PSI - Issue 77

D.C. Gonçalves et al. / Procedia Structural Integrity 77 (2026) 79–86 Gonçalves et al./ Structural Integrity Procedia 00 (2026) 000 – 000

82 4

2.2. Fracture Propagation A wide variety of crack propagation criteria are available, ranging from strain/stress based criteria to energy-based approaches. In this application, the critical energy release rate criterion is implemented, a classical method within adhesive joints applications. Depending on mode I or mode II fracture propagation, the crack tip is propagated if ( )=1 or ( )=1 , being the criterion function defined as, ( )= (Mode I fracture) (7) ( )= (Mode II fracture) Where and are the fracture energies at the crack tip, and and are the critical energy release rates of the adhesive material. and can be obtained experimentally. and are calculated at each increment and determine if the crack tip is propagating. If at a given increment, the criterion function equals 1, the crack tip is propagating and local remeshing is required to account for the crack tip propagation in the numerical model. In this work, the nodes and integration cells are locally rearranged around the crack tip using an approach presented in detail in reference [12]. The fracture energy can be obtained in DCB and ENF resorting to various methods. In this application, the Direct Beam Theory (DBT), the Corrected Beam Theory (CBT), and the Compliance Based Beam Method (CBBM) [13], [14] were implemented to calculate the fracture energy at the crack tip, and also to construct the resistance curves and determine the and values. 3. Results 3.1. Experimental Testing Fig. 3 shows the geometry and boundary conditions of the DCB and ENF specimens. The adherend thickness is 3 mm in both tests, and the adhesive layer thickness are 1 mm and 0.2 mm, respectively, in the DCB and ENF tests. Both joints have a 25 mm width. In the numerical model, the crack length, a, is an average of the crack lengths measured of the specimens tested experimentally. In both cases, the aluminum alloy AW 6082-T651 ( = 70.1 GPa,ν = 0.33) was used to manufacture the adherends, which were bonded with the strong and brittle Araldite AV138 adhesive ( = 4.89 GPa,ν = 0.35) . Fig. 4 shows a DCB (Fig. 4a) and an ENF (Fig. 4b) specimen ready for testing. A camera was placed to capture the crack length evolution along with the load, displacement and time data from the machine. A measuring tape was glued to the specimens’ side, allowing to posteriorly synchronize the crack length data with the load and displacement values at each time step. The results for valid and reproducible tests are shown in Fig. 5. Considering the experimental load-displacement curves, it is possible to construct the resistance curves ( − and − ) using the data reduction schemes mentioned in the previous section, and to define the critical energy release rates, for the mode I and mode II scenarios. The average and values for the DCB and ENF tests, obtained with the DBT, CBT, and CBBM techniques are presented in Table 1. These and values are incorporated into the numerical analysis to evaluate the crack initiation function.

Fig. 3. (a) DCB geometry; (b) ENF geometry.