PSI - Issue 18

Chmelko, V., Berta, I./ Structural Integrity Procedia 00 (2019) 000 – 000

4

Vladimír Chmelko et al. / Procedia Structural Integrity 18 (2019) 600–607

603

Fig. 2 The bilinear material model parameters as an approximation of true tensile diagram.

Putting relations 12 into eq. (11) and applying physically clear boundary conditions ( ) 1 1 r r p  = − ( ) 3 3 r r p  = − it is possible to obtain relations for radial and tangential stress in the elastic-plastic region (

(13)

)

1 2 r r r   in the form

of

 

  

r

h r

2

1 1

 +  +



2

p

ln

=

+

− −



K

K

rp

2

1

2 h r r

2

h r

1

1

+ 

3

3

1

1

  

  

  

  

r

h r

2

1 1



2

p

1 ln

=

+ +

+ −



K

K

(14)

tp

2

1

2 h r r

2

h

r

1

1

+

3

3

1

1

3. Fully plastic state in cross-section

To determine the burst pressure, it is necessary to consider the state where the entire cross-section of the vessel is in a plastic state. It is necessary to solve the above derived equations in modified form

d

1 d dr r  t

r r    − − t r

(

)

0

=

  = −

a

(15)

r

t

dr

Using the relationship between stress intensity and strain intensity for a bilinear material model (Eq. 12), applying a constant volume condition at plasticization (ν = 0.5) and calculat ing integration constants from boundary conditions ( ) 1 1 r p r = −  ( ) 0 3 = − = 3 r p r  , (16) it is possible to obtain the resulting relationship for destructive pressure by criterion Hubert-Mises-Hencky ( ) 2 2 2 2 red t r z t r r z z t           = + + − + + (17)