## 4 Results and Discussion
### Material Properties  
For each set of print settings 9 specimens were produced, totaling 154 specimens. Out of the 154, tensile data could only be collected for 142 specimens. Out of these 142 specimens, only 64 failed within the grips. Therefore, fracture characteristics could only be gathered for 64 specimens. For each data point, nine specimens were prepared to eliminate experimental error. Table 3 displays the results for every set of parameters. Column 8 in Table 3 shows the final number of samples with usable test data. Figure 11: Variation in the amplitude and wavelength of vibrations with varying motor speeds. Error bars represent (\(\pm\)) 1 S.E. Figure 12: A line was drawn at S26, before and after the collapse, likely due to the pen rubbing on the paper. Figure 13: Lines drawn at different motor speeds as viewed through the microscope. The most significant improvement in mechanical properties came from adding induced vibration for specimens printed in the lower right area of the print bed, with 3600 mm/min print speed and 205 \({}^{\circ}\)C extrusion temperature. This increased tensile strength from 36.7 MPa to 39.6 MPa, and elastic modulus from 2933 MPa to 3095 MPa. The two specimens (vibration and no vibration) with the highest tensile strength from this set are shown in Figure 14. The average mechanical property values are listed in Table 4.  
Induced vibration did not produce any change in dimensional accuracy. No vibration specimens were on average 3.57 mm thick and 13.12 mm wide, while vibrated specimens were 3.58 mm thick and 13.12 mm wide. Specimens were too long to measure length by micrometer, so they were measured by caliper. Due to the resolution of the calipers, they were not included as a metric for judging dimensional accuracy, and a standard length of 168.5 mm was used to calculate the volume of each specimen. Each specimen was within \(\pm\)0.2 mm of 168.5 mm lengthwise. Porosity is defined as the volume of pores in the specimen divided by the volume of the specimen itself:  
\[\%\ P porosity=\frac{V_{p}}{V_{s}} \tag{1}\]  
\(V_{p}\) can also be expressed as the volume of the specimen minus the volume of water displaced (\(V_{s}-V_{d}\)):  
\[\%\ P porosity=1-\frac{V_{d}}{V_{s}} \tag{2}\]  
Specimens subjected to induced vibrations had lower values of porosity. Values for porosity were smaller than those reported in [PERSON] et al. [24]. This is due to the size of the nozzle and bead width used in combination with layer height. The bead width used was five times larger than the layer height used, producing relatively flat beads. Rounder beads result in more porosity, since the corners of these beads will be empty space, while rectangular beads with have more material at these interfaces. Specimens without induced vibration had an average porosity of 4.0% volume, while those subjected to induced vibration had 3.2% porosity on average, as shown in Figure 15.  
Inducing vibration appeared to alter the shape of the rasters. Inducing vibration is also shown to cause fusing between rasters, making it difficult to identify individual beads. The fusion present in the induced vibration specimen gives it the appearance of more homogenous material. While this fusion likely increased mechanical properties by decreasing porosity and increasing bead adhesion, it also made rasters thinner at certain \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Tensile Strength**} & \multirow{2}{*}{**Strain at Tensile Strength**} & **Elastic** & **Fracture** & **Strain at Fracture** \\  & & **Strength** & **Modulus** & **Strength** & **Strength** \\  & **(\%)** & **(MPa)** & **(MPa)** & **(MPa)** & **(\%)** \\ \hline No Vibration & 34.5 & 1.8 & 2859 & 28.7 & 3.2 \\ Vibration & 37.1 & 2.0 & 2914 & 33.3 & 2.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average mechanical property values for each category of printed parts. Figure 15: Porosity of specimens with and without induced vibration. sections, creating weak points susceptible to fracture.