## 4 Hybrid Fiber Composition
### Steel--Steel Hybrid Fiber
#### 4.1.2 Mechanical Properties
The mixture with straight and twisted fibers achieved the highest flexural strength for a fiber content of 1% each. Increasing the content of twisted fibers to 1.5% resulted in the lowest increase in flexural tensile strength, with only a 0.6% improvement compared to the mix with 2% straight steel fibers. [PERSON] [171] and [PERSON] et al. [172] analyzed the cracking patterns of the bending samples. In the case of longer fibers, damage was observed over larger distances, requiring cracking of a relatively larger concrete surface. The slip resistance of straight fibers is provided solely by interfacial friction, while the hooked-end fibers exhibit both friction and mechanical anchorage generated by the end hooks [173; 174]. When a straight fiber reaches its maximum pull-out load, it detaches from the matrix and begins to slide out. In contrast, for hooked-end fibers, a sudden drop in strength is observed because of the need for fiber straightening or matrix cracking, whereas this occurrence is not present for straight fibers. According to [175], the average spalling area was greater for longer fibers and the spalling of the matrix occurred before the maximum load was reached, which reduced the effective length of the anchor compared to the initial length of the fiber. A UHPC mix with the addition of two types of straight steel fibers with a length/diameter of 6, 10, or 13/0.12 mm and a total fiber content of 1.5% was tested for splitting tensile strength [48]. The addition of fibers transformed sudden cracking into ductile cracking after reaching maximum load. The highest strength was recorded for the mix containing 0.5% fibers with a length of 10 mm and 1% fibers with a length of 13 mm, showing a 75% increase compared to the control mix. The larger matrix-fiber contact surface for longer fibers resulted in more effective crack bridging, inhibiting crack propagation after matrix damage. The load is transferred to the fibers, allowing for a further increase in load until the fibers fail or are pulled out of the matrix. A mixture containing straight steel fibers with a length/diameter ratio of 19.5/0.2 mm and hooked fibers of 13 or 25/0.2 mm, with a total fiber content of 1%, was tested for axial tensile strength [140]. In each of the mixes, replacing a portion of straight steel fibers with hooked-end fibers resulted in a strength increase ranging from 0.9% to 14.4%. The highest strength improvement was achieved with a 0.5% substitution of straight fibers for 25 mm hooked-end fibers. The hooked ends of the fibers exhibited a beneficial effect by increasing the energy required to remove them from the concrete matrix. However, the matrix surrounding the fibers was mechanically fragmented and crushing could appear, especially with shorter embedding lengths [176]. Tensile strength is related to the strength of the interfacial bond between the fibers and the matrix. The resistance mechanism can be improved by using fibers with rough surfaces, increasing the fiber-matrix contact area, and improving the matrix strength [177]. [PERSON] et al. [178] conducted tests to determine the pull-out forces of steel fibers with the following length/hook-end configurations: 30 mm/single hook with a 5 mm bend at 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\); 25 mm/single hook with a 2.5 mm bend at 45\({}^{\circ}\); and 30 mm/double hook with a 5 mm bend at 45\({}^{\circ}\), tested through axial pull-out from a UHPC matrix. The shortest 25 mm fiber was pulled from the matrix before reaching the maximum load of the sample, indicating limited use of its load-bearing capacity. For the remaining types of fibers, the fiber rupture occurred without significant matrix damage, which was due to the pull-out resistance of the fiber exceeding the tensile strength of the single fiber. A UHPC mix containing straight steel fibers (19.5/0.2 mm) in the amount of 0.5% and hooked fibers (13/0.2 mm) with a total content of 0.5% achieved the highest elastic modulus [140].