An experimental study of fibre waviness and its effects on compressive properties of unidirectional NCF composites

Accepted Manuscript An experimental study of fibre waviness and its effects on compressive properties of unidirectional NCF composites D. Wilhelmsson, R. Gutkin, F. Edgren, L.E. Asp PII: DOI: Reference:

S1359-835X(18)30054-X https://doi.org/10.1016/j.compositesa.2018.02.013 JCOMA 4927

To appear in:

Composites: Part A

Received Date: Revised Date: Accepted Date:

3 November 2017 30 January 2018 8 February 2018

Please cite this article as: Wilhelmsson, D., Gutkin, R., Edgren, F., Asp, L.E., An experimental study of fibre waviness and its effects on compressive properties of unidirectional NCF composites, Composites: Part A (2018), doi: https://doi.org/10.1016/j.compositesa.2018.02.013

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An experimental study of fibre waviness and its effects on compressive properties of unidirectional NCF composites D. Wilhelmssona , R. Gutkinb , F. Edgrenc , L.E. Aspa,∗ a Industrial

and Materials Science, Chalmers University of Technology, H¨ orsalsv¨ agen 7A, SE-41296 G¨ oteborg, Sweden b Swerea SICOMP AB, G¨ oteborg, Sweden. c GKN Aerospace Sweden AB, Flygmotorv¨ agen, SE-46181 Trollh¨ attan, Sweden

Abstract In this paper a comprehensive experimental study on effects of different fibre waviness characteristics on the compressive properties of unidirectional non-crimp fabrics (NCF) composites is presented. The fibre waviness ranges from periodic to random with medium to large misalignment angles. As expected, fibre waviness is found to strongly impair the compressive mechanical properties of the composite. It is demonstrated that the maximum fibre misalignment alone can be used to accurately predict strength with analytical kinking criteria. Furthermore, there is a direct correlation between waviness and a knock-down factor on stiffness with approximately 5 %/degree mean fibre misalignment angle. Analysis of the extension of the misaligned regions (defects) provides additional evidence that defect extension in the transverse direction is more critical than in the longitudinal direction, supporting earlier theoretical predictions in the open literature. Keywords: A. Carbon Fibres, A. Fabrics/textiles, D. Microstructural analysis, D. Mechanical testing

1. Introduction With ever increasing traffic levels, the civil aircraft industry is in constant need of new technologies to make air travel environmentally sustainable [1]. One such technology is lightweight materials for reduced fuel consumption. For example, the amount of carbon fibre reinforced composites (CFRP) in the Airbus A350XWB is 53 % by weight [2], mainly in its fuselage and wings. ∗ Corresponding

author Email addresses: [email protected] (D. Wilhelmsson), [email protected] (R. Gutkin), [email protected] (F. Edgren), [email protected] (L.E. Asp)

Preprint submitted to Composites Part A

February 9, 2018

CFRP fan-blades were successively introduced in a civil aircraft engine (GE90) in 1994 [3] and there is now interest to increase the use of CFRP in cold and moderately high temperature parts of the engines. The outlet guide vanes is an example of such a part. The current research is carried out in response to an industrial interest of cost-effective CFRP components in load carrying parts of the engine. The preferred manufacturing process is an automated, out-of-autoclave method based on resin transfer moulding (RTM) and non-crimp fabric (NCF) as reinforcement. One problem for the use of NCF composites in these applications is their lower compressive strength due to higher waviness of the carbon fibres compared to tape-based unidirectional (UD) composites. The complex meso-structure of NCF composites and its effect on the compressive strength is currently not well understood. Robust sizing methods, relying on such understanding for these applications are needed. The compressive failure mechanism in this context is formation of kink-bands and it was understood already in 1972 [4] that this process is driven by matrix-shearing and thus governed by initial fibre misalignments with respect to the laminate and loading direction. It is a topic studied for many years but mainly for UD tape-based composites where the fibre arrangement is fairly homogeneous within each ply. NCF composites have fibres organised in a fabric with e.g. glass fibre weft yarns resulting in imperfections on the meso-scale, which affect how the composite behaves under compressive loading [5]. In this study we provide fundamental understanding of how fibre waviness, fibre volume fraction Vf and laminate thickness influence the compressive stiffness and strength of NCF composites. This information is generated via an extensive experimental study of unidirectional NCF composites, varying these characteristics. Furthermore, to assess the influence of fibre waviness on compressive properties, we use an in-house method for measurements of fibre orientations [6, 7]. The microscopy method is utilized to characterise the out-of-plane waviness for a large number of specimens and relate these to the measured stiffness and strengths in compression tests. To date, most studies seeking to quantify influence of variations in the fibre waviness have used modelling while considering idealised waviness characteristics in terms of amplitude and wavelengths [5, 8–13]. Our approach has instead been to link the experimentally measured waviness to compressive properties by statistics such as the mean and maximum fibre misalignment angles. The obtained fibre waviness is ”authentic” in all samples, meaning that it is generated only by the material architecture and the RTM manufacturing process. The measured fibre waviness ranges

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from periodic to random spatial distributions and from medium to high in magnitude. Numerical studies by Liu et al. [14] and Sutcliffe [15] have suggested an imperfection size effect on compressive strength of composites. In the current study, we examine measured fibre waviness characteristics to see if such size effects can explain subtle differences in observed strength for different laminates with random waviness. To the best of our knowledge, this is the first experimental study performed on this topic. The fibre waviness is more representative for NCF composites than prepregs but the findings are considered relevant for all types of continuous CFRP architectures. This novel study provides a comprehensive database to deepen our understanding of compressive failure in NCF composites.

