Composites: Part A 103 (2017) 168–177
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Micro-level mechanisms of fiber waviness and wrinkling during hot drape forming of unidirectional prepreg composites K. Farnand, N. Zobeiry ⇑, A. Poursartip, G. Fernlund Composites Research Network, The University of British Columbia, Vancouver, BC, Canada
a r t i c l e
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Article history: Received 27 July 2017 Received in revised form 19 September 2017 Accepted 9 October 2017 Available online 10 October 2017 Keywords: A. Polymer-matrix composites (PMCs) B. Defects E. Forming E. Prepreg processing
a b s t r a c t Fiber misalignment in composites in the form of in-plane waviness and out of-plane wrinkling, is a major defect arising from processes such as hot drape forming. This work studies the micro-level mechanisms of forming in-plane fiber waviness and out-of-plane wrinkling. An out-of-autoclave unidirectional prepreg system by SOLVAY (CYTEC), CYCOM 5320/T650-35 was used to conduct multiple forming experiments and study the effects of various parameters including forming temperate and lay-up sequence. The effect of partial impregnation, or ‘Engineered Vacuum Channels’, in out-of-autoclave prepreg systems on the intra-ply separation/slippage and consequently fiber misalignment was studied and found to be a significant contributor to micro-level mechanisms. Cross sectioning and microscopy of the parts and examination of the end termination profiles were used to analyze the effect of forming parameters on ply end-shortening and consequently fiber misalignment. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction and background During the last decade, advanced composites have experienced a rapid rise in adoption for commercial products such as aircraft (e.g. Boeing 787, Airbus A350 and Bombardier C-series) and road vehicles (e.g. BMW i3 and i8). Compared to their metallic counterparts, aside from excellent inherent properties such as high specific stiffness and strength, a variety of parameters have contributed to this surge in use. This includes reduction in raw material cost, recent advancements in automation, new regulations and standards to promote lighter and more efficient designs, and introduction/implementation of new processing methods. Uncertainties associated with the manufacturing methods, however, have introduced many challenges in the adoption of composites e.g. [1]. Multi-year delays have been observed in ambitious composites manufacturing programs such as the Boeing 787 and the Bombardier C-Series. In general, inadequate control of key process parameters leads to the formation of defects in composite parts. This includes defects such as porosity [2,3], residual stresses/dimensional changes and micro-cracks [4–6]. In addition, each manufacturing process may exacerbate specific types of defects, such as the fiber waviness and wrinkling commonly observed in the hot drape forming (HDF) process [7–11]. ⇑ Corresponding author at: 309-6350 Stores Road, Vancouver, BC V6T 1Z4, Canada. E-mail address:
[email protected] (N. Zobeiry). https://doi.org/10.1016/j.compositesa.2017.10.008 1359-835X/Ó 2017 Elsevier Ltd. All rights reserved.
Fiber misalignment defects are of particular importance due to their impact on mechanical properties and their effect on the part outer dimensions. This often leads to interference during assembly followed by costly trimming and shimming operations or part rejection [12]. Fiber misalignment poses additional risk as it often go undetected. For instance, wrinkling internal to the part cannot be seen from the outside surface. In addition, ultrasonic inspection cannot detect in-plane misalignments and CT scans are not feasible for large structures. An increased understanding of the onset, evolution, and detection of fiber misalignment will lead to manufacturing inspection cost reductions, lighter parts, and increased manufacturing throughput. Buckling of fibers, tows, and plies have shown to be the main driving mechanism for fiber misalignments [13,14]. However, considering many available manufacturing methods and composite material systems, several parameters at different steps of the process may contribute to fiber misalignment formation. For Liquid Composite Moulding (LCM) processes such as high-pressure Resin Transfer Moulding (RTM), for example, fiber misalignment may be introduced during the deposition of dry fabrics. During the injection step, however, fiber wash-out may further contribute to this misalignment [15–17]. Other examples include wrinkle formation during material deposition using automated processes such as Automated Tape Laying (ATL), as well as wrinkle formation during the hot drape forming process. Regarding fiber misalignment, attention has mainly been paid to understanding, characterizing and simulating the formability
