PSI - Issue 77

P.D.A. da Silva et al. / Procedia Structural Integrity 77 (2026) 103–110 Silva et al. / Structural Integrity Procedia 00 (2026) 000–000

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weight ratio and ability to bond different adherends (Eusébio and Campilho 2019, Pinheiro et al. 2022). However, a detailed analysis of these joints and its ability to comply with the demanding requirements of various industries is due. In this context, numerical modelling and strength prediction of tubular adhesive joints are commonly conducted. Tubular joints can be modelled in two-dimensional (2D) axisymmetric models to analyse stresses, or in three dimensional (3D) analyses for torsional loading scenarios (Oliveira et al. 2021, Sukhaya and Aimmanee 2022). Adherends are typically modelled as solid elements, while the adhesive layer fracture can be modelled with continuum mechanics, fracture mechanics, CZM, or eXtended Finite Element Method (XFEM) (Adediran et al. 2025). The CZM approach is particularly useful to predict the behaviour of thin adhesive layers (Campilho et al. 2013). Additionally, the XFEM, which establishes enrichment functions for displacement near crack tips, can be used to model crack growth and separation between the crack faces, applied to both adherends and adhesive, or only to the adhesive layer (Ghandriz et al. 2020). Eusébio and Campilho (2019) used the XFEM to model the tensile behavior of single-lap tubular joints, with different overlap lengths ( L O ), of 20 and 40 mm, and adhesives. For both adhesives and L O , the use of maximum stress (MAXS) and quadratic stress (QUADS) criteria has proven to be effective. Rosas et al. (2021) addressed single-lap tubular adhesive joints with aluminium adherends and the adhesive Araldite ® 2015 by axisymmetric CZM modelling. Three geometrical modifications were assumed: adherends inner chamfer, adherends outer chamfer, and adhesive fillet at the overlap ends. The numerical analysis highlighted the outer chamfer potential in reducing adhesive’s stresses, but adhesive fillets were most effective in increasing P m . Lavalette et al. (2020) conducted a comprehensive study on the effect of geometrical factors such as bonding area, L O , adherend thickness ( t p ), tapering angle, and adhesive thickness ( t a ) on the performance of carbon fiber-aluminum tubular adhesive joints. Using a trapezoidal CZM, the authors validated the models through experimental tests. P m significantly increased with L O and inner diameter. Moreover, the t a and taper lengths influenced the uniformity of τ xy stresses, especially at higher L O . Silva et al. (2021) studied the impact strength of tubular joints with aluminium adherends and Araldite ® AV138 adhesive by CZM, using different L O and tube thicknesses. Higher L O promoted a higher contact area, augmenting P m and the absorbed energy. However, proportionally, the contact area increase is much more pronounced, as big overlaps are affected by peak stresses. This study presents a numerical investigation of tubular adhesive joints under impact, with different adhesive types. The impact damage was simulated using an adapted CZM implemented in Abaqus ® . A parametric study was conducted including θ , α , and β . The results include distributions of σ y and τ xy stresses, P - δ behaviour, E a , and P m . 2. Methods 2.1. Adherends and adhesives The adherends were manufactured from DIN 55 Si7 steel, a material of high mechanical strength. The choice of such material aimed to prevent premature plastic deformation during testing. The mechanical properties of the adherends, including Young’s modulus ( E ), tensile yield stress ( σ y ), tensile strength ( σ f ), tensile failure strain ( ε y ), Poisson’s ratio ( v ) and density ( ρ ), are summarized in Table 1.

Table 1. Mechanical properties of DIN 55 Si7 adherends.

Property

E [GPa]

σ y [MPa]

σ f [MPa]

ε y (%)

ρ ( g/cm

3 )

v

Value

210

1078

1600

6

0.3

7.8

Two brittle (Araldite ® AV138 and Nagase Chemtex ® XNR6852 E-2) and two ductile (Momentive ® RTV 106 and 3M ® DP8005) adhesives were chosen. To determine E and cohesive tensile strength ( t n 0 ), tensile tests were performed, while the cohesive shear strength ( t s 0 ) was obtained using thick adherend shear tests. Lastly, double cantilever beam and end-notched flexure tests were used to determine the fracture toughness in mode I ( G IC ) and II ( G IIC ). Table 2 summarizes the collected properties, including values provided by the manufacturers ( ρ and v ).