9 This article examines the e ect of braid angle on the mechanical 10 performance of carbon-epoxy braided tubes in tension and compres- 11 sion. Vacuum-assisted resin transfer moulding is used to produce a 12 variety of tubes with several combinations of 15and 20braid an- 13 gles. As uniaxial tensile testing of cylindrical tubes is not trivial, 14 two tensile testing xture designs are explored. It is found that a 15 combination of mechanical and adhesive gripping produces repeatable 16 fractures between the grips, with no slipping. Tubes with lower braid 17 angles exhibit higher strengths both in tension and compression, as 18 well as absorbing greater amounts of energy in compression. 19 Keywords 20 Biaxial braided tubes; carbon bre composites; braid angle; grip design; 21 vacuum-assisted resin transfer moulding 22 1 1 Introduction 23 Braided composites consist of interwoven yarns embedded in a resin system 24 [1]. Thanks to their high strength-to-weight ratio and performance under 3- 25 D stress states, tubular braided composites are increasingly used in a variety 26 of applications, including biomedical [2], sports [3, 4], aerospace [5] and mil- 27 itary [6, 7]. In contrast to laminated composites, braided composites exhibit 28 greater impact resistance [8] and the opportunity to make near net shape 29 preforms. Recent studies have shown that carbon bre braided tubes are ex- 30 cellent candidates for space applications structures due to their high speci c 31 sti ness, thermal stability and superior fatigue resistance [9, 10]. In biaxial 32 tubular braiding, bre strands/tows are intertwined around a tubular man- 33 drel in clockwise and counterclockwise directions, resulting in a bidirectional 34 helically interlaced structure (Figure 1) [11]. The helix angle with respect to 35 the tube axis is known as the braid (or braiding) angle and has theoretical 36 values between 0and 90. Due to manufacturing constraints, braid angles 37 range from 15to 75. A braid angle of 0indicates a tow oriented axially 38 and not wrapped around the component, whereas 90indicates a tow that 39 wraps around the structure but does not progress along the main axis, similar 40 to lament winding. 41 Figure 1: 2-D biaxial braids (adapted from [12]). 2 The braid angle greatly a ects the mechanical properties of composite 42 braids, and many studies have examined its e ect on the mechanical perfor- 43 mance of braided composites [13, 14, 15, 16, 17, 18, 19]. Previous studies have 44 established that an increase in braid angle is accompanied by a decrease in 45 tensile strength [20, 21], peak failure load [22, 23] and tensile modulus [23, 24], 46 and by an increase of axial failure strain [25] and stress wave propagation 47 speed [26]. 48 Tensile testing of intact tubes is dicult for a number of reasons [27, 28]: 49 1) custom grips are required; and 2) specimen slipping is a common occur- 50 rence. As a result, much of the available literature on braided composites 51 focuses on testing of at specimens [24, 29, 30, 31, 32, 33]. While this ap- 52 proach gives a good indication of the behaviour of braided tubes, it also 53 presents some drawbacks [34]: 54 •Edge e ects : premature failure can occur at the free edges of at spec- 55 imens; 56 •Fibre relaxation : braided fabrics lose some of their integrity and straight- 57 ness when cut; 58 •Void content and distribution : the void content and its distribution in 59 at specimens may di er from those in tubular specimens. 60 A number of approaches for gripping intact tubes during tensile testing 61 have been reported in the literature [35, 27, 13, 14, 15, 17, 18, 19]. The 62 most common design is a double mounting grip in which the braided tube is 63 clamped between inner and outer circular xtures as shown in Figure 2. 64 This design is able to accommodate tubes of large diameters, however the 65 contact surface between tube and centre clamp is limited, which may result 66 in increased slipping. Moreover, this design does not o er much exibility 67 on the tube geometry as it is restricted to tubes of uniform cross section and 68 xed diameter. Any alteration in the design to accommodate di erent tube 69 geometries and sizes would be challenging to manufacture. 