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Composites Part B

journal homepage: www.elsevier.com/locate/compositesb

Automated detection of yarn orientation in 3D-draped carbon fiber fabrics and preforms from eddy current data

Georg Bardl a' *, Andreas Nocke a, Chokri Cherifa, Matthias Pooch b, Martin Schulze b, Henning Heuer b'c, Marko Schiller d, Richard Kupke e, Marcus Klein e

a Institute of Textile Machinery and High Performance Material Technology (¡TM), TU Dresden, Dresden, Germany b Fraunhofer Institute for Ceramic Technology and Systems, Material Diagnostic (IKTS-MD), Dresden, Germany c Electronic Packaging Laboratory, Chair of Sensor Systems for Non-Destructive Testing, TU Dresden, Dresden, Germany d HTS GmbH, Coswig, Germany e SURAGUS GmbH, Dresden, Germany

ARTICLE INFO

ABSTRACT

Article history: Received 28 January 2016 Received in revised form 24 March 2016 Accepted 14 April 2016 Available online 23 April 2016

Keywords: A. Carbon fibre A. Preform

D. Non-destructive testing

E. Forming

High frequency eddy current testing

Ensuring the correct fiber orientation in draped textiles and 3D preforms is one of the current challenges in the production of carbon-fiber reinforced plastics (CFRP), especially in resin transfer molding (RTM). Small deviations in fiber angle during preforming have a considerable effect on the mechanical properties of the final composite. Therefore, this paper presents an automated method for determining local yarn orientation in three-dimensionally draped, multi-layered fabrics. The draped fabric is scanned with a robot-guided high-frequency eddy current sensor to obtain an image of the sample's local conductivity and permittivity. From this image, the fiber orientation not only of the upper, but also of the lower, optically non-visible layers can be analyzed. A 2D Fast Fourier Transform is applied to local segments of the eddy current image to determine the local yarn orientation. Guidelines for processing the eddy current data, including phase rotation, filtering and evaluation segment size, are derived. For an intuitive visualization and analysis of the determined yarn orientation, reference yarn paths are reconstructed from the determined yarn angles. The developed process can be applied to quality inspection, process development and the validation of forming simulation results.

© 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

In the production of carbon fiber reinforced plastics (CFRP), one of the current challenges is the quality assessment along the process chain. This is especially true for the resin transfer molding (RTM) process, which involves the steps of textile production, preforming and the injection of the resin in a closed mold. The preforming step, in which dry textiles are cut, stacked, draped to a 3D shape and bonded, is critical for the quality of the final composite part. Any deviations in the fiber orientation can lead to a drastic loss of strength in the composite part. E.g., a fiber misalignment of 10° results in a loss of 30% or more in compression strength for unidirectional-reinforced composites [1—4]. It is therefore of great importance to ensure the correct fiber

* Corresponding author. ITM TU Dresden, Hohe Str. 6, 01069, Dresden, Germany. Tel.: +49 351 463 33766; fax: +49 351 463 34026.

E-mail address: georg.bardl@tu-dresden.de (G. Bardl).

orientation. Furthermore, forming defects like gaps and wrinkles need to be eliminated.

Different methods have been applied for the detection of the fiber orientation in 3D-draped textiles and preforms. Most researchers and industrial users rely on optical methods [5—8], which are fast and low-cost. However, optical methods only allow measurement of the uppermost fabric or preform layer, which is insufficient for typical preforms consisting of 10 or more fabric layers. Ultrasonic inspection, which is state of the art for the quality assessment of the finished composite part, is in general not applicable to stacks of dry textiles, which lack a solid medium for wave propagation [9,10]. Although air-coupled ultrasound techniques can be operated on dry materials, the attainable resolution and contrast are not sufficient for fiber orientation analysis [11,12]. High-resolution thermography has been shown to be able to detect the fiber orientation in draped textiles [13,14]. Challenges, in this case, are the limited penetration depth and the required technological adaptions for high-resolution measurement.

