Following the effect of braid architecture on performance and damage of carbon fibre/epoxy composite tubes during torsional straining

The torsional performance of bi-axially braided carbon fibre reinforced polymer 20 (CFRP) tubes as a function of braid architecture is investigated. It is found that for a given braid pattern, the 45 braided CFRP tubes have higher shear moduli and lower shear strength than the 35 braids. In general, 2/2 (regular) braided CFRP tubes exhibit both higher shear strength and higher shear modulus than 1/1 (diamond) braids. However, beyond the peak load, the shear strength of 2/2 braided CFRPs exhibits 25 sudden, steep drops, resulting in a lower remnant shear strength than 1/1 structures after the shear strain exceeds 4.5%. Moreover, the damage evolution is monitored in-situ by synchrotron X-ray computed tomography during torsional straining. It showed that for a 2/2 structure, inter-tow debonded regions are vertically interconnected


Introduction
In the drive to reduce carbon emission and improve energy efficiency in industries such as aerospace and automotive, employing light-weight materials is an attractive approach [1]. Carbon fibre reinforced polymers (CFRPs) exhibit higher strength-to-weight and stiffness-to-weight ratios than metals and alloys, as well as offereing other advantages 40 including high corrossion resistance attractive to the oil and gas industry for example [2]. Thus, CFRP structures are increasingly being considered as candidates to replace metal components. For example, in the Airbus A350 XWB and Boeing 787 aircraft more than 50% (by weight) of the components are made of CFRPs [3]. Moreover, the application of CFRPs has expanded their consideration from secondary structures to 45 load-bearing structures. Composite structures also offer a wide range of gometries and archetectures, from laminated panels to complex three-dimensional (3D) woven/braided architectures. Among these, tubular structures are widely used in industrial applications, such as the drive shafts in hybrid/electric automobiles, drive shafts for aircraft control surfaces, the body frame of drones, the casing of aero-engines and pipelines in the oil 50 and gas industry. For the safe and reliable application of tubular CFRPs, there is a need to further our understanding of the dependence of the mechanical performance on the fibre architecture for this materials class.
Braided and filament wound architectures are well suited to tubular structures. Filament wound structures are much more susceptible to large-scale delamination than braided 55 ones [4]. Two-dimensional (2D) bi-axial braiding is a highly automated technique and is thus commonly used [5]. It involves interlacing fibre tows oriented at a braiding angle of ±θ with respect to the long axis of the tube continuously in a helix. A number of studies have reported the failure mechanisms of braided composite laminates under tension [6,7], compression [8], shear and impact [9,10]. Perhaps surprisingly, there have 60 been limited studies on the mechanical performance of braided composite of tube structures, especially under torsion, which is a common loading scenario in industrial applications [11]. Melenka and Carey [12] studied the tensile and torsional performance of both 1/1 and 2/2 braided Kevlar fibre/epoxy composite tubes with braid angles of 35°, 45° and 55°. They found that tensile strength and Young's modulus decrease with 65 increasing braid angle for both 1/1 and 2/2 braid patterns; however, there is no distinct trend for the torsional/shear properties across different braid archetectures. Potluri et al. [13] found that the shear modulus and shear strength of the braided composites decrease with increasing braid angle in 1/1 braided glass fibre/epoxy composite tubes with braid angles of 31°, 45° and 60°, which was attributed to the difference in fibre volume 70 fraction (Vf) and the sensitivity to tube diameter variation in the used testing configuration. Harte and Fleck [14] reported that the shear strength of braided composites increase with increasing braid angle in 2/2 braided glass fibre/epoxy composite tubes with braid angles of 23°, 40° and 55°, in contrast to that in 1/1 braids.
With regards to braided CFRP tubes, the torsional/shear properties of CFRP tubes of 75 different braid architectures haven't yet been reported in literature.
Apart from the lack of macro-mechanical studies, little is known about the damage mechanisms that give rise to the difference in torsional properties across composite tubes having different braid structures. Lomov et al. [15] summarised a variety of nondestructive techniques to study damage evolution in textile composites, including digital 80 image correlation [6,16], acoustic emission [17], X-ray radiography [18] and X-ray comupted tomography (CT). Although acoustic emission could identify the damage modes including matrix cracking, debonding between fibre tow and matrix, and fibre fracture, in the torsional failure of 3D braided CFRP tubes, the 3D distribution of the various damage modes cannot be mapped. X-ray computed tomography (CT) is a 85 promising technique to assess microstructure and damage in braided tubes owing to its 3D non-destructive nature. Time-lapse X-ray CT under in-situ loading has been used increasingly to obtain insights into the damage mechanisms in unidirectional [19,20] and woven [21] CFRPs as reviewed by Garcea et al. [22] and Wang et al. [23]. With regards to braided composites, Melenka et al. [24] reported the first use of X-ray CT to 90 assess the 3D braid structure and defects in 2D 1/1 braided Kevlar fibre/epoxy composite tubes, where the actual interlacing paths of individual braid Kevlar fibre tows were extracted in 3D. Zhou et al. [9] used post-mortem X-ray CT to assess the impact damage in 3D braided CFRP tubes of different braid angles, in which they found that impact damage is more severe with decreasing braid angle because of their looser 95 structure. Due to the intrinsic complexity associated with the in-situ mechanical testing of tubular shaped structures, time-lapse X-ray imaging of the damage evolution in braided composite tubes under load has not been realised until recently. We recently reported the first real time 3D imaging of damage development under torsion [25]. The damage in 2D 1/1-45° braided CFRP tube was mapped in 3D during torsional straining 100 and the damage sequence was observed to initiate through radial intra-tow cracking and circumferential inter-tow debonding, followed by fibre micro-buckling and ultimately kink-band formation [25].
This paper aims to compare and contrast the damage behaviour for braided CFRP tubes having different braid interlacement topologies in order to extend our understanding of 105 the effect of braid architecture on the mechanical performance of braided CFRPs under torsion. The torsional/shear properties of 1/1 and 2/2 braided CFRPs tubes having braiding angles of 35° and 45° are compared and time-lapse synchrotron X-ray CT used to provide insights into the key damage mechanisms involved in failure. The findings reported here provide important information for the design of braided composite tubes 110 bearing torsional loads.

