Post-Forming Limits of Carbon Fibre Reinforced Thermoplastic Tubular Structures in a Rotary Draw Bending Process

This paper presents the post-forming limits of polyamide 6 carbon (CF/PA6) thermoplastic tubes to facilitate design and process optimisation of bent tubular CF/PA6 part manufacturing. Straight CF/PA6 tubes can be post-formed using rotary draw bending at elevated temperature to achieve desired curvatures. Forming limits of the tubes are predicted based on their winding angles, tube geometry, and bending radius, presented as the relation between tube winding angle and bending ratio. Additionally, the corresponding principal shear strain limits are derived from the winding angle limits and tube axial strains. Three sets of CF/PA6 tubes with the configurations of [±30°]4, [±45°]4, and [±60°]4 are heated to 220 °C and post-formed to a bending angle of 90° with a bending ratio of 2. Micro computed tomography imaging is performed to analyse tube geometry after forming to identify forming and failure modes for tubes beyond the forming limits.


Introduction
The demand for composite materials has been growing over the past decades, especially in the automotive industry for the pursue of lightweight and high performance applications [1]. Carbon fibre reinforced thermoplastic tubes are highly desirable for such applications as they offer high stiffnessto-weight ratios of composites combined with the design versatility of tubes, enabling more possibilities in the making of structural components [2,3]. Currently, straight tubes can be rapidly manufactured by laser assisted thermoplastic automated tape placement (TP-ATP) [4]. The use of thermoplastic polymer matrix system opens the possibility of rapid production and customisation of carbon reinforced composite parts. Fibre relocation and re-orientation are possible via re-heating of the matrix system into a soft and formable state [5]. Therefore, formation of complex curvatures from straight thermoplastic tubes is possible via post-forming operations such as rotary draw bending (RDB) akin to metallic tubing [6].
As a post-forming technique, RDB at elevated temperature is relatively simple with notable advantages including high design freedom, reduced instrument cost, and the possibility of automation [7]. In a thermoplastic composite RDB process, it is possible for the tube undergo forming when the temperature in the bending zone is sufficiently high for significant matrix softening. In this study, a straight tube is first fed into the RDB setup, and the whole assembly is heated to the formable temperature of the tube [6,8]. The heated tube is then bent to the desired curvature defined by a bending angle under isothermal conditions [6,8]. To enable prediction of tube deformation, laminate changes, and the related mechanical property changes for design optimisation, it is important to understand the forming limits of tubes, which can be defined by tube winding angle and bending ratio between the bending radius and tube diameter.
This study will investigate the relation between CF/PA6 tube winding angles and their influence on the post-forming behaviour in a RDB post-forming process. Three sets of CF/PA6 tubes, namely [±30°] 4 , [±45°] 4 , and [±60°] 4 will be post-formed under isothermal conditions to a bending angle of 90°. Micro computed tomography (micro-CT) will be conducted on the post-formed tubes to analyse the geometrical changes and to identify the change of forming modes. A forming limit diagram on tube winding angle and bending ratio based on the parameters used in this study, validated by the forming experiments will be presented by this study. Based on the validated forming limits, the corresponding principal shear strains are derived and compared against the tube axial strains.

Experimental Materials and Setup
Straight CF/PA6 tubes were manufactured at AFPT GmbH via TP-ATP using Celanese Celstran® CFR-TP PA6 CF60-01 tapes. Each tape is 12 mm wide, 0.13 mm thick, and has a fibre volume content of 48%. The tape placement rate was 12 m/min with a consolidation force of 200 N at a process temperature of 280 ℃. The tapes were wound around a chrome steel bar with the diameter of 20 mm, following a conventional helical filament winding pattern, with a shaft parameter of one (N s = 1) defined by [9], and 5, 4 and 3 circuits (P) per ±30°, ±45°, and ±60° layer pair respectively. The manufactured tubes were measured with an average tape width of 12.5mm, inner diameter ( ) of 20 mm, and outer diameter ( ) of 22.6 mm and had 8 plies, resulting in an average wall thickness of 1.3 mm. The winding angle of the ith ply, θ 0,i is computed based on the tube ply circumference, 2πr i , the tape width, w, and P.
A bespoke rotary draw bender was manufactured for the post-forming experiments. The bender contains key elements akin to a traditional metal tube bender with modifications including the polytetrafluoroethylene (PTFE) pressure and wiper dies to minimise heat loss during forming, and the addition of a bending angle selector for curvature setting and a silicone mandrel for internal support. The main bending die has a mid-line bending radius of 46mm, making the bending ratio 2.

Experimental Procedure
Post-forming of CF/PA6 tubes requires heating of the tubes to their formable temperature of 220℃ to soften the thermoplastic matrix prior to forming [6,8]. In this post-forming experiment, a silicone mandrel with its diameter equivalent to d i and length greater than the tube bending zone length, was inserted into the tube. An Omega 5SC-TT-K-40-36 fine wire K-type thermocouple was inserted between the mandrel and the tube bending zone to monitor temperature change in the experiment. A National Instruments cDAQ-9188 data logger was used to record the temperature data readings.

