3.1. Uniaxial Tensile Results and Stress–Strain Analysis
Figure 10 shows the failure mode of each group of specimens under uniaxial tension, and
Figure 11 shows the stress–strain curve under uniaxial tension. The test phenomenon and stress–strain curve show that in the initial stage of loading, the ECC specimen is in the elastic stage and the tensile force is mainly borne by the cement matrix. When the cracking strength of the cement matrix is reached, the specimen exhibits the first crack, and the stress–strain curve suddenly drops. Cracks continue to appear as the tensile force increases and the stress–strain curve repeatedly fluctuates, exhibiting strain-hardening characteristics. During the failure process of the test piece, the continuous sound of fibers being pulled out or broken can be heard. The reason for this is that the PE fiber plays a bridging role after the cement matrix breaks, bears the load from the matrix and makes the surrounding matrix continuously generate new cracks until the PE fiber fails in its bridging role, resulting in multiple cracks and a large deformation.
The shape and distribution of the two groups of fractures are basically consistent based on the comparative analysis of Group A with desert sand and Group B with ordinary sand as both have a spacing of approximately 2–3 mm and a fracture width of less than 100 μm. The number of cracks is 40–50, which demonstrates the characteristics of the dense, saturated multiple cracks. The deformation of the two groups is mainly generated by the cumulative width of these multiple cracks. For ordinary sand, Group B exhibits dense, saturated multiple cracking characteristics. Although Groups C, D and E also exhibit multiple cracking characteristics, they exhibit unsaturated multiple cracking. The cracks are unevenly distributed, and the maximum spacing of the cracks can reach 15 mm, which indicates that the reinforcement effect of the fibers has not been fully utilized. The deformation of materials is mainly obtained through the final main-crack cracking, which limits the final deformation ability of the materials. In total, the number of cracks becomes increasingly fewer as the particle size increases. A coarse particle size is not conducive to the realization of multiple cracking in the ECCs, especially for particles larger than 0.6 mm. Desert sand and ordinary sand with a 0.075–0.3 mm particle size show excellent multiple cracking characteristics and the ability to control the crack width.
The uniaxial tensile properties of the ECCs with different particle sizes and ages are shown in
Figure 12. From the perspective of the initial crack strength, the 7-day initial crack strengths of Group A with desert sand and Group B with ordinary sand are 2.09 MPa and 2.06 MPa, respectively, and the 28-day initial crack strengths are 2.51 MPa and 2.64 MPa, respectively, under the same change trend. For ordinary sand, the initial crack strength of the ECCs tends to increase along with the increase in the sand particle size, but the initial crack strength of Groups C–E at 28 days does not significantly increase, which may be caused by the random difference in the cement matrix’s defect size.
According to the 28-day tensile elastic modulus, for Groups A and B, the tensile elastic moduli are 3.76 GPa and 3.31 GPa, respectively. The tensile elastic modulus of the ECCs with desert sand is higher, but the difference is not significant. For ordinary sand, the tensile elastic modulus of Group B with fine particles is higher than the tensile elastic modulus of Groups C–E. The tensile elastic modulus decreases as the particle size increases.
Comparison and analysis of the desert and ordinary sand reveal that the tensile strengths of Group A at 7 and 28 days are 4.47 MPa and 4.97 MPa, respectively, and those of Group B are 4.06 MPa and 4.57 MPa, respectively. The tensile strength of the desert sand is slightly higher than that of Group B with ordinary sand. The tensile strains of Group A at 7 and 28 days are 5.80% and 6.78%, respectively, whereas those of Group B are 4.06% and 8.13%, respectively. The tensile strain of ordinary sand at 28 days is slightly higher than that of the desert sand, and the tensile deformation of both is much higher, being 2% more than the minimum limit value of the ECCs defined by the general rules, which indicates that the deformation capacity of the ECC materials prepared from desert sand is excellent and can completely replace ordinary sand.
