Characterization of multilayer structures in fiber reinforced polymer employing synchrotron and...

Oliver Wirjadia , Michael Godehardta , Katja Schladitza , Björn Wagnera , Alexander Rackb ,

Martin Gurkac , Sebastian Nisslec , Andreas NollcaFraunhofer ITWM, Kaiserslautern, GermanybEuropean Synchrotron Radiation Facility, Grenoble, Francec Institute for Composite Materials IVW, Kaiserslautern, Germany

Characterization of multilayer structuresin fiber reinforced polymer employingsynchrotron and laboratory X-ray CT

Specimens of carbon or glass fiber reinforced polymer canbe imaged using both conventional laboratory X-ray mi-cro-computed tomography equipment and synchrotron lightsources. The image quality when using intense (partially)coherent synchrotron light is still superior, especially whenapplying phase-retrieval algorithms. In the resulting vol-ume images, the fiber direction distribution and other me-chanically relevant parameters such as volume fractions orlayer thickness can be determined. In this contribution, wewill demonstrate how fiber direction results can be used todetect regions with locally different fiber orientations incarbon or glass fiber reinforced polymer which arise in themolding process of such samples. To this end, we evaluatethe three-dimensional fiber orientation tensor locally acrossthe thickness of different specimens. For each resulting in-dividual layer, we can automatically detect the layer thick-ness and the preferred fiber direction. These methods havebeen successfully applied to various commercial speci-mens. We will demonstrate results on volume images ofsamples from both synchrotron and laboratory micro-com-puted tomography and discuss the specific advantages anddisadvantages in this application.

Keywords: Image analysis; Computed tomography; Fiberorientation; Mechanical properties

1. Introduction

Due to their high weight-specific stiffness and strength,composite materials play an increasingly important role inlightweight construction. Glass and carbon fiber reinforcedpolymers (GFRP and CFRP) especially are now used in awide variety of applications. In general, parts from such fi-ber reinforced materials should be produced such that thefibers are aligned with the main loading direction in the fi-nal application to ensure high strength and stiffness. Yet, itis known that depending on fiber lengths and processingconditions during the injection or molding procedures usedto form a fiber-reinforced part, complex and inhomoge-neous fiber direction distributions can result. An overviewof structure formation during processing and its effects onmechanical parameters is given in [1]. References [2, 3]

summarize guidelines for optimization of injection andcompression molding of various specific material combina-tions, while [4] gives some insight into fatigue behavior ofGFRP components, depending on their structure. These ef-fects seem to be insufficiently understood and simulationsoftware is currently not yet capable of fully describingthem. Three dimensional (3D) imaging using micro-com-puted tomography (lCT) and image analysis may be usedto describe the phenomenology and as a powerful tool foranalyzing the relations between production processes andfiber distribution in the final component.

The goals of the present paper are: First, to provide 3D-image analysis tools capable of extracting mechanically re-levant parameters from lCT-reconstructions of fiber-rein-forced polymers; second, to compare laboratory (lXCT)and synchrotron X-ray micro-tomography (lSCT) regard-ing their usability for characterizing CFRP, which are diffi-cult to analyze by normal lXCT due to the small differ-ences in X-ray absorption of carbon fibers and surroundingmatrix.

A quantitative correlation of microscopically determinedstructural parameters (orientation tensor, layer thickness,volume fraction) with mechanical properties needs exhaus-tive modeling and simulation studies, for which a qualita-tive starting point will be given with the mechanical analy-sis presented in this manuscript. The high complexity ofsuch a simulation study follows from the fact that injec-tion-molded GFRP and CFRP with fiber lengths in themm-scale have a far more complex geometry than high-per-formance composites reinforced by endless, unidirectionalfibers. This renders simple, one-parameter descriptionssuch as the direct relationship between a scalar angle andE-modulus presented in [5] infeasible for our data. Yet, wedo give some hint at how geometrical characteristics de-rived from CT-data can be used in Section 4.2, where wepresent an analytical estimation of stiffness based on fibervolume fraction.

