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

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1997). One of the most prominent examples is the Mosquito, in 1940 (Bishopp 2005). Benefits of this joining process include joining of different base materials, no drilling required, lightweight arising from the joint and using different materials, specific strength, and improved stress distributions (Ebnesajjad and Landrock 2014). The main limitations of this technique are the poor strength under humid and high temperature conditions, design uncertainties and disassembly difficulties after curing. Apart from these, joint design should focus on the reduction of peel (  y ) stresses, appearing due to the loading or part’s shape. In fact, except for peel loadings, adhesive joints should be mostly subjected to shear ( τ xy ) and compression stresses (Petrie 2008). Different base geometries are available and studied in the literature, whose use depends on the application, with design data and parametric studies to address the geometrical and material effects, aiming to aid the design. The single-lap joint (SLJ) is the recurrent geometry, while double-lap joints (DLJ) and scarf joints are also studied in detail (Moya-Sanz et al. 2017, Stuparu et al. 2017, Sun et al. 2020). T-joints are a market niche encountered in specific industries (for example aeronautical and marine), in joints like those between the ship bulkheads and hull (Di Bella et al. 2010). T-joints perform well in joining orthogonally oriented components, which are a common necessity. T-joints are also addressed, but seldom compared to the most common geometries. Few issues must though be considered, such as strength under direct peel or subjected to bending. Conversely, under compressive transverse stresses the strength is acceptable (Duan et al. 2004, Yang et al. 2013). Adhesive joints need techniques that can reliably infer their behavior under service loads, including failure loci, damage onset and strength, such that the confidence in their use grows to enable their dissemination. With this goal, different analytical models were initially proposed before the advent of numerical computation. Volkersen (1938) was the first to propose an analytical model, but considering only  xy stresses. Although it was developed for SLJ, this formulation is also applicable to DLJ, since this geometry reduces the non-considered peel effects (de Sousa et al. 2017). However, analytical modelling becomes more complicated in the scope of adhesive ductility or plastic adherends. In these cases, it is easier to resort to numerical methods, including the FEM (Li et al. 1999). Possible FEM approaches to bonded joints can be continuum mechanics and fracture mechanics, even though conventional fracture mechanics cannot deal with crack propagation (Weißgraeber et al. 2016). Cohesive Zone Modelling (CZM) was first proposed by Barenblatt (Barenblatt 1959, Barenblatt 1962) to simulate brittle crack growth. The main limitation is the necessity to place the cohesive elements at the potential fracture planes. The XFEM is not affected by the aforementioned CZM limitation, since it can initiate and grow cracks according to specified criteria. Actually, this technique uses stress or strain damage initiation criteria to start the cracks anywhere in the models, and damage laws to propagate them. This method was first developed by Belytschko and Black (1999) and Moës et al. (1999), consisting of introducing local functions around the crack area, to promote the separation between the crack faces. There is published work on the XFEM application to bonded joints, aiming to predict the failure modes and strength. Campilho et al. (2011) evaluated the XFEM against experimental SLJ and DLJ data. Both CZM and XFEM formulations of Abaqus ® (Dassault Systèmes, Vélizy-Villacoublay, France) were tested to simulate various geometries (including different overlap lengths), to directly compare both methods. The CZM was accurate in reproducing the experimental behavior. On the other hand, the XFEM revealed to be unsuitable in the crack propagation part when using principal stresses and strains to infer damage initiation. Stuparu et al. (2016) predicted the SLJ strength, in joints with different adherends (carbon fiber/aluminum), with CZM and hybrid CZM-XFEM modelling. CZM modelling was done with triangular damage laws (i.e., linear softening), and the quadratic nominal stress (QUADS) criterion to infer onset of damage. For the hybrid models (CZM-XFEM), CZM was applied to simulate an interfacial failure (between the adhesive and adherends), using CZM elements with no thickness. On the other hand, the adhesive and adherends were considered as XFEM regions to make possible crack growth without restrictions. With this hybrid technique, In the XFEM parts, cracking was set to initiate by the principal strains or stresses, i.e., when the limiting values of these stresses were reached. The comparison between both approaches showed identical predictions, even though the maximum load ( P m ) was marginally above the experiments for both numerical techniques. Sadeghi et al. (2020) evaluated different modelling techniques based of FEM to emulate SLJ behavior with varying values of adhesive thickness ( t A ), namely virtual crack closure technique (VCCT), CZM, surface-based CZM and XFEM. All evaluated techniques except XFEM gave identical results, which were equally precise, provided that the damage laws’ parameters were properly defined. However, with small t A , the XFEM renders less precise because of incipient damage gro wth in the adherends’ direction because of the