PSI - Issue 72

552 José A.F.O. Correia / Procedia Structural Integrity 72 (2025) 547–556 The local fatigue criteria determine fatigue failure using a parameter ψ , which usually decreases as total life increases, represented by ψ=q(N f ) (12) Then, the generic power function, given by Figure 4, used to describe the material fatigue curve based on local criteria (e.g., stress, strain, energy), can be written as ψ=κ(2N f ) α +ψ 0 (13) where ψ 0 is the fatigue limit, κ is the fatigue resistance coefficient corresponding to the fatigue parameter, and α is the fatigue resistance exponent to the fatigue parameter.



Log 

α

1

 0

2N L

Log (2N f )

Fig. 4. Generic power law to describe fatigue life resistance (adapted from Correia et al., 2017). The ψ parameter can be represented by various fatigue parameters based on stress, strain, and energy methods. For example: ψ=σ a (14) ψ=ε a (15) ψ=σ max ∙ε a =SWT (16) ψ=ε a ( 1 2 - R ) 1 - γ̂ =ε a,w (17) ψ=∆W t = 1 - n ' 1+n ' ∙∆σ∆ε P + 2 1 E ( ∆ 2 σ +σ m ) 2 (18) In these equations, the following variables are defined:

- σ a : Stress amplitude; - ε a : Strain amplitude; - σ max : Maximum stress; - : Smith-Watson-Topper parameter; - R : Strain ratio; - γ̂ : Walker fitting constant; - ε a, : Walker-type strain amplitude;