Permeability of flax fibre mats: Numerical and theoretical prediction from 3D X-ray microtomography images
Introduction
Biosourced composites reinforced with plant-based fibres represent a credible alternative to composites reinforced with glass or other synthetic fibres that are commonly used as structural or semi-structural parts in many industrial applications [1], [2]. Several architectures of plant-based fibres are encountered: woven fabrics, knitted fabrics, and non-woven materials such as unidirectional veils of fibres and fibre mats. Fibre mats are versatile fibrous materials that consist of an intricate network of individualised fibrous elements such as discontinuous fibres, or discontinuous fibre bundles or both types of elements. The ease of their manufacturing offers the possibility to obtain various fibrous architectures varying for instance their fibre content, areal density and fibre orientation [3], [4]. In addition, they offer a good compromise with respect to other types of reinforcements because of their good processability (e.g. large deformation properties) in several composite manufacturing processes, and their ability to provide good reinforcement effect to polymer matrices [5], [6].
The manufacturing of composites parts with biosourced fibre mats can be done using either wet, e.g. Liquid Composite Moulding (LCM), or dry forming, e.g. compression moulding, processes [2], [7], [8]. These processes involve the deformation of these reinforcement materials and their simultaneous or subsequent impregnation by a fluid polymer matrix to obtain either a prepreg material or a composite part with the desired shape. For plant-based reinforcement materials such as flax fibre woven fabrics, a poor control of the deformation mechanisms of these materials in their dry state is known to induce several defects such as wrinkling, buckling or tearing that affect the reinforcement architecture and integrity [9], [10], [11]. Similarly, the impregnation of the same reinforcements by fluids such as filled thermoset resins or thermoplastics may result in voids inside and between tows [11], [12]. It has been established that the impregnation of fibrous reinforcements is mainly controlled by their anisotropic permeability properties [13], [14], [15] which are also strongly coupled with their deformation state [16]. At the flow front, capillary effects also play an important role on the impregnation phenomena [17]. Far from the flow front, in saturated zones, the impregnation phenonema occurring in composite forming processes are usually modelled by assuming the Darcy’s law [18], which is, strictly speaking, valid for the flow of incompressible Newtonian fluids through rigid porous media at negligible Reynolds number. Vast research efforts are still ongoing to reveal the links between the components of the permeability tensor of the Darcy’s law and the deformability of various natural fibrous materials with more or less disordered architectures [19]. For biosourced fibre mats, the prediction of the permeability components is all the more difficult to establish as the fibrous microstructure of these materials is strongly disordered and fibres exhibit large morphological variations [16], [20], [21].
Several experimental studies dealt with the determination of the out-of-plane and in-plane permeability of biosourced fibre mats [22], [21], [23], [24]. The effect of the compaction was also determined and allowed highlighting the effect of the porosity or conversely the fibre volume fraction on the permeability properties. Some authors reported that the evolution of the permeability components could be empirically fitted using either empirical power-law functions of the fibre volume fraction [14] or the Kozeny-Carman model [25], [26], [27]. This equation is widely used to estimate the permeability of isotropic porous media:
where is the specific surface area, is the tortuosity (defined as the ratio between the mean flow path length and a characteristic length of the porous media). The Kozeny-Carman model assumes that the porous medium is equivalent to an assembly of parallel tortuous capillaries with equal length and diameter and circular cross sections. The assembly of capillaries has the same equivalent fibre volume fraction and specific surface area as the porous medium. The parameter can be seen as a phenomenological corrective term to account for flows in cylinders with any cross section geometry [25], [26], [27], [28], [29], [30]. The Kozeny-Carman model was used by Bizet et al. [23] to fit the evolution of the out-of-plane permeability component of flax fibre mats by determining the best value for for fitting experimental data. The parameter was shown to depend non-linearly on the fibre volume fraction.
The Kozeny-Carman equation thus relates the permeability to some key microstructure descriptors of the porous media and , the parameter coupling the fluid flow with the structure. It is thus crucial to determine accurately these descriptors and their evolution with the deformation. Several studies used 3D X-ray microtomography imaging techniques to characterise the porous and fibrous architecture of biosourced mats [21], [31] and paper-like materials [32], [33], [34]. Thanks to the analysis of 3D images, the authors could measure several crucial descriptors such as the mean porosity , the specific surface area and tortuosity . They also used these parameters in the Kozeny-Carman equation and compared the prediction of this model for the out-of-plane permeability of wood-based fibre mats with results obtained experimentally or by numerical simulation performed on 3D X-ray microtomography images [21], [35]. The chosen value of the parameter did not allow a good prediction of the out-of-plane permeability of the studied materials [35]. Their choice was governed by considering the geometry of the pore cross sections (circular or flat cross section of pores) that is presumably far from the real geometry of the pores in the investigated anisotropic fibrous networks. This shows that this parameter is critical and also difficult to estimate using uniquely image analysis of 3D fibrous networks. To circumvent this difficulty, Koponen et al. [36] performed flow simulations through the thickness of numerically generated realistic fibrous networks with planar fibre orientation representative of the structure of paper-like materials. Hence, they determined the out-of-plane permeability of these materials, thereby estimating the value of by an inverse method for this particular direction. They also proposed an empirical non-linear law for the evolution of as a function of the fibre volume fraction .
