Electro-Heating of Polymer Nanocomposites for Aeronautical Composite Structures ^†

Abstract

This work presents an approach for designing 3D-printed heaters with tunable electrical resistance by optimizing both printing and geometrical parameters. To this end, acrylonitrile butadiene styrene reinforced with carbon nanotubes (ABS-CNTs) has been processed through fused filament fabrication (FFF) in a manner that favors electrical current flow along the printing direction and enables adjustment of electrical resistance to meet the scalability needs and limitations of the power supplier available in the application field. The as-developed 3D-printed heater has been integrated into an aeronautical fiberglass composite as proof of its possible application as a de-icing system.

1. Introduction

Electro-thermal heating based on the Joule effect has emerged as a versatile solution for a wide range of applications, including de-icing strategies [1], out-of-autoclave processing [2,3], and welding operations [4,5]. Despite its potential, achieving uniform heat distribution, simplified design, and high energy efficiency remains challenging [6]. These objectives require materials capable of efficiently converting electrical energy into heat, as well as manufacturing processes that allow customization of heater characteristics to meet specific performance requirements and application constraints—such as available power supply, heating area, and target steady-state temperature.

Recent advancements in composite materials and additive manufacturing technologies have opened new opportunities in this field. The incorporation of conductive nanofillers (e.g., carbon nanotubes [7,8,9], graphene [10,11,12], mxene [13,14]) into polymer matrices enables the development of lightweight, flexible heating elements that can conform to complex geometries [15]. Literature reports indicate that achieving high electro-thermal efficiency typically requires adding conductive fillers beyond the electrical percolation threshold [16], which allows for significant temperature increases at relatively low applied voltages. However, this approach alone may not suffice for large-scale industrial applications, where the required voltage strongly depends on both the heater dimensions and the intrinsic electrical conductivity of the material.

Rather than solely modifying material composition, geometrical optimization of the heater design combined with careful selection of processing parameters offers a promising strategy to address these limitations. Fused filament fabrication is a 3D-printing technology capable of creating complex geometries without material waste by depositing molten thermoplastic materials layer by layer [17]. Combining the functional properties of nanocomposites with the design flexibility of additive manufacturing enables the fabrication of customized devices tailored to specific application needs.

In this context, the present work investigates design and optimization approaches for Joule-effect-based heating elements, with particular emphasis on scalability, flexibility, and energy efficiency. The aim is to propose solutions that enable integration into complex structures while ensuring reliable thermal performance under demanding operating conditions.

2. Materials and Methods

The ABS filled with carbon nanotubes (ABS–CNT) was sourced from 3DXTECH Additive Manufacturing (Grand Rapids, MI, USA) as spooled filament whose diameter was 1.75 mm. The nanofiller concentration is reported as below 10 wt% in the technical datasheet. Three distinct geometries of 3D-printed heaters were fabricated (see Figure 1) using an Original Prusa i3 MK2 3D printer (Prusa Research, Prague, Czech Republic). Printing settings were configured in Slic3r Prusa Edition (Prusa Research) and kept consistent across all tested samples. During the CAM phase, the infill pattern of the sample has been designed in such a way as to complete each geometry through concentric perimeter repetitions. Considering the position of the electrical contacts, this strategy allows the current to flow in the direction parallel to the deposited filaments (see Figure 1). In a recent work [18], the authors have demonstrated that the electrical conductivity along the printing direction is about two orders of magnitude higher than the electrical conductivity in the direction perpendicular to the printed filaments.

The other printing parameters are an extrusion temperature of 250 °C, a bed temperature of 80 °C, a nozzle diameter of 0.4 mm, an infill density of 100% and a printing speed of 80 mm/s. The layer height was set to 0.3 mm for the first layer and to 0.2 mm for the following layers. These parameters have been chosen to ensure the high quality of the final object (e.g., lower porosity [19] allowing the material to relax internal stresses [20]). To demonstrate its suitability for de-icing applications, the H3 printed heater was embedded in the middle plane of a fiberglass composite as a functional heating element. The sandwich panel consisted of four fiberglass prepreg layers (Krempel BD 2808, twill 2,2, Krempel GmbH, Vaihingen/Enz, Germany) arranged in a (0°/90°/0°/90°) stacking sequence on both sides of the embedded heater, in an oven at 80 °C for 3 h within a vacuum bag system. The selected curing cycle allowed the 3D-printed heater to be consolidated in the composite structure without softening and without losing its morphology since 80 °C is well below the glass transition temperature of ABS-CNTs, which is 110 °C [21]. The electrical characterization method and Joule heating test procedure are summarized in

Table 1. Electrical characterization and Joule heating test methods.

