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Numerical simulation on bursting pipe using damagemodel with pressure and Lode angle dependence

Marcelo Paredes

Tomasz W ierzbicki


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Outline Introduction

Brief review of Material properties andCalibration procedures

Modified-Mohr Coulomb model

Crack Propagation in Bursting pipe simulation Summary

1Numerica l simula tion on bursting pipe using damage model with pressure andLode angle dependence

Marcelo Paredes and Tomasz Wierzbicki


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Numerica l simula tion on bursting pipe using damage model with pressure andLode angle dependence


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INTRODUCTION

X100 provides economic advantages

by increasing strength with reductionin wall thickness.

Current standards and design codesestablish that the allowable stressdepends partially or completely onyield tensile strength.

These type of material exhibits lowerwork hardening capacity, lower strainto failure and softening of their HAZ.

A complete characterization of stressstate around the crack defect isrequired when it propagates.


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3

Material of investigation: X100, OD=48,t=18.4mm

Anisotropy Performance of the quasi-static tests on flat

dog-specimens using DIC Determination of the Lankford parameters in

0, 45 and 90 degree angles

F G H L M N0.62 0.7 0. 30 2.02 1.5 1.5

X100 R2

r 0 0.988 0.988

r 45 1.035 0.993

r 90 0.482 0.954

Kofiani, K, Nonn, A., Wierzbicki , T., Experimental and Fracture Modeling of High Strength pipelines for high and low stress triaxialities The Proceedings of The Twenty-second (2012) International OFFSHORE AND POLAR ENGINEERING CONFERENCE, Rohdes, Greece

Hill48 anisotropic yield condition parameters


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Theory of anisotropic plasticityTheoretical model

Isotropic Hardening law

= ( + ) A [MPa] n 1006.5 0.0384 0.0008


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Classical Mohr-Coulomb

ModifiedMohr-Coulomb

(MMC)

(Bai and Wierzbicki, 2010)

1 2 f nmax c c

Modified Mohr-Coulomb Model:


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6

Modified Mohr-Coulomb Model:

1

2

13 3 1

2

13 11 sec 1 cos sin

6 3 6 3 62 3

n

f

c Ac c c

c

In strain space (Modified Mohr-Coulomb model ):

0( )

( , )

p p p

f

d D

( ) 1 f

c D D

Damage accumulation rule:

At fracture initiates.

1 2 f nmax c c

In stress space (Classical Mohr-Coulomb model):

T r a n s f o r m a

t i o n

23

m

Mises

p

J

Stress triaxiality:

61

1 1 Normalized Lode angle:

6


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Hybrid experimental/numerical process

7

7

P, curve crit

, crit

FEM

Experiments3DFL

Matlab Monte-Carlo simulations


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3D Fracture surface

Fracture parameters



8

Hybrid experimental/numerical process

8

8

C1 C2 C3 R0.029 535 0.90 98%



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Validation results X100

9

9


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- C3D8R, eight-node brick elementwith reduced integration

- Moment free grips- Capability of predicting both first stageof crack propagation up to completeseparation


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10

, =

+3

2 3 1 sec

6 11 +

3 cos

6 + +13 sin

6

, = 1 +

3+

, = 1 +

3cos

6+

13

sin

6

MMC Fracture criteria c1, c2, c 3

Burst Pressure: Limiting Cases

MMC Fracture criteria Pressure dependence: = 0, c 3 = 1

MMC Fracture criteria Lode dependence: = 0, c 3 = 1

0.0

0.1

0.20.3

0.4

0.5

-1 -0.5 0 0.5 1 1.5

0.0

0.5

1.0

1.5

2.0

-1 -0.5 0 0.5 1


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Modified Mohr Coulomba/t = 0.5

/

/



0.0

1.0

2.0

3.0

4.0

0 0.2 0.4 0.6 0.8 1

Thicknessx/D = 1x/D =22

x/D = 45x/D =77

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Thickness x/D = 1x/D = 22

x/D = 45

x/D =77

T=0.4680P = 38.2 MPa

T=0.4740P = 38.5 MPa

* x/D = normalized vertical distance of control points from crack tip.

