PSI - Issue 33

R.V.F. Faria et al. / Procedia Structural Integrity 33 (2021) 673–684 Faria et al. / Structural Integrity Procedia 00 (2019) 000 – 000

683 11

Fig. 8 evaluates the numerical P m against the test results for the mentioned propagation conditions and purely welded, bonded and hybrid joints. The XFEM percentile errors over the experiments are given in Table 4. Results of the exponential damage law clearly overshoots the experimental P m , with a minimum error of 33.7% for the purely welded joint and a maximum of 73.7% for the bonded joint. On the other hand, the XFEM results were good using a linear damage law (best for  =0.5). The P m errors over the experiments ranged from -0.5% (purely welded joint) to 3.5% (bonded joint). Nonetheless, no major difference was found for both  =1 and 2. Considering  =1, the offsets were between 1.1% (hybrid joint) and 3.9% (bonded joint), while being almost identical for  =2. In view of these results, this work shows that only the linear softening law should be used in design of T-peel joints, while the exponential law is not recommended. This offset is linked to overshooting the maximum displacements in the damage laws with this damage formulation to keep the area under the damage law constant, resulting in higher P m .

Table 4. Percentile P m errors between the XFEM data and experiments - damage propagation criteria.

Linear α =0.5

Linear α =1

Linear α =2

Exp α =1 33.7 73.7 41.4

Joint condition Spot-welded Bonded 2015 Hybrid 2015

-0.5 3.5 -1.3

2.7 3.9 1.1

2.9 3.9 1.3

5. Conclusions This work presented an XFEM criteria evaluation for T-peel joints, in the variants of purely welded, bonded and hybrid methods. The XFEM accuracy was checked by reproducibility of failure modes and P m comparison. The numerical analyses accounted for varying damage initiation criteria, damage laws and  . The test results were initially presented, and revealed that the bonded and hybrid joints experienced failures in the adhesive layer (cohesive failure) at small loads. In which regards P m , the hybrid joint largely excelled the bonded joint, due to the premature cracking of the latter case with the adhesives due to adhesive cracking onset at low loads (297.0% increase). The hybrid joint also behaves better than the welded joint, with the significant improvement of 40.3%. These variations were discussed with stress distributions’ data . Actually, the addition of a thin adhesive layer to the purely welded joint highly improved the join performance due to reduction of associated peak stresses, and also more paths for peel load transfer. The XFEM evaluation consisted of two studies. In the damage initiation study, the best results reported to the QUADS and MAXS stress criteria. In the damage propagation study, the exponential damage law is not recommended due to offset results, oppositely to the linear damage law. References Barenblatt, G. I., 1959. The formation of equilibrium cracks during brittle fracture. General ideas and hypothesis. Axisymmetrical cracks. Journal of Applied Mathematics and Mechanics 23, 622-636. Barenblatt, G. I., 1962. The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Advances in Applied Mechanics 7, 55-129. Belytschko, T. and Black, T., 1999. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45(5), 601-620. Bishopp, J. (2005). Chapter 5 Aerospace: A pioneer in structural adhesive bonding. Handbook of Adhesives and Sealants. P. Cognard, Elsevier Science Ltd. 1 : 215-347. Bishopp, J. A., 1997. The history of Redux® and the Redux bonding process. International Journal of Adhesion and Adhesives 17(4), 287-301. Campilho, R. D. S. G., Banea, M. D., Neto, J. A. B. P. and da Silva, L. F. M., 2013. Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. International Journal of Adhesion and Adhesives 44, 48-56. Campilho, R. D. S. G., Banea, M. D., Pinto, A. M. G., da Silva, L. F. M. and de Jesus, A. M. P., 2011. Strength prediction of single- and double lap joints by standard and extended finite element modelling. International Journal of Adhesion and Adhesives 31(5), 363-372. Campilho, R. D. S. G., Pinto, A. M. G., Banea, M. D. and da Silva, L. F. M., 2012. Optimization study of hybrid spot -welded/bonded single-lap joints. International Journal of Adhesion and Adhesives 37, 86-95. Curiel Sosa, J. L. and Karapurath, N., 2012. Delamination modelling of GLARE using the extended finite element method. Composites Science and Technology 72(7), 788-791. de Sousa, C. C. R. G., Campilho, R. D. S. G., Marques, E. A. S., Costa, M. and da Silva, L. F. M., 2017. Overview of different strength prediction techniques for single-lap bonded joints. Journal of Materials: Design and Application - Part L 231, 210-223. Di Bella, G., Borsellino, C., Pollicino, E. and Ruisi, V. F., 2010. Experimental and numerical study of composite T-joints for marine application.