*3.4. Pullout Stress Recovery Starting Time (Tr) during the Heat Treatment*

As observed in the pullout stress versus time curves of the SMA fibers during the short-term heat treatment in both Figures 6 and 7, their pullout stress first decreased at the beginning of the heat treatment and then began increasing to the end of the heat treatment. The pullout stress recovery starting time was quite different based on the type of SMA fiber geometry and alloy. Table 5 provides the recovery starting times (Tr) of the pullout stress relative to the test series during the short heat treatment period. The average Tr values of the test series (NT\_S\_H, NT\_D\_H, NTN\_S\_H, and NTN\_D\_H) were 2.20, 1.42, 2.94, and 1.95 min, respectively. The NT fibers usually produced faster Tr than the NTN fibers, while the D-shaped fibers produced faster Tr than the S fibers. The earlier pullout stress recovery of the dog-bone-shaped SMA fibers is thought to originate from their higher PE values, indicating a superior pullout resistance. Accordingly, the SMA fibers with a deformed geometry generating a larger PE are favorable for generating a faster crack closing ability. However, the parameters influencing the recovery start time (Tr) require further investigation.


**Table 5.** Pullout stress recovery starting time during heating (Tr).

#### *3.5. Pullout Stress Recovery Ratios*

The ratios R1 and R2, between the pullout stresses, P0.5,re, P0.5,rc, and P0.5,rp, were calculated to quantify the crack closing ability of the SMA fibers during and after the short-term heat treatment. The ratio between the P0.5,rc and P0.5,re is denoted as R1, which represents the potential crack closing ability. The ratio between the P0.5,rp and P0.5,re was additionally analyzed and denoted as R2, which is thought to correlate with the ability to prevent crack reopening. Both R1 and R2 ratios are provided in Figure 9b. The NT fibers generally produce higher recovery ratios than the NTN fibers, as shown in Figure 9b; the values of R1 were 2.78, 2.28, 0.59, and 0.80 for NT\_S\_H, NT\_D\_H, NTN\_S\_H, and NTN\_D\_H, respectively, while those of R2 were 3.79, 4.79, 3.05, and 1.65 for NT\_S\_H, NT\_D\_H, NTN\_S\_H, and NTN\_D\_H, respectively. The R1 ratios of the NT fibers were higher than 1.0, whereas those of the NTN fibers were less than 1.0. Therefore, the pullout stress recovery during the short heat treatment period is higher for the NT fibers than the NTN fibers. Additionally, R1 values below 1.0 are not sufficient for closing cracks, whereas those higher than 1.0 are indicative of a satisfactory or strong crack closing capacity. The R2 ratios of the NT fibers were also higher than the NTN fibers. Therefore, the NT fibers after the heat treatment displayed a higher pullout resistance during the second pullout process.

**Figure 9.** (**a**) Pullout stress and (**b**) pullout stress ratios owing to the heat treatment, for the different samples.

#### *3.6. Pullout Energy Ratios*

The short heat treatment period also noticeably increased the amount of pullout energy after the 0.5 mm initial slip to complete fiber pullout, as provided in Table 4 and Figure 10a.

The enhanced SMA fiber pullout energy after the heat treatment originated from the lateral recovery of the fiber diameter due to shape memory effects. To quantitatively compare the heat treatment effect on the PE, the pullout energy ratios between samples with and without heat treatment were estimated and are shown in Figure 10. The pullout energy ratios of the NT\_S, NT\_D, NTN\_S, and NTN\_D were 1.71, 1.18, 3.29, and 1.20, respectively. The higher pullout energy ratio is thought to be favorable for resisting crack reopening. The NTN\_S fiber produced the highest pullout energy ratio, while the NTN\_D fiber produced the highest pullout energy. In addition, it was also evident that the smooth fibers generated higher pullout energy ratios than the dog-bone-shaped fibers because the pullout energy of the D fiber was much higher than that of the S fiber for the series without heat treatment. The *PE* value of NTN\_S\_N was 494.3 MPa-mm, while that of NTN\_D\_N was 2375 MPa-mm.

**Figure 10.** (**a**) Pullout energy (for samples with heating (grey) or without heating (white)), and (**b**) pullout energy ratio owing to the heating treatment.

#### **4. Conclusions**

This study investigated the effects of applying a short heat treatment period (10 min) to shape memory alloy (SMA) fibers on their geometry and pullout resistance. The short heat treatment time clearly activated the shape memory effects, eventually generating the pullout stress recovery of SMA fibers in mortar. The conclusions below can be drawn from this experimental study:


Self-healing concrete can close (heal or fill) cracks; however it requires a few days minimum to heal the cracks. Consequently, in this study, we found that the SMA-FRCCs have a fast crack closing capacity (just only 10 min). The crack-closing behavior of SMA-FRCCs under a load is now under investigation and the parameters influencing the recovery start time require further investigation. Moreover, it is also necessary to investigate the residual stress of SMA-FRCCs [26].

**Author Contributions:** M.K.K., D.J.K., Y.-S.C., and E.C. conceived, designed, and wrote the manuscript; M.K.K. performed the experiments.

**Funding:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Project No. 2019-R1A2C2008542).

**Conflicts of Interest:** The authors declare no conflicts of interest.