70 Perillo et al. proposed a customised grip design as shown in Figure 3. 71 This design allows the testing of tubes of various diameters; however the 72 3 Figure 2: Existing approach for the tensile test of braided tubes (adapted from [27]) V-shaped clamping grip may result in increased local stress regions, which 73 may induce cracking. 74 In the present article, we describe an alternative tensile testing procedure 75 for tubular braided composite structures, as well as characterising braided 76 tubes in tension and compression for a variety of braiding angles. 77 The remainder of this article is structured as follows: Section 2 describes 78 the materials used and sample preparation steps. Section 3 describes the 79 tensile and compression testing methods, as well as the design of a novel 80 gripping procedure for full tube tensile tests. A nite element model of the 81 tensile test is also reported. The results and discussion are given in Section 82 4, and Section 5 brie y outlines the conclusions of the work. 83 2 Materials and Tube Fabrication 84 2.1 Materials 85 Two types of carbon bre biaxial braided sleeves (15and 20) were pro- 86 vided by Burgmann Packings Ltd [36]. Each sleeve is composed of approx- 87 4 Figure 3: Custom grip design by Perillo et al. (adapted from [35]) imately 3000 yarns (7 m diameter) bundled into 128 individual threads; 88 these threads are braided together in a diamond pattern and oriented at an 89 angle of with respect to the sleeve's axis. An IN2 Infusion epoxy resin 90 system was used with the AT30 slow curing agent (100:30 mixing ratio by 91 weight) [37]. 92 2.2 Tube Fabrication 93 Each tube is manufactured with four layers of braided sleeves; the following 94 sleeve stacking sequences are examined (from the inside towards the outside 95 of the tube): 96 5 (a) Mould assembly (b) Vacuum seals (in blue) Figure 4: Mould used to manufacture the braided tubes. •BR-15 : [15]4 97 •BR-20/15 : [20=15]2 98 •BR-20 : [20]4 99 The tubes are infused in a two-part aluminium mould with a 25 mm 100 diameter steel mandrel provided by Burgmann Packings Ltd [36] (Figure 4). 101 The infusion process by Vacuum Assisted Resin Transfer Molding (VARTM) 102 consists of the following steps (a schematic representation of the process is 103 given in Figure 5): 104 1. The mandrel and mould cavity are coated with the Easy-Lease releasing 105 agent [37] to facilitate demoulding; 106 2. Four layers of braided sleeves are pulled over the mandrel, according 107 to the chosen design (BR-20, BR-15 or BR-20/15); 108 3. The mandrel wrapped with braided sleeves is placed in the cavity, and 109 the mould is bolted closed. The mould is then placed in a vertical 110 orientation with the inlet at the bottom and outlet at the top; 111 4. The resin is preheated to 40C and degassed. Subsequently, a vacuum 112 pressure of -1 bar is applied to the mould causing the resin to infuse 113 into the mould. 114 The infusion process takes 10 minutes; 115 6 5. Once the resin reaches the outlet, some extra resin is allowed to bleed 116 out for a few minutes to remove air bubbles in the resin ow and the 117 inlet and outlet gate valves are closed. The vacuum port is kept open 118 until the remaining resin in the reservoir has cured. The tubes are then 119 left to cure for 30 hours at room temperature; 120 6. Once the mould is opened, the tube is pushed o the mandrel from one 121 end of the assembly while holding the cured tube rmly using a custom 122 extraction tool; 123 7. The tubes are post-cured at 80C for 2 hours; 124 8. The cured tubes are cut into segments of the required length with a 125 band saw cutter. 126 Figure 5: Infusion process setup. The outer diameters and wall thicknesses of the tubes after curing are 127 given in Table 1. 