PSI - Issue 41

J.E.S.M. Silva et al. / Procedia Structural Integrity 41 (2022) 36–47 Silva et al. / Structural Integrity Procedia 00 (2019) 000 – 000

37

2

1. Introduction Structural adhesive joints have been used in various industries such as aeronautics, aerospace, automotive, civil, electronics, footwear, and wood structures. Adhesive bonding gives the designer freedom to combine different materials for optimising the st ructures’ properties aiming for the best possible solution. Due to the absence of drilled holes, used in bolted or riveted connections, more uniform stress distributions are achieved and adherend over design can be prevented. Adhesive bonding, like all joining methods, presents disadvantages regarding the manufacturing process such as the need for surface preparation, control of the environmental conditions, the limitations of the production methods and resin curing time, as well as production costs inherent to the particularities of the manufacturing processes (Adams, 2005). Several configurations are available for designing adhesive joints. One of the most employed is the single-lap joint (SLJ) due to its manufacturing simplicity, applicability to thin adherends, and being manly subjected to shear stresses. However, in SLJs, the adherends are not aligned, which induces a bending moment that originates peel stresses, compromising the service life of this type of joint (Petrie, 2000). This drawback led to the development of other geometrical variations aiming to reduce peel loads. Geometrical variations such as the stepped-lap joint, in which the adherends are aligned, or as the double-lap joint (DLJ) that when subjected to tensile loads can minimise, or even eliminate, the transverse deflection of the joint. Another variation is the joggle-lap joint (JLJ), leading to smaller stress concentrations at the bonding edges when compared to the SLJ (Taib et al., 2006). Strap joints are an alternative to lap joints for thicker substrates. The adherends in strap joints are aligned (Petrie, 2000). Furthermore, a single-strap is not symmetrical and is susceptible to bending stresses, whilst the double-strap joint is a better alternative. In fact, both lap and strap joints can present several geometrical variations to reduce peak stresses (Campilho et al., 2009). Chamfering of the adherends at their ends to create a scarf joint increases joint strength; the shear-resistant area increases exponentially by reducing the scarf angle (  ), which is relatively easy to perform by machining (Wu et al., 2018). The butt-lap joint configuration also improves the load capability of butt joints; in this case, the adherends are also self-centred, and present a larger area for adhesive bonding, contributing to higher joint strength (Petrie, 2000). In addition, cylindrical or tubular adhesive joints are employed to join tubes and rods. The tubular lap joint (TLJ), one of the most common, has a working principle like the SLJ but is axisymmetric. These joints could be subjected to axial and torsional loads. Axially loaded TLJs present stress concentrations in the adhesive layer as SLJs. Joint strength is then improved by producing a scarf joint in a cylindrical configuration, known as tubular scarf joint (TSJ), which has a larger bonding area. However, most of the suitable geometrical solutions for cylindrical joints require machining of the adherends; furthermore, the quality of these joints is difficult to inspect in their final form (Barbosa et al., 2018a). Regarding strength prediction of adhesive joints, Volkersen (1938), and Goland and Reissner (1944) developed the first works, proposing analytical methods with close form expressions suitable for single and double-lap joint configurations but only with linear elastic materials. Therefore, these methods are not applicable to more complex geometries or different material behaviours. Adams and Peppiatt (1974) presented one of the first applications of the finite element method (FEM) to predict the strength of bonded joints. The authors developed a method that is based on the knowledge of the stress distribution and the implementation of an adequate failure criterion based on continuum mechanics. An acceptable agreement was found between the stress distributions obtained by the FEM and by traditional analytical methods. Nowadays, one of the most used and well-accepted methods is cohesive zone modelling (CZM) (Rocha and Campilho, 2018; Woelke et al., 2013) which makes it possible to predict the strength of adhesively bonded joints with good accuracy regardless of the joint complexity. The accuracy of the CZM method relies on the proper assessment of the cohesive strengths in tension ( t n 0 ), shear ( t s 0 ), fracture toughness in mode I ( G IC ), and mode II ( G IIC ) (Campilho et al., 2012). As an alternative, the eXtended Finite Element Method (XFEM) was developed by Belytschko and Black (1999) and consists of enrichment functions for the nodal points of the finite elements around the crack path/tip. Thus, crack growth is not constrained to a pre-defined path which is an advantage when compared to the CZM technique (Campilho et al., 2011b). In consequence, this method can also be applied to predict the strength of adhesive joints. Different strength prediction methods had been employed for tubular bonded joints, for example, Nguyen and Kedward (2001) proposed a simple analytical model to estimate the shear stresses distribution of the adhesive layer in a chamfered tubular joint subjected to tensile loading. Their approach is an extension of the Volkersen (1938)