# Mechanical and Fiber-Bridging Behavior of Slag-Based Composite with High Tensile Ductility
## 3 Results and Discussion
### Micromechanical Properties  
Single fiber pullout load and pullout distance curves of specimens for micromechanical analysis are shown in Figure 7. Single fiber pull-out test results showed that there were two stages. In the initial stage, the load increased with a constant slope until the maximum load was reached; in the next stage, the load gradually decreased. As mentioned above, the proportional (linear) increase in load (in the first stage) was attributable to elongation of the fibers according to their elastic modulus. Meanwhile, the load decreased after exceeding the maximum value because the fibers started to be pulled out. Load drops were observed in all specimens directly after load peak and gradual drops were observed after that. Table 5 lists the micromechanical properties obtained from the matrix fracture toughness and the fiber pullout tests, including the matrix fracture toughness (\(K_{m}\)), and the interfacial properties between the matrix and fiber, i.e., the frictional bond strength (\(\tau_{i}\)), chemical bond strength (\(G_{i}\)), and strain-hardening coefficient (\(\beta_{i}\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(N_{c}\) in Gauge Length (80 mm) & \(S_{c}\) (mm) & **Deformation in Gauge Length (mm)** & \(W_{c}\) (\(\mu\)m) \\ \hline
100 (\(\pm\)7) & 0.8 (\(\pm\)0.1) & 6.0 (\(\pm\)0.3) & 59.8 (\(\pm\)3.3) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Cracking patterns.  
Figure 5: Cracking pattern of uniaxial tension test specimen (unit of number: cm).  
Figure 6: SEM images of composite.  
\(K_{m}\) was calculated using Equation (1) [15].  
\[K_{m}=\frac{P_{Q}S}{\sqrt{BB_{N}}W^{\frac{3}{2}}}.f(\frac{a}{W}) \tag{1}\]  
Here, \(P_{Q}\) is the load, \(S\) is the distance between each node, \(B\) is the specimen thickness, and \(W\) is the specimen height. \(f(\frac{a}{W})\) in Equation (1) was calculated using Equation (2) below:  
\[f(\frac{a}{W})=3\sqrt{\frac{a}{W}}.\frac{1.99-(\frac{a}{W})(1-\frac{a}{W})[2.1 5-3.93\frac{a}{W}+2.7(\frac{a}{W})^{2}]}{2(1+2\frac{a}{W})(1-\frac{a}{W})^{ \frac{3}{2}}} \tag{2}\]  
Here, \(a\) is the notch length.  
\(\tau_{i}\) can be calculated with the peak pullout load \((P_{f})\). When \(P_{f}\) if exceeded, fiber pull-out begins. The frictional bond strength was calculated using Equation (3) [18]:  
\[\tau_{i}=\frac{P_{f}}{\pi d_{f}L_{e}} \tag{3}\]  
Here, \(d_{f}\) and \(L_{e}\) are the diameter and embedment length of fibers, respectively.  
Using Equation (4) [18], \(\beta_{i}\) was calculated from the initial slope of the pullout load and pullout distance curves at the point of \(P_{f}\).  
\[\beta_{i}=(d_{f}/L_{e})[(\frac{1}{\tau_{0}\pi d_{f}})(\frac{\Delta P}{\Delta S ^{\prime}})_{S^{\prime}\to 0}\ +\ 1] \tag{4}\]  
Here, \(\Delta P\) is the variation in fiber pull-out load and \(S^{\prime}\) is the slip between matrix and fiber.  
In the present work, the chemical reaction between PE fiber and the matrix was not considered. Instead, the slip softening behavior in the fiber pullout test results was reflected by the strain-hardening coefficient, which was a constant value of zero when the pullout load decreases linearly as the pullout  
Figure 7: Single fiber pullout load and pullout distance curves of specimens (Different colors of lines indicate different samples with identical mixture.).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(K_{m}\) (MPa m\({}^{1/2}\)) & \(\tau_{i}\) (MPa) & \(G_{i}\) (J/m\({}^{2}\)) & \(\beta_{i}\) \\ \hline
0.34 & 1.49 (\(\pm 0.11\)) & 0 & \(-0.06\) (\(\pm 0.03\)) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Matrix fracture toughness and interfacial properties.  
distance increases. The strain-hardening coefficient had a negative value because slip softening behavior was observed in the specimens.