PSI - Issue 54

I.R.S. Araújo et al. / Procedia Structural Integrity 54 (2024) 406–413 Araújo et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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such as mechanical fastening, welding, riveting, among others. Adhesively bonded joints provide significant advantages (Petrie 2007), such as more uniform stress distribution throughout the adhesive layer, with reduced stress concentrations. This distribution allows for higher stiffness and load transmissions, promoting weight reduction and lower cost. Drawbacks can also be identified, e.g., minimization of peel loads required, limited resistance to extreme conditions of temperature and humidity due to the polymeric nature of the adhesives, need for clamping jigs during the curing process, and careful surface preparation. The single-lap joint (SLJ) is widely used due to the ease of manufacture and predominant shear loading. Scarf joints present high strength, due to reduction of stress gradients in the adhesive. On the other hand, due to the need to machine the overlapping area, these joints have higher costs. In scarf joints, the strength depends on the scarf angle (Kumar et al. 2005). The Finite Element Method (FEM) is the most commonly used technique for the analysis of adhesive joints, having been initially applied by Harris and Adams (1984). Continuum mechanics was then used to predict the strength of adhesive joints, which requires stress distribution and an appropriate failure criterion. FEM can also be combined with fracture mechanics techniques to predict strength, either by the stress intensity factor or by energetic approaches such as the virtual crack closure technique. However, these modelling techniques make the process of evaluating crack growth difficult due to the need to recreate the mesh in the path of crack propagation (Sosa and Karapurath 2012). Numerical modelling has seen major advances, such as cohesive zone models (CZM). This technique couples conventional FEM models for regions where damage is not expected with fracture mechanics, through the use of cohesive elements to promote crack propagation. The concept of CZM began with studies by Barenblatt (1959) and Dugdale (1960), who described the damage in the fracture process zone in front of the crack under the effect of static loads. The implementation of CZM can be done in spring elements or, more conventionally, in cohesive elements (Duan et al. 2004). The XFEM uses enriched shape functions to represent a continuous displacement field. XFEM is a recent evolution of CZM, which allows the analysis and modelling of damage growth to predict fracture in structures, based on the strength of materials for damage initiation and deformations for failure assessment, instead of values of t n 0 / t s 0 or  n 0 /  s 0 (peak tractions and displacements in tension and shear, respectively) used in the CZM. Comparing to CZM, in XFEM it is no longer necessary that the crack follows a pre-defined path, which is a significant advantage. Thus, the crack can propagate freely without the need for the mesh to coincide with the geometry of the discontinuities and without the need to apply the mesh close to the crack (Mohammadi 2008). This method is based on the concept of partition of unity, and can be implemented in the FEM by introducing local enrichment functions for the displacements near the edge of the crack. Recent studies carried out to predict the strength of scarf joints are available in the literature. Alves et al. (2018) presented an experimental and numerical study of hybrid scarf joints. Carbon fiber reinforced polymer (CFRP) and aluminum adherends were bonded with Araldite ® AV138 and Araldite ® 2015, brittle and ductile adhesive, respectively, considering different scarf angles (  ) . Using the FEM, the peel (  y ) and shear stresses (  xy ) were obtained, while CZM was used to predict joint strength. The numerical results showed that the magnitude of  y and  xy increases with  , although this increase is more significant for  y . The experimental maximum load ( P m ) increases exponentially with the reduction of  for the two tested adhesives, due to the increase in adhesive area and a more uniform stress distribution. The P m values obtained by CZM are very close to those obtained experimentally. In the work of Sun et al. (2020), an experimental and numerical study was carried out on the tensile performance of scarf adhesive joints. A ductile adhesive was used and CFRP adherends were considered. Experimentally, scarf joints were tested with different values of  (3°, 5°, 10°, 15°, 20° and 30°). Numerically, to validate the prediction accuracy of a user defined CZM, the numerical results were compared with the experimental data. A triangular damage law was also used. Experimentally, it was found that P m increases exponentially with  decrease, except for joints with adherends with the stacking sequence [45/0/-45/90] 3S . The stress distribution in the adhesive is not uniform and depends on  and the adhesive stacking sequence. Comparison of results shows that the user defined CZM was able to predict joint strength and displacement to failure with higher accuracy than the triangular damage law, which underestimated the experimentally obtained values. The objective of this work is the parametric numerical study of scarf adhesive joints in tension with different adhesives (Araldite ® AV138, Araldite ® 2015 and Sikaforce ® 7752) and different scarf angles or  (3.43°, 10°, 15°, 20°, 30° and 45°) by the XFEM. The developed numerical work includes the distribution of the damage variable and joint strength. With the work carried out, the coherence of the numerical results with the experimental ones was observed, with emphasis on the joint strength as a function of  .