1

Study of the influence of dent depth on critical pressure of

pipeM. Allouti

ENIM Metz France

2

1) INTRODUCTIONCauses and percentage of incidents on gas pipes

External Interference

Construction defect/ material failure

Corrosion

Ground Movement

Hot-Tap made by Error

Other and Unknown

49.6%

16.5%

15.3%

7.3 %

4.6%

6.7%

One notes that mechanicals damages (external interference) are the major cause of service failures in Europe and in transmission pipelines. These types of damage can be classified into gouges and dent.

3

DENTEA dent in a pipeline is a permanent plastic deformation of the circular cross-section of the pipe without wall thickness reduction A dent causes a local stress and strain concentration and a local reduction in the pipe diameter.

The critical variables relating to plain dents are :•Dent depth H,•Pipe geometry (ratio of diameter to wall thickness),•Profil curvature of the dent R.

European Pipeline Research Group (EPRG) acceptance criterion

%10≤eD

H

H = dent depth in the non pressurized condition, in. (mm)De = pipe outside diameter, in. (mm)

correlation between the dent depth on a nonpressurized pipe and a pressurized pipe

043.1 HH =4

5

DENT + GOUGE

The following geometrical parameters describe the gouge:•Length 2c•Depth a•Radius ρ•Width W•Gouge angle Ψ

6

PIPE FAILURE MODE

7

ROAD MAP FOR DEFECT ASSESMENT IN PIPES

DEFECTS Brittle quasi brittle

ductile

FAD

MNFAD

Limit analysisKICJIC, δc

MNFAD

Limit Analysis

Critical strain

Limit analysis

Currently used In progress

TOOLS FOR DENTE AND GOUGE NOCIVITY ASSESSMENT

8

9

2) DENTS ASSESSMENT

• EPRG empirical criterion• Limit Analysis by Oryniak• Ductility criterion (Present study)

24

2

2

1 ⎟⎠⎞

⎜⎝⎛−+⎟

⎠⎞

⎜⎝⎛==

Vc

tV

Vc

tV

tPR

uσα

OYANE’S DUCTILITY CRITERION

11

01

2

20

1

=⎟⎠⎞

⎜⎝⎛ +=

=⎟⎠⎞

⎜⎝⎛ +=

∫

∫

εσ

σ

εσ

σ

ε

ε

dCC

I

CdCI

f

f

m

m

fε is the equivalent strain at which the fracture occurs,

is the hydrostatic stress,

is the equivalent strain,

C1 and C2 are the material constants.

mσ

fε

10

11

Experimental studyPipe geometry

L= 600mm

t =3.2mm

De=88.9mm

Steel A37

Caps Steel A37

12

Pipes with dentes

Vessel # 1 2 3 4 5 6Displacementindentator (mm)

28 mm 17 mm 14.5 mm 11.2 mm

9 mm 4.8 mm

Relativedent depth (mm)

28 % De 16 % De 13 % De 10 % De 8 % De 4 % De

13

Strain Gauges

Near dentFar from dent

J3

J1

J2

J7J8

J9J4

J5

J6

Env. 210 mm

R2R3

R1

A proximité de l’enfoncement

Résults with strain gauges (Exp-Num)

14

15

NUMERICAL ANALYSIS

Indentation Elastic back spring. Internal pressure acting on pipe with dent.

Step1

Step 3Step2

Yield stress (MPa)

Ultimate

strength

(MPa)

Young’s

modulus

(MPa)

Elongation

at failure (%)

K Hollomon’s

constant

StrainHardeningexponent n

355 432 202500 30 532 0.115

16

Results: Load displacement curves (Exp-Num)

17

18

Application of failure criterion

11

01

2

=⎟⎠⎞

⎜⎝⎛ +∫ ε

σσε

dCC

rm

20

1 CdCr

m =⎟⎠⎞

⎜⎝⎛ +∫ ε

σσε

C1 0.0227 -0.0447 -0.172 0.057 (*) -0.043(**)

C2 0.3 0.3 0.3 0.29 0.22

(*) et (**) from literature)

Before pressurization (during denting test)

After pressurization

19

20

Cause of non failure in dent

Mean Vickers microhardness

Standard deviation uσ (MPa) PL (MPa)

Outside of dent 136 5.4 431 31.0 At base of dent 177 15.2 561 40.4

Strain hardening in dentincreases ultimate strength enough to protectdent against failure.

21

3) DENTE +GOUGE ASESSMENT BY COMBINED

CRITERION (EFFECTIVE STRESS AND STRESS

TRIAXIALITY)

• Batelle formula • British Gas Formula • New criretion based on effective stress

and stress triaxiality

22

Batelle formula( )

90300 6.0−

=Q

f

rσσ

σ 0 is the flow stress and σy the yield stress

σo = yσ + 69 MPa

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

ta

cR

dCvQ

g

e

d 22

Q parameter

Cv charpy energy dd : dent depth (mm),ag gouge depth 2c : gouge length : Re external pipe radius (mm).

23

British Gas Formula

( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ −−

+−−=2

1738.0lnexp

22.1028.1112

5.1113exp1cos2

,

,K

KvC

etDdRd

YeDdd

YgAaf

E

LN

cN

σ

ππσ

σ

⎪⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪

⎬

⎫

=

==

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

pdd

gggg

gggg

gyLN

dd

KK

ta

ta

ta

ta

Y

ta

ta

ta

ta

Y

ta

43.1

57.019.1

141.1332.739.112.1

4.307.216.1023.012.1

115.1

2

1

432

2

432

1

, σσ

24

DENT + GOUGE GEOMETRY

semi-elliptical notch notchique

25

Application of BG formula

STRESS DISTRIBUTION AT GOUGE TIP

26

Stress triaxiality

eq

m

σσ

β =Stress Triaxiality

β c =1

Xefcβ r( )dr

0

Xef∫Average critical stress triaxiality

27

FAILURE CRITERION

ef ,0cσ c,0β ≤ ef

cσ cβ

ef ,0cσ and

c,0β

the value of the critical effective stress and average triaxiality for a single gouge

28

29

Application of the failure criterion

Dent depth 4% De 10% De 16% De Effective stress (MPa) 677 659 637 Effective distance (mm) 0.81 0.72 0.66 Slope α -6.38 -6.7 -6.9 Average critical stress triaxiality cβ

0.85

0.8

0.75

σ effc βc 575

527 477

failure gouge Smooth wall Smooth wall

30

4) CONCLUSION• Gouges, dent and combined gouge +dent defects cannot

be considered as crack like defect and treated by classical fracture mechanics.

• Gouges and combined gouge+dent defect induce elastoplastic failure and can be assess by limit analysis or Notch fracture Mechanics.

• Both method are appropriate and give safety factor which are very close.

• Dent is not a severe defect. • The empirical rule of tolerance of dent with a depth less

than 10% of the pipe diameter is very conservative.• It is then preferable to use a failure criterion based on

ductility. • In this case, the increase of fracture resistance due to

strain hardening during dent formation needs to be taken into account.