PSI - Issue 47

J.E.S.M. Silva et al. / Procedia Structural Integrity 47 (2023) 70–79 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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loading which induces  y stresses in the adhesive layer, reducing joint strength (Petrie 2000). Consequently, other joint configurations had been developed to reduce the loading eccentricity, namely the stepped-lap joint, the double lap joint (DLJ), and the joggled-lap joint (JLJ). Scarf joints maintain the adherends’ alignment while increasing the bond area (Taib et al. 2006). There are other joint configurations meant for transverse loadings through perpendicular adherends, like those presented in aircraft and maritime applications (Moreira and Campilho 2015). The described joints are flat configurations, but these can also be arranged around an axis forming tubular joints, which are employed to transmit axial and torsional loads. However, even in the tubular configuration, there are stress concentrations in the adhesive layer and the joint strength is proportional to the bonded area. Therefore, chamfering the tubular adherends to produce TSJ increases joint strength while maintaining adherends’ alignment (Parashar and Mertiny 2012). The strength of adhesive joints can be estimated by means of analytical models or by using numerical techniques like the Finite Element Method (FEM). The most known analytical model for SLJ and DLJ was developed by Volkersen (1938) and later expanded by Goland and Reissner (1944). The sandwich model is applicable to many joint configurations, and a recent application have been described by Weißgraeber et al. (2014). Adams and Peppiatt (1974) performed one of the first numerical models to determine stress distributions in adhesive layers using different failure criteria depending on the adhesive ductility. The predictions obtained with the FEM agreed with previous analytical models. CZM provide accurate estimations of joint strength (Woelke et al. 2013). The CZM is based on cohesive laws that represent the adhesive’s damage behaviour. Although there are different cohesive law shapes (Alfano 2006), the triangular law provides accurate predictions for adhesive joints, as reported in the literature (de Sousa et al. 2017). Alfano (2006) provided a thorough description of the cohesive laws and the parameters necessary for their implementation. Despite its accuracy, the CZM requires that the fracture path be known or assumed beforehand, so other formulations also based on the FEM and CZM were developed to overcome this limitation, which in the case of adhesive joints has little influence because the failure occurs in the bond line. The eXtended Finite Element Method (xFEM) is based on the unit partition and enrichment functions around the crack tip (Belytschko and Black 1999). The xFEM does not require predefined crack paths while still employing the CZM parameters. The xFEM has been successfully applied to adhesive joints (Campilho et al. 2011b), although the CZM is still the preferred method, as described by Sadeghi et al. (2020) after a thorough analysis of an SLJ using different numerical techniques. For tubular adhesive joints, analytical models were developed to calculate the shear stresses along the bond line considering an elastic-plastic behaviour of the adhesive (Nguyen and Kedward 2001). Numerically, Labbé and Drouet (2012) studied TLJ through a parametric study, finding that TLJ with large bonded areas and thin adhesive layers show the best performance when loaded in tension. Later (Ferreira et al. 2019), studied TLJ subjected to tensile loading using the CZM. The study involved three different structural adhesives, aluminium adherends, and two lap lengths. The CZM was found suitable to analyse this joint configuration. Following a similar line, Kaiser and Tan (2020) studied TLJ with composite and titanium adherends using the FEM and CZM. Also, a bi-adhesive bond line was evaluated. The bi-adhesive approach provided an increase of up to 81.6%, as long as the bond line thickness is thin (0.25 mm) and the joint contains spews. The torsional behaviour of tubular adhesive joints was later studied numerically (Hosseinzadeh et al. 2007), which also included evaluating the Ramber-Osgood plasticity model, and finding it adequate. Although there are studies related to TLJ, studies related to TSJ are more scarce. This work addresses the tensile performance of TSJ with aluminium adherends. The effect of  on P m was evaluated by varying it from 3.43º to 45º. Three adhesives, from brittle to ductile, were also considered. A numerical approach based on the FEM and CZM was considered, which was validated through experimental testing of TLJ. Finally, the study provides an ample spectrum of data including  y and  xy stress distributions, and P m , which would provide valuable information for the design of this type of joint configuration. 2. Experimental methods 2.1. Joint geometry The schematic representations of the TLJ and TSJ are presented in Fig. 1 a) and b), respectively. The experimental work and numerical validation were performed in the TLJ and subsequently a numerical study was performed involving the TSJ. In Fig. 1 a) the dimensions for the TLJ are as follow: adhesive thickness ( t A )=0.20 mm, thickness of the inner tube ( t SI )=2 mm, thickness of the outer tube ( t SE )=2 mm, inner tube diameter ( d SI )=20 mm, outer tube