Meso-scale FE analyses of textile composite reinforcement deformation based on X-ray computed tomography
Introduction
Finite element modelling methods applied to design and manufacturing processes are under investigation as a means of generating a predictive design tool for engineers to use when designing composite parts. A large part of these simulations are performed at the macroscopic scale (the global scale of the composite part) (Fig. 1a). In particular, the simulations of the reinforcement preforming [1], [2], [3] and of the resin flow in L.C.M. processes (Liquid Composite Moulding) [4], [5], [6] are performed at the macroscale. Nevertheless it is necessary to carry out analyses at lower scales to analyse some phenomena. Some studies are conducted at the scale of the fibre (microscopic scale Fig. 1c) to analyse motion and friction between the fibres [7], [8], [9]. At the mesoscopic scale (Fig. 1b) the composite is seen as a set of tows (warp and weft yarns in case of 2D woven reinforcements) with or without resin depending on the type of analysis. For periodic structures, mesoscopic models consider the smallest elementary pattern, which can represent the whole fabric by in-plane translation. That domain is called the representative unit cell (RUC) [10], [11], [12], [13]. The mesoscopic analyses allow to compute homogenised properties of the composite [10], [12], [14], damage initiation and propagation [12], [15]. The deformation analysis of a reinforcement RUC (with no resin) during the preforming stage provides the geometry of the yarns when the resin is injected. The simulation of the resin flow within these deformed tows allows to compute the permeability of the reinforcement for different local deformations [16], [17]. The deformation of the mesoscale geometry of the reinforcement during manufacturing can also be taken into account in the mechanical behaviour of the composite part [18].
The quality of the result of the meso FE modelling strongly depends on the initial FE mesh, its geometry and the associated data in particular the fibre directions. The geometry can be obtained from textile geometrical modelers such as TexGen or WiseTex [19], [20]. Nevertheless they provide a simplified geometry of the reinforcements. Moreover the reinforcement architecture are numerous especially for the 3D fabrics [21], [22] and they are not all described by these modelers. Finally some interpenetrations can occur between the yarns defined by the modelers in some configurations. In the present study, the initial geometry of meso-FE analyses is directly achieved from a X-ray Micro Tomography (XRMT) [23], [24], [25], [26], [27] also called micro computed tomography (μCT). This fairly recent technics allows detailed, accurate and non-destructive 3D observations inside the material [24]. It allows to distinguish yarns and even fibres defining the anisotropy directions of the material. In the present paper, a methodology is proposed to build automatically finite element models from X-ray micro CT images of the composite or composite reinforcement. These models take into account the specificities of the geometry of the analysed material. They can be obtained for any type of weaving or architecture of the reinforcement. The meso FE modelling of the deformation of a carbon twill weave reinforcement is taken as an example. The determination of the fibre directions within the yarn is a point of main importance. The hypoelastic behaviour used for the FE analysis of the deformation is based on the fibre rotation [28], [29]. The meso FE model obtained from μCT images of the carbon twill are used first to identify the parameters of the hypoelastic model of the tow and secondly to simulate biaxial tensile and compaction tests. In the latter case, it is shown that the meso FE model obtained from μCT gives a result closer to experiments than a model built from a textile geometrical modeler.
Section snippets
Material and method
The Hexcel G0986® fabric (Fig. 2a) is taken as an example to present the different stages of the method. This fabric is a 2 × 2 carbon twill weave which characteristics are summarised in Table 1. Images have been acquired using a laboratory tomograph Phoenix V tome X which principles and main functionalities are described in [23], [24], [25], [26], [27]. The size of the focus, and thus the resolution is adjustable from 1 to 5 μm. The detector used is made of 1920 × 1575 pixels each with a size of 127 ×
Mesh generation
At mesoscopic scale, the mechanical analysis of composite reinforcements is based on the finite element method. This method relies on subdomains that are defined by a mesh. The mesh generation boils down to building a “triangulation” that precisely catches the domain described in practice by a discretization of its boundary [43]. The aim of the present section is to transform the tomography image into discrete geometry.
Simulation and discussion
Fig. 12 shows a X-ray tomography imaging of a textile reinforcement yarn. This yarn is composed of nearly parallel fibres and can be considered as a transversally isotropic material. This has been confirmed by experimental observations [48], [49]. In particular, covariance analyses, providing information about the spatial distribution of fibres for different deformations, justify this assumption [48]. When the yarn is considered as a continuous material the main attribute of such a material
Conclusions
X-ray Micro Tomography is one possible way to define meso FE models directly from a composite or composite reinforcement specimen. This method can be used for any type of reinforcement and in particular for those that have not be taken into account in textile modellers. The specificities and variability of the reinforcement are taken into account. The different steps to obtain the FE model have been detailed. In particular the definition of the fibre directions is a key point for the mechanical
Acknowledgements
The collaboration with SNECMA is gratefully acknowledged. This work was supported under the PRC Composites, Research project funded by DGAC, involving SAFRAN Group, ONERA and CNRS.
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