Issue 49

F.J.P. Moreira et alii, Frattura ed Integrità Strutturale, 49 (2019) 435-449; DOI: 10.3221/IGF-ESIS.49.42 445 promotes stresses to be concentrated in small areas, flexible and ductile adhesives behave best. In one hand, the flexibility tends to increase the area along which stresses are being transferred (Fig. 5). On the other hand, the ductility permits plasticization of the adhesive at the stress concentration sites while the regions in the vicinity becomes loaded, resulting in an overall improved behaviour. Numerical evaluation of the XFEM initiation criterion The XFEM initiation criteria described in Section “XFEM formulation” are evaluated against the experimental data, by directly comparing P m with the experiments. At this stage, the linear energetic criterion, considering  =1 in Eqn. (5), is considered in all simulations. As it was previously discussed, the use of the MAXS, MAXE, QUADS and QUADE criteria results in crack onset and growth parallel to the adhesive layer, while MAXPS and MAXPE criteria leads to cracking perpendicular to the maximum principal stresses or strains, which subsequently makes the crack grow in the direction of the adherends. Fig. 8 shows the P m comparison for all t P2 between the different XFEM initiation criteria and the experiments for the adhesives Araldite ® AV138 (a), Araldite ® 2015 (b) and Sikaforce ® 7752 (c). a) b) c) Figure 8: Experimental and numerical P m comparison, considering different XFEM initiation criteria, for the T-joints bonded with the Araldite ® AV138 (a), Araldite ® 2015 (b) and Sikaforce ® 7752 (c). For the Araldite ® AV138, the QUADS and MAXS criteria are closest to the experimental points, and the respective curves are practically overlapped in the figure. Averaged over the experiments, the maximum relative deviations were +8.8% ( t P2 =2 mm) and +9.5% ( t P2 =2 mm), respectively, for these two criteria. The MAXPS criterion revealed to be unsuited, in the manner that it was used, since P m highly underestimates the tests (up to -82.5% for t P2 =1 mm). Oppositely to this behaviour, the strain-based criteria (QUADE, MAXE and MAXPE) overshoot the experimental data, with emphasis to the QUADE and MAXE. The highest offsets for these criteria were +113.3% (QUADE), +117.3% (MAXE) and +31.3% (MAXPE), in all cases for t P2 =2 mm. Qualitatively, the P m predictions for the Araldite ® 2015 by the six criteria agree with those of the Araldite ® AV138. Thus, the QUADS and MAXS criteria are quite close to the experimental values, with a negligible difference between them. The maximum P m deviations were, in both cases, obtained for t P2 =4 mm, attaining -8.9% (QUADS) and -8.6% (MAXS). The MAXPS criterion was offset up to -81.3% ( t P2 =1 mm), whilst the maximum deviations for the strain-based criteria attained maximums of +110.7% for both QUADE and MAXE ( t P2 =1 mm), and +55.2% the MAXPE criterion ( t P2 =2 mm). Finally, the results for the Sikaforce ® 7752 were much alike those of the former adhesives although, in this case, even the QUADS and MAXS criteria showed bigger variations to the experimental P m (up to -13.3% 0 1 2 3 0 1 2 3 4 P m [kN] t P2 [mm] Exp MAXS QUADS QUADE MAXE MAXPS MAXPE 0 2 4 6 0 1 2 3 4 P m [kN] t P2 [mm] Exp MAXS QUADS QUADE MAXE MAXPS MAXPE 0 4 8 12 16 20 0 1 2 3 4 P m [kN] t P2 [mm] Exp MAXS QUADS QUADE MAXE MAXPS MAXPE