2. Experimental 2.1. Material and Specimens The composite material is based on HTS45 carbon fibres from Toho Tenax [16] and LY556 epoxy resin produced by Huntsman [17]. The UD-textile was supplied by Porcher industries [18] and consists of 12k bundles held together by a polyamide/glass yarn in the weft direction, see Fig. 1. There are 2.4 bundles/cm and 1 weft yarn/cm. The thickness of the textile is 0.3 mm and becomes 0.2 mm at a Vf of 53 %. The areal mass is 205 g/m2 for the textile and 192 g/m2 for the fibres without sizing. Laminates were manufactured with RTM according to Table 1. 1.6 mm glass/epoxy laminate tabs were then adhesively bonded on each side before water-cutting the specimens. The specimens were produced for testing with ASTM D6641 and ASTM D3410 standards [19, 20] with nominal size of 140 × 12 × 2 mm (length × width × thickness) and a gauge section length of 13 mm. An ultrasonic C-scan technique was used to verify a low porosity level in all laminates. The laminates presented in Table 2 have different fibre volume fractions and thicknesses which are based on realistic variations in a future aeroengine component. These laminates have been divided into three groups A, B and C based on their manufacturing details, which are presented in Table 1. Plate A1 according to Tables 1 and 2 have been manufactured and previously tested by Bru et al. [21]. The laminates with a nominal thickness of 2 mm from group B all have a greater out-of-plane waviness than laminates from groups A and C. The most probable cause for this is that the textile preforms were compressed longitudinally by the ”small” RTM tool used for this group, which

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would amplify any waviness already present.The extensive out-of-plane waviness resulting from manufacture of Plates B would never be allowed in a material qualification test-campaign for the aerospace industry. Nevertheless, they are included in the current study to add diversity given their extreme waviness. 2.2. Compression tests Compressive testing was performed according to ASTM D6641 [19] and ASTM D3410 [20] with the ambition to characterise the material strength and stiffness. The main difference is that the former introduces load by shear and end load via the combined load compression (CLC) fixture and the latter by shear exclusively (ITRII fixture). The CLC fixture was made at Swerea SICOMP according to ASTM D6641 [19] and the ITRII fixture was manufactured by Wyoming Test Fixtures. The ITRII fixture was used to rule out any influence of the test fixture on the bending. No significant differences in test results between the two methods were observed in the current work. Thus confirming earlier results by Wegner and Adams [22]. For this reason all tests on the C laminate and on the majority of the B-laminates were performed in the CLC fixture. The usage of these two methods is reported in Table 3. Testing was conducted at the Swerea SICOMP laboratory in M¨olndal, Sweden, in a 100 kN MTS 20/M load rig. Compressive loading was applied at a rate of 1.3 mm / min until a drop in load was indicating failure. Potential bending was checked with strain measurements on a few specimens from each laminate according to ASTM standards [19, 20]. Both of these standards allow a maximum of 10 % bending at failure for a test to be considered valid and it is noted in Table 3 that most of the laminates exceeded this requirement. Bending of specimens in compressive testing can potentially lower the strength and yield inaccurate results. The authors have analysed any potential effect from a flexural contribution on the compressive load in detail to avoid misinterpretation of or scepticism towards the presented experimental results. Another phenomena, which can be confused with bending but not necessarily related is Euler buckling (instability). The proofs presented below is therefore twofold, firstly that bending does not have a significant effect the compressive results and secondly that Euler buckling does not occur in any of the tested specimens: i) There is no correlation between the strength data of individual specimens and bending at failure, i.e., specimens with high bending at failure may have high strength and specimens with low bending

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at failure may have low strength. ii) Dimensions of the specimens are according to the ASTM standards [19, 20], such that no Euler buckling shall occur. It should be noted that the theoretical prediction is similar to a pin-ended column, which is considered to give a conservative assessment. iii) Fractographical evidence which proves that fibre kinking is the failure mechanism also for specimens with high recorded bending values is presented in Fig. 2 and Fig. 3. Such fibre terraces show fibres which have failed at equal length and subsequently leading to formation of kink-bands [23]. These are a key characteristic of compressive failure and rule out the possibility of Euler buckling. Further morphological evidence for kinked fibres such as the compression / tension faces on individual fibres has been observed in these samples but is not presented here. A separate study has also been performed by the authors to study the effect of out-of-plane fibre waviness on bending [24]. It was concluded that a combination of the wavy textile architecture and too small strain gauges both are contributing factors to the recorded bending. Up to approximately 10 % bending can be caused by the out-of-plane fibre waviness alone. The conclusion from the investigation on bending is that failure by kinking is the dominant failure mechanism. For these reasons the results from tests on specimens with high bending can be included in the study even though they deviate from the limit set by the standards. The physical motivation to why bending does not necessarily affect the compressive strength could be explained by the strain gradient effect reported by Wisnom [25]. 2.3. Measurements of out-of-plane fibre waviness This study is limited to characterisation of the out-of-plane waviness since kinking exclusively occurred out-of-plane in the compression tests of UD NCF composites loaded in parallel with the fibres. This observation agrees with previous studies on the compressive strength of NCF composites [5, 26]. The method proposed by Wilhelmsson and Asp [6, 7] has been used for measurements of fibremisalignment angles in section planes parallel to the nominal fibre direction as seen in Fig. 4. Two sections, each with a length of 20 mm were sampled from each specimen as shown in Fig. 5. These regions were chosen as close as possible to the gauge section, but were not to contain any damage. The number of sections analysed for fibre waviness from each laminate (nθ ) is specified in Table 4. The method for characterisation of fibre waviness is based on image analysis, where the angle of individual fibres are measured explicitly from detailed micrographs. The method is direct, meaning