CFRP tube manufacture
Toray T700-12K carbon fibre and IN2/AT30 epoxy resin were used to manufacture all 115 the braided composite tubes in this study. The single layer 2D braided sleeves were fabricated into two patterns -diamond (1/1) and regular (2/2) onto a 10 mm-diameter steel mandrel (pre-treated with release agent to aid demoulding) using a maypole braiding machine (Cobra Braiding Machinery Ltd) as shown in Fig. 1a. Braids with two braiding angles (35° and 45°) were prepared for each braid pattern, thus providing four 120 braid structures (1/1-35°, 1/1-45°, 2/2-35° and 2/2-45°). The braided sleeves (on the mandrels) were then infused with IN2/AT30 epoxy resin using the vacuum assisted resin infusion (VARI) method, followed by consolidation at 100 °C for 3 hours. The manufactured tubes have a 10 mm inner diameter and were cut into 55 mm lengths (15 mm gauge length). The final 20 mm at the ends of each specimen was glued into end-125 tabbing fixtures, comprising an insert and an outer shell (adapted from ASTM standard D5448/D5448M [26]), by epoxy adhesive (3M™ Scotch-Weld™ EC-9323 B/A). from the X-ray CT images inset.
In order to reduce defects (such as wrinkles, voids and uneven wall thickness) induced by the resin infusion process, the moulds for the VARI system were modified as shown in Fig. 1b. An extra outer-shell mould was added outside the braid (following [13] and [25]). The resulting tubes had a smooth surface finish and a wall thickness of ~1.3mm, 135 which contains about 0.3-0.4 mm thick resin-rich area (considering both inner and outer surfaces). The fibre volume fractions of the braided tubes were calculated based on segmented CT images (see section 2.4), excluding the resin-rich skins caused by the mould.