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and wrinkle formation in dry textile fabrics [18–20]. In several studies, drapeability of dry textile fabrics and the effect of the shear locking angle have been studied extensively [21–25]. However, as industry more and more focuses on drape forming of unidirectional (UD) prepreg systems, there is a shift in attention towards understanding the formation of fiber misalignment in prepreg applications. Aside from geometry, ply sequence and intraply properties, has been shown that the formation of wrinkling and inplane waviness is largely affected by interply shear properties and interply slip. This in turn is affected by process parameters such as temperature, forming rate and forming pressure [26]. Although most researchers have focused on studying the formability of thermoset prepregs, some have considered UD thermoplastic prepregs e.g. [27]. Using several toughened epoxy-based prepregs, Larberg et al. [28] studied the effect of material system on interply friction using a dedicated friction rig. They discovered that a combination of several factors including type of thermoplastic tougheners (i.e. surface particles or miscible liquid), fiber volume fraction and forming temperature significantly influence the coefficient of interply friction and consequently wrinkle formation. Hallander et al. [10], studied the effect of lay-up sequence during forming process of a spar geometry. More recently, they showed that by co-stacking critical layers, it is possible to increase buckling resistance of layers and consequently avoid wrinkle formation [29]. Lightfoot et al. [30], studied the effect of tool/part interaction and ply slippage on formation of fiber waviness and wrinkling using a U-shaped tool. Erland et al. [26] studied the effect of various parameters including the effect of forming rate, forming pressure and forming temperature. Of particular interest was their observation that by increasing the forming temperature, initially the critical interply shear stress decreases but as the temperature reaches around 90 °C, the critical stress increases. This study aims to better understand the micro-level mechanisms leading to formation of fiber misalignment including inplane waviness and out-of-plane wrinkling during the hot drape forming process of prepreg laminates. In this study, an out-ofautoclave material system (CYCOM 5320/T650-35) was selected to form C-shape parts from flat charges. It is shown that the existence of Engineered Vacuum Channels in the form of a dry (i.e. unimpregnated) prepreg core in out-of-autoclave material systems may introduce/promote intraply slippage/separation. The coupling of intraply and interplay slippage during forming, introduces micro-level mechanisms leading to fiber misalignment. The effect of several parameters including lay-up sequence, laminate thickness, flange length and forming temperature on fiber waviness and wrinkling are studied. By analyzing the termination angle of the Cshape parts and correlating it to missing ply length and wrinkle formation, the effect of forming parameters are investigated.
2. Experimental studies 2.1. Experimental setup The drape forming process for C-shape parts involves laying up a flat laminate charge and subsequent forming onto a tool (otherwise known as a mandrel or mould). This is done by means of a pressure differential created by pulling vacuum under an extensible elastomer sheet. A schematic of the experimental setup and forming process is shown in Fig. 1. A forming assembly consisting of a forming box (600 mm 600 mm aluminum plate with welded aluminum square tubing walls), a silicone membrane (Torr Technologies Inc. 1 mm-thick EL80 flat sheet adhered to an aluminum frame), and a release agent-covered aluminum tool (101 mm 101 mm 101 mm aluminum block with corner radii of 9.5 mm)
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was used in this study as shown in Fig. 1. The release agent used in this study was Frekote 700-NC from Henkel Adhesives. CYCOM 5320/T650-35 unidirectional prepreg sheets were used in fabrication of all parts. Prepreg sheets were removed from the freezer and left to sit for 30 min at room temperature. 228 mm 76 mm (300 900 ) quasi-isotropic laminates were then laid up by facing the prepreg backing paper upward and compacting each ply with a roller prior to the removal of the backing paper. A fixed aluminum block was used to align one edge of the laminate during this process and ensure an initial 90 degree edge angle. Once the laminate was laid up in full, it was covered with an aluminum block and the assembly was then placed under full vacuum for 10 min for debulking at room temperature. Given the aluminum block’s greater area, the laminate was calculated to have been consolidated with 1.4 atm. of pressure. After this process, the none-buttressed end of the laminate was trimmed using an ultrasonic knife. 