PSI - Issue 52

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

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Fig. 9. Base drop (height 1.2m) - Plastic strain contour plot of the centre of the base (uncracked model)

6.2. Base centre assessment

Initially, Annex M of BS7910 (2019) was used to calculate K I assuming a plate solution subject to bending and tension. The results indicated that both surface and embedded flaws would not meet existing inspection criteria. Subsequently, Annex N of BS7910 (2019) was applied to consider constraint e ff ects. When comparing results to FEA cracked body models for the calculation of T-stress it was found that enhanced T-stress values could be obtained with FEA - the reason for this is explained in Appendix A of this paper. Quarter symmetry cracked body models were produced for the base centre to represent a plate of dimensions 540mm x 540mm x 105mm with surface and embedded elliptical flaw of 5x25mm (2a x 2c), Fig. 10 and 11. The model was created in Abaqus (2023) and solved using Abaqus / Standard. The crack front was modelled with a spider web mesh and 5 contour integrals were su ffi cient to demonstrate path independence for K and T-stress solutions. The crack tip was modelled to represent a r − 1 / 2 singularity, the mid-side nodes of the collapsed C3D20R elements adjusted to the quarter point position and the nodes at the crack tip dependent on neighbouring elements. The model was loaded in biaxial tension and bending, applying Q m = 92MPa andQ b = 753 MPa. Biaxial loading is considered for T-stress calculations following Annex N of BS7910 (2019). Fig. 10 shows the cracked body model for the 1x5mm surface flaw and the resulting T-stress and K I values about the crack front. The results are summarised in Table 4 and K r is calculated with and without considering constraint e ff ects applied to K mat . It is evident that by consideration of constraint e ff ects the existing inspection criteria can be satisfied.

Table 4. Base centre outer surface 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]

(a x 2c) [mm]

[MPa]

92 92

753 753

540 540

105 105

1x5 1x5

34 34

N / A -410

N / A 50.5

44.6 43.8

1.31 0.87

Fig. 11 shows the cracked body models and results for the 5x25mm embedded flaw (thin ligament p = 1.5mm). Table 5 summarises the results, including the fracture ratio, K r , with and without the e ff ects of constraint. Again, the existing inspection criteria are satisfied with constraint e ff ects applied to K mat .

6.3. Base radius assessment

Initial assessments applying Annex M and P of BS7910 (2019) without taking account of constraint e ff ects resulted in unsatisfactory results for both surface and embedded flaws. Again, cracked body models of a flat plate loaded in