# Accelerated Testing and Reliability of FDM-Based Structural Electronics
## 2 Materials and Methods  
The experiment for the determination of SE reliability used in this work was accelerated life testing. It was decided to operate the electrical systems at elevated temperatures and calculate the mean time to failure using the formula [19]:  
\[MTTF=\frac{D\cdot H\cdot A_{f}}{r} \tag{1}\]  
where \(MTTF\) is mean time to failure, \(D\) is number of devices tested, \(H\) is test hours per device, \(r\) is number of failures, and \(A_{f}\) is acceleration factor from the Arrhenius equation, described by:  
\[A_{f}=e^{\frac{E_{a}}{L}\cdot(\frac{1}{I_{\text{size}}}-\frac{1}{I_{\text{total }}})} \tag{2}\]  
where \(E_{a}\) = 0.7 eV is activation energy (eV) of the failure mode, \(k\) = 8.617 \(\times\) 10\({}^{-5}\) eV/K is Boltzmann's Constant, \(T_{\text{size}}\) is operating temperature (in K) (usually room temperature), and \(T_{\text{test}}\) is test temperature (in K). To simulate structural electrical systems, 2 types of samples were prepared. The first had 6 single traces in 3 different widths, ended with measurement pads at each end. The second type had an additional 0 \(\Omega\) resistor in the middle of each path. Both types of samples also had a single meandering trace to simulate more complex shapes. The samples were prepared in a multistep process. First, glycol-modified polyethylene terephthalate (PET-G) substrates were printed using a fused deposition modeling (FDM) printer from Graften (Poland). The FDM process involves heating and extruding a thermoplastic material through the printer head and applying it to the required area [20,21]. PET-G filament was purchased from Nebula (Poland) and extruded according to the manufacturer's recommendations, i.e., with a nozzle temperature of 230 \({}^{\circ}\)C and a table temperature of 50 \({}^{\circ}\)C. The substrates contained cavities for traces and resistors (if needed). In the next step, FDM printing was stopped, and 0 \(\Omega\), 1218 SMD resistors from Vishay (Malvern, PA, USA) were placed (this step was skipped in the samples without resistors). Then, cavities were partially filled with PM-460A paste from Henkel (Dusseldorf, Germany) using a custom-built automated dispensing system. Dispensing was performed by extruding paste through the tip using controlled pneumatic pressure [22, 23, 24]. In the next step, the paste was dried at 50 \({}^{\circ}\)C for 15 min by FDM printer hot plate, and then the plate covering the traces and resistors was 3D printed on top of the substrate. The cured ink layer was lower than the surrounding polymer layer, so the first layer of covering plate was printed in midair over traces and resistors, but the small size of cavities (less than 10 mm) is not a challenge for FDM techniques. Figure 2 shows the fabrication steps and the appearance of the samples at each step. Finally, 70 samples were produced and divided into three groups. Group A consisted of 3 meandered paths and 4 paths without resistors in each tested width (0.5 mm, 1 mm, or 2 mm) and 2 paths with resistors in each width. Group B consisted of 2 meandered paths and 4 paths with resistors in each width. Group C consisted of 5 meandered paths and 6 paths without resistors in each tested width and 4 paths with resistors in each width. In each group, samples were connected in series to equalize the flowing current, and then all samples were placed in a climatic test chamber CTS C-70/200 at 344 K (71 \({}^{\circ}\)C). The temperature at which the accelerated life tests were performed was limited by the glass transition temperature of PET-G, which is approximately 350 K (77 \({}^{\circ}\)C). After connection to the power supply system, the series of samples was connected to an automated data acquisition system to determine the time when failure of any of the samples in the series occurred. It was assumed that after some time, the circuit would break, indicating failure, which was registered as a state in which the measured current value dropped below 20 mA.