PSI - Issue 82

4

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

47

(1 − η ) R 2

2 o

(1 − η ) R 2

2 o

R 2

2 o

R 2

2 o

i − η R o − R

i R

i − η R o − R 2 i

i R

σ θθ ( r ) P i

σ rr ( r ) P i

;

(4)

2 i −

=

=

+

2 i ) r

2 i ) r

R 2

( R 2

2

R 2

( R 2

2

o − R

o − R

3. Results and Discussions

3.1. Stress Distribution in the Uncracked Annulus

A parametric study using MATLAB was carried out to analyze radial and hoop stress distributions in thick-walled cylinders under varying pressure ratios and geometries, based on normalized Lame´ eqs. (4). The results in Fig. 2 show that at low pressure ratios, the hoop stress peaks near the inner surface due to high circumferential tension, while increasing external pressure flattens the distribution. Radial stress varies from compressive at the inner surface to tensile or compressive at the outer surface depending on the pressure ratio, with higher external pressure making the outer surface compressive beyond η > 0 . 5. Geometry also plays a key role—thinner cylinders ( R i / R o close to 1) exhibit steeper stress gradients and higher hoop stress peaks, whereas thicker ones show smoother, more uniform distributions that enhance structural stability. Overall, the combined influence of pressure ratio and wall thickness governs the stress response, providing a normalized basis for the T-stress evaluations.

1.5

0

2

1

1.5

-0.2

1

0.5

-0.4

0.5

0

-0.6

0

-0.5

-0.8

-0.5

-1

-1

-1

0

0.2 0.4 0.6 0.8

1

0

0.2 0.4 0.6 0.8

1

0

0.2 0.4 0.6 0.8

1

(a)

(b)

(c)

Fig. 2: Normalized (a) radial and (b & c) hoop stress distributions in an annulus with (a & b) R i / R o = 0 . 2 and (c) R i / R o = 0 . 6 for varying pressure ratios η = P o / P i .

3.2. Evaluation of T-stress in Inner and Outer Edge Cracked Annuli Using Weight Functions

The T-stress component was evaluated for double-edge cracked circular rings using the weight function method, with the uncracked stress field obtained from the parametric Lame´ formulation. Four annular geometries, characterized by radius ratios R i / R o = 0 . 2 , 0 . 3 , 0 . 5 , and 0 . 6, were analyzed to represent progressively thinner configurations. For each geometry, the normalized crack length a / w was varied from 0.2 to 0.7, while the pressure ratio η = P o / P i was incremented from 0 to 1.0 in steps of 0.2. The normalized T-stress, defined as T / P i , was determined from the corresponding weight function integrals for each crack configuration and loading condition. 3.2.1. T-Stress Behavior in Inner Edge Cracked Annuli Figure 3 illustrates the variation of normalized T-stress ( T / P i ) with normalized crack length ( a / w ) for di ff erent annular geometries and pressure ratios. For the thickest configuration ( R i / R o = 0 . 2), the T-stress remains negative for η = 0 . 0 and 0 . 2 across all crack lengths, indicating a uniformly low crack-tip constraint. However, for higher pressure ratios ( η = 0 . 4–1 . 0), the T-stress, initially negative at small crack lengths, transitions to positive values as a / w increases, signifying a gradual shift from a compressive to a tensile stress state ahead of the crack tip. A similar trend is observed for R i / R o = 0 . 3, where lower pressure ratios ( η ≤ 0 . 4) yield entirely negative T-stress profiles, while