Issue 49

F.J.P. Moreira et alii, Frattura ed Integrità Strutturale, 49 (2019) 435-449; DOI: 10.3221/IGF-ESIS.49.42 446 for the QUADS, considering t P2 =4 mm, and +13.3% for the MAXS, considering t P2 =1 mm). Identically, the curves for these two criteria overlap. Due to the aforementioned approximations, the MAXPS criterion showed P m values much below the expected, with a maximum deviation of -85.8% ( t P2 =3 mm). The strain-based criteria significantly over predicted P m , in line with the previous adhesives. The maximum offsets, all by excess, were +197.8% for the QUADE ( t P2 =2 mm), +214.7% for the MAXE ( t P2 =4 mm) and +160.5% for the MAXPE ( t P2 =2 mm). It was shown in a previous work [23] that damage initiation is ruled by the adhesive layer’s stresses rather than the strains (which also vary by a large amount between adhesives). On the other hand, using strain-based criteria can result in major deviations to the real joint behaviour, with an over prediction tendency. This is why the QUADS and MAXS criteria generally work very well. The QUADE and MAXE criteria, being based on strains, naturally present wrong P m results and should not be considered in the design process of bonded joints. The MAXPS and MAXPE criteria, due to its intrinsic formulation, are unable to promote a realistic damage growth path, since the crack growth direction is ruled by the maximum principal stresses or strains, in a sense that crack initiates and grows perpendicularly to the principal directions. As a result, adherend detaching by the adhesive through all the adhesive layer is rendered unfeasible because the mixed-mode loading induced in the adhesive results in short crack growth in the adhesive before the crack hits the adherend interface. Since P m was assessed by the damage initiation load, i.e., at the time the first crack appears in the model, the results do not match the real joint behaviour. Moreover, since stresses and strains in FEM modelling are traditionally mesh dependent [11], the direct use of initiation criteria to assess failure, i.e., without failure criteria, should promote mesh-dependent P m . Numerical evaluation of the XFEM propagation criterion The study of the propagation criterion relied on the use of the QUADS initiation criterion, due to the consistency of results shown in the previous Section, and consisted of changing the mixed-mode exponent  in expression (5) using the linear damage law, by considering  =0.5, 1 and 2, and also testing an exponential damage law with  =1. Usually, from reported data [32], the triangular law manages to represent with accuracy the behaviour of the adhesive layer, but changing this parameter leads to different mixed-mode conditions for element failure, which may or not prove to have a noteworthy influence on the results. Fig. 9 depicts the experimental and numerical P m comparison under the mentioned modelling conditions, for the T-joints bonded with the Araldite ® AV138 (a), Araldite ® 2015 (b) and Sikaforce ® 7752 (c). a) b) c) Figure 9: Experimental and numerical P m comparison, considering different XFEM propagation models, for the T-joints bonded with the Araldite ® AV138 (a), Araldite ® 2015 (b) and Sikaforce ® 7752 (c). 0 1 2 3 4 0 1 2 3 4 P m [kN] t P2 [mm] Exp Tri P1 Tri P0.5 Tri P2 Expon P1 0 1 2 3 4 5 6 0 1 2 3 4 P m [kN] t P2 [mm] Exp Tri P1 Tri P0.5 Tri P2 Expon P1 0 4 8 12 16 0 1 2 3 4 P m [kN] t P2 [mm] Exp Tri P1 Tri P0.5 Tri P2 Expon P1