PSI - Issue 47

Domenico Ammendolea et al. / Procedia Structural Integrity 47 (2023) 488–502 Author name / Structural Integrity Procedia 00 (2019) 000–000

496

9

The first example, reported in Section 4.1, is a symmetric four-point bending test inducing pure Mode-I fracture conditions, which is used to assess the ability of the procedure described in Section 3.1 to determine accurate R curves for nano-filled UHPFRCs. The second example, reported in Section 4.2, is an asymmetric four-point bending test inducing Mixed-Mode fracture conditions, which is used to investigate the reliability of the proposed Moving Mesh approach to capture crack propagation along arbitrary crack paths under general loading conditions. 4.1. Mode-I four-point bending test The pre-notched beam considered for the present Mode-I four-point bending test, already investigated from an experimental point of view by (Meng and Khayat, 2016), is sketched in Figure 4(a), together with the adopted boundary conditions and computational mesh used for its spatial discretization. Moreover, a zoomed view of the same mesh around the crack tip is depicted in Figure 4(b). The geometric parameters appearing in Figure 4(a) are L = 305 mm and l = 203 mm, whereas the cross-section has a squared shape with a side of 76 mm. Four different mixtures of UHPFRC have been considered: one without nano-reinforcement and the others containing 0.1%, 0.2%, and 0.3% graphite nanoplatelets (GNPs), respectively. The Poisson’s ratio is equal to 0.2 for all these mixtures, whereas the Young’s modulus, computed on the basis of the initial linear part of the experimental load-displacement curve, is found to be 25, 40, 32, and 39 GPa for the same mixtures, respectively.

Figure 4. Mode-I four-point bending test: (a) geometry and boundary conditions; (b) zoomed view of the mesh around the crack tip region.

Figure 5 depicts the R -curves determined by using the procedure detailed in Section 3.1. For all the considered mixtures, the R -curves exhibit a monotonically increasing behavior and, in particular, a superlinear trend in the final stage, which can be explained by considering the additional toughness provided by the nano-filler. Moreover, the role of the GNP content in influencing the overall UHPFRC’s fracture toughness is clearly shown in the figure. After deriving the R -curves for all the considered mixtures, the relevant failure responses for the same Mode-I fracture test have been simulated by using the crack propagation algorithm described in Section 3.2. The predicted load-deflection curves are shown in Figure 6(a), which also reports the corresponding experimental curves obtained by (Meng and Khayat, 2016) for comparison. It can be easily observed that the numerical results are in excellent agreement with the experimental findings, thus confirming the accuracy of the present approach in predicting the failure response of nano-filled UHPFRC structural members. For the sake of completeness, Figure 6(b) reports the snapshots of the deformed configurations obtained for the different mixtures at the beam deflection of 1.2 mm.