PSI - Issue 47

Francesco Ascione et al. / Procedia Structural Integrity 47 (2023) 460–468 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The numerical analyses have been performed by considering different meshes, in order to assess the potential mesh dependency of the proposed model. In particular, three meshes have been built by changing the number of cohesive elements along the bonded concrete/FRP interface. 15, 30, and 60 cohesive elements are employed for Mesh 1 (coarsest mesh), Mesh 2, and Mesh 3 (finest), respectively, as depicted in Fig. 3b. The main cohesive parameters required by the adopted traction-separation law for concrete, illustrated in Section 2.1, are the tensile strength t f and fracture energy f G , and here chosen equal to 3.1 MPa and 100 N/m, as reported in the reference experimental work (Irshidat and Al-Saleh, 2016). The cohesive elements along the concrete/FRP interface are equipped with a bond-slip law explained in Section 2.2, whose required parameters for CNT modified adhesive are reported in Table 1.

Table 1. Adopted parameters for the bond-slip law. δ 1 δ 2

G f

δ f

τ max

CNT-modified epoxy resin

0.01

0.695

0.705

3.6

2500

Fig. 4a shows the predicted structural response obtained by the proposed mode with different computational discretizations. All loading curves, in terms of bond stress vs slip, are almost in good agreement with each other and the experimental outcome. However, the coarsest mesh, Mesh 1, exhibits a higher value of the slip than Mesh 2 and 3, leading to a failure mode slightly different from that predicted by the other meshes. As a matter of fact, a combined debonding failure mode characterized by the partial detachment of the concrete substrate is obtained by Mesh 1, with respect to Mesh 2 and 3 where the complete concrete substrate detachment occurs (see Fig. 4b). However, all loading curves are in good agreement with the experiment, thus validating the proposed model for analyzing FRP-reinforced concrete elements.

a

b

Mesh 1

Mesh 2

Mesh 3

Fig. 4. Numerical results of the double lap shear test: (a) bond stress vs slip and (b) failure modes of the specimens with different mesh sizes.

3.2. Failure analysis of nano-enhanced FRP-plated RC beam The proposed model is here employed to analyze a reinforced concrete beam retrofitted with an FRP plate bonded to the concrete surface by a nano-modified epoxy resin, subjected to a four-point bending test. The geometry and boundary conditions are reported in Fig. 5. The adopted Young’s modulus, taken from (Irshidat et al., 2016), is equal to 20 GPa for concrete and 200 GPa for steel rebars. The external reinforcing system consists of a 1 mm thick carbon fiber plate, already employed in the validation test, whose Young’s modulus and tensile strength are equal to 28 GPa and 4900 MPa, respectively. The FRP plate is bonded to the concrete surface by nano-modified epoxy resin. In particular, the concentration of carbon nanotubes (CNTs) in the nano-modified epoxy resin was equal to 3.4 wt%. The tested beam is discretized by 2D triangular elements arranged by a Delaunay tessellation for the concrete phase and 1D truss elements for rebars. A mapped mesh with quadrilateral elements is employed to discretize the FRP system. The cohesive parameters, required by the traction-separation law, are set equal to 2.0 MPa t f = and 100 N/m f G = ,