## 3 Results and Discussion
### Quasi-Static Mechanical Characterization
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name** & \(\sigma_{N}\) **[MPa]** & \(\sigma_{L}\) **[MPa]** & \(\sigma_{R1}\) **[MPa]** & \(\sigma_{R2}\) **[MPa]** & \(\sigma_{R3}\) **[MPa]** & \(\sigma_{R4}\) **[MPa]** & \(W_{F}\) **[N m]** \\ \hline FCLC-0.0 & 0.7 (0.2) & 0.3 (0.1) & 0.1 (0.0) & – & – & – & 0.21 (0.05) \\ FCLC-0.3 & 0.9 (0.1) & 0.3 (0.0) & 0.3 (0.1) & 0.2 (0.1) & 0.1 (0.0) & 0.34 (0.06) \\ FCLC-0.6 & 0.7 (0.2) & 0.3 (0.0) & 0.4 (0.2) & 0.2 (0.1) & 0.2 (0.1) & 0.1 (0.0) & 0.36 (0.11) \\ FCLC-0.9 & 1.1 (0.2) & 0.3 (0.0) & 0.8 (0.2) & 0.5 (0.2) & 0.4 (0.1) & 0.3 (0.1) & 0.59 (0.12) \\ FCLC-1.2 & 1.1 (0.1) & 0.3 (0.0) & 1.0 (0.1) & 0.6 (0.1) & 0.4 (0.0) & 0.3 (0.0) & 0.67 (0.06) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mode I fracture dynamic test results at a displacement rate of 4 mm/s (\(v_{2}\)): \(\sigma_{N}\), flexural strength; \(\sigma_{L}\), flexural strength for 0.05 mm of vertical displacement; \(\sigma_{R1}\), residual flexural strength for 0.5 mm of vertical displacement; \(\sigma_{R2}\), residual flexural strength for 1.5 mm of vertical displacement; \(\sigma_{R3}\), residual flexural strength for 2.5 mm of vertical displacement; \(\sigma_{R4}\), residual flexural strength for 3.5 mm of vertical displacement; \(W_{F}\), work of fracture up to 0.5 mm of vertical displacement (mean values, standard deviation in parentheses). Figure 6: (**a**) \(\sigma_{R2}\) and (**b**) \(\sigma_{R3}\) for higher velocity (in notched prismatic specimens, \(420\times 100\times 100\) mm\({}^{3}\), length \(\times\) height \(\times\) width). Figure 7: Evolution of flexural strengths: (**a**) \(\sigma_{N}\) (quasi-static regime); (**b**) \(\sigma_{Ri}\) (dynamic regime). displacement under the loading point (Figure 4b). As anticipated, in the dynamic regime, the \(W_{F}\) value is higher than in the quasi-static regime, except for \(\phi_{f}=0.006\) of fiber content. Given that the average \(W_{F}\) values are quite similar, and the standard deviation is relatively high at both speeds, the most likely explanation for this atypical trend is the lack of uniformity in the distribution and quantity of fibers crossing the fracture section. Figure 5 compares the obtained values of \(\sigma_{L}\) and \(\sigma_{R1}\) for both regimes. In the quasi-static regime, as \(\phi_{f}\) increases, so does \(\sigma_{L}\), reaching the optimum value at \(\phi_{f}=0.009\). Meanwhile, in the dynamic regime, \(\sigma_{L}\) remains constant as \(\phi_{f}\) increases (Figure 5a). Regarding residual flexural strength, only the evolution of \(\sigma_{R1}\) can be compared since it is the only measurable parameter in both regimes (Figure 5b). In the quasi-static regime, a similar trend to \(\sigma_{L}\) is observed; as \(\phi_{f}\) increases, so does \(\sigma_{R1}\), reaching the optimal value again at \(\phi_{f}=0.009\). In the dynamic regime, the value of \(\sigma_{R1}\) increases with the increase in \(\phi_{f}\). Figure 6 illustrates the dynamic regime evolution of residual flexural strength values for 1.5 mm and 2.5 mm of vertical displacement, \(\sigma_{R2}\) and \(\sigma_{R3}\), respectively. Both strength parameters are enhanced as \(\phi_{f}\) is increased. Figure 7a compares the evolution of flexural strength parameters measured in the quasi-static regime (\(v_{1}=4\times 10^{-4}\) mm/s). Except for the unreinforced matrix, \(\sigma_{N}\) and \(\sigma_{L}\) coincide for different fiber quantities. It is also observed that the values of \(\sigma_{R1}\) follow a similar trend to \(\sigma_{N}\) and \(\sigma_{L}\) for various \(\phi_{f}\) values, reaching their maximum values at \(\phi_{f}=0.009\). This indicates that, for the studied hydraulic lime concrete matrix design, there exists an optimal fiber volume fraction (\(\phi_{f}=0.009\)) in the quasi-static regime, beyond which distortion occurs, leading to reduced flexural strengths.