1 Introduction

Polymer heat sinks and heat exchangers can be viable in many applications [1], especially where lightweight thermal solutions are important such as aerospace, automotive, and electronics applications [2,3,4]. Thermal performance can be limited by the polymer thermal conductivity [5]; however, by leveraging the additive manufacturing (AM) of polymer composites, thermal performance can be improved by both higher conductivity composite materials [6] and through the freedom to design and fabricate complex geometries for improved convection [7, 8]. For these reasons, there has been recent interest in studying AM polymer composite heat exchange technologies [9,10,11,12]; however, these composites have been exclusively discontinuous which limits their thermal conductivity [13, 14].

The shortcomings of discontinuous composites can often be improved using continuous fiber composites [15]. Historically, the continuous fibers used are typically natural, glass, and polyacrylonitrile (PAN) carbon fibers (CF) [16,17,18,19]. These fillers, (especially PAN CF) in conjunction with improved fused filament fabrication (FFF) 3D-printing techniques, have allowed for significant improvements in mechanical properties of the resulting polymer composites [20] and typically result in composites with better mechanical properties than those with discontinuous fillers [21]. Thermal conductivity, which is important for lightweight heat exchange applications, is often overlooked and most studies which investigate the thermal conductivity of FFF composites also focus on discontinuous fillers [22,23,24]. Notable exceptions are studies by Ibrahim et al. [25], which characterized the effective thermal conductivity of continuous PAN carbon fibers, and Ibrahim et al. [26], which developed a continuous metal wire FFF process for increased effective thermal conductivity [27].

In contrast to PAN carbon fibers (which are derived from a synthetic polymer), pitch carbon fibers (PCF) are derived from petroleum or coal tar pitches and undergo a graphitization process. As PCFs can have very high thermal conductivities (up to ≈800 W/mK in the case of Mitsubishi Chemicals K13D2U), they have been employed in FFF in discontinuous form by Ji et al. to fabricate samples with thermal conductivities of 7.36 W/mK using a volume fraction of 12% PCF [28]. If PCF can be printed in a continuous form, models suggest that only 20% volume fraction is required to achieve an effective thermal conductivity of 167 W/mK which would rival the performance of many aluminum alloys used in heat exchange applications but with only half the density [25]. The printing of continuous PCF in FFF processes is challenging, however, due to the brittle nature and high tensile modulus of PCF [29, 30]. FFF extruders typically extrude at a right angle to the print bed and such a sharp bend causes the PCF to break upon exiting the nozzle.

A method for 3D printing pitch-based carbon fiber composites was developed previously and used to print multi-layer composite samples with unidirectional fibers. This approach used a print nozzle that was angled at 45° from the print bed to help mitigate breakage [31]. The resultant composites demonstrated very high stiffness [32] and thermal conductivities of up to 37.1 W/mK with a relatively low volume fraction of pitch carbon fiber (9.5%) [31]. However, in both studies, the stiffness and the effective thermal conductivity were significantly lower than theoretically predicted. Micro-computed tomography analysis showed a degree of fiber breakage had occurred resulting in discontinuities in the heat flow paths [31]. Moreover, this process was limited to printing only unidirectional samples.

An alternative to conventional FFF printers is to employ a 6-axis robot to serve as the motion control platform. A robot arm with a large working area and sufficiently high accuracy and repeatability can improve print quality through better control of fiber alignment and more complex geometries, and support the fabrication of larger components [33]. Yao et al. showed that using the greater mobility of a 6-axis robot can be leveraged to print on non-flat surfaces while avoiding staircase effects and collision resulting in parts with improved strength compared to conventional flat slicing [34]. High-performance continuous PAN carbon fiber composites have also been printed using a robot arm by Miri et al. which demonstrated high strength and stiffness [35] and Abedi et al. with good electromagnetic shielding properties [36]. The improved range of motion offered by robot arms was used by İpekçi and Ekici to 3D print continuous carbon fiber and successfully printed hollow tubes with bends and without any staircasing [37].

Here we present a new method for printing continuous PCF using a 6-axis robot arm which leverages the additional degrees of freedom to angle the print nozzle relative to the build plate such that the bending stress applied to the PCF at the nozzle exit be reduced to better mitigate fiber breakage. Moreover, this angled nozzle can be articulated to follow the raster path, allowing for curved rasters to be printed. This approach can potentially afford design flexibility for components with internal high-conductivity pathways and strategically designed thermal networks. We investigate these methods by quantifying the effective thermal conductivity of single 3D-printed PCF composite rasters to understand factors which contribute to fiber breakage. In this way, the continuous PCF 3D-printing process can be improved to result in 3D-printed composite materials with improved thermal properties more suitable for lightweight heat exchange applications.

