# Mechanical and Fiber-Bridging Behavior of Slag-Based Composite with High Tensile Ductility
## 4 Conclusions  
This study investigated the mechanical properties of a strain-hardening slag-based composite with high ductility of up to 7.5% and also the micromechanical characteristics of the composite. The fiber-bridging behavior of the composite was theoretically analyzed to investigate the mechanism of strain-hardening and highly ductile behavior. The following conclusions have been drawn:  
1. The PE fiber-reinforced slag-based composite with a moderate compressive strength of 36.8 MPa showed excellent tensile performance. Although the first cracking strength (3.4 MPa) was similar to that of normal concrete with a similar range of compressive strength, the tensile strength of the composite after strain hardening reached 8.5 MPa. Composite also showed also excellent tensile ductility of up to 7.5%. It was found that the values of coefficient of variation of tensile strength and tensile ductility were similar to that of the compressive strength. The composite also showed saturated cracking patterns. The crack width and crack spacing of the composite were 59.8 \(\upmu\)m and 0.8 mm, respectively.
2. From single-fiber pullout test, the frictional bond strength between matrix and fiber was found to be 1.49 MPa. The slip softening behavior of the fiber pullout test results was considered by the strain-hardening coefficient. Therefore, the strain-hardening coefficient had a negative value because slip softening behavior was observed.
3. The maximum fiber-bridging stress was just 2.3% higher than the tensile strength of the composite, a negligible gap. It seems that the theoretical fiber-bridging curve simulate the tensile behavior of the composite well, especially considering the variation of the matrix properties and the fiber distribution. This implies that the fiber-bridging analysis performed in this study is appropriate to investigate the fundamental mechanism of the strain-hardening and highly ductile behavior of the composite.
4. The stress performance index of the composite was 2.5, which is approximately two times higher than the value (=1.3) in the practical design criterion. The energy performance index of the composite was 8.9, which is approximately three times higher than the value (=2.7) in the practical design criterion. Both indices explain the strain-hardening and steady-state multiple cracking behavior of the composite and supports the excellent tensile behavior of the composite.  
Conceptualization, J.-I.C. and B.Y.L.; methodology, J.-I.C. and B.Y.L.; software, J.-I.C. and B.Y.L.; validation, H.-K.K. and B.Y.L.; formal analysis, J.-I.C.; investigation, J.-I.C.; writing--original draft preparation, J.-I.C. and B.Y.L.; writing--review and editing, H.-K.K. and B.Y.L.; visualization, J.-I.C.; supervision, H.-K.K. and B.Y.L.; funding acquisition, B.Y.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A2C4069794).  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(I_{tip}\) (J/m\({}^{2}\)) & \(I_{b}\)\({}^{{}^{\prime}}\) (J/m\({}^{2}\)) & \(I_{EP}\) \\ \hline
11.3 & 100 & 8.9 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Energy condition.