PSI - Issue 61

G.J.C. Pinheiro et al. / Procedia Structural Integrity 61 (2024) 71–78 Pinheiro et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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by the slope or scarf angle (  ) of the adherents. Altering the angle of the joint allows to control the balance between peel and shear stresses, and adhesive are resisting separation. As with any other joint design, the main objective is to improve stress distribution and, cons equently, maximize overall strength. Scarf bonded joints’ adhesive layer area is affected by  and adherent thickness, and smaller  may require the use of thicker adherents. Used for general structural bonding as well as in composite structures repair, this type of design is commonly found in aerospace and aeronautical applications (Barbosa et al. 2018). Kumar et al. (2005) experimentally studied the compression loading of scarf joints with aluminum reinforced carbon-fiber reinforced plastics (CFRP) adherents. Cohesive failures occurred for  above 3º. Conversely,  below 3º resulted in adherent failure. It was observed that the smaller  , the higher strength is achieved. Strength improvement on externally reinforced aluminum structures with adhesive repairs was researched by Moreira and Campilho (2015). Cohesive zone modelling (CZM) simulations were conducted with the adhesive Araldite ® 2015 and  values between 10º and 45º. Several configurations of external reinforcement were evaluated, such as bonded reinforcements on one or both repair faces, including varying bonding lengths. Adding reinforcements improved joint strength, attaining maximum strength with internal and external reinforcements. An exponential increase in strength when decreasing  was also verified. The eXtended Finite Element Method (XFEM) is an alternative method to CZM, relying on stress or strain-based criteria for damage initiations, and energetic concepts to assess softening and damage propagation. Damage and failure are achieved using XFEM via selected continuum mechanics-based initiation criteria and damage laws between paired nodes. Maximum stress and maximum strain can be used to employ damage initiation criteria and material softening up to failure can either occur linearly or exponentially (Abaqus ® 2013). Discontinuous enrichment functions were proposed by Belytschko and Black (1999), which can be implemented in numerical models allowing crack nucleation and growth (Moës et al. 1999). This method allows for damage propagation within the entire model subject to study instead of being limited to a predefined crack growth path such as CZM. Therefore, the crack can evolve throughout the model without requiring remeshing surrounding the crack (Mohammadi 2008). However, the results of Fernandes et al. (2015) revealed that the joint strength is affected by the element size. It was found by Mubashar et al. (2014) that the benefit of predicting crack propagation when running a model with combined XFEM and CZM fracture possibilities outweighed the shortcomings of a predefined path setup. CZM and XFEM methods were compared by Campilho et al. (2011a) in single and double-lap joints bonded with ductile adhesives. It was concluded that XFEM is not the best suited method for adhesive layer damage propagation under mixed-mode using principal stress/strain damage initiation criteria, while CZM delivered accurate results. In XFEM, the crack growth direction was found to be perpendicular to the principal directions, resulting in crack propagation towards the adherents instead of following the adhesive layer. This behavior opposed the experimental findings, but could be improved by using different criteria for damage initiation. This work presents an analysis on the tensile strength of scarf adhesive joints, considering  and the adhesive type as design parameters. A detailed numerical evaluation is presented, based on the XFEM, following the technique validation with experimental data, for adhesives with different characteristics. The XFEM technique was tested with varying damage initiation and propagation criteria. 2. Materials and methods 2.1. Scarf geometry and dimensions Different geometries were evaluated, all of them based on a scarf design (Fig. 1). General adherent dimensions were kept unchanged and adherent thickness, varying  values across configurations (Table 1).

Fig. 1. Geometry and main dimensions of a scarf joint.