2.2. Forming experiments For the forming experiments, the forming assembly, tool and prepreg charge were heated to the forming temperature in an oven. To study the effect of flange length, once ready for forming, the rectangular charge was aligned off-center on the aluminum tool to form a C-shape part with two different flange lengths of approximately 38 mm (1.500 ) and 76 mm (300 ). The prepreg charge was covered with a release film before forming commenced inside the heated oven. The vacuum line valve was then opened, initiating drape forming of the flat charge onto the tool with an average forming rate of 6.4°/s (0.11 rad/s). Five minutes after the forming process was completed, while under vacuum pressure, the part was cured using the manufacturer’s recommended cure cycle (i.e. MRCC) of 1.0 °C/min ramp to 121 °C, followed by a 3 h hold. No post cure was performed on the parts. This cycle was chosen as vitrification occurs during the 3 h hold. After vitrification and while the resin is in the glassy state, no fiber buckling can occur to create additional waviness/wrinkling. During the forming process, the laminates were unsupported laterally. Industrial practice has over the years shifted from unsupported forming to supported forming to reduce forming defects such as wrinkles and waviness. The reason unsupported forming was used in this study was to have a direct comparison with the baseline, hand-lay process, giving the same boundary conditions for all samples studied. Aside from flange length and forming temperature, the effect of other parameters including lay-up sequence and charge thickness were also considered in this study. All forming experiments are listed in Table 1. The forming experiment with configurations of sample #1 was repeated twice and the results were evaluated to determine the repeatability of the test method. Comparison of results showed similar trends and details of wrinkle formation in both samples. After this evaluation, no further repeats was performed for the other forming tests. In addition to the forming experiments, a baseline test was also conducted using the traditional hand lay-up method with a lay-up similar to forming sample #1 (Table 1). In this test, plies were laidup on the tool one at a time by hand. Each ply was held into place for approximately five seconds allowing for adequate adhesion to the previous ply. A roller was then used to compact the laminate after laying-up each ply. No intermediate vacuum debulk was conducted during the lay-up process. After placing all layers on to the tool, a 10 min debulked was performed at room temperature before curing the part. 2.3. Material and process The out-of-autoclave material CYCOM 5320/T650-35 was used in all the forming experiments. CYCOM 5320 is a toughened epoxy
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Fig. 1. Hot drape forming process of a C-shape part, (a) heating of the charge in preparation for forming, (b) formed geometry. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Forming experiments. Sample #
Lay-up
Nominal thickness
Forming temperature
Resin viscosity during forming
1 2 3 4 5 6
[90/+45/45/0]4S [90/+45/45/0]2S [90/+45/45/0]8S [90/+45/45/0]4S [0/45/+45/90]4S [0/45+45/90]4S
4.32 mm 2.16 mm 8.64 mm 4.32 mm 4.32 mm 4.32 mm
30 °C 30 °C 30 °C 70 °C 30 °C 70 °C
19.1 kPa.S 19.1 kPa.S 19.1 kPa.S 0.3 kPa.S 19.1 kPa.S 0.3 kPa.S
(32 (16 (64 (32 (32 (32
plies) plies) plies) plies) plies) plies)
where thermoplastic tougheners initially are in the form of a miscible liquid in the epoxy resin. As shown in other studies, prepregs with thermoplastic particles on the surface exhibit much higher interply friction compared to prepregs with liquid thermoplastic tougheners [28]. Consequently, the choice of material system in this study promotes interply slippage by reducing interply friction. Moreover, out-of-autoclave prepregs and even some autoclave prepregs, are manufactured with ‘Engineered Vacuum Channels’ in the form of dry prepreg core. These vacuum channels for CYCOM 5320 prepreg are shown in Fig. 2 using scanning electron microcopy (SEM). SEM images of the surfaces and cross sections of two prepreg samples at room temperature and at an elevated temperature of 70 °C are compared in Fig. 2. No debulking was performed on these prepreg samples. As shown in these images, even at an elevated temperature of 70 °C, the viscosity of resin is high enough that it doesn’t completely fill the dry core of the prepreg. For the selected forming temperatures of 30 °C and 70 °C, and for the selected MRCC, viscosity development and degree of cure (i.e. DOC) were calculated using models developed by Kratz et al. [31] and exercised by RAVEN software [32] and are shown in Figs. 3and 4 respectively. These figures show viscosity of 19.1 kPa.s and 0.3 kPa.s during forming at temperatures of 30 °C and 70 °C respectively. At these low forming temperatures engineered vacuum channels stay open as was previously indicated by Ridgard [33]. He introduced the approach of a ‘Super Ambient Dwell’ at a temperature around 60 °C to keep the vacuum channels open for effective and fast debulks. This ensures rapid removal of volatiles and moisture through these vacuum channels.
