PSI - Issue 75

Sgamma M. et al. / Procedia Structural Integrity 75 (2025) 709–718 Author name / Structural Integrity Procedia 00 (2025) 000–000

710

2

In response to these challenges, frequency-domain methods have gained prominence as e ffi cient and statistically reliable alternatives [4, 29, 40, 25, 35]. Unlike their time-domain counterparts, frequency-domain techniques uti lize statistical characteristics derived from the Power Spectral Density (PSD) of stress or strain signals. By directly interpreting PSD data, these methods eliminate cumbersome cycle-counting procedures and considerably reduce com putational e ff orts, making them especially advantageous in contexts involving random vibration environments. Con sequently, frequency-domain approaches o ff er engineers a robust yet computationally lean alternative to traditional fatigue analyses, delivering both practicality and accuracy [12, 3, 19, 11, 37, 33]. Among established multiaxial fatigue criteria, the Critical Plane (CP) approach, notably represented by the Fatemi–Socie criterion (FSC), has demonstrated high reliability and correlation with experimental results across var ious materials and loading conditions. The FSC’s key strength lies in its explicit consideration of the orientation dependence of crack initiation, e ff ectively accounting for non-proportional loading e ff ects common in real-world ap plications [17, 8, 36, 23, 31, 9]. However, the classical FSC implementation remains predominantly time-domain oriented, creating a clear gap when attempting to extend its application to frequency-domain analysis [28, 29, 39]. Bridging this gap involves addressing substantial theoretical and practical issues, primarily concerning the probabilis tic representation of stress and strain conditions and the statistical identification of the critical damage plane. This paper aims precisely at filling this gap by introducing and validating an adaptation of the FSC suitable for frequency-domain applications, specifically tailored for Gaussian random load scenarios. By employing statistical methodologies and PSD-based formulations, the proposed adaptation provides an e ffi cient yet rigorous approach to identifying critical damage planes and assessing multiaxial fatigue life without resorting to extensive cycle-counting. Furthermore, the approach facilitates practical integration of mean stress e ff ects, an important consideration for accu rate multiaxial fatigue predictions under realistic operating conditions [34, 9, 27]. In 1988, Fatemi and Socie introduced a critical-plane methodology for multiaxial fatigue [17]. Under this frame work, the fatigue parameter P FS is assumed to remain constant for various loading configurations at a given fatigue life N f . They define this parameter as: P FS = γ a , max 1 + k σ n , max σ y = const , (1) where γ a , max is the maximum shear strain amplitude on the critical plane, σ n , max is the corresponding maximum normal stress, σ y represents the yield strength, and k is a material constant. The ratio σ n , max /σ y ensures that the term inside the parentheses in equation 1 remains dimensionless. Since P FS must align with a shear strain-based fatigue characteristic, Fatemi and Socie also related P FS to the shear strain fatigue curve: 2. Fatemi–Socie Criterion

τ ′ f G

b 0

c 0 ,

+ γ ′ f (2 N f )

(2 N f )

(2)

P FS =

where τ ′ f is the fatigue strength coe ffi cient for shear stress, G is the shear modulus, and γ ′ f denotes the fatigue ductility coe ffi cient in torsion. The exponents b 0 and c 0 arise from experimentally determined shear strain–life data. In practice, however, it is often di ffi cult to obtain experimental torsional data from strain-controlled tests on un notched tubular specimens. Consequently, Fatemi and Kurath derived an alternative formulation [16]: