Methods to Determine the Permeability of Textile

Transcription

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www.kunststofftech.com
© 2014 Carl Hanser Verlag, München
Zeitschrift Kunststofftechnik
4Autor
Titel (gegebenenfalls gekürzt)
Journal of Plastics Technology
www.kunststofftech.com · www.plasticseng.com
archivierte, peer-rezensierte Internetzeitschrift
archival, peer-reviewed online Journal of the Scientific Alliance of Plastics Technology
1.1.1.1.1.1.1
10 (2014) 4
eingereicht/handed in:
angenommen/accepted:
14.03.2014
25.05.2014
Reinhold Meier, Dr. Andrew Walbran, Christoph Hahn, Swen Zaremba, Prof. Dr.-Ing.
Klaus Drechsler
Institute for Carbon Composites, Technische Universität München, Faculty of
Mechanical Engineering, Boltzmannstraße 15, D-85748 Garching b. München, Germany
Methoden zur Bestimmung der Permeabilität
von Verstärkungstextilen
Die Permeabilität trockener Verstärkungstextilien ist eine wichtige Materialeigenschaft, die zu einem
besseren Verständnis des Infiltrationsprozesses in Flüssigimprägnierverfahren beiträgt. Zur
Bestimmung der Permeabilität textiler poröser Medien sind verschiedene Methoden bekannt, jede mit
ihren Vor- und Nachteilen. In diesem Aufsatz werden Prüfstände zur Bestimmung der gesättigten und
ungesättigten Permeabilität vorgestellt, welche den Prinzipien für eindimensionalen (1D) und radialen
(2D) Fluss folgen. Neben den Messergebnissen werden der dazu notwendige Zeit- und
Materialeinsatz der verschiedenen Methoden zur Bestimmung der Permeabilität in Bauteilebene
verglichen. Außerdem wird ein Simulationsansatz zur Bestimmung der Permeabilität vorgestellt,
welcher auf der digitalen Abbildung des Materials mit einem Scanner beruht.
Methods to Determine the Permeability of
Textile Reinforcements
Reinforcing textile permeability is an important material property used to better understand the
infiltration phase of Liquid Composite Molding processes. A range of methods exists to determine the
permeability of textile porous media all with their respective advantages. In this work, facilities to
characterize the saturated and unsaturated in-plane permeability using rectilinear (1D) or radial flow
(2D) methods are presented. A comparison of the in-plane permeability results obtained using each
test method was carried out, together with the required testing time and material usage. Furthermore,
a simulation approach to predict the permeability based on scanned images is presented.
© Carl Hanser Verlag
Zeitschrift Kunststofftechnik / Journal of Plastics Technology 10 (2014) 4
Meier, Walbran, Hahn, et al.
Permeability Measurement Methods
Methods to Determine the Permeability
of Dry Textile Reinforcements
R. Meier, A. Walbran, C. Hahn, S. Zaremba, K. Drechsler
Reinforcing textile permeability is an important material property used to better
understand the infiltration phase of Liquid Composite Molding processes. A
range of methods exists to determine the permeability of textile porous media all
with their respective advantages. In this work, facilities to characterize the
saturated and unsaturated in-plane permeability using rectilinear (1D) or radial
flow (2D) methods are presented. A comparison of the in-plane permeability
results obtained using each test method was carried out, together with the
required testing time and material usage. The results of the two in-plane
methods are in good agreement. The time required to fully characterize a
material using the 1D method was more than three-times the time required
when using the 2D method. The material used for testing with the 1D method
was also three times greater than for the 2D method. Furthermore, a simulation
approach to predict the permeability based on scanned images is presented.
1. INTRODUCTION AND MOTIVATION
In Liquid Composite Molding (LCM) processes, a textile reinforcement structure
is placed in a mold cavity and is impregnated with mostly thermoset resins [1].
After complete infiltration of the porous structure and curing of the resin the part
is demolded. The quality and the mechanical properties of the part are defined
by the quality of the infiltration process and the degree of cure of the matrix
material. Porosity or dry spots have therefore to be avoided. In LCM processand tool-design, the permeability of the fibrous reinforcement is a very important
parameter to consider. Theoretically, permeability is a geometric property and
quantifies the hydraulic conductivity of porous media to fluid flow. One widely
accepted model to describe the impregnation step in LCM processes is Darcy’s
law, where the permeability of the textile reinforcement together with the
dynamic viscosity of the liquid matrix material represent the characteristics of
the materials for fluid flow [2].
The most straightforward use for permeability measurement is the
determination of material data to design the filling process of complex parts.
The results can be used to predict process properties, such as fill time and
injection pressures. In addition, tool design and part quality can be optimized
and flow in areas with complex fiber architecture (such as T-junctions and
overlapping areas) can be simulated. In series production processes,
Journal of Plastics Technology 10 (2014) 4
91
permissible variability from the ideal handling- and processing conditions
influencing the permeability can be derived, resulting in reduced scrap, lower
process time and energy consumption. For example, the effects of varying
binder content and variations in the corresponding activation process (activation
temperature and time) on the permeability can be quantified [3] and the
influence on the filling process can be predicted.