Similar algorithms to ours exist in the literature, e. g. [6–11], and structural studies of fiber reinforced polymersbased on lCT data have also appeared elsewhere, e. g. [4,5]. However, this paper presents to the best of our knowl-edge the first detailed quantitative comparison of the influ-ence of injection rate on the resulting 3D-microstructure,and the first paper which is able to demonstrate reproduci-

O. Wirjadi et al.: Characterization of multilayer structures in fiber reinforced polymer employing X-ray CT

Int. J. Mater. Res. (formerly Z. Metallkd.) 105 (2014) 7 645

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bility of image analysis results using different lCT technol-ogies for GFRP. Furthermore, we present a novel method toidentify and measure the thickness of regions with differ-ently oriented fibers from local fiber orientation measure-ments.

Among the previously proposed algorithms for measur-ing fiber orientation in polymers, there are 2D methods [6]and some which do not allow for a quantification of localeffects [9]. In contrast, morphological approaches such as[7, 8], or filter-based methods [10] would also be applicablein our case. Yet, algorithms using partial gray value deriva-tives [11, 12] are more closely related to our method, andwe expect these could produce similar results to those pre-sented here. Nevertheless, we will use the local estimationof fiber directions based on the three-dimensional Hessianmatrix in this paper, which we have previously describedin [13], and which resembles one of the two algorithms usedby Salaberger et al. [12]. This method does not require seg-mentation of individual fibers and is therefore also applic-able at medium resolutions and high fiber density. In thepresent context, a medium resolution means that the pixeldistances in the reconstructed volume images are just belowthe fiber diameter (typically 10–15 lm for glass fibers andbelow 10 lm for carbon fibers).

Applying lCT to study fiber-structures in polymers doesnot only introduce challenges in terms of spatial resolvingpower: additionally, sensitive contrast modes are requiredin order to depict the only weakly varying density changesin the samples [14, 15]. Here, the usage of synchrotron lightwith its partial spatial coherence as well as intense photonflux is highly beneficial for lCT. It allows one to obtainimages with high spatial resolution as well as high signal-to-noise ratio and, even more important, to exploit the fullcomplex-valued refractive index of the specimen in termsof contrast. Especially the contrast related to the real partof the refractive index, frequently termed X-ray phase con-

trast, is of high interest as it is orders of magnitude largerfor low-Z materials such as polymers than the imaginarypart (absorption) [16]. X-ray phase contrast allows one todepict specimens with either negligible absorption contrastor where the absorption contrast between different constitu-ents is weak, e. g., as in the case of carbon fibers in poly-mers [13–18] or even water-enriched regions in hardeningcement [19].

2. Materials

Two different types of samples were investigated. GFRPsamples, made from polypropylene (PP) and long glass fi-bers (LGF) (average length of 7 mm, diameter of about16 lm) as well as CFRP samples, made from polypheny-lene sulfide (PPS) and short carbon fibers (SCF) (averagelength of 100–150 lm, diameter of about 8 lm). All sam-ples were injection molded with an Allrounder 320S (Ar-burg GmbH, Germany) machine to type 1A shouldered testbars based on DIN EN ISO 3167. The different fiber con-tents and injection rates for the GFRP and CFRP samplesare listed in Table 1. For the GFRP samples #1 and #5 with60 wt.% (35 vol.%) fiber content Factor LGF 60-N7 (Cela-nese Corporation) was used and the fiber content was re-duced to 30 wt.% (13.3 vol.%) with Moplen EP 340 K(LyondellBasell) for samples #9 and #13. The CFRP sam-ples #17 and #18 were made from Fortron 0214C1 (TiconaGmbH) and Tenax-A HT-C723 fibers (TohoTenax EuropeGmbH, Germany).

For mechanical testing the samples were used as made byinjection molding. For X-ray tomographic analysis smallsamples ( 10� 4� 10 mm3) were cut out at the position asdepicted in Fig. 1. There, we also depicted the position ofthe sprue, from where the molten polymer-fiber compoundwas injected into the mold.


646 Int. J. Mater. Res. (formerly Z. Metallkd.) 105 (2014) 7

Table 1. Material and injection parameters of the different samples. Note that even though these five specimens have been used, six vol-ume images were analyzed in total. This is due to the fact that GF-60 slow was imaged using both mXCT and mSCT, see also Table 2.

