# Investigation into the Flexural Toughness and Methods of Evaluating Ductile Concrete
## 4 Methods of Evaluating Bending Toughness of High-Ductility Concrete
### Discussion for Practical Implementation  
To prove the effectiveness of the evaluation method of bending toughness based on the peak load, the method was used to measure the flexural toughness of HDC, which produced a strain-hardening effect. These results are useful for practical applications.  
As shown in Figure 12, the equivalent bending strength \(f_{\text{n}}\) of HDC significantly increased with the increase in fiber content, but the increase gradually reduced. When the fiber content increased from 0% to 2%, the initial crack equivalent bending strength\(f_{0.35}\) of high-ductility concrete increased by 29%, 25%, and 33%; and the peak equivalent bending strength \(f_{1}\) increased by 170% and 40%, respectively. The equivalent bending strength \(f_{0.85}\) increased by 182%, 38%, and 34%, and the equivalent bending strength\(f_{0.2}\) after the peak increased by 140%, 45%, and 24%, respectively. This was because the initial cracking performance of the HDC mainly depended on the strength and deformation capacity of the material matrix, so the increase in the amount of fiber to the initial bending equivalent bending strength \(f_{0.35}\) was smaller than that of other stages. In addition, the effects of the water-binder ratio and age on the equivalent bending strength of HDC were relatively small, and the range of change was between 2% and 13%.  
It can be seen from Table 3 that, compared with the bending toughness ratio of plain concrete, the increase in the bending toughness ratios of the HDC beams \(R_{1}\), \(R_{0.85}\), and \(R_{0.2}\) reached 184%, 190%, and 143% at the maximum, respectively, indicating that HDC exhibited good cracking performance. A good pseudo-strain hardening effect was achieved and the toughness of plain concrete was significantly improved. This was due to the incorporation of fibers, which made the test piece crack. The fibers at the cracks continued to participate in the force until the fibers were completely pulled out or disconnected. In the process, the energy consumption continued to increase, and the deflection continued to increase. The bending toughness of HDC was significantly better than that of plain concrete.  
It can be seen from Figure 13 that the bending toughness ratio \(R_{\text{n}}\) of HDC had an increasing trend with an increase in the fiber content, but the increase gradually decreased, especially when the fiber content increased from 1.5% to 2%. The bending toughness ratio was basically unchanged. The main reason was that the greater the amount of fiber, the easier it was to obtain the strain hardening effect and the development of multiple cracks. The stronger the energy consumption capacity, the better the bending toughness of the material. However, when the fiber content reached a certain value, the effect of further increasing its value on the toughness of the material was not obvious. In addition, as seen in Figures 12 and 13, among the bending toughness indicators of HDC, \(f_{0.85}\) and \(R_{0.85}\) were the largest, indicating that the HDC specimen continued to show a good holding load after the peak load of 0.85 \(F_{\text{max}}\), and the load-deflection curve slowly decreased.  
Above all, it could be seen that the evaluated results were in good agreement with the experimental specimens, and the novel toughness evaluation method overcame the drawbacks of traditional methods such as an over-dependence on the unstable first cracking characteristics and the uncertain deformability of ductile materials. In addition, the peak load was unique and stable, which provided a determinate foundation of toughness  
Figure 12: Effect of fiber content on \(f_{\text{n}}\): (**a**) 56 d; (**b**) 28 d.  
for evaluating ductile cementitious composites, especially for fiber-reinforced concrete. Therefore, the toughness evaluation based on the peak load is of great help when assessing the performance of novel ductile materials.