As a standard test method for evaluating permeability currently does not exist, a
number of different methods have been developed [4]. Experimental and
simulation-based approaches are the most promising, in contrast to analytical
approaches such as the Kozeny-Carman equation, to capture the effects in
complex parts with respect to accuracy and repeatability. Both approaches are
presented in this paper. In terms of the experimental methods, measurement
results of the most commonly used test methods are presented and compared
with respect to time and material effort.
2 THEORY OF PERMEABILITY MEASUREMENT
The permeability of a porous material is an inverse measure of the resistance to
fluid flow through that material, thus high permeability values account for low
resistance and vice versa. In theory, permeability is dependent only on
geometrical quantities of the fibrous reinforcement such as the fiber volume
fraction Vf, the reinforcement architecture (type of textile and degree of shear),
the number of layers and the degree of saturation. The permeability of fiber
reinforcement typically varies with direction and is commonly described by
Darcy’s law for flow through porous media [5]:
(1)
where is the fluid velocity vector, is the dynamic viscosity of the fluid,
is
the pressure gradient and is the permeability tensor of the material. While
Darcy’s law assumes fully saturated flow in the porous media, typical LCM
processes involve an unsaturated, wetting flow front. However many authors
have used Darcy’s law to model this case [6]-[9]. Darcy’s law also assumes that
the fluid is Newtonian and of constant viscosity, whereas resins used in
composites manufacturing are distinctly non-Newtonian and the viscosity can
change during processing.
For the general three-dimensional case, permeability is a symmetric positive
definite 2nd order tensor [10]-[11], and can therefore be diagonalized. The
major permeability tensor can be graphically described as an ellipsoid. In
practical applications, especially for thin-walled structures, it is common to
simplify the permeability tensor and devide it into an in-plane tensor, which has
the shape of an ellipse that is defined by the two principal permeabilities, K11
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and K22, and one “out-of-plane” or “through-thickness” permeability, K33. It has
been shown previously that K33 is typically one or more orders of magnitude
lower than K11 and K22 [12].
3 PRINCIPLES OF PERMEABILITY MEASUREMENT
Permeability test methods can be divided into three categories: analytical,
experimental and simulation approaches.
There are various analytical methods available to determine permeability in a
fast manner, such as the Kozeny-Carmann equation [13]. However, all
analytical approaches have the drawback that they rely on a certain model
assumption which does not represent reality in terms of material type and
preform architecture. Nevertheless the Kozeny-Carman equation is frequently
cited in papers on textile permeability and is often used by textile engineers as a
rule of thumb [14]. Furthermore, for an interpolation of experimental results with
varying Vf, the Kozeny-Carman equation gives promising results for Vfs close to
the measured ones [15].
The work of the First Permeability Benchmark Exercise [4] shows that two
experimental methods are most frequently used to determine the in-plane
permeability, the rectilinear (1D) and the radial (2D) flow method, as shown
schematically in Figure 1. These methods both neglect flow in the thickness
direction of the preform, as the thickness of composite laminates is typically
orders of magnitude lower than the in-plane dimensions. Both methods have in
common that a Newtonian fluid is injected into the porous fibrous media
whereupon the governing flow direction lies within the sample plane. The flow
velocity is determined together with the applied injection pressure and the
pressure at the flow front (the borderline between wet and dry textile). The flow
front pattern generally is of linear and elliptical shape for the rectilinear and
radial method, respectively. In the case of isotropic materials, with respect to
the in-plane permeability properties, a circular flow front pattern is observed in
the radial method.
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a)
b)
Figure 1: Schematics of the rectilinear (a) and radial (b) filling scheme for
evaluation of in-plane permeability values.
Flow velocity can be determined by monitoring the flow front evolution (for
unsaturated measurements) or the mass flow of the test fluid (for saturated
measurements).The “saturated permeability” is consistent with the assumptions
of Darcy’s law. The difference between saturated and unsaturated permeability
values mainly results from capillary effects which contribute to the driving forces
of the flow in addition to the applied pressure difference between the inlet and
outlet. However, other phenomena e.g. geometrical rearrangements of the fiber
bundles or air entrapments can also lead to differences between unsaturated
and saturated permeability.
The flow front position can, for both methods, be monitored using a clear mold
half, often manufactured from perspex, polycarbonate or glass and reinforced to
counter the low bending stiffness of such materials. This is necessary to avoid
local bending of the clear mold half which affects the cavity thickness on a local
scale, leading to a varying Vf and as a consequence to inaccurate
measurements. Alternatively, dielectric sensors [16], pressure transducers [17],
optical fibers [18], ultrasonic transducers [19], or thermocouple sensors [20] can
be used to monitor flow front progression for permeability characterisation.
The saturated rectilinear flow method can also be used to determine the
through-thickness permeability, K33. Fluid is forced through the thickness of the
textile reinforcement and the mass flow is measured to evaluate the average
flow velocity according to Equation 1. Other than the interactions between the
applied pressure difference and the resulting preform compaction, the principles
are the same as for the 1D in-plane method. These three experimental methods
are explained more detailed in the following sections, which discuss the testbenches available at the Institute for Carbon Composites (LCC).
