Non-destructive characterisation of out-of-plane fibre waviness in carbon fibre reinforced polymers by X-ray dark-field radiography

Abstract

Fibre waviness is a frequently encountered problem in composite design and manufacturing as it can severely influence mechanical properties of components. In this work, we propose a new method for the detection and quantification of out-of-plane fibre waviness in carbon fibre composites using Talbot-Lau grating interferometry. The sensitivity of X-ray dark-field imaging to the orientation of carbon fibres is exploited to visualise fibre waviness by radiographic imaging and reduce measurement times in comparison to full computed tomography scans. We show that fibre waviness can be qualitatively detected by single radiographic images providing a valid option, for example, for in-line monitoring of similar specimens. Furthermore, quantitative evaluation of fibre waviness angles can be performed by repeated radiographic imaging over an angular range of roughly 10°. Therefore, the number of required projection images can be reduced significantly. With this method, we evaluated wave angles at an error of less than ±1.5° compared to results achieved by full computed tomography scans.

Full text

Non-destructive characterisation of out-of-plane fibre waviness in
carbon fibre reinforced polymers by X-ray dark-field radiography
Jonathan Glinz
a,b,
*, Michael Thor
b
, Joachim Schulz
c
, Simon Zabler
d
,
Johann Kastner
b
, Sascha Senck
b
a
Institut für Werkstoffwissenschaft und Werkstofftechnologie, TU Wien, 1060 Wien,
Austria
b
University of Applied Sciences Upper Austria, 4600 Wels, Austria
c
Microworks GmbH, 76137 Karlsruhe, Germany
d
Lehrstuhl für Röntgenmikroskopie, Universität Würzburg, 97074 Würzburg, Germany
*corresponding author: jonathan.glinz@fh-wels.at

Non-destructive characterization of out-of-plane fibre waviness in
carbon fibre reinforced polymers by X-ray dark-field radiography
Fibre waviness is a frequently encountered problem in composite design and
manufacturing as it can severely influence mechanical properties of components.
In this work we propose a new method for the detection and quantification of out-
of-plane fibre waviness in carbon fibre composites using Talbot-Lau grating
interferometry. The sensitivity of X-ray dark-field imaging to the orientation of
carbon fibres is exploited to visualize fibre waviness by radiographic imaging
and reduce measurement times in comparison to full computed tomography
scans. We show that fibre waviness can be qualitatively detected by single
radiographic images providing a valid option, e.g. for in-line monitoring of
similar specimens. Furthermore, quantitative evaluation of fibre waviness angles
can be performed by repeated radiographic imaging over an angular range of
roughly 10°. Therefore, the number of required projection images can be reduced
significantly. With this method, we evaluated wave angles at an error of less than
±1.5° compared to results achieved by full computed tomography scans.
Keywords: out-of-plane fibre waviness, Talbot-Lau grating interferometry, dark-
field radiography, radiographic testing
1 Introduction
Out-of-plane fibre waviness is one of the most frequently encountered defects in carbon
fibre reinforced polymer (CFRP) parts which can originate from different stages of the
design and manufacturing process [1-3]. Most commonly, waviness develops at inner
radii [4] where fibre layers fail to follow the curvature because of path length
differences. Furthermore, foreign objects in the fibre layup such as electronic
components [5] as well as the inherent undulation in fibre fabrics cause deviations from
the intended fibre orientation. While wave amplitude and length are commonly used to
describe fibre waviness, the maximum angular deviation of carbon fibres θ
max
influences mechanical properties most significantly [1,2,6]. For example, Hörrmann et
al. [7] showed that out-of-plane fibre misalignment angle negatively influences the

