BRITTLE FRACTURE & BRITTLE to DUCTILE …matperso.mines-paristech.fr/Donnees/data02/255-Summer...1...

1

BRITTLE FRACTURE & BRITTLE to DUCTILE FRACTURE TRANSIT ION MICROMECHANISMS

André PINEAUCentre des Matériaux - Ecole des Mines de Paris. ParisTech

UMR CNRS [email protected]

I. INTRODUCTION : Various Scales / History of Fracture Mechaniscs

II. BRITTLE CLEAVAGE FRACTURE – THEORYII.1. Main characteristics of Brittle Cleavage FractureII.2. Weibull – Beremin TheoryII.3. Multiple barrier modelsII.4. Effect of Deformation – Second Order approximation

III. DUCTILE FRACTURE – THEORY (Introduction)III.1. Cavity initiation, growth & coalescence. GTN modelIII.2. Computational strategies to simulate ductile crack growth

IV. DUCTILE TO BRITTLE TRANSITION IN STEELSIV-1. Qualitative explanations for the existence of DBTIV-2. Fracture toughness transitionIV-3. Impact Charpy test

V. CONCLUSIONS

Summer School on Fracture, CARGESE, 07-19 June 2010 A. Pineau

2








V. CONCLUSIONS


3


10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

100(m)

(µm)(nm)

1

10

100

1000

10

100

1000

First Talk

Second Talk

A. Pineau, IJF, 2008

Y. Bréchet, Mat. Nuc., 2008Pareige, JNM, 2007

2 ¼ Cr – E. Bouyne, 1998

4

Standard Fracture Toughness specimens and wide plate components linked with the equivalent CTOD ratio β


2c

a

2a

σσσσ∞∞∞∞

t

ca

σσσσ∞∞∞∞c a

a

a


t



t

σσσσ∞∞∞∞σσσσ∞∞∞∞

t


Standard fracture toughness specimens

Equivalent CTOD ratio β

Surface crack

Surface crack

Through-thickness crack


Center surface crack panel (CSCP) Center through-thickness crack panel (CTCP)

Edge surface crack panel (ESCP) Edge through-thickness crack panel (ETCP)

B = t

W a0= BH H

S = 4W

1.25W

0.6W

a0 = BW

B = t

0.6W

Structural components

(0.45 < a0 / W < 0.55)

3-point bendCompact

5


10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

100(m)

(µm)(nm)

1

10

100

1000

10

100

1000

Bouchard,(NH),1978, R.M. Pelloux

Fe-3%Si- Qiao, Argon, 2003

A. Lambert-Perlade, 2001

A. Lambert-Perlade, 2001

6


10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10

100(m)

(µm)(nm)

1

10

100

1000

10

100

1000

2IC m/J62G −=

2GBIC

GBIC

m/J20020G

mMPa62k

−=

−=

23IC

IC

m/J10100G

mMPa10050K

×=

−=

X 10X 1000

23IC

IC

m/J1082G

mMPa4020K

×−=

−=

X 0.10

X 1000

7

( )mma∆

J(KJ/m2)

�

�

��

��

�

DUCTILE TO BRITTLE TRANSITION - DEFINITION

� T1

T2 > T1

OR DECREASING STRAIN RATE


8

WARM-PRESTRESS EFFECT

*

LUCF

*LCF

T1TEMPERATURE

FRACTURE

TOUGHNESS

( )mMPa

T2

See also D.J. Smith, CSI 2003, pp. 289-345


9

Crack

εεεεσσσσ,

x

GLOBAL APPROACH

Fieldεεεε−−−−σσσσSingle parameterK, J, CTOD

K-T; J-QTwo parameters

LOCAL APPROACH

Crack Tip

Fieldεεεε−−−−σσσσ+ Physically-based

Fracture Criteria

COMPUTATIONAL FRACTURE MECHANICS

1960 1970 1980 1990 2000

LEFM

EPFM

1981ICF5

2010

LAF

1986

1st Sem.1992AIME

Sem.

19962nd Sem.

20063st Sem.


10

I - EXPERIMENTS

• Mechanical Tests

• Microstructural Observations

• Micromechanisms

II - MODELS

• Constitutive Equations

• Damage Modelling

III - IDENTIFICATION

• Tuning of Models Parameters

IV - SIMULATION

• Laboratory Tests

V - SIMULATION

• Industrial Components

• Complex Loading Conditions


11

MECHANICAL TESTS OBSERVATIONS


12

(((( )))) (((( ))))(((( )))) (((( ))))(((( ))))(((( ))))

2,1i;K

R11F1

p

1

RFp

pbexp1Qpbexp1QRT,pR

EQUATIONSVECONSTITUTI

in

ii

21

22110

====−−−−σσσσ====εεεεεεεε

++++εεεε

========

−−−−σσσσ====

−−−−−−−−++++−−−−−−−−++++====

⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅

⋅⋅⋅⋅

elsmodCoupled

elsmodUncoupled

RUPTUREDUCTILE

dVV1

exp1P

STRESSWEIBULL

FRACTURECLEAVAGE

MODELLINGDAMAGE

m/1mI

uw

m

u

wR

−−−−−−−−••••

σσσσ====σσσσ

σσσσσσσσ−−−−−−−−====

••••

∫∫∫∫


13

CLEAVAGE FRACTURE

Probabilistic Model

Weibull Stress

DUCTILE RUPTURE

Coupled Models

• Gurson-Tvergaard-NeedlemanPotential with an acceleratingfunction

• Rousselier Potential

• Statistical models in DuplexStainless Steels

Charlotte Bouchet


14

NS (AE)