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3.1 1D In-Plane Facilities
For rectilinear in-plane flow measurements, a rectangular sample is assembled,
placed in a mold and Newtonian fluid is injected along one short edge of the
preform to ensure in-plane fluid flow. The cavity height is determined by the
thickness of a spacer frame which is mounted to the lower mold before sample
loading. The minimum frame thickness is 2 mm. At the LCC, two separate 1D
in-plane setups are available. These differ in the way the flow front position is
detected. In one case the flow front is tracked optically (compare Figure 1)
through a transparent mold half made of polycarbonate and in the other case by
pressure transducers. The latter is necessary as this mold is manufactured from
35 mm thick aluminium to reduce mold deflection and thus local variations of Vf
(compare Figure 3). The advantage of the rectilinear flow method over the radial
flow method is that unsaturated and saturated flow experiments can be
conducted. Saturated measurements fulfil the assumptions of Darcy’s law. In
this case the flow velocity is calculated based on the measured mass flow
through the sample.
Camera
Pressure
pot
D
Mold
Preform
Outlet
Scale
P
T
Thermocouple
U
U
P
Pressure
transducer
Data
acquisition
unit
U
T
U
Figure 2: Schematic of the single-cavity 1D test setup with a clear upper mold
and a video camera for optical flow front tracking.
The rectilinear flow method is very sensitive to “race-tracking” of the test fluid
along the edges of the sample. Race-tracking is the preferential flow of fluid
along the higher permeability regions at the edges of the sample which is
further promoted by samples not fitting the mold perfectly [21]-[25]. These
effects are overcome by placing silicon strips between the side edges of the
fibrous preform and the cavity. The silicon strips are slightly thicker
(approximately 10 %) than the spacer frame which is used to adjust the desired
thickness of the sample. When the cavity is closed, the silicon deforms and fills
the gaps at the edges of the preform, eliminating race-tracking. Furthermore,
the silicon helps to avoid fiber squeezing between the frame and the mold
halves which could lead to deviations in the Vf and leakage of the cavity. To
determine the major in-plane permeability tensor with the 1D method, three
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experiments must be conducted in order to identify the three unknown
quantities – the principle permeabilities K11 and K22 and the rotation angle (θ)
between the major axis of the ellipse and the warp and weft directions of the
textile.
The 1D facilities respect the recommendations of the 2nd Permeability
Benchmark Exercise [26] in which the LCC took part. The goal of this roundrobin study was to determine the accuracy of the unsaturated 1D permeability
measurement method. Identical textile material was sent to 13 academic
laboratories around the world from which the unsaturated in-plane permeability
tensor for a defined Vf and number of layers was determined. One outcome of
the exercise was that the variability of the principle permeability values including
the ellipse-orientation was below ± 20 % when using the least square fit method
for analysis. This method is also incorporated in LCC’s analysis tools for the 1D
setups. Compared to the results of the other laboratories, the LCC values are in
the middle of the range. The variability of the LCC values is around ± 15 % for
K11, ± 17.5 % for K22 and ± 22.5 % for the orientation of the in-plane tensor.
Figure 3: Four-cavity setup that allows four parallel measurements of in-plane
permeability values.
To reduce the time effort for determining in-plane permeability values with the
rectilinear flow method a four-cavity setup was developed at the LCC which
allows four parallel measurements. The inlets of the four cavities are connected
to the same fluid reservoir providing the same injection pressure. Each cell is
equipped with its own thermocouples as well as pressure and force transducers
to evaluate the mold temperature as well as the unsaturated and saturated
permeability of four different preforms at the same time. Measurement of the
mold temperature is required to determine the fluid viscosity based on the
average temperature of the test. Race tracking can be detected with pressure
sensors at the edges of the sample to guarantee validity of results.
All experimental process data (the pressure at the inlet and outlet, mold
temperature, mass flow and flow front arrival at the pressure sensors) is
gathered by a data acquisition system and is automatically analyzed after the
test. As a result, a measurement protocol is generated containing the most
relevant data together with a plot of the principle in-plane permeability tensor.
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3.2 2D In-Plane Facility
The radial-flow in-plane permeability evaluation tool is presented in Figure 4. In
addition to permeability values, this test facility allows the measurement of the
through-thickness compaction behavior of the textile reinforcement which is
important to calculate the clamping force in many LCM processes, such as resin
transfer molding (RTM), RTM Light and Compression RTM or to adjust a
specific Vf in vacuum bag processes. It consists of a lower glass platen with an
upper aluminum platen. The facility is mounted in a universal testing machine,
providing accurate cavity thickness and mold closure control. The Vf of the
sample can be adjusted continuously and the compaction response can be
investigated as a function of the part thickness and mold closure velocity. The
glass platen is mounted in a frame above a camera which is used to record the
flow front position as discrete images at a set time interval (typical values are
between 3 and 10 s), allowing the flow front speed to be calculated. Test fluid is
injected via a central hole in the top platen. The injection pressure at the inlet is
measured, and laser sensors monitor the cavity thickness during injection. All
experimental data is gathered by a data acquisition system and is automatically
analyzed after the test.
