# Cracking Behavior of Fiber-Reinforced Concrete Beams Made of Waste Sand
## 2 Mechanisms of Cracks  
Concrete is a fundamental building material classified as a brittle substance. To enhance its homogeneity, short steel fibers are incorporated, resulting in the formation of fiber-reinforced concrete. One of the primary advantages of fiber-reinforced concrete is its capacity to transfer tensile stresses across cracks. The inclusion of dispersed reinforcement in the matrix transforms the originally brittle material into a more ductile one [13; 58; 59; 60]. Figure 1 illustrates the force-deformation relationship of axially stretched samples made from both ordinary concrete and fiber-reinforced concrete. The results indicate that the addition of fibers prevents the sudden failure typical of conventional concrete elements. This improved performance is attributed to the ability of the fibers to distribute stresses at points of discontinuity within the concrete [12; 17; 31]. Figure 2 depicts the distribution of tensile stresses across cracks for both ordinary and fiber-reinforced concrete. The fiber interlinking, akin to aggregate interlinking, is influenced by a variety of factors. In evaluations aimed at assessing the effectiveness of fibers, a single fiber positioned perpendicular to a crack is analyzed. This fiber is assumed to play a role in energy dissipation through several mechanisms, which include: the rupture of the matrix and its debonding, the detachment of the fiber-matrix interface, friction between the fiber and matrix post-bonding (fiber pullout), the breakage of the fiber itself, as well as abrasive wear and plastic deformation or yielding of the fiber (see Figure 3). The mechanical performance of fiber-reinforced composites (FRC) is certainly affected by the quantity of fibers, their orientation, and significantly by their behavior during pullout in relation to the applied load (or load-displacement characteristics). Specifically, fiber pullout is contingent on the type and mechanical/geometric properties of the fibers, the mechanical characteristics of the fiber-matrix interface, the angle of the fiber relative to the load direction, and the mechanical properties of the matrix itself [12; 13; 15; 60; 63; 64; 65; 66; 12; 16]. When analyzing the behavior of a reinforced concrete element, two fundamental situations can be identified: one in which the element is uncracked and another in which it is cracked. The transition from the first situation to the second depends on the tensile strength of the concrete, which is evidenced by the appearance of the first crack. This initial crack typically forms in the area where the bending moment is at its maximum and the shear force is relatively low. The cracks generally develop in a direction that is more or less perpendicular to the bending stress. Consequently, the element is classified as being in phase I (uncracked). As illustrated in the load-deflection diagram, there comes a point  
Figure 1: Relationship between force-elongation of an axially stretched sample made from ordinary concrete and fiber-reinforced concrete [61]. Figure 2: Stress distribution of tensile stresses across a crack for ordinary concrete and fiber-reinforced concrete, according to RILEM TC-1 62-TDF [62]. where the behavior transitions from linear to nonlinear (see Figure 4b), indicating a move to phase II (cracking). The cracking mechanism of reinforced concrete elements involves the appearance of the first crack at the point of maximum bending moment and the lowest tensile strength of the concrete matrix. Subsequent cracks emerge adjacent to the first one, continuing in this manner until a stabilized crack pattern is achieved. This means that no new cracks develop, and only the existing ones widen and extend their range [50]. In the case of reinforced concrete elements additionally reinforced with dispersed reinforcement, the process of crack formation and development is similar to that in reinforced concrete elements, but not identical. There is a noticeable difference in the development of cracks and their widths.