PSI - Issue 57

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Nesrine Majed et al. / Procedia Structural Integrity 57 (2024) 502–509 Nesrine Majed et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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5. Numerical simulation A finite element simulation is used to find the stress in the vicinity of the defect for alternating tension stress. For this, the mesh is refined and optimized around the defect by tetrahedral elements C3D10. Figure 4 illustrates the mesh employed during the use of a quadratic tetrahedron solid element with 10-node C3D10. The finite element (FE) results indicate that the plane perpendicular to the direction of the maximum principal stress is identified as the Highest Loaded Plane (HLP) as shown in figure 5.b. Nadot 's (2006) et al findings further support this observation as depicted in the figure 5.a. Their findings demonstrate that in a material containing defects under fatigue loading, the crack initiates at the tip of the defect and propagates perpendicular to the direction of the maximum principal stress. Consequently, σ eqCr will be evaluated on the critical plane, considering various defect sizes ( √ ) and different load ratio.

Fig. 4. Refined mesh in the vicinity of a spherical defect.

Figure 5. a) Crack initiation at the defect tip (tension loading), (b) Stress distribution in front of a defect (tension loading)

Rotella et al. (2020) have concluded that the material behavior can be described using a non-linear Kinematic hardening law after having conducted a strain-driven cyclic hardening test. Consequently, they have identified the A357- T6 parameters (C et γ) and Le Pen et al. (2001) have identified these parameters for the cast alloy A356-T6, their value is given in Table 3. This work-hardening model is based on the approach proposed by Lemaitre et al. (2009). Table 3. Kinematic hardening material parameters for A357-T6 and A 356 -T6 aluminium alloys. 5.1. Identification of affected depth parameter The affected depth is a critical length. It is a material parameter identified from an experimental endurance limit of the defect material. depends on the type of the material and on the load ratio as it is proved by Nasr et al (2017). Thus, to identify this parameter, we need an experimental result for each load ratio. Numerical simulations are carried out to a sample with a spherical defect (size = √ = 200 µm), and it is subjected to its experimental defective fatigue limit equal to 91 MPa under the same tension loading at load ratio = −1 . Experimental values were assessed by Mu et al (2014). However, the torsion fatigue limit of this material is 38−1 = 80 MPa which is investigated by Munoz et al (2020). Consequently, the identified value is = 350 μm. Aluminum alloy C (MPa) γ A 357 150 000 1400 A 356 58 000 680