Locking
alignment unit
Laser sensor
Fluid injection
Pressure
sensor
Upper mould
platen
Sample
Lower glass mould
platen
Frame
Camera
b)
a)
Figure 4: 2D in-plane permeability and through thickness compactions
measurement facility: a) installed in testing machine, b) schematic.
3.3 1D Out-of-Plane Facility
The 1D out-of-plane setup allows the determination of the saturated
permeability in through-thickness direction of the preform by measuring the
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mass flow through the compacted fibrous textile via a force transducer
connected to the outlet. Flow and compaction of the textile material in the
thickness direction is enabled by the application of perforated plates. The fluid
pressure at the in- and outlet is monitored by pressure transducers. In contrast
to the in-plane flow method, the applied pressure difference leads to an
additional preform compaction thus increased Vf and decreased permeability.
As a consequence, the measured permeability value depends on the applied
pressure difference. Although the edge permeability has a minor effect on the
bulk permeability of the sample [23], an o-ring is placed between the preform
and the spacer frame to reduce the influence of race tracking on the measured
permeability. The minimum cavity height is 2 mm and is determined by the
thickness of the spacer frame.
Preform
Perforated plate
P
Scale
U
P
U
Pressure pot
T
U
T
U
Data
acquisition
unit
a)
b)
Figure 5: a) 1D through-thickness permeability measurement facility, b)
schematic of facility.
4 MEASUREMENT PROCEDURE
The general procedure for any permeability test involves five main steps;
sample preparation, sample loading, mold closure, infiltration and finally
analysis. This is common for in-plane rectilinear and radial as well as out-ofplane testing, however each method has specific details which will be discussed
in the sections 4.1 – 4.3.
Sample preparation
The samples must be cut from the material roll. Generally there are several
cutting procedures; manual cutting with a roller cutter or a knife, stamping in a
press and an automated CNC cutter. For 1D measurements, the quality and
accuracy of the cut edge is very important due to the sensitivity to race-tracking
of this method. For this reason, the faster methods (stamping and CNC cutting)
might not be appropriate for some materials as for example UDs or satin
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weaves. The problem in these cases often is the rough surfaces of the underlay
in which filaments easily get caught and as a consequence outer rovings are
pulled out of the sample. This issue is less of a concern in manual cutting since
smooth glass plates can be used as underlay.
For 2D measurements edge quality is less important since the flow front does
not reach the outer edge of the preform. The injection holes to ensure in-plane
flow in the middle of samples for radial flow measurements are always stamped.
The sample orientation must also be considered. For radial flow experiments,
each layer within a sample must be oriented correctly. In the case of rectilinear
experiments it is also necessary to test samples in different orientations to
calculate the in-plane permeability tensor. Therefore, consistency between the
samples with respect to fiber orientation must also be maintained. Before the
fiber stacks are transferred to the mold, each sample is weighed. This data is
required to calculate the actual Vf and is a measure of the material variability
and the cutting quality achieved.
Sample loading
When the layers are transferred into the mold, distortion of the layers must be
avoided. Furthermore, the samples must be positioned in a repeatable manner.
Here, spacer blocks between the mold edge and the sample edge are used.
Mold closure
During mold closure, distortion and displacement of the layers must be avoided,
in particular of the upper most layer of each sample. The stack is compacted in
the thickness direction without in-plane displacement of single layers until the
desired fiber volume fraction is reached.
Infiltration
Before infiltration the test fluid should have the same temperature as the mold
and the samples. This can most easily be achieved by storing the test fluid, the
mold and the samples in the same room.
The infiltration pressure must be low enough to avoid fiber washing or distortion
of the preform due to the fluid stream. Furthermore, mold deflection is lower at
lower injection pressures resulting in a more homogeneous Vf of the sample.
For tests with constant volume flow and tests with constant injection pressure
the fluctuation of these values should be reduced to a minimum in order to
measure reliable permeability values especially when the squared flow front
approach is utilized in the analysis process of the rectilinear flow method [26].
Analysis
To achieve high reproducibility, automated data acquisition and analysis
processes are suggested, always following the same criteria e.g. when the flow
front has reached a certain position in the unsaturated 1D rectilinear
measurement.
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4.1 1D In-Plane Testing
For measurement of the unsaturated and saturated in-plane permeability,
samples of 400 mm x 200 mm are placed in the lower mold platen between two
silicon stripes to avoid race tracking. Larger samples are less sensitive to
possible perturbations such as race-tracking effects or defects in the raw
material. However, with increasing sample size the measurement time and
material usage also increases. The aspect ratio of the sample geometry is also
important in the case of rectilinear measurements to ensure one dimensional
flow even for highly anisotropy textile lay-ups [27]. A minimum number of five
layers per sample is suggested, depending on the areal weight of the material,
to reduce the influence of the outer most layers on the final permeability value.
Having direct contact to the rigid mold halves, these layers are compacted
differently compared to the other layers and therefore will influence the
permeability of thin fiber stacks. Smaller cavity heights than 2 mm lead to
extensive deformations of the spacer frame which compresses the o-ring
between the lower mold and the frame. Too high deformations lead to race
tracking and as a consequence to incorrect results. Hence, depending on the
areal weight of the fabric, a minimum number of layers is needed for the 1D inplane method. To determine the permeability of thin preforms or even single
layers, the 2D radial flow method is suggested.
