Unified constitutive equations to describe elastoplastic ...matperso.mines-paristech.fr/Donnees/data00/63-Ecf16.pdfUni ed constitutive equations to describe elastoplastic and damage

Unified constitutive equations to describe

elastoplastic and damage behavior of an X100

linepipe steel

T.T. Luu1,2 B. Tanguy1, J. Besson 1, A. Pineau 1, G. Perrin2

1Centre des Materiaux/UMR 7633Ecole des Mines de Paris/CNRS

2Institut Francais du PetroleReuil-Malmaison, France

Supported by : IFP, EUROPIPE, TOTAL, GDF

Experimental results for plate and pipe steelsConstitutive equations for plate material

Conclusions

Aim of the study

Use of high strength steel : grade X100 (Re>690MPa)

Characterization and simulation of fast crack propagation andcrack arrest of X100 linepipe steel

Global approach to fracture : Charpy energy minimum(Battelle, AISI, etc), CT0D (Kobayashi, Kanninen).

empiric formula

10

6.67

10

55

⇒ Failed for grade X100

Local approach to fracture (Pineau, Beremin)ECF16, 5 july, Alexandroupolis, Grece Ductile rupture of X100 : experiment and modelling


Conclusions

Prediction of crack propagation and crack arrest on pipe

v=20

−40m

/s

3700

LT

S

LT

S

CT−TL

685

250 difficult extraction

Forming process

L T

S

19

18.4

20

CT

KCV

3700

CT−LT

KCV−TLKCV−LT

v=50−200m/s

1600

1900

X100!

ECF16, 5 july, Alexandroupolis, Grece Ductile rupture of X100 : experiment and modelling


Conclusions

Microstructure of X100 pipe

High strength steel low alloyed, low sulfur content

Microstructure consisting of ferrite grains and bainite bands,Martensite-Austenite constituents

Inclusions : calcium sulfide (CaS), oxides (Al2O3, MgO),titanium nitride (TiN)


Outline

1 Experimental results for plate and pipe steels

2 Constitutive equations for plate materialModel for plastic anisotropic behaviorModel for ductile tearingApplication to simulate ductile tearing test

3 Conclusions


Conclusions

Elastoplatic and damage behavior of X100 plate and pipe

Testssmooth tensile tests(L,T,S)

axisymmetrically notchedtensile tests

compact tension tests

Charpy V-notch tests

dynamic ductile tearingtests

Objectivesplastic anisotropy of plate and pipesteel

characterization of elastoplastic anddamage behavior for higher plasticdeformation

determination of fracture toughnessand identification of modelparameters

determination of upper shelf energyunder both dynamic and staticconditions and validate the model

characterization of fast crackpropagation and crack arrest



Conclusions

Mechanical properties of plate and pipe steels

Yield strength (YS) and ultimate tensile strength (UTS)

690MPa

PipePlatePipePlate

UTSYS 0.2%

R(M

Pa)

STLSTLSTLSTL

850

800

750

700

650

600

550

X100 steel plate and pipe mechanical propertiesPlate Pipe

7.2 4.1



Conclusions

Plastic anisotropy of plate steel

Nominal stress-strain curves and fracture surfaces for plate steel

Plastic anisotropy of material : Lankford ratio

RL = ln(ΦT /Φ0)ln(ΦS/Φ0)

, et RT = ln(ΦS/Φ0)ln(ΦL/Φ0)

RL RT RS

Plate 0.508 1.252 1.171

Pipe 0.69 1.149 —



Conclusions

Fracture toughness of X100 plate and pipe

Crack growth resistance : J-∆a curves

delaminationdelamination

delamination

J0.2 = 231J0.2 = 316

J0.2 = 431

J0.2 = 614

CT T-LCT L-T

PipePlate

∆a (mm)

J(k

N/m

2)

2.52.1.510.502.1.51.0.50

1200

900

600

300

0

Upper shelf energy of Charpy V-notch

sollicitationPlate Pipe

dynamic static dynamic static

L-T 296 J 237 J 277 J 211 J

T-L 309 J 234 J 237 J 178 J



Conclusions

Dynamic ductile tearing tests

4000kN dynamic tensile testing machine

Velocity of crack propagation : 20-40m/s

Ductile slant crack propagation as observed in pipe burst

20mm

propagation



Conclusions

Results

Loading curves and evolution of crack length

E8 crack lengthE6 crack length

E8 loadE6 load

Displacement (mm)

crac

kle

ngt

h(m

m)

Loa

d(k

N)

80

120

160

200

240

80706050403020100

2000

1600

1200

800

400

0

Energy dissipation rate : R = dUdissB.da (J/mm2)

crack length (mm)

R(J

/mm

2)

80 110 140 170 200 230 250

10

8

6

4

2

0


Outline



3 Conclusions


Conclusions

Model for plastic anisotropic behaviorModel for ductile tearingApplication to simulate ductile tearing test

