PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1590–1600 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2020) 000–000

1594

3. Finite element modelling For modelling the fracture behaviour of SLJs during the tensile test, surface based-cohesive model approach was used in the present study. In this approach, a cohesive connection between the adherents and the adhesive is modelled with a zero-thickness interface which its damage constitutive law is based on the Traction-separation Law (TSL) . To attain a better understanding of the strain variation on the adhesively bonded joints different 2D and 3D symmetric model were developed by using ABAQUS. To investigate the influence of different element types on the measured longitudinal strain as well as the location of ZSP, two different 2D FE models were considered in the present study. In fact, both adherents and the adhesive layer were modeled once with plane strain elements (CPE4R) and another time with plane stress (CPS4R) elements. For the 3D symmetric SLJ model, C3D20R were chosen for both adherents and the adhesive layer. The constitutive damage response is assigned in the property of the contact interaction between the adherent and adhesive (contact to contact surface). TSL can have different shapes and the simplest approach is a bilinear softening law which was used in the present study. The properties needed for the adhesive layer 3M Scotch Weld DP 490 by using the CZM properties used for modelling the adhesive based on surface based-cohesive model is given in Table 1.

Table 1-material properties of 3M Scotch-Weld DP 490. Property

Value

Young modulus (N/mm 2 )

1730 a

Poisson’s ratio

0.43 b

Tensile failure strength (N/mm 2 )

30.8 a

Shear failure strength (N/mm 2 )

23.6 a

G IC (N/mm)

2.7

a

G IIC , G IIIC (N/mm)

10.8

a

Power Law exponent

1

a from manufacturer’s data

4. Results and discussions The representative comparative load-displacement curves between different FE models developed in the present work and experimental results have been depicted in Fig. 4. The comparison between the FE models and the experimental results show a good agreement. The average fracture load achieved for experimental results is: 13976 ± 749 N, the maximum load achieved for the 3D FE model; 2D plane stress and plane strain are respectively 13861 N, 14300 N, 14800 N. The fracture pattern in all specimens were cohesive failure and no plasticity was observed on the steel adherents (Fig. 5).The deformation and Von-Mises stress counter of the 3D FE symmetric model developed in the present work for a time step in which the damage is developed from both sides is shown in Fig. 6. As it can be seen, the damage in the FE model is propagated symmetrically from the both ends of the bonded area. The position of the ZSP was detected by the 3D FE model which was 8.5 mm from the both ends of the bonded area which is expected from the FE model due to symmetric boundary condition and the joint geometry. Base on the detected location of ZSP, two strain gauges were mounted on both sides of the bonded area (in the middle of the bonded area). The variation of strain variation at ZSP and the corresponding load versus displacement of the joint by using FE analysis is shown Fig. 7. The trend of the strain at ZSP can be divided to three different regions: in the first region, the crack is still on the initiating phase and therefore the strain remains without change over the time recording very small values of strain. Once the crack has propagated from both overlap ends of the joint, the strain gauge evolves (region two). In the third region, the strain values rises hastily which is followed by the rapture of the adhesive bond in the joint.