Sample Name Material Fiber content

(wt.%)

Fiber content

(vol.%)

Injection rate

(mm s–1)

Injection time

(s)

#1 GF-60 slow GFRP 60.0 35.0 10 4.3

#5 GF-60 fast GFRP 60.0 35.0 50 0.9

#9 GF-30 fast GFRP 30.0 13.3 50 0.9

#13 GF-30 slow GFRP 30.0 12.3 10 4.3

#17 CF-30 CFRP 30.0 24.3 41.5 /

Table 2. Overview of the specimen sizes used for our experiments.

Sample Name Specimen size

(mm3)

Evaluated volume

(mm3)

mXCT mSCT

#1 GF-60 slow 10�4�10 6�4�6 yes yes

#5 GF-60 fast 10�4�10 6�4�6 yes no

#9 GF-30 fast 10�4�10 6�4�6 yes no

#13 GF-30 slow 10�4�10 6�4�6 yes no

#17 CF-30 10�4�10 10�4�6.7 no yes

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3. Methods

3.1. Synchrotron X-ray micro-computed tomography

Experiments were carried out using beamline ID19 of theEuropean Synchrotron Radiation Facility (Grenoble,France) [20]. In order to reach for a homogeneous incomingwave front for X-ray imaging, ID19 was operated in pinkbeam mode, i. e. only X-ray absorption filters were used tonarrow the bandwidth of the radiation emitted by the beam-line’s insertion devices. Two configurations were deployed,with a mean energy of 36 keV (U17.6 undulator with gap15 mm and 2 mm Al plus 0.5 mm Cu filters) and 65 keV(W150 wiggler with gap 50 and 2 mm Al plus 0.25 mm Cuplus 0.2 mmW filters). The choice of the energy was drivenby the need for reducing the dose to the sensitive samples.The specimens were placed approximately 1 m upstreamof the X-ray imaging detector in order to acquire fringe-dominated images (inline X-ray phase contrast) suitablefor single-distance phase-retrieval [21]. The indirect detec-tor consisted of a 47-lm thick Eu-doped Gd3Ga5O12 sin-

gle-crystal scintillater on top of an undoped Gd3Ga5O12

substrate, its luminescence image is projected by a long-working distance objective (OptiquePeter, France, NA =0.18, 4 · magnification) on the CCD-chip of the ESRF in-house-developed camera FReLoN (type e2v). The resultingeffective pixel distance is 3.75 lm. The tomographic fieldof view was laterally 1.7 · extended by shifting the axis ofrotation to the border of the field of view of the detector,performing a 360 degree tomographic scan and then com-bining corresponding radiographic images which are at a180 degree angular distance. If necessary, single-distancephase retrieval was applied to increase the contrast by usingan adopted version of Paganin’s approach via the ESRF in-house tomographic reconstruction software PyHST_2 [22,23]. The required values of the refractive index of the speci-men were trimmed manually.

3.2. Laboratory X-ray micro-computed tomography

The laboratory X-ray tomograms were scanned using a Na-notom 180 NF CT device (GE Phoenix X-Ray, Germany)



(a) GF-60 slow, lXCT (b) GF-60 fast, lXCT

(c) GF-60 slow, lSCT (d) CF-30, lSCT

Fig. 1. Volume renderings of four from the total of six 3D datasets that will be used in the present paper. See Table 1 for details. Both glass fiber(GF) and carbon fiber (CF) reinforced specimens will be investigated, imaged using either conventional laboratory X-ray micro-computed tomo-graphy (lXCT) or synchrotron radiation-based micro-computed tomography (lSCT) at ID19 of ESRF, Grenoble.

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with a 180 kV nano focus tube, a 2300� 2300 Hamamatsudetector and a tungsten target. For all scans the pixeldistance was 4 lm, the tube voltage was 100 kV and themeasurement current was 80 lA. 1500 pictures averagedfrom 5 frames were taken with a recording time of 500 msper frame for each scan. Phoenix datosx 2.0 was used forthe reconstruction of the 3D-volume. The reconstructionsystem limited the reconstructed size of the samples to6� 4� 6 mm. The samples were positioned at right anglesto the detector and the nano focus tube to ensure that thereis no influence of the alignment of the reconstructed vol-ume data on the analyzed fiber orientation.