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that the angles are measured by tracing individual fibres one at a time. The micrograph is read into Matlab and then divided into smaller regions called cells, such that curved fibres appear straight and the angle can be measured by straight line-segments. The cell size determine the spatial resolution and it has been possible to achieve a spatial resolution of 55 µm from an optical magnification of only 50 times. The cells consists of 50 pixels × 50 pixels at this resolution, which is equal to 1.1 µm per pixel. With a ply thickness of approximately 200 µm, the result is four cells per ply. Typically, between three and four fibres per cell are measured, which give a total of 50,000 fibres with approximately 12,000 cells in the whole domain. Once the mean misalignment angle for each cell has been calculated, the spatial distribution and probability distribution of the fibre misalignment angles can be plotted. The mean angle for the global-micrograph-domain, i.e. the mean misalignment angle, is calculated as n

1X ¯ θ¯ = |θi |, n i=1

(1)

where |θ¯i | is the absolute value of the mean fibre misalignment angle in the i:th cell and n is the number of cells containing a measurement. Typically, around 97 % of all cells have measurements. This deviation from 100 % is due to the matrix-rich regions and weft yarns. A number of spurious measurements of fibre misalignment angles are typically obtained for each measured sample, either due to the image analysis algorithm or due to fibres having an abnormal orientation. The maximum misalignment angle of all fibres is thus not representing the true maximum misalignment. The number of spurious measurements are typically less than a few permille of all measurements. Therefore, we define the maximum misalignment angle θmax as the value of the 99:th percentile of the experimentally characterised distribution for |θ¯i | and thereby obtain a margin related to these spurious measurements. The fibre waviness in this study is random for some of the laminates and it is not feasible to characterise the waviness in terms of amplitude and wavelength by conventional spatial measurements in such cases. The approach adopted in this study is to transfer results from the spatial domain to the frequency domain by Fourier transform as done by Clarke et al. [27]. In that study, the waviness spectral contributions were characterised in terms of slopes, motivated from previous work by Slaughter and Fleck [28]. The misalignment data as shown in Fig. 6 is used directly for the analysis, where a 2D discrete Fourier transform is performed in Matlab using the fft2 (fast Fourier transform) function, where 7


the slopes are obtained as tan θ¯i . The sampling frequency is dictated by the spatial resolution of 55 µm, which results in a sampling frequency of 18.2 slope-values per mm. If we assume that 10 sampling points are needed per wavelength, then the minimum detectable wavelength in this analysis is 0.55 mm or 1.82 Hz. The spectral contributions of slopes from the 2D fft are clustered at the lowest frequencies for the thickness direction and we are only interested in the spectral contributions along the longitudinal direction. Therefore, the 3D data is reduced to 2D by averaging of the five lowest frequencies in the thickness direction. This gives a spectral density distribution of slopes for one measured micrograph, i.e the slopes as a function of spatial frequency. Since there are 10-12 samples per laminate, a laminate spectral density distribution of slopes is calculated as the mean of these. The results of this analysis are presented in section 3.1.

3. Results and discussion The main results for waviness, stiffness and strength are summarised in Table 4. Section 3.1 shows results of the measured waviness and highlights differences between the different laminates. The mean fibre misalignment angles are then related to the stiffness reduction in section 3.2. The effect of waviness on strength is presented in section 3.3 with two subsections. Section 3.3.1, presents the maximum fibre misalignment angles with respect to the strength reduction and compares to analytical kinking criteria. Finally, the effect of size and extension of misaligned regions is presented in section 3.3.2 3.1. Fibre waviness characteristics ¯ θmax ) for each laminate are presented The mean and maximum fibre misalignment angles (θ, in Table 4 together with the coefficient of variation (CV) for θ¯ (CVθmax ≈ CVθ¯). Two groups can be identified in terms of these waviness statistics. The group B1, B2 and B3 have a high relative waviness (θ¯ ≈3 ◦ , θmax ≈8 ◦ ) and the group A1, B4, C1, C2, C3 and C4 have a low relative waviness (θ¯ ≈1.5 ◦ , θmax ≈5 ◦ ). These groups are hereafter referred to as high and low waviness. The spatial distribution of fibre misalignment angles is presented in Fig. 6 for representative measurements on laminates. Note that these plots are based on raw data from the measurements and no averaging or smoothing has been done. Results for B3 and C2 come from the same specimens and measurements as in Fig. 4 and Fig. 7, respectively. The distributions for B1 and B2 are represented 8

by a sample from B1 since they are similar. The complete analysis on waviness characteristics is presented below but it may already at this point be noted that the waviness ranges from periodic to random. For the characterisation of fibre waviness in terms of slope and wavelength, results are presented in Fig. 8, based on the method described in section 2.3. These results are presented as two plots, one for high waviness Fig. 8(a) and one for low waviness Fig. 8(b). The curves are normalised with the maximum value of the slopes in Fig. 8 and plotted against the spatial frequency which is equal to the inverse of the wavelength. The shape of the slope spectra for laminates B4,C1,C2,C4 were similar and thus combined into one curve as the average of these. Fig. 8(a) reveals that the highest slopes for B1 and B2 are associated with a dominant wavelength of 11 mm (1/0.09). Reasonably, this characteristic wavelength originates from the textile architecture and more specifically from the longitudinal spacing of weft yarns in each ply, which is 10 mm. Laminate B3 has an additional wavelength of 5.5 mm associated with high slopes, which is half the characteristic wavelength. The results in Fig. 8(b) show that the laminates with low waviness have slopes that are more distributed with different wavelengths. The flat topped slope spectra is associated with random waviness and this analysis confirms the assumptions made by Slaughter and Fleck [28] in studies of random fibre waviness when no characterisations of this kind where available. Interestingly, laminates which appear to be random (B4,C1,C2,C4), also have a wavelength where the highest slopes can be related to the periodicity of the textile. It should be stated that the results in Fig. 8 can also be obtained by performing the Fourier transform directly on fibre angles instead of slopes. The waviness characteristics are summarised for the two groups of high and low waviness below, based on the presented results:

