PSI - Issue 41

A.E.S. Pinheiro et al. / Procedia Structural Integrity 41 (2022) 60–71 Pinheiro et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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8

0 2 4 6 8

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σ y [MPa]

σ y [MPa]

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-6 -4 -2

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x / L O P&C FEM

x / L O P&C FEM

a)

b)

Fig. 5. Absolute  y stresses in the 2015 by the models of Pugno and Carpinteri, and FEM, for L O =20 (a) and 40 mm (b).

Table 3. Peak σ y [MPa] comparisons for the three adhesives by the Pugno and Carpinteri model and the FEM. Adhesive AV138 2015 7752 L O (mm) 20 40 20 40 20 40 FEM 2.60 2.60 1.57 1.53 0.77 0.34 Pugno and Carpinteri 16.68 16.68 5.82 5.82 1.55 1.55 Δ σ y (%) 541.5 541.5 270.7 280.4 101.3 355.9

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τ xy [MPa]

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x / L O P&C N-H FEM

x / L O P&C N-H FEM

a)

b)

Fig. 6. Absolute  xy stresses in the 2015 by the models of Nayeb-Hashemi et al., Pugno and Carpinteri, and FEM, for L O =20 (a) and 40 mm (b).

Fig. 6 shows the absolute  xy stresses in the 2015 by the models of Nayeb-Hashemi et al., Pugno and Carpinteri, and the FEM, for L O =20 mm (a) and L O =40 mm (b).The  xy curves’ shape agrees with the expected, with peaks at the overlap edges caused by the shear-lag effect, and higher magnitude at x / L O =0 due to the different cross-sectional area of the adherends (Barbosa et al. 2018). The models by Nayeb-Hashemi et al., and Pugno and Carpinteri provide an identical  xy stress distributions, since both are based on the axial strain model. Compared with the FEM stress distribution, the analytical models generally have a good approximation both at the ends of the overlap and at the central region. According to the peak  xy values shown in Table 4, the AV138 led to the highest stress values and a good accuracy in comparison to the FEM results. The largest difference of both theoretical models was 21.0% (by excess) to the FEM, for L O =20 mm. The 2015 gave a better agreement, with excess deviations of 5.2% for L O =20 mm and 5.4% for L O =40 mm. The 7752 provided the closest results, with difference of 4.3% for L O =20 mm and 114.6% for L O =40 mm, both overshooting the FEM predictions. Identically to  y stresses, the reducing difference by the presented order of adhesives is related to the increasing ductility. Table 4. Peak  xy [MPa] comparisons for the three adhesives by the Nayeb-Hashemi et al., Pugno and Carpinteri model and the FEM. Adhesive AV138 2015 7752 L O (mm) 20 40 20 40 20 40 FEM 2.43 2.43 1.72 1.67 1.15 0.48

Nayeb-Hasehmi et al. 2.94 2.93 1.81 1.76 1.20 1.03 Pugno and Carpinteri 2.94 2.93 1.81 1.76 1.20 1.03 Δ τ xy (%) N-H / P&C 21.0 20.1 5.2 5.4 4.3 114.6