PSI - Issue 77

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

15 5

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

Fig. 2. Thermographic estimation methods: (a) bilinear approach (Luong method); (b) maximum normalized angle change; (c) minimum curvature radius; (d) maximum perpendicular distance to the chord (knee method).

The mean fatigue strengths obtained using the ∆ T s – σ method were 160.3 MPa (GFRP), 130.1 MPa (GFRP-GNPs), and 180.4 MPa (GFRP-HNPs), while the ˙ q – σ method yielded 170.9, 127.9, and 192.2 MPa, respectively. These values were in close agreement with fatigue strengths determined from classical testing at 10 7 cycles presented in Table 1. Importantly, the ∆ T s – σ approach showed an average relative error of only 2 . 7% when compared to σ SN at 10 7 cycles. In contrast, referencing fatigue strengths at 10 6 cycles resulted in a significantly higher average error of 20 . 9%. This point out the importance of selecting an appropriate reference fatigue life when using thermographic technique. Based on observed better accuracy for σ TT referred to N ( σ SN ) = 10 7 , all subsequent relative error evaluations were referred to σ SN at 10 7 cycles. Table 3 reports relative errors for both thermographic methods, excluding results with RMSE values exceeding 0.03, which were considered unreliable in terms of the goodness of fit of data approximation. The ∆ T s – σ approach exhibited an average relative error of 5 . 5%, while the ˙ q – σ approach showed a substantially lower average error of 0 . 6%, indicating higher estimation accuracy, taking into account results obtained using di ff erent estimation methods. Among the estimation techniques, the MPD method ( σ MPD TT ) provided the most accurate and consistent results, with an average relative error of − 5 . 2%for ˙ q – σ and − 1 . 3%for ∆ T s − σ approach. Although the negative sign indicates a tendency toward overestimation, and thus, nonconservative outcomes, it remains the most precise method across the dataset. Although the ∆ T s – σ method shows lower accuracy compared to the ˙ q – σ approach across various estimation techniques, it still provides reliable results when combined with the MPD method.

Table 1. Source data and information on conducted tests and used methods No. Source Material

R [-]

f [Hz]

σ SN (at10 7 cyc.) [MPa]

σ SN (at10 6 cyc.) [MPa]

1 2 3

Amraei and Katunin (2025)

GFRP

241.1 157.5 206.5

180.5 121.0 191.0

-1 -1 -1

40 40 40

Amraei et al. (2025) Amraei et al. (2025)

GFRP-reinforced GNPs GFRP-reinforced HNPs