http://dx.doi.org/10.1016/j.compositesb.2016.04.040

1359-8368/© 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

One technology with the potential to fill this current gap, and thereby provide an inspection technique for multi-layered textile stacks and preforms, is the high-frequency eddy current inspection technique. Due to the considerably lower conductivity of carbon fiber materials compared to metals, higher frequencies can be used to increase sensitivity on carbon fibers (1—50 MHz, compared to 0.1—1 MHz for the eddy current testing of aluminum). Although the feasibility of eddy current testing for carbon fiber composites had already been shown in the 1970s [15,16], early research focused on the detection of cracks in composites [17—23]. Only with the recent development of high-resolution testing equipment, it was possible to use local changes in conductivity to trace individual yarns and thereby detect fabric and preform defects such as gaps, local wavi-ness and fiber orientation [24—27]. In recent years, high-resolution, high-frequency eddy current measurement has been successfully applied for the online-inspection of non-crimp fabric production [28] and automated fiber placement [29], as well as in the online areal weight (grammature) testing of carbon fiber nonwovens [28,30].

Fig. 1 (left) shows an example eddy current scan for a quadraxial (+45/90/-45/0) carbon fiber non-crimp fabric (four layers of ca. 300 g/m2 area weight each). As can be seen, yarns from both the upper and the three lower layers can be distinguished as stripe patterns.

By integrating a high-frequency eddy current measurement system with an industrial 6-axis robot, it was shown that the yarn orientation in three-dimensionally draped textiles and preforms can be visualized [28]. The result is a 3D map of the local electrical properties of the sample, in which individual yarns from the different layers can be distinguished (Fig. 1 right).

A dedicated inspection software, EddyEva by Suragus GmbH [31], is available for the automated analysis of eddy current scans from multi-layer carbon fabrics and preforms. Different layers can

be separated and quality parameters like yarn orientation, fiber distribution, gaps and waviness can be automatically evaluated, with the option to check user-defined critical thresholds and to generate automatic reports for each sample. The inspection can be applied for the local analysis of both 2D and 3D scan results (Fig. 2).

However, no research has been reported so far on the global analysis of 3D eddy current scan results. From the perspective of process development and quality assessment in RTM preforming, as well as for the validation of draping simulations, it would be desirable to not only determine local yarn orientations for the whole 3D surface automatically, but to use this local fiber orientation to reconstruct the actual yarn paths over the 3D surface. This would finally allow for an easy comparison between different samples, e.g. with different draping parameters, and could serve as input e.g. for infusion or structural simulation [32].

Therefore, this paper aims at developing such an automated, robust method for the extraction of local yarn angles from 3D eddy current data and for the reconstruction of local yarn paths. The detection of the yarn orientation will be done by a local Fourier transform of projected segments of the measurement data; in order to provide a general background, the concept of using Fourier analysis for the determination of fiber orientation will be explained briefly.

Supplementary data related to this article can be found online at http://dx.doi.org/10.1016/j.compositesb.2016.04.040.

2. 2D-Fast Fourier analysis for the evaluation of fiber orientation

As was shown above, high-frequency eddy current scanning can be used to generate a conductivity map in which the individual yarn systems are visible as overlaid stripe patterns. For the

2D eddy current scan 3D eddy current scan

Fig. 1. Eddy current scan results for a planar quadraxial non-crimp fabric (left) and for a hemispherically draped biaxial non-crimp fabric.

File Tools Into

• - ■ am J- g

Fig. 2. EddyEva detection of local yarn positions and gaps for a biaxial fabric (left and center), and of a critical gap width (right) in a 3D eddy current scan.

analysis of such periodic patterns, Fourier analysis been used in a variety of textile and related applications. It has been successfully applied for the detection of local fabric defects in weaves [33—44] and knitted fabrics [45]; the determination of fiber orientation in paper sheets [46], nonwovens [47,48] and biological cell networks [49]; and the measurement of fiber orientation in planar non-crimp fabrics, based on optical inspection [50]. It has also been used for the evaluation of 2D eddy current measurements [51,52].