Using high-resolution 3D X-ray microtomography images of fibre networks appear to be a powerful approach to estimate the permeability of fibrous materials with complex architectures [32], [33], [34], [37], [38], [39], [40], [41]. The current progress made in 3D X-ray microtomography imaging allow acquiring 3D images during in situ and in real time experiments that mimic the real forming conditions the composite fibre reinforcements are subjected [42], [43], [44].
Hence, the objectives of this work were to investigate the microstructure and its evolution during transverse compression of thermolinked flax fibre mats, mimicking compaction phenomena that occur in many composite forming processes. For that purpose, in situ compression experiments were performed using synchrotron X-ray microtomography. Image analysis allowed quantifying the evolution of several key microstructure descriptors of the mats during their compaction. The components of the permeability tensor were estimated by direct numerical simulations on the 3D images for the various compression stages. Then, the microstructural data were used as input parameters of a modified anisotropic Kozeny-Carman model. To account for the anisotropy of the flax fiber mats, the tortuosity and an equivalent term to the aforementioned parameter of the Kozeny-Carman model were seen as directional parameters. Following the approach proposed by Koponen et al. [36], the directional values of were identified by an inverse method from permeability calculations performed using numerically generated 3D fibre networks. Finally, the relevance of the modified Kozeny-Caman model was discussed and tested for another type of biosourced mat.
Section snippets
Flax fibre mats
The first type of mats was made of 90 wt% of flax fibres combined with 10 wt% of polypropylene fibres. These mats, denoted M1 in the following sections, were fabricated by the Gemtex laboratory using carding, overlapping and needle punching nonwoven technologies [45]. These mats were also consolidated using thermolinking. During thermo-linking, the polypropylene fibres melted, allowing them to bond flax fibres after cooling. This process is usually used to increase the mechanical strength of
Specific surface area
A stereological technique [55], [52] based on intercept lines was used to estimate the specific surface area of the solid phase, i.e. flax fibre phase plus the polypropylene phase. The specific surface area was calculated as follows [56]:
where is the mean number of intercepts per unit of intercept lines. was calculated from the measurements of the number of intersection with the solid phase of 500 intercept lines the directions of which were randomly distributed in the
Evolution of the pore volume fraction
Fig. 4a shows the variation of the local volume fraction of pores along the thickness of the sample for the different stages of compression shown in Fig. 2. This figure shows that the volume fraction of pores decreases with the increase in the compression loading and increases after unloading. However, in the initial state and during the deformation of the sample, the volume fraction of pores varies slightly along the thickness. After unloading, the volume fraction of pores is different from
Proposition of an anisotropic Kozeny-Carman permeability model
Based on the previous studies devoted to the prediction of the permeability properties of fibrous materials with disordered fibrous architectures such as papers [36], boards or reinforcements for composites made of discontinuous fibres [21], [35], [38], [39], [40], we propose the following adaptation of the Kozeny-Carman (KC) model for anisotropic porous materials where the principal components of the dimensionless permeability tensor are written as follows:
with
Conclusion
In situ out-of-plane compression tests were performed on a thermolinked flax fibre mat, using a micro-press installed on a synchrotron microtomography beamline. This technique allowed us to show that (i) the porous phase evolved significantly as shown by the measurements of the mean porosity, pore size distribution, and the directional tortuosities, (ii) the cross sections of the flax fibres remained almost unchanged, and (iii) the specific surface area increased with increasing the compaction.
CRediT authorship contribution statement
T.A. Ghafour: Conceptualization, Investigation, Writing – review & editing. C. Balbinot: Conceptualization, Investigation, Writing – review & editing. N. Audry: Conceptualization, Investigation, Writing – review & editing. F. Martoïa: Conceptualization, Investigation, Writing – review & editing. L. Orgéas: Conceptualization, Investigation, Writing – review & editing. P.J.J. Dumont: Conceptualization, Investigation, Writing – review & editing. P. Vroman: Conceptualization, Investigation, Writing
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
C. Balbinot gratefully acknowledges the French Ministry of Higher Education and Research for her PhD research grant. We acknowledge EcoTechnilin (Valliquerville, France) and would like to thank Karim Behlouli for supplying mat M2. The experiments done on mat M1 were performed on beamline ID19 at the European Synchrotron Radiation Facility (ESRF) in the framework of the long term project “Heterogeneous fibrous materials” (MA 127), Grenoble, France. We acknowledge the Paul Scherrer Institut
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