PSI - Issue 82

M.S. KannanKulavan et al. / Procedia Structural Integrity 82 (2026) 44–50 KannanKulavan et al. / Structural Integrity Procedia 00 (2026) 000–000

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negative, approaching zero for higher pressure ratios. The influence of pressure ratio is also less pronounced for outer cracks—while increasing η reduces the magnitude of T-stress, the e ff ect is weaker than that observed in inner-cracked geometries. Overall, these results suggest that outer-edge cracks experience persistently low constraint levels and are less sensitive to geometric and loading variations under combined pressure loading.

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(a) R i / R o = 0 . 2

(b) R i / R o = 0 . 3

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(c) R i / R o = 0 . 5

(d) R i / R o = 0 . 6

Fig. 4: Variation of normalized T-stress ( T / P i ) with normalized crack length ( a / w ) for five outer double edge cracked annular geometries with radius ratios R i / R o = 0 . 2 to 0 . 6. Each subfigure presents results for a specific geometry, showing the influence of pressure ratio η = P o / P i on constraint behavior. The curves are obtained using weight function integration with stress fields derived from the parametric Lame´ solution. An additional observation at higher radius ratios reveals a distinct convergence behaviour (leading to a concurrent point) among the normalized T-stress ( T / P i ) curves for di ff erent pressure ratios. For inner-edge cracked annuli with R i / R o = 0 . 5and0 . 6, the curves merge near a / w ≈ 0 . 3, indicating that beyond this point, the T-stress becomes primarily governed by geometry rather than loading. In contrast, outer-edge cracked annuli exhibit a similar convergence at larger crack lengths around a / w ≈ 0 . 7, where the influence of pressure ratio diminishes. This behavior suggests that, for both crack locations, there exists a geometry-dominated regime where the constraint state becomes nearly invariant to loading, occurring earlier for inner cracks than for outer ones.

4. Conclusion

This study examined the T-stress behavior in double-edge cracked circular annuli subjected to combined internal and external pressure using the weight function method integrated with the parametric Lame´ formulation. The re-