PSI - Issue 75

Yuki Ono et al. / Procedia Structural Integrity 75 (2025) 176–183 Author name / Structural Integrity Procedia (2025)

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2.2. Numerical simulation example for a notch model

Fig. 2 presents an example of finite element (FE) simulations used to determine fatigue effective stress and strain [Ono and Remes (2024)], referred to as Step 1 in Section 2.1 . The simulation model is a notch model that is a smooth notched plate containing a small imperfection with 40 μm in width and 10 μm in depth. The material under analysis is S690QL, which has a plate thickness of 6 mm and the nominal yield strength of f y = 832 MPa. The model exhibits a compressive residual stress field near the imperfection in loading direction, characterized by stress levels of -0.5 f y up to a depth of 0.5 mm. Beyond this depth, the stresses gradually shift to tensile residual stress side through the plate thickness. The material model is a combined non-linear isotropic-kinematic hardening model, known as Voce Chaboche’s model. The hardening layer (HL) near the surface is systematically accounted for in the following segments: HL1 ( σ y = 1154 MPa and d 99% = 5 μm) up to 50 μm depth, HL2 ( σ y = 952 MPa and d 99% = 6 μm) from 50 to 100 μm depth, HL3 ( σ y = 811 MPa and d 99% = 8 μm) from 100 to 200 μm depth, and BM ( σ y = 745 MPa and d 99% = 10 μm) beyond 200 μm dept h. Here, σ y refers to the yield strength at zero plastic strain for Voce-Chaboche ’ s model. A uniaxial cyclic loading ( ΔS = 0.36 f y and R = 0.23) is applied at the end of the notch model. To model the crack growth in FE simulation, the element deletion method built in Abaqus is employed, a method previously utilized in some studies, e.g., [Al-Karawai (2021) and Banno et al. (2021)]. Element deletion method allows for the deactivation of specific elements as a step, as similar to loading and boundary conditions. Thus, this approach achieves a continuous,

Step n = 1 to n = 25

- Joint / notch geometry - Material modelling - Defining elements to be deleted Simulation model

Step n = 0

- Final failure Simulation ending

Residual stress implementation

Element deleting

Applied loading

Applied loading

Example of n=6 to n=7

Contour at maximum loading

Step n=7

Step n=6

σ xx (MPa)

a 6 = 0.11mm

a 7 = 0.16mm

Element deleting of 0.05 mm

Stress averaging within d 99%

y

x

z

(a) Flowchart of crack growth simulation

10.000 10

a 0 = 0 mm, no fatigue crack growth a 25 =2.3 mm, critical crack length

σ eff,2

0.100 0.1 Crack length, 0.01 + a n (mm) 1.000 1.0

σ eff,1

σ eff,3

Symmetric boundary condition for other planes

σ eff,1 : Maximum principal stress σ eff,2 : Intermediate principal stress σ eff,3 : Minimum principal stress

0.010 0.01

0

10

20

30

Step n

(c) Continuum-single element model (CSEM)

(b) Crack length at each step

Fig. 2 An example of FE simulation procedure and tools to determine fatigue effective stress and strain for a notch model, adapted from Ono and Remes (2024).