PSI - Issue 33

M.F.M.O. Rosas et al. / Procedia Structural Integrity 33 (2021) 115–125 Rosas et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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act as stress concentration singularities, allow weight reduction and reveal good fatigue resistance, among other advantages (Pascoe et al. 2013, Ramalho et al. 2020). There are several adhesive joint geometries and configurations employed in various industrial sectors, such as aeronautical, automotive, naval, wind energy, and many others. The most common configuration is the single-lap joint, which is considered of simple manufacturing and loads the adhesive mainly in shear. However, the non-collinear adherends (specific characteristic of the single-lap geometry) give rise to a bending moment that generates peel stresses (  y ) at the overlap edges (Zhao et al. 2014). In addition,  xy peak stresses caused by the shear-lag effect are also present at the overlap edges (Adams and Davies 1996). In order to overcome these drawbacks, double-lap, stepped-lap or joggle-lap joints can be alternatively used (Moreira and Campilho 2015, Carvalho and Campilho 2016, Moreira and Campilho 2016, Machado et al. 2019). In more specific applications, it is possible to use butt joints, T-joints, corner joints and tubular adhesive joints configurations (Petrie 2000). In general, tubular joints present larger bonded areas and higher flexural strength owing to their overall stiffness. Nowadays, in the piping industry, adhesives are extensively used in tube joining. The initial methods developed for the strength prediction of adhesive bonded joints were based on analytical stress analysis and further evolving to numerical methods such as finite elements (FE). These initial methods (e.g. Volkersen (1938) or Goland and Reissner (1944)), are based on closed-form expressions, that disregard several material and geometrical specifics. In fact, when solving problems that present more complex geometries or boundary conditions, these methods reveal some inaccuracy and the predictions become unrealistic. Since the 70’s decade that FE analyses are the most used method to characterize the behavior of adhesive joints. To perform the strength prediction of bonded joints, Adams and Peppiatt (1974) proposed a simple method that only required the knowledge of the stress distribution and the use of an adequate failure criterion, which was based on a continuum mechanics approach. In the work of He (2011) it is stated that early FE-based strength prediction was accomplished either by continuum or fracture mechanics approaches. In the present days, the most used and accepted method is CZM (Campilho et al. 2009, Woelke et al. 2013). With this method, that relies in the use of fracture properties, it is possible to accurately model bonded joints, which are considered structures that undergo high stress variations. The precision of the CZM modelling technique depends on properly determining the values for the cohesive strengths in tension and shear ( t n 0 and t s 0 , respectively), and for the fracture toughness in tension and shear ( G IC and G IIC , respectively) (Campilho et al. 2012). Despite tubular adhesive joints are understudied in the literature, relevant research works are available. In the work of Albiez et al. (2019), the authors experimentally studied the influence of geometrical factors variation on the strength of steel tubular joints loaded in tension, and also analyzed two different adhesives (polyurethane and epoxy). It was concluded that there is a difference between the strength values of the two adhesives. The joint strength increased with the increase of the overlap length ( L O ), but the tendency was not linear. Finally, the experimental results showed that the increase of the adhesive layer thickness ( t A ) affects negatively the joint strength. Nguyen and Kedward (2001) proposed an analytical model to determine the  xy stress distribution in a tubular adhesive joint under tension, with aluminum adherends. The authors also performed a FE study to validate the proposed analytical model. The results showed a good agreement between the analytical model and the FE results. According to the obtained results, the joints with a 10° chamfer in the adherends showed a more uniform stress distribution and a lower value of stress when compared to tubular joints’ without chamfer. Lavalette et al. (2020) analyzed several geometrical parameters ( L O , internal and external diameter of tubes) of a tubular joint composed by aluminum and carbon-fiber reinforced plastic (CFRP) adherends and loaded in tension. The authors performed experimental tests and numerical simulations with a CZM. The numerical results show a good agreement with the experimental ones. It was found that the strength of the tubular joint increases with the increase of L O and the internal diameter. Moreover, the thickness of the adherends and the chamfer length affect the  xy stress distribution. Overall, the authors concluded that the geometrical parameters influence the joint strength and also have an impact on the joint weight. This work numerically analyzed by CZM the tensile performance of aluminum tubular joints bonded with the adhesive Araldite ® 2015, considering geometric changes that potentially promote a strength improvement. Prior to the numerical study, axisymmetric CZM modelling for this purpose was validated by comparing with experimental results. The geometric changes tested in this work consisted of an outer chamfer, an inner chamfer (both in the adherends), and adding an adhesive fillet at the overlap ends. Moreover, the combined effect of the inner chamfer and adhesive fillet were evaluated.