PSI - Issue 14

V. Viswanath et al. / Procedia Structural Integrity 14 (2019) 442–448

447

V Viswanath/ StructuralIntegrity Procedia 00 (2018) 000 – 000

6

The crack FAP is computed using the stress intensity factor from an elastic analysis and the reference stress at the given load. Lr is evaluated using the equation (4) where  ref is the reference stress at the evaluation load, usually the design or operation load.



ref

r L



(4)



y

The Kr value is computed using the elastic stress intensity, KI, and the material toughness Kmat with equation (5):

r K K K 

I

(5)

mat

K I is evaluated using the Newman-Raju relation given by Newman et al (1984). The stress at the assumed weld crack location has two components namely due to tank internal pressure and due to residual stress. In fracture analyses, the stress arising from the applied mechanical load, in the current case internal pressure, is classified as primary stress. While the residual stress due to welding is classified as secondary stress. Secondary stresses being self equilibrating across the structure, the net force and bending moment are zero as has been explained earlier in section 2. This separation is imperative since primary stresses contribute to plastic collapse while secondary stresses do not. However, the K factor determination is based on both primary and secondary stresses, with only the primary stresses accounted for the determination of reference stress for evaluation of ligament yielding factor Lr. For small scale yielding, KI may be taken to be the sum of p I K and s I K . However, the situation becomes complicated for contained and net-section yielding due to plasticity and relaxation effects where in the resulting K-factor is no longer the sum of p I K and s I K . In such cases, an additional interaction or correction term, ‘V’, is incorporated, where in, Kr is given by equation (6)

mat K K K V K    p I r

s

I

(6)

A simplified route for evaluation of ‘V’ is given in Zerbst et al (2007) which is used in this paper. In absence of availability of fracture toughness corresponding to tank thickness, the plane strain fracture toughness is used for K mat . FAD for tank weld material is given in Fig 6.It may be noted that s I K exists even in absence of any loading (primary stress). Therefore, the origin of the loading curve in FAD shifts to (0, s I K ). Point ‘A’ on FAD is the FAP corresponding to crack 3. Table 1 gives the parameters and MOS against failure in presence of the three cracks.

Table 1: Margin of safety (MOS) for the three assumed cracks at weld location

s MPa  m

I p MPa  m

p , N/mm 2

Crack No

Surface crack size (2c x a)

K I

K

V

L

K r

MOS



r

Crack 1 Crack 2 Crack 3

7.62 x 0.76 3.3 x 1.65 6.44 x 3.22

5.12 5.31 8.62

4.31 4.47 7.26

80 80 80

1.143 1.143 1.143

0.5714 0.5714 0.5714

0.409 0.424 0.689

0.67 0.65 0.23

Fig. 6.Failure Assessment Diagram (FAD) for the nozzle weld region in presence of residual stress.