Predominant PlaneStrain condition

High Stress

Triaxiality


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-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Axial

x/D =1

x/D =13

x/D = 17

13

/

/




0.0

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8 1

Axialx/D = 1

x/D = 13

x/D =17

T=0.4820, P = 38.9 MPa

T=0.4900, P = 39.3 MPa

Strong Influence of

Lode angle SlantFracture

Low Stress

Triaxiality


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0.0

1.0

2.0

3.0

4.0

0 0.2 0.4 0.6 0.8 1

Thicknessx/D = 1x/D = 19

x/D = 31x/D = 89

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Thicknessx/D = 1x/D = 19x/D = 31x/D = 89

/

/



T=0.6040P = 41.9 MPa

T=0.6220P = 42.2 MPa

T=0.6260P = 42.3 MP

Fluctuations on reveals 45 plane ofMax. Plastic Strain

(zigzag pattern)

High Stress

Triaxiality


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0.0

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8 1

Axialx/D =1

x/D = 25

x/D = 62

x/D = 77

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Axial

x/D =1

x/D = 25x/D = 62x/D = 77

/

/




T=0.6220, P = 42.2 MPa

T=0.6240, P = 42.3 MPa

T=0.6300, P = 42.4 MPa

Peak on leads toslant fracture pattern


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/

/

Modified Mohr Coulomb: Lode dependencea/t = 0.15



-1.0

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Thickness

x/D = 1x/D = 10x/D = 40x/D = 100

-1.0

-0.5

0.0

0.5

1.0

0 0.2 0.4 0.6 0.8 1

Axial

x/D =1x/D = 10x/D = 50x/D = 130

T=0.4300P = 37.3 MPa

T=0.4380P = 37.5 MPa

T=0.4300 T=0.4380 T=0.4440Thickness

Axial

Stress State tends toPlane Strain condition(verti cal fracture pattern )

Strong variation on creates new fracture

surfaces far fromcrack tip


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-1.0

-0.5

0.0

0.51.0

1.5

2.0

0 0.2 0.4 0.6 0.8 1

Thickness

x/D = 1x/D = 10x/D = 40x/D = 100

-1.0

-0.5

0.00.5

1.0

1.5

2.0

0 0.2 0.4 0.6 0.8 1

Axial

x/D =1x/D = 10x/D = 40x/D = 100

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/

/

Modified Mohr Coulomb: Pressure dependencea/t = 0.15



T=0.3360P = 22 MPa

T=0.3380P = 23 MPa

T=0.3360 T=0.3380

Thickness

Axial

Same triaxiality leve ls leadto similar fracture pattern(straight w/o slant crack

propagation )


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Modified Mohr Coulomb: Mapping the cracka/t = 0.15



x/D = 1

x/D = 19

x/D = 31

x/D = 89

1

2

3

x/D = 1

x/D = 25

x/D = 62 x/D = 77

1

2

3

Thickness directionAxial direction

Stress state in shallow crack pipes exhibit more dispersionin thickness than axial direction up to fracture.

The growing crack goes from plane strain to axisymmetrictension condition in both directions.

Cut off region

Plane Stress Condition(magenta color line)


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Modified Mohr Coulomb: Mapping the cracka/t = 0.50



x/D = 1

x/D = 22 x/D = 77

x/D = 45

1

2

3

x/D = 1

x/D = 13

x/D = 17

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Thickness directionAxial direction

Stress state in deep crack pipes exhibit a narrow dispersionin thickness than axial direction up to fracture.

The growing crack tends to remain in plane straincondition ( ) in thickness direction.

Cut off region

Plane Stress Condition(magenta color line)


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Modified Mohr Coulomb: Burst Pressure



10

15

20

25

30

35

40

45

50

10 15 20 25 30 35 40 45 50

Pb-FEA

Pb-PRED

Pb-FEA = Pb-PRED

a/t = 0.15 MMCa/t = 0.15 Pressa/t = 0.15 Lodea/t = 0.50 MMCReference (*)

=1 /

1 /

= 1 + 1.61/

With :

=+2

(*) Erdelen-Peppler, Hillenbrand, H-G, Kalwa , C., Suitable HAZ testing to predict linepipe safety. PipelineTechnology Conference, 2009.

ASME Code Section XI :


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Comments There are two competing fracture mechanisms controlled by the stress state

in terms of triaxiality and lode angle.

The stress triaxiality has a strong influence on ductile crack growth inthickness direction, causing a rapid propagation.

On axial direction the lode angle prevails rather than the triaxiality whichleads to the occurrence of slant fracture.

The burst predictions through code design formula yield to conservativesolutions compared to FE as well as experimental results.

The limiting cases for each condition reduces the effect of stress state parameters , on ductile crack propagation and thus decreasing the bursting pressure in pipes.

21Numerica l simula tion on bursting pipe using damage model with pressure andLode angle dependence


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