PSI - Issue 54

Luís D.C. Ramalho et al. / Procedia Structural Integrity 54 (2024) 390–397 Lu´ıs D.C. Ramalho et al. / Structural Integrity Procedia 00 (2023) 000–000

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3. Results

3.1. Geometry and properties

The joint analysed in this section is a SLJ, whose dimensions are presented in Fig. 2, subjected to an impact load. Most dimensions are fixed, but three di ff erent overlap lengths ( L O ) were tested: 12.5 mm, 25 mm and 50 mm. The joint is composed of three di ff erent materials: an adhesive, a CFRP substrate and an impact material. The CFRP substrate has the following properties E x = 109GPa, E y = E z = 8 . 819GPa, ν xy = ν xz = 0 . 342, ν xz = 0 . 380, G xy = G xz = 4315, G xz = 3200 and density ρ = 1227 kg / m 3 Peres et al. (2022). Two di ff erent adhesives were tested, whose properties are shown in Table 1. The impact material has the following properties: 1000 GPa, ν = 0 . 3 and ρ = 23 . 22 × 10 6 kg / m 3 . This density combined with an impact velocity of 1.75 m / s ensures an impact energy of 40 J, the same as the experimental tests performed by Peres et al. (2022), used to compare to the numerical results. The discretizations have between 7859 and 13081 nodes, depending on the L O , joints with longer L O have more nodes. The discretization is biased toward the adhesive / adherent interface corners, which are the most critical areas, this is shown in Fig. 3. The simulations were all performed assuming plane strain conditions. The stress analysis show in Fig. 4 shows that under impact the stress in the adhesive mid-thickness line, be it τ xy or σ yy , is not completely symmetric like it happens in static analysis. Comparing the di ff erent numerical methods, the two meshless methods used in this work provide stress distributions similar to the FEM, regardless of the adhesive used or the L O . The more ductile adhesive, Sikaforce ® 7752, shows a more uniform stress distribution, and the stress peaks at the overlap ends are not as pronounced, especially when looking at the τ xy . Comparing the di ff erent L O , it is possible to conclude that shorter L O result in higher stress concentrations near the overlap ends, which was observed for all numerical methods and the two di ff erent adhesives. Fig. 5 shows the evolution of the force applied to the joint and the maximum τ xy , which is what was used to predict the strength of the joints. It its important to note that these values were obtained using a moving average with 40 data points. The black dots in the figure represent the point where the failure was predicted for each simulation. Looking at the force, for both adhesives there is almost no di ff erence between the three numerical methods. The figure also shows that longer L O also have a higher force than shorter L O for a given displacement, regardless of the adhesive. The maximum τ xy progression is similar for all numerical methods and L O up until the failure point, in the Araldite ® AV138 joints. For the Sikaforce ® 7752 there are small di ff erences between the numerical methods and the di ff erent L O . For a given displacement, the NNRPIM predicts a higher maximum τ xy , followed by the FEM and the RPIM predicts the lowest. The L O comparison shows that the longer the L O the lower the maximum τ xy will be for a given displacement up until the predicted failure point. The strength predictions using the maximum τ xy are shown in Fig. 6 the three numerical methods show similar predictions, with the RPIM generally predicting a higher strength than the other two numerical methods. The maxi 3.2. Results

Imposed Velocity

0.2

3

L O 200

25

Figure 2: Scheme of the SLJ, measurements in mm (not to scale)

Table 1: Mechanical properties of the adhesives Peres et al. (2022)

3 )

Material

E (GPa)

ν τ f (MPa)

ρ (kg / m

Araldite ® AV138 4.89 0.35 51.7 Sikaforce ® 7752 0.49 0.33 26.4

1700 1530