SCALE EFFECTS ON FRC COMPOSITES: BRITTLE, PERFECTLY-PLASTIC, SOFTENING POST-PEAK REGIMES

In the framework of Fracture Mechanics, the present work aims to analyse the mechanical behaviour of Fiber-Reinforced Concrete (FRC) structural elements subjected to monotonic bending. The Bridged Crack Model is proposed as a Fracture Mechanics based approach able to describe the crack propagation process occurring in the cross-section of FRC structural elements. After a brief introduction, the model’s features are described: the concrete matrix is assumed as elastic-perfectly brittle, whereas the bridging action of the fibers is modelled with suitable constitutive laws, describing the pull-out mechanisms. These mechanisms are defined by pull-out tests results, reported in the scientific literature. On the basis of equilibrium and compatibility conditions, defined in the framework of Linear Elastic Fracture Mechanics, the response of the cracked cross-section is described in terms of applied moment vs localized rotation curve. Experimental studies reported in the scientific literature suggest to describe the flexural response of FRC beams, by subdividing it into three stages. Considering a notched FRC specimen subjected to bending, the related applied load vs deflection diagram starts with a linear elastic ascending branch (stage I), up to the initiation of the fracturing process. From this point forward, the post-cracking phase (stage II) of the element takes place, during which the main crack gradually propagates while the reinforcing fibers exert their bridging action. Depending on several conditions, including the fiber volume content, different post-cracking behaviour of the composite can be obtained, such as the perfectly-plastic one. The flexural response experiences finally a descending softening branch (stage III), where the fiber pull-out from the matrix (fiber slippage) is the dominant phenomenon. By applying the Buckingham Pi theorem, the dimensional analysis reveals two dimensionless parameter, NP and NW, as crucial in the identification of the mechanical response of the composite in the post-cracking regimes. The first one depends on the fiber volume fraction, the matrix fracture toughnes, the mechanical and geometrical properties of the fiber, and the beam characteristic size. The second one depends on the matrix fracture toughness, the matrix Young’s modulus, the beam characteristic size, and the average embedded length of the fiber into the matrix. Numerical simulations conducted by the Bridged Crack numerical algorithm, pointed out the effect of the dimensionless parameters on the global response of the composite. It is found that the reinforcing brittleness number, NP, governs the stage II of the response, whereas a fixed value of NW, provides the collapse of the curves onto a unique final branch, related to the stage III. In the second part of the work, the model is validated on the basis of bending test on FRC specimens, carried out by other Authors. A comparison between numerical results and experimental data proved the effectiveness of the Bridged Crack Model in the material identification. For each experimental campaign four identifying parameters are determined, so the model is able to evaluate the minimum reinforcement condition, required to achieve a stable post-cracking response. Finally, three experimental campaigns conducted on specimens of different sizes are analysed and reproduced, confirming the model’s ability to understand in a comprehensive manner size effects in the structural behaviour of FRC.