PSI - Issue 77

Tomasz Rogala et al. / Procedia Structural Integrity 77 (2026) 11–17 Tomasz Rogala et al. / Structural Integrity Procedia 00 (2026) 000–000

16

6

Table 2. Fatigue strength σ TT results obtained using di ff erent thermographic approches ∆ T s − σ , ˙ q − σ and with the application of di ff erent estimation methods BL, AC, MCR, MPD T s − σ ˙ q − σ No. σ BL TT / RMSE σ AC TT / RMSE σ MCR TT / RMSE σ MPD TT / RMSE σ BL TT / RMSE σ AC TT / RMSE σ MCR TT / RMSE σ MPD TT / RMSE

173.2 ∗ / 0.021 135.5 / 0.031 191.6 / 0.019

186.9 ∗ / 0.018 152.0 / 0.042 204.7 / 0.022

1

151.5 / 0.034 147 / 0.043 183.6 / 0.021

140.6 / 0.027 111.8 ∗ / 0.023 159.0 ∗ / 0.011

176.2 / 0.027 126.1 ∗ / 0.023 195.3 ∗ / 0.011

148.3 / 0.069 124.5 / 0.039 204.7 / 0.022

160.7 / 0.018 109.0 ∗ / 0.016 162.6 ∗ / 0.011

187.8 / 0.018 125.9 ∗ / 0.016 196.9 ∗ / 0.011

2

3

∗ value reported in the source

Table 3. Comparison of fatigue strength estimation using ∆ T − σ approach and ˙ q − σ with reference to N ( σ SN ) = 10 7 cycles T s − σ ; N ( σ SN ) = 10 7 ˙ q − σ ; N ( σ SN ) = 10 7 No. σ SN − σ BL TT σ SN − σ AC TT σ SN − σ MCR TT σ SN − σ MPD TT σ SN − σ BL TT σ SN − σ AC TT σ SN − σ

MCR TT

MPD TT

σ SN − σ

σ SN

σ SN

σ SN

σ SN

σ SN

σ SN

σ SN

σ SN

1 2 3

4.0

- -

22.1

2.32 -4.2 -2.2

-3.5

- -

10.9

-4.0 -4.0 -7.7

-

7.6

-

9.9

-0.3

3.9

16.7

14.8

-3.1

-7.7

5. Conclusions

This study demonstrated the e ff ectiveness of thermographic methods for estimating fatigue strength in polymer ma trix composites (PMCs), specifically GFRP materials, and GFRP reinforced with graphene and hybrid nanoparticles. By comparing classical high-cycle fatigue (HCF) test results with thermographic estimates obtained through ∆ T s – σ and ˙ q – σ approaches, it was shown that thermographic techniques can yield accurate fatigue strength predictions when appropriate reference cycles are used. Among the approaches evaluated, the ˙ q – σ approach consistently provided lower relative errors compared to ∆ T s – σ , with an average estimation error of just 0 . 6% when referenced to fatigue strength at 10 7 cycles for the results estimated usingdi ff erent methods. The MPD method further proved to be the most reliable estimation technique, independently of the applied approach ˙ q – σ or ∆ T s – σ , o ff ering the highest accuracy despite a slight tendency toward nonconser vative overestimation. These results underscore the importance of both reference selection and method selection in thermographic fatigue evaluation.

Acknowledgements

This work was supported by the Rector’s Pro-Quality Grant at the Silesian University of Technology (grant number: 10 / 060 / RGJ25 / 2062), under the Initiative of Excellence - Research University (IDUB) program.

References

Adam, T.J., Horst, P., 2017. Fatigue damage and fatigue limits of a gfrp angle-ply laminate tested under very high cycle fatigue loading. International Journal of Fatigue 99, 202–214. doi: 10.1016/j.ijfatigue.2017.01.045 . Amraei, J., Katunin, A., 2022. Recent advances in limiting fatigue damage accumulation induced by self-heating in polymer–matrix composites. Polymers 14, 5384. doi: 10.3390/polym14245384 .