Torsion testing 140
Torsion tests (zero axial load) on the braided CFRP tubes were carried out on an Instron 8802 machine to investigate the torsional behaviour and also to validate the in-situ tests.
Three specimens were tested for each of the four braid architectures. During each test, 100 bar gripping pressure was applied to hold the samples and loading was performed at 2°/min. High-resolution videos of the samples throughout the loading process were 145 recorded using LaVision Imager E-lite (105 mm lens), to track the damage on the sample surface at a frame rate of 5 Hz.
The composite mean shear stress , ̅ , was inferred from the torque, T, according to Equations 1 and 2, which are obtained by assuming that the sum moment caused by the mean shear stress equals the torque applied on the specimen. The mean shear strain, ̅ , 150 was inferred from the torsion angle (φrad) according to Equation 3. Considering the difficulties in installing strain gauges on small-diameter tubes with a short gauge length (L), φrad has been computed from the crosshead rotation angle after applying appropriate compliance correction (crosshead compliance has been estimated using a steel bar of known properties). In the following equations, r is the radius of the annular element on 155 the cross-section of the specimen, dA is the area of the annular element, dr and dθ are the thickness and angle of the annular element, respectively, , and ̅ are the outer, inner and mean radius of the tube, respectively .

In-situ torsion test
The in-situ torsion tests were performed on the Deben-Manchester Open Frame Rig 160 (Mark II) which exploits a pair of independently controllable rotating grips. It was mounted on the I13-2 Diamond-Manchester beamline, Diamond Light Source, UK. The in-situ test specimens have the same gauge length as those for Instron 8802 tests, but metal tabs were specially designed with two parallel side surfaces for gripping to apply the torque (see Fig. 2). The torsional load was applied by rotating the top grip relative to 165 the bottom one while maintaining zero axial load. The progressive evolution of damage was monitored in real-time by interrupting the test 170 at different stages for synchrotron X-ray CT imaging. A parallel polychromatic 'pink' (20-24 keV) beam was used for CT imaging with the radiographs recorded on a PCO.4000 camera providing a cropped field of view (FoV) of 10.8 mm × 7.2 mm at a voxel size of (3.6 μm). In each CT scan, the two opposing grips were rotated in synchrony such that 4500 radiographs/projections were acquired at an exposure time of 175 0.12 s over 360° rotation using an off-centred imaging approach [27]. The acquisition time for each tomogram was about 30 minutes. To facilitate the CT scan, the control of the rig was switched from load control (for torsional straining) to position control (for imaging with minimal sample movement). The load was stabilised for 20 minutes at each load step prior to starting the CT scan. 180

X-ray CT image processing
The acquired projections were reconstructed into 32-bit float CT data using in-house python codes. The pre-processing pipeline incorporated the following elements: 1) Flatfield correction; 2) distortion correction [28]; 3) converting 0-360° sinograms to 0-180° sinograms [29]; 4) zinger removal; 5) blob removal [30]; 6) ring removal [30]. Then the 185 GRIDEC algorithm was used for reconstruction [31,32]. 3D image analysis was performed in Avizo 2019.1 software. The CT images were firstly transformed into 8-bit (from 32-bit), in order to reduce the data size thus accelerate the following image analysis processes. The non-local means filter was applied to remove noise. With the help of the image segmentation toolbox in Avizo, the bias fibre tows and the damage 190 types can be segmented semi-automatically based on their different greyscale levels.
Thus, the topology of the braided structure can be extracted and visualised in 3D as shown in Fig. 3. Moreover, the volumes of the braid tows (including intra-tow resin) and the composite were obtained from the CT images based on the segmentation results to facilitate the measurement of Vf, which was calculated by the volume of fibres 195 divided by the volume of the composite. The volume of fibres equals the volume of tows multiplied by the intra-tow fibre volume fraction. The intra-tow fibre volume fraction was calculated by the area of carbon fibres (obtained from known parametersthe fibre diameter and the number of fibres in each tow) divided by the area of the tows (obtained from CT image sections) [33]. 200 The level of crimp is a crucial factor for textile composites as it directly influences the 205 mechanical behaviour of the composite [34]. The crimp angle (Φc) was measured by unwrapping CT slices from the tubular shape to form a virtual flat panel using the Polar Transformer plugin in Fiji ImageJ [24,35]. The unwrapped flat panel has a height equal to the imaged tube height, a thickness equal to the wall thickness and a width equal to the mean circumference of the tube. In addition, the damage area fraction in the tubular 210 specimen was calculated based on the unwrapped data, as will be discussed in Section 5.