3.3. Mechanical testing

Tensile tests in accordance with DIN EN ISO 527–1 to –5were performed to characterize the mechanical propertiesof the different samples. The significant properties to bemeasured in tensile tests are the tensile modulus, the tensilestrength and the elongation at break. The tested sampleswere type 1A shouldered test bars based on DIN EN ISO3167 with a parallel length of 80 mm, a width of 10 mmand a thickness of 4 mm. The tests were made on a tensiletesting machine with a crosshead speed of 1 mm min–1 forthe GFRP-samples and 5 mm min–1 for the CFRP-samples.The tensile modulus was determined as secant modulus be-tween 0.05 and 0.25% strain.

3.4. Image analysis

The image analysis algorithm that we applied to the threedimensional image data created as described above workson gray scale images. Images were prepared by linearlytransforming the input to 8 bit gray scale, rotation aboutthe z-axis using bi-linear interpolation in order to compen-sate for minor sample misalignment, followed by a3� 3� 3 median filter to reduce noise. No further prepro-cessing has been applied to the images.

The algorithm starts by computing the symmetric Hes-sian matrix H of smoothed second partial derivatives ofthe gray values for every point x in the three dimensionalimage f,

H ¼

f rxx f rxy f rxzf rxy f ryy f ryzf rxz f ryz f rzz

0

@

1

A;

where f rxy ¼q2

qxqyf � gr denotes the second partial deriva-

tive of the image convolved with an isotropic Gaussian ker-nel with parameter r in x- and y-directions. The remainingentries are defined analogously. Since H is symmetric, ithas only six degrees of freedom in 3D. The Hessian matrixencodes information about the local gray value curvaturein an image at size scale r. Since we are interested in ana-lyzing fiber systems in the present context, r will be chosento correspond to approximately half of the (known) fiberdiameter, cf. Section 4 for details regarding parameter se-lection. Assume that each fiber can be modeled by a differ-entiable random curve C in R3. The local fiber direction isthen given by the tangent direction on the unit sphere atsome point x 2 Ci in curve i. To model fiber thickness, wecan dilate each C by a disk of radius r > 0 orthogonal to

vðxÞ, resulting in a fiber system. Thus, each fiber is locallycylindric and we can estimate the fiber directions vðxÞ fromH using an eigen decomposition: The eigenvector corre-sponding to the smallest eigenvalue will be approximatelyparallel to v �ð Þ for all points within the fiber system,x 2 U, see [24] for details. To compute orientation tensors[25] we average the tensor products of the thus estimateddirection vectors across the fiber system,

T ¼1

vol Uð Þ

X

x2U

v �ð ÞvtðxÞ:

Note that this results in a volume-weighted version of theorientation tensor which, in case of fibers with constant ra-dii, is equivalent to the length-weighted one.

Long glass fiber reinforced polymers in particular areknown to possess non-stationary fiber orientation distribu-tions [1–3]. In such situations, T is therefore not suitableto characterize these local effects when computed on theentire specimens. To resolve this problem, we compute lo-cal orientation tensors Ti in regions Wi; i ¼ 1; 2; . . . ;m,where m is the number of regions into which an image is se-parated. These regions could have some general shape orposition. But, in order to avoid a bias in some direction,we always use cubic windows. Furthermore, for the purposeof this paper, we consider non-overlapping regions, only,i. e., Wi \Wj ¼ ; for i 6¼ j. This results in a \tiling" of thevolume under consideration, where each tile is a cube defin-ing a region in a three dimensional image. For each Wi, thelocal three dimensional orientation tensor can be computedas

Ti ¼1

vol Wi \Uð Þ

X

x2Wi \U

v �ð ÞvtðxÞ:

This allows for a characterization of non-stationary fiberorientation distributions down to the length scale deter-mined by the size of the windowsWi. Of course, the choiceof the window size is crucial: It must be small enough tomeasure local effects, but it must also be large enough tocorrectly measure the statistical properties within the win-dow. Note that this is a very typical problem related to thechoice of a representative volume element (RVE, see e. g.[26]).

A numerical evaluation of the image analysis method de-scribed in this section is beyond the scope of this paper, but



Fig. 2. Test bar with sprue, direction of injection and position of sam-ples for tomographic analysis.