2 Experimental methods

2.1 Materials and fiber preparation

The pitch carbon fiber investigated in the present study was manufactured by Mitsubishi Chemical Carbon Fiber and Composites with the specified properties summarized in Table 1.

Table 1 Pitch carbon fiber properties [38]
Full size table

Prior to 3D printing, the PCF was first coated with molten polylactic acid (PLA) pellets (3DXTECH) which was allowed to solidify to create a rigid PCF filament amenable to printing through a direct drive extrusion system. This coating was performed using a custom pultrusion setup, as shown in Fig. 1a, which included the molten PLA bath through which the PCF was passed. After the polymer bath, the PCF was pulled through an 0.8-mm nozzle and allowed to cool at room temperature and solidify. Expansion after the nozzle resulted in a continuous PCF filament approximately 1 mm in diameter and the resulting volume percentage of this filament was approximately 24% PCF as shown in Fig. 1b (estimated using the specified fiber count and fiber diameter from Table 1).

Fig. 1
figure 1

a Coating pitch carbon fiber tows with PLA, b cross-section of PLA-coated PCF

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2.2 Continuous fiber printer extruder and movement control

In the two previous investigations which 3D printed continuous pitch carbon fiber, the 3D printer used a fixed angle hot end which resulted in the PCF extruding at a constant 45° relative to the print bed [31, 32]. The fixed angle limited the printer to only printing unidirectional samples along the x-axis, severely limiting the complexity of printed parts. To overcome these limitations, a new extruder was designed and fitted on a 6-axis robot arm, which allows the nozzle to be angled in any direction and for full articulation of the nozzle during printing. In this way, the angled nozzle can be articulated to follow the path of a curved raster.

The extruder design is shown in Fig. 2a. It consists of a V6 hot end (E3D-Online) with a custom nozzle which was machined to be longer and slenderer such that the entire extruder could be angled to a large degree without hitting the printing surface (Fig. 2a).

Fig. 2
figure 2

a Schematic of the continuous PCF extruder nozzle including detailed view of nozzle, b photograph of the extruder mounted to the robot arm illustration nozzle articulation

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An all-metal V6 extruder (E3D-Online) served as basis for this extruder and uses the original heatsink, hot-end, heat-break, heater, and thermistor. However, the nozzle was custom machined to be longer and slenderer than the stock nozzle and allows for the whole extruder to be angled up to 65° from vertical without hitting the printing surface (illustrated in Fig. 2b). To decrease friction between the filament and extruder walls, the internal walls of the extruder and nozzle were coated with a polytetrafluoroethylene (PTFE) spray (Synco Chemical).

The extruder was mounted on an ABB IRB 1200 7–0.7 6-axis arm as shown in Fig. 2b and the arm and a heated print bed were mounted to a steel table. The print bed was coated with a 0.15 mm polyethylenimine (PEI) sheet (Spool3D) to promote raster adhesion, and bed leveling was performed using four compression springs adjusted with screws at the corners of the print bed.

The robot arm motion was controlled via an IRC5 compact controller, and the extruder was controlled with a RAMPS 1.4 control board. G-code was prepared and ran simultaneously on the two controllers to print samples. For the straight samples, the G-code was written by hand. For the curved samples, the open-source tool FullControl GCode Designer was used (Loughborough University) to generate the G-code. The G-code was then converted to motion in the robot arm using RobotStudio 3D Printing PowerPac (ABB).

For this study, the single raster samples were 3D printed at a speed of 13.3 mm/s, hot end temperature of 220 °C, and a bed temperature of 60 °C.

2.3 Fiber and raster thermal conductivity measurement apparatus

The steady-state fiber conductivity approach developed in the present study is shown in Fig. 3a and is akin to setups developed by Piraux et al. [39] and May et al. [40].

Fig. 3
figure 3

Apparatus for measuring the thermal conductivity of 3D-printed continuous fiber rasters a schematic of approach, b close-up photograph of sample test section, c photograph of experimental setup

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The sample under test is clamped between a heater, which applies a known input power to the sample, and a cooling block which holds the other end of the sample at fixed temperature as shown in Fig. 3a. Temperature sensors placed along the sample measure the temperature gradient and at steady state, the thermal resistance of the sample can be computed.

The heater consists of small copper clamp with an embedded thermistor (GAG22K7MCD419, TE Connectivity) which served as a heating element. Electrical power (Qinput) to the heater was supplied and measured using a Keithley 2400 SourceMeter. The other end of the sample was clamped to a copper cooling block which was temperature controlled using a PID controlled thermoelectric water chiller. The resulting temperature gradient along the sample was then measured using two carefully calibrated thermistors placed in contact with the samples at a known spacing, L. The two sensing thermistors were measured using a Lakeshore Model 370 AC Resistance Bridge to accurately measure their resistance with minimal self-heating using a four-wire configuration. The thermistors were calibrated together against a reference probe (5606 Full Immersion PRT, Fluke) in a uniform temperature environment like that described in Ref. [41], such that the resistors were found to show the same temperature reading with a maximum uncertainty of approximately ± 0.02 K.