128 7 Braid con guration Outer diameter (mm) Wall thickness (mm) BR-15 30.21 0.05 2.60 0.03 BR-20/15 30.14 0.16 2.57 0.08 BR-20 30.09 0.06 2.54 0.03 Table 1: Mean outer diameters and wall thicknesses after curing, with stan- dard deviations. 3 Methods 129 3.1 Tensile Testing 130 The braided tubes are cut to a length of 150 mm and constrained in tension 131 with a hydraulic Instron universal testing machine and a 250 kN load cell 132 according to the ASTM D5450 standard [38]. The test apparatus can be seen 133 in Figure 6. The tests are carried out with a constant crosshead displacement 134 of 1.3 mm/min. The tubes are loaded to failure and the load and the failure 135 displacements are recorded. The axial engineering stress within the tubes is 136 calculated by dividing the load by the initial cross-sectional area. The failure 137 strain is computed by dividing the displacement at failure by the distance 138 between the grips (100 mm). 139 Each test is repeated three times. Given the tubular shape of the speci- 140 mens as well as the loads involved, the design of a suitable gripping mecha- 141 nism is critical to ensure repeatable testing. With this in mind, two separate 142 gripping system designs are examined, as described in Section 3.3 below. 143 3.2 Compression Testing 144 Compression testing is performed according to the ASTM 695-02 [39] stan- 145 dard, as shown in Figure 7. The specimens are cut to a height of 30 mm, 146 yielding a unity height-to-diameter ratio. Once again, testing is performed 147 on a hydraulic Instron universal testing machine with a 250 kN load cell. The 148 specimens are compressed between two parallel smooth and at steel plates 149 8 Figure 6: Experimental setup for the tensile test of braided tubes. at a rate of 1.3 mm/min, and the force is recorded. In addition, the failure 150 mechanism is noted. These tests are repeated thrice. For each tensile and 151 compression test, the three following metrics are computed: 152 •The strength, de ned as the rst load peak divided by the undeformed 153 cross-sectional area; 154 •The axial sti ness, de ned as the strength divided by the strain at 155 break. 156 •The energy density, de ned as the area under the force{displacement 157 curve per unit volume: 158 Ed=1 VZlmax 0P(l) dl (1) 9 wherePis the load, lis the vertical displacement and Vis the volume 159 of the specimen; 160 Figure 7: Experimental setup for the compression testing of braided tubes. 3.3 Design of a Novel Gripping System for Tensile 161 Testing of Tubes 162 Following the general speci cations of the ASTM D5450 standard (tensile test 163 method for hoop-wound composite cylinders), two grips designs are proposed. 164 3.3.1 Design I 165 The rst design (Figures 8 and 9) is based on an internal cup and cone placed 166 inside each end of the tube, which are then bolted to the external xture of 167 the testing machine. This design has a much greater surface contact area as 168 compared to the designs proposed by Roy et al [27]. The external xture 169 consists of a clamping disk/cylinder which ts around the end of the tube. 170 As the internal bolt is tightened, it pushes the internal cone against the 171 internal cup, causing mechanical gripping. The outer surface of the cup 172 is sand-blasted to increase its friction coecient. The external clamping 173 10 disk/cylinder provides support against this internal pressure to avoid damage 174 of the tube, as well as gripping the tube from the outside. As the bolt heads 175 are within the tube, an internal alignment pin is inserted to allow tightening 176 of the bolt at the other end. This alignment pin remains in place during 177 testing but does not hold any force in tension. As the tensile test progresses, 178 the increasing axial force on the internal bolts results in increasing gripping 179 pressure applied by the cone via the internal cup. 180 Inner Cone (11.5°) Outer cone (2°)Lower plate Upper plate Cap Screw Cup part (yellow) Braided tubeAlignment pinSpacer ring Figure 8: Design I grip schematics. This design is an elegant gripping approach that does not