static strength as well as fatigue life of resin transfer moulded CFRP specimens.
Consequently, the detection of fibre waviness in an early stage of production is crucial
to prevent extensive rejects or even failure during operation. The currently most
established technique for the inspection of CFRP components in industry is ultrasonic
testing (UT) since it is comparably cheap and available for on-site investigations.
Although, it is mostly only used for the localization and shape/type identification of
fibre waviness rather than a detailed quantification [2]. X-ray computed tomography
(XCT) on the other hand is an invaluable technique for the three-dimensional
characterization of the (micro-)structure in CFRP specimens [8,9]. However,
restrictions in specimen dimensions combined with typically low contrast between
carbon fibres and conventional matrix materials limit its applicability for the inspection
of fibre waviness in industrial applications.
In this work, we present a new method for the detection and quantification of
out-of-plane fibre waviness by X-ray dark-field contrast (DFC) radiography. The dark-
field modality can be extracted via Talbot-Lau grating interferometry (TLGI) which was
introduced by Pfeiffer et al. [10] in 2006 and enables the grating interferometry
technique for low brilliance laboratory X-ray devices. TLGI uses a phase stepping
approach which creates a sinusoidal intensity modulation on each detector pixel. The
amplitude of this sine wave decreases due to scattering caused by a specimen in the
beam path [11]. Thus, the DFC modality represents the small angle scattering of X-rays
caused by microstructures in a component. This is particularly useful for the
visualization of carbon fibres as they cause high scattering and consequently high
contrast of fibre bundles compared to standard attenuation contrast (AC) radiography
[12-14]. Furthermore, the signal amplitude in DFC is sensitive to the direction of
scattered X-rays and consequently can be utilized for the extraction of fibre orientation

information [15-17]. Carbon fibres aligned with beam direction cause a distinct peak in
the dark-field signal [18]. In this work, we exploit the angular sensitivity for the
detection and quantification of out-of-plane fibre waviness. The low requirements in
spatial resolution of the method allow for increased specimen dimensions at reduced
measurement time in comparison to XCT.
2 Materials and methods
2.1 Specimen preparation
Two test specimens with dimensions of 16×9×7.5 mm³ were cut from a plate produced
from IM7-8552 (Hexcel Corporation, USA) pre-impregnated polymer composite [19] in
a sequence of 46 unidirectional layers alternating between 0° and 90° orientation. Each
specimen includes non-uniform out-of-plane fibre waves with an amplitude of 2 mm at
a length of 15 mm (S1) and 10 mm (S2) respectively. A reference (ref) specimen with
dimensions of 14×8×7.5 mm³ was cut out of a similar plate not including fibre
waviness. Photographs of the specimens are visible in Figure 1.
Figure 1. Photograph of specimen S1 (a), S2 (b), and reference specimen without
waviness (c).
2.2 Data acquisition
Image data was recorded on a SkyScan 1294 TLGI-XCT system (Bruker microCT,
Belgium), featuring two absorption and one phase grating. The gratings are fabricated at
periods of 4.8 µm and positioned in a symmetric setup as shown in Figure 2a. The first
absorption grating G0 is positioned close to the X-ray source and creates multiple line

sources which are mutually incoherent but individually have sufficient transverse spatial
coherence. If grating periods and inter-grating distances are chosen correctly, these line
sources interfere constructively at G2 and enable Talbot-Lau imaging using low
brilliance X-ray sources [10]. The actual image formation is achieved by the phase
grating G1 in combination with the absorption grating G2. The phase shifting G1 causes
an interference pattern which projects a self-image of G1 onto the detector. Typical
laboratory XCT setups lack the required spatial resolution to visualize this interference
pattern directly, which is why the analyser grating G2 is needed. By a stepwise lateral
movement of G2 over at least one period a sinusoidal intensity modulation can be
recorded by each detector element. This procedure is generally referred to as phase
stepping [20]. The visibility of the recorded sine function is defined by   

, with
the signal amplitude A and mean intensity I
0
. By comparison to reference data without a
specimen in the beam path the attenuation contrast (AC) and dark-field contrast (DFC)
can be calculated as follows:
  




   




 (1)
For image acquisition, the 60 kV micro-focus tube of the SkyScan 1294 was
operated at 35 kV tube voltage and 1300 µA current using a 0.25 mm aluminium
prefilter. Projection images were recorded using a 4000×2672 pixel CCD camera at an
exposure time of 650 ms in 4×4 binning mode, resulting in an isometric pixel size of
22.8 μm. For the extraction of DFC data, 4 phase steps were performed and images
were averaged over 7 frames for reduction of image noise.
For the assessment of fibre waviness by DFC radiography, the rotary table was
used to apply a tilt angle φ to the specimen around the y-axis from 0 to 180° at an
interval of 1°. The specimen positioned perpendicular to the grating orientation

