# Enhancing Structural Performance of Short Fiber Reinforced Objects through Customized Tool-Path
## 3 Material Characterization
### Fiber Orientation  
The major assumption underlying the proposed method is that short fibers are fully aligned with the direction of extrusion. Although the fiber orientation of parts was indirectly verified through lab tests, visual verification is required to understand the potential and limitation of the proposed method caused by the inherent drawback of short carbon fibers. The orientation of short fibers embedded in printed parts was investigated by an optical microscope. For this task, the specific method developed \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **Direction** & **CFRP-Nylon** & **ASTM** \\ \hline Young’s Modulus & 0\({}^{\circ}\) & 4.14 GPa & \\ Shear Modulus & 90\({}^{\circ}\) & 2.15 Gpa & D638 \\ Shear Modulus & \(\pm\)45\({}^{\circ}\) & 1.12 Gpa & D3518 \\ Tensile Strength & 0\({}^{\circ}\) & 56.6 Mpa & D638 \\ Shear Strength & 90\({}^{\circ}\) & 28.3 Mpa & D3518 \\ Shear Strength & \(\pm\)45\({}^{\circ}\) & 11.9 Mpa & D3518 \\ Elongation & 0\({}^{\circ}\) & 2.30\% & D638 \\  & 90\({}^{\circ}\) & 1.59\% & \\ Poisson’s ratio & \(\
u_{12}\) & 0.391 & D638 \\  & \(\
u_{21}\) & 0.203 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of carbon fiber-reinforced polymer (CFRP)-Nylon. Figure 5: Test specimens (**a**) tensile (“dog bone”, lower) and shear (rectangular, upper) and (**b**) SHIMAZU tensile machine. Figure 6: Stress vs. strain data for CFRP-Nylon printed at 0\({}^{\circ}\) (**a**), 90\({}^{\circ}\) (**b**), and \(\pm\)45\({}^{\circ}\) (**c**). by [PERSON] [35] was followed to characterize the short fiber orientation of the printed samples. Figure 7. Shows an SEM image of CFRP-Nylon fractured surface, as shown, most of the fibers are aligned in a single direction. Figure 8. shows an optical microscope image of a printed CFRP part. The methodology for fiber alignment analysis is based on the simple geometrical assumption that, ideally, cylindrical fiber should appear on the section as either circular or elliptical shape. However, as shown in Figure 9a, due to variations of fiber tip geometry, such as covering of the matrix material on the fiber tips surface or breakage of fiber tip surface, some of the cross-sectional shapes of fibers are not suitable for fiber alignment analysis--thus, those were excluded. Figure 8: Sample micrographs of a polished specimen obtained from optical microscope: (**a**) Cross-section at 0\({}^{\circ}\) (printing direction), magnitude 50\(\times\); (**b**) cross-section at 0\({}^{\circ}\), magnitude 20\(\times\); (**c**) cross-section at 90\({}^{\circ}\), magnitude 50\(\times\); (**d**) cross-section at 90\({}^{\circ}\), 20\(\times\). Figure 7: SEM image of CFRP specimen printed at 45\({}^{\circ}\) direction. Assuming the length and diameter of the short carbon fibers are uniform as approximately 100 \(\upmu\)m and 5 \(\upmu\)m, the measurement was processed to find only the ends of the major axis. Each image was broken into pixels; each pixel has a value corresponding to the intensity of light at its Cartesian location. These digital images are first subjected to a threshold operation, making each pixel either black or white, as shown in Figure 8(b). The next step is to identify a group of pixels representing each fiber and determine the relevant dimensions. It measured the chord length in several directions and then took the maximum and minimum values as the major and minor axes, respectively. Using the cross-sectional area and major/minor diameters, each cross-section is checked to confirm they are roughly either circular or elliptical. If those fibers whose cross-sections are not circular or elliptical, they would not be used for fiber orientation analysis, and these fibers are filtered out, as shown in Figure 9(b). Using the processed fiber images, such as Figure 9(b), second-order tensors of fiber orientations in the directions of 1, 2, and 3, were computed.