PSI - Issue 33

A.F.M.V. Silva et al. / Procedia Structural Integrity 33 (2021) 138–148 Silva et al. / Structural Integrity Procedia 00 (2019) 000–000

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driven by its inherent features and advantages over other joining methods (Adams 2005). Actually, adhesive bonding offers the possibility to join different types of materials with different thicknesses, while providing more uniform stress distributions, since holes are not required. It also works as a flexible gap filing, with corrosion protection and improved aesthetics (Petrie 2000). One of the main features is the good strength-weight and cost-effectiveness ratios (Da Silva et al. 2011), which is the primary goal of structural designers. Drawbacks of bonded joints include, among others, the disassembly difficulty without causing damage, the requirement of a surface treatment, and planning the design orientated towards the elimination of s y stresses (Adams 2005). Several joint architectures are available, enabling to choose the one that best performs over the project demands. SLJ, the double-lap, scarf, stepped, and tubular joints are among the most used. The SLJ is the simplest and the most studied design, inclusively for analytical or numerical methods’ validation. Tubular joints are seldom addressed in the literature, but they are widely used in vehicle frames (airplanes, cars, buses) (Barbosa et al. 2018), truss structures (Lavalette et al. 2020) and used to join complex piping assemblies, by replacing flanged connections (Dantas et al. 2021). They have a large bonded area and a higher flexural strength due to their overall stiffness (Petrie 2000). It is important to refer that many of the principles which govern lap joints also apply to tubular joints. On the one hand, the revolving symmetry benefits the load transfer, while on the other hand transverse peel loads are still present and should be considered in the design process (Adams and Peppiatt 1977). The use of bonded structures is likely to significantly increase. All the advances in material properties, joint architectures and simulation methods, combined with a detailed knowledge of the joint behavior, will provide to the engineers the tools to design efficient bonded structures. Researchers have been developing tools capable of capturing the structural strength and their failure behavior. Analytical methods (Volkersen 1938, Goland and Reissner 1944, Hart-Smith 1973) are straightforward and provide quick results. Nonetheless, with the development of new adhesives, with a high degree of plasticity, the analytical models become outdated. Finite element models (FEM) were developed and tested over the years, capable of capturing the plastic behavior of both adherends and adhesives, providing accurate strength prediction results. Barenblatt (1959) and Dugdale (1960) proposed the CZM concept to study the damage onset and growth, i.e. modelling the fracture behavior. This methodology simulates damage along a predefined path by the establishment of traction–separation laws that associate the cohesive tractions ( t n for tension and t s for shear) with the relative displacements ( d n for tension and d s for shear). Different criteria can be used to assess damage initiation and growth (Rocha and Campilho 2017). For a trustworthy CZM strength prediction of adhesive joints, the adhesive should be characterized under identical geometrical conditions in which the resulting laws will be used in the simulations (Li et al. 2016). Impact loadings are relevant for many industrial applications involving adhesive joints, and several methodologies were proposed along the years that can predict and comprehend the complete failure phenomenon. Strength prediction can be accomplished with analytical models, e.g., by applying Kelvin-Voigt (Miyagi and Yamamoto 1987) or Maxwell viscoelastic models (Wenchang et al. 2003) the elastic deformation of an adhesive as a function of time can be computed. This allows to replicate experimental stress-strain curves of structural adhesives and infer failure by suitable failure criteria. Johnson and Cook (1985) proposed a viscoplastic model that expresses the strain to fracture as a function of the strain rate, and that was later applied to create failure criteria for adhesive materials. By using FEM, complex models such as CZM, typically embedded in commercial software, are skilled to capture the impact phenomenon and can be applied to model an impact in any structure, from a simple sandwich coupon to a space shuttle, within a reasonable execution time (He 2011). However, the analysis should be explicit to account for time dependent effects, and the material properties should translate their behavior at identical test speeds of the structures that are being analyzed (Valente et al. 2020). Currently, the study of the adhesive joints behavior under impact loading is a very active field of research, driven by a significant industrial interest, mainly from the automotive industry. Machado et al. (2017) performed an exhaustive investigation on the available research of this topic. The work presents a review that also include materials’ strain rate dependency, environmental conditions effect on impact behavior, and impact modelling procedures. On the subject of the strain rate, it was found that adhesives are moderately sensitive, both in tensile, shear and fracture properties. Moreover, when subjected to large strain rates, the joint behavior is ruled by the adherends’ performance, in addition to the adhesives properties. Therefore, to design joints skilled to withstand impact events, it is imperative to be aware of the materials properties and their strain rate sensitivity. Regarding the environmental effects, it was generally found that most of the experimental tests are being performed at room temperature and without humidity, showing that a higher degree of maturity in this field is required to understand the