In Fourier analysis, the 1D or 2D signal is decomposed into sine functions, which, when summed up with their respective frequency and amplitude, generate the original signal [33]. The Fourier transform, therefore, can be used to analyze the periodic components of a signal. For an example, see the striped black-white pattern in Fig. 3 (left). It can be represented as a single sine wave with the respective angle (45°), spatial frequency (ca. 0.03 mm-1) and amplitude, which are shown in the Fourier transform (Fig. 3, right). Since the Fourier transform is symmetrical to the origin, all frequencies are present twice, resulting in two red peaks for the main frequency. The angle between the vertical axis and the line formed by these peaks represents the angle of the periodicity of the pattern. The stripe or "fiber" orientation is perpendicular to the axis of the periodicity and can thus be easily derived from the Fourier transform.

When two perpendicular sine waves of the same frequency are overlaid, the result will be a pattern as in Fig. 4, with the Fourier transform showing both components at their respective angles (+45° and -45° in this case).

3. Experimental procedures

3.1. Tested material

All experiments were carried out with bidiagonal [+45/-45] carbon fiber non-crimp fabrics. The textiles were manufactured at the ITM, TU Dresden on a Karl Mayer Malimo 14024. Table 1 contains the material specifications.

3.2. Draping test stand

For the purpose of this research, a draping test system was designed and manufactured by HTS Coswig GmbH in a joint research project (Fig. 5). The test system features a hemispherical punch which can be extended at different speeds and to set heights. Force and displacement are measured and logged to a control PC. For tensioning, the circular blank-holder is divided into 8 blank-holder segments, whose forces can be adjusted individually.

Table 1

Material specification.

Fiber orientation [+45/—45]

Areal weight 580 g/m2

Fiber material Toho Tenax HTS45 E23 800 tex

Fiber spacing 2.76 mm

Stitch length 4 mm

Binding Tricot

Fourier transform

(mm) fx <1/mm>

Fig. 3. Stripe pattern (left) and its Fourier transform (right).

signal Fourier transform

-0.1 0 0.1

f (1/mm)

Fig. 4. Two overlaid sine waves at +45° and -45° (left) and corresponding Fourier transform (right).

Table 2 shows the available options for the draping test stand, their limits and the selected values for the first experiment.

3.3. Robot-guided eddy current measurement system

After draping, the surface of the draped textile is scanned with a high-frequency eddy current sensor mounted on an industrial 6-axis robot (Fig. 6). Due to symmetry, a representative part of the hemisphere was used for scanning. Within this area, parabolic paths are projected onto the surface, along which the sensor scans the draped multi-layered textile. For the sensor and the measurement hard- and software, the commercially available EddyCus® Integration Kit by Fraunhofer IKTS, Dresden, was used (see Ref. [28] for further details). At defined time intervals, the complex impedance signal (conductivity and permittivity of the sample) is measured and recorded. The testing is done simultaneously with four eddy current excitation frequencies

(schematic) (left), picture (right).

(test frequencies). Best results were obtained for a test frequency of 6 MHz, so only data for this frequency was used for evaluation. Table 3 lists the scanning parameters.

4. Development of image analysis algorithm

4.1. Automatic phase rotation of eddy current data

The measurement provides a data set of ca. 60,000 complex electrical impedance values (real and imaginary components) of the eddy current signal, with each value associated with a point in 3D space. In order to visualize the data and to apply image analysis algorithms to it, this complex (2D) signal value at each point has be transformed to a real (1D) signal which can be represented as a gray value.

Fig. 7 (left) plots the real and imaginary components of all data points. The real components spread out between ca. 7000 and 10,000 digits, the imaginary components between 1000 and 5000 digits. By

Table 2

Experimental values for draping experiments.

Min Max Selected value

Displacement 0 mm 100 mm 100 mm

Speed 0.3 m/s 13.3 m/s 0.3 m/s

Blank holder force (individually for each of the 8 blank holders) 0 96 N 0 N

Fig. 6. Draped textile at punch extension height 100 mm (left), area used for scanning (center), scanning process by EddyCus® robot at Fraunhofer IKTS-MD (right).

Table 3

Eddy current scanning parameters.