When sample loading is completed, the upper platen is placed on the fiber stack
with the aid of aligning pins and the bolts are tightened to 50 Nm. The
unsaturated measurement starts when fluid starts to fill the linear inlet and ends
when the flow front reaches the edges of the sample. As soon as no bubbles
are flowing out of the outlet and a constant mass flow is measured, the
saturated measurement begins and lasts for approximately five minutes. The
duration of the unsaturated measurement depends on the permeability of the
textile investigated, the applied injection pressure (usually 1 bar) and the fluid
viscosity (approximately between 50 – 100 mPas for the applied sunflower oil);
typical times are around 25 minutes per sample. This procedure must be
undertaken with three samples oriented at 0º, 45º and 90º from the warp
direction to calculate the in-plane permeability tensor. For statistical purposes a
minimum of three repeats of each test is undertaken.
The raw data is automatically analyzed using a Matlab-based analysis tool. At
the end of the analysis an Excel-based result sheet is created summarizing the
important data of the investigated material.
4.2 2D In-Plane Testing
For the radial permeability and through-thickness compaction test facility, the
sample size is 280 mm x 280 mm, with a 250 mm diameter test surface defined
by the upper mold platen. Samples can be comprised of any number of layers,
however six layers is typical. Consistence in orientation of the single layers of
one stack must be ensured. A 15 mm diameter hole is punched in the center of
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each sample to enforce two-dimensional in-plane fluid flow. Material variations
close to the inlet hole have to be avoided since they severely influence the
measured permeability as the pressure gradient is highest there [27]. For this
reason, the analysis program considers only the last third of the images
recorded when assessing the final permeability.
After sample loading, the upper platen is lowered until it just contacts the fiber
stack. The compaction test is then started, beginning with a constant-speed
compaction to the desired cavity thickness and hence target Vf. The
permeability test begins 60 s after the cavity thickness is achieved. This is to
allow the majority of relaxation of the compaction stresses to occur, giving a
more consistent condition for the fluid flow where rearrangement of the fiber
bundles should be avoided. Fluid is injected until the flow front reaches the
edges of the upper platen. Typical testing time is around 8 - 10 minutes per
sample, depending on the permeability of the sample, the injection pressure
(usually between 1 – 5 bar) and the viscosity of the test fluid (approximately 50
– 100 mPas for the applied sunflower oil). For statistical purposes a minimum of
three repeats of each test is undertaken.
After completion of the testing, the raw data is automatically analyzed using an
Matlab tool developed at the University of Auckland [28]. The tool generates the
flow front pattern based on a grey scale analysis of the images recorded from
the camera during injection (compare chapter 3.2), fits the ellipse and finally
calculates the principle permeabilities and the orientation angle.
4.3 1D Out-of-Plane Testing
The samples for determining the saturated through-thickness permeability have
a diameter of 130 mm. Corresponding to the ASTM standard D5493 “Standard
Test Method for Permittivity of Geotextiles Under Load” a minimum diameter of
50 mm is suggested to minimize the influence of hydraulic edge-effects. Circular
samples have the advantage that no care must be taken when considering the
orientation during cutting. The correct sample orientation can easily be adjusted
during layup in the mold as long as no alternating stacking e.g. 0/90° or +-45° is
needed. In this case, the whole preform is stacked outside the mold before
cutting. The samples are manually placed on the lower perforated plate. The
diameter of the o-ring which seals the preform against the spacer frame is
slightly (approximately 10%) larger than the desired cavity thickness. This seal
reduces the influence of edge effects especially for low permeability preforms.
The top perforated plate is placed on top of the fiber stack. The perforation
patterns coincide with each other. The mold is closed and the screws are
tightened to 11 Nm.
Once the desired injection pressure is adjusted in the pressure pot, the
saturation process starts which is considered completed as soon as no bubbles
can be observed in the outlet hose and a constant volume flow is measured
with the force transducer. The volume flow is monitored for approximately two
101
minutes together with the pressure in the upper and lower fluid chamber of the
setup and the mold temperature. After this period, the injection pressure is
increased as the applied fluid pressure leads to an additional compaction of the
preform thus to a decreasing permeability [29], [30]. This relationship between
compaction state and permeability must be taken into account when flow
processes in the through-thickness direction are considered. For statistical
purposes a minimum number of three repeats of each test is undertaken.
5 SIMULATION APPROACH
Another approach to determine the permeability of sheared and compacted
preforms is to use simulation techniques. The method used at the LCC is based
on fabric images, image processing and textile modeling [32]. The core of the
approach is comprised of algorithms for image processing conducted on images
obtained using a scanner together with a transparent compaction mold. This
technique provides the advantage of fast and repeatable permeability
determination and abstains from time- and material-consuming flow
experiments. Figure 6 illustrates the data flow of the simulation approach.
Figure 6: Data flow for the simulation approach of permeability prediction.
Digital images of the scanned fabric, information such as lay-up thickness and
desired fiber volume fraction, together with some numerical parameters for the
embedded third party tools WiseTex and FlowTex developed at KU Leuven
[33], [34] are required input for the simulation approach. The outcome is a
material card that can be directly imported to the desired RTM solver of the
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filling simulation software. Furthermore, the results from image processing can
be used for fabric quality inspection.