require the 181 use of any adhesive. However after several tensile test trials, the following 182 limitations are noted: 183 •Signi cant machining time is required to produce the internal cup and 184 cones components. In addition, a number of cone angles needed to be 185 considered to yield a design that does not slip. 186 •The strength of the internal bolts provides an upper limit on the force 187 supported by the grips, where the maximum bolt size that can be used 188 is limited by the internal diameter of the tubes to be tested. One must 189 11 Figure 9: Design I grip assembly. ensure that the largest bolt that ts inside the tubes is strong enough 190 to perform the test; 191 •Many times during testing, the tubes starts to slip inside the grips, 192 thus invalidating the tests. 193 3.3.2 Design II 194 The second design consists of a T-shaped mild steel section with a central 195 protruding column, as shown in Figures 10, 11 and 15. The protruding 196 column is inserted into the end of the tube and a pair of external side xtures 197 are simultaneously clamped to each other (M10 bolts) as well as to the T- 198 shaped section (M8 bolts). 199 This design allows the external side xtures to mechanically grip onto the 200 tube. Initial testing found that this setup is able to successfully perform ten- 201 sile testing on braided tubes, however intermittent slipping is still an issue. 202 To overcome this, experimental grade fast-curing adhesive [40], supplied by 203 Henkel Ireland, is applied to the T-shaped section and the inner side of the 204 tube. The adhesive is cured at 110C for 15 minutes. Through the combi- 205 nation of mechanical and adhesive gripping, this gripper design eliminates 206 slipping during testing. There are however a number of limitations with this 207 12 Braided tubeM10 screws M8 screwsT-shaped Grips holders Adhesive (In red)Inner coreFigure 10: Design II grip schematics. design: 208 •In order to avoid premature failure of the braided tubes at the grips, 209 the external side bolts should not be over-tightened. Through trial- 210 and-error, this value was found to be to 90 Nm for the current setup; 211 •As adhesive from previous tests must be removed between each test, 212 multiple gripping xtures must be manufactured. Alternatively, only 213 one tube can be tested at a time. 214 Nevertheless, this approach is found to be sucient robust and is used 215 for tensile testing. 216 3.4 Finite Element Model 217 The tensile testing of has been modelled in nite element software Abaqus 218 [41] in order to compare the trends observed experimentally. The braided 219 tubes are modelled as a quarter cylinder with length 100 mm and a diameter 220 corresponding to the con guration modelled (approximately 30 mm, see Ta- 221 ble 1). Symmetrical boundary conditions are imposed on the two long free 222 13 Figure 11: Design II grip assembly. edges. A fully constrained boundary condition is applied to the edge at z = 223 0 and a vertical upward displacement of 3 mm is imposed on the opposite 224 edge. The model is meshed with 2200 S4R elements, which are 4-noded shell 225 elements based on the rst-order shear theory, featuring reduced integration, 226 a large-strain formulation and hourglass control. 227 Each braided sleeve is modelled as a laminated composite layup of 2 228 orthotropic plies whose bres are oriented at an angle of from the tube 229 axis. This modelling choice is adopted to represent the braiding as a uniform 230 component without having to model its microstructure. The ply thickness 231 is de ned as the tube wall thickness divided by the number of plies. For 232 example, the BR-20/15 tube is composed of 8 plies of thickness 2.57/8 mm 233 (approximately 0.3 mm) with the following ply orientation sequence: [+20 = 234 20=+ 15=15]2. The material properties of the carbon-epoxy material are 235 given in Table 2. Theses values are tted to the experimental stress-strain 236 curves shown in the result section and are comparable to those reported by 237 14 RTZ123100 mm 30 mm3 mmFigure 12: Mesh and dimensions of the nite element model. Shi et al. [42]. 