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

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The formed crimp creates a high concentration of tensile membrane stresses σ m =σ 2 . The theoretical stress concentration factor for these stresses can be estimated according to the layout of eccentric tension of the unit bar with eccentricity h that creates bending and tensile stresses in the inner surface at the crimp top. Thus the total maximal elastic stresses caused by tension and bending are:

h

* max

1 6 m

.

(21)

According to Makhutov (2008) in the crimp zone (Fig. 2) one can define the changes of the metal properties through formulas (2) and (6):

F m

e

max

.

(22)

y cr

y F

e

y F

If σ y =293MPa, e max cr =0.27, m F =0.17 and σ y F =711 MPa then the strain hardening exponent m cr of the damaged metal in crimp zone can be estimated taking into account the equation (6):

lg( / S

)

c y r

c

m

.

(23)

cr

lg(

/ e e c cr

)

y cr

For the given design case according to expression (23) m cr =0.067. If the pipeline with crimp is loaded by inner pressure, some secondary plastic deformations will take place in its inner side at the crimp top. The strain concentration factor K e will exceed the theoretical stress concentration factor K t ( K e > K t ). Then according to Makhutov (2008) normalized secondary local elasto-plastic strains can be determined by the following expression: 2 / (1 ) max cr m cr n t e e K , (24) where n e is normalized nominal strain in the smooth part of the pipeline ( / n nF y e e e ; / n cr nF y cr e e e ; / y cr y cr e E ). The nominal fracture strain can be derived from expression (24) using the strain-based fracture criterion:

1

(1 ) / 2 cr m

e

e

.

(25)

n cr

c cr

K

t

Fig. 3 Examples of pipeline failure in crimp zone

For the considered case

0.316 n cr e . Nominal fracturing stress in the crimp zone

MPa as for

224

n cr

n cr

y cr

elastic deformation of the pipeline . This stress is less than the yield stress limits for steel σ y , σ y cr , and the fracture membrane stress σ m =σ 2 =σ θ c /2. In the pipeline damaged by crimp the nominal fracture stress σ n cr corresponds to fracture pressure p c cr : 0.316 n cr n cr e