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can be found in [27]. All image processing and analysis re-sults reported in the present manuscript were obtained usingthe MAVI software package version 1.5 beta (FraunhoferITWM, Germany).

4. Results

Next, we summarize the results from imaging, mechanicaltesting and image analysis. The section closes with a dis-cussion regarding the consistency of the results.

4.1. Tomographic imaging

The five samples investigated in the present paper were im-aged as described above. Note that the lXCT was unable toyield any contrast suitable for image analysis when imagingthe carbon fiber specimen CF-30. Therefore, that samplewas only imaged at ESRF using synchrotron light. There,on the other hand, only the specimen GF-60 slow of all four

GFRP specimens was imaged, thus enabling us to compareresults between lXCT and lSCT, on that dataset.

Figure 3 shows examples of slices through the tomo-graphic reconstructions. Since all the datasets have verysimilar pixel distances, it is possible to compare the qualityof the different images. For the glass fiber specimen GF-60slow, the image qualities achieved using laboratory andsynchrotron lCT are very similar, with a slight advantagefor the synchrotron data which seems to have sharper edges(cf. Fig. 3d and f). This can be explained by the edge-en-hancement, an effect related to X-ray inline phase contrast.For the carbon fiber sample CF-30, image quality obtainedfrom lSCT is again very high, showing a higher noise levelthan the glass fiber samples, but satisfactory contrast. Pixeldistances were small enough in all cases to resolve the fibercross-sections with several pixels, which is sufficient for allimage analysis tasks in this paper.

Single-distance phase retrieval was applied in order to in-crease the contrast by using an adopted version of Paganin’s



(a) GF-30 slow, lXCT, 4 lm pixel spacing (b) GF-30 fast, lXCT, 4 lm pixel spacing

(c) GF-60 slow, lSCT with phase retrieval, (d) GF-60 slow, lXCT, 4 lm pixel spacing

3.75 lm pixel spacing

Fig. 3. Example grayscale slices from different specimens and tomograms used for the present papers. These slices show the gray values after ap-plying a 3� 3� 3 median filter and linearly spreading the gray value range from the original 12/16-bit data to 8 bit grayscale.

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approach via the ESRF in-house tomographic reconstruc-tion software PyHST_2 [22, 23]. Phase-retrieval by meansof holotomography or other less sophicsticated approacheshas already been demonstrated to be highly beneficial forthe study of fiber systems in terms of contrast enhancementand noise reduction which support a subsequent volume im-age analysis [17]. As inline X-ray phase contrast enhancesborders, the applied phase retrieval can also be useful in alater stage to measure exact size.

In our case, phase retrieval reduced noise, but did notlead to a significant increase in quality (see Fig. 3c vs.Fig. 3f and Fig. 3g vs. Fig. 3h). Thus, for the purpose ofthe present paper, phase retrieval turned out not to be neces-sary and will not be considered any further in the presentpaper.

4.2. Mechanical testing

Results from mechanical tests as described in Section 3 aresummarized in Figs. 4 to 6. Clearly, the mechanical proper-ties of the GFRP samples are dominated by fiber content:The two GF-samples with 60 wt.% fiber content have a ten-sile modulus almost 10 GPa above the one of the specimens

with only 30 wt.% (Fig. 4), and a tensile strength that ishigher by almost 50 MPa (Fig. 5). Also, the specimens withhigher fiber content exhibit less deformation (Fig. 6). How-ever, the different injection times of 4.3 sec and 0.9 sec forthe slow and fast specimens, respectively, induce signifi-cant differences at both tested fiber content levels in thetensile modulus (6.9% for GF30 and 7.6% for GF60) aswell as in the tensile strength (7.8% for GF30 and 5.6%for GF60). This can be seen in the magnification insets inFig. 4 and in Fig. 5.