238 At each time step, the vertical reaction force of the nodes at the top 239 short edge of the tube is summed and recorded, together with its associated 240 vertical displacement. The Hashin criterion is used to model damage in the 241 composite and the model parameters are reported in Table 2. 242 4 Results and Discussion 243 4.1 Tensile Testing 244 The stress-strain curves of all tension sample are shown under tensile load is 245 shown in Figure 13, both from experimental testing and nite element anal- 246 ysis. All tests exhibit an approximately linear region followed by a sudden 247 brittle failure, accompanied by a loud sound. The failure is sudden with al- 248 most no observable damage prior to fracture. It can be seen that the strength 249 and sti ness of the BR-15 sample (i.e. the tube with the lowest average braid 250 angle) is the highest, followed by the BR-20/15 and BR-20 samples. Simi- 251 lar trends are observed in nite element analysis. These results agree with 252 15 Material property value Longitudinal elastic modulus - E0 1 87 GPa Transverse elastic modulus - E0 2=E0 3 10.3 GPa Longitudinal shear modulus - G0 12=G0 13 6 GPa Transverse shear modulus - G0 23 3.7 GPa Longitudinal Poisson's ratio - 12=13 0.3 Transverse Poisson's ratio - 23 0.4 Tensile strength in the bre direction - XT3000 MPa Compressive strength in the bre direction - XC2370 MPa Tensile strength perpendicular to bre direction - YT123 MPa Compressive strength perpendicular to bre direction - YC354 MPa Longitudinal shear strength - SL202.5 MPa Transverse shear strength - SL90 MPa Fracture energy dissipated in bre tension - GC ft 9160 J/m2 Fracture energy dissipated in bre compression - GC fc 7990 J/m2 Fracture energy dissipated in matrix tension - GC mt 2200 J/m2 Fracture energy dissipated in matrix compression - GC mc 1100 J/m2 Viscosity coecients - ft=fc=mt=mc 0.001 Table 2: Material properties of the carbon-epoxy material. the theory and literature: the tubes with bres most aligned in the axial 253 direction are stronger and sti er [21, 23]. 254 Examining the failure modes in Table 4, it can be seen that failure is 255 due to a combination of bre breakage and matrix cracking. In all samples, 256 failure occurs between the two grips and not at the gripping location. This 257 suggests that the gripping xtures are e ective at constraining the sample in 258 tension without causing any excessive damage while gripping the sample. 259 4.2 Compression Testing 260 In compression, all tubes behave elastically up to an initial peak followed by 261 a drop in load, corresponding to crack initiation and propagation, see Figure 262 14. As the displacement increases, the stress continues to decline slowly 263 while the tube is being crushed. Similar to the tensile tests, the tubes with 264 the lowest braid angle (BR-15) shows the highest strength, while the BR- 265 16 0.0 0.5 1.0 1.5 2.0 2.5 Strain (%)0.00.10.20.30.40.5Stress (GPa) BR-15 (exp) BR-15 (FE) BR-20/15 (exp) BR-20/15 (FE) BR-20 (exp) BR-20 (FE)Figure 13: Stress strain curves of the three tube con gurations obtained both from experiments and nite element analysis. 20/15 and BR-20 con gurations exhibit comparable strengths. As crushing 266 progressed, the stress carried by the BR-20/15 tube reduces at a slower rate 267 than the other tubes, meaning that more energy is absorbed by the BR-20/15 268 tube at comparable strength. This suggests that alternating plies with low 269 and high bre angles contribute to increasing the energy absorption capacity 270 of braided tubes in compression. 271 The failure modes of the samples under a 9 mm compressive displacement 272 are characterised by a combination of matrix cracking, bre breakage and 273 interply delamination, see Table 4. 