Microstructure of the braided tubes 215
The 3D microstructure of the braided CFRP tubes can be assessed by X-ray CT. Other than qualitative visualisation of the braid architecture and manufacturing defects, quantitative measurement of the braid parameters such as crimp and fibre volume fraction are also of importance in comparing the behaviours. The crimp angle has been calculated based on unwrapped images as shown in Fig. 3c. Unsurprisingly, the crimp 220 angles for the 1/1 braids are higher than those for the 2/2 braids (see Table 1) because that the tow interlacing interval for the 1/1 structures is shorter than for the 2/2 structures, which results in larger waviness at tow cross-overs. For a specific braid pattern, the crimp angle for 45° structures are relatively higher than that for the 35° structures. Table 1 also shows the fibre volume fractions of the composites having the 225 different braid structures measured following the approach reported in [25].

Torsional performance of braided CFRP tubes
The shear stress-strain behaviours of the test-pieces were calculated from the applied 230 torque and twisting angle according to Equations (1) and (2). Typical curves for the four braid structures are plotted in Fig. 4a. It is noteworthy that for 1/1 braided tubes the stress-strain curve is rather stable after the peak stress (indicating stable damage accumulation); whereas the shear stress response for the 2/2 braided tubes typically exhibits several steep drops upon exceeding the ultimate shear strength (peak load), 235 suggestive of bursts of rapid damage accumulation. This also results in a lower remnant shear strength for the 2/2 braided structures than 1/1 at large shear strains (>4.5%).
Moreover, the torsional performance is observed to be broadly repeatable from sample to sample. Fig. 4b shows the shear stress-strain curves for all three 2/2-45° specimens tested on the Instron 8802 alongside the 2/2-45° specimen tested in-situ. It is also 240 reassuring that the in-situ tested specimen behaves similarly to the off-line tested specimens, which means that the damage evolution observed in-situ by X-ray CT is likely to be representative of the general behaviour of this braid structure. Note that the large stress drops at steps S3-36 for the in-situ specimen were caused by both the

Damage mechanisms in braided CFRP tubes 270
The damage evolution in the 1/1-45° braided CFRP tube has been reported previously [25]. In that case we found that torsional damage tends to initiate from axial compression/transverse tension induced radial intra-tow cracking, followed by circumferential inter-tow debonding between oppositely biased tows (where the compressive tows are on the outside and the tensile ones the inside) followed by fibre 275 micro-buckling in the axially compressed tows. In this section, the distribution and evolution of torsional damage in the 2/2-45° braided CFRP tube is explored from the time-lapse X-ray CT images. Under the applied torque (shear stress), the +45° tows are approximately in a state of axial tension and transverse compression, whereas the -45° tows are under axial compression and transverse tension. For clarity in the following 280 discussions, the +45° tows which are loaded in axial tension are termed AT tows (colorcoded yellow in Fig. 3), and the -45° tows which are being axially compressed are termed AC tows (color-coded green in Fig. 3).

