PSI - Issue 72

L.A.S. Maia et al. / Procedia Structural Integrity 72 (2025) 43–51

46

P 0 , E m g h   

(1)

being E P the potential energy, m the mass of the weight, g the gravity acceleration, and h 0 the height of the dropping weight. Since the height of the fall was not considered in numerical modelling, the next equation gives the kinetic energy ( E C ) used to obtain the velocity of the mass ( v ) at the moment of impact, which is equal to 1.75 m/s

1

2

.

C 2 E m v   

(2)

Aiming to simulate the impact of this mass, a volume was created in the numerical models by defining its dimensions and calculating its density to match the real mass. This procedure gives rise to a density of 2.476×10 7 kg/m 3 to achieve a total energy of 40 J and replicate the experimental tests. 2.4. Numerical simulations The numerical analysis was carried out in the Abaqus ® software, which is based on the FEM and accounts for advanced fracture solutions such as CZM. The numerical analysis conditions presented next are valid for both the validation study, with single-adhesive joints, and the numerical study on DSLJ. Two-dimensional (2D) models were built to simplify the simulations and reduce the computational effort. The adherends and the artificial mass were homogeneous solid elements. The adhesives (flexible and rigid) were modelled by a single row of cohesive elements with triangular damage law. A detailed description of this model is presented in a previous work (Valente et al. 2019). All relevant properties were defined as shown in section 2.2. The definition of the explicit step included establishing field outputs for further analysis, such as the stiffness (SDEG) parameter. Under history output recordings, the RF1 parameter records the reaction force along the longitudinal specimens’ direction. The U1 parameter records the corresponding displacement which, when combined with RF1, allows the load-displacement ( P - δ ) curve to be obtained. The opposite adherends’ edge to the artificial mass was clamped, while the edge adjacent to the mass was restricted in the specimens’ transverse direction, while only longitudinal movement was allowed. The impact loading was emulated by assigning v =1.75 m/s to the artificial mass, which corresponds to an impact energy of 40 J on the joint based on the mass volume and density. A mesh was created with quadrilateral elements with a side dimension of 0.2 mm. Two types of elements were used. For the adherends and mass, plane-strain CPE4R elements were selected, resulting in 13050 elements. For the adhesives, 4-node COH2D4 cohesive elements were defined, resulting in 125 elements. In total, a mesh with 13175 elements was obtained. 3. Results and discussion 3.1. Numerical technique validation To validate the numerical approach, experimental results and numerical reference values of single-adhesive joints obtained by Valente et al. (2019) are considered. A comparative analysis of experimental and reference P m values for the adhesives AV138, DP8005, and XNR6852E-2 alongside the numerical P m results derived in this study using the CZM model is illustrated in Fig. 2 and detailed in Table 4, including the numerical P m deviation (  P m ). In the case of AV138 joints, the deviation observed was within an acceptable range, with the numerical P m value calculated here being 6% lower than the reference numerical result and 16% off from experimental findings. For the DP8005 adhesive, results were satisfactory, as the P -  curve closely mirrored the reference data, despite some irregularities. The numerical result showed only a 1% difference from the numerical reference, while the experimental P m was approximately 15% lower. For the XNR6852E-2 adhesive, the numerical P m value differed by 5% from the numerical reference and was 16% higher than the experimental reference. Despite minor differences, the CZM approach was considered validated for design applications.