Model for plastic anisotropic bahavior

Mises and Hill criterion : no satisfactoryModel of Bron and Besson :

σ =

"

αψ1 + (1 − α)ψ2

2

#1/a

(1a)

ψ1

=˛

˛

˛S

12 − S

13

˛

˛

˛

a+

˛

˛

˛S

13 − S

11

˛

˛

˛

a+

˛

˛

˛S

11 − S

12

˛

˛

˛

a(1b)

ψ2

=3a

2a−1 + 1

“˛

˛

˛S21

˛

˛

˛

a+

˛

˛

˛S22

˛

˛

˛

a+

˛

˛

˛S23

˛

˛

˛

a”

(1c)

where Ski=1−3 are the principal values of two modified stress deviators s

∼

k = L∼

∼

k :σ∼

, k = 1, 2

BronHill

experiment

∆ΦL/Φ0

∆ΦS/Φ0

∆ΦT/Φ0

1TR S1TR T1TR L

∆L/L0

∆Φ

/Φ

0

F/S

0(M

Pa)

0.06

0.05

0.04

0.03

0.02

0.01

00.120.090.060.0300.090.060.0300.090.060.030

900

750

600

450

300

150

0


Outline



3 Conclusions


Conclusions


Model for ductile tearing

Extension of GTN model to plastic anisotropy (Rivalin,1998)

Φ = σ∗ − R(p)

σ2

σ2∗

+ 2q1f∗cosh

(

q2.3

2

σm

σ∗

)

− (1 + q21f

∗2) = 0

with f ∗ =

{

f if f < fcfc + δ × (f − fc) otherwise

σ is Bron equivalent stress

Evolution of the porosity : f = (1 − f )trace(εp) + Anp

An =

{

A0n if ps < p < pe

0 otherwise

q1 = 1.6, q2 = 1, f0 = 1.5 × 10−4 (images analysis)

Model parameters ajustement : δ, fc , mesh size



Conclusions


Results for axisymmetrically notched specimens

NT1 NT2 NT4

x

y

z

x

y

z

x

y

z

experimentsimulation

AE4L

AE2L

AE1L

AE4T

AE2T

AE1T

∆ΦS/Φ0

F/S

0(M

Pa)

0 0.1 0.2 0.3 0 0.1 0.2 0.3 0.4

1500

1200

900

600

300

0



Conclusions


Results for CT specimens

x

y

z

l

l

T

S

h

propagation

Mesh CT : h=200µm, lP=250µm, lS=600-1000µm

experimentssimulations

CT L-TCT T-L

Load line displacement (mm)

∆a

(mm

)

Loa

d(k

N)

5

4

3

2

1

00 1 2 3 4 0 1 2 3 4 5

20

16

12

8

4

0



Conclusions


Resulats for Charpy V notch specimens

x

y

z

staticdynamicsimulation

Charpy L-TCharpy T-L

Displacement (mm)

Loa

d(k

N)

0 4 8 12 16 20 0 4 8 12 16 20 24

24

20

16

12

8

4

0


Outline



3 Conclusions


Conclusions


Simulation of ductile tearing

3D mesh : h=200µm, lp=315µm, lS=1187.5µm

x

y

zx

y

z

Load-displacement, crack length displacement and R-da curves

E11-X100E10-X100E8-X100E6-X100

simulation

displacement (mm)

crac

kle

ngt

h(m

m)

Loa

d(k

N)

250

200

150

100

50403020100

2000

1500

1000

500

0experiments

simulation

crack length (mm)

R(J

/mm

2)

26023020017014011080

16

12

8

4

0



Conclusions


Simulation of ductile tearing

3D mesh : h=200µm, lp=315µm, lS=1187.5µm

x

y

zx

y

z

x

y

z

0 0.00106140.00212290.00318430.00424570.00530710.00636860.007430.00849140.00955290.0106140.0116760.0127370.0137990.01486

ft map:251.000000 time:21.5521 min:340282346638528859811704183484516925440.000000 max:-340282346638528859811704183484516925440.000000

Load-displacement, crack length displacement and R-da curves

E11-X100E10-X100E8-X100E6-X100

simulation

displacement (mm)

crac

kle

ngt

h(m

m)

Loa

d(k

N)

250

200

150

100

50403020100

2000

1500

1000

500

0experiments

simulation

crack length (mm)

R(J

/mm

2)

26023020017014011080

16

12

8

4

0



Conclusions

Conclusions

Deformation and rupture of X100 plate and pipe materialswere investigated

Unified constitutive equations able to describe theelastoplastic and damage behavior : taking into accountplastic anisotropy.

Good representation of all mechanical tests for both L and Tloading directions.


Unified constitutive equations to describe elastoplastic ...matperso.mines-paristech.fr/Donnees/data00/63-Ecf16.pdfUni ed constitutive equations to describe elastoplastic and damage

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