PSI - Issue 75

Okan Yılmaz et al. / Procedia Structural Integrity 75 (2025) 435 –441 O. Yılmaz and D. Van Hoecke / Structural Integrity Procedia 00 (2025) 000–000

438

4

Component Wöhler (S-N) curve (P RAM - N)

Material properties for steel

Shifting factors

Calculation of fatigue initiation life

Linear elastic FEA

P RAM damage parameter

Neuber’s method

Fig. 3. Calculation routine to construct component Wo¨hler curve per material, P RAM damage parameter, and fatigue crack initiation life.

We start with the finite-element simulation of the formed specimen. Using an elastoplastic material model, the ma terial is bended to 90°. Then, the deformed mesh is used as an input for the linear elastic analysis of the specimen under fatigue loading. The result of the analysis is then used to calculate P RAM , an adaptation of the Smith-Watson-Topper (SWT) damage parameter (Smith et al., 1970) including the mean stress e ff ects. Figure 3 presents the calculation routine to construct component Wo¨hler curve per material, P RAM damage parameter, and fatigue crack initiation life. P RAM damage parameter is denoted with P RAM =  ( σ m + k · σ a ) · E · ε a , (1) where σ m is the mean stress, σ a and ε a are is the mean stress and strain amplitudes, E is the Young’s modulus, and k is a parameter to include the mean stress e ff ects. k is calculated using a material dependent mean stress sensitivity term, M σ : k =   M σ · ( M σ + 2) for σ m ≥ 0 M σ 3 ·  M σ 3 + 2  for σ m < 0 . (2) Mean stress sensitivity term is a function of the ultimate tensile strength R m and obtained through the following equation where a M and b M are material constants.

M σ = a M · 0 . 001 · R m + b M .

(3)

Fatigue life for the component as a function of the damage parameter P RAM is calculated as

N =  

P RAM , Z  P RAM , Z 

10 3 ·  P RAM 10 3 ·  P RAM

1 / d 1

for P RAM ≥ P RAM , Z for P RAM < P RAM , Z ,

(4)

1 / d 2