Fanuc ARC Mate 120iC

Sensor

- Coil configuration

- Coil diameter

- Shape of coil

Eddy current test frequency

Distance between data points (average)

Distance between parallel paths (average)

S14148

- "Half-transmission" (separated excitation and pick-up coil, both on same side of material)

- 3.3 mm

- Helical 6 MHz 0.6 mm 0.5 mm

Complex eddy current data Visualization

Fig. 7. Complex plot of eddy current scan data (left), visualization as gray values after projection of complex data (right).

projecting this point cloud onto the real axis (i.e., only taking the real component), the complex 2D signal at each data point can be reduced to 1D data, which can be interpreted as a gray value (with 7000 digits = white, 10,000 = black). Fig. 7 (right) visualizes the result, where at each sample point in 3D space the gray value derived from the measurement is plotted. Notice that the paths of individual yarns can be distinguished, although with low contrast. Also, yarns of both layers — both the upper +45° and the lower -45° layer, which wouldn't be accessible with optical methods — are visible.

The contrast between individual yarns in Fig. 7 can be considerably improved by applying an additional phase rotation to the complex data. What appears as different brightness between the (darker) left side and the (brighter) lower-right part of the surface is actually the result of a lift-off effect (a small air gap between the sensor and the fabric), which occurred in the lower-right part during the scanning process. The lift-off effect and the electrical conductivity of the sample are the two dominating contrast mechanisms during eddy current scanning, with both contrast effects occurring at different phase angles. The difference between these phase angles is ca. 90°. Thus, by applying an appropriate phase rotation to the data set, the effect of the lift-off can be mapped mostly to the imaginary axis and the effect of the conductivity on the real axis. The absolute value of the required phase rotation angle will be influenced by parasitic effects from the measurement instruments.

Fig. 8 shows the point cloud rotated by different phase angles. For the marked sample point, the phase angle is changed from a0 to a0 +30° etc.

The rotated point clouds are again projected onto the real axis (only the real component is taken) and visualized on the 3D surface (Fig. 9). Rotations above 180° are not considered, since a rotation of 180°+a only inverts the real and imaginary components compared to a rotation of a.

Comparing the results of the different rotations, it can be found that the best contrast between individual yarns is achieved for a phase rotation of 60°. At this rotation, the lift-off influence is

Fig. 8. Phase rotation of complex impedance data.

considerably decreased, with the different brightness between the left part and the right tip of the surface is removed.

In order to automatically determine the appropriate phase rotation for removing liftoff and compensating parasitic effects, it is assumed that the standard deviation caused by the lift-off is equal or higher compared to the standard deviation caused by the sample's electrical properties, which is a valid assumption for Fig. 7. Thus, when a regression line is calculated for the complex data set, the direction of the regression line — which by definition is the direction of the highest standard deviation — will indicate the direction of the lift-off. By rotating the point cloud so that this regression line stands vertically (Fig. 10), the lift-off effect will be mapped mostly to the imaginary axis and is therefore removed when the data is projected to the real axis.

For the current sample, this procedure results in a calculated lift-off angle of 62°, which is in good agreement with the analysis of Fig. 9 as discussed above. Furthermore, it was found that a phase rotation calculated by this procedure gives best detection results for

Fig. 9. Visualization after phase rotation.

Calculation of rotation angle

10000 8000 6000 4000 2000 0

H Ц ^ Rotated

Original

f 9 /m

V Regression line

0 5000 10000

Re (digits)

Fig. 10. Procedure for automatic phase rotation.

the other samples discussed in this paper, too. The automatically calculated phase rotation is therefore applied to the complex measurement data set prior to image processing.

4.2. Image segmentation, orthogonal projection and local Fourier transform

In order to extract information about local yarn orientation, the image is evaluated at individual points (centers marked with circles

in Fig. 11). In this chapter, section (2,2) will be used for the illustration of the algorithm. For the discussion of the algorithm parameters, results from sections (2,2) and (5,2) will be compared (both marked red).

