*3.2. Flexural Performance*

Test results of 15 × 50 × 350 mm specimens subjected to flexural test after 28 days are shown in Figure 10. The results were obtained by averaging the flexural results of three samples for each series. The maximum increase in flexural strength was obtained for 1 NCa specimen. Accordingly, the increase in the nanocalcite content in the mixes increased the flexural strength values. Sun et al. [51] found that the content of nano-CaCO3 improved the flexural performance of ECC. In addition, increasing the nanocalcite content in the blends increased the flexural strength values to 13.1, 14.31, 16.9, and 15.31 MPa for 0, 0.5, 1, and 1.5 NCa series, respectively. In general, the increase in the flexural strength values with the addition of the nanomaterials would be further beneficial for applying ECC-steel bar reinforced composite beams. In this case, the ECC with higher flexural strength could carry developing tensile stress under flexural loading and the steel reinforcement rebar after cracks. This, in turn, results in a much higher load-carrying capacity for the composite.

Moreover, mid-span displacement, strain, and stress-deflection curves were obtained from the flexural strength test. The strain, mid-span displacement, flexural toughness, and ductility index results obtained from the stress-deflection curves are shown in Table 4. This table indicates that 1 NCa samples have the highest strain and mid-span displacement values. Thus, the increase in the content of nanocalcite increased the flexural performance and compressive strength of the samples. In addition, by examining the stress-deflection curves of 15 × 50 × 350 mm specimens shown in Figure 11, the content of NCa improved the flexural performance. The maximum deflection values (deflection capacity) of the samples subjected to the flexural strength test were obtained from the endpoints of the flexural stress-deflection curves. The increases in the deflection capacity of the 0.5 NCa (11.74 mm), 1 NCa (12.88 mm), and 1.5 NCa (12.51 mm) series were 46.70%, 61.01%, and 56.39%, respectively, compared to the 0 NCa (8 mm) series. Furthermore, the flexural strength increases of 0.5, 1, and 1.5 NCa series were 8.68%, 31.55%, and 18.68, respectively, compared to the 0 NCa series. Thus, series 1 NCa exhibited the best flexural properties, having the highest flexural stress and deflection values. Ding et al. [39] found that the content of nano-CaCO3 increased the strength of UHP-ECC, and an NC content of three percent (by mass of cement) was considered ideal. In their study, they replaced the NC material with PC only, but if they had replaced the NC material with a binder (FA and PC),

the ratio they used would have been approximately 1–1.5% by mass of the binder. Thus, their conclusion was close to the conclusion of this study.

**Figure 10.** Flexural strength results of NCa-ECC.


Ductility and flexural toughness can be evaluated using flexural load-deflection curves, as indicated in the literature [52,53]. The area under the whole load-deflection curve is used

to compute flexural toughness, and the load–deflection curves were also used to calculate ductility. The ductility index (μ) calculated using the formula;

$$
\mu = \delta \mathbf{u} / \delta \mathbf{y} \tag{2}
$$

where δu is the ultimate displacement and δy is the yield displacement. After calculating the ductility indexes of the samples, the percent increases of the ductility indexes of the samples compared to the 0 NCa series were calculated and given in Table 4. NCa-containing mixtures exhibit considerably greater deflections in the ultimate state and higher loads when compared to the 0 NCa mixture. This results in a greater area under the loaddeflection curves, which may indicate increased toughness. In addition, it can be concluded that adding NCa to the ECC mixes improves the ductility and flexural toughness of the mixes. In this study, the highest flexural toughness and ductility were obtained for 1 NCa specimen. Ye¸silmen et al. [54] used nano-silica and nano-CaCO3 in ECC mixtures, and they found that the nano- CaCO3 contained ECC mixtures had the highest ductility. The higher fracture toughness and improved multiple cracking behavior associated with the nanoparticle reinforced mix can make ECC effectively improve the unstable crack propagation caused by the surrounding concrete or old/new concrete interface. This, in turn, reduces the common early damage types in repair structures such as spalling and interlaminar fracture [55].

