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ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 1
CONCEPT FOR A PERMEABILITY MODEL FOR NON-CRIMP
FABRICS
D. Droste1, A. Dimassi1 and A.S. Herrmann1
1Faserinstitut Bremen e.V., Modelling and Simulation, 28359 Bremen, Germany
Email: droste@faserinstitut.de, Web Page: http://www.faserinstitut.de
Keywords: Liquid Composite Moulding, Permeability, Computational Fluid Dynamics, Darcy’s Law
Abstract
Permeability is the decisive textile parameter for the design and simulation of liquid composite moulding
processes. Since the determination of permeability is both time consuming and costly, the development
of a valid permeability model is important for a fast estimation during the design phase. In this paper,
the first systematic steps to develop the model for a non-crimp fabric are demonstrated. In the first step,
a virtual model of the meso-structure is created, in which the variations of the textile are considered.
The influences of individual model parameters on the permeability are analysed using flow simulations
on the generated structures.
In this study, the used modulus of elasticity shows a major impact on the compacted structure, which
influences the permeability. Bad chosen values lead to unrealistic meso-structures and bad results of the
permeability. The shift of layers during the stacking could change the out-of-plane permeability
drastically. A linear correlation between roving breadth and permeability was recognised. Further results
are necessary to build up the model and validate it with experimental results.
1. Introduction
Liquid composite moulding (LCM) processes are one of the most important manufacturing processes
for fibre reinforced plastic (FRP) components in various industries. Depending on the requirements,
high-quality components can be produced in this process.
Process simulations are carried out to fully understand and optimise the process. The permeability of
the dry fibre material is an important parameter in the process alongside the viscosity of the resin and
must therefore be known. The most common method is experimental determination. A standard [1] has
recently become available for determining in-plane permeability. The determination of the out-of-plane
permeability is still in the benchmark phase [2]. The experimental determination of permeability has the
disadvantage of high experimental and financial effort. For this reason, simulations for virtual
permeability determination represent a promising way [3]. However, the effort required to create the
meso-geometry, using micrographs and µCT data, is too high to obtain a quick permeability estimate
for a specific material.
Permeability models represent the third possibility. Models for woven or non-crimp fabrics (NCF) must
consider the hierarchy of the textile structure [4]. Current models instead focus primarily on the micro
level and work with parameters that can only be determined by analysing the micro-structure of the FRP
component, they cannot be applied to estimate the meso-permeability. For this reason, a concept will be
presented in this paper, in which the meso-permeability can be estimated using a permeability model
based only on known textile parameters (e.g. fibre diameter, areal weight, stitch distance).
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 2
1.1. Influences on the meso-permeability
There are a large number of studies in the literature on the influence of various textile parameters on
permeability. In addition to the influence of the fibre volume content, other parameters have been
identified in studies on woven fabrics. The type of fabric, the ratio between weft and warp and the
openness of the fabric showed an influence on the experimental results [5]. In the case of NCF, the areal
weight was recognised as a relevant factor. A higher areal weight is associated with a higher out-of-
plane permeability [6]. The out-of-plane permeability is also influenced by the change in the layer
structure of unidirectional NCF (change in angle). The rotation of the layers led to an increase in
permeability [7]. The stitch density also influences the out-of-plane permeability [8]-[9]. A linear
relationship between stitch density and out-of-plane permeability was derived from experimental studies
[9].
The aim of this paper is to show the first steps to build a textile-parameter based permeability model for
NCF. As the model is to be based on simulation data and experimental results, the NCF structure is first
analysed and transferred to a digital twin. The twin is used to analyse the influence of different model
parameters, as the textile parameters can be easily adjusted by simulation. The influence of several
model parameters is discussed. The next steps (experimental investigations, modelling and validation)
will be described in further work.
2. Materials and Methods
2.1. Material
In this paper, the results for a unidirectional NCF are described, which has a small proportion of 90°
rovings and stitch threads in addition to the 0° rovings as the main layer.
2.2. Generation of virtual non-crimp fabrics
A parametric model for the generation of the meso-structures is created using micrographs and µCT
images of the dry textile and different laminates. The relevant model parameters are identified by
analysing these image data. The identified model parameters for unidirectional NCF are listed in table
1. In addition to the textile parameters, further parameters are required for automated geometry
generation. These parameters ensure that the meso-structures are generated with a certain variation for
a specific textile parameter set. As the textile has variations due to the production and handling, this is
also considered in the model (cf. figure 1).
Figure 1. Two meso-structures with specific textile parameter set, but different model parameters
(offset between the layers. A: 0%, B: 25%). Grey: 0° rovings, Yellow: 90° rovings and Black:
Stitching.
The rovings are modelled as a porous medium. The micro-permeability for the rovings is computed on
different micro-structures. The correlation of local and global fibre volume content is considered.
Depending on the local fibre volume content and the fibre diameter, a transverse isotropic micro-
permeability is defined for the rovings. The generation of the meso-structures is implemented in the
GeoDict software from Math2Market GmbH using an additional Python script. A comparison between
the virtual meso-structure and the micrograph is shown in figure 2.
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 3
Table 1. Model parameters for digital twin of unidirectional NCF.