corresponds to φ = 0° as shown in Figure 2a. The DFC signal will show a distinct peak
when fibres are aligned with beam direction. Consequently, only layers with fibres
oriented in x
s
-direction can be evaluated and fibre waviness will cause peaks in the DFC
signal apart from φ = 90° as exemplarily shown in Figure 2b. Full TLGI-XCT scans of
each specimen were performed for reference.
Figure 2. a) Specimen placement and tilt angle φ around the y-axis in TLGI-XCT. The
specimen is shown in φ = 0° orientation. b) Schematic visualizing the projected scatter
profile P(φ,x) at φ = φ
p
and the corresponding wave angle θ in the x
s
-z
s
-plane of the
specimen coordinate system. Peaks in the scatter signal caused by fibre waviness are
visible in the projection profile.
2.3 Image processing and evaluation
For comparison to the radiographic method proposed in this work, fibre misalignment
angles in both specimens were assessed in VGStudioMax 3.4 (Volume Graphics,
Germany) via fibre composite analysis of the TLGI-XCT volume data. Since the DFC
in radiographic images is only sensitive to fibres oriented in x
s
-direction, exclusively
these layers of the volume data were evaluated. Prior to this evaluation, a non-local
means filter using a search window of 10 pixels, a local neighbourhood value of 5
pixels and a similarity value 2 was applied to the TLGI-XCT volume data in Avizo 3D

2021.1 (Thermo Fisher Scientific Inc., USA) in order to reduce noise while preserving
image contrast between fibre layers.
For the assessment of fibre waviness via DFC radiography, projection images
were median-filtered in y-direction with a kernel size of 15 pixels. Thereby noise is
reduced significantly while avoiding additional blur between layers as they are oriented
in the vertical direction (y-direction). Since the DFC signal is maximised when fibres
are aligned with beam direction, the corresponding wave angle θ can be determined by
  

   (2)
at tilt angle φ
p
where the peak occurs. However, the cone beam X-ray source of
standard laboratory devices affects the evaluation of fibre misalignment angle.
Consequently, Equation 2 has to be corrected for perspective error arising from the cone
beam geometry by
 !

 " #$%&
'
()*
+, -
.
! (3)
where α is the cone beam opening angle, ∆φ is the angular step between
projection images and -
.
is the sign sensitive pixel distance in x-direction of the
respective DFC peak to the optical axis. Perspective error can also be corrected by
applying the tilt added in Equation 3 to the projection image stack around the y-axis if
projections are oriented in the x-y-plane as shown in Figure 2a. A qualitative
assessment of fibre waviness can be performed by visual inspection of the projection
images since fibre waviness causes distinct peaks in the DFC signal apart from φ = 90°.
For a more detailed assessment of fibre wave angles, image data is evaluated in the
sinogram domain. Mean values and standard deviation
/
were calculated from 17

sinograms distributed equidistantly across the height of the specimens to minimize the
influence of local differences.
3 Results
3.1 DFC: X-ray computed tomography
The fibre composite analysis performed in VGStudioMax revealed wave angles of up to
26° in specimen S1 and 29° in specimen S2 as visible in Figure 3a. Carbon fibre layers
have been numbered from left to right to indicate layers with maximum wave angle. To
distinguish between the top and bottom slopes of the waves, histograms for the top and
bottom halves of the specimens were plotted separately as can be seen in Figure 3b. From
these histograms, maximum wave angles of top = 25.8° and bottom = 22.3° were found
in layer L25 of specimen 1 and of top = 29.0° and bottom = 27.9° in layers L17 and L15
of specimen 2 respectively. These results serve as a reference for the following
evaluations via DFC radiography. Note that XCT wave angles peak at ~1° because layers
are not perfectly parallel to the specimen contour which was used for the alignment of
specimens. For the reference specimen without fibre waviness (see Fig. 1c) no analysis
was performed.

Figure 3. a) DFC-XCT cross-section images of specimens S1 & S2. Results of the fibre
composite analysis are color-coded in the right images respectively. Layer numbers in
which maximum and minimum detectable wave angles occur are indicated with arrows.
b) Histograms of the fibre waviness results of specimens S1 & S2 with maximum wave
angles indicated. Values for top and bottom half of the specimens were plotted
separately to distinguish between top and bottom slope of the waviness.
3.2 DFC: radiography
Figure 4 shows the sinograms of the reference specimen without fibre waviness (a) and
specimen S1 (c) over a tilt angle range of 180°. In addition, exemplary projection
images at φ = 68° for the respective specimens are shown in Figure 4b) and 4d). As
shown in Figure 4c) and 4d), an increase in the scatter signal from
0
= 62° to 115° in S1
is clearly visible - in the sinogram as well as in the respective projection image. In
contrast, the increase in scatter in the reference specimen is notable in a narrower range
from
0
= 84° to 96° causing significantly different sinogram shape compared to the

