PSI - Issue 47

Luciano Feo et al. / Procedia Structural Integrity 47 (2023) 800–811 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Model calibration and results An inverse identification procedure was performed to assess the accuracy of the modified model to predict the cracking and post-cracking response of nano-enhanced HPFRC beam elements. The main goal of this Section is to determine the values of the model parameters that minimize the difference between the experimental results and the numerical ones with reference to Force-Displacement curves. In particular, seven different mixtures obtained by fixing both the UHPC matrix and the volume fraction of steel fibers (i.e., 0.5%) and varying the weight fraction of nanofibers (CNFs) in the set 0%, 0.10%, 0.15%, 0.20% and 0.3%, were considered. Steel fibers with a diameter, � , of 0.2 mm, a length, � , of 13 mm and with no hooked and CNFs (50-200 m in length) with a diameter equal to 100 nm and a surface area of 45 m 2 /g were used. The mechanical properties of both steel fibers and carbon nanofibers are listed in Table 1. In addition, for each percentage by weight of nanofillers, Table 2 summarizes the mechanical properties of UHPFRC mixtures, in terms of average value of compressive strength, tensile strength and flexural strength. Compressive and bending tests were carried out in accordance with the ASTM C109 (1999) and ASTM C1609 (2005), respectively. The size of the samples used for testing and for input data of the model are shown in Figure 5. Table 1. Mechanical proprieties of the fibers used (Meng and Khayat (2016)). Fiber type Elastic modulus (GPa) Tensile strength (GPa) Steel fiber 203 1.9 Carbon nanofiber (CNF) 240 30

Table 2. Compressive, tensile and flexural strength (Meng and Khayat (2016)).

Content (%)

Compressive strength (MPa)

Tensile strength (MPa)

Flexural strength (MPa)

0

174 174 175 177 179 181

5.84 7.01 7.65 7.97 8.36 9.09

7.73 8.17 8.28

0.05 0.10 0.15 0.20 0.30

10.70 11.12 11.26

Because of their random spatial distribution and orientation, the number of  bers crossing the cracked section is variable. Therefore, several runs were conducted (i.e., three for each mixture), assuming a number of layers, � , equal to 20 and a length of the flexible part, , equal to 150mm. The proposed inverse identification procedure begins to calibrate the fracture energy parameters for both the mixture without nanofibers (i.e., 0%), and for those with nanofibers (i.e., 0.05%, 0.10%, 0.15%, 0.20%, 0.30%). In particular, the increase in the percentage of nanofillers was taken into account by modifying the parameters � , �� and ��� and leaving the point 0.2 ∙ ��� and the final crack opening width, � , of the concrete stress-strain diagram in tension, unchanged (Figure 3b). Subsequently, the parameters of the bond-slip law were calibrated. Starting from the mixture without nanofibers, all five parameters were calibrated. Then, only the two bond stresses (i.e., �� and � ) were calibrated again on the bending response of renforced samples while all slip parameters (i.e., �� , � and � ) were considered constant. The input data of both the fracture energy parameters and of the bond-slip law considered for the numerical analysis are summarized in Tables 3-4, respectively, while their qualitative trend is plotted in Figures 6-7. The results in terms of fracture energy, for each percentage of nanofibers content are listed in Table 5.