## 3 Results and Discussion  
### Resistivities of Filaments and Printed Parts  
In FDM, the filaments were heated into a semi-molten state and extruded into thin fibers from a nozzle of the 3D printer. The fibers were deposited layer by layer according to the sliced model design to build 3D models (Figure 1a). To compare the resistivity of the ABS/CB composites in different shapes, the resistivities of the filaments, fibers, and the cubic samples (Figure 1b) at frequencies of 1 Hz-1 MHz were measured and are shown in Figure 1c, wherein cubic samples were fabricated by a default process parameter combination (layer thickness: 0.2 mm, raster width: 0.4 mm, air gap: 0.00 mm). The resistivities of differently-shaped parts were relatively constant from 1 Hz to 100 kHz, and then decreased gradually from 100 kHz to 1 MHz. The resistivities of the cubic samples are much higher than those of the filaments, as reported previously for ABS/GO composites [15], and the resistivities of the extruded fibers wereslightly lower than those of the filaments. In addition, the resistivities of the cubic samples significantly varied in different directions (Figure 1c), which is consistent with previous reports [18]. For instance, at a frequency of 1 kHz, the resistivities of the filaments, the fibers, the samples in the horizontal direction and the samples in the vertical direction were 29.06 \(\pm\) 0.77 \(\Omega\cdot\)m, 26.55 \(\pm\) 0.50 \(\Omega\cdot\)m, 42.59 \(\pm\) 1.94 \(\Omega\cdot\)m and 101.60 \(\pm\) 6.85 \(\Omega\cdot\)m, respectively. It can, thus, be concluded that the resistivities of the cubic samples increased compared to the fibers, but the resistivities of the filaments did not increase compared to the fibers. Consequently, the possible reason was due to the internal structural features of the printed parts produced during deposition of the fibers but not to the heating and extruding process of the materials. To investigate why the resistivity changed from fibers to the printed samples, a finite element model was established to simulate the printed structure that was created from the fibers. The cross-section of the fiber is circular when the material extrudes from the nozzle, but the fiber becomes squeezed and deformed when deposited. The fiber was modeled with two straight sides and two rounded sides [28], as shown in Figure 1a. The advantage of this model was that the mass density decrease from the solid model to the printed structure model was similar to the actual case considering the existence of voids for printed parts. Specifically, the density decreased from 1.178 g/cm\({}^{3}\) for the ABS/CB composite filament to 1.051 g/cm\({}^{3}\) for the printed parts and the density ratio of the printed structure to solid structure was 0.891 for simulation models. The simulation results indicated that the resistivities of the printed structure in the vertical and horizontal directions are 1.85 and 1.38 times of those of the cubic solid model, respectively, as shown in Figure 1d. In fact, the measured values were 3.83 and 1.60 times. Therefore, voids may not be only factor to determine the resistivities of cubic samples. Although using a greater void fraction in the simulation model could increase the predicted resistivity, it also unavoidably decreases the density further, inconsistent with the actual case. The fibers extruded from the nozzle are semi-molten [27; 28; 36] and not completely fused. The imperfect bonding conditions between adjacent fibers may cause contact resistivity. Hence, besides voids, the influence of this contact resistivity between fiber layers on the resistivity in the vertical direction was also examined in the simulation model. As shown in Figure 1e, the resistivity indicated by the model increased with contact resistivity. The relationship between the resistivity in the vertical direction and the contact resistivity was given in Figure S4.