The thermal resistance of the sample is quantified as

$$R_{{\text{sample}}} = \frac{T_1 - T_2 }{{Q_{{\text{sample}}} }}$$
(1)

where T1 and T2 are the measured temperatures across the sample and Qsample is the heat transfer rate through the sample quantified using the electrical input power less any heat loss to the ambient (described below). The effective thermal conductivity of the fibers in the sample was then calculated as

$$k_f = { }\frac{L}{{\left( {R_{{\text{sample}}} } \right)A_f }}$$
(2)

where L is the distance between the temperature measurements measured using calipers (with an estimated uncertainty of 1 mm), and Af is the cross-sectional area of the conductive fibers calculated from the specified diameter of the fibers and the fiber count per tow (this assumes that all heat flow through the sample is conducted through fibers and not the polymer).

This method relies on the assumption that all input power to the heater flows through sample and therefore minimal heat loss to the ambient. This was achieved by placing the whole test section under vacuum to minimize heat transfer through the ambient air like Refs. [39] and [40]. The bell jar setup shown in Fig. 3c was used to enclose the sample test section. Electrical and fluid feedthroughs were used to connect the thermistor wires and to temperature control the cooling block. Vacuum was achieved using a rotary vane pump (Edwards V5) which is specified for 10–3 mbar. A Pirani gauge (EDWARDS APG-L-NW16) was used to measure the vacuum within the chamber. Outgassing was minimized by thoroughly cleaning and heating the inner surfaces of the chamber to remove any contaminants. Sample thermal measurements were only considered once the chamber pressure reached 2 × 10–3 mbar to lower the thermal conductivity of air to 4% of its nominal value at atmospheric pressure [42] and obtain sufficiently accurate measurements of kf using this technique.

During measurements, the cold block was held at ≈14 °C and the hot clamp was supplied with approximately 40 mW. The ambient temperature in the chamber was kept at 22 °C. The distance between thermistors T1 and T2 on the samples was approximately 20 mm for each sample such that a sufficiently large temperature difference could be measured with good accuracy (typically 3 to 5 K depending on thermal conductivity of the sample for input powers of on the order of ≈10–2 W). Temperature and input power measurements were collected and displayed by a MATLAB script. All tests were run until steady state was achieved.

2.4 Uncertainty analysis and heat loss calibration

A summary of the measured quantities, their measurement technique, and their associated uncertainties is presented in Table 2.

Table 2 Measured parameters and uncertainties
Full size table

The uncertainty of kf was quantified using the individual measurement uncertainties and the error propagation method described by Kline and McClintock [43]. The uncertainty of the calculated quantity, UZ, is expressed generally as

$$U_Z = \sqrt {{\mathop \sum \limits_{i = 1}^n \left[ {\frac{\partial Z}{{dx_i }}U_i } \right]^2 }}$$
(3)

where Z is the calculated quantity expressed in terms of the measured quantities, xi, having the uncertainties Ui. The resultant uncertainty in kf was approximately 8%.

The vacuum bell jar does not eliminate all heat loss during sample testing and a heat loss calibration was performed to account for the small heat leakage from the heater clamp to the ambient environment by suspending the clamp within the evacuated bell jar and inputting relatively small input powers to the heater thermistor. A relationship between the steady-state heat transfer rate and the temperature difference between the clamp and ambient temperature was established to account for this loss and provide a better estimate of Qsample used in Eq. 1.

3 Results and discussion

3.1 Baseline thermal conductivity measurements

The accuracy of the thermal conductivity apparatus was verified by measuring the thermal conductivities of different metal wires with known thermal conductivities over a range of input powers. Figure 4 shows the measured thermal conductivities of a 28 AWG Copper 110 wire, an 18 AWG Aluminum 1100 wire, and a 1.5 mm diameter 99% tin solder wire as a function of heater input power. The average measured thermal conductivity of the aluminum and tin samples was 214.7 W/mK and 64.8 W/mK, respectively, which agrees well with the accepted values of 220 W/mK and 66 W/mK, respectively, the measured values being only 2.45% and 1.9% away from the accepted values. For the coper wire sample, the average measured thermal conductivity was 409.8 W/mK which is about 5% higher than the accepted value 390 W/mK. Uncertainty propagation led to high uncertainties for the copper wire sample, which stemmed from its relatively small wire diameter (the aluminum and tin wire samples had lower uncertainty due to larger diameters).

