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

13

5

1

lg( /

) / lg 1 /

ln

m S

e

.

(6)

c

y

y

1

c

With the above-shown standard characteristics of pipe steels m =0.18-0.22. Using equations (2) – (6), one can calculate the intensity of true fracture s tresses σ ic or strains e ic taking into consideration the reduction of the cross sectional area due to local strains. Then according to strain-based or stress-based fracture criterion one can get: 1/ m i c i c y c y e e e , (7)

m

e e

S

c

.

(8)

i c

y

c

y

As pressure p in the pipeline grows tending to its critical value ( p → p c ) and accounting for the reduction of the wall thickness, the fracturing (critical) pressure p c will be defined according to the moment of reaching the state of instability of plastic strains characterized as: 0 / 0 i i d de , (9) where σ i 0 is the intensity of engineering stresses, that are calculated without taking into account the changes of the original dimensions in the process of deformation. Condition (9) corresponds to the finite uniform strain at the level of the pipeline strength limit:

0 i u e e m

(10)

Then using equations (7) and (10):

m

e

i u

.

(11)

i c

y

e

y

If the pipeline ( D 0 =1200 mm and δ=18mm) is made of steel whose characteristics are: σ y =320 MPa, ψ c =0.6, E =2·10 6 MPa, then according to (6) m =0.178, and to (10) e u = m =0.178. With the increase of cross sectional area F from the cross sectional area of a smooth standard specimen F 0 =80mm 2 up to the pipeline cross sectional area F =π D 0 δ=6.78·10 4 mm 2 design yield stress σ yF and ultimate stress σ uF as well as the relative narrowing ψ cF will be reduced according to scaling laws:

0 0 ( / ) , ( / ) , ( / ) , Y u m m m F F F F F F 0

yF

y

(12)

u F

u

cF

c

where m y , m u and m ψ are scaling law exponents that are assumed to be material constants. For the considered pipe steel according to Makhutov (2008), m y = m u =0.013 , m ψ =0.03. According to expressions (12) and (5), σ yF =293MPa, σ uF =494MPa, ψ cF =49%, S cF =832MPa, m F = e iuF = 0.17. As was shown in Makhutov (2008) the decrease of plasticity e uF due to multiaxiality of the stress state of the pipeline with the components of relative principle stresses 1 1 1 / € , 2 1 2 / € , 3 1 3 / 0 € is estimated using the value of D en that characterize the reduction of ultimate plasticity due to multiaxiality of the stress state: