PSI - Issue 28

I.J. Sánchez-Arce et al. / Procedia Structural Integrity 28 (2020) 1084–1093 Sánchez-Arce et al. / Structural Integrity Procedia 00 (2019) 000–000

1090

7

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Peak difference (%)

12,5

25

37,5

50

Normalized L O Peel Shear

Figure 4. Difference, in percentage, between the peak stresses estimated from the NNRPIM method compared to the FEM.

In the τ xy case, the maximum difference was 6.56%, corresponding to L O =50.0 mm. The smallest was 4.92%, corresponding to L O =25.0 mm (Figure 4). In the peel stress case, the maximum difference was 4.34%, corresponding to L O =12.5 mm. The smallest difference was 0.60%, observed at L O =50.0 mm, as shown in Figure 4. Such small differences indicate the NNRPIM method provides rather similar results to those predicted by well established methods as the FEM. Difference between peak stress values comparing meshless to FEM have been reported before [24]; however, the difference found by Mubashar and Ashcroft [24] was five times larger than the one observed here. Such a big difference can be attributed to the node density; in this study, the mean distance between nodes in the adhesive layer was 0.03 mm whilst the distance in [24] was two-fold larger. 4.3. Strength prediction The P max calculated from the FEM and NNRPIM predictions were compared with the P max determined experimentally (Figure 2). It was found that the experimental P max is higher than the numerical. Nevertheless, the lowest difference was observed with L O =12.5 mm, which is a standard (i.e., ASTM [5]). In all cases, both experimental and numerical, the joint strength increased proportionally (approximately linearly) with L O , as can be observed in Figure 2, Figure 5, and Figure 6. Considering the maximum shear stress criterion (MSSC), the minimum difference between experimental and numerical data was found at L O =12.5 mm where the numerical techniques under-predict the joint strength by 52.9% and 55.7% (FEM and NNRPIM, respectively). On the other hand, the maximum difference was observed at L O =50.0 mm, where these techniques provided strengths equivalent to 45.5% and 48.1% (FEM and NNRPIM, respectively), with respect to the experimental measurements, as shown in Figure 5. In addition, P max was determined by means of the maximum peel stress criterion (MPSC). Similar to the MSSC, this criterion also underpredicts P max . The minimum differences from the FEM and NNRPIM predictions were also observed at L O = 12.5 mm, being 56.2% and 54.6% below the experimental data, respectively. Again, the maximum difference was observed at the longest L O . In such a case, the predictions (FEM and NNRPIM) correspond to 41.1% and 40.3% of the experimental values, respectively, as shown in Figure 6. Both criteria underpredicted P max ; however, under the conditions evaluated here, those predictions derived from the MSSC were slightly closer to the experimental data than those from the MPSC. Regardless of the numerical method (FEM or NNRPIM), the MSSC’s predictions are, on average, half of the experimental measurements. The MPSC’s predictions were on average 41% of the experimental value. Moreover, with both criteria, the NNRPIM provided higher mean predictions ( ≤2.5% higher to FEM).