To compare the differences of tensile properties of different types of fiber-reinforced UHPC, the typical tensile stress–strain curves of each group of specimens are shown in Figure 6. Due to the large ultimate deformation of hybrid fiber-reinforced UHPC, to more intuitively compare the differences in the whole failure process of different specimens, the process from loading to cracking of each group of specimens was enlarged and placed at the upper right of Figure 6. The tensile stress–strain curves of different hybrid fiber-reinforced UHPC can be divided into two parts: ascending and softening branches. Due to the different types and volume content of fibers, the tensile stress–strain curves can be divided into two different types (Type A and Type B). The ascending branches of the tensile curve of the two types of strain-softening UHPC were similar, and the softening branches were different, as shown in Figure 7.

Type A: generally, the tensile stress–strain curve of UHPC with low fiber content or hybrid steel fiber and long or coarse non-metallic fiber. It can be divided into four stages: 1) Ascending stage: The relationship between stress and strain is approximately linear until microcracks appear in the specimen. At this stage, the single-doped steel fiber or hybrid fiber effectively reduces the possibility of stress concentration in the matrix. When the tensile stress increases to the initial crack stress, microcracks appear in the component, the cracked UHPC loses its bearing capacity, and the fibers crossing the cracks begin to play a role. Generally, some microfibers have low elastic modulus but have a large number, which can significantly inhibit the development of early microcracks. Compared with ordinary concrete, the generation and expansion of initial cracks of fiber concrete are delayed; 2) Softening stage I: rapid descending stage. After the specimen reaches the tensile strength, it cracks, and the bearing capacity decreases rapidly. This kind of curve often shows that the fiber content is low, or the steel fiber is mixed with long or coarse non-metallic fibers, and these fibers begin to play a bridging role gradually after the specimen cracks. Therefore, the bearing capacity of the specimen decreases suddenly at the moment of cracking. This stage is closely related to the type and content of fiber in the specimen. When the fiber content or type is appropriate, the bearing capacity of the specimen decreases only slightly. On the contrary, the bearing capacity of the specimen will decrease greatly; 3) Softening stage II: stable descending stage. At this stage, with the increase in crack width, the fibers between cracks, especially some macrofibers, begin to play a bridging role. The fiber is well bonded with the matrix, which can effectively delay and prevent the expansion of cracks, improve the toughness of the matrix, and maintain the stability of bearing capacity; 4) Softening stage III: fast descending stage. As the fibers are continuously pulled out or broken, the fiber-bridging effect is gradually weakened, and the bearing capacity of the specimen decreases rapidly with the increase in specimen deformation.

Type B: generally, the UHPC tensile stress–strain curve with high fiber content or hybrid steel fiber and fine non-metallic fiber. It can be roughly divided into two stages: 1) Ascending stage, which is similar to the ascending section of type A. Since microfibers can inhibit the development of early microcracks, strain hardening is more likely to occur before specimen cracking than type A. 2) Softening stage: After the specimen is cracked, the fibers between the cracks effectively play a bridging role to control the extension of macrocracks, and the bearing capacity does not decrease rapidly. Compared with the tensile stress–strain curve of type A, the softening section is gentler and shows good toughness.

It can be seen from the tensile stress–strain curve of the hybrid PP fiber in Figure 6A that the coarse PP fiber had little effect on the ascending stage, but the tensile peak strain was slightly increased. After the specimen S1.3PP0.5-40 cracked, the tensile stress dropped significantly. The reason was that the diameter of the PP fiber was too coarse, and the effect of controlling the expansion of microcracks before cracking was not obvious. When the specimen was cracked, the PP fibers between the cracks cannot immediately play a bridging role, so the stress decreased. Compared with the single-doped steel fiber specimen S1.3, the descending stage of the specimen S1.3PP0.5-40 was gentler, and the toughening effect was obvious.

It can be seen from the tensile stress–strain curve of hybrid PVA fiber in Figure 6B that before cracking, the specimens S1.3PVA0.5-12a, S1.3PVA0.5-8, and S1.3PVA0.5-12b had obvious strain-hardening characteristics, reflecting the good crack resistance of PVA fiber. Among them, fiber PVA-12-0.04 had the best crack resistance, followed by PVA-8-0.2, and PVA-12-0.2 was inferior. The reason was that the diameter of the three PVA fibers was relatively small, and the elastic modulus was medium. Before cracking, they can effectively delay the development of microcracks, improve the crack resistance of the specimen, and improve the tensile strength of the specimen, which had an obvious effect of strengthening the crack resistance. Compared with specimen S1.3, the descending section of the specimens S1.3PVA0.5-12a, S1.3PVA0.5-8, and S1.3PVA0.5-12b was gentle, and the ultimate deformation was large. The reason was that there were hydroxyl groups on the surface of the PVA fiber, which was well bonded with the UHPC matrix and which can effectively control the development of macrocracks, reflecting the good toughening effect of the PVA fiber.