Figure 7 presents the transparent mold for fabrics scanning (on the left) and a
collection of results from image processing (on the right); the stitching yarns and
the typical “fish-eyes” for Non-Crimped-Fabrics (NCF) are detected and
measured automatically. Based on the information obtained from image
processing a unit-cell model of the preform is set-up using the meso-level fabric
processor WiseTex. The discretized form of the model is then used in a CFD
analysis automatically conducted with FlowTex. The resulting pressure
gradients and flow velocity field is then used to determine the permeability using
Darcy’s law (Eq. 1). In the last step, the permeability results are post-processed
and can be written to a RTM solver material card.
a)
b)
Figure 7: Transparent compaction mold for fabric scanning (a) and result
overview from image processing (b).
6 RESULTS
In the following sections results gathered with the different test methods are
presented and compared with each other. Next to permeability values, the time
and material efforts of the two in-plane methods are compared. Furthermore,
example results of a through-thickness permeability and compaction
measurement are shown carried out in the 1D off-plane permeability cell and
the 2D in-plane test facility, respectively.
6.1 Compaction Response
Figure 8 demonstrates the variability of a bidiagonal carbon fiber NCF material
with an aerial weight of 540 g/m², ±45° fiber orientation and a warp stitching
pattern. During the compaction experiments the sample was compacted to a
given thickness (and hence Vf) and then held constant. The cavity thickness
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was adjusted based on the mass of each sample to ensure that constant Vf was
achieved for each test. The average peak compaction stress was
123.91 kPa + 6.0/-6.8%. The long term or relaxed stress exhibited a small
increase in variability, at +5.5/-7.9% from the average of 90.25 kPa (at t = 15s).
At each point, the stress is highest in sample R4 and lowest in R1. The stress
relaxation is most likely caused by the rearrangement of the fibers within the
fiber tows. The source of the increased variability could be due to unequal
rearrangement of the fibers within the tows. The NCF material exhibited
considerably lower variability compared to previous research on textile
reinforcements [35], [36]. This was likely due to the architecture of the NCF
material; it was very consistent. It was also much less susceptible to nesting
than woven materials.
Figure 9 presents the average compaction stress curves as a function of final Vf
and as a function of the compaction speed, ̇ . As has been previously shown,
the compaction stress increased considerably with volume fraction. It is
interesting to note that the peak compaction stress was much lower than
reported previously for various glass-fiber reinforcements; the peak stress
achieved at a final target Vf of 52.5% (46.46 kPa) is much lower than reported
for similar Vfs for random mat and 0/90º non-crimp glass fiber reinforcements
[37]. This supports previous views that reinforcement compaction response is
dependent on more than reinforcement or fiber type and basic architecture.
Previous studies have shown a strong viscoelastic response for fibrous
reinforcements – the compaction stress increases considerably with increasing
̇ [37]. However, while there was some increase in peak compaction stress with
increasing ̇ (peak stress of 108.50 kPa at 2 mm/min increasing to 123.91 kPa
at 10 mm/min and 126.00 kPa at 25 mm/min), this is significantly lower than
was expected and what previous studies have shown [35], [36]. The cause of
this low increase in compaction stress with increasing ̇ is presently unknown
and is the subject of current investigation.
R1
R2
R3
R4
R5
Average
Compaction Stress (kPa)
100
50
0
-10
0
10
20
Time (s)
Figure 8: Compaction stress curves at Vf = 0.60 and ̇ = 10 mm/min.
104
a)
b)
Figure 9: Average compaction stress as a function of Vf (a) and ̇ (b).
6.2 In-Plane Permeability
The unsaturated in-plane permeability of the NCF material was determined in
the stitching direction (analogous to the warp direction in woven textiles). Single
layers were cut and placed on each other without any rotation. For both
methods, the 1D single-cavity and 2D radial, each preform consisted of 7 layers
which were compacted to 4 mm resulting in a target Vf of 53.4 %. The same
material was investigated in the 1D four-cavity setup for two other Vfs [38]. In
this case, the preforms consisted of 8 layers and were compacted to 4.8 and
4.4 mm resulting in target Vfs of 50.9 and 55.5 %, respectively.
105
1D single-cavity
1D 4-cavity
2D
1,00E-10
Log Permeability [m²]
1,00E-11
50,00
51,00
52,00
53,00
54,00
55,00
56,00
Fiber volume fraction [%]
Figure 10: Comparison of the unsaturated permeability results gathered in
different test setups. Each data point is the mean value of five
repeats and the error bars represent the standard deviation.
Figure 10 presents the permeability results over the Vf on a logarithmic scale.
The 1D results can be approximated as a function of Vf using a simple
exponential model, which is a commonly-used approach [35]. The mean
permeability determined with the 2D method is about 30 % higher than the
theoretic value calculated with the fitted power law model based on the 1D
results for the appropriate Vf. Regarding the results of the 2nd permeability
benchmark study [26] this difference is in the common range and can therefore
be seen as expected, in particular since two different methods are incorporated
here in contrast to the 2nd benchmark study (where only 1D test methods were
used). Nevertheless, further research is required to explain and reduce the
observed variability. One possible explanation might be the difference in the
mold design. In the 2D setup the preform is free to expand around its edges
whereas in the 1D cavity the preform is surrounded by a rigid mold. This may
lead to denser packing in the 1D cavity and thus higher Vf and as a
consequence to lower permeability values. However, this explanation needs to
be proven with additional measurements.
