Woven fabric permeability: From textile deformation to fluid flow mesoscale simulations F. Loix a , P. Badel b , L. Orgéas a, * , C. Geindreau a , P. Boisse b a Laboratoire Sols-Solides-Structures-Risques (3SR), CNRS – Université de Grenoble (INPG-UJF), BP 53, 38041 Grenoble Cedex 9, France b Laboratoire de Mécanique des Contacts et des Structures (LaMCoS), CNRS – INSA Lyon, Bâtiment Jacquard, Rue Jean Capelle, F69621 Villeurbanne Cedex, France article info Article history: Received 5 September 2007 Received in revised form 15 February 2008 Accepted 19 February 2008 Available online 5 March 2008 Keywords: A. Fabrics/textiles B. Shear deformation B. Permeability C. Finite element analysis (FEA) E. Multiscale modelling abstract A two-step methodology is proposed in order to estimate from numerical simulations the permeability of deformed woven fabrics. Firstly, the shear deformation of a glass plain weave until the shear locking is studied from a mesoscale analysis achieved with a representative volume element (RVE) of the periodic plain weave. Simulations have been carried out within the scope of large transformations, accounting for yarn–yarn contacts, and assuming that yarns behave as hypoelastic materials with transverse isotropy. From the simulated deformed solid RVE, a complementary periodic fluid RVE is then built and the slow flow of an incompressible Newtonian fluid within it is investigated. This allows to compute, in a second step, the permeability of the deformed plain weave. The role of the shear deformation on the permeability of multi-layers or single layer preforms is discussed. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction It is essential to accurately predict flows in fibre preforms for a number of liquid molding processes among which the resin trans- fer moulding process (RTM). Nevertheless, the determination with a high precision of the permeability, which is one of the most important parameter influencing those flows, still remains diffi- cult. Woven fabrics’ manufacturers can provide a material property list which sometimes contains the permeability of fabrics, usually measured when fabrics are not deformed. However, during the preforming stage of RTM woven fabrics undergo mechanical load- ings which can induce very large deformations of the textiles of which dominant mode is the shear deformation [1]. This can strongly affect their permeability and has to be understood and quantified. Indeed, the relation between deformation and perme- ability being determined and the deformation pattern of the fabrics being known, the related permeability pattern can be drawn for the entire reinforcement in order to better predict the flow within the preform [2]. A possible way to circumvent the above difficulty is to perform numerical simulations in order to predict the permeability of a de- formed fibre reinforcement. For that purpose, two steps have to be performed. The first step consists in modelling the pre-deforma- tion of the dry woven textile, taking into account mechanical prop- erties of the yarns as well as their interactions. The second step consists in simulating the flow of the polymer resin through the as-deformed textile in order to compute the permeability. Within such a framework, 2D simplified permeability models which have been validated with experimental measurements have already been developed [3–8]. These studies showed the significant influ- ence of shear on principal permeabilities of reinforcements. Some of them [3,5–7] also highlighted two relevant factors when consid- ering experimental flows in sheared fabrics, i.e. the ratio of princi- pal permeabilities and the direction of principal axes of the permeability tensor with respect to the shear deformation of the fibre reinforcement. When the shear angle is below the locking an- gle of the woven fabric, rather good agreement is generally ob- served between the permeability model prediction and measurements [8]. 3D models of the permeability have also been developed [9–13]. Simacek and Advani [9] and Dungan et al. [10] highlighted the influence of the number of layers and of the nest- ing effect on the permeability. A decrease of the in-plane perme- ability with the number of layers was indeed shown [10]. Nevertheless, no detail is brought on the mechanical model used to describe the 3D pre-deformation of the dry reinforcement in [9–11]. Finally, Laine et al. [12,13] investigated two ways to con- struct the fluid volume around the deformed textile. The first con- sists in using ‘‘voxelization” of a real representative volume element (RVE) obtained from X-ray microtomography. In that case, 0266-3538/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2008.02.027 * Corresponding author. Tel.: +33 4 76 82 70 73; fax: +33 4 76 82 70 43. E-mail address: laurent.orgeas@hmg.inpg.fr (L. Orgéas). Composites Science and Technology 68 (2008) 1624–1630 Contents lists available at ScienceDirect Composites Science and Technology journal homepage: www.elsevier.com/locate/compscitech