## 3 Results
### Stress-Strain Curve  
As was mentioned earlier in Section 2.3, the stress-strain curve of some specimens is presented based on the average value of all four strain gauges. The results for all specimens, classified by the age of specimens in the testing time, are provided in Figure 6a-h. In this figure, the mathematical models (bi-linear diagram or/and four-point stress-strain curve) for CSFRC behavior prediction are proposed, given the loading time, in addition to the experimental results. Figure 6: Stress-strain curves of specimens at the ages of 9 (**a**), 14 (**b**), 21 (**c**), 28 (**d**), 35 (**e**), 49 (**f**), 70 (**g**), and 91 days (**h**). The CSFRC load-bearing behavior can be divided into the three \"life periods\":  
1. The growing up period or \"childhood\";
2. Maturity or \"the best period of life\";
3. The \"old age period\". The 9- and 14-day-old specimens belong represent the first \"life period\". Figures 2 and 6a,b show that in this period, the CSFRC has not achieved the full tensile strength. As a consequence, the corresponding specimens suffer significant strain (Figure 6a) and damage (Section 3.5), which is especially obvious at the age of 9 days. These concrete specimens have lower strength, so new cracks will open before the fibers rupture. Therefore, significant nonlinearity of CSFRC already appears at about 55% of the CSFRC tensile strength at the age of 9 days (Figures 3 and 5a), which causes elasticity modulus softening in this region. For that reason, the bi-linear model may underestimate the damage in the region where the stress ranges from 55% to 100% of the CSFRC tensile strength (Figures 2, 3 and 6a). Hence, to predict CSFRC behavior after 9 days of age, the stress-strain model through four points is proposed together with the bi-linear model (Figure 6a). Because of significant damage in the CSFRC, there is large energy dissipation, and hence the introduction of a huge amount of external energy is required to break the specimen. This is because the average ultimate tensile strain, as shown in Figure 6a, is about 3.5%. At the age of 14 days, specimens have slightly higher concrete tensile strength, but the elasticity modulus also increases. For this reason, a stronger connection between fibers and concrete is achieved, given that there is only slight softening of the CSFRC elasticity modulus in the region between the appearance of first micro-cracks (about 55% of CSFRC tensile strength--Figures 2 and 3) and the CSFRC reaching sufficient tensile strength (Figure 6b). Sudden strain growth (red and blue line in Figure 6b at stress of 10-12.5 MPa) indicates that full bonding between the concrete and the fibers has not yet been achieved through the entire specimen. Since there is only slight softening of the elasticity modulus, a bi-linear diagram is proposed (Figure 6b) for behavior prediction. As these specimens are less damaged, they dissipate lower amounts of energy, so their average ultimate tensile strain is around 1.5 %. Concrete shrinkage also contributes to differences in behavior between specimens at the ages of 9 and 14 days, but since there are two different parallel processes in this life span in addition to aging and shrinkage development, it is impossible to define their particular influence on specific details without further comprehensive research. The second period--\"the best period of life\" or maturity--comprises specimens tested at the ages of 21, 28, 35, and 49 days (Figure 6c-f). The latter is actually in a state of transition from period two to three. From all 12 specimens in this period, it is obvious that the CSFRC elasticity modulus softening in the region of micro-nonlinearity (stress between 60% and 100% of the CSFRC tensile strength) can be ignored, so the bi-linear diagrams are proposed as behavior prediction models (Figure 6c-f). The average ultimate strains of specimens 21, 28, and 35 days old are 2.65%, 2.45 %, and 2.8%, while specimens tested at the age of 49 days have an average ultimate strain of 1.90% (Figure 6c-f).