PSI - Issue 41

A.R.F. Soares et al. / Procedia Structural Integrity 41 (2022) 48–59 Soares et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction In recent decades, the use of adhesive joints has increased due to their competitive characteristics compared to traditional joining methods, such as welded, riveted or fastened joints. Adhesive joints are lighter, allow joining different materials, have lower stress concentrations and also have good behaviour under cyclical or fatigue loads (Petrie, 2000). These are used in a wide variety of structural applications and can be subjected to tensile stresses (pure mode I), shear (pure mode II) or mixed-mode (mode I+II), as seen in most real situations. To increase confidence in the design of adhesive structures, it is important to be able to accurately predict their strength. In this context, the Fracture and Damage Mechanics approaches present significant advantages over the Strength of Materials methods, mainly in structures with stress singularities and plastic behaviour (Campilho, 2017). Frequently, the Fracture Mechanics approach is applied by an energetic analysis, and the fracture toughness ( G C ) is the main parameter to be determined to predict the evolution of damage and failure, which can be divided into the tensile ( G IC ) and shear components ( G IIC ) (Naghipour et al., 2009). Due to mixed-mode loading conditions often present in bonded joints, it is necessary to establish a fracture criterion that promotes the propagation of damage under these conditions. Fracture characterization tests in mixed mode I+II enables obtaining the fracture envelopes to define the most adequate fracture criterion (Fernlund and Spelt, 1994). Thus, it becomes possible to use strength prediction methods such as cohesive zone models (CZM). CZM consist of a fracture mechanics-based method that uses strength of materials for crack initiation and fracture mechanics for crack propagation, while the mixed-mode behaviour is typically defined by a power-law criterion (Santos and Campilho, 2017). Generally, fracture characterization tests in adhesive joints are based on Linear Elastic Fracture Mechanics (LEFM), considering that the adhesive remains linear and elastic during loading and that any plasticity is limited to a small region in front of the crack tip (Shih and A, 1991). However, in an adhesive joint, the surrounding adherends affect the behaviour of the adhesive, since they can influence the size of the plastic zone that forms at the crack tip, which consequently limits G C (Pardoen et al., 2005). Therefore, tests on adhesive joints are important to characterize G C for given geometrical conditions. Mode I corresponds to the opening mode due to the effect of tensile loads. It is the most critical mode since stresses are concentrated in smaller portions in the adhesive and the joint presents less resistance to peel than to shear (Bendemra et al., 2015). The most common test setups in mode I are the double cantilever beam (DCB) and tapered double-cantilever beam (DCB). The DCB test consists of two bonded adherends of constant thickness, while in the TDCB test the adherends’ thickness varies with a specific function to enable a linear variation of the compliance or displacement/load ratio ( C =  / P ) with the crack length ( a ). As a result, it is possible to derive a G IC expression from the Irwin – Kies equation that is independent of a (Lopes et al., 2016). Mode II is considered the sliding mode due to shear. There is no standard for the shear fracture characterization of adhesive joints, and most of the published works are based on fracture characterization for composite materials (Rajendran et al., 2019). The most relevant tests are the end-notched flexure (ENF), four-point ENF (4ENF) and end-loaded split (ELS) tests. The ENF test is the simplest and consists of a three-point bending setup applied to a cracked specimen at one end, promoting pure mode II at the crack tip. The 4ENF test uses a four-point bending setup, it is more stable relating to crack propagation, but the setup is more complex and it is sensible to friction between the crack faces (de Morais and Pereira, 2007). The ELS test consists of transversely loading a cracked cantilevered specimen, but it is less used due to large displacements and sensitivity to the gripping conditions (Pérez-Galmés et al., 2016). Few mixed-mode tests allow the variation of the ratio between mode I and mode II and, thus, to analyse the influence of the mixed-mode ratio on the joint strength (Watson et al., 2020). The asymmetric DCB (ADCB) test consists of two adherends of different materials or thicknesses to induce mode mixity (Arouche et al., 2019). The asymmetric tapered DCB (ATDCB) test (Park and Dillard, 2007) consists of a hybrid configuration, where one adherend has a constant section and the other adherend is similar to the TDCB test, resulting in a range of mode mixes from 0° to approximately 20° during the test. The single-leg bending (SLB) test, proposed by Yoon and Hong (1990) as a modified ENF test specimen, presents a limited mix range when compared to the MMB test, although the SLB test requires less equipment and its experimental procedure is easier (Szekrényes and Uj, 2004). The MMB test, developed by Reeder and Crews Jr (1990), presents a relatively complex configuration, but it allows the variation of the mixed-mode ratio practically without limitations. Several studies on the MMB test were presented, which cover the development of different configurations, as well as methods for G C estimation. Most works focus