High waviness: • Laminates B1 and B2 show the same distribution, which is periodic with a dominant wavelength of 11 mm and a peak amplitude of 0.1 - 0.15 mm. • Laminate B3 is periodic but to a lower degree than B1 and B2. Low waviness: • Laminate A1 is periodic. However, the periodic occurrence of weft yarns in the longitudinal direction has a special effect on the waviness which is not seen in any of the other laminates. It 9

results in longer distances with straight fibres in-between the regions with high misalignment angles. • Laminate B4 has random waviness in general but weak signs of periodic waves were seen in some samples. • Laminate C1 has random waviness in general but weak signs of periodic waves were seen in some micrograph samples. This is confirmed by the highest amplitude for a wavelength of 11 mm, which is related to the textile architecture. • Laminates C2 - C4 have random waviness. The probability distributions of experimentally characterised fibre misalignments for more than 50,000 fibres per laminate is plotted in Fig. 7 together with fitted normal probability density functions (PDF). The probability distribution for B2 is representative for B1, B2 and B3, which have periodic waviness and high amplitude and the probability distribution for C2 is representative for B4, C1, C2, C3 and C4, which have random waviness and low amplitude. Note that a laminate with random waviness (C2) is more closely related to a normal distribution than is a laminate with periodic waviness (B3). Laminates with periodic waviness are more sensitive to the size of the measured region (2 mm × 20 mm) than laminates with random waviness, considering their ”main” wavelength of 11 mm. This may be one explanation to the larger deviance from a normal distribution. A1 is a special case with periodic but non sinusoidal waviness where the probability distribution is close to a normal distribution but with higher peak and longer tail. Although a number of the laminates in the current study are reported to have a periodic waviness, the observed periodicity is not fully periodic, i.e. with a constant wavelength as suggested in earlier studies for cross-plies or quasi-isotropic laminates [5, 12]. The waviness is more random due to the non-periodic occurrence of weft yarns in the longitudinal direction. Furthermore, the weft yarns contribute more to the waviness than intended in these laminates. If the micrograph in Fig. 4 (a) is studied, one can see that some of these weft yarns retain their original circular shape, which has a great effect on the waviness in the nearby region. Sutcliffe et al. [29] performed a similar characterisation of out-of-plane waviness for an RTM processed CFRP component and reported a standard deviation of the misalignment angles of 1.63◦ . Laminates A1, B4 and C1 - C4 have a similar waviness magnitudes with standard deviations of 1.7 2.0◦ . Laminates B1 - B3 have standard deviations of 3.4 - 3.8◦ . 10

3.2. Effect of fibre waviness on stiffness The compressive elastic modulus is evaluated from the mean strain between 0.1 and 0.3 % according to the standards [19, 20]. The measured compressive elastic moduli for the laminates are presented in Fig. 9. The stiffness is ranging from 100 - 140 GPa and is greater for increased Vf as expected. The significant variability of the B - group laminates is noted and this is due to the problems with bending as explained in section 2.2. Interestingly, the average values seem trustworthy based on the expected response from varying the fibre volume fraction. The measured compressive elastic moduli are compared to the analytical, homogenized, stiffness by the rule of mixture (ROM) in Fig. 10, where the experimental results have been divided into two groups based on out-of-plane waviness. The material data for fibre and matrix used in ROM is presented in Table 5. As reported above, laminates A1, B4 and C1 - C4 have a low waviness (θ¯ ≈1.5 ◦ ) and laminates B1 - B3 have a high waviness (θ¯ ≈3 ◦ ). A reduction in the experimental elastic modulus to the analytical prediction by ROM is observed with the reduction being greater for the group of laminates with high waviness than for the group of laminates with low out-of-plane waviness. A difference in slope of the two groups can also be seen, meaning that an increase of Vf has greater impact on the stiffness for laminates with low waviness than for those with high waviness. We define the reduction in stiffness with a knock-down factor as   Eexp Knock-down factor η = 1 − × 100, EROM

(2)

where Eexp is the the experimental stiffness and EROM is the analytical value by ROM. The knockdown factor η is plotted in Fig. 11 where the knock-down factor is a function of the mean angle. The curve fit to experimental data shows an increase of approximately 5 % / degree mean misalignment angle in the range 1 - 3◦ . Note that this plot is only based on the out-of-plane waviness and the correct response is dependent also on the fibre misalignments in-plane. It is then interesting to observe that an extension of the fitted curve towards a mean misalignment angle of zero results in a knock-down factor close to zero. This suggests, either that the magnitude of in-plane waviness is dependent on the out-of-plane waviness or that the in-plane waviness is small with respect to the out-of-plane waviness. Relating the knock-down factor to a mean angle is convenient since it requires no assumptions on the type of waviness, which is often assumed to be periodic [5, 12].