274 The sti ness, strength and energy density of all the braided tube con g- 275 urations are compared in Table 3. Overall, the tube with the lowest braid 276 angle (BR-15) exhibit the best mechanical performance in terms of sti ness, 277 strength and energy density, both in tension and in compression. This is in 278 agreement with the results found in the literature, suggesting that the grip- 279 ping methodology adopted here is robust. Furthermore, the braided tube 280 con gurations considered here perform signi cantly better in tension than in 281 compression. On average, the braided tubes in tension are sti er, stronger 282 and absorb more energy than the same tubes loaded in compression. 283 17 0 2 4 6 8 10 Strain (%)0.0000.0250.0500.0750.1000.1250.1500.1750.200Stress (GPa)BR-15 BR-20/15 BR-20Figure 14: Stress-strain curve of the braided tubes under compressive loading. 5 Conclusion 284 In this study, the experimental characterisation of composite braided tubes 285 under axial tensile and compressive loads is carried out. FOr tensile test- 286 ing of full tubes, a new gripping desing is proposed that successfully avoids 287 slipping and premature fracture. It is found that the braiding angle has a 288 signi cant e ect on the ultimate tensile and compressive strengths. In tensile 289 testing, the load-carrying capacity of the BR-15 con guration is found to be 290 24% and 38% higher than that of the BR-20/15 and BR-20 con gurations, 291 respectively. In compression testing, the peak load, compressive strength 292 and energy absorption capabilities are reported for comparison. It is found 293 that the BR-15 con guration showed the highest crushing load compared to 294 the BR-20 and BR-20/15 con gurations. The BR-15 tube absorbed 24% and 295 6.7% more energy than the BR-20/15 and BR-20 con gurations, respectively. 296 6 Acknowledgements 297 Financial support is gratefully acknowledged from the Irish Composites Cen- 298 tre (IComp), as well as technical assistance and advice from Alojz Ivankovic, 299 18 Test con guration Sti ness (MPa)Strength (MPa)Energy density (KJ/m3) BR-15 - tension - exp 188.6 2.2 427.9 16.9 5125 452 BR-20/15 - tension - exp 172.5 17.6 343.5 9.2 3854 434 BR-20 - tension - exp 156.4 1.9 308.7 10.0 3361 276 BR-15 - tension - FE 309.1 486.1 4959 BR-20/15 - tension - FE 282.3 450.4 4516 BR-20 - tension - FE 253.5 429.5 3290 BR-15 - compression - exp - 191.8 7.5 3617 917 BR-20/15 - compression - exp - 167.1 6.1 3389 502 BR-20 - compression - exp - 166.9 1.3 2911 258 Table 3: Sti nesses, strengths and energy densities of all tube con gurations in compression and tension. Michael Donohue, John Gahan and Tatiana Stefanov from University College 300 Dublin. Materials are provided by Greg Byrne at Burgmann Packings Ltd. 301 7 Declarations 302 7.1 Ethics approval and consent to participate 303 Not applicable. 304 7.2 Adherence to national and international regula- 305 tions 306 Not applicable. 307 7.3 Consent for publication 308 Not applicable 309 19 BR- 15 BR- 15/20 BR- 20 3 mm 3 mm 6 mm 9 mm tension compression compression compression Table 4: Failure modes of the braided tubes in tension and compression. 7.4 Availability of data and material 310 Raw data were generated at University College Dublin. Derived data sup- 311 porting the ndings of this study are available from the corresponding author, 312 PC, on request. 313 7.5 Competing interests 314 The authors declare that they have no competing interests. 315 20 7.6 Funding 316 Financial support is gratefully acknowledged from the Irish Composites Cen- 317 tre (IComp), which is jointly funded by Enterprise Ireland and IDA Ireland. 318 7.7 Authors' contributions 319 Conceptualisation, P.C. and U.J. and P.A.; methodology, P.C. and U.J. and 320 P.A.; software, P.C. and P.A.; writing|original draft preparation, U.J.; 321 writing|review and editing, P.C. and U.J. and P.A.; supervision, P.C.; 322 project administration, P.C.; funding acquisition, P.C. 323 7.8 Acknowledgements 324 Technical assistance and advice are gratefully acknowledged from Alojz Ivankovic, 325 Michael Donohue, John Gahan and Tatiana Stefanov from University College 326 Dublin. Materials are provided by Greg Byrne at Burgmann Packings Ltd. 327