PSI - Issue 38

Hamza Abbad El Andaloussi et al. / Procedia Structural Integrity 38 (2022) 238–250 245 Hamza Abbad El Andaloussi, Luc Mouton, Firas Sayed Ahmad, Xabier Errotabehere, Stéphanie Mahérault-Mougin, Stéphane Paboeuf/ Structural Integrity Procedia 00 (2021) 000 – 000 8

Figure 6 Geometry of the single-strap samples – 2D Abaqus model

The type of elements used in the 2D model are 4-node bilinear plane strain quadrilateral with reduced integration, hourglass control (CPE4R). For the IDL (which exhibits a hyperelastic behavior), a 4-node bilinear plane strain quadrilateral, hybrid, constant pressure with hourglass control element (CPE4RH) is used. The general mesh size is 2 mm and mesh size at interface is between 0.25 and 2 mm. The total number of elements of the model is 32883. A displacement is imposed at the free edge of the sample as illustrated Figure 6. The other end was clamped. Then, as the numerical calculation is non-linear and incremental, the analysis is performed at the targeted load range regarding the loading test considered. The Table 2 gives the materials properties used in this model:

Table 2 Materials properties used in the numerical model

Steel substrate

Superduplex

IDL

Adhesive

Behavior E (GPa)

Elastic

Hyperelastic

Elastic

Elastic

203

-

3.4 0.4

209.0

υ

0.3

0.49

0.3

This numerical model has been validated by comparison with strain gauges results from tensile experimental tests. This is not further detailed in this article as the focus is made on the S-N curve calculation. Numerical Results As already shown previously [1] , this new reinforcement technology is compatible with a stress-based strength criteria. Hence, from the numerical model presented in the previous paragraph, the maximum peel and shear interfacial stresses are extracted at the bondline and for relevant load ranges. Those are not related to the mesh size as the design, and in particular the IDL allow the stress concentration at the edge to converge to a finite value. Thus, it was shown [1] that the mesh size used presently enables to reach this value, a thinner mesh would not increase the maximum stress. Table 3 presents maximum peel and shear stresses, as well as quadratic interfacial stresses for each load range tested in the frame of this fatigue tests campaign.

Table 3 Calculation of quadratic interfacial stress at bondline

Interfacial stress Absolute max.

Quadratic interfacial

% of ultimate tensile capacity

Shear (MPa)

Load range (kN)

Peel (MPa)

Stress (MPa)

530 440 395 350

15.0 12.2 10.8

75.0% 62.5% 56.5% 50.0%

10.8

10.4

8.8 7.8 7.0

8.4 7.5 6.7

9.7

Thanks to this numerical work, the acting interfacial stresses at the bondline are known. These quadratic interfacial stress values are then used as inputs for the statistical analysis to determine the interfacial S-N curve of the reinforcement.