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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4.2. Heat dissipation rate induced by fatigue damage To extract the irreversible energy release that drives structural degradation, the reversible frictional contribution represented by Line I in the original trilinear model (Amraei and Katunin, 2025) was subtracted from the total dissipation release using Eq. (4). The plotted curves in Fig. 2 illustrate only the heat generated by damage processes under fatigue loading for different loading frequencies, ranging from 10 to 100 Hz. Figure 2, therefore, shows the heat dissipation rate induced by damage extracted from increasing and constant amplitude tests (IATs and CATs), represented by Lines II and III, respectively, after subtraction of the frictional term, so that the frictional term itself is not shown. Removing the frictional contribution is essential, because it excludes recoverable energy exchanges and leaves only the irreversible heating that produces entropy and directly correlates with progressive structural damage. For the frequencies of 20, 30, 40, and 50 Hz, the stress boundaries of these regimes were determined directly from experimental observations. To extend the model to other frequencies within the 10–100 Hz range, the upper limit of stress within the Line II was scaled in proportion to the reduction in fatigue strength. For example, the decrease of approximately 20% in fatigue strength due to the increase of frequency from 50 to 60 Hz was reflected by a corresponding 20% stress reduction in the Line II boundary. The upper stress boundary of the damage-dominated regime (Line III) was then extrapolated based on the empirical observation that it consistently occurs at stress levels about one-third higher than the Line II boundary. This procedure preserves continuity with measured behaviour while extending the damage-driven heat dissipation model ( − ) across the full frequency range. The resulting − curves exhibit a clear dependency on both stress and frequency: damage-induced heat dissipation increases with stress amplitude, and for a given stress level, the irreversible heating grows with loading frequency. These trends highlight why damage-induced heating, rather than total heat generation, must be used as the thermodynamic driving variable in entropy-based life prediction, providing the critical thermodynamic input required for subsequent fracture fatigue entropy calculations and the fatigue-life predictions presented in this study.

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Fig. 2. Relationship between the applied stress and the heat dissipation rate response induced by fatigue damage for different loading frequencies, ranging from 10 to 100 Hz.