computational approach to model the forming stage of dry HiTape® stacks. The HiTape® ply is a slender structure, exhibiting a transversely isotropic behaviour in large deformations as well as a non-linear bending behaviour. Another particularity is that the bending stiffness of the ply is not directly related its membrane stiffness. When stacks are considered, inter-ply phenomena (opening and sliding) appear and greatly influence the bending stiffness of the structure. To model every of these specificities, diverse techniques are used: solid-shell elements are considered to answer the ply slenderness, embedded elements approach helps to model the membrane/bending behaviours decoupling, frictional cohesive zone model stands for inter-ply phenomena and the particular behaviour of the ply is described using a non-linear physical-invariant based hyperelastic constitutive. The finite element (FE) software Abaqus will be used in this work.

In the context of developing competitive liquid composites molding processes for primary aircraft structures, modeling the forming stage of automatically-placed initially flat stacks of dry reinforcements is of great interest. In the case of HiTape®, a dry unidirectional carbon fiber reinforcement designed to achieve performances comparable to state-of-the-art pre-impregnated materials, the presence of a thermoplastic veil on each side of the material for both processing and mechanical purposes should also be considered when modeling forming in hot conditions. As a dry unidirectional reinforcement, HiTape® is expected to exhibit a transversely isotropic behavior. Computation cost and strong characterization challenges led us to model its behavior at the forming process temperature (above the thermoplastic veil melting temperature) through a homogeneous equivalent continuous medium exhibiting four ‘classical’ deformation modes and a specific structural mode, namely out-of-plane bending. The response of both single plies and stacks of HiTape® to this latter structural mode was characterized at the forming process temperature using a modified Peirce flexometer . Results on single plies showed a non-linear softening moment-curvature behavior and a corresponding flexural stiffness much lower than what can be inferred from continuum mechanics. Moreover, testing stacks revealed that the veil acts as a thin load transfer layer between the plies undergoing relative in-plane displacement, i.e. inter-ply sliding. This inter-ply response was then characterized separately at the forming process temperature thanks to a specific method relying on a pull-through test. Experiments performed at pressures and speeds representative of the forming stage revealed that a hydrodynamic lubricated friction regime predominates, i.e. a linearly increasing relationship between the friction coefficient and the modified Hersey number. From an industrial point of view, high forming pressures and low speeds are therefore recommended to promote inter-ply slip to limit the occurrence of defects such as wrinkles.

In this article, a statistical study on transverse permeability of random fibrous medium is performed. For that purpose, numerous random numerical microstructures are generated with constant or randomly varying fibre radii. Their statistical representativity with respect to experimental data is first briefly discussed. Flow simulations are then performed on these digital microstructures to retrieve their full transverse permeability tensor. The representative volume element (RVE) size is determined by studying convergence of permeability distribution when domain size increases. This allows to characterise the medium isotropy as well as the impact of geometrical randomness on permeability. The approach also integrates Gaussian process regression, that is a Bayesian machine-learning model, to consider variability within interpolation in the proposed permeability predictive model. In addition, this paper considers the impact of fluid slip at liquid/fibre interface on permeability for random fibrous media. An analytical expression is proposed to describe precisely the transition from a no-slip to a free-slip regime. This allows us to propose a probabilistic model that links permeability to both the fibre volume ratio and slip length. This finally yields two bounds for transverse permeability of fibrous media: a first related to statistical scattering and a second purely linked to fluid slip.

2D and 3D numerical permeability of fibrous media are studied based on Stokes and Stokes-Darcy flows simulated by a Finite Element Modelling (FEM). A monolithic approach stabilised by an Algebraic Sub-Grid Scale (ASGS) method and implemented in a FEM software (Z-set) is used. The 2D geometries have been generated according to ideal arrangements and 3D geometry are representative of a highly anisotropic ply-to-ply interlock unit cell. For both geometries, yarns have been first considered as impermeable, and then the same calculations have been conducted with various intra-yarn permeabilities. The main novelty of this work is to address the dual-scale permeability problem with a Stokes-Darcy modelling so as to override numerical strategy robustness issues. An empirical law has been proposed to link the effective permeability to the intra-yarn one: this allows to generalise previously established results to real 3D materials with complex structures. An intra-yarn permeability threshold (asymptotic value) from which yarns can be considered impermeable has also been highlighted. This study underlines the importance of unit cell definition when it comes to computing permeability of 3D structures numerically generated, especially non-periodicity issues. Two methods to decrease the impact of preferential flows are then discussed. (C) 2020 Elsevier Ltd. All rights reserved.

Capillary wicking of liquids in natural fibrous reinforcements is a significant phenomenon in fibre-reinforced composites manufacturing through Liquid Composite Moulding (LCM) processes. Such phenomenon is however difficult to analyse due to heterogeneous, multiscale and variable fibrous medium during flow. Taking into account the fibre swelling, a modified Washburn’s model is proposed to predict the capillary rise of liquids in flax fibres. Particularly, swelling and wicking are studied at two different scales, i.e. elementary fibres and individual yarns. Swelling effects have been considered in the model and a modified Washburn’s theory has been developed. The proposed model satisfactory fits experimental results from capillary wicking tests, and hold for a 60% fibre volume fraction (Vf) of fabric on a relatively short duration while it fits well on a longer duration for lower Vf.