For the comparison of the time effort to determine the complete in-plane
permeability tensor it was assumed that the test facilities are prepared for the
first measurement i.e. all the sensors are calibrated, the spacer frames are
mounted to the molds and the 2D facility is installed in the Universal Testing
Machine. Sample preparation time was discounted. The time to analyse the
experiments was also discounted from this comparison as for both methods
106
automated tools are available that calculate the permeability values based on
the raw data.
The measurement time is primarily dependent on the permeability of the textile
material under investigation. Therefore, the time until the flow front reaches the
edges of the preform is compared for the 1D and 2D method. In the case of the
2D method this time was determined by the principle permeability K11 and was
calculated with the following equation [4]:
{
[
(
)
]
}
(2)
where x2D represents the flow front position in the direction of the principle
permeability K11 and r is the radius of the inlet hole. The corresponding equation
for the 1D method is [26]:
(3)
where x1D represents the flow front position in the direction of the principle
permeability K11. When assuming the same viscosity η, the same fiber volume
fraction and the same injection pressure the quotient of t1D devided by t2D is
defined as:
[
(
)
]
(4)
For the specific dimensions of the test facilities presented in this work the
determination of the principle permeability K11 with the 1D method takes about
4.4 times longer than with the 2D method. This drawback is diminished when
using the four-cavity setup where four experiments can be run in parallel.
Nevertheless measurements in three different directions are needed in case of
the 1D method to completely determine the in-plane permeability tensor.
Consequently the 2D method is at least three times faster than the 1D method.
Furthermore, four molds must be prepared in case of the four-cavity setup. This
includes the time to cut the preforms, to install the spacer frames with the
required thicknesses and to clean the four cavities after the test. Moreover, the
equipment of a 1D test bench is needed four times which causes a considerable
invest. But the expenses for the equipment of the 2D test setup are also high
since a universal testing machine is necessary.
The inherent property of the rectilinear flow method to measure the permeability
in three different directions also becomes crucial when the required material is
compared to the radial flow method. The material effort to characterize the
complete in-plane permeability tensor for the presented preform dimensions is
3.1 times higher for the rectilinear method than the radial flow method.
107
6.3 Out-of-Plane Permeability
In terms of the saturated out-of-plane permeability a bidiagonal NCF with a total
aerial weight of 266 g/m² was characterized including the weight of the powder
binder system which was activated before testing. The cavity height was 2 mm
resulting in a target Vf of 42.3 and 56.4 % for a 6 and 8 layer preform,
respectively. The volume flow was measured for 150 s at each pressure
difference.
6 layer
8 layer
1,2E-12
1E-12
Permeability [m²]
8E-13
6E-13
4E-13
2E-13
0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
Pressure difference [bar]
Figure 11: Dependency of the measured saturated through thickness
permeability for a 6 and 8 layers NCF preform on the applied
pressure difference. The data points show the mean values of three
repeats and the error bars represent the standard deviation [39].
In Figure 11 the dependency of the saturated through thickness permeability on
the applied pressure difference is demonstrated, in particular for the 6 layer
preform. The maximum pressure difference was limited by the capacity of the
pressure pot. Due to the large cross-section area of the preform through which
the fluid is forced and the high pressure gradient, as a result of the small
preform thickness, a considerable higher volume flow appears compared to the
1D in-plane test, limiting the time until the pressure pot is drained. Higher
pressure differences can also be achieved with the given setup by increasing
the oil the viscosity or by increasing the jumps between the pressure
differences. The applied injection pressure causes additional preform
compaction leading to decreasing permeability values. Furthermore, the
permeability decreases with increasing number of layers thus increasing Vf. The
108
change in permeability between the lowest and highest pressure difference
decreases with increasing number of layers. This can be explained with the
non-linear relationship between preform thickness and compaction pressure
(compare Figure 9). With increasing Vf relatively more pressure is required to
further increase the Vf since the packing density of the filaments converges to
the physical maximum [40], [41]. For the 8 layer preform no considerable
decrease in the mean permeability values is measured. These observations are
in agreement with other results in literature [29], [30], [31]. It has further been
shown that not only overall preform compaction causes reduced permeability,
but also an increasing inhomogenity in Vf across the preform thickness [29].
This inhomogeneous compaction also appears for relatively high initial Vfs (e.g.
Vf = 0.597 in [29]) and it also depends on the applied pressure difference.
7 CONCLUSIONS
Four different test facilities were presented to experimentally determine the
complete 3D permeability tensor of textile reinforcements. A simulation
approach to predict permeability was also presented. The test facilities can be
distinguished between in-plane and out-of-plane flow through thin-walled
materials. For in-plane flow, they can be further distinguished between one
dimensional (rectilinear) and two dimensional (radial) flow methods.