Damage initiation and propagation
The mechanism by which damage first initiates in 2/2 regular braided CFRP tube is 285 different from that in the 1/1-45° braided architecture [25]. The first cracks to appear at a torsional strain of around 1.2% are the result of a new damage moderadial inter-tow debonding (see Fig. 6a (bottom)), which occurs between the paired AC tows (see Fig.   6b). This mode is not available for the 1/1 braids; by contrast the first damage to appear in the 1/1-45° braid is circumferential inter-tow debonding between ±45° tows (see the 290 schematic in Fig. 6a (top)) and intra-tow cracking. Although adjacent AC tows tend to buckle under the shear-induced axial compression, the locations of the two buckles are shifted by the width of an AT tow, thereby generating a shear stress between the two adjacent AC tows and resulting in the radial inter-tow debonding between them. This damage mode is also clearly visible on the surface of the specimen as shown in Fig. 6c. 295 The sequence of damage development in the 2/2-45° structure can be established from the time-lapse sequence of the virtual 2D X-ray CT section oriented parallel to the tow (fibre) directions (see Fig. 7) and compared with that for the 1/1-45 case reported previously [25]. As discussed above, damage initiates through radial inter-tow 305 debonding between adjacent AC tows in locations where they lie on the outside of the tube at a shear strain of 1.2% (see Feature A in Fig. 7). It is worth noting that subsequently this radial inter-tow debonding is also observed towards the interior of the tube (i.e. between two AC tows lying inside the AT tow) after a shear strain of 2.0% (see Feature B). The fact that damage tends to initiate from the outer surface of the tube, 310 rather than the inner surface, can be attributed to the stress gradient along the tube radius observed in non-thin-walled tubes [36]. In the meantime, circumferential intertow debonding (Feature C) induced by the shear stress (similar to that observed in the 1/1-45° structure [25]) has occurred along the interface between the oppositely biased tows by 2.0% strain, where AC tows lie outside AT tows. We can see that it tends to 315 extend as far as the width of the AC tows on this section. By 2.9% strain (S4), intra-tow cracks (Feature D and F) start to appear and develop in AC tows. It is also worth noting that debonding between AC tows and the matrix (Feature E) is observed at the interior of the CFRP tube at this stage, accompanied by wavy deformation of the tube inner surface. 320 Based on the observations above, we can conclude that damage occurs predominantly along interfaces (between adjacent AC tows and between outer AC tows and inner AT tows) and within the AC tows. Fig. 8 shows a time series for a virtual section parallel to an AC (green) tow with increasing strain. It can be seen that the length of the circumferential inter-tow debonding along the AC tow is shorter than that along the AT 330 tow (see Feature C in Fig. 7 and Fig. 8). Here, the debond extends to about two-thirds the width of two AT tows, as the AC tow is constrained in the through-the-thickness direction by the AT tows at the tow cross-over points. Moreover, the inner and outer surfaces of the tube both take up an increasingly wavy conformation with increasing shear strain due to tendency for the AC tows to protrude radially and the AT tows to 335 intrude. As the shear strain reaches 5.4%, the axial compression along the AC tow, together with the shear stress concentration at the tow cross-over points, promotes fibre micro-buckling and fibre kinking, see Fig. 8. Moreover, as shown in Fig. 7 and Fig. 8, it is evident that under increasing shear strain, the AT tows become straighter (lower crimp) under shear induced axial tension, while the AC tows become wavier (higher 340 crimp) under shear induced axial compression. As illustrated in Fig. 9a, the 2/2 pattern gives rise to waviness (crimp) in the fibre tows with a half-wavelength of about two times the tow-width. Given that fibre misalignment and waviness can significantly degrade the compressive strength of unidirectional CFRP [37], the intrinsic waviness in the braid structure makes the braided CFRP susceptible to 350 shear (torque) induced axial compressive stress along the AC tows. Various conformations of fibre micro-buckling and fibre kinking have been observed in the 2/2-45° specimen (see Fig. 9b-d). Fibre micro-buckling and fibre kinking tend to occur within the AC tow segments lying outside the AT tows (Fig. 9b-c), accompanied by circumferential inter-tow debonding, similar to that developed from a notched region 355 under four-point bending reported in Wang et al [38], due to the lower through-thethickness constraint near surface. Two typical positions for fibre kink bands to develop have been observed, either close to one tow cross-over point (see Fig. 9b) or in the middle between the two cross-over points (see Fig. 9c), depending on the local stress distribution. In addition, fibre micro-buckling/kinking can also be found in the AC tow 360 segments lying inside the two AT tows (see Fig. 9d

Overall damage distribution
Apart from the detailed examination of various damage modes within a region-of-375 interest as discussed above, the overall damage distribution in the 2/2-45° structure under torsion can also be assessed by 3D volume rendering of the X-ray CT images. Fig. 10 shows the 3D rendered volume of the 2/2-45° CFRP tube under increasing shear strain, where the damaged regions appear lighter than the undamaged ones. It is evident that the damage is localised into vertically interconnected bands (columns) parallel to 380 the tube axis. This damage has occurred in regions where the AC tows lie outside the AT tows (i.e. the green columns in the colourized rendering in Fig. 10). In these locations the AC tows have buckled outwards under the shear (torque) induced axial compression and the interface between the outer AC tow and the inner AT tow have debonded.
Overall, the damage in the 2/2-45° structure has propagated by almost simultaneous 385 circumferential debonding for all the (green) patches down a vertical column, and then sequentially (green) column by (green) column thereby causing the sequential load drops with increasing shear strain, as highlighted by the dashed boxes in the loading sequence shown in Fig. 10.

