PSI - Issue 77

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

212

6

4.3. Thermal response The prediction of fatigue life also required establishing the relationship between absolute temperature rise and applied stress at different frequencies. For 20, 30, 40, and 50 Hz, experimental results reported in Amraei and Katunin (2025) were employed. At 40 and 50 Hz, the regression models including slopes and intercepts were directly available, while at 20 and 30 Hz the slopes were derived from measured temperature rise-stress ( ∆ ) relations and the intercepts were calibrated to reproduce the measured temperature rise at the fatigue strength. These experimentally determined curves provided the basis for constructing temperature–stress relationships across a wider frequency range. For frequencies not covered experimentally, interpolation and extrapolation procedures were applied under controlled assumptions to maintain physical consistency. At 10 and 15 Hz, the slopes were scaled from the 20 Hz trend, reflecting the reduced contribution of self-heating at lower loading rates. Intermediate frequencies such as 25 and 35 Hz were obtained using cubic Hermite interpolation to preserve smooth transitions between available datasets. For higher frequencies above 50 Hz, extrapolation with moderated slopes and constrained intercepts was used to capture the experimentally observed trend of smaller temperature rises at higher loading rates. In this way, a continuous and physically consistent set of stress–temperature curves were constructed across the 10–100 Hz domain, as shown in Figure 3, and these served as key input for the subsequent entropy-based fatigue life predictions.

390

10 Hz

15 Hz

20 Hz

25 Hz

30 Hz

35 Hz

40 Hz

50 Hz

60 Hz

70 Hz

80 Hz

90 Hz

100 Hz

380

370

360

350

340

330

320

Absolute Temperature, T [K]

310

300

290

0

100

200

300

400

500

600

700

Maximum Stress from Bending,

[MPa]

Fig. 3. Dependency of the absolute thermal response on the applied stress level for a wide range of frequencies from 10 to 100 Hz.

4.4. Fatigue life prediction using fracture fatigue entropy concept The final step involved predicting the fatigue life of the composite using FFE framework, which links the energy dissipated per unit volume with the corresponding thermal response and frequency-dependent effects. The regime based FFE values for low-cycle, intermediate-cycle, and high-cycle fatigue were taken from the earlier study of Amraei and Katunin (2025). By combining the damage-induced heat dissipation rates established in this work with the absolute temperature–stress relationships derived for each frequency, frequency-dependent stress-life ( ) curves were constructed for the entire range of 10–100 Hz, as presented in Fig. 4. The predictions demonstrate a strong dependence of fatigue life on loading frequency. At lower frequencies (10– 20 Hz), lifetimes exceed 10 6 cycles for moderate stress amplitudes, whereas with increasing frequency, fatigue life decreases sharply due to the combined effects of reduced fatigue strength, higher levels of damage-induced heating, and accelerated entropy accumulation. At 100 Hz, the fatigue life drops below 10 4 cycles even at relatively low stress