Test Type	Method/Setup	Equipment Used	Conditions
Electrical properties	Two-probe method; silver paint for contacts (green and red areas in Figure 1).	Silver paint (RS 196-3600, RS PRO, Corby, UK); Electrometer Keithley 6517A (0–25 V, 10 steps) (Keithley Instruments, Inc., Solon, OH, USA); Multimeter Agilent 3458A (Agilent, Santa Clara, CA, USA).	Voltage sweep: from 0 to 25 V and from 25 V to 0 V (to check hysteresis).
Joule Heating Test	DC mode with a constant selected voltage.	Power supply EA-PSI 8360-10T (0–360 V, 0–10 A, 1000 W max) (EA Elektro-Automatik GmbH & Co. KG., Viersen, Germany); Data Logger TC-08 (Pico Technology Ltd., St Neots, UK); PicoLog software (version 6.2.8).	Temperature evolution at sample center. Static air, both sides at 25 °C.
Temperature Measurement	Thermocouples and IR imaging.	Type K thermocouples (Omega Engineering Ltd., Manchester, UK); IR Camera Fluke Ti401 Pro Thermal Imager (Fluke Corporation, Washington, DC, USA).	Local temperature and surface temperature map.

.

3. Result and Discussion

3.1. Electrical Characterization of 3D-Printed Heaters

Considering the position of electrical contacts (green and red areas in Figure 1), H1, H2 and H3 can be schematized as resistances composed of several resistive branches in parallel. Based on this, the overall equivalent resistance value ($R_{eq}$) is described by the following equation:

$${\displaystyle \frac{1}{R_{eq}}}= {\sum }_{i=1}^n{\displaystyle \frac{1}{R_i}}$$

(1)

where $n$ is the number of resistive branches in parallel and $R_i$ is the electrical resistance of each of them. If all branches have the resistance value ($R$), Equation (1) becomes:

$$R_{eq}={\displaystyle \frac{R}{n}}$$

(2)

Substituting the second Ohm’s law in Equation (2), a simple model describing equal resistances in parallel is obtained as follows:

$$R_{eq}={\displaystyle \frac{1}{n}}\times \rho \times {\displaystyle \frac{L}{W\times s}}$$

(3)

where $\rho$ is the electrical resistivity of the material, $L$ is the length, $W$ the width and $s$ the thickness of the sample.

In the present case, the material composition remains unchanged for all three geometries; thus, the same electrical resistivity value has to be considered. As expected from Equation (3), the total equivalent resistance can be tuned by varying the number of branches in parallel $\left(n\right)$, their length $\left(L\right)$, width ($W$) and thickness ($s$). In this way, it is possible to reduce the equivalent resistance without changing the filler concentration in the building material. This approach is particularly advantageous for 3D-printed heaters for two main reasons: (i) the free-form manufacturing easily allows for the production of customized heaters whose geometry has been optimized based on electrical resistance requirements, differing from traditional production processes requiring suitably designed molds; and (ii) it is not necessary to increase the filler concentration to reach a low resistance value, avoiding common issues during the printing such as clogging during the processing of nanocomposite materials. H1 geometry was inspired by commercially available metallic resistors. The values of $n, L, W$ and $s$ for H1 are reported in

Table 2. Geometric parameters and electrical resistance values of the three experimental 3D-printed heaters.

	H1	H2	H3
$n$	2	15	150
$L$ [cm]	73.6	10	1.25
$s$ [mm]	2	2	0.5
$W$ [mm]	2	2	2
$R_{eq}$ [Ω]	30,834	823	30

. However, the experimental value of $R_{eq}$ for the H1 sample was too high to apply H1 as a heater, since very high voltages would have been necessary to heat it. Passing from H1 to H2, the printing area occupied by the samples has been kept constant and equal to the value of 30 cm². At the same time, to reduce the total equivalent resistance, the number of branches in parallel increased from two to 15, and their length was reduced from 73.6 cm to 10 cm. This choice resulted in lowering the total equivalent resistance by about two orders of magnitude. Although the H2 configuration demonstrates reduced electrical conductivity as expected from Equation (3) compared to H1, it was not flexible. However, flexibility remains a key factor for the integration of electro-thermal heaters into composite structures, particularly those with curved geometries (e.g., the leading edge of an airplane). To get flexibility, the thickness decreased from 2 mm to 0.5 mm. To compensate for the effect of thickness reduction on the $R_{eq}$ (it causes an increase in total resistance, according to Equation (3)), $n$ was increased from 15 to 150, and $L$ was reduced from 10 cm to 1.25 cm, while keeping the area to be heated (30 cm²) constant. H3 could be represented as a long series of 150 branches in parallel; however, by folding it and overlapping the equipotential surfaces of the electrical contacts, a more compact comb structure was obtained. The value of equivalent resistance for H3 is 30 Ω, about one order lower than the equivalent resistance of H2 and three orders lower than that of H1. The geometric parameters and the respective $R_{eq}$ values for H1, H2, and H3 are summarized in Table 2.