Effect of braid pattern on torsional damage evolution
Comparing the damage evolution of 1/1-45° CFRP reported by Chai et al [25] with that 395 of the 2/2-45° CFRP reported here, we can explore the effect of braid pattern, diamond (1/1) or regular (2/2), on the damage mechanisms under torsion. Fig. 11 shows typical shear stress-strain curves alongside photographs of the specimen surfaces for the 2/2-45° specimen (a1-a4) and the 1/1-45° specimen (b1-b4) at the corresponding stages of the torsional straining. From these photographs we can see that damage propagates quite 400 differently for the two structures. As discussed above for the 2/2 structure from the 3D CT renderings in Fig. 10, the vertical bands of damage (highlighted by ellipses in Fig.   11) are evident on the specimen surface. For the 1/1-45° braided structure, intra-tow cracking damage (marked by the small ellipses) is evident on the specimen surface.
These damage features are localised and are evenly distributed almost uniformly across 405 the tube. By correlating the video sequence with the stress-strain response it is evident that each steep drop in the shear strength of the 2/2-45° specimen corresponds to the occurrence of a new 'damaged column' caused by the deformation of AC tows together with the circumferential 'popping' of interface between the outer AC tows and the inner AT tows. In the 2/2 structure, failure (buckling and debonding) of a single tow leads to a 410 dynamic transfer of load to the adjacent tow: this stimulates failure of the adjacent tow, whereas for the 1/1 structure this local load-transfer effect is not evident.
For the 1/1-45° specimen, damage initiates in the form of radial intra-tow cracks in the AC tows along with circumferential inter-tow debonding between the bias tows in regions where the AC tows are outermost (the green patches (see Fig. 1b)). whereas in 415 the 2/2-45° specimen, damage initiates from radial inter-tow debonding followed by circumferential inter-tow debonding. The radial intra-tow cracks in AC tows observed in 1/1-45° specimen are similar to the longitudinal splitting in unidirectional CFRP developed under axial compression, which is likely to occur along the fibre/matrix interface. Thus, in both braid patterns interfacial performance is critical during the early 420 stages of torsional damage. As damage propagates, circumferential inter-tow debonding becomes the dominant mechanism of strain relief in both structures. In order to understand the difference in the propagation of circumferential inter-tow debonding between the 1/1 and 2/2 braids, the inter-tow debonding damage was extracted from the X-ray CT images of the 1/1-45° and 2/2-45° specimens at ̅ = 2.0% 430 (just after the peak in shear stress). The unwrapped segmented circumferential inter-tow debonding damage is projected throughout the wall thickness onto one image (see Fig.   12). The area fraction of the debonding damage was calculated at ̅ = 2.0% from Fig.   12. The debonded area fraction in the 2/2-45° specimen (18%) is larger than that of the 1/1-45° specimen (15%). More importantly, each debonded 'patch' is much larger than 435 that for the 1/1-45° specimen. This is because the tow interlacing distance is doubled in the 2/2-45° structure, which gives rise to a larger individual interfacial area between bias tows. The denser array of tow cross-over points in the 1/1-45° braid structure helps to constrain the extent of circumferential inter-tow debonding. Further, the fact that the regions where the AC tows are outermost are connected as vertical bands in the 2/2 440 case, but distributed into a chequer board pattern for the 1/1 braid means that the strain relief and hence strength drop caused by the buckling of AC tows and the propagation of the circumferential cracks means that the degradation in strength for the 2/2 stress strain curve is less gradual than for the 1/1 braid once the peak strength has been exceeded. 445 During the latter stages of torsional failure, fibre micro-buckling and kink-band formation (along with fibre fracture) in the AC tows are the key damage modes in both 1/1-45° and 2/2-45° structures. In the 1/1-45° structure, fibre micro-buckling and kink bands tend to develop close to tow cross-over points [25], while in the 2/2-45° structure, 455 the mid-point between two tow cross-overs is also susceptible to fibre kinking (see Fig.   9c). This might be due to the fact that the tow interlacing distance is almost doubled in the 2/2 structure compared with the 1/1 structure, which imposes less through-the-thickness constraint thereby promoting fibre micro-buckling/kinking. For the 1/1 braid, kink bands were only observed where the AC tow segments lie at the outer surface of 460 the tube, whereas for the 2/2 braid, fibre kink bands were also observed where the AC tow segments lie at the inner diameter of the tube (see Fig. 9d). It is also noteworthy that under the excessive buckling of the AC tows in the 1/1-45° structure intra-tow cracking occurred rapidly in AT tows, while in the 2/2-45° structure the AT tows were barely damaged even at γ ̅ = 6%. 465