Textile Parameter
Model Parameter
Lower Limit
Upper Limit
Shape of Roving
Shape of Roving
Elliptical
Rectangular
0° Roving Breadth
0° Roving Breadth
1.5 mm
2.5 mm
90° Roving Breadth
90° Roving Breadth
0.8 mm
1.4 mm
Stitching Breadth
Stitching Breadth
0.325 mm
Areal Weight
0° Roving Thickness
0.6 mm
0.9 mm
90° Roving Thickness
0.075 mm
Stitching Thickness
0.325 mm
Stitching length
Stitching Length
2.5 mm
5.0 mm
Gap between 0° Roving
Gap between 0° Roving
0.2 mm
0.3 mm
Fibre type
Fibre type
Carbon
Glass
Number of Rovings
3
Number of Layers
2
6
Undulation
0%
50%
Randomness
10%
Shifting of Layer
0%
50%
Rotation of Layer
5°
Seed
Variable
Offset in z-direction
-0.1 mm
0 mm
Figure 2. Comparison between micrograph and virtual meso-structure.
Grey: 0° rovings, Yellow: 90° rovings and Black: Stitching.
2.2. Virtual compaction and permeability measurements
The virtual compaction and permeability determinations are calculated in GeoDict. Mechanical
properties must be defined for the different materials (fibre bundles, stitches and pore space) for the
compaction simulation. These properties can be regarded as further model parameters as they show an
influence on the compacted structure (see section 3).
The flow simulations on the meso-structures are done according to the Stokes-Brinkman-Equation. A
pressure drop of 0.02 Pa is defined in flow direction. Inflow and outflow areas are defined in front and
behind the unit cell. Symmetric boundary conditions are applied in tangential direction. The
permeability of the different meso-structures is calculated based on the pressure drop, calculated
velocity, viscosity and media thickness using Darcy's law.
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 4
3. Results and Discussion
In order to find the input parameters and their influence on the permeability for the model, various
parameter studies were carried out. Exemplary, three influences will be considered in more detail. In the
results, K1 (0° direction) and K2 (90° direction) form the in-plane permeability. The out-of-plane
permeability is described by K3. Five simulations were performed for each textile parameter set.
3.1 Shifting parameter
Before the compaction of the meso-structures takes place, the individually generated layers must be
assembled into one meso-cell. The layers can be perfectly stacked on top of each other or shifted in
relation to each other by a defined shifting parameter (cf. figure 3 A, B). The influence of this parameter
is obvious for the thickness direction. In a perfectly layered laminate, vertical flow channels are created,
through which the flow is favoured. As soon as the layers are shifted towards each other, the flow must
flow around the roving, as the flow follows the least resistance (pore space). Due to the direction change
of the flow, a greater pressure difference is required and the determined permeability decreases. As seen
in figure 3 C, the change in the out-of-plane permeability varies more than one order of magnitude by
changing this parameter.
Figure 3. Influences of the shifting parameter on the fluid flow in thickness direction.
A: Shifted 0° rovings (25%). B: No shift for 0°-Rovings. C: Results of the simulations.
3.2 Compaction parameters
In order to perform the compaction virtually, a modulus of elasticity must be defined for the rovings
𝐸𝐹𝑖𝑏𝑟𝑒 and the pore space 𝐸𝑃𝑜𝑟𝑒. The compacted meso-structure is significantly influenced by the change
of the modulus of elasticity (cf. figure 4 A-C). If the ratio of the modulus of elasticity (𝐸𝐹𝑖𝑏𝑒𝑟 𝐸𝑃𝑜𝑟𝑒
⁄) is
set too high, the horizontal pore space between the rovings is compressed completely, which influences
the permeability both in thickness direction and in 90° direction. When the ratio is set too low, the
rovings are compacted too strongly.
Due to the disappearance of the horizontal pore space (high ratio of modulus), the resin has no free path
between the rovings. It must pass through the rovings. In this case, the determined permeability depends
massively on the micro-permeability. If the rovings were modelled as solids, no flow would be possible.
A similar picture emerges for the out-of-plane permeability, although here it depends on the shift of the
different layers relative to each other.
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 5
Figure 4. Influence of the compaction parameters.
A: Compacted structure with high modulus ratio.
B: Compacted structure with middle modulus ratio.
C: Compacted structure with low modulus ratio.
D: Results of the simulations with different modulus ratios.
3.3 Roving breadth
As a textile parameter, the roving breadth of the 0° roving is considered here as an example. Changing
the roving breadth changes the ratio between the pore space and rovings in the thickness direction. As
the roving breadth increases, the less pore space is available in relation to it. This results in a reduction
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 6
in permeability in the thickness direction. The same effect can be observed for K1 (cf. figure 5 A). The
analogue explanation applies. A smaller effect is recognisable for K2.
The influence of the roving breadth on the permeability can be described by a linear model (cf. figure 5
C). The Pearson correlation coefficient is over 0.96 for all directions, which indicates a strong linear
relationship between the parameters.
Figure 5. Influence of the 0° roving breadth on the permeability.
4. Conclusions and future work
In this work, the influence of different parameters was investigated. The shifting parameter and the ratio
of modulus of elasticity show a significant influence on the permeability. The textile parameter (roving
breadth) shows a smaller influence on the results. If the influence of the textile parameters is too small
compared to the other model parameters, the prediction of the model will be weak. This needs to be
investigated further.
The investigation of the other textile parameters (table 1) and the extension to a biaxial fabric are
required to build up the NCF permeability model. With the help of a subsequent sensitivity analysis, the
relevant parameters are determined and transferred to the model. In parallel, the validation and
calibration of the simulation results and thus the validation of the model will be carried out.
Acknowledgments
We are grateful to the Forschungskuratorium Textil for the financial support of the research project
moToPerm (IGF – No. 22174 N/1), which is supported by the Federal Ministry for Economic Affairs
and Climate Action on the basis of a decision by the German Bundestag. We would also like to thank
Math2Market GmbH for their support and advice during the modelling phase.
ECCM21 – 21st European Conference on Composite Materials
02-05 July 2024, Nantes, France 7
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