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Incorporation of fibers is vital to improve the crack resistance and fracture toughness of UHPC. Steel fiber is the most common used fiber to improve the toughness of UHPC, and extensive studies have been conducted in this area [2]. The reinforcement effect of steel fiber on the UHPC matrix is influenced by the fiber content, fiber shape, fiber length and aspect ratio [2,3,8]. When the steel fiber content is below 3%, the existing research showed that the strength of UHPC increased at different magnitudes with the increase of steel fiber content under compressive, tensile and flexural loading [3]. However, further increase of fiber content in UHPC led to the decrease of flowability and the presence of fiber agglomerate, resulting in the decline of the mechanical properties of UHPC [3,9,10]. The results of research on the influence of fiber shape on the mechanical properties of UHPC explored by different researchers were not consistent. Some research indicated the deformed fibers, i.e., hook-end fiber, twist fiber and corrugated fiber, are beneficial for the mechanical properties of UHPC compared to the straight fibers [11,12,13], whereas some other researchers reported the opposite results [8,14]. Yoo et al. [15] demonstrated that straight steel fibers exhibited higher fiber numbers per unit volume and a better distribution condition, which may be the reason for the better mechanical properties of UHPC containing straight steel fibers. Moreover, some other studies have been carried out to investigate the influence of steel fiber length and aspect ratio on the mechanical behavior of UHPC. The results showed that steel fiber length and aspect ratio have a positive effect on the tensile and flexural behavior of UHPC [11,16,17], but they have no obvious influence on the compressive behavior [18]. Compared with plain concrete, steel fiber reinforcement can improve the cracking resistance and fracture toughness of UHPC, but the mode of single crack failure is still the main failure pattern; the crack width has not been effectively controlled, and the ultimate strain capacity is still limited [2,3].
Ultra-high molecular weight polyethylene (PE) fibers with 2% vol. were used in the UHPC specimens. The mix design of the UHPC matrix is given in Table 3. PE fiber has a high modulus of elasticity and fiber strength. There are 5 types of PE fiber, namely PA fiber, PB fiber, PC fiber, PD fiber, PF fiber (i.e., PF fiber is PF type polyethylene fiber). The morphology and basic parameters are shown in Figure 1 and Table 4, respectively.
There is still no set of systematic and comprehensive evaluation methods regarding the tensile toughness of UHPC. According to the performance grading scheme proposed by Naaman and Reinhardt [32], as shown in Figure 13, the tensile properties of UHPC can be divided into the five levels: Level 0 was used to illustrate the tensile behavior of plain UHPC without fibers as a control group. The tensile stress-strain curve has only an elastic phase, and the matrix cracks and fails after reaching the peak load. With the addition of fibers, the tensile behavior of the UHPC can be improved due to the fiber bridging effect. As illustrated in Level 1, the tensile stress-strain curve of the UHPC exhibits the stress-softening section. In Level 2, the softening section of the tensile stress-strain curve is more obvious, and the energy absorption capacity of the composite is improved. However, the cracking formed in the composite is still the single crack. In Level 3, the composite exhibits strain-hardening behavior under tensile loading. The cracking mode of the composite changes from the single crack to the multiple crack pattern. The ultimate tensile strain of the specimen is greatly improved. In Level 4, the composite exhibits higher ultimate tensile strength and ultimate tensile strain. The strain-hardening section of the composite becomes more obvious, and the energy absorption capacity greatly improves.
where G is the energy release rate of the crack. Energy release rate is the elastic energy per unit film thickness that would be released if the crack were to extend by a unit distance along the interface. In this analysis, deviation of the crack trajectory from the interface (e.g. in cohesive failure) is assumed to be small so that the energy release rate G can be computed by assuming the crack is right on the interface.
In summary, a fracture mechanics model is used to explain why small free-standing membranes are more resistant to detachment. We show that detachment can be prevented by making the membrane smaller for a given pre-strain and W, which is consistent with our experimental observations. A useful expression for critical radius of the membrane is obtained and may guide future design of free-standing membrane systems. 2ff7e9595c
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