2.4. Cross sectioning and microscopy After the laminate was formed and cured, microscopy was performed on several cross sections. A cross-sectional plane running through the middle of the flange (38 mm from the edge of the part) was chosen for microscopy. Samples were mounted in room temperature curing epoxy, and polished using a Buehler EcoMet 300 auto-polisher. Micrographs were captured at 200 magnification using a Keyence digital microscope. Images were then automatically stitched together using the Keyence microscope software. 2.5. Termination angle When forming a laminate over a tool with male radius as shown in Fig. 5(a), the assumption of ideal slippage of plies and negligible ply thickness change leads to a flange termination angle of hideal as depicted in Fig. 5(b). This is due to the difference in path lengths between inner and outer plies. Fig. 5(c) shows a close-up of the laminate end termination. For concentric arcs at the corner, assuming that the S1 and S2 are the bottom and top ply arc lengths as shown in Fig. 5(b), and assuming that R is the corner radius and h is the laminate thickness, we can calculate the ideal slip angle, hidal , as follows:
h h ¼ tan1 p p S2 S1 ðR þ hÞ 2 ðRÞ 2 2 ¼ 32:5 ¼ tan1
hidal ¼ tan1
p
ð1Þ
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Fig. 2. SEM Microscopy of a CYCOM 5320/T650-35 unidirectional prepreg (not debulked) at different temperatures: (a) surface of the prepreg at room temperature, 20 °C, (b) surface of the prepreg at 70 °C, (c) cross sectional view of the prepreg at room temperature, 20 °C and (d) cross sectional view of the prepreg at 70 °C.
Fig. 3. Temperature cycle, viscosity profile and degree of cure calculated using models by Kratz et al. [31] in RAVEN software [32] for CYCOM 5320/T650-35. Drape forming at 30 °C is followed by the manufacturer’s recommended cure cycle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
If there is laminate compaction during forming, this angle is reduced to reflect the reduction in ply thickness during cure. For the measured ratio of cured ply thickness to uncured ply thickness
of 82%, this angle is further reduced to about 27°. In this study, based on the above discussion and also experimental observations, an ideal slip angle in the range of 27°–32° is assumed.
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Fig. 4. Temperature cycle, viscosity profile and degree of cure calculated using models by Kratz et al. [31] in RAVEN software [32] for CYCOM 5320/T650-35. Drape forming at 70 °C is followed by the manufacturer’s recommended cure cycle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. End termination of a symmetric C-shape part formed on a male tool: (a) before the forming process, and (b) after the forming process with h as the end termination angle, and (c) wrinkling formation and the missing length effect on ply termination.
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3. Experimental results and discussions 3.1. Forming temperature The choice of forming temperatures in the current study are discussed below: – Forming at 30 °C: As shown in Fig. 2(a), at low temperatures, resin is not distributed uniformly on the prepreg surface with patches of the dry fabric remaining visible. This rough prepreg surface combined with high resin viscosity (19.1 kPa.s), results in high interply friction that promotes fiber misalignment during forming. In addition, at low consolidation pressures at the beginning of the forming, the dry core of the prepreg shown in Fig. 2(c), promotes intraply separation. – Forming at 70 °C: As shown in Fig. 2(b), by elevating the temperature, resin viscosity drops to create a smoother prepreg surface. This reduces the interply friction and consequently reduces the formation of fiber misalignment in the part. Although the center of the prepreg remains dry, resin is transferred toward the center of the prepreg through the capillary effect to reduce intraply separation during forming. 3.2. Missing ply length Dodwell et al. [13] introduced the idea of excess length whereby a laminate being formed or consolidated to a curved surface (an external radius, for example), will develop an excess ply or fiber path lengths if the generated compressive strain cannot be relieved by shear or slip. As shown in Fig. 5(c), this excess length leads to formation of wrinkling or fiber waviness and manifests itself as missing length at the end termination. Therefore, missing length can be correlated to the amount of fiber misalignment in each ply. Fig. 6, for example, compares the ply missing length observed in two forming experiments with different forming temperatures: Fig. 6(a) shows the end termination in experiment #5 (as listed under Table 1) with a forming temperature of 30 °C and Fig. 6(b) shows the end termination in experiment #6 (as listed under Table 1) with a forming temperature of 70 °C. This comparison shows a smaller missing ply length for the forming experiment at the elevated temperature of 70 °C. As expected, by increasing the forming temperature, resin viscosity drops and interplay friction decreases. During forming, this leads to ply slippage and consequently smaller fiber misalignment. Experiment #5, however, shows larger missing ply length as an indication of higher fiber misalignment in the form of waviness and wrinkling.