The 1D in-plane method allows the determination of the unsaturated and
saturated permeability tensor which is important for scientific investigations e.g.
the influence of capillary effects on the filling process in LCM processes.
Furthermore, all the applied equations are valid without restrictions only for the
saturated flow. The two rectilinear setups presented differ in the method the
flow front is tracked in the unsaturated stage. In the single cavity setup the flow
front is tracked optically whereas in the four-cavity setup pressure sensors are
used. The time required to completely characterize the in-plane tensor could be
reduced by approximately a factor of four by running four trials in parallel in the
four-cavity setup.
The 2D method allows a fast and material-saving characterization of the
unsaturated in-plane permeability tensor together with the measurement of the
compaction response of the textile.
The unsaturated in-plane permeability values gathered in the 1D methods are in
very good agreement. When compared to the results of the 2D method a
difference of around 30 % was observed. This difference is small considering
the variability of the materials and is considered typical in the field of
permeability measurements, particularly when comparing two different
measurement methods.
The out-of-plane measurement cell presented allows the determination of the
saturated permeability in the thickness direction of a textile reinforcement. The
109
inherent effect of additional material compaction due to the applied pressure
difference on the determined permeability value is presented. The mean
permeability values of the 6 layer preforms decreased by 21.7 % for pressure
differences between 0.2 and 0.8 bars.
The advantages and functionality of a simulation approach to permeability
characterization was shown. The advantage is that no time- and materialconsuming flow experiments are needed although additional tests are strongly
recommended for validation and calibration purposes. The approach is based
on digital images of the material recorded in a scanner. The digital images are
processed and transferred to a material model for CFD simulations. Finally the
permeability can be determined based on the simulation results applying
Darcy’s law.
8 FUTURE WORK
In the future the observations gathered in the off-plane permeability cell will be
coupled with the results of the compaction measurement in the 2D facility to
model the fluid-structure interaction for through thickness flows. For this
purpose, also experiments in which compaction response and fluid flow is
measured in parallel are planned. These investigations are useful for the design
of manufacturing processes such as Compaction RTM.
Furthermore, the effect of softening binder material at elevated temperatures on
the permeability will be studied. Both 1D facilities, the off-plane and the in-plane
cell, will be equipped with an electrical heating device and a piston injection
machine will be used to inject the heated fluid. Hence, the permeability of
bindered preforms can be measured at process temperature. The influence of
the binder activation process on the permeability of textile reinforcements has
already been demonstrated in literature but permeability tests have only been
conducted at room temperature.
The long term goal is the combination of experimental and simulation
approaches to account for complex areas in real parts such as radii, Tjunctions, ending layers and sheared zones.
Acknowledgments
The authors gratefully acknowledge the support of the Institute for Carbon
Composites, the TUM Graduate School of the Technische Universität München
and European Union through the Marie Curie Actions International Incoming
Fellowships (IIF) program, under the FP7 ‘Peoples’ framework.
110
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Stichworte:
Harzinfiltrationsverfahren, Permeabilitätsmessung,
Unidirektionalflussmethode, Radialflussmethode, Bildverarbeitung
Keywords:
Liquid composite molding, Permeability Measurement, Rectilinear Flow
Method, Radial Flow Method, Image Processing
115
Autor/author:
Dipl.-Ing. (Univ.) Reinhold Meier (Autor)
Dr. Andrew Walbran (Autor)
M. Sc. Christoph Hahn (Autor)
Dipl.-Ing. Swen Zaremba (Autor)
Prof. Dr.-Ing. Klaus Drechsler (Professor)
Technische Universität München
Institute for Carbon Composites
Faculty of Mechanical Engineering
Boltzmannstraße 15
85748 Garching b. München
Herausgeber/Editor:
Europa/Europe
Prof. Dr.-Ing. Dr. h.c. Gottfried W. Ehrenstein, verantwortlich
Lehrstuhl für Kunststofftechnik
Universität Erlangen-Nürnberg
Am Weichselgarten 9
91058 Erlangen
Deutschland
Phone: +49 (0)9131/85 - 29703
Fax.:
+49 (0)9131/85 - 29709
E-Mail-Adresse: ehrenstein@lkt.uni-erlangen.de
Verlag/Publisher:
Carl-Hanser-Verlag
Kolbergerstraße 22
D-81679 München
Tel.: +49 (0)89 99830-613
Fax: +49 (0)89 99830-225
E-Mail-Adresse:
meier@lcc.mw.tum.de
Webseite: www.lcc.mw.tum.de
Tel.: +49 (0)89/289-15054
Fax: +49 (0)89/289-15097
Amerika/The Americas
Prof. Prof. hon. Dr. Tim A. Osswald,
responsible
Polymer Engineering Center,
Director
University of Wisconsin-Madison
1513 University Avenue
Madison, WI 53706
USA
Phone: +1/608 263 9538
Fax.:
+1/608 265 2316
E-Mail-Adresse:
osswald@engr.wisc.edu
Redaktion / Editorial Office:
Dr.-Ing. Eva Bittmann
Christopher Fischer, M.Sc.
Beirat / Advisory Board:
38 Experten aus Forschung und
Industrie, gelistet unter
116

Methods to Determine the Permeability of Textile

Transcription

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