An exact calculation of theoretical stiffness values for in-jection-molded structures requires micromechanical mod-eling and FE-methods [28]. As a quantitative correlationbetween the results of the mechanical tests and the mea-sured fiber orientation is not a goal of this paper, we dis-pensed with a detailed comparison between the theoreticalstiffness and the measured value. For this reason, the theo-retical stiffness EC is estimated as indicated by Thomason[29] by:

EC ¼ g0 � E1 þ 1� g0ð Þ � E2;

where g0 is the orientation parameter and E1 and E2 are themoduli of a unidirectionally reinforced laminate calculated



(e) GF-60 fast, lXCT, 4 lm pixel spacing (f) GF-60 slow, lSCT, 3.75 lm pixel spacing

(g) CF-30, lSCT, 3.75 lm pixel spacing (h) CF-30, lSCT with phase retrieval. A void is visiblein the top-right part of this slice, 3.75 lm pixel spacing

Fig. 3. (continued)

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from the Halpin–Tsai equations [30]. For our purpose, wecomputed g0 by dividing the orientation tensor’s diagonalcomponent corresponding to the injection direction by thetrace of T, cf. Section 4.3. A comparison between the calcu-lated and the measured stiffness values can be found in Ta-ble 3. The predictions based on VV measured from CT-images are closer to the measured stiffness results than

those when using the theoretical values. Furthermore, val-ues of VV measured from CT-reconstructions allow for pre-diction of differences due to injection parameters (slow/fast). The differences in stiffness caused by injection speedin our experimental measurements and based on our mea-sured VV agree well, see Table 3. Only for the CFRP speci-men, for which we assumed an isotropic behavior of thecarbon fibers, is there a large deviation between the mea-sured and the calculated stiffness. One reason for this couldbe that the calculated values are based on an equation forlong fiber materials. In [31] the modulus is obtained de-pending only on a change of VV, which then leads to goodresults (&19.5 GPa).

The CFRP sample CF-30 exceeds the GFRP specimensboth in terms of tensile modulus and in terms of tensilestrength due to different materials properties of fibers (car-bon fiber) and matrix (PPS instead of PP). Note howeverthat the carbon fiber reinforced specimen has been includedin the present study not for the purpose of comparing itsmechanical properties to GFRP, but rather to test the applic-ability of lXCT and lSCT as well as image analysis to bothmaterials.

4.3. Image analysis

In a first step, the local orientation tensors Ti were com-puted in regions Wi of size 50� 50� 50 pixels (corre-sponding to a volume of (200 lm)3 in case of the lXCTdata), completely covering the imaged areas of each data-set. Then, the components of Ti were averaged orthogonallyto the thickness direction of each sample. The thickness di-



Fig. 4. Tensile modulus. Enlarged insets show details of the 30 wt.%and 60 wt.% results. The slowly injected specimens were measured tohave a higher tensile modulus by 0.4 GPa and 1.1 GPa at 30 wt.% and60 wt.% fiber content, respectively, when compared to the correspond-ing specimens with shorter injection times. Note that CF-30 is includedhere for completeness, only. As noted above, the glass and carbon fibersamples have different matrix materials with E PPð Þ � 1:4GPa (GF-30and GF-60) and E PPSð Þ � 3:4GPa (CF-30).

Fig. 5. Tensile strengths. Enlarged inset shows detail of the 30 wt.%and 60 wt.% results, respectively. The slowly injected specimens weremeasured to have a higher tensile modulus by 5.9 MPa and 6.3 MPa at30 wt.% and 60 wt.% fiber content, respectively, when compared to thecorresponding specimens with shorter injection times.

Fig. 6. Elongation at break for the tested glass fiber samples, only.These results are in line with the measurements from Fig. 4 andFig. 5. Here, the more slowly injected specimens can be seen to exhibita lower degree of deformation prior to failure.

Table 3. Comparison between calculated and measured stiffness values of the analyzed samples. Measured fiber volume fractions VV

taken from Table 4.

Measured stiffness

(GPa)

Theoretical stiffness

(theoretical VV) (GPa)

Theoretical stiffness

(measured VV) (GPa)

g0

GF-30 slow 6.0 7.3 6.3 0.65

GF-30 fast 5.6 7.1 5.6 0.62

GF-60 slow 15.2 16.0 14.9 0.59

GF-60 fast 14.1 15.6 13.6 0.57

CF-30 19.7 33.6 30.6 0.62

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rection is the normal direction of the flat surfaces of eachtest bar. This procedure results in the plots in Fig. 7, wherethe diagonal components of Ti corresponding to the direc-tion of injection in Fig. 2 are plotted across the thicknessof each specimen. As the fibers should be aligned along thisinjection direction, larger values are expected. Yet, as canbe seen in Fig. 7 (left), the GFRP samples show a signifi-cant drop of fiber fraction aligned to the injection directionin the central areas. This is true independently of the fibercontent and injection speed. But the specimens injected atlower speeds retain a statistically significantly higher de-gree of alignment especially in those central areas – bothat 30 wt.% and 60 wt.% fiber content, cf. Fig. 7 (left).