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3.3. Effect of fibre waviness on strength 3.3.1. Experimental results and comparison to analytical models The measured compressive strength for all laminates is presented in Fig. 12 and the strain to failure cu is presented in Table 4. As for stiffness two groups are identified where laminates with high fibre waviness (i.e. B1 - B3) have a compressive strength of approximately 400 MPa, whereas laminates with lower waviness (B4, C1 - C4) have a compressive strength around 750 MPa. The strength of laminate A1 is in between these groups but closer to group C. The compressive strength is shown together with the maximum misalignment angle θmax in Fig. 13 with the compressive strength on the left Y-axis and the maximum misalignment angle on the right Y-axis. The main purpose of this graph is to show trends within the groups. A clear correlation exists between the maximum out-of-plane misalignment angle and the compressive strength for the two groups of laminates, with high waviness (B1 - B3) and and low waviness (B4, C1 - C4). The experimental error in terms of CV in Table 4 for both the strength data and waviness measurements are similar. Consequently, these results support the conclusion by Liu et al. [14] that large variations in fibre waviness cause the large scatter typically observed in compression strength data. Another observation based on the presented strength data is that any effect of laminate thickness on strength is subordinate the effect of waviness. Laminate C4 has a similar waviness to laminate C2 and also similar strength, whereas laminate B4 has higher strength than laminates B1 - B3 with a higher waviness. One of the aims of this study is to quantify the initial fibre misalignments in unidirectional NCF laminates and relate them to the compressive strength. It is clear that this variable has a significant effect on the compressive strength. Predictions of compression strength by models typically involves a parameter which describes the initial fibre misalignment. The kinking criteria by Argon [4] in Eq. 3 and Budiansky [30] in Eq. 4 are evaluated to see how these can be related to the experimental results via the maximum misalignment angle. The compressive strength Xc is predicted as τy , φ0 τy = , γy + φ0

Xc,Argon = Xc,Budiansky

(3) (4)

where τy is the shear yield limit, φ0 is the initial fibre misalignment angle and γy is the additional fibre rotation angle from loading. The parameters τy and γy are derived from the experimental 12

characterisation by Bru et al. [21] on the same material system. A shear strength S13 of 56.7 MPa is used as input for the shear yield limit τy . The fibre rotation angle from loading γy is calculated from the elastic response as γy =

S13 , G13

(5)

where G13 is the shear modulus out-of-plane with a magnitude of 3.7 GPa, calculated between 0.2 % and 0.4 %. The predicted fibre rotation (engineering shear strain) γy at kinking then becomes 1.5 % which is equivalent 0.86◦ . The analytical predictions by Argon and Budiansky are plotted with the experimental data in Fig. 14, where the initial fibre misalignment angle φ0 is estimated by the maximum fibre misalignment angle θmax . There is good agreement between the kinking models and the experimental results when the maximum fibre misalignment angle θmax is used as input for the initial fibre misalignment angle. In Fig. 14 the θmax is given by the 99:th percentile of the measured maximum misalignment angle. The maximum misalignment angle θmax is sensitive to the choice of percentile since it is related to the tail of a normal distribution. The estimated maximum angle drops approximately 20 % when changing the percentile from 99 to 95. Detailed studies of the waviness in micrographs and the corresponding measurements reveals that the 99:th percentile is a pertinent choice for the proposed methodology. It provides a sufficiently high filter for spurious angles associated with the measurement method and maintains a sufficiently low filter on ”real” fibre misalignment angles. 3.3.2. Effect of size and shape of misaligned regions When the spatial distributions of fibre-misalignment angles were studied in more detail for each measured section, an interesting difference between laminate C2 and C3 was observed. Laminate C2 appeared to have misaligned regions with a larger extension in the longitudinal direction than C3. Lemanski and Sutcliffe [31] studied the effect of wavy regions with a finite size using finite element analysis. They concluded that the extension of wavy regions in the transverse direction to the fibres results in a significant reduction of compressive strength whereas an extension in the longitudinal direction does not. This is a plausible explanation to the lower strength for laminate C3 compared to C2 despite its higher fibre volume fraction. To our knowledge, this is the first time the postulated effect of size of the wavy region on compressive strength [31] is confirmed experimentally. In the current study, the analysis performed to quantify the effect of misalignment region size is based on the work by Liu et al. [14], where it was concluded that the ellipse is a suitable shape to represent

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defects (misaligned regions). Three representative samples from laminates C2 and C3 are shown in Fig. 15 where the defects are represented by white cells. These cells are identified by a threshold value of the misalignment angle, which in this case is set to 2◦ and a white region is created from connecting cells. Available functions in Matlab are used for the image analysis, where the centre of gravity is first identified followed by identification of the major and minor axes. The largest distance through the thickness is then extracted from all defects as the projection of the principal axes on the Z-axis, where the largest value is selected. The average values of 10 measurements for each laminate are 0.91 mm for laminate C2 and 1.24 mm for laminate C3. It should be noted that the coefficient of variation is approximately 25 % in these measurements for both laminates. As presented in the previous chapter, there is a good correlation between the maximum misalignment angle θmax and the compressive strength, and if the C - group of laminates is considered, there is also a decent correlation within the group, where laminates C1 and C3 have lower strength and higher maximum misalignment angle than laminates C2 and C4. As presented in the previous paragraph, we have been able to give one explanation to the difference in strength between laminates C2 and C3 with different extension of the misaligned regions through the thickness. However, we have not been able to identify which defect that is critical based on Weibull statistics for strength of brittle materials. For this type of analysis, one must consider the intricate relation between fibre misalignments and defect size. Liu et al. [14] approached this problem numerically by constructing a look-up table of strength for different relations between fibre misalignment and defect size. This table was then used to asses the compressive strength of a domain with random waviness based on the critical defect. Sutcliffe [15] used finite element analysis (FEA) to explore the effects of defect size and the study showed that although FEA is powerful for identifying critical defects, it is difficult to draw firm conclusions of their effect on compressive strength. It would be interesting with a similar study based on experimentally characterised fibre waviness and strength combined with numerical identification of the critical defect to fully understand the complex relationship between these quantities. Another interesting approach for future studies with micro-computed tomography would be to characterise the fibre orientations of a ”large” gauge section in 3D and subsequently identify initiation of kink-band formation and correlate to the fibre waviness of the initiation site. One example of state-of-the art for these type of studies is presented in [32]. Our approach in which the maximum misalignment angle is extracted as the 99:th percentile implies that strength cannot be directly linked to a specific defect. It is instead related to the

