PSI - Issue 41

T.F.C. Pereira et al. / Procedia Structural Integrity 41 (2022) 14–23 Pereira et al. / Structural Integrity Procedia 00 (2019) 000 – 000

17

4

Table 1 – Elastic orthotropic properties of a unidirectional lamina with the fibers aligned in direction 1 (Campilho et al. 2005).

E 1 [MPa] E 2 [MPa] E 3 [MPa]

109000

G 12 [MPa] G 13 [MPa] G 23 [MPa]

4315 4315 3200

0.342 0.342

 12  13  23

8819 8819

0.38

Table 2 – Properties of the Araldite ® AV138 (Campilho et al. 2011).

Property

Value

Young’s modulus, E (GPa)

4.89±0.81

Shear yield strength,  y (MPa)

25.1±0.33 30.2±0.40

Poisson’s ratio, 

0.35 a

Shear failure strength, 

f (MPa)

Tensile yield strength,  y (MPa) Tensile failure strength,  f (MPa) Tensile failure strain,  f (%)

36.49±2.47 Shear failure strain,  f (%)

7.8±0.7

39.45±3.18 Toughness in tension, G IC (N/mm)

0.20 0.38

1.21±0.10

Toughness in shear, G IIC (N/mm)

Shear modulus, G (GPa)

1.81 b

a manufacturer’s data b estimated from the Hooke’s law using E and 

2.2. Impact testing The impact testing corresponds to a known weight falling a known distance, hence transferring its potential energy to the tested specimen. Consequently, the specimen is subjected to a load that can be measured using a load cell. Experimental testing was performed using a Falling Weight Impact equipment (Rosand ® 5 HV) at a speed of 1.75 m/s, as described in a previous work (Valente et al. 2019). The energy imposed on the specimens is 40 J. To impose this energy into a numerical model, as discussed later, it is necessary to know the mass and impact speed. Based on the conservation of energy and knowing the test speed ( v ), a mass ( m ) of 26 kg was calculated. 2.3. Numerical modelling The experimentally tested specimens (Section 2.1) were modelled into a Finite Element Analysis software (ABAQUS ® 2017, Dassault Systèmes. RI, USA). As previously mentioned, DIN 55 Si7 steel adherends were used for the validation process, while composite adherends were considered in the numerical analysis. These materials were modelled as isotropic and orthotropic, respectively. The adhesive was considered isotropic. The joint geometries were modelled as plane-strain cases. The adherends were meshed using four-node quadrilateral elements (CPE4). The adhesive was modelled by a single layer of cohesive elements (COH2D4) with an approximate element size of 0.2 mm×0.2 mm in the adhesive layer (Fig. 2). As boundary conditions, the left edge (Fig. 1) was constrained in both vertical and horizontal directions ( U x= U y=0). In the right edge (Fig. 1), m =26 kg and v =1.75 m/s acting in the horizontal direction were added, as determined in Section 2.1. The models are dynamic and were solved using the explicit solver. The time period for the models was 0.005 s, which was controlled by the software.

Fig. 2 – Details of the mesh at the adhesive layer's right end.

2.4. CZM formulation

Cohesive laws represent the behavior of materials from loading until failure. These laws can present different shapes, depending on the material, to best suit its behavior. In addition, these can represent pure and mixed-mode conditions. In adhesive joints, mixed-mode is often present due to the complex loadings. The most common CZM