The advantage of this strategy also relies on the possibility of scaling up H3 by properly tuning the $R_{eq}$ value according to the area to be covered and to the power supplier available in the application field. This aspect will be clearer in the following section, where the Joule heating performance of H1, H2, and H3 is discussed.

3.2. Joule Heating Performance of 3D-Printed Heater

Joule heating tests have been carried out on the three experimental heaters to understand their performance in terms of the required voltage value needed to reach a determined temperature. Due to the high equivalent resistance value of H1, a high voltage value of 350 V has been applied to obtain an increase in the temperature of 25 °C (∆T) at steady-state conditions (from an initial value of 20 °C to the plateau value 45 °C). By lowering the total resistance by two orders of magnitude, passing from H1 to H2 geometry, a lower voltage value (100 V) was enough to reach a higher temperature, 97 °C, at a steady state, corresponding to a ∆T of about 77 °C. The value of the electrical power applied to H1 and H2 is summarized in

Table 3. Electro-thermal heating performance of H1, H2, and H3.

	H1	H2	H3
$R_{eq}$ [Ω]	30,834	823	30
$P$ [W]	4	12	11
∆V [V]	350	100	18
∆T [°C]	25	77	56
∆tss [s]	160	200	120

along with the applied voltage (∆V), the steady-state temperature variation (∆T), and the time needed to reach the steady-state temperature (∆t_ss). The temperature profiles of H1 and H2 during Joule heating tests are shown in Figure 2a and Figure 2b, respectively, together with the IR thermal camera image captured at steady-state conditions (300 s).

In the case of H3, the low value of equivalent resistance (30 Ω) allows for applying a low voltage value (18 V) to reach a steady-state temperature of about 76 °C (∆T = 56 °C). Thermal IR images reported in Figure 2a–c show a quite homogeneous temperature distribution on the surface of all three experimental 3D-printed heaters.

Adapting the electrical resistance to the voltage values available in the application field can be very useful. For example, when the heater is intended for use as an aircraft de-icing system, the onboard power supply typically provides voltages of 28 V or 110 V [22]. Conversely, if the same system is designed for integration into civil buildings to prevent roof icing in cold climates, the power source would generally be the domestic electrical grid—230 V in Europe and 120 V in the United States [23]. In automotive applications, the available onboard voltage is usually 12 V or 48 V [24]. Figure 3 shows how ∆T depends on the applied electrical power values. As expected from the heat balance at steady-state conditions described by Equation (4), by increasing the applied power, the steady-state temperature increases linearly.

$$P\approx G=h\times \left(T_{ss}-T_{air}\right)\times S$$

(4)

where $G$ is the heat generated inside the sample by the Joule effect, strictly determined by the applied electrical power $P$, $h$ is the heat transfer coefficient due to free convection toward the air, $T_{ss}$ is the steady-state temperature of the sample, and $T_{air}$ is the temperature of the surrounding ambient, while $S$ is the exchange surface between the sample and the air.

3.3. Joule Heating Performance of the 3D-Printed Heater Integrated in the Fiberglass Structure

The topological optimization implemented in this study establishes a framework for designing heating elements that can be effectively scaled for large-area applications. Among the proposed configurations, H3 represents a notable example of a low-resistance heater that combines scalability with mechanical flexibility. When an increase in the heating surface is required, the comb-like architecture of H3 can be replicated following the schematic representation in Figure 4a. This modular approach allows for an increase in the number of branches, with their lengths adjusted to preserve constant equivalent resistance, as defined by Equation (3). Furthermore, the H3 configuration exhibits remarkable flexibility, as evidenced in Figure 4b, which underscores its suitability for integration in curved structures, shown in Figure 4c. Joule heating tests were repeated on the H3 integrated into the fiberglass curved structure at two different power values, 5 W and 16 W. The data obtained are reported in Figure 4d. Even in these two cases, thermal camera images at steady-state conditions show an overall homogeneous temperature distribution on the fiberglass composite. This result means that the 3D-printed heater survived the integration procedure and the curing phase without undergoing any defects.

4. Conclusions

This present paper shows a case study of the fabrication of ABS-CNT heating elements via fused filament fabrication (FFF), having tunable performance based on application-specific requirements such as target temperature, available power supply, and geometric adaptability. Firstly, 3D-printed heaters have been printed in such a way as to favor the current flowing along the printed filaments. Without changing the material composition, a design strategy regarding the electrical resistance of the 3D-printed heaters based on the model of ì resistive branches in parallel was proposed and validated. Three different electro-thermal heaters (H1, H2, and H3) have been produced following this strategy, resulting in a reduction in the equivalent resistance by about three orders of magnitude (from ~30 kΩ of H1 to ~30 Ω of H3). The optimized heater H3 was successfully integrated into a curved fiberglass composite thanks to its flexibility. These results highlight how, by properly combining the smart function of nanocomposite materials (e.g., electro-thermal heating) with the 3D-printing potential (e.g., free-form fabrication), it is possible to produce customized devices meeting application requirements.