PSI - Issue 52

A.D. Cummings et al. / Procedia Structural Integrity 52 (2024) 762–784 A. Cummings / Structural Integrity Procedia 00 (2023) 000–000

777

16

(a)

(b)

(c)

(d)

Fig. 10. Cracked body model and contour integral results for a 1x5mm (a x 2c) surface breaking, semi-elliptical flaw in the base centre. K I and T-stress calculated with FEA - where φ = 0 ◦ is at the free surface and φ = 90 ◦ is at the deepest point within the body (a) 1 / 4 symmetry cracked body model (b) Mesh at crack tip (c) K I about crack front (d) T-stress about crack front

Table 5. Base centre embedded flaw assessment Q m Q b W B

c mat

Flawsize

K mat

T-stress

K

K I

K r

[MPa.m 0 . 5 ]

[MPa.m 0 . 5 ]

[MPa.m 0 . 5 ]

[MPa]

[MPa]

[mm]

[mm]

(2a x 2c) [mm]

[MPa]

92 92 92 92

753 753 753 753

540 540 540 540

105 105 105 105

2x7

34 34 34 34

N / A N / A -819

N / A N / A 86.4

44.1 73.7 43.0 78.1

1.30 2.17

5x25

2x7

0.5

5 x25

-1014

116.2

0.67

tension and bending were used to predict T-stress and K I . In this instance the models were only loaded in the crack opening direction as stresses perpendicular to the flaw were low. The value of L r = 0.67 is calculated applying Annex P BS7910 (2019) for σ ref , from the integrated stress lineariza tion across the section, which essentially removes the peak stress component. The K r values are calculated applying the membrane and bending stress components linearised across the 1mm flaw depth. The results for K r are calculated with and without consideration of the e ff ects of constraint, see Table 6. Table 7 shows the results of the embedded flaw assessment. Again, the L r values are calculated based on the inte grated stress linearization across the section using Annex P solutions from BS7910 (2019). The K r values calculated based on bending and membrane stresses linearised across an embedded flaw with a ligament plus flaw depth of