It can be seen from the tensile stress–strain curve of hybrid PET fiber in Figure 6C that before cracking, specimen S1.3PET0.5-30a had strain-hardening characteristics, while specimen S1.3PET0.5-30b had no strain hardening characteristics. After cracking, the descending section of S1.3PET0.5-30a was gentle, and the ultimate strain was large, which reflected the good crack resistance and toughening effect of fiber PET-30-0.75. The tensile stress of specimen S1.3PET0.5-30b decreased greatly after cracking, and the descending section was also relatively gentle, which also reflected the crack resistance and toughening effect of the fiber PET-30-0.9. A comprehensive comparison found that the crack resistance and toughening effect of the fiber PET-30-0.9 were weaker than that of the fiber PET-30-0.75. The reason was that the diameter of the fiber PET-30-0.9 was too thick, and the number of fibers per unit cross-sectional area was too small. Therefore, it was suggested that the diameter of fiber PET should not exceed 0.75 mm.

It can be seen from the tensile stress–strain curve of hybrid BF fiber in Figure 6D that before cracking, the specimen S1.3B0.5-12 had obvious strain-hardening characteristics, and the tensile strength had been significantly improved. At the moment of cracking, the bearing capacity decreased obviously, and then the descending section was gentle. It can be seen that the BF fiber had a fine diameter and high elastic modulus, which has an obvious strengthening and toughening effect.

To better quantitatively compare the differences in tensile properties of each group of specimens, the strength corresponding to the peak point was taken as the tensile strength (σ _p), and its corresponding strain was taken as the peak strain (ε _p). Take the slope of the connecting line between 5% and 50% of the maximum stress in the ascending stage of the tensile stress–strain curve of the specimen as the elastic modulus (E _t). To evaluate the performance differences of the different specimens after cracking, fracture energy (G _F) was defined to characterize the energy absorption capacity of the specimens and characteristic length (L _ch) to characterize the brittleness of the specimens. All the above results were the average values of the same group of parallel specimens, and the results are listed in Table 5.

The tensile strength σ _p of UHPC in each group is listed in Table 5. When the steel fiber content increased from 0 to 1.3% and 1.8%, the tensile strength of UHPC increased by 13.70% and 25.24% respectively, indicating that the tensile strength of UHPC can be significantly improved by adding steel fibers. In addition, the addition of steel fibers also changed the brittle failure characteristics of the plain UHPC. After the peak tensile strength, the descending section of specimen S1.8 was gentler than that of S1.3. This was because the steel fibers played a great role before and during the cracking of UHPC. The steel fiber exerted its bridging function and continuously transmitted the stress to the surrounding matrix so that the matrix can continue to work under the stress after it was cracked, which cannot only increase the tensile stress but also improve the ability to resist tensile deformation.

Compared with S1.3, the tensile strength of S1.3PP0.5-40 and S1.3PET0.5-30b decreased by 9.73% and 11.63%, respectively, and the tensile strength of S1.3PVA0.5-12a, S1.3PVA0.5-8, S1.3PVA0.5-12b, S1.3PET0.5-30a, and S1.3B0.5-12 increased by 8.46%, 0.03%, 4.65%, 7.19%, and 15.01%, respectively. Generally speaking, microfibers can effectively prevent the development of microcracks, and macrofibers can effectively prevent the development of cracks after macrocracks appeared (Fantilli et al., 2017; Stahli and Mier 2007). Therefore, some fine fibers such as PVA-12-0.04 and BF-12-0.02 had an obvious enhancement effect on the matrix. Some coarse fibers such as PP-40-0.6 and PET-30-0.9 cannot prevent the development of microcracks well before the specimen cracked, so the tensile strength of the specimen was significantly reduced.

The tensile strength of the specimen hybrid with three different sizes of PVA fiber and steel fiber was improved. The reinforcement effect of the two PVA fibers with a length of 12 mm was better than that of the PVA fiber with a length of 8 mm. The length of fiber PVA-12-0.04 and PVA-12-0.2 was the same as 12 mm, but the diameter of fiber PVA-12-0.04 was only 0.04 mm, so its reinforcement effect was the best.

