PSI - Issue 57

Kalle Lipiäinen et al. / Procedia Structural Integrity 57 (2024) 785–792 Lipiäinen et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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4. Finite element analysis Finite element analyses were carried out to obtain the fatigue notch factors, K f , for the fatigue assessments (see Section 5) using local approaches as per the critical distance approach. Two different two-dimensional (2D) linear plane strain element models were prepared using FEMAP with Nx Nastran version 2022.2 (Siemens PLM software) – one for the unnotched component with an initial crack located at the hot-rolled surface (Fig. 6a) and one for the notched ( d = 10 mm) component with an initial crack located at the root of the geometrical notch (Fig. 6b). The linear material model, with Young’s modulus of E = 210 GPa and Poisson’s ratio of v = 0.3, was applied. The models were analysed applying different crack sizes with lengths of 0 (no crack), 25 μm, 50 μm, 75 μm and 100 μm as representative values found in the fractography analyses. Fig. 6 exemplifies the stress distributions for the crack length of 50 μm. For the unnotched component, the cross-sectional model was created. For the notched component, the geometrical specimen shape, applying the half-symmetry, was modelled. No mesh convergence study was conducted within this work, but based on the previous work by (Lipiäinen, Ahola, Kaijalainen, et al., 2022)., an element side length at the critical location was set as 0.0625 mm to enable sufficient accuracy in fatigue notch factors with the critical distances more than 0.125 mm (in a case of more than two elements over the critical distance). Both models were loaded with uniform 1 MPa unit load, and models were analysed with linear static analyses. For the unnotched component, the notch stress concentration was obviously K t = 1.0. For the notched component, stress concentration factor of K t = 2.5 was found (referring to the net cross section of the notched area).

Symmetry plane

1 MPa

1 MPa

t

b/2

σ mp (MPa)

σ mp (MPa)

7.0

mp (MPa)

σ

σ mp (MPa)

0 2 4 6 8 10

0 2 4 6 8 10

2.0

6.25

0.0

0.0

1.875

K t = 2.5

K t = 1.0

5.50

0.1

0.1

1.75

4.75

1.625

4.0

0.2

0.2

1.50

x (mm)

3.25

x (mm)

0.3

1.375

0.3

2.5

1.25

1.75

0.4

0.4

1.125

1.0

(a)

(b)

1.0

Fig. 6. Finite element models for (a) unnotched component, and (b) notched component. 5. 4R method application

The local material properties based on ultimate tensile strenght and defect sizes are used as inputs in the fatigue strength assessment model. Local hardness based value including strain hardnening could be also used in the analysis. The input values are given in Table 1. The analysis are conducted with neutral residual stress state for unnotched and 400 MPa (+0.5f y ) for shear cut specimens based on measurements with X-ray diffraction technique (Stresstech G3). The procedure for 4R method has been explained e.g., in (Ahola et al., 2020; Lipiäinen, Ahola, Kaijalainen, et al., 2022). The method applies the local cyclic stress at the notch in the Smith-Watson-Topper (SWT) mean stress correction (Fig. 7a). The applied mean stress- corrected stress, Δ σ k,ref , can be expressed as follows (Eq. 1): k k,ref local 1 R     = − , (1) where Δ σ k is the linear-elastic effective stress at the notch, and R local is the local stress ratio obtained based on the minimum and maximum stress, σ min and σ max , at the notch (see also Fig. 7a): min local max R   = (2)