Figure 1 RDB operation for CF/PA6 tubes (a) tube loading and heating, (b) tube bending and clamping
The tube was then loaded into the bender, which was heated until the thermocouple read 220℃ in a Steridium O75 Oven. The duration of heating phase was approximately five hours per tube. The loaded tube was bent by turning the main bending die to 90° at a bending rate of approximately 45° per second and held in place until tube temperature dropped below 100℃. This allowed for the resolidification of the thermoplastic matrix while the bent tube was constrained at the desired geometry to minimise spring-back [6].

Post-Forming Tube Characterisation
Using micro-CT imaging of the post-formed CF/PA6 tubes, tube diameter, d, and tube bending zone length, l are characterised to determine tube axial strain, ε x and ovality changes during forming to identify possible changes in forming modes for tubes with varying θ 0 . ε x is formulated based on the characterised bending zone length before (l 0 ) and after (l 1 ) forming.
The post-formed tubes were imaged using a HeliScan™ micro-CT instrument at the Australian National University (ANU) CTLab. The instrument was equipped with a 60kV X-ray micro-focus source and a 3040 x 3040 pixels flat panel detector. 2D radioscope projections were taken of individual specimens, placed on a rotating motor-controlled stage, after each rotation. Volumetric images of the complete 3D post-formed CF/PA6 tube geometry were obtained from the processing of the 2D projections using a proprietary ANU reconstruction algorithm [10]. Total acquisition time was ~17 hours, total number of projections was 8778, and scanning resolution (i.e. voxel size) was ~45 μm for the tubes bent to 90°. CF/PA6 tube post-forming limits can be expressed in terms of its winding angle limits corresponding to a given bending ratio based on the post-forming fibre orientation prediction model by Eckardt et al [8]. The fibre orientation prediction model predicts the ultimate fibre angle, θ 1 (maximum and minimum) in a post-formed tube based on the initial fibre angle, θ 0 and the bending radius, r b and tube ply radius, r i . The model assumes a pure textile tube deformation during forming, in which only rotational displacement of the crossing tapes at their points of intersection is possible according to [8]. In the formulation of θ 1 , fibre lengths are assumed to be constant due to their high stiffness relative to the molten thermoplastic matrix and the tube circular cross section represented by r i is also assumed to be constant. Additionally, the model neglects slipping effects, resulting in a constant distance between two intersection points [8]. After forming, the maximum and minimum fibre angles can be found at the intrados and the extrados respectively, where the maximum axial strains are experienced by the tube during forming.

CF/PA6 Tube Winding Angle Limits
During forming, the extrados experiences a tensile strain and elongates while the intrados experiences a compressive strain and compresses. Consequentially, the extrados fibres align towards the axial direction (θ = 0) parallel to the tube axis due to the axial tension and the intrados fibres align towards the hoop direction (θ = 90°) normal to the tube axis due to the axial compression. As the fibres are wound between the axial and hoop directions and cannot completely align with the axes, θ 1,ex > 0 and θ 1,in < 90°. Hence, the limits of θ 0 can be derived to satisfy these conditions based on Eq. (3) and (4).
The limits of θ 0 of a given set of bending parameters can be obtained by substituting the parameters into Eq. (5) and (6). The lower limit of θ 0 from Eq. (5) is valid when r i ≠ r b and r i < r b , suggesting that θ 0 is inversely proportional to the bending ratio. The upper limit from Eq. (6), on the other hand, is always satisfied with fibres oriented between the axial and hoop directions. Based on the parameters used in the forming experiments, the lower limit is valid in this study and are computed to compare with θ 0 of each laminate configuration of the experimental CF/PA6 tubes in Table 1. A ±2° variation was observed from the measured θ 0 of the tube outer plies in the experiment.

CF/PA6 Tube Post-Forming Mode Change
Eq. (3) and (4) predict that tubes with smaller θ 0 experience larger fibre angle change during forming. For tubes with θ 0 smaller than the lower limit, axial strain during forming acts predominantly in the fibre direction. In this case, when the required fibre angle change is greater than θ 0 , the forming mode changes from fibre realignment reflected by the smooth surface finish of the  Fig. 3. At tube intrados, compression of axially-aligned fibres in the axial direction forces fibres to buckle rather than to realign. At tube extrados, as the fibres realign to the axial direction due to tension to form the elongated extrados, inward displacement of extrados towards the bending die may occur as a result of the realigned fibres being unable to span the full length of the extrados. For the tubes beyond the forming limits, the inward extrados displacement were accompanied by horizontal expansions of the extrados half of the tubes as well as elongated d 1 . As the tube intrados was constrained by the main bending die, the outer wall of the intrados maintained the desired curvature and ovality of the tube.
The extrados deformation of the tubes beyond the forming limits may be caused by the joint effect of both the intrados and extrados under the forming strains. Buckling was induced at the intrados due to compressive strain. The thickened intrados wall due to buckling pushed the silicone mandrel against the extrados, forcing the extrados to expand, hence resulting in elongated d 1 . On the other hand, tensile strain experienced by the extrados resulted in its inward displacement as it could not be stretched to cover the increased extrados length after forming, hence forming the flattened extrados surface. The extrados surface was flattened more in tubes with smaller θ 0 as the extrados fibres were more axially aligned. As the tube extrados was not constrained, the compression by its inward displacement induced horizontal expansions on the unconstrained sides.