to create larger wrinkles. For sample #5 with 0° ply against the tool, as shown in Fig. 8, a combined mechanism is observed for wrinkle formation. First, excess length leads to the formation of in-plane fiber waviness. This can be observed in Fig. 8(b) where the cross sections of 0° fibers gradually transforms to an elliptical shape as an indication of fiber waviness. Based on the methodology developed by Yurgartis [34], fiber waviness up to 45° can be measured in this cross section. This method stipulates that if a fiber is cut at an angle x from the fiber axis, the angle can be calculated from the ratio of the resulting ellipse minor diameter, d1, and major diameter, d2, using the following relationship:
3.3. Micro-Level mechanisms
sin x ¼
Depending on parameters such as lay-up, temperature and material properties, the excess length that leads to formation of fiber misalignment manifests itself in different ways. This includes internal wrinkles (i.e. out-of-plane fiber misalignment not visible on the part surface), external wrinkles (i.e. out-of-plane fiber misalignment visible on the part surface) and waviness (i.e. internal fiber misalignment in a ply). For parts with a 90° ply against the tool and forming temperature of 30 °C (samples # 1–3), formation of internal wrinkling was observed through folding and rolling of 90° fibers as shown in Fig. 7. If interplay slippage is prevented when the charge is formed, wrinkles are generated due bendinginduced excess length. Plies closer to the mould with larger excess length buckle under compression and generate wrinkles. At higher temperatures and under vacuum pressure, 90° fibers roll over each other and flow to fill the cavity created by wrinkle formation during the forming process. In some cases, the ply may fold over itself
Fig. 8(c), shows that similar to the 90° plies, rolling of these misaligned 0° fibers eventually leads to formation of an internal wrinkle. In addition, at the curved section of the C-shape parts, partial fiber waviness can be observed in all 0° plies though the laminate thickness as shown in Fig. 9. Since fiber waviness indicates bending-induced compression, existence of partial waviness zones in 0° plies shows that only parts of each ply have undergone compression while the rest of the ply was under tension. This is behavior is not expected if no interply slippage occurs. With no interply slippage, the half of the formed laminate close to the tool undergoes compression and the other half undergoes tension. Consequently, the existence of these partial waviness zones in all 0° plies, is an indication that interply slippage occurred during forming thus creating compressive and tensile zones within each 0° ply. This combined with a dry prepreg core (i.e. Engineered Vacuum Channels), leads to formation of intraply separation and partial
Fig. 6. End termination of two formed samples: (a) sample #5 that was formed at 30 °C and (b) sample #6 that was formed at 70 °C. Ideal slip line and missing ply lengths are identified in 0° layers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
d1 d2
ð2Þ
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Fig. 7. Wrinkle formation through rolling of 90° fibers in the ply at the mould surface in sample #3 (64 layers formed at 30 °C). During forming and under applied shear stress, fibers roll over each other to increase ply thickness and form an internal wrinkle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Wrinkle formation in the 0° layer in sample #5: (a) wrinkled region, (b) start of in-plane fiber waviness in the 0° layer, and (c) combination of in-plane waviness and rolling of the misaligned 0° fibers to form a wrinkle. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
waviness throughout the part thickness. The bending induced compression is likely due to the conformation of the flat plies to the curved tool surface. However, debulking of individual plies is expected to create a similar effect and may add to the observed waviness. 3.4. Effect of thickness The effect of part thickness on forming of C-shape parts is shown in Figs. 10 and 11 for samples #1 (32 plies), #2 (16 plies) and #3 (64 plies). In Fig. 10, the termination angle of these samples are compared. This shows that by increasing the laminate thickness, the termination angle decreases and becomes closer to the perfect slip angle. This indicates a higher degree of fiber misalign-