The tensile strength and tensile deformation of ordinary sand with a 0.075–0.3 mm particle size show an increasing trend alongside the increase in age, whereas when the particle size exceeds 0.6 mm, a decreasing trend occurs. The reason for this is that the strain-hardening property of the coarse-grain-sized sand decreases as the grain size increases, which leads to the premature occurrence of the main cracks in the test piece and leads to a decrease in the tensile deformation and tensile strength. The tensile strain of the four groups of the ECC specimens with different particle sizes exceeds 2%, which is consistent with the identification of the ECCs in this study. Sand with a grain size of less than 0.3 mm can effectively improve the deformation capacity and tensile strength of the ECCs. The 0.3–0.6 mm grain size increases with age, and the change range of the tensile strength and tensile deformation is not obvious. A coarse-grain size of more than 0.6 mm can reduce the deformation capacity and tensile strength, which is not conducive to achieving strain strengthening in the ECC materials.
3.2. Three-Point Bending Test Results and Fracture Energy of the Cement Matrix
Figure 13 shows the failure mode of the three-point bending test piece. Because PE fiber was not added to the cement matrix, each group of the test pieces was brittle when they were damaged, and they all broke from the notch. Equations (3)–(6), which are recommended by Tada [
42], show that, based on the peak load of the specimen failure, the mass of the specimen and the elastic modulus measured under uniaxial tension, the fracture energy of the five groups of matrixes can be obtained, as listed in
Table 4 and
Figure 14.
For Group A and Group B, the fracture energies are 72.5 J/m2 and 67 J/m2, respectively, which are small and conducive to achieving a high toughness. For ordinary sand, the matrix fracture energies of Groups B to E are 67.0 J/m2, 90.6 J/m2, 109.6 J/m2 and 96.5 J/m2, respectively. The matrix fracture energy of Group B was the smallest, and that of Group C, Group D and Group E was 35.2%, 63.6% and 44.0% higher than that of Group B. It can be seen that the larger the particle size is, the higher the fracture energy is.
3.4. Analysis and Discussion of Fracture Toughness
The multiple cracking performance (MCP) and the pseudostrain hardening (PSH) could be obtained, respectively, according to the matrix’s fracture energy
Jtip, the complementary energy
J′
b and the initial crack strength, which was measured by the three-point bending test, the single-seam tensile test and the uniaxial tensile test, respectively, as shown in
Table 6 and
Figure 17.
The MCP of Group A with desert sand and Group B with ordinary sand is 2.88 and 2.33, respectively. The desert sand group’s MCP is slightly larger than that of the ordinary sand group, and both are greater than 1.3, which meets the requirements of the strength criteria in Equation (1). Both groups of specimens have obvious characteristics of multiple cracking, which have been verified via the uniaxial tensile stress–strain curve and the specimen failure phenomenon. The PSH of the two groups of specimens is 8.76 and 8.17, respectively, which are both much larger than 2.7. The desert sand group’s PSH is slightly larger than that of the ordinary sand group, and both meet the requirements of the energy criteria in Equation (2). The higher PSH of the desert sand group is conducive to achieving a high toughness.
For ordinary sand, the MCP of Groups B to E is 2.33, 2.44, 2.45 and 2.40, respectively, which are all greater than 1.3 and meet the requirements of the strength criteria in Equation (1). The four groups of specimens have the characteristic of multiple cracking. The PSH of the four groups of ordinary sand specimens are 8.17, 5.39, 5.05 and 6.00, which are all greater than 2.7 and meet the requirements of the energy criteria in Equation (2). It can be seen that the smaller the grain size of the ordinary sand is, the easier it is to achieve stable multiple cracking and strain hardening. Similar conclusions were reflected in M. Sahmaran’s research [
33]. In that research, dolomite limestone sand and gravel sand with a maximum particle size of 1.19 mm and 2.38 mm were used to replace micro-silica sand with maximum particle sizes of 0.2 mm when preparing the ECCs, and the production cost of the ECCs was reduced. The tensile strength and deformation of the ECC materials prepared by using larger grains of sand were reduced to varying degrees.