In a first step, the tangential plane is determined at the considered evaluation point and a normal projection of the whole

Fig. 11. Evaluation points.

surface is carried out (Fig. 12, left). From this normal projection, a square section of defined edge length around the center point is taken for evaluation (Fig. 12, right). Notice that the pattern in the projected section generally resembles the pattern generated by two overlaid sine waves in Fig. 4 above.

On this projected section, a 2D Fourier transform is applied in order to carry out a frequency analysis (Fig. 13, left). In the Fourier transform image, yellow and red colors correspond to higher energy, which indicate a periodicity in the corresponding direction and at the corresponding frequency. The angle of these peaks, as measured form the vertical, thus indicates the direction of the periodicity. Thus, the analyzed section shows periodic components at angles of 57°, 100° and 142° (Fig. 13, right).

4.3. Detection of yarn orientation

Since the yarn direction is perpendicular to the direction of the corresponding frequency peak, the actual yarn angles ayarn can be calculated from the frequency angles afreq:

ttyarn = a

Table 4 shows the frequency and corresponding yarn angles along with the frequencies and wave lengths of the individual peaks found at these angles. Note that several high-energy peaks with different frequency are present at the angles of 57° and 142°, indicating periodic information of different frequencies at these angles.

In order to automatically detect the yarn angles from the Fourier transform, the energy for all pixels at a certain angle is summed up and the frequency angles are converted to the actual yarn angles (Fig. 14, left). This energy distribution clearly shows two peaks which correspond to the two yarn directions, as can be confirmed from Fig. 14 (right). The third frequency peak at 10° is most likely an artifact from the measurement. The corresponding wave length of ca. 4 mm indicates that it might be related to the distance between the excitation and pick-up coil in the sensor, which is roughly the same length [28].

From Fig. 14 (left), an automatic detection of the fiber angles is possible if the intervals in which the yarn directions are presumed are known. In this case, it is known that there are two yarn systems and that the angles of these yarn systems are between 20 and 85 and -20 and -85°, respectively. These intervals have been marked

Fig. 12. Normal projection at point (2,2) (left), derived evaluation section (right).

2D Fourier transform

Angles with maximum energy

0.9 0.8 0.7 • 0.6 ; 0.5 -0.4 0.3 1 0.2 0.1

/--- /

/ 100°

\ 142° Z' J

Fig. 13. Fourier transform of section (2,2) (left), angles with maximum energy (right).

Table 4

Determined angles from Fourier transform.

Frequency angle (in degree) Corresponding yarn angle (in degree) Frequency (in 1/mm) Wave length (in mm)

57 -33 0.11, 0.19, 0.33 8.9, 5.3, 3.0

100 10 0.25 4.1

142 52 0.18, 0.28 5.6, 3.5

i (degree)

Fig. 14. Energy distribution (left), visualization of fiber orientation with maximum energy (right).

with a dotted gray vertical line in the energy distribution. The maximum within these intervals is taken to be the actual yarn direction. In future research, this procedure can be extended to preforms with multiple fabric layers, since each additional yarn system with a distinct angle will be represented as an additional peak in the energy distribution.

It should be noted that in the 2D-Fourier transform (Fig. 13 above), the main red and yellow energy peaks are not, as would be expected, at the frequency of 0.36 mm-1 (which would correspond to the original yarn distance of ca. 2.8 mm), but at ca. half this frequency (corresponding to twice the yarn distance). The reason for this can be seen in Fig. 15. For both yarn directions, a grid has been fitted to the image, with the yarn distances of 3.1 and 3.3 mm chosen so as to best match the white stripes (yarns) in both directions. When the underlying image is compared to this grid, it can be seen that two neighboring yarns (white stripes) usually appear as "merged", which might be caused by the distance between sensor's excitation and pick-up coil, which is of the same magnitude as the yarn distance. In the Fourier transform, the main periodicity thus appears at twice the yarn distance.

5. Influence of algorithm parameters and filtering on the results

5.1. Evaluation sections

The detection of the yarn orientation can be influenced by two factors: the size of the evaluation segment, and an optional frequency filtering, which can improve the results. These influences are discussed for sections (2,2), which had been used for the illustrations above, and section (5,2), which is one of the most difficult sections of the surface: the fabric is highly draped, while at the same time the section features an edge and has reduced information (yarn only in 50% of the area) (Fig. 16).