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whole distribution of misalignment angles since misalignment angles close to the 99th percentile may come from different defects. This is an approach proven in this study to work well for UD NCF composites. It has been shown that consideration of the maximum misalignment angle alone provides sufficient input for reliable strength predictions for these materials.

4. Conclusions The current experimental study investigates influence of intrinsic material variations on performance of unidirectional NCF composites loaded in compression. In conjunction with the compression tests, an in-house method to measure fibre misalignment angles with high accuracy and spatial resolution has been used. The obtained fibre misalignment angles from section planes along the fibres were used to study how the out-of-plane waviness influences the longitudinal stiffness and strength of the composites. Only the out-of-plane waviness was considered in the study since all specimens failed by kinking out-of-plane. As such, this is the largest experimental characterization of the spatial variation of fibre waviness and its effect on compressive performance of UD composites to date. Analyses of the fibre waviness revealed that the probability distribution of fibre misalignments was close to normal for all laminates studied. Interestingly, the observed waviness covers the whole spectrum from periodic to random spatial distributions and the magnitude ranges from medium to high. The obtained waviness was not generated by any special manufacturing principle, but instead caused by the different fibre volume fractions, laminate thicknesses and RTM processes. In that sense, the waviness in this study is authentic and can be expected to occur under certain conditions in production. We have been able to show experimentally the relation between the mean fibre misalignment angle, i.e. fibre waviness, and stiffness reduction. A knock-down factor was calculated as the reduction in percent of the measured stiffness relative the theoretical stiffness for an ideal laminate with straight fibres. The calculated knock-down factor of the studied laminates range from 10 - 20 % with mean misalignment angles of 1.5 - 3◦ , corresponding to a stiffness knock-down of 5 % per degree in the studied range. It is also shown that the stiffness knock-down is dependent on fibre waviness. That is, an increase in fibre volume fraction in a laminate with low waviness has a stronger effect on stiffness than has a similar increase in fibre volume fraction in a laminate with high waviness.

15

As expected, fibre waviness is found to have a strong adverse effect on the compressive mechanical properties of the composite. The measured compressive strength was reduced to half as the maximum fibre misalignment angle was doubled. A group of laminates with low out-of-plane waviness ( θmax ≈4.5 ◦ ) had a compressive strength of approximately 750 MPa, while another group with high out-of-plane waviness ( θmax ≈8 ◦ ) resulted in a compressive strength of approximately 400 MPa. It is found that the maximum fibre misalignment angle can be used to accurately predict the compressive strength with simple kinking criteria, both for periodic and random waviness. Using the 99:th percentile of fibre misalignment angles as the maximum, a conservative prediction of the compressive strength is obtained with models by both Argon [4] and Budiansky [30]. Consideration of the maximum misalignment angle alone offers reliable prediction of the compressive strength of UD NCF composites. Characterisation of the waviness spectral contributions reveals that the largest misalignment angles or slopes are associated with a wavelength induced by the textile. This relation is strong for laminates with periodic waviness and fades as the waviness becomes more random. For the first time experimental data are presented, which show the effect of size and orientation of misaligned regions on compressive strength. These experimental results confirm observations in previous numerical studies [14, 31] where it was found that the extension of a misaligned region in the transverse direction is more critical than an extension in the longitudinal direction. Both qualitative and quantitative experimental evidence is provided that confirm the adverse effect on compressive strength with the extension of misaligned regions through the thickness. Thus, identification of the importance of the size of the misalignment regions adds to the overall understanding of compressive failure in UD composites and merits further study.

5. Acknowledgements This work has been performed within the Swedish Aeronautical Research Program (NFFP), Project 2013 - 01119, jointly funded by the Swedish Armed Forces, Swedish Defence Materiel Administration, the Swedish Governmental Agency for Innovation Systems and GKN Aerospace. Peter H¨ allstr¨ om performed major parts of the compressive testing at Swerea SICOMP. His work is gratefully acknowledged. David Carlstedt at Chalmers University of Technology is gratefully acknowledged for his help with taking the SEM images. Siavash Shoja at Chalmers University 16

of Technology is gratefully acknowledged for valuable discussions regarding the Fourier analysis. Sweden’s innovation agency, VINNOVA, is also gratefully acknowledged for funding via LIGHTer SRA1.

