PSI - Issue 72

P.D.A. da Silva et al. / Procedia Structural Integrity 72 (2025) 52–60

53

1. Introduction Adhesive joints offer certain advantages, but also disadvantages, over conventional mechanical joining methods (Kinloch 2012). These allow for a more uniform distribution of stresses along the adhesive, reduction of stress concentrations, and joining of different materials. Disadvantages are the low resistance to  y stresses and possible requirement of temperature and pressure to finalise the adhesive’s curing process. Among the fields of application that most use these types of joints, the aeronautical and automotive industries stand out (Jeevi et al. 2019). Tubular adhesive joints are made up of two tubes joined by an adhesive layer. As tubular adhesive joints have a high strength-to-weight ratio and the ability to join different adherends, and with a low thickness, it is advantageous to use these joints to the detriment of other types of joints as a structural connecting element (Eusebio and Campilho 2019). In the case of axial loading, there are stress concentrations at the ends of the overlap, as in overlap joints with flat adherends. In the case of torsion, there is only the effect of differential deformation (Barbosa et al. 2019). Tubular adhesive joints are widely used in various industries, such as oil, energy (e.g., gas), water, automotive, aeronautical, construction and aerospace (Barbosa et al. 2019). There are currently many methods to estimate the strength of an adhesive joint. Conventional analytical methods rule out plastic behavior or make the calculation quite complex. The finite element method (FEM) becomes the most widely used method. The related techniques incorporate factors such as joint rotation, the plasticity of the adherends, the plasticity of the adhesive, and the influence of the fillet. Opposed to static loads, dynamic loadings vary over the time. Under this scope, variable strain rate and impact studies are divided into continuum mechanics, damage mechanics and CZM models (Ramalho et al. 2022). Continuum mechanics is used to evaluate stresses and strains in adhesive joints. Damage mechanics makes it possible to simulate the progressive degradation of the material until final failure along an arbitrary path. CZM models are the most used models to study and predict the impact strength. These are used in a similar way to static loading, and the properties used to define the cohesive laws are dependent on the strain rate. Therefore, adhesive characterisation tests must be carried out under different strain rates (Valente et al. 2020). Different works are available in the literature under dynamic analysis of adhesive joints. Rao and Crocker (1990) used a theoretical model to study the bending vibration of overlapping joints. First, the equations of motion in the joint region are derived mathematically using a differential calculus approach. The transverse displacements of the upper and lower beam are considered to be different. The model can be used to predict the natural frequencies, modal damping ratios and mode shapes of the system for free vibration. Esmaeili et al. (2015) carried out a fatigue study on the effect of the tightening torque on bolted and hybrid (bonded/bolted) joints with different cyclic longitudinal loads. The fatigue of the specimens was predicted using six different multiaxial fatigue criteria by means of the local stress and strain distribution obtained from FEM analyses. The hybrid joints showed better fatigue life compared to the bolted joints. In the work of Hazimeh et al. (2015), a three-dimensional (3D) FEM study was carried out for double-lap joints of similar composite adherends, under quasi-static and impact loads, to study the geometric and material influence on the distribution of shear stresses in the adhesive layer. The adhesive shear stiffness was found to raise the average  xy stress and increase the significance of stress heterogeneity. Conversely, an increase in the adherends’ longitudinal stiffness results in higher average  xy stress. This work addresses the CZM numerical analysis of adhesive tubular joints subjected to impact loads, considering different adhesives. A parametric numerical study carried out on the influence of L O and t p on the strength of the adhesive joints. Plots with the distribution of  y normal stresses and  xy shear stresses are presented, as well as P -  curves, E a and P m for all joints tested. 2. Experimental and numerical details 2.1. Materials The material adopted for the adherends is DIN 55 Si7 (Silva et al. 2022), aiming to avoid plastic deformation of the adherends during the numerical study and to ensure that the failure is cohesive in adhesive (Table 1). A brittle adhesive (AV138) and two ductile adhesives (DP 8005 and XNR6852 E-2) were used. Tensile tests provided the Young Modulus ( E ) and tensile cohesive stress ( t n 0 ), while the shear modulus ( G ) and the shear cohesive stress ( t s 0 ) were obtained through thick-adherend shear tests (TAST). The double-cantilever beam (DCB) tests provided the