waviness specimen. Consequently, the respective projection image at φ = 68° (Fig. 4b)
also shows no increase in the scatter signal in the form of vertical dark bands. For
comparison, the standard AC sinogram and projection images in Figure 4e) and 4f) are
dominated by differences in transmission length and no indications of fibre waviness
are evident.
Figure 4. a) DFC sinogram of reference specimen without fibre waviness. b) DFC
radiography projection image of reference specimen at θ = 68°. c) DFC sinogram of
waviness specimen S1. d) DFC radiography projection image of waviness specimen S1
at θ = 68°. e) AC sinogram of waviness specimen S1. f) AC radiography projection
image of waviness specimen S1 at θ = 68°. Horizontal green lines in the sinograms
indicate the projection angle of b), d), and f). Pixel values shown are as extracted before
normalization. Images have been corrected for perspective error as explained in chapter
2.3.

Extracting line profiles from the respective projection images, we visualized the
influence of transmission length on DFC and AC data (see Figure 5). Although DFC
shows a reduced sensitivity to changes in transmission length compared to AC, a
correction for specimen thickness has to be considered for detailed evaluation of
waviness angles. Therefore, we calculated the normalized scatter
% 
.12
32
(4)
which is decoupled from the specimen thickness by setting the scatter in relation
to the absorption signal [21]. While peaks caused by fibre waviness are easily
perceivable in the DFC signal as well, the quantification of fibre misalignment angles
will be more precise after correction for transmission length.
Figure 5. Line profiles through specimen S1 at θ = 68°. Distinct peaks in DFC due to
fibre waviness and reduced sensitivity to transmission length compared to AC are
obvious (top and middle). The bottom line profile shows the normalized DFC (nDFC)
calculated to remove the influence of transmission length on the evaluations. Note that
nDFC is dominated by noise in regions where transmission length approaches zero.

Consequently, further evaluations were performed on nDFC data as shown in
the sinograms in Figure 6. The increased scatter signals in these sinograms are
detectable over a range of 54° in S1 and 66° in S2 but farthest from φ = 90° in fibre
layers L25 in specimen S1 (see Fig. 6a) and L15 and L17 in specimen S2 (see Fig. 6c).
This is a strong indicator that maximum wave angles will be found in these layers as
well. Consequently, only these layers were further evaluated. The nDFC signals evoked
at each angular step position within the respective layer and indicated region are plotted
in Figure 6b and d. Within these graphs the maximum nDFC signal indicates the tilt
angles corresponding to the maximum wave angle θ
max
. Standard deviation
/
indicates
the variance between the 17 evaluated sinograms along the height of the specimens.
Table 1 gives a comparison of θ
max
evaluated from 3D-XCT versus limited angle
sinogram data.
Figure 6. Zoomed sections of nDFC sinograms from S1 and S2 in a) and c) respectively.
Regions evaluated for θ
max
are indicated by red brackets. Layers with minimum
detectable wave angles are indicated with red arrows. In b) and d) maximum nDFC

signal per image line in the evaluated regions indicated in a) and c) are plotted over the
corresponding wave angle. Maximum wave angles are indicated by vertical red lines.
Table 1: Results of maximum wave angle θ
max
evaluated from sinogram data in
comparison to values evaluated from XCT volume data via VG fibre composite
analysis. Standard deviation indicates the variance between the 17 evaluated sinograms
along the height of the specimens.
Specimen
Layer/Region
θ
max
Sinogram
θ
max
XCT
∆
S1
L25
-
Top
25
±
1.
3
°
25.
8
°
-
0.
8
°
L25
-
Bottom
21
±1.2
°
22.
3
°
-
1.
3
°
S2
L17
-
Top
30
±0.7
°
2
9
.
0
°
+1.
0
°
L15
-
Bottom
29
±0.6
°
27.9°
+1.1°
Furthermore, for the estimation of the smallest detectable waviness angle, layers
with low wave angle were investigated as well. As the central ±6° region around φ =
90° in the sinogram of the reference specimen also evokes a strong scatter signal despite
the absence of waviness, this can be considered a limiting factor for the detection of low
wave angles. However, as we have seen from maximum wave angle investigations, the
scatter signal starts to increase at an angle of approximately 3° earlier than the actual
wave angle. Consequently, wave angles of 4° should theoretically still evoke a visible
scatter signal outside the central ±6° region. For example, evaluations of XCT volume
data revealed wave angles of roughly 4° in layer L41 - Top of specimen S1 and 5° in
layer L39 - Top of specimen S2. (see Fig. 3a) In the sinogram domain, these layers
show an increase in scatter signal at angles of up to 7° and 8° respectively and therefore
are discernible from the central ±6° region (see Fig. 6a & c). This means that despite the
waviness angle being smaller than 6°, detection is still possible to a minimum angle of
approximately 4°.