Figure 7 (right) repeats the measurement results on GF-60 slow, and adds the results from the two lSCT recon-structions: Measurement results on laboratory and synchro-tron lCT data are in good agreement, with statistically in-significant differences in the central areas and an accuratematch in positioning the misaligned central area. Further-more, Fig. 7 (right) reveals that the carbon fiber reinforcedspecimen CF-30 retains a high level of fiber alignment ininjection direction all throughout the specimen. Note onceagain that CF-30 could not be imaged using a lXCT systemand hence that sample appears only in one of those plots.

Although the results in Fig. 7 are consistent, they do notyet explain the significant differences in tensile modulusand strength reported in the previous section. Mechanicalproperties in such samples are dominated by fiber content.Therefore, fiber volume fractions (also known as volumedensity, VV ) were computed on binarized versions of thelCT-reconstructions, see Table 4. Threshold values werechosen manually such that the binarized images representedthe visible fiber system well. The resulting values of VV

match fairly well to the theoretical values of 13% and35% corresponding to 30 wt.% and 60 wt.% fiber content,

respectively, but significant differences between measuredand theoretical fiber volume fractions exist (see Table 4).The reason for this difference is unknown. These discrepan-cies may be caused by inhomogeneity, but, as the theoreti-cal results from Section 4.1 show, the volume fractions de-termined by image binarization seem to fit better to theresults from mechanical testing than the theoretical fibervolume contents. The slowly injected GFRP samples bothhave a higher fiber volume fraction than their more quicklyinjected counterparts, but those differences are not statisti-cally significant (error margins of VV in Table 4 correspondto standard deviations of the fiber volume fraction com-puted in (400 lm)3 windows across each dataset). The fibervolume fraction did not vary strongly through the thickness,especially in the specimens with 30 wt.% fiber content, cf.Fig. 8. In the case of 60 wt.% fiber content, we observesome density variations at about 1 mm and 3 mm from thesurface, which corresponds to the points of fiber reorienta-tion in Fig. 7.

Another relevant point is the thickness of the misorientedregions in the GFRP specimens. To this end, we identifiedthe regions Wi in every image of the GFRP specimens forwhich the diagonal components in injection direction ofthe respective orientation tensor Ti dropped below a valueof 0.6. Then, we computed the minimal volume boundingbox using the MAVIparticle toolbox (Fraunhofer ITWM,Germany). Note that this minimal volume box is not neces-sarily aligned with the coordinate system on the image;thus, define the thickness of the misaligned fiber regionsas the thickness of this box. Results are also given in Ta-ble 4. Using this definition, the misaligned fiber areas inthe slowly injected GFRP specimens are always thinnerthan the ones in their more quickly injected counterparts.Results between synchrotron and laboratory X-ray lCT dohowever disagree by almost half a millimeter. This last



Fig. 7. Orientation tensor components plotted across the thickness of the samples. Left: Comparison of the four glass fiber-reinforced specimensfrom conventional lXCT (4 lm pixel spacing). Right: Comparison of results regarding GF-60 slow from conventional lXCT against results onlSCT data, and measurement results on CF-30 (lSCT only).

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point requires further investigation for the possible causes.In summary, consistent drops in fiber alignment could be

measured in all GF specimens, where the datasets GF-30slow and GF-60 slow have only thinner misaligned layersthan GF-30 fast and GF-60 fast, respectively. This can beinterpreted as a geometric explanation for the small yet sta-tistically significant differences between the measured ten-sile properties at each glass fiber weight level.

5. Discussion

Micro-computed tomography is a suitable imaging technol-ogy for quantitative, local analysis of both glass and carbonfiber systems in reinforced polymers. Results regardingglass fiber systems from conventional lXCT and lSCTare in good agreement, both in terms of image quality andquantitative analysis results [32–34].