Among all the hybrid fiber-reinforced UHPC specimens, the tensile strength of specimen S1.3B0.5-12 was the highest, even higher than that of specimen S1.8, indicating that the reinforcement effect of fiber BF-12-0.02 was the best among all non-metallic fibers because its minimum diameter was only 0.02 mm, and its elastic modulus was the highest among all non-metallic fibers. Therefore, selecting fine fibers with high elastic modulus was the most effective way to improve the tensile strength of materials.

The peak strain ε _p of UHPC in each group is listed in Table 5. When the steel fiber content increased from 0 to 1.3% and 1.8%, the peak strain of UHPC was close.

Compared with S1.8, the peak strain of S1.3PET0.5-30b decreased by 22.73%, and the peak strain of S1.3PP0.5-40, S1.3PVA0.5-12a, S1.3PVA0.5-8, S1.3PVA0.5-12b, S1.3PET0.5-30a, and S1.3B0.5-12 increased by 10.00%, 110.00%, 74.55%, 5.45%, 26.36%, and 71.81%, respectively. Similar to the effect of hybrid fibers on tensile strength, in general, microfibers can effectively prevent the development of microcracks, and macrofibers can effectively prevent the development of cracks after macrocracks appeared (Fantilli et al., 2017; Stahli and Mier 2007).

For three different sizes of PVA fiber and steel fiber hybrid-reinforced UHPC specimens, the peak strain of specimens S1.3PVA0.5-12a, S1.3PVA0.5-8, and S1.3PVA0.5-12b decreased in turn. The reason was that the diameter of fiber PVA-12-0.04 was only 0.04 mm, and the number of fibers contained in the unit cross-sectional area was the largest, which also reflected the contribution of micro-fibers to slowing down the initiation and development of microcracks.

Compared with S1.3PET0.5-30a, the peak strain of S1.3PET0.5-30b decreased by 38.85%. The same reason was that the diameter of fiber PET-30-0.9 was too coarse, and the number of fibers contained in the section of the same area reduced, resulting in a decrease in peak strain.

In all fiber hybrid-reinforced UHPC tensile specimens, PVA-12-0.04, PVA-8-0.2, and BF-12-0.02 had a significant increase in peak strain because these three fibers had fine diameter, high elastic modulus, and excellent enhancement effect.

Based on the assumption that the specimen does not crack before peak load, and the residual deformation does not increase after the peak load, the schematic diagram of UHPC tensile stress–total deformation curve is shown in Figure 8, and the total deformation δ (Deng et al., 2009) of hybrid fiber-reinforced UHPC in the tensile process is: δ = δ e + δ 0 + w (1) where w is the macrocrack width, and δ _e and δ ₀ are the elastic deformation and residual deformation outside the fracture zone of the specimen, respectively, and then: δ e = σ l E t (2) δ e 0 = σ p l E t (3) δ 0 = δ p − δ e 0 (4) where σ and σ _p are the axial tensile stress and the peak stress, respectively, δ _p and δ _e ⁰ are the total deformation and elastic deformation corresponding to peak stress, respectively, E _t is the elastic modulus, and l is the gauge distance of the specimen.

The crack propagation width w is independent of the length of the specimen, and there is no macrocrack before the maximum load (Deng et al., 2009). According to Eq. 1, the w is: w = δ − δ e − δ 0 (5)

The tensile stress–crack width curves are shown in Figure 9. Different hybrid fiber-reinforced UHPC had significant differences due to the different characteristics of non-metal fibers. To better evaluate the difference in tensile stress–crack width curves of different tensile specimens, the evaluation index of fracture energy (G_F) was introduced (see the Effect of hybrid fibers on fracture energy section for details).

Fracture energy G _F (Deng et al., 2009) is the energy consumed to form cracks per unit area, that is, the ratio of the area under the tensile stress–crack width curves to the cross-sectional area of the specimen, and G F = ∫ 0 w f σ ( w ) d w (6)

The fiber-reinforced UHPC had large deformation. To compare the toughness differences of different specimens more accurately, it was uniformly taken that the load was reduced to 20% of the cracking load. The calculation results of the fracture energy of the different specimens are listed in Table 5. The fracture energy value reflected the energy consumed by UHPC during the fracture process. The greater the fracture energy, the greater the energy consumed by UHPC during the fracture process, and the more significant the crack resistance effect of the fiber.

Plain UHPC specimen S0 had a brittle fracture, and the fracture energy was not considered. The fracture energy of UHPC increased by 197.62% when the content of steel fiber was increased from 1.3% to 1.8%, indicating that steel fiber had a significant toughening effect on UHPC.