4 Discussion
For the realisation of the proposed method the approximate orientation of fibre
waviness needs to be known a priori for the correct application of specimen tilt
direction, which must be applied around the same axis as the wave angle. However,
expected waviness location and orientation often can be predicted from manufacturing
parameters and mould shape. Otherwise, repeated measurements around different tilt
axes or preliminary inspections to determine wave orientation are necessary.
Furthermore, since the change in scatter signal is based on the change in fibre
orientation caused by the waviness, the method will only work for fibres oriented
parallel to the wave.
Although the scatter signal increases with specimen thickness or transmission
length respectively, fibre waviness is still easily discernible from scatter caused by
specimen thickness in radiography projection images and sinograms. Consequently, the
calculation of nDFC is only necessary for more accurate quantitative determination of
the wave angle. For qualitative detection of waviness, the standard DFC signal proved
to be sufficient. The main advantage of the inspection of fibre waviness via DFC
radiography is the reduced measurement time compared to full computed tomography
scans and the additional information available in comparison to alternative non-
destructive testing methods such as ultrasonic testing. During this work, radiography
images over 180° tilt angle were recorded. However, the increase in scatter signal
caused by waviness was visible over a range of approximately ±30° around φ = 90°
orientation, offering a relatively large angular window in which fibre waviness can be
detected qualitatively. This means in most cases fibre waviness can be detected by only

a few projection images recorded around φ = 90° orientation, which are available for
live inspection in modern devices.
For the quantitative evaluation of an unknown maximum waviness angle a
possible measurement procedure could be to sample the specimen in 10° steps starting
at φ = 90±10°. If the first projection image shows an increased scatter signal,
subsequent projections in 10° steps are recorded until the increased scatter signal seizes.
Then the range between the last two projections is sampled in detail, e.g., by 1° steps.
By this procedure, a maximum of 18 projection angles per waviness slope need to be
recorded for quantitative waviness evaluation. For the specimens investigated in this
work a total of 24 projection angles for S1 and 26 projection angles for S2 would be
required following this procedure.
However, due to high noise in DFC data median filtering e.g., of several
projection images should be considered as well as adequate angular step size with
respect to required precision. Ultimately, higher angular deviations are easier to detect
with the proposed method, while smallest detectable wave angles will mostly depend on
specimen dimensions as projection images closer to φ = 90° might be prevented by
collision of the specimen with interferometer gratings. Furthermore, if specimen
dimensions allow the acquisition of projection images over 180° as shown in this work,
the layers in which the waviness occurs can be determined, giving some information
about the depth of the waviness within the composite laminate. The importance of the
position of waviness in the cross-section of a composite was previously shown by
Caiazzo et al. [22]. However, in completely unidirectional specimens, where individual
layers cannot be differentiated, this might not be possible right away.
5 Conclusions

We presented a new method for the detection and quantification of fibre waviness by
application of dark-field contrast imaging. Although there are some restrictions
regarding detectable fibre orientation and some a prior knowledge is required to
minimize measurement time, the method provides a valid option, e.g., for in-line
monitoring, where specimens of similar features and waviness are expected. With the
approach presented, we were able to determine the maximum occurring wave angle in a
unidirectional CFRP laminate with non-uniform out-of-plane fibre waviness at less than
±1.5° error in comparison to results achieved by computed tomography. While TLGI-
XCT is known to be a rather time-consuming technique, this approach allows for a
significant reduction of projection images, to around ten to twenty images depending on
required precision, compared to typically several hundred in XCT. Further outlooks of
this work will include the application of the proposed method to bigger and more
complex CFRP structures at different layer sequences such as completely unidirectional
or woven fabric specimens.
Acknowledgements
This work was financed by the project "Phad-CT" funded by the federal government of
Upper Austria [FFG grant number: 875432] and by the project “FatAM” in the course
of COIN “Aufbau” [FFG grant number: 884101].
Declaration of competing interests
The authors report there are no competing interests to declare.
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