PSI - Issue 25

R.M.D. Machado et al. / Procedia Structural Integrity 25 (2020) 71–78 Machado et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction

Adhesively bonded joints emerged in last decades as a strong alternative joining technique to those that prevail for long such as welding, fastening and riveting. Actually, the aeronautic industry was the one that most contributed to the development of such technology. Nowadays, several industries become enthusiasts of this method mainly due to its intrinsic advantages. In fact, this method allows the possibility of joining dissimilar materials and preserves the joint integrity, while providing more uniform stress distributions along the bonded area. In addition, it enhances the possibility to obtain lightweight and strong structures. Nevertheless, few limitations of bonded joints can be appointed, such as disassembly difficulties, low resistance to humidity and temperature, and joint design orientated towards the elimination of peel stresses (  y ), i.e., the joint should be designed so that the in-service loads should stress the adhesive mainly with shear stresses (  xy ) (Davis and Bond 1999). A large number of joint configurations is available, offering several joining choices. Among these, single-lap joints (SLJ), double-lap joints (DLJ) and scarf joints are the most common. In addition, the stepped-lap joint design is considered one of the most efficient, capable to endure higher loads through the relief of stress concentrations at the overlap ends (Bendemra et al. 2015). This design includes a number of steps in the bonded area, combining both scarf and SLJ architectures. Actually, the stepped design promotes multiple stress concentrations zones, as an alternative of stresses being focused at the bonded length edges, and it allows a gradual load transfer from step to step. In order to enable a widespread use of bonded joints, one should b e able to accurately predict the joints’ behavior, evaluating stresses and strains resulting from the submitted loads and predicting the possible points of failure. Finite Element Method (FEM) models arisen decades ago, and this technique is the focus of continuous improvements. Barenblatt (Barenblatt 1959), in the late fifties/early sixties, developed the Cohesive Zone Modelling (CZM) concept to describe crack propagation in perfect brittle materials, assuming that finite molecular cohesion forces exist near the crack faces. Subsequently, CZM was improved in order to simulate damage initiation and propagation in adhesive joints and composites. This method does not require an initial flaw, and it takes advantage of traction-separation laws between stresses and relative displacements to simulate damage along pre-specific paths. The accuracy of this method is invariably linked to an accurate evaluation of the cohesive strengths in tension and shear ( t n 0 and t s 0 , respectively), and also the tensile ( G IC ) and shear toughness ( G IIC ). An innovate FEM development is the Extended Finite Element Method (XFEM) approach, which uses damage laws based on the bulk strength of materials to capture damage initiation and strain to assess failure along an arbitrary path, thus overcoming the main restriction of CZM, in which damage can only grow along the predefined paths. Belytschko and Black (1999) and Moës et al. (1999) were pioneers of this technique by introducing local enrichment functions in the surrounding area of the crack, capable to capture the displacement jump and near-tip structure of the crack. Several authors applied this method to assess crack patterns and perform strength predictions. Among those, de Sousa et al. (2017) compared different analytical and numerical methods in the strength prediction of SLJ with different overlap lengths ( L O ). With this purpose, adhesive joints were produced between aluminum adherends, bonded with the adhesives Araldite ® AV138, Araldite ® 2015 and Sikaforce ® 7888. Different analytical methods were considered, together with two numerical techniques: CZM and XFEM. The analytical methods showed that they only give relatively accurate results in very specific conditions. The CZM analysis with the triangular law revealed to be a very accurate method, except for joints with very ductile adhesives. On the other hand, the XFEM analysis revealed some limitations due to crack propagation miscalculations arising from the significant joint deflections. This work aims to validate the XFEM to predict the behavior of stepped-lap joints with different L O values bonded with the Araldite ® 2015 (from Huntsman, Basel, Switzerland). For the XFEM strength prediction, different damage initiation criteria were used based on either stresses or strains. The damage law shape was also evaluated, namely the linear and exponential damage propagation laws.

2. Experimental work

2.1. Materials

The adherends were made-up with a ductile aluminum alloy, grade AA6082 T651, chosen for its high strength and wide structural applications. This alloy was previous characterized in the work of Campilho et al. (2011), where the