Conclusions
In this study, we have investigated the torsional behaviour of T700 carbon fibre/epoxy resin braided composite tubes with various braid architectures. The key findings can be summarised as follows,  In general, 2/2 braided CFRPs exhibit both higher shear strength and higher 470 shear modulus than 1/1 braided CFRPs. This is related to the lower crimp (crimp angle) associated with the 2/2 braids. However, the shear strength for the 2/2 braided CFRP drops significantly beyond the peak stress showing significant and sudden load drops. By contrast the 1/1 braids show very modest falls in strength after the peak stress and the degradation in strength is gradual, thus 475 exhibiting a degree of 'ductility' under torsion. As a consequence, the 1/1 has a higher remnant strength at torsional strains in excess of 4.5 %.
 While 45° is the optimum angle for a filament-wound tube under torsion, for braided tubes, the braid angle has a complex relation with the shear modulus and strength. For a given braid pattern, the 45° braided CFRPs have higher shear 480 moduli and a lower shear strength than the 35° braids. It appears that the torsional strength of a braided tube is highly sensitive to the crimp angle, which could be attributed to the susceptibility of crimped tows to axial compression.
 Through time-lapse synchrotron X-ray CT monitoring of the stress-strain behaviour the damage sequences have been captured. For the 2/2-45° braided 485 CFRP tube, damage initiates from radial inter-tow debonds between adjacent AC (i.e. under shear (torque) induced axial compression) tows, followed by circumferential inter-tow debonding between ±45° biased tows in locations where the AC tows are outermost. At higher strains intra-tow cracking, fibre micro-buckling and kink-band formation (fibre fracture) are also observed in AC 490 tows. The significant drops in shear strength recorded for the 2/2 braids have been shown to be related to the occurrence of the buckling of AC tows together with the propagation of circumferential debonding of the AC tows from the AT tows down vertical zones. The chequer board nature of the tows for the 1/1 structures prevents the formation of such interconnected damage zones. 495  The fibre/matrix interfacial strength is important, as it controls damage initiation under torsion. Tow cross-over density is a key factor in controlling damage propagation under torsion. Tow cross-overs can arrest circumferential inter-tow debonding, thus gives rise to smaller debonding area in the 1/1 structure than 2/2 structure. However, the crimp caused by the tow cross-overs contributes to the 500 occurrence of fibre micro-buckling. It is found that the fewer tow cross-overs in 2/2 structure gives rise to larger tow interlacing distance which imposes less through-the-thickness constraint that could promote fibre micro-buckling.
The above key findings provide key insights into the design of braid architecture for torsionally loaded components. For applications requiring high shear strength and/or 505 high shear modulus, 2/2 braided CFRP tubes are advantageous over 1/1 braided CFRP tubes. However, for applications that require higher structural integrity once damage has started to develop, 1/1 braided CFRP tubes could be a better option since 2/2 structures suffer from significant drops in shear strength once damage starts to propagate.
In the current study the lack of radial constraint of the AC tows is critical in terms of 510 damage propagation in the form of debonding and fibre micro-buckling. This suggests that the additional through-the-thickness constraint offered by through-the-thickness binders, hoop-winding or multiple layers may improve torsional strength. Future research could focus on developing novel braided structures with low crimp angle (for strength) but increased number of cross-over points (for damage tolerance). 515