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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1. Introduction Polymer-matrix composites (PMCs), including carbon and glass fiber-reinforced polymers (CFRPs and GFRPs), are increasingly used in the energy (e.g., wind turbines) and transportation sectors (e.g., aviation, rail, and marine) owing to their excellent strength-to-weight ratio, longevity, environmental durability, and design flexibility. Nevertheless, the lack of knowledge of their fatigue responses necessitates conservative design approaches, often resulting in over-designed structures to mitigate the risk of significant damage accumulation under prolonged cyclic loading and prevent premature failure. This not only imposes the weight and cost penalties but also limits the structural design optimization. Therefore, understanding the fatigue response of PMCs under different loading regimes is essential for developing predictive fatigue strength and life models. A central challenge in fatigue research is to characterize the material response across the entire spectrum of loading regimes, from low- to very-high-cycle fatigue (Amraei et al., 2024a). Conventional fatigue testing at low frequencies (≤5 Hz) is often impractical . For example, a single fatigue test reaching 10 9 cycles would take over six years at 5 Hz, nearly one-fifth of an aircraft’s service life. Accelerated testing at higher frequencies is a practical pathway. However, due to the viscoelastic nature of polymers (Amraei et al., 2024b), high-frequency loading results in the self-heating effect, and consequently, thermo-mechanical synergy occurs. The self-heating phenomenon generally follows three phases (Amraei and Katunin, 2022): (i) an initial rapid temperature increase primarily driven by friction, (ii) a quasi-stabilized regime where heat generation and dissipation reach equilibrium, and (iii) a sudden thermal acceleration linked to damage accumulation and softening. The transition between stable and unstable regimes is marked by a critical self-heating temperature, frequently used as a parameter for the determination of the beginning of rapid fatigue damage accumulation (Katunin et al., 2017; Amraei and Katunin, 2025). If the temperature increase is limited (e.g., <3 °C), self-heating can even be implemented as an alternative heat source for the non-destructive damage assessment of composite structures (Amraei et al., 2025a). Otherwise, excessive heating accelerates micro- and macro-scale damage such as interfacial debonding, matrix cracking, fiber breakage, and delamination (Rose et al., 2021; Katunin et al., 2025; Amraei et al., 2024a). To reduce experimental demands, thermographic approaches have been developed to estimate fatigue strength and life based on temperature evolution. Pioneering works, such as Luong’s Δ − approach (Luong, 1998; La Rosa and Risitano, 2000; Huang et al., 2020; Palumbo et al., 2016; Pathak et al., 2025), estimate fatigue strength by correlating stabilized temperature rise with applied stress levels. Alternative techniques based on heat dissipation analysis (Amraei and Katunin, 2025; Amraei et al., 2025b) have also demonstrated effectiveness for fatigue strength determination. These approaches significantly reduce testing duration, while their applicability and accuracy may be dependent on material type and testing conditions. For example, under fully reversed bending, the heat dissipation–stress ( ̇ − ) method has been reported to provide closer agreement with fatigue strength values obtained from conventional stress– life ( − ) curves compared to the Δ − approach (Amraei and Katunin, 2025; Amraei et al., 2025b). Furthermore, entropy-based approaches provide a robust framework for evaluating the influence of self-heating on fatigue response of PMCs, as they remain applicable across different loading frequencies and regimes. Within this context, entropy generation, governed by the second law of thermodynamics (Mohammadi and Mahmoudi, 2018), is influenced by parameters such as loading type (Mehdizadeh and Khonsari, 2021), environmental temperature (Amooie and Khonsari, 2023), applied stress level, and loading frequency (Mehdizadeh and Khonsari, 2018; Amooie et al., 2023). Since entropy generation is inherently linked to irreversible processes, the fracture fatigue entropy (FFE) concept has been proposed as a material property, which aims to predict fatigue response of composites. By applying the first and second laws of thermodynamics, FFE accounts for energy dissipation through matrix cracking, fiber fracture, delamination, and interfacial debonding. Several studies have demonstrated the potential of entropy-based models for predicting fatigue life in composite materials (Huang et al., 2020; Mohammadi and Mahmoudi, 2018; Naderi and Khonsari, 2013; Mahmoudi and Mohammadi, 2019; Huang et al., 2022; Premanand et al., 2024; Premanand and Balle, 2025). Despite these advancements, most existing studies assumed a constant heat capacity ( ) and applied a single average FFE value to predict the fatigue life of PMCs. More recent investigations have addressed these shortcomings by considering temperature-dependent and defining regime-based FFE values for low- (up to 10 5 cycles), intermediate- (between 10 5 and 10 6 cycles), and high-cycle (above 10 6 cycles) fatigue (Amraei and Katunin, 2025).