PSI - Issue 51

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P.A.R. Ferreira et al. / Procedia Structural Integrity 51 (2023) 115–121 P.A.R. Ferreira et al. / Structural Integrity Procedia 00 (2022) 000–000

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Fig. 1. Geometry of the curved joggled-lap joint (JLJ) subjected to an internal pressure ( p ).

Eight different values of L O were evaluated, from 10 mm to 80 mm; in addition, three t P values were considered, 1.2 mm, 2.4 mm, and 3.6 mm. Finally, three different values of R were tested, 1000 mm, 2000 mm, and 3000 mm. All the joints had composite substrates bonded with an epoxy-based ductile adhesive, Araldite® 2015. The substrates' material is CFRP based on a prepreg (HS160), which mechanical properties are listed in Table 1, while the mechanical properties of the adhesive are listed in Table 2.

Table 1. Mechanical properties of the substrate material. Adapted from (Abdelfattah et al., 2022). Elastic modulus Poisson’s ratio Shear modulus (GPa) (-) (GPa) E 11 109.000  12 0.342 G 12 4.315 E 22 8.819  13 0.342 G 13 4.315 E 33 8.819  23 0.380 G 23 3.200 Table 2. Mechanical properties of the Araldite® 2015. Adapted from (Campilho et al., 2011). Property value Property value E (MPa) 1850±0.21 τ Y (MPa) 14.60±1.30  0.35 τ U (MPa) 17.90±1.80 S Y (MPa) 12.63±0.61 γ F (%) 43.90±3.40 S U (MPa) 21.63±1.61 G IC (N/mm) 0.43±0.02 ε F (%) 4.77±0.15 G IIC (N/mm) 4.70±0.34 G (MPa) 560±0.21

A numerical model was created following the geometry of Fig. 1 and the dimensions listed above. The model was made parametric to allow exploring the effects of varying t P , L O , and R . In this case, the geometry allows for a 2D model, being a plane strain case. All the modelling was performed using the ABAQUS® software (ABAQUS® 2017, Dassault Systèmes. U.S.A.). Then, the corresponding mechanical properties were assigned using the data reported in Table 1 and Table 2. Geometrical and material non-linearities were considered in all the models. The geometry represents a sector of a cylindrical surface; thus, a polar coordinate system was created to allow the imposition of boundary conditions. Both ends of the substrates were constrained in the tangential direction (θ) while left free in the radial direction ( � ), as shown in Fig. 1. Subsequently, a pressure of 1 MPa was imposed on all the internal surfaces, such value is higher than the observed at cruise altitude (Sforza, 2014), being the pressure the only force acting in the geometry. On the other hand, the chosen boundary conditions allow for the expansion of the geometry due to the internal pressure. The geometry was meshed with two different element types, plane strain four-node solid elements (CPE4) on the substrates, and four-node cohesive elements (COH2D4) for the adhesive and interlaminar layers, the latter were