# Mechanical and Fiber-Bridging Behavior of Slag-Based Composite with High Tensile Ductility
## 3 Results and Discussion  
### Composite Properties  
The value of \(f_{cs}\) of the composite was 36.8 MPa; the coefficient of variation of \(f_{cs}\) was 4.5%. The value of \(f_{cs}\) of the composite is lower than that of the previous study, which had an identical water-to-binder ratio [8]. This is attributed to the fact that the chemical compositions of the slag used in this study are different from those of previous study and the fiber volume fraction (1.50%) in this study is lower than that (1.75%) of the previous study. The tensile stress and tensile strain curves of the composite are shown in Figure 4. Strain-hardening behavior, a further increase in stress and strain after first cracking, was clearly observed in all specimens. Because the stresses of the matrix and of existing cracks are released when a new crack occurs, the stress after first cracking fluctuated until it reached maximum stress. The compressive strength and representative values of tensile behavior, i.e., the first cracking strength (\(f_{1 cs}\)), tensile strength (\(f_{ts}\)), and tensile ductility of the composite, are listed in Table 3. Note that the first cracking strength implied a proportional limit, i.e., a maximum stress of the mixture that is directly proportional to strain. The value of \(f_{1 cs}\) of the composite was 3.4 MPa and the ratio of \(f_{1 cs}\) to \(f_{cs}\) was 9.3%, similar to that of normal concrete [19]. This demonstrates that the value of \(f_{1 cs}\) of this composite was affected by the strength of the matrix and that the effect of fiber on \(f_{1 cs}\) is not significant. It should be noted that the coefficient of variation of \(f_{1 cs}\) was 27.5%p higher than that of \(f_{cs}\). The value of \(f_{ts}\) of the composite was 8.5 MPa, and the ratio of \(f_{ts}\) to \(f_{cs}\) was 23%. This ratio is 2.3 times higher than that of normal concrete, whose \(f_{ts}\) is approximately 10% of \(f_{cs}\); also, normally, the value of \(f_{ts}\) of normal concrete is identical to \(f_{1 cs}\). This indicates that the value of \(f_{ts}\) of the composite depends on the fiber-bridging behavior. \(I_{SP}\) refers to the ratio of \(f_{ts}\) to \(f_{1 cs}\). When the index is greater than 1, multi-cracking occurs. The value of \(I_{SP}\) of the composite was 2.5, which means that the composite satisfied the stress condition for strain-hardening and steady-state multiple cracking behavior and is approximately two times higher than the value (=1.3) in the practical design criterion proposed by [PERSON] and [PERSON] [11]. From this analysis, it can be expected that the composite will show high tensile ductility based on multiple cracking. Figure 3: Fiber pullout test: (**a**) dimensions of specimen and (**b**) test setup. The tensile ductility was defined as the tensile strain corresponding to the tensile strength. The tensile ductility of the composite was 7.5%, which is approximately seven hundred times higher than that of normal concrete. The high tensile ductility of the composite is due to multiple micro-cracking and controlled crack width. It should be noted that the values of the coefficient of variation of \(f_{\text{fs}}\) and the tensile ductility were similar to that of \(f_{\text{cs}}\). Toughness represents the comprehensive energy absorption capacity of a composite, encompassing \(f_{\text{fs}}\) and the tensile ductility. Toughness was calculated using the tensile strength and the area that represents the tensile ductility. The toughness of the composite was 0.44 MPa m/m, 16% higher than that of UHPC, with a compressive strength of 166 MPa [20]. Figure 5 shows the representative cracking pattern of the composite. As expected from the tensile stress and strain curves, the composite showed saturated multiple cracks and controlled crack width. It can be assumed that tensile deformation of the composite was mainly induced by crack creating and growth, which are related to the fiber reinforcement, rather than by the deformation of the matrix itself. That deformation is negligibly small compared to the crack width.