PSI - Issue 20

Nikolay A. Makhutov et al. / Procedia Structural Integrity 20 (2019) 9–16 Nikolay A. Makhutov et al. / Structural Integrity Procedia 00 (2019) 000 – 000

14

6

2

2

2

€

€ €

€

1

1

2

2

3

3

en D K

,

(13)

D

€ € 2 1

2

3

where K D the material constant lies in the range K D = 0.8-1.3. Let K D =1 than D en =0.577 and 0.098 v iuF iuF en e e D ,

(14)

where superscript “ν” designates a volumetric strain. On the basis of the given above design data and according to (11) the intensity of nominal fracture stresses is σ v icF = 598MPa. For an undamaged pipeline if σ 3 << σ 1 and μ=0.5.

1 0.85 , 0.89 , e

i

(15)

i e

1

The first true principle stress will amount to σ 1 F =σ θ F =598/0.85=703MPa. Taking into account the reduction of ψ uF and the wall thickness at fracture:

1 (1 ) F uF .

(16)

1

c

c

Here ψ uF is defined by the relationship: 1 ln 1 i u F u F e ,

(17)

with e iuF =0.17, ψ uF =0.156, σ θc =593MPa. The fracturing pressure will be defined by the expression:

2

p

.

(18)

c

c

D

0

Then for the considered undamaged pipeline p c =17.8MPa. The allowable pressure [ p ] can be estimated as:

0 2 , y u y u D n n

[ ] 2[ ] p

.

(19)

D

0

min

For n y =1.25 and n u =1.7 one will get [ p ]=7.68MPa. Pressure [ p ] is lower than fracturing pressure p c for an undamaged pipeline and the safety factor for limit pressure equals to 2.32. If in the process of pipeline operation, an asymmetric crimp occurs, then according to experimental data the maximal local elasto-plastic strain in the crimp will be e max cr =27%. For K age =1.3 one can estimate the residual plasticity of metal in the crimp zone (Fig. 2):

1

ln

e

D

age K e

.

(20)

max

c cr

en

cr

1

c F

The plasticity of metal defined by relation (20) equals 0.037, which is essentially (24.7 times) lower than the initial one e c that was obtained using formula (5) and 4.6 times lower than fracture strain e iuc of the undamaged pipe calculated using relation (14).