Compared with the single-doped steel fiber specimen S1.3, the fracture energies of S1.3PP0.5-40, S1.3PVA0.5-12a, S1.3PVA0.5-8, S1.3PVA0.5-12b, S1.3PET0.5-30a, S1.3PET0.5-30b, and S1.3B0.5-12 increased by 25.29%, 156.10%, 187.07%, 102.72%, 117.01%, 15.37%, and 53.88%, respectively. The steel fiber content of all hybrid fiber-reinforced UHPC was 1.3%, and the fracture energy was significantly improved by adding non-metallic fiber of fiber content 0.5%, which showed that the steel fiber and non-metallic fiber were mixed with complementary advantages and gave full play to the strengthening and toughening effects of fibers of different varieties and sizes. In general, long fibers can more effectively limit the development of macrocracks than short fibers, to improve the ductility of UHPC and achieve the effect of toughening. In the test, the fibers PVA-12-0.04, PVA-8-0.2, PVA-12-0.2, PET-30-0.75, and BF-0.02 all showed good toughening effects.

The fracture energy of the specimens S1.3PVA0.5-8, S1.3PVA0.5-12a, and S1.3PVA0.5-12b decreased sequentially in three different sizes of PVA fiber and steel fiber hybrid-reinforced UHPC specimens, which showed that among the three types of PVA fibers, fiber PVA-8-0.2 had the best toughening effect, followed by PVA-12-0.04, and PVA-12-0.2 was the worst.

Compared with the specimen S1.3PET0.5-30a, the fracture energy of S1.3PET0.5-30b was reduced by 47.99%. The reasons were also that the diameter of fiber PET-30-0.9 was too thick, the number of fibers contained in the section of the same area was reduced, and the bonding force between the fiber and the matrix was reduced, resulting in the decrease in fracture energy.

Compared with other non-metallic fibers, the fracture energy of all steel fiber–PVA hybrid fiber-reinforced UHPC was very high, indicating that PVA fiber had a good toughening effect due to its relatively high elastic modulus, tensile strength, and excellent dispersion. In addition, the fracture energy of the specimen S1.3PET0.5-30a was also higher, which reflected the good toughening effect of the fiber PET-30-0.75.

The fracture energy of all hybrid fiber-reinforced UHPC was lower than that of specimen S1.8, indicating that steel fiber played an important role in strengthening and toughening in the whole process of specimen tension. However, high steel fiber content would increase the cost and reduce the workability. When the crack width of steel fiber was small, the crack resistance and reinforcement effect were obvious. When the deformation was large, the steel fiber would slip obviously, and the toughening effect was reduced. Through the above test results, it can be found that the hybrid of steel fiber and non-metallic fiber can complement the advantages of each other, give full play to the strengthening and toughening effect of different varieties and different sizes of fibers, not only improve the fracture energy and toughness of UHPC but also reduce the preparation cost, and promote the development of UHPC preparation technology and engineering application.

The characteristic length L _ch (Deng et al., 2009) proposed by Hillerborg is usually used to express the brittle fracture performance of concrete, and L ch = E t G F ( f t ) 2 (7) where the units of L _ch and E _t are mm and GPa, respectively, and the units of G _F and f _t are N/m and MPa, respectively. The smaller the L _ch, the more brittle the material.

The calculation results of the characteristic lengths of different specimens are listed in Table 5. The plain UHPC specimen S0 had a brittle fracture, and the characteristic length was not considered. In the specimens with single steel fiber, when the content of steel fiber increased from 1.3% to 1.8%, the characteristic length of UHPC increased by 222.73%, which showed that steel fiber had a significant toughening effect on UHPC and reduced the brittleness of the material.

Compared with the specimen S1.3, the characteristic lengths of the specimens S1.3PP0.5-40, S1.3PVA0.5-12a, S1.3PVA0.5-8, S1.3PVA0.5-12b, S1.3PET0.5-30a, S1.3PET0.5-30b, and S1.3B0.5-12 were increased by 64.83%, 167.80%, 209.33%, 200.36%, 17.36%, 259.39%, and 50.12%, respectively. The average characteristic length of ordinary mortar was 110 mm, the average characteristic length of ordinary concrete and polypropylene fiber concrete were 600 and 650 mm, respectively, the characteristic length of engineered cementitious composite (ECC) was between 1,405 and 3,461 mm (Deng et al., 2009), and the characteristic length of hybrid fiber-reinforced UHPC was between 19,700.21 and 60,542.86 mm, which reflected the good toughness of hybrid fiber-reinforced UHPC. The reason was that hybrid fiber had good crack control ability, delayed the development of cracks, and prevented the extension of macrocracks.