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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0.2 0.3 0.4 0.5 0.6 0.7 -1

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

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

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0.2 0.3 0.4 0.5 0.6 0.7

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

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

Fig. 3: Variation of normalized T-stress ( T / P i ) with normalized crack length ( a / w ) for five inner 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.

higher pressure ratios ( η ≥ 0 . 6) lead to a transition from negative to positive values with increasing crack length. For R i / R o = 0 . 5, the T-stress remains negative for η = 0 . 0–0 . 8, becoming positive only for η = 1 . 0 at longer cracks ( a / w ≳ 0 . 6), reflecting a marginal increase in crack-tip constraint. In contrast, for the thinnest annulus ( R i / R o = 0 . 6), the T-stress remains consistently negative for all pressure ratios and crack lengths, indicating a persistently low level of constraint. Overall, the results demonstrate that as the annulus becomes thinner (increasing R i / R o ), higher external-to internal pressure ratios are required for the T-stress to attain positive values. Positive T-stress corresponds to elevated crack-tip constraint and a more brittle-like fracture tendency, whereas negative T-stress indicates reduced constraint and enhanced ductile behavior. Thus, for thin annuli, the dominance of negative T-stress suggests a lower susceptibility to brittle fracture under combined pressure loading. 3.2.2. T-Stress Behavior in Outer Edge Cracked Annuli Figure 4 shows the variation of normalized T-stress ( T / P i ) with normalized crack length ( a / w ) for outer-edge cracked annuli with radius ratios R i / R o = 0 . 2 to 0 . 6. Each subfigure corresponds to a specific geometry and includes curves for di ff erent pressure ratios η = P o / P i . In all cases, the T-stress values remain negative, indicating a low constraint crack-tip environment. Compared to the inner-cracked configurations, the magnitude of negative T-stress is smaller and its variation with crack length is more gradual. As the crack length increases, T-stress becomes less