5.2. Filtering

High-pass filtering is a standard tool in image analysis for taking out low-frequency components, thus sharpening the image and highlighting any edges. Therefore, different high-pass filters which correspond to multiples of the yarn distance are tested on the image (see Table 5).

Yarn distance

5 10 15

u (mm)

Fig. 15. Analysis of yarn distances.

0 10 20 30

u (mm)

Fig. 16. Normal projection for section (5,2).

Table 5

Filter frequencies and corresponding wave lengths.

Frequency Wave length

0.08 mm-1 12 mm

0.11 mm-1 9 mm

0.17 mm-1 6 mm

0.33 mm-1 3 mm

0 (no filtering) Infinite

Fig. 17 shows the Fourier transform for both sections. Notice that the peaks for section (5,2) are much wider, indicating that slightly different fiber angles are present in the evaluation segment. The minimum frequency for each filter is shown as circle. When calculating the energy distribution, only energy content outside of the filter radius is considered.

Fig. 18 shows the energy distribution of the two samples for the different filter widths. The detected fiber directions are drawn into Fig. 19.

fx (1/mm)

Fig. 17. High-pass filter radii in Fourier transforms for section (2,2) (left) and (5,2) (right).

Fig. 18. Energy distribution for different high-pass filters, sample (2,2) (left) and (5,2) (right).

Calculated fiber orientations, section (2, 2) Calculated fiber orientations, section (5, 2)

The results show that the detection of the fiber orientation for section (2,2) is rather independent of the chosen filter. Small deviations in the -31 ... -35° angle are to be expected, since yarns with slightly different orientations and slightly different yarn distances are present in the evaluation section due to draping. Based on the analysis of this section, all filter widths, including 0 mm-1 (no filtering) would be suited for the automated detection.

For section (5,2), on the other hand, the different filters lead to noticeable different results. Without filtering (fm;n = 0 mm-1, red curve), the orientation of the yarn at ca. +56° was not detected (the maximum of the red curve was found at 82.5). Thus, the application of a filter is necessary in this case. Also, note that the filtering at fmin = 0.33 mm-1 (magenta curve) accentuates the peaks at ca. ± 5° and leads to rather big secondary peaks within the detection intervals (at ca. 70° and -65°). The filter sizes of 0.08, 0.11 and 0.17 mm-1 all lead to reasonable results, but it can be seen that the blue and green lines best match the orientation of the yarns in the evaluation segment's center. Thus, a filter width of 0.11 mm-1 (blue line) is chosen, which corresponds to a wave length of three times the yarn distance.

only the average yarn orientation for a bigger section. It is, therefore, desirable to have a section as small as possible.

Fig. 20 shows the included area for different sizes of the evaluation section; Fig. 21 shows the calculated energy distribution. A high-pass filtering of 0.11 mm-1 was applied.

The comparison of the calculated yarn orientations with the scanning results can be seen in Fig. 22. For section (2,2), the detected angles for widths 15, 20 and 30 mm are almost equal. However, a width of 40 mm leads to a slight change for both yarn angles, which is most likely due to a variation in yarn angle in the outer parts of the increased evaluation section.

For Section (5,2), it can be seen that a minimum width of 30 mm is necessary for proper detection of the yarn angles. Thus, a filter of 0.11 mm-1 and a segment size of 30 mm (corresponding to roughly ten times the yarn distance) is chosen for further evaluation. Notice that the distance between the evaluation points was chosen as 20 mm, so an evaluation segment width of 30 mm will lead to some overlap, which however doesn't affect the calculation.

6. Visualization of the results

5.3. Influence of segment size

The size of the evaluation segment influences the detection results. The bigger the size, the more yarns and thus periodical patterns are present, resulting in higher peaks in the 2D Fourier transform. However, since the surface is draped, the bigger the evaluation section, the higher the variety of yarn angles in the evaluation segment will be, leading to wider peaks. The determined angle will represent

The described algorithm is applied to determine the local yarn orientation at all evaluation points (Fig. 23, left). From the pictures, it can be seen that the calculated yarn directions correctly show the directions of the yarns in the fabric at all evaluation points.