ment in thinner samples. Fig. 11 on the other hand, compares the termination angle of the samples for different flange lengths. It shows smaller termination angle on the side with smaller flange length. Since the termination angle for the smaller flanges is less than the ideal slip angle and termination angle for the larger flange is larger than the ideal slip angle, this indicates a laminate slip toward the larger flange side. This can be explained by the asymmetry of the part and the fact that shear stresses applied on the part surface, through stretching of the silicone bag during forming, push the plies toward the longer flange. In addition, Fig. 11 shows that the average termination angle of both flanges in each forming experiment is still larger than the ideal slip angle (45°, 34° and 32° for 16, 32 and 64 plies respectively). This is an indication of missing ply length and consequently
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Fig. 9. Formation of partial waviness in 0° layers throughout the thickness of part #5 due to bending-induced compression. Partial waviness is an indication of inter-ply slippage to create both tensile, T(+), and compressive, C(), zones in 0° layers. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
fiber misalignment in all parts, with greater misalignment in thinner parts. It should be noted that the effect of thickness may not be generalized to other geometries and material systems. The observations on flange length cannot be generalized to other geometries. For example, as the flange length is decreased, the total interply friction force is also decreased which further promotes inter-ply slippage. This may affect the micro-level mechanisms of wrinkle formation observed in current study.
3.5. Effect of curing Unlike formed samples, microscopy of the baseline hand lay-up sample did not show any wrinkles. This highlights the fact that the wrinkles observed in the forming experiments are forminginduced and not curing-induced. Microscopy of the baseline hand lay-up sample also showed partial waviness in 0 degree plies, similar to forming samples. This is expected as the hand lay-up method also involves bending individual plies, which creates a compressive zone in each ply. This compression leads to formation of fiber waviness. In cases where wrinkles are generated during the forming process, some of the out-of-plane wrinkles may transform into in-plane waviness due to the further drop in viscosity combined with applied pressure during cure. The hand lay-up and
forming data suggest that in-plane waviness is bending-induced but may be further exacerbated during the curing process.
4. Summary and conclusions In this study, micro-level mechanisms for wrinkle formation and general fiber misalignments were analyzed. An out-ofautoclave material that contains engineered vacuum channels in the form of a dry core was used in the current study. It was shown that the combination of these channels and low forming temperature, promotes intraply separation of fibers in 0° plies that leads to partial waviness of the ply during forming. For 90° plies, rolling of fibers was observed as the micro-level mechanism that leads to wrinkle formation during bending-induced compression. In comparison, for 0° plies, a combination of in-plane waviness of fibers and rolling of misaligned fibers was observed as the micro-level mechanism leading to wrinkle formation. In general, by increasing temperature, as observed in other studies, interply friction is reduced to promote slippage. This reduces missing length and fiber misalignment during forming. For the current geometry, forming parameters and material system, by increasing laminate thickness, fiber misalignment is reduced. This obviously may not be generalized to other geometries and material systems. Finally, it was
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Fig. 10. Comparison of the termination angles in samples with various thicknesses: (a) sample #2, 16 plies, (b) sample #1, 32 plies and (c) sample #3, 64 plies. Microscopy images are taken from the termination section of long flanges of samples. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Acknowledgments The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and the industrial members of the Composites Research Network (The Boeing Company, Convergent Manufacturing Technologies, Toray Americas, Avcorp Industries) for their financial support. We would also like to acknowledge many fruitful discussions with colleagues at the Composites Research Network (CRN). References
Fig. 11. Effect of flange length and laminate thickness on termination angle and ply slippage. Average termination angle for each part is higher than the perfect slip angle. This is an indication of missing ply lengths to form in-plane fiber waviness and out-of-plane wrinkles. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
shown that by analyzing the end termination of the flanges, missing ply length can be correlated to fiber misalignment level in each layer.
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