PSI - Issue 39

Andrea Pranno et al. / Procedia Structural Integrity 39 (2022) 688–699 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3.1. Plain nano-enhanced UHPFRC beam specimens The following numerical results are based on the experimental four-point bending test performed in quasi-static loading conditions by Meng and Khayat (2016) on small-sized plain UHPFRC beams containing 0.5% of volume fraction of straight steel fibers with diameters D = 2 mm and length L f = 13 mm. The geometrical parameters of the computational model are depicted in Figure 4. Three different mixtures have been investigated: one without nano reinforcement (UHPFRC) and two containing 0.05% (UHPFRC GNP 0.05%) and 0.1% (UHPFRC GNP 0.1%) of graphene nanoplatelets.

Fig. 4. Geometry of the plain nano-enhanced UHPFRC beam specimen.

For all the investigated mixtures the concrete Young’s modulus E and the Poisson’s ratio is ν are assumed equal to 40 GPa and 0.2, respectively, assuming that for low volume fraction of nano reinforcement such material parameters are not influenced. The mechanical parameters of the steel reinforcing fibers and the graphene nanoplatelets are reported in De Maio et al. (2020a), while the fracture parameters of the embedded cohesive interfaces for the investigated UHPFRC mixtures were obtained from an accurate calibration process. Thus, the fracture parameters reported in Table 1 are assumed as reasonable values giving an accurate prediction of the load-deflection curve for the investigated cases.

Table 1. Fracture parameters of the embedded cohesive interfaces for the investigated UHPFRC mixtures. t f [MPa] UHPC f G [N/m] F UHPC G [N/m] F UHPFRC G [N/m] c CTOD [mm]

f w [mm]

UHPFRC

5.71 1

40

350

1800

0.005

3.25

UHPFRC GNP 0.05%

6.14 1

50

375

2800

0.005

3.25

UHPFRC GNP 0.1%

60

400

3800

0.005

3.25

6.81 1

1 for additional details see the work of Meng and Khayat (2016)

In Figure 5, comparisons between the obtained numerical load-deflection curves and the experimental ones (reported in Meng and Khayat (2016)) have been reported. It has been highlighted that the proposed trilinear traction– separation law is consistent for determining the structural behavior of nano reinforced UHPFRC elements. The obtained numerical curves are in good agreement with the experimental ones giving percentage errors on the predicted load peak equal to 3.62%, 3.58%, and 4.51%, for the three mixtures UHPFRC, UHPFRC GNP 0.05%, and UHPFRC GNP 0.1%, respectively. A slight local divergence in the softening branches between the reported curves was highlighted due to the probable appearance of dynamic phenomena induced by high speeds of crack propagation which is neglected in the numerical simulation based on quasi-static loading conditions. As already known from the experimental results found in literature and confirmed by the obtained numerical results, the peak load and the energy absorbed energy can be increased with the addition of low contents of graphene nanoplatelets. Such strengthening and toughening effects are due to the development of higher cohesive forces between cement paste and steel fibers, and between cement paste and fine aggregates.