At each evaluation point, the two determined yarn angles represent the slope of the two yarn systems in the fabric. This information can now be used to draw reference yarn paths onto the surface, which provide an intuitive visualization:

Normal projection, section (2, 2)

Normal projection, section (5, 2)

40 35 30 25 .20 15 10 5 0

A VQmm

fvlLl^ll

jl 5 20 mm ^

40 35 30 25 20 15 10 5 0

20 mm 15 mm

Fig. 20. Visualization of different evaluation segment sizes for section (2,2) (left) and (5,2) (right).

Fig. 21. Energy distribution for different evaluation segment sizes, sample (2,2) (left) and (5,2) (right).

Calculated fiber orientations, section (2, 2)

35 30 25

Calculated fiber orientations, section (5, 2)

Fig. 22. Calculated fiber orientation for different evaluation segment sizes, sample (2,2) (left) and (5,2) (right).

Fig. 23. Calculated yarn directions at evaluation points (left) and calculated reference yarn paths (right) for sample 1.

- From the known slopes at the evaluation points, the slope ofthe yarn can be calculated at any given point on the surface by means of 2D interpolation from the neighboring evaluation points.

- Starting from any given point on the surface, the path of a yarn can be reconstructed by numerical integration of the slope field: the yarn direction is determined at the starting point, and a small step is taken in this direction, arriving at a new point. The process is repeated until the path of this yarn is fully reconstructed.

Fig. 23 (right) shows the paths for a set of reference yarns for the evaluated sample. In order to limit the number of lines in the picture, the distance between the starting points of the reference yarns was set to 10 mm. Each reference yarn thus represents several yarns of the fabric. It can be seen that the reference yarns follow the paths of the actual yarns very closely. This serves as the final validation of the developed algorithm.

The calculation and comparison of reference yarns can be used to easily visualize the effect of different forming parameters on the yarn paths. Fig. 24 shows the detected yarn paths for two additional samples. In sample 2, the blank holder force of all eight blank holder segments was set to 48 N each, resulting in a total blank holder force of 348 N. In sample 3, a blank holder force of 96 N per segment (768 N total) was used.

Comparing the yarn paths on the surface shows the influence of the blank-holder force (Fig. 25). As expected, the displacement of the yarns by draping is highest for sample 1 (red) and restricted for samples 2 and 3. Interestingly, the difference in yarn paths between samples 2 and 3 is much smaller than between samples 1 and 2.

7. Conclusions

In order to process 3D eddy current measurement data, an algorithm was developed that automatically determines and visualizes the yarn orientation on the surface. It was shown that the yarn orientation can be derived from a 2D Fourier transform. With proper choices for a high-pass filter and for the size of the evaluation section, it is possible to determine the yarn paths even in highly draped border regions of the surface. By drawing reference yarn paths onto the surface, the influence of different experimental settings on fiber orientation can be easily evaluated. The presented evaluation method is not limited to eddy current measurement data, but may be used for optical inspection of draped fabrics, too, although in this case only the yarn paths for the upper layer may be reconstructed.

The developed algorithm is not only of high usability for the evaluation of draping results, but can also be used for the validation

Reference yarn paths, sample 2 (F=384 N) Reference yarn paths, sample 3 (F=768 N)

x in mm x in mm

Fig. 24. Reference yarn paths for samples 2 (left) and 3 (right).

x in mm "" y in mm

Fig. 25. Comparison of yarn paths for samples 1, 2 and 3.

of textile forming (draping) simulations. The simulation results, usually shear angles, can be processed to compute simulated yarn paths, too, which can be compared to those derived from experimental results. Current research at the ITM is aimed at using the determined fiber orientation as input for infusion and structural FEM simulation.

Acknowledgment

This research was funded by the European Union Regional Development Fund (EFRE) and the Free State of Saxony (grant "3D-Fast", number 100224749). The authors would like to thank the mentioned institutions for providing the funding.

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