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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Table 3. Joint dimensions, in mm.

Geometry

Overlap length ( L O )

Adhesive thickness ( t A )

Adherend thickness ( t P )

Adherend width

Total length ( L T )

SLJ DLJ

0.2 0.2

3

12.5/25/50

15

200

1.5( t Po ) / 3( t Pi )

The SLJ specimens were fabricated by manually stacking 20 layers of prepreg, unidirectionally, which are then submitted to heat cycle under 3 bar. When fully cured, all specimens are trimmed to design specification. The adhesive bonding area of each specimen was sanded to promote adhesion and all joints were assembled. Experimental impact testing was performed using a drop-weight testing device. Necessary procedures were applied to avoid misalignment and rupture of adherends during testing. The 30 kg weight was dropped from a pre-set height, resulting in a kinetic energy impact of 40 J. A laser beam was used to read the joints’ displacement under evaluation. Experimental details, including joint fabrication, impact testing and data analysis, are available in previous works (Valente et al. 2019). 2.3. Numerical simulations Abaqus ® was the chosen software to simulate an impact loading on the studied joints, with dynamic explicit formulation. All studies were conducted considering a triangular CZM law. To reduce the complexity of calculations, the simulation models were designed in two-dimensions (2D), thus reducing the number of elements subject to calculations. Symmetry conditions – mirroring along the axis corresponding to impact testing direction – were applied to DLJ design in all its configurations, where only one of the outer adherends was modelled and thickness of the inner adherend was halved. The cohesive failure of the adhesive layer was assured to occur within all simulations’ total testing time and data collection took place at evenly spaced time intervals for each numerical testing. The amount of available data, from start to rupture, ensured that maximum load could be accurately identified from the P - δ plot curves. To simulate the weight used in a drop-weight testing machine, rigid elements were defined at the end of one of the adherends. Respective properties were defined to result in a 40 J impact at a 1.75 m/s starting velocity, replicating impact loadings of experimental testing. Geometrical constraints were set to replicate the experimental testing device, in which test samples are restricted in movement except for the impact load direction and, as a result, decreasing the effect of buckling adherends as result of stress propagation. Both SLJ and DLJ models’ mesh were generated using sweep control. Element size was controlled by applying bias, resulting in smaller element size in areas nearing bonding elements. Neighbouring regions suffer greater stress fields variation, whereas areas with bigger mesh elements are expected to experience more progressive stress distributions. The adhesive layer was modelled with a single layer of COH2D4 mesh elements with quadratic stress damage initiation, having damage propagation into consideration by a linear energetic criterion. All adherends and simulated mass comprise CPE4 structural elements. CZM laws establish a connection between cohesive elements’ nodes and their relationship in stress and displacement, enabling the study of materials until reaching mechanical limits (Alfano et al. 2007). Several models have been developed over time, being applied for different materials and behaviours for which they can provide improved accuracy (Campilho et al. 2013). In this study, the triangular shaped law was used for both adhesives. Not only it is simple to configure and use in numerical analysis software, but it also provides accurate results within short processing time. As this model can be applied in impact loading scenarios on adhesives with varying properties and behaviours, it also provides consistency in comparison between different adhesive joints subject to analysis (Valente et al. 2020). Suitability of this approach was validated by comparison between experimental and numerical work in a SLJ configuration submitted to impact. After a first stage following elastic behaviour, damage initiation in pure mode begins to take place when reaching t n 0 or t s 0 (Sane et al. 2018). Stress and energy criteria from pure-mode laws are usually combined to be applied under mixed-mode scenarios. Under mixed mode, damage initiation occurs when the mixed mode cohesive strength ( t m 0 ) is attained. For this study, damage initiation relies on the quadratic nominal stress criterion (Rocha and Campilho 2018). On the other hand, mixed-mode crack propagation is evaluated by a linear energetic criterion depending on G IC and G IIC (Dimitri et al. 2015). 2.4. CZM model