PSI - Issue 77

Jafar Amraei et al. / Procedia Structural Integrity 77 (2026) 207–214 Author name / Structural Integrity Procedia 00 (2026) 000–000

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The current study builds on previous advances by predicting the heat dissipation rate induced by fatigue damage evolution and consequently employing the regime-based FFE concept for fatigue life prediction of PMCs under a wide range of loading frequencies from 10 to 100 Hz, and different loading regimes. By incorporating the FFE-based framework, this study aims to provide a more generalized and reliable methodology that minimizes experimental effort while enabling accelerated life prediction of fatigue-loaded PMCs. 2. Thermodynamic process of entropy generation for fatigue life prediction During cyclic loading, heat generation in PMCs is primarily due to their thermoviscoelastic behaviour, with most dissipated energy converting to heat under loading frequencies above 10 Hz. When a fatigue-loaded PMC reaches a stabilized self-heating temperature (phase II), the heat stored balances the heat dissipated: ̇ = ̇ = − | = , (1) where is density, is the heat capacity, and ⁄ represents the cooling rate exactly after unloading at time . For glass/epoxy composites, varies with temperature as (Kalogiannakis et al., 2004): = 828.7 + 2.71 ∙ (°C), (2) Below the fatigue strength, heat dissipation arises mainly from recoverable internal friction (i.e., ̇ = ̇ ) while above the fatigue strength, additional irreversible heat is generated by damage ( ̇ ), so that: ̇ = ̇ + = ̇ + ̇ . (3) The heat dissipation rate induced by damage ( ̇ ) can be determined as a function of stress by: ̇ = ̇ + ( ≥ ) − ̇ ( < ). (4) By implementing the second law of thermodynamics, the total volumetric entropy generation ( ) can then be quantified by (Huang et al., 2020): FFE= � ̇ 0 . (5) The cumulative entropy, termed as FFE, generated for multiple load levels within increasing amplitude testes (IATs) can be determined using (Mehdizadeh and Khonsari, 2018): FFE= � ̇ =1 , (6) where indicates the number of load levels, is the loading frequency, is the stabilized temperature in Kelvin, denotes the number of load cycles, and ̇ is the damage-induced heat dissipation rate at the -th step. Once the FFE is determined for the fatigue-loaded PMCs under different fatigue regimes, fatigue life for arbitrary stress levels above the fatigue strength value for a given loading frequency can be estimated using: ( , )=FFE ∙ ( , ) ̇ ( , ) . (7) However, applying Eq. (7) requires establishing the relationship between the thermal response, loading frequency, and applied stress. In particular, it is necessary to capture how stabilized temperature and heat dissipation vary with frequency and stress level, as these correlations govern the accurate prediction of fatigue life. 3. Materials and testing procedure The investigated composite was the glass-fiber reinforced epoxy laminate (EP GC 201, Izo-Erg S.A., Poland), consisting of 14 layers of unidirectional plies with a 200 g/m² plain weave E-glass fabric. Specimens were cut into rectangular geometry with dimensions of 100 × 10 × 2.4 mm³ and an effective span length of 39 mm.