PSI - Issue 17

Konstantinos Kouzoumis et al. / Procedia Structural Integrity 17 (2019) 347–354 Konstantinos Kouzoumis / Structural Integrity Procedia 00 (2019) 000 – 000

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4.3. Option 3 – Constraint Corrected

A constraint corrected FAL is generated according to equation (6)

(6)

1 ) ] k

( ) [1 ( r r K f L a L  =  + − r

BS 7910 contains analytical solutions for β and L r in the case of uniaxially and equibiaxially loaded plates, however the current geometry does not directly relate to a plate and the T-stress and L r values calculated from FEA are used for the determination of β and consequently equation (6). These values are shown in Table 5. Table 5: Structural constraint parameter ( β ) of specimens ‹ƒš‹ƒŽ‹–› ”ƒ–‹‘ k=0 k=0.5 k=1 k=2 β Ǧ ǦͳǤͳͷͶ ǦͲǤ͸͵͵ ǦͲǤͲͷͳ ͲǤͷͷͳ From Table 5 it is seen that as biaxiality increases the constraint relaxation decreases, i.e. becomes less negative, leading to positive T-stresses and no constraint relaxation at a ratio of k=2 . The resulting graph with the Option 3 and Option 3-constraint corrected FALs along with the FEA derived assessment points are shown in Figure 5.

1.8

2.5

K MC,5%

1.6

K MC,5%

2

1.4

K MC,5%

K MC,20%

1.2

K MC,5%

K MC,5%

K MC,20%

1.5

k=1 k=2

1

K r

K MC,20%

K MC,5%

K r

K MC,20%

K MC,5%

K MC,20%

0.8

1

0.6

k=1

K MC,20%

K MC,20%

k=0.5

0.4

k=0.5

0.5

k=0 - FEA k=0.5 - FEA k=1 - FEA k=2 - FEA

k=0

k=0 - FEA k=0.5 - FEA k=1 - FEA

0.2

k=0

0

0

0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.4

0.6

0.8

1

1.2

L r

L r

Figure 5: Constraint modified Option 3 FALs

Figure 4: Option 3 FAD

Given that for k=2 no constraint relaxation was experienced, that specimen is not included in this analysis and in Figure 5. Additionally, for k=1 constraint relaxation is almost insignificant, and the constraint modified FAL lies on the original Option 3 FAL. For biaxiality ratios of k=0.5 and k=0 the constraint correction seems to widely increase the safe zone of the FAD in accordance with k . Using a very conservative estimate of fracture toughness, i.e. the 5% probability Master Curve value, gives safe results for all the biaxiality ratios. However, with the 20% Master Curve toughness values both k=0 and k=0.5 assessment points would be lying in the safe zone. This could be due to assumptions included in the definition of the constraint dependent fracture toughness curve or the limited dataset out of which the Master Curve originates. In any case it does raise concern over the use of advanced methods in assessing a component without a high number of fracture toughness tests or a conservative definition of K mat .

Concluding remarks

Biaxially and uniaxially loaded cruciform test results have been analysed in accordance with the current BS 7910 and R6 fracture assessment procedures as well as with the use of tailor made FEA analyses. The initial “ A ” assessments generate safe results, i.e. all the failed specimens have been safely predicted to be in the unsafe zone of the FAD, while assessments’ B L r values decrease or increase in a similar manner to the FEA