Le but de ce travail, qui represente le cœur de la chaire industrielle entre Mines Saint-Etienne et Hexcel, est de mettre au point un chainage numerique robuste pour prendre en compte les effets locaux d’impregnation de fibres par une resine liquide dans des simulations a l’echelle du procede. Les effets locaux sont donc modelises a l’echelle des fibres pour capturer les effets capillaires et calculer ainsi des parametres, tels que la pression capillaire, a exporter a l’echelle superieure. Ceci a ete rendu possible par des stabilisations et enrichissements des methodes elements finis utilises pour simuler des ecoulements de Stokes et Darcy ainsi que leur couplage. Les contraintes capillaires (pressions capillaires dans les directions principales) sont alors inclues dans les simulations d’elaboration par procedes directs de pieces aeronautiques. Le but ultime de cette approche est de developper un modele robuste permettant de predire l’impregnation et la post-infusion de renfort fibreux pour des applications industrielles.

Transient flows through porous media can be controlled by local capillary forces. In an attempt to ease the representation of these complex multi-scale flows, this article presents a new numerical approach to account for these local forces, viewed as a global pressure discontinuity acting in bi-fluid flows through smeared-out porous media. A finite element discretization of the Darcy's equations is considered and a pressure enriched space is locally introduced at the fluid interface in order to capture the pressure discontinuity. Then, a Variational Multiscale Stabilization (VMS) method is selected to take into account the subgrid effects on the finite element solution and hence ensure the consistency of the finite element formulation. The fluid front is represented by a level set function, convected with the fluid velocity thanks to a finite element scheme stabilized with a Streamline-Upwind/Petrov-Galerkin (SUPG) method. Both convergence and implementation are first validated with the Method of Manufactured Solution (MMS) and the model shows a good convergence. Second, a comparison with experimental measurements in the case of capillary wicking of water into carbon reinforcements shows a very good correlation between experimental and numerical results.

Specific technologies such as Liquid Resin Infusion (LRI) processes have been developed in the aeronautics industry to manufacture high performance composites with the quality required (low void contents, high fiber volume fraction. . . ) for primary aircraft parts. The aim of the present work is to simulate theses processes which consist in coupling fluid-solid mechanics at different stages. First, the filling step consists in infusing or impregnating a stacking of fibrous preforms (assimilated to orthotropic porous media) with a thermo-reactive liquid resin (the fluid) under a vacuum pressure. During the impregnation of the porous medium, a competition between viscous and capillary effects may occur leading to the formation of porosities [1]. Then, still under vacuum pressure, the supply of fluid is cut off. Due to the porous medium deformation the fluid flow continues after the filling stage is complete as it does take a finite resting time for the pressure field to become uniform during this post-filling period. In this work, the fluid mechanics problem describes the fluid flow into a distribution medium and then into the porous medium. Hence we have to deal with the coupling of Stokes and Darcy equations to describe the filling step where capillary forces may act as a complementary pressure discontinuity on the flow front. The fluid flow is coupled with the non-linear solid mechanics problem which describes the finite deformations undergone by the preforms due to both an external mechanical pressure applied during the compaction stage and the fluid pressure acting in the porous medium. The Stokes-Darcy coupled problem is solved using a Finite Element Method (FEM) based on a linear approximation for the velocity and the pressure (P1-P1). A pressure enriched space may be locally introduced at the fluid interface in order to capture the pressure discontinuity due to capillary forces. Then, a Variational Multiscale Stabilization (VMS) method is selected to take into account the subgrid effects on the finite element solution and hence ensure the consistency of the finite element formulation. The fluid front is represented by a level set function, convected with the fluid velocity thanks to a finite element scheme stabilized with a Streamline-Upwind/PetrovGalerkin (SUPG) method [1]. The coupled problem is validated both on numerous tests cases and various 2D and 3D simulations. Comparisons with existing experimental measurement are also discussed. Finally, the governing equations to model the post-filling flow, in which the porous medium is allowed to deform, are based on a poromechanics approach with saturated medium assumptions [2]. The coupled fluid-solid mechanics is developed to simulate the time dependent pressure distribution during the post-filling stage. The model is implemented using a FEM. The change in pressure distribution inside the porous medium during the post-filling stage is discussed for different conditions (drained and undrained conditions).

Le but de la presente etude est de prouver l’effet d’une modification d’energie de surface de fibres de lin par traitement thermique sur le comportement mecanique de composites bio-sources. Il a ete montre que ce traitement ameliore le mouillage des fibres par de la resine epoxy en reduisant le taux de porosite dans le composite. Des tests visant a evaluer les proprietes mecaniques des fibres elementaires, des fils et du composite ont ete menes. La conclusion est que, meme si les fibres elementaires et les fils ont ete fragilises et que le travail d’adhesion a diminue, comme le mouillage a ete ameliore, le comportement mecanique des composites renforces par des fibres traitees, elaboree par infusion, est meilleur.