Issue 48

J.P.S.M.B. Ribeiro et alii, Frattura ed Integrità Strutturale, 48 (2019) 332-347; DOI: 10.3221/IGF-ESIS.48.32 333 K EYWORDS . Bonded joint; Finite Element analysis; Cohesive zone models; Mixed-mode fracture; Fracture envelope. I NTRODUCTION n the present time, adhesively-bonded joints are used in numerous industrial fields due to several advantages over other joining methods, e.g. welding, riveting and fastening. In fact, from a simple shoe to a space shuttle, adhesives are employed to bond similar and dissimilar materials. The aeronautic industry, continuously looking for new techniques to reduce fuel consumption and costs, was the one that most contributed to the development of adhesive joints [1]. Moreover, the use of composite materials such as carbon fibre reinforced polymers (CFRP) in structures has significantly increased during the last years. In the automotive industry, CFRP is usually joined to other composites, aluminium or steel through adhesive bonds [2]. This technique’s advantages include preserving the integrity of the parent materials, since it avoids any structural damage (i.e. no holes or heating), thus providing a better stress distribution along the bonded area [3]. Additionally, improved strength-weight and cost-effectiveness ratios can be attained, which are highly relevant for the industry and designers in the pursuit of better products [1]. Few other benefits such as flexible gap filing, noise and vibration damping, excellent insulation and improved aesthetics are inherent to this method. Nevertheless, some drawbacks still persist, such as the requirement of a surface treatment, disassembly issues without causing damage, low resistance to temperature and humidity, and joint design orientated towards the elimination of peel stresses [4]. A number of joint architectures is available depending on the different applied loads. Among those, the SLJ is the most studied one. In fact, SLJ are simple to manufacture, although the adherends are not aligned, causing major peel (  y ) stresses at the overlap ends [3]. The DLJ, slightly more difficult to produce, manages to decrease the bending moment due to its balanced design, thus reducing both  y and shear (  xy ) stresses. Despite that, internal bending moments may occur, triggering  y stresses at the ends of the inner adherend. The scarf joint, which also presents manufacturing difficulties (in cutting the taper angle) keeps the loading axis collinear with the joint, therefore promoting more uniform  y stresses in the adhesive layer and helping the joint to endure higher strengths compared to lap joints [5]. Moreover, one may find commonly other joint architectures, such as butt, strap, step, tubular and T-joints. The development of trustworthy predictive methods is required for a widespread use of adhesively-bonded joints. Despite few analytical solutions being capable to quickly predict the joints’ behaviour, the process could become extremely complex when composite adherends are used or in the presence of adhesives with high plasticity. The Finite Element (FE) method is capable to overcome such issues and is by far the most common technique used in bonded joints [6]. Several approaches were developed along the years, such as continuum mechanics, fracture and damage mechanics techniques. Later, during the sixties, Barenblatt [7] and Dugdale [8] proposed the concept of cohesive zone to describe damage under static loads. This method simulates the damage along a predefined crack path thru the establishment of a load-displacement ( P -  ) correlation, known as traction-separation law. These laws associate the cohesive tractions ( t n for tension and t s for shear) with the relative displacements ( δ n for tension and δ s for shear). To obtain good agreement between the predicted strength and the experiments, a truthful estimation of the cohesive strengths in tension and in shear ( t n 0 and t s 0 , respectively), and G IC and G IIC is essential. Usually, an adhesive joint may be put under  y or  xy stresses, although in most cases it is subjected simultaneously to both, thereby creating a mixed-mode loading. Despite the importance of the correct estimation of the CZM parameters, standardized methods are not yet available [9]. Nevertheless, few techniques are available to assess the cohesive parameters: the property identification method, the direct method and the inverse method [1]. The property identification technique involves the separated calculation of each one of the cohesive law parameters by proper tests. This approach is particularly critical if bulk tests are used due to reported deviations between the bulk and thin adhesive bond cohesive properties [10]. The direct method provides the precise shape and the complete CZM laws by measuring the J - integral and crack-tip normal or shear displacements, through the differentiation of G I or G II with respect to δ n or δ s , respectively [11]. On the other hand, the inverse method involves estimating the CZM parameters by iterative fitting the FE prediction with experimental data (e.g. the R -curve, the crack opening profile or the P - δ curve), considering a precise description of the experimental geometry and approximated cohesive laws [12]. The value of G IC or G IIC is input in the FE model and, to completely define the CZM law, approximate bulk values can be used for t n 0 or t n s for the initiation of the trial and error iterative process. I