Issue 49

F.J.P. Moreira et alii, Frattura ed Integrità Strutturale, 49 (2019) 435-449; DOI: 10.3221/IGF-ESIS.49.42 436 stresses, ease of manufacture, possibility of joining different materials and low cost are the main advantages of adhesive bonds. The main disadvantages are related to the requirement of surface preparation, low peel strength and difficulties in quality control and safety. The most common adhesive joint configurations are single-lap joints (SLJ), double-lap joints (DLJ) and scarf joints [1]. SLJ are the most common. However, they develop major  y peak stresses. DLJ are more difficult to manufacture but, on the other hand,  y stresses greatly diminish. Scarf joints are highly efficient when compared to SLJ because of the reduction of stress concentrations [1]. Although these types of joints are the most used in the industry, other types of joints have specific applications. Stepped-lap configurations can be used in composite joining due to the easiness to make the step design during the materials’ fabrication process [2]. T-joints find application in the naval and aeronautical industries. In the naval industry, they allow joining panels with the hull [3] and the fiberglass hull with anti-flood panels [4]. In the aeronautical industry, they are used to join wing panels and fuselage sections [5]. Several works were carried out to evaluate T-joints, using either analytical or numerical techniques [6, 7]. The number of approaches to predict the strength of adhesive joints has increased over the years. Actually, analytical and numerical techniques have become more and more refined and with higher accuracy. Numerical methods are typically founded on the FEM. The FEM allows modelling complex geometries with high precision, due to the computational advancements and Computer Aided Engineering (CAE) tools. Within this scope, the use of ContinuumMechanics supposes using the obtained stresses or strains, whose maximum values are used in appropriate failure criteria to assess failure. However, this technique has limited applicability because of stress singularities (which make the predictions dependent on the applied mesh) and neglecting of fracture mechanics concepts [8]. Actually, in a bonded joint FEM analysis, stresses near the singular regions increase with the mesh refinement, making convergence impossible [9]. Traditional Fracture Mechanics- based techniques can be applied to the study of the behaviour of structures that contain defects, such as cracks. These cracks can result from stress concentrations, usually located in holes, notches or interfaces between different materials. However, it is not mandatory that the structures to be analysed already have cracks, which is a limitation of this method [10]. Cohesive Zone Models (CZM) were developed to describe damage under static loads in the cohesive process zone around the crack tip. They are based on cohesive elements, which allow connecting solid elements of two-dimensional (2D) and three- dimensional (3D) structures, using pre-established traction-separation laws [11]. CZM were tested and optimized to promote structural damage initiation and crack propagation simulations on cohesive and interfacial fracture problems, and delamination in composites. The use of CZM to model structures enables to create one or more regions or interfaces in which damage nucleation and growth is made possible by the softening and release of homologous nodes of the cohesive elements [12]. FEM simulations based on continuum mechanics wrongly consider that the solid elements undergo plasticization without taking damage. Damage mechanics simulations work by inducing damage to the elements through the reduction of transmitted loads between solid elements. Thus, it is possible to perform the simulation of crack growth, in which the cracks can assume a pre-defined trajectory or an arbitrary trajectory within a finite region [8]. In Damage Mechanics, a damage parameter is established to cause a change in the response of the constituent materials through the depreciation of the strength or stiffness, as occurs in adhesive layers, or in composite delaminations, to model damage during loading [13, 14]. The insertion of a damage variable in the constitutive law of the material enables simulating damage before and after crack nucleation. Two types of damage variables can be introduced in the models: variables that empirically depreciate the properties of the materials, without any relation to the damage mechanism, and variables that have a physical significance, by directly relating to the observed type of damage (for example the size of porosities or micro-cavities) [15]. The growth of damage is usually ruled by the load function for static simulations [16] and as a function of the number of cycles for fatigue modelling [17, 18]. The XFEM is a recent variant of the FEM to model damage growth in structures, although it is yet seldom studied within the context of bonded joints. This method uses damage laws to predict fracture, based on strength concepts to infer damage initiation of damage and deformations for failure. Comparing the XFEM with CZM, the XFEM has the clear advantage of not requiring the crack to follow a predefined path by the user. This is because crack propagation occurs freely inside the material, without the geometry of the discontinuities being coincident with the mesh or the necessity to correct the mesh in the crack vicinity [19]. The XFEM is based on the concept of partition of unity, and its implementation in the FEM can be accomplished by introducing local enrichment functions for the displacements near the crack tip, allowing damage to grow and respective separation between the cracked faces [20]. Mubashar et al. [21] carried out a study on the damage and failure modelling of adhesively-bonded SLJ with spew fillets at the overlap ends, combining two methods: XFEM (to perform the modelling of the crack in the fillet region where the crack path is unknown) and CZM (applied to model crack progression and damage along the adhesive bond interface). The numerical analysis was performed in Abaqus ® . Aluminium alloy 2024 T3 adherends were bonded with the epoxy adhesive FM73-M, and the adhesive was modelled with elastoplastic properties, obtained in tensile tests. This work allowed to conclude that the XFEM is capable of predicting, with a high degree of precision, the crack onset location and path within the spew fillet. Moreover, it is possible to combine the XFEM with CZM to more accurately predict crack initiation and growth in bonded joints,