Fig. 4
figure 4

Measured thermal conductivity of different wires at different input power values

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3.2 Effect of extruder angle

The effective fiber thermal conductivity was measured for individual straight rasters printed using nozzles angled from 45° to 60° from normal (see Fig. 2b) and the results are plotted in Fig. 5. All samples were printed using the same parameters and g-code settings, except for print angle which was varied in 5° intervals from 45° to 60°. At 45°, the measured kf was 521 W/mK but this increased with nozzle angle achieving 621 W/mK when the extruder was oriented at 60° from vertical. This suggests that that shallower print angles between the heated bed and nozzle result in less PCF breakage during printing; this results in higher thermal conductivities that are much closer to those of the original unprocessed fiber with the 60° sample having a kf of 82% of specified K13D2U thermal conductivity.

Fig. 5
figure 5

Measured thermal conductivity of PCF rasters printed at varying nozzle angles

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3.3 Effect of curvature radius

The previous section demonstrated that shallower nozzle angles resulted in increased effective thermal conductivity of the printed composite; however, to fully leverage the benefits of continuous PCF for thermal applications, the ability to design and control the directionality of the conductive fibers is essential for many applications. To assess these effects, curved continuous PCF rasters were printed with the nozzle held at a constant 55° from vertical and articulating to stay tangent to the curve during printing to evaluate the effect of curvature radius on the effective thermal conductivity of the printed raster. This angle was used because it achieved a reasonably kf and allowed for consistent sample adhesion to the print bed. Samples with a range radius of curvature were printed as shown in Fig. 6a, and the resultant effective thermal conductivity of these fibers, kf, is plotted in Fig. 6b. Samples printed with a radius between 30 and 50 mm had thermal conductivities nominally the same (within measured uncertainty) as the previously measured linear raster printed at 55° of 582 W/mK. The sample printed at a radius of 20 mm was then shown to decrease thermal conductivity and at a radius of 15 mm, the lowest thermal conductivity of 376 W/mK was measured (or 53% less than the original K13D2U fiber thermal conductivity).

Fig. 6
figure 6

a Measured fiber thermal conductivities as a function of printed of radii of curvature, rc, b representative images of samples prior to cutting for thermal testing (rc = 15 mm sample not shown)

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3.4 Effect of cornering technique

The ability to print corners is also important for more complex 3D-printed parts; hence, samples which underwent local changes in direction were also printed. Like the previous section, the PCF rasters were printed with the nozzle held at a constant 55° from vertical. The samples were then printed with a straight approach section, followed by a corner creation process, and then a straight exit path. The turning point process involved the nozzle instantaneously turning to create a corner with varying angles (150°, 120°, 90°) as shown in Fig. 7a (i.e., with an rc of ≈0). It was found that sharp corners printed by turning the nozzle instantaneously at the corner yielded additional breakage, as evidenced by the markedly lower thermal conductivity measured in these samples (Fig. 7b). For a corner with an angle of 120°, a fiber thermal conductivity of 345 W/mK was measured (43% of the original thermal conductivity of K13D2U) while corners at 90° had full breakage.

Fig. 7
figure 7

a Corner samples printed using a turn point method, b corresponding fiber thermal conductivities, c corner samples printed using a constant turning radius, d corresponding fiber thermal conductivities

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Although sharp corners performed relatively poorly (especially at smaller angles), the use of a constant radius of curvature instead of a sharp corner achieved the same general shape and change in printing direction as shown in Fig. 7c. Incorporating a radius of curvature, rc of 20 mm at the corners yielded thermal conductivities consistent with the continuous rc = 20 mm case from Fig. 5, for all turning angles, as shown in Fig. 7d.

4 Summary and outlook

A method for fabricating high-conductivity continuous pitch carbon fiber composites using 6-axis robot arm FFF 3D printing is presented. Continuous pitch carbon fibers were coated in a PLA before being printed using a custom extruder mounted to a 6-axis robot arm. The robot arm was used to angle the printer nozzle with respect to the print bed to decrease the amount of continuous fiber breakage and increase the effective thermal conductivity of the printed rasters. The robot arm further allowed for the nozzle to be angled and articulated in the direction of printing, thereby affording more complex continuous fiber raster paths. Continuous curves with a range of curvature radii were investigated; radii of curvatures of less than 30 mm should be avoided to maintain fiber thermal conductivity. Moreover, approaches to creating corners within raster traces were investigated and showed that sharp corners with low radii of curvature should also be avoided.

Future research should address improvement of the nozzle design itself to further mitigate fiber breakage and understand impacts on raster adhesion. Microscopic imaging to understand the precise mechanism of fiber breakage may also be useful.

This understanding can help support the fabrication of larger-scale continuous PCF composites with controllable anisotropic heat flow paths. It will further support the design of functional thermal composites for lightweight heat exchange applications in the automotive, aerospace, and electronics cooling sectors.