Tensile modulus and strength of GFRP specimens aredominated by the fiber content, but significant differences

in the efficiency of the materials were observed dependingon the speed of injection. These differences could success-fully be correlated with the thickness of misaligned regionsof the fiber systems. This agrees well with results reportedelsewhere (e. g. [1] and references therein). A three dimen-sional image analysis algorithm to quantify this effect wasproposed in the present paper.

For carbon fiber systems, the state of the art in lCT stillseems to require researchers to turn to synchrotron radia-tion. There, high quality three dimensional reconstructionscan be achieved. Given such a reconstruction, we were ableto demonstrate in the present paper that the image analysismethods applicable to glass fiber reinforced polymers eas-ily transfer to carbon fiber reinforced ones.

Three dimensional image analysis of fiber reinforcedpolymers is not limited to volume fractions and fiber orien-tation tensors, as suggested in the present paper. Fiberthicknesses, inter-fiber distances, matrix defects and othercharacteristics can also be determined. Yet, those two geo-metric characteristics seem to be sufficient to explain thedifferences observed during mechanical testing of the spe-cimens that were investigated, here. Quantitative analysisof fiber reinforcements from tomographic reconstructionsis currently hindered by the tradeoff between resolutionand field of view, which is inherent to this imaging technol-ogy: High resolutions are achievable with laboratory X-rayCT systems, i. e., in the order of 1 lm pixel distance. Atthose high resolutions, segmentation of individual fibers ispossible at least in some cases. However, long glass fiberswith lengths of several millimeters can no longer be ob-served completely. Also, spatial inhomogeneity such as dis-cussed in the present paper is difficult to judge due to scale.Going to lower resolutions, i. e., in the order of 10 lm pixeldistance, enlarges the field of view to image spatial homo-geneity and to a size scale beyond the expected fiberlengths, but segmentation of individual fibers is no longerfeasible there due to missing details.

The focus of the present paper is aiming at the explana-tion of measured mechanical differences. The results of thispaper, however, open the path for future research regardingmodeling and virtual material design of composites.

This work was partially funded by the German Federal Ministry of Edu-cation and research project \AMiNa" (BMBF grant 05M10AMA). Theauthors are grateful to Helga Riedel for help with visualizations.



Table 4. Image analysis results on the specimens. Standard deviations for the fiber volume fractions were computed using (400 mm)3

subfields. Fiber volume fractions were measured using manually chosen threshold values, and the resulting volume densities deviatefrom the theoretical ones. However, these measured volume fractions yielded a better fit to the measured mechanical behavior of thespecimens than the theoretical ones (Section 4.2). Note that the thicknesses of the misoriented layers were measured in terms of theminimal volume bounding boxes of regions where the diagonal entry of the orientation tensor corresponding to the injection directiondropped below 0.6. This box does not lie parallel to the coordinate system, in general.

Theoretical fiber

volume fraction (%)

Measured fiber

volume fraction (%)

Thickness of misoriented

layer (mm)

GF-60 slow 35.0 31.2 ± 5.7 3.13

GF-60 fast 35.0 29.1 ± 5.0 3.47

GF-30 slow 13.3 10.8 ± 1.5 1.98

GF-30-fast 13.3 9.5 ± 1.6 2.68

GF-60 slow, synchrotron 35.0 31.5 ± 2.5 2.64

CF-30, synchrotron 24.3 22.0 ± 0.7 n/a

Fig. 8. Fiber volume fractions in the four GFRP specimens against thethickness, in steps of 400 lm. Note that the evaluated thicknesses varydue to the necessity to crop the image data at the borders in order to ob-tain regions which are entirely filled with material, and due to the factthat the slices were 400 lm thick, here.

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(Received September 15, 2013; accepted April 7, 2014; on-line since May 13, 2014)

Correspondence address

Dr. Oliver WirjadiFraunhofer ITWMFraunhofer-Platz 167663 KaiserslauternGermanyTel: +49-631-316004396Fax: +49-631-316005396E-mail: [email protected]

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DOI 10.3139/146.111082Int. J. Mater. Res. (formerly Z. Metallkd.)105 (2014) 7; page 645–654# Carl Hanser Verlag GmbH & Co. KGISSN 1862-5282



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