Issue 48

F.A.L. Viana et alii, Frattura ed Integrità Strutturale, 48 (2019) 286-303; DOI: 10.3221/IGF-ESIS.48.29 287 K EYWORDS . Adhesive joint; Structural adhesive; Cohesive zone models; Inverse method; Parameter identification. I NTRODUCTION dhesive is a substance that joints two materials together, known as adherends, in a strong and permanent way [1]. Bonding is by far the most universal joining technique. Essentially, all useful materials can be joined throughout this surface-to-surface joining technique. Adhesive bonding has been used as a joining technique since 4000 b.C. by the Mesopotamians, using asphalt for constructions [2]. In the early 1900s, synthetic polymeric adhesives replaced natural ones, giving products with stronger adhesion and superior resistance [1]. The aviation and aerospace industries, with their inherent history of innovation, novel designs and technologies, were the ones that most contributed for the widespread use of adhesive bonding. From the very early days of structural adhesives, they have been used in order to enable the construction of lighter, stronger and more long-lasting airframes and aircrafts. Major advantages of adhesively-bonded joints are the possibility to join different materials, more uniform stress fields along the bonded area, more efficient load transfer, fluid sealing, corrosion resistance, high fatigue strength and better aesthetics (without bolts heads, rivets or welding). On the other hand, as disadvantages one may refer the need of the joint design to be oriented towards the elimination of peel stresses, low resistance to temperature and humidity and the requirement of a surface treatment [1, 3]. In an ideal joint, the adhesive should be only subjected to shear stresses and the load-bearing area should be as large as possible but, due to design limitations, this cannot always be applied [4]. Different joint architectures give the engineers a wide range of solutions depending on the application. SLJ are easy to manufacture, can be used with thin adherends and the adhesive is mostly loaded by shear (  xy ) stresses. However, the adherends are not collinear, which leads to significant peel (  y ) stresses at the overlap end [1]. On the other hand, DLJ have a balanced construction that decreases the bending moment. Nonetheless, the internal bending moments cause peel stresses at the ends of the inner adherend. Recent solutions included wavy and reverse-lap joints. Ávila and Bueno [5] evaluated the wavy-lap joint architecture and concluded that the maximum load ( P m ) supported by those joints was in average 41% higher than that carried by equivalent SLJ. Scarf joints’ manufacture is difficult due to the adherends’ tapering at the bond region. However, this design keeps the axis of loading in line with the joint, which is prone to reduce  y stresses in the adhesive layer. Thus, these joints endure higher strengths compared with the above-mentioned lap joints, for the same bonded area. Undoubtedly, it is necessary to provide accurate tools to predict the strength, possible points and paths of failure of adhesive joints. This is essential to enable the widespread applicability of this technology in different industrial fields. This quest began about eighty years ago with a simple analytical analysis of SLJ performed by Volkersen [6]. However, the analysis requirement of several joint designs and novel adhesives with high plasticity degree, rendered the analytical analyses unpractical. The development of Finite Element (FE) techniques brings new horizons to the P m prediction of bonded joints, notwithstanding the design, load conditions and adhesives’ plasticity. Among several approaches, the cohesive zone modelling (CZM) technique, presented by Barenblatt [7] and Dugdale [8], is currently the most used. This method relies on the establishment of tensile and shear traction-separation laws, linking the cohesive tractions ( t n for tension and t s for shear) with the relative displacements (  n for tension and  s for shear). Moreover, different criteria to assess mixed-mode damage initiation and growth are used. Using this methodology, damage is simulated along a predefined crack path, which can be an inconvenient if this path is not known beforehand. However, in bonded joints this does not constitute a limitation, since failure is usually confined to the adhesive layer and respective interfaces, or in the worst case to parallel adherend delaminations when using composite adherends [9]. Provided that the modelling conditions are properly established for a specific structure and that the cohesive parameters, namely, the shear cohesive strength ( t s 0 ), the tensile cohesive strength ( t n 0 ), the fracture toughness in tension ( G IC ) and shear ( G IIC ), are accurately characterized, CZM is a precise technique for strength prediction of adhesively-bonded joints [10]. Thus, one must assure the correct determination of the cohesive parameters. For that purpose, one possible method is the property identification technique, which estimates each one of the cohesive law parameters by suitable tests [9]. On the other hand, the direct method provides the precise shape and the complete CZM laws because it uses experimental data from the DCB or ENF fracture tests. This is accomplished through the differentiation of the fracture energy in tension ( G I ) or the fracture energy in shear ( G II ) with respect to  n or  s , respectively [11]. The inverse method consists of the estimation of the CZM parameters by iterative fitting the numerical prediction with experimentally measured data (typically the P -  curve), considering a precise description of the experimental geometry and approximated cohesive laws. The inverse characterization of adhesive bonds should be applied individually for each tested specimen to account for slight geometry variations between specimens. The value of G IC or G IIC , usually A