#### *3.3. Fractal Analysis*

In the literature, there are various methods (cube counting, variance methods, etc.) for extracting and then calculating the cracking map and fractal dimension of surface cracks at the fractured 15 × 50 × 350 mm samples shown in Figure 12. Box-counting is the most preferred and practical technique for measuring the borders of a form by measuring the distances between points on it using square boxes. Erdem and Blankson [36] described the techniques in depth in prior research.

**Figure 12.** (**a**) An example of the crack on the studied sample (**b**) the extracted map of the crack.

The fractal dimension values of the surface cracks provided by the Image J program are illustrated in Figure 13. The results clearly show that the ECC mix with 1% nanocalcite particles (1 NCa) has the highest fractal dimension value among the NCa-ECC series. In addition, the other nanocalcite dopped ECC samples had a fractal dimension higher than the control ECC series (0 NCa). The greater fractal dimension of the 1 NCa mixture resulted in higher fracture energy dissipation at the macro scale level, as verified by the findings shown in Table 5. The greater fractal dimension values with the adding nanoparticles most likely indicate that the filling effect of nanocalcite particles refines the pore structures and reduces unsaturated bonds, resulting in improved bondability between and creating the deformation hardening method along the fracture front and voids. However, using more than 1% nanocalcite particles decreases fractal dimension and fractural energy. In general, the previous studies [37,55] show that the fractal of general cementitious materials has a value of 1 and 2. The results of this study are consistent with the existing literature.

**Figure 13.** Fractal dimensions of the (**a**) 0 NCa, (**b**) 0.5 NCa, (**c**) 1 NCa, and (**d**) 1.5 NCa samples.

**Table 5.** The summary of the fractal analysis of the mixtures.


Figure 14 illustrated 3D views of the cracked surfaces' crack surface roughness. According to the findings, the sample containing 1% nanocalcite particles had the greatest energy value during fracture initiation and propagation. The 3D surfaces curves of the mixtures corresponding with the depth of the sample locations are shown in Figure 14. The findings showed that the more fibers associated with, the larger surface area would be available to bridge cracks during the crack propagation process under flexural loading. This would, in turn, result in much higher fiber bridging complementary energy in terms

of the micromechanical principles. In general, the strong bridging ability could confirm the excellent deflection capacity with the increase in the content of the NCa particles.

**Figure 14.** 3D surface graphs of the fracture surfaces of the (**a**) 0 NCa, (**b**) 0.5 NCa, (**c**) 1 NCa, and (**d**) 1.5 NCa samples.

#### *3.4. SEM Analysis*

The ECC matrix without nanomaterials is shown in Figure 15. The micrograph in Figure 15 indicates that the composites were relatively loose, with unhydrated fly ash particles clustered with distinct interfaces. It consists of dense calcium silicate hydrate (CSH) gel, unhydrated FA particles, amorphous and crystallized calcium hydroxide (CH). The micromorphology of a modified ECC sample matrix with nanocalcite (1 NCa) is shown in Figure 16. The matrix compactness improved after nanomaterials were added, and although unhydrated fly ash particles were retained, their distribution was uniform and had no clear interfaces. The main explanation for this was that the nanoparticles have a similar particle size to hydrated calcium silicate [56]. In addition, the newly formed hydration products slightly increased the density of the matrix, which improved the mechanical properties.

Conversely, the matrix did not exhibit visible micro-cracks. This, in turn, indicates that the addition of NCa particles can increase the fracture toughness of the matrix. The improvement of the matrix fracture toughness would be attributable to the shielding effect on crack tips [57]. As found in the Due et al. [58] study, the active ingredients of FA in 28-day samples prepared in this study reacted together with Ca(OH)2. This reaction effectively improves the growth rate of matrix strength and imparts good strength to NCa-ECC.

**Figure 15.** SEM of the 0 NCa sample magnified at 5000 times.

**Figure 16.** SEM of the 1 NCa sample magnified at 5000 times.