CF/PA6 Tube Forming Limits
With the validated forming limit derivation by the experimental results, the forming limit diagram of the CF/PA6 tubes in terms of the minimum θ 0 required for a given bending ratio based on the parameters used in this study is established. In the forming limit diagram (Fig. 4), diameter of the ply is set as 20 mm, the diameter of ply 1, as it has the lowest winding angle, and tape width as 12.5 mm. The bending ratios range from 1 to 20 by adjusting r b while keeping other parameters consistent. From Fig. 4, the minimum winding angle shows an exponential decrease as bending ratio increases.

CF/PA6 Tube Post-Forming Strain Limits
In terms of fibre shear during forming, the shear strains experienced by the tapes and the tube can be related by a transformation matrix [T] based on the sine (s) and cosine (c) operations of θ 0 . The x and y axes of the tube correspond to its axial and hoop directions respectively as shown in Fig. 2. The tube normal strains, ε and the shear strain, γ on the x and y axes are transformed into principal material coordinates, corresponding to the axial and transverse fibre orientations of the tape.
As the fibre angle prediction model assumes a constant r i , no hoop strain is experienced by the tube during forming, which is reflected by ε y = 0 in Eq. (7). In addition, fibres are assumed to be non-stretchable, hence ε 1 = 0 in Eq. (7) for fibres under tension at the extrados. It is worth noting that ε 1 may become negative at the intrados due to buckling of fibres under compression.
Based on the above assumptions and the known parameters, shear strain experienced by the fibres, 12 at the extrados can be derived using Eq. (8) based on ε x calculated in Eq. (2). The factor − c s suggests that a greater shear is experienced by the fibres with smaller θ 0 at the extrados, resulting in greater fibre angle change from smaller θ 0 predicted by Eq. (3) and (4). Due to the cross-winding pattern of the tubes, the magnitude of shear strain limit, � 12, � for the extrados is compared with the extrados axial strain, ε x,extrados in Fig. 5. � 12, � is derived based on the limits of θ 0 from Fig. 4 and ε x,extrados . The fibre angle prediction model assumptions may become invalid when beyond the principal shear strain limits of �γ 12,max � < |γ 12 | < 0, resulting in the mode of tube post-forming to change from fibre relocation and reorientation to fibre buckling in the context of this study.

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Achievements and Trends in Material Forming Figure 5 Comparison of tube extrados axial strains and extrados principal shear strains From Fig. 5, both strains decrease as bending ratio increases. Between the strains, �γ 12,max � has a larger magnitude than ε x,extrados at bending ratio ≥ 2, where the minimum θ 0 < 45°; �γ 12,max � < ε x,extrados at bending ratio 1 when the minimum θ 0 > 45°. For the bending ratio of 2 used in this study, the minimum θ 0 of 34.815° translates to the maximum γ 12 of -0.313.

Conclusion
In this study, the forming limits of CF/PA6 tubes are presented in terms of a forming limit diagram and the corresponding strains to facilitate design and process optimisation of CF/PA6 component manufacturing. Analysis of micro-CT images revealed that when θ 0 exceeds the limits, forming mode changes from fibre realignment and reorientation to fibre buckling through the following failures captured: • Buckling at the intrados due to compressive strains; • Elongated tube circumferential cross section due the silicone mandrel displaced by the buckled intrados wall; • Flattened extrados wall as a result of its inward displacement as the extrados fibres cannot be stretched to cover the increased extrados length; and • Horizontal expansions on the extrados side walls due to compression of the silicone mandrel induced by the inward displacement of the extrados. Using a general orthotropic off-axis strain transformation, the shear strains experienced by the tapes can be determined based on tube strains. The magnitude of extrados principal shear strains decreases towards 0 as the bending ratio increases and they surpass the extrados tube axial strain when the bending ratio is greater than 2.
Future work will include further validations and improvements in the forming limit model via postforming of CF/PA6 tubes at larger bending ratios. Additionally, experimental characterisation may be conducted to further investigate and validate the strain predictions. Slow motion capture of the forming process may also be implemented to further investigate tube geometrical changes during forming, hence the change of forming modes.