PSI - Issue 80

Yuhang Pan et al. / Procedia Structural Integrity 80 (2026) 43–52 YuhangPan / Structural Integrity Procedia 00 (2023) 000–000

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length prediction. Among them, γ ′ exhibits distinct advantages over β ′ : in addition to achieving baseline free monitoring, it facilitates fully automated in-service crack detection, thereby enhancing the robustness and practical applicability of the method in real-world engineering contexts. Building upon these findings, the present work applies the Dynamic Piecewise Linear (DPL) method, originally introduced in Pan et al. (2025), to the experimental data obtained in this paper. The DPL method dynamically performs piecewise linear fitting of harmonic parameters, enabling e ff ective segmentation and feature extraction across di ff erent stages of crack growth. Importantly, this analysis is conducted without reliance on prior baseline information. The results obtained from the DPL method on specimen T1 are presented in Fig. 5.

Fig. 5: Results of crack detection based on γ ′ : (a) The change of the γ ′ with respect to the fatigue loading cycles on T1, (b) The running details of dynamic fitted lines between second and third stage, (c) The di ff erent fatigue stages divided by the DPL method, and the crack size detected by the method. Fig. 5 presents the results obtained using the proposed DPL method. As shown in Fig. 5(a), the change of γ ′ during the fatigue process can be divided into three distinct stages. In the initial stage, γ ′ exhibits a sharp increase as the number of fatigue cycles increases. This is followed by a decreasing trend, reaching its minimum around 12,000 cycles. In the subsequent stage, γ ′ gradually rises again and stabilizes within the range of approximately 1 . 6 × 10 − 3 to 1 . 7 × 10 − 3 . Once γ ′ exceeds 1.7, its value starts to increase rapidly, marking the onset of the final stage. Notably, this rapid growth phase is well aligned with the trend of mea surable crack propagation, as shown by the crack length curve. This correlation suggests that the transition point between the second and third stages represents a critical indicator for crack detection. To further quan tify this behaviour, the DPL method was applied to fit the data, as illustrated in Fig. 5(b). During the early stage of fatigue loading, the slope of the fitted segments obtained from di ff erent moving windows remains relatively high. As the loading progresses, the slope gradually decreases, and distinct ”spikes” appear at the transition points due to the reduced degree of overlap between fittings. The final classification results derived from the DPL method are presented in Fig. 5(c). Three fatigue stages are clearly identified, and the method