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technology-and-innovation/ [3] CFAN, History of the 50/50 joint-venture cfan between ge aircraft engines and snecma (2016). URL http://www.c-fan.com/history/ [4] A. S. Argon, Fracture of composites, Treatise on materials science and technology 1 (1972) 79–114. [5] S. Drapier, M. R. Wisnom, Finite-element investigation of the compressive strength of noncrimp-fabric-based composites, Composites Science and Technology 59 (8) (1999) 1287–1297. [6] D. Wilhelmsson, On matrix-driven failure in unidirectional NCF composites - A theoretical and experimental study (Licentiate thesis), Department of Applied Mechanics, Material and Computational Mechanics, Chalmers University of Technology, 2016. [7] D. Wilhelmsson, L. E. Asp, A direct method for characterisation of fibre misalignment angles in composites, To be submitted for publication 2017. [8] S. Kyriakides, R. Arseculeratne, E. Perry, K. Liechti, On the compressive failure of fiber reinforced composites, International Journal of Solids and Structures 32 (6-7) (1995) 689–738. [9] H. Hsiao, I. Daniel, Effect of fiber waviness on stiffness and strength reduction of unidirectional composites under compressive loading, Composites Science and Technology 56 (5) (1996) 581– 593.

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[10] M. Romanowicz, Initiation of kink bands from regions of higher misalignment in carbon fiberreinforced polymers, Journal of Composite Materials 48 (19) (2013) 2387–2399. [11] R. Joffe, D. Mattsson, J. Modniks, J. Varna, Compressive failure analysis of non-crimp fabric composites with large out-of-plane misalignment of fiber bundles, Composites Part A: Applied Science and Manufacturing 36 (8) (2005) 1030–1046. [12] F. Edgren, L. E. Asp, Approximate analytical constitutive model for non-crimp fabric composites, Composites Part A: Applied Science and Manufacturing 36 (2) (2005) 173–181. [13] J. Zhu, J. Wang, L. Zu, Influence of out-of-plane ply waviness on elastic properties of composite laminates under uniaxial loading, Composite Structures 132 (2015) 440–450. [14] D. Liu, N. A. Fleck, M. P. F. Sutcliffe, Compressive strength of fibre composites with random fibre waviness, Journal of the Mechanics and Physics of Solids 52 (7) (2004) 1481–1505. [15] M. P. F. Sutcliffe, Modelling the effect of size on compressive strength of fibre composites with random waviness, Composites Science and Technology 88 (2013) 142–150. R [16] Teijin Toho Tenax, Technical data sheet, Delivery programme and characteristics for Tenax

HTS filamet yarn (2011). R R [17] Huntsman, Technical data sheet, Araldite LY556 / Aradur 917 / Accelerator DY 070, Hot

curing epoxy matrix system (2007). [18] Porcher Composites, Technical data sheet, Style 4510 Finish F9773 (2014). [19] ASTM, ASTM D6641 - Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials Using a Combined Loading Compression ( CLC ) Test Fixture, Tech. Rep. Clc, West Conshohocken, PA (2014). [20] ASTM, ASTM D3410 - Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials with Unsupported Gage Section by Shear, Tech. Rep. Reapproved 2008, West Conshohocken, PA (2008). [21] T. Bru, P. Hellstr¨ om, R. Gutkin, D. Ramantani, G. Peterson, Characterisation of the mechanical and fracture properties of a uni-weave carbon fibre/epoxy non-crimp fabric composite, Data in Brief 6 (2016) 680–695. 18

[22] P. M. Wegner, D. F. Adams, Verification of the Combined Load Compression ( CLC ) Test Method, Tech. Rep. August, University of Wyoming (2000). [23] E. S. Greenhalgh, Failure analysis and fractography of polymer composites, Woodhead Publishing Limited, Cambridge, UK, 2009. [24] D. Wilhelmsson, L. E. Asp, R. Gutkin, F. Edgren, Fibre waviness induced bending in compression tests of unidirectional NCF composites, in: ICCM21, Xi’an, China, 2017. [25] M. R. Wisnom, The effect of fibre waviness on the relationship between compressive and flexural strengths of unidirectional composites, Journal of Composite Materials 28 (1) (1993) 66–76. [26] F. Edgren, L. E. Asp, R. Joffe, Failure of NCF composites subjected to combined compression and shear loading, Composites Science and Technology 66 (15) (2006) 2865–2877. [27] A. R. Clarke, G. Archenhold, N. C. Davidson, W. S. Slaughter, N. A. Fleck, Determining the power spectral density of the waviness of unidirectional glass fibres in polymer composites, Applied Composite Materials: An International Journal for the Science and Application of Composite Materials 2 (4) (1995) 233–243. [28] W. S. Slaughter, N. A. Fleck, Microbuckling of fiber composites with random initial fiber waviness, Journal of the Mechanics and Physics of Solids 42 (11) (1994) 1743–1766. [29] M. P. F. Sutcliffe, S. Lemanski, A. Scott, Measurement of fibre waviness in industrial composite components, Composites Science and Technology 72 (16) (2012) 2016–2023. [30] B. Budiansky, Micromechanics, Computers & Structures 16 (1983) 3–12. [31] S. L. Lemanski, M. P. F. Sutcliffe, Compressive failure of finite size unidirectional composite laminates with a region of fibre waviness, Composites Part A: Applied Science and Manufacturing 43 (3) (2012) 435–444. [32] Y. Wang, T. L. Burnett, Y. Chai, C. Soutis, P. J. Hogg, P. J. Withers, X-ray computed tomography study of kink bands in unidirectional composites, Composite Structures 160 (2017) 917–924.

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Captions

Figure 1: Illustration of the textile architecture.

Figure 2: Terraces of kinked fibres for specimen B1-4 with a recorded bending at failure of 39 %.

Figure 3: Terraces of kinked fibres for specimen C1-6 with a recorded bending at failure of 43 %.

Figure 4: Representative micrographs of waviness out-of-plane for laminate B3 and C2. The length is 20 mm in the fibre direction (1 - dir).

Figure 5: Location and size of the studied regions for out-of-plane waviness.

