PSI - Issue 66

Bineet Kumar et al. / Procedia Structural Integrity 66 (2024) 337–343 Author name / Structural Integrity Procedia 00 (2025) 000–000

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cracking and enhancing the load-carrying capacity. As the cracks propagated, the 30 mm fibers offered resistance through a bridging mechanism, a phase known as the fiber-bridging stage, where the load-bearing capacity increased with the widening of the cracks. However, after reaching a certain point, the load capacity gradually decreased due to the fiber pull-out phenomenon. The behavior across different stages of fracturing, such as micro-cracking, fiber-bridging, and fiber pull-out, showed variation depending on specimen size. Therefore, understanding the relative dominance of these zones and their dependence on the specimen size is critical. To analyze and predict the post-peak fracture behavior, an inverse analysis approach has been employed, following by the study, Kumar et al. (2024). This method allows for deriving the tensile properties of the UHPFRC beams and predicting fracture characteristics, including the fracture process zone and variations in crack width concerning specimen size. 3. Analytical formulation In this section, closed-form expressions for different phases of the tensile stress–strain behavior (as shown in Fig. 2) of composite beam specimens have been developed through inverse analysis. The proposed material model, derived from experimental observations of center-point loading tests on beams, is illustrated in Fig. 2. The compressive stress profile has been modelled by assuming an elasto-plastic behavior typical of concrete under compression. Meanwhile, the tensile stress profile has been defined using a combination of stress-strain and stress-crack width approaches. Initially, it is assumed that the UHPFRC exhibits elastic behavior. As loading continues, micro-cracking and matrix cracking emerge, leading to fiber slippage and a sudden drop in the resisting bending stress. Following this, the composite enters the fiber-bridging phase, where the bending stress provided by the beam increases. Up to this point, the stress-strain approach is applicable, as no major crack formation has occurred. However, once substantial matrix-cracking is present, macro-crack propagation begins, accompanied by fiber pull-out. At this stage, the stress strain model is no longer suitable due to the clear separation of crack surfaces, making the traditional gauge length definition ineffective. Therefore, a stress-crack width criterion has been employed for this phase. The hooked-end fibers used in the composite contribute two primary forms of resistance. Firstly, resistance arises from fiber yielding at the two bend points during pull-out (Alwan et al. (1999), Accornero et al. (2022), Carpinteri et al. (2023)). Secondly, frictional resistance also plays a role. In this fourth phase, the bending stress provided by the beam starts to diminish. As more fibers length get pulled out, the stress reduces further, with yielding localized to only one point along the fiber bend. During the final stage of fiber pull-out, resistance comes from a combination of single-point fiber yielding and friction. Stress gradually declines to zero as the fibers are completely pulled out of the concrete matrix. Additionally, the present model incorporates the effect of fiber orientation by accounting for the effective fiber length. This effective length considers the wall effect, which also contributes to the size effect observed in fiber-reinforced concrete. 4. Calibration and validation The proposed material model has been developed, and a closed-form expression for the load–CMOD relationship has been derived. This model has been calibrated against experimental data for all three specimen sizes and both fiber contents, as illustrated in Fig. 3. The model parameters, which vary depending on fiber percentage and specimen size, have been quantified accordingly. Further, the crack length predicted from the model has been compared with result obtained from digital image correlation technique (DIC). The comparison showed that the results from the proposed model closely match those obtained DIC results.