PSI - Issue 33

M.F.M.O. Rosas et al. / Procedia Structural Integrity 33 (2021) 115–125 Rosas et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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2.4. Triangular CZM model CZM are based on relationships between stresses and relative displacements connecting homologous nodes of the cohesive elements. These laws simulate the elastic behavior up to a peak load and subsequent softening, to model the gradual degradation of material properties up to complete failure. The areas under the traction-separation laws in tension or shear are equaled to G IC or G IIC , respectively. Under pure mode, damage propagation between two connected nodes occurs when the stresses become nil in the traction-separation law linking the two nodes. Under mixed mode, energetic criteria, i.e. based on parameters such as G IC and G IIC , are often used to combine tension and shear (Kim 2015). In this work, triangular pure and mixed-mode laws, i.e. with linear softening, were considered. The elastic behavior of the cohesive elements up to the tipping tractions is defined by an elastic constitutive matrix relating stresses and strains across the interface, containing E and  as main parameters. Damage initiation under mixed-mode can be specified by different criteria. In this work, the quadratic nominal stress criterion was considered for the initiation of damage. After the cohesive strength in mixed-mode ( t m 0 ) is attained, the material stiffness is degraded. Complete separation is predicted by a linear power law form of the required energies for failure in the pure modes. For full details of the presented model, the reader can refer to Campilho et al. (2011). 3. Results 3.1. Validation with experimental results Fig. 3 presents the experimental and numerical values of P m as a function of L O for the tubular joints bonded with the Araldite ® 2015. The numerical strength predictions reveal that the values obtained by CZM, in regard to P m , are in close agreement with the values obtained experimentally. For L O =20 mm, a 6.1% difference was found between the average of the experimental results and the numerical one, being the values obtained by CZM higher than the experimental average. This is considered an acceptable discrepancy, and in fact it is a very small difference, since the experimental results average is P m ≈27 kN and the numerical result is P m ≈29 kN. On the other hand, the percentile difference between the experimental results average and the numerical predictions is even smaller for L O =40 mm, since it is approximately 2.9%. The experimental results average is P m ≈39 kN and the numerical result is P m ≈40 kN. Despite the small differences observed, which are acceptable in view of experimental processes, the values obtained by the CZM predictions are considered as adequate. Thus, the parametric study that follows in section 3.2, will only consist of a numerical analysis, due to the positive results of the validation study.

50

40

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P m [kN]

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10

0

0

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L O [mm]

Experimental

Numerical

Fig. 3. Experimental and numerical values of P m vs. L O for the tubular joints with the adhesive Araldite ® 2015.

3.2. Geometric modifications

In this section, stress analysis and joint strength of tubular adhesive joints with geometric changes are carried out. These geometric modifications consist of the creation and variation of the angle of the outer chamfers, inner chamfers and adhesive fillets at the ends of the aluminium tubes. In this analysis, tubular adhesive joints with L O =40