PSI - Issue 47

L.A.R. Gomes et al. / Procedia Structural Integrity 47 (2023) 94–101 Gomes et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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improved stress distribution uniformity over riveting or welding, which involve holes or heat (Petrie 2000). The main limitation include low resistance to temperature and humidity, typically permanent character of the joints, and exacerbated sensitivity to  y stresses (Adams 2005). To be able to evaluate the performance and strength of an adhesive joint, analytical or numerical methodologies based on the FEM are used. The widespread use of this technology requires a deep knowledge of the joint strength and failure modes, giving more freedom to the designer, and the ability to quickly test different solutions. Theoretical analyses were initially performed (Allred and Guess 1978), but with limitations. On the other hand, FEM analyses are versatile, since these can model plasticity of both adherends and adhesives, and provide accurate solutions for different geometries (Jousset and Rachik 2014). Between the different numerical and FEM-based techniques, CZM is definitely the most widespread (Rocha and Campilho 2018). CZM-FEM analyses simulates crack onset and growth along pre-specified paths by the user by merging continuum with cohesive elements that include traction – separation laws linking the cohesive tractions ( t n in tension; t s in shear) and displacements (  n in tension;  s in shear). To assure accurate predictions, the cohesive properties should be indexed to the specific adhesive thickness ( t A ) that is being tested (Li et al. 2016). Nowadays, static simulations are widely studied in scientific works (Sukhaya and Aimmanee 2022), which does not occur for dynamic loads. However, in real applications, adhesive joints are also subjected to dynamic loads, such as impact (Silva et al. 2022). Due to the scarcity of literature on the behaviour of adhesive joints under impact, its study has become relevant. Few analytical models are described in the literature, such as the model of Johnson and Cook (1985), consisting of a viscoplastic model specifying the strain to fracture as a function of the strain rate, which was later applied to create failure criteria for adhesive materials. A suitable alternative consists of using CZM with cohesive parameters tuned for the specific strain rates (Valente et al. 2020), making it possible to model impact loadings without geometric restrictions, and with low computational cost (Lißner et al. 2020). This modelling approach takes advantage of explicit solvers. Presently, bonded joint impact analysis is a relevant research area, mainly promoted by the automotive and military industries. Liao et al. (2011) performed a three-dimensional (3D) FEM stress analysis and strength evaluation of SLJ subjected to impact tensile loads. In the test, the deformation rate of the adhesive was taken into account. The Cowper Symonds method for dynamic analysis was considered, leading to joint failure onset at the interface. The effects of Young ’ s modulus of the adherend, L O , t A and initial impact velocity on stress wave propagations and interface stress distributions were evaluated. The measured results confirmed the numerical predictions and joint performance, described by the impact energy, was between 5.439 and 5.620 J. Hazimeh et al. (2015) analysed the geometric and material effects in DLJ subjected to dynamic loads in the plane. The dynamic analysis was accomplished by the Hopkinson bar. In the analysis of the results, it was observed that higher shear stiffness of the adhesive and higher adherend longitudinal stiffness increase the average  xy stress at failure. On the other hand, stress uniformity in the adhesive layer was better achieved for smaller shear stiffness of the adherends. Peres et al. (2022) evaluated the L O and adhesive type effects on the impact strength of composite SLJ, considering experimental testing and CZM. The numerical models enabled output of stresses, damage evolution and joints’ strength . Higher L O increased the joint strength, especially when using a flexible and ductile adhesive, which prevents significant stress concentrations and absorbs peak stresses. Overall, the impact CZM was able to predict the impact joints’ strength with good accuracy. This work aims to predict the behaviour and strength of composite DLJ under impact loads, under different L O . Numerical simulations by FEM and CZM are considered. The adhesives used for this numerical study are the Araldite ® AV138 and the Sikaforce ® 7752. As adherend, the pre-preg Seal ® Texipreg HS 160 RM was used. Initially, a study was carried out with SLJ experimental data, to validate the proposed technique. DLJ analysis was based on elastic  y and  xy stresses, P -  curve analysis, and strength prediction. 2. Methods 2.1. Material description A SLJ configuration was used to validate the CZM impact model used in this study. A DLJ design was then subject of a numerical analysis. Both joint architectures share the same adherend material, Texipreg HS 160 RM from SEAL ® , a high stiffness material composed of epoxy resin reinforced by carbon fibre (CFRP). The adherends were cut from manually fabricated plates, composed of 20 layers of this prepreg, unidirectionally stacked in line with the loading

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