Figure 6: Representative spatial distributions of fibre misalignment angles with a spatial resolution of 55 µm. The angle is defined as positive clockwise. Note that some regions exceed the minimum and maximum limits in the colorbar.

Figure 7: Representative fibre misalignment distributions for laminate B3 and C2 with corresponding fits of normal PDF:s. Note that a laminate with random waviness (C2) is more closely related to a normal distribution than is a laminate with periodic waviness (B3).

Figure 8: Spectral density distributions of fibre slopes for (a) high waviness and (b) low waviness.

Figure 9: Compressive elastic modulus, with the associated standard deviations, measured between 0.1 and 0.3 % strain for all laminates. The fibre volume fraction and thickness is presented below each value.

Figure 10: Compressive elastic modulus as a function of fibre volume fraction for two groups of laminates and ROM.

20

Figure 11: The knockdown factor η as a function of the mean misalignment angle θ¯ with a second order least square fit.

Figure 12: Compressive strength for all laminates with the associated standard deviations. The fibre volume fraction and thickness is presented below each value.

Figure 13: The compressive strength Xc and maximum misalignment angle θmax for all 0◦ laminates. Note that the right y - axis is reversed with increasing angles downwards.

Figure 14: The compressive strength Xc as a function of the maximum misalignment angle θmax with analytical estimates by Argon and Budiansky.

Figure 15: Examples of misaligned regions for C2 and C3 seen as white areas. The dashed lines represent the major axes and the dotted lines represent the minor axes of ellipses fitted to these regions.

21

Table 1: Processing details of the groups of laminates. The laminates have a size w (width) × l (length) with the fibre orientation in the length direction.

Plate- Curing Postgroup A

Infusion/cure Infusion type

Laminate size RTM tool

curing pressure [bar] 4 h 80◦ 4 h 140◦ 3 / 3

w x l [mm] Surrounding periphery in-

w x l [mm]

1000 × 280

1130 × 320

327 × 227

340 × 240

let with centralized outlet B

16 h 80◦ 4 h 140◦ 2 / 2

”Edge injection, long side” to long side

C

16 h 80◦ 4 h 140◦ 2 / 2

Surrounding periphery in- ∼500 × 250

1130 × 320

let with centralized outlet

Table 2: Basic properties of manufactured laminates where n is the number of specimens and t is the thickness. The fibre volume fraction Vf is calculated based on the areal weight and density of the fibres.

Laminate

n

Layup

t (mm)

Vf (%)

A1

6

[0]10

1.77

61

B1

5

[0]9

2.03

48

B2

7

[0]10

2.03

53

B3

6

[0]11

2.03

59

B4

6

[0]20

3.92

55

C1

20

[0]8

1.68

52

C2

20

[0]9

1.68

58

C3

20

[0]10

1.70

64

C4

16

[0]20

3.70

59

22

¯f Table 3: The number of specimens with strain gauges n , ITRII or CLC fixture and average bending at failure B within a laminate.

Laminate

n

ITRII/CLC

¯f (%) B

A1

6

6/0

11

B1

5

2/3

61

B2

7

1/6

44

B3

6

1/5

15

B4

6

4/2

6

C1

5

0/20

19

C2

5

0/20

14

C3

4

0/20

11

C4

3

0/16

7

Table 4: Summary of compressive tests and waviness measurements with associated errors.

¯ ◦ ) θmax (◦ ) nθ CVθ¯(%) cu (%) Laminate XC (M P a) CVXC (%) E(GP a) CVE (%) θ( A1

1

631

9

134

3

1.3

4.8

10 9

0.48

B1

379

12

95

17

2.8

7.3

10 11

0.42

B2

394

13

102

16

3.1

8.0

10 14

0.39

B3

408

10

115

6

2.7

8.2

10 7

0.35

B4

669

9

115

4

1.7

5.0

10 4

0.56

C1

689

9

108

4

1.5

4.5

12 9

0.59

C2

812

10

122

1

1.3

4.4

10 6

0.68

C3

728

13

139

2

1.4

4.9

10 7

0.52

C4

826

9

122

1

1.3

4.4

10 10

0.68

23

Table 5: Longitudinal elastic moduli for fibres and matrix [16, 17].

Constituent

Longitudinal elastic modulus (GPa)

Fibres

240

Matrix

3.2

24

Carbon fibre bundles

Polyamide / glass weft yarns Figure 1

Figure 2

Figure 3

25

a) B3 3

b) C2

1 Figure 4

2

1

20 mm

20 mm Figure 5

26

A1 B1

B3 -4 B4

-2

0 C1 C2

2

C3

4

C4 3 1 Figure 6

27

Figure 7

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0 0

0.1

0.2

0.3

0.4

(a)

0

0.1

0.2

(b) Figure 8

28

0.3

0.4

140 64% 120

61% 58%

100

80

59%

55%

B3

B4

59%

52%

53% 48%

60

40 A1

B1

B2

C1

C2

C3

C4

Figure 9

160

140

120

100

80 45

50

55

Figure 10

29

60

65

70

25

20

15

10

5

0 0

0.5

1

1.5

2

2.5

3

3.5

Figure 11

1000 900 800 700 600 500

59%

58% 61%

55%

52%

B4

C1

64%

400 300

48%

53%

59%

B1

B2

B3

200 100 0 A1

Figure 12

30

C2

C3

C4

1000 900

3

800

4

700

5

600

6

500

7

400

8

300

9

200 A1

B1

B2

B3

B4

C1

C2

C3

C4

Figure 13

900 800 700 600 500 400 300 0

2

4

Figure 14

31

6

8

a) C2

b) C3 3 1 Figure 15

32