CT

CHARPY V NOTCH

SIMULATION

B. Tanguy & J. Besson


15

SIMULATIONPRESSURE VESSEL

ALOHA, 1988


16








V. CONCLUSIONS


17

BRITTLE FRACTUREMAIN CHARACTERISTICS

• SCATTER

• SIZE EFFECT

• GEOMETRICAL DEPENDENCE

• LOADING RATE EFFECT

• EFFECT OF METALLURGICAL

VARIABLES & INHOMOGENEITIES


18

0

50

100

150

200

250

300

350

400

-200 -150 -100 -50 0 50

KIC (NS)

KIC (S)

KJ (NS)

KJ-Kcpm(S)

Kcpm (NS)

DIDR

Code RCC-M

Fra

ctur

e T

ough

ness

(MP

am1/

2)

T - RTNDT (°C)

C. Naudin, A. Pineau and J.M. Frund (2001), 10th Conf. on environmental degradation


19

Size Effect

I. Iwadate et al., Nucl. Eng. Design (1985), Vol. 85, pp. 89-99


20

Short

Crack

Effect

CONSTRAINT EFFECT- W.A. Sorem et al. Int. J. Fracture, (1991), 47, 105-126- D. Tigges et al. ECF 10, (1994), 1, 637-646


21

E36 Steel (-50°C)

0

50

100

150

200

250

300

0,00 0,20 0,40 0,60 0,80

a/W

J IC

(KJ/

m²)

SENB 0.03 < a/W < 0.77CCP 0.63 < a/W < 0.77

Sumpter 1993


CONSTRAINT EFFECT

22

0

50

100

150

200

250

300

350

-220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20

TEMPERATURE (°C)

FR

AC

TU

RE

TO

UG

HN

ES

S (

MP

am1/

2 )

Pr=90%

Pr=10% Pr=90%

Pr=10%

.K

MPam1/2/s

4102

2

. •o Theoretical curves for failure

Probabilities of 10% and 90% (Beremin model)

Henry et al., 1985A 508 Steel


23

Weld structure Correspondingthermal cycles

CorrespondingHAZ microstructures

Run #1

Run #2

Run #3

A

BC

D

Coarse gained HAZ(CG HAZ)

Intercritically reheatedCG HAZ

Supercritically reheatedCG HAZ(fine grains)

~ CG HAZ

A

B

C

D

METALLURGICAL

INHOMOGENEITIES

A. Lambert-Perlade et al., Metall. And Mater. Trans. A (2004), Vol. 35A, pp. 1039-1053


24

10µm

10µm10µm

30 µmtransverse direction

short transversedirection

E 450BASE METAL CGHAZ-25

ICCGHAZ-25 CGHAZ-120

A. Lambert-Perlade et al., Metall and Mater. Trans. A, (2004), Vol. 35A, pp. 1039-1053


25

martensite

austenite

5 µm

1 µm

martensite

austenite

1 µm

martensite

austenite

MARTENSITE - AUSTENITECONSTITUENTS

E 450 STEEL

A. Lambert-Perlade et al., Metall. and Mater. Trans. A, (2004), Vol. 35 A, pp. 1039-1053


26

0

50

100

150

200

250

300

-200 -150 -100 -50

Base metal

KJc (MPa.m1/2)

T (°C)

base metal

0

50

100

150

200

250

300

-200 -150 -100 -50 0 50

CGHAZ-25

KJc (MPa.m1/2)

T (°C)

CG HAZ 1

0

50

100

150

200

250

300

-200 -150 -100 -50 0 50

ICCGHAZ-25

KJc (MPa.m1/2)

T (°C)

IC CG HAZ 1

0

50

100

150

200

250

300

-200 -150 -100 -50 0 50

CGHAZ-120

KJc (MPa.m1/2)

T (°C)

CG HAZ 2

ductile stable crack propagation over > 0.2 mmA. Lambert-Perlade et al., Metall. Mater. Trans. A, (2004), Vol. 35A, pp. 1039-1053

T0 = - 130°C T0 = - 45°C

T0 = - 12°C T0 = - 6°C


27








V. CONCLUSIONS


28

V

V0

WEAKEST LINK THEORY. WEIBULL-BEREMIN MODEL

(((( )))) (((( )))) (((( ))))

(((( ))))

σσσσ∫∫∫∫−−−−−−−−====

σσσσαααα====→→→→

∫∫∫∫====σσσσ→→→→ ∞∞∞∞

0PZR

2c

00l000

VdV

pexp1P:V

lGriffith

dllppdllp:Vc

(((( ))))

22m

VdV

;exp1P

VdV

exp1P

l/lp

LawPower

m/1

0

m1PZw

m

u

wR

0

m

u

1PZR

00

−−−−ββββ====

σσσσ====σσσσ



γγγγ====

∫∫∫∫

∫∫∫∫

ββββ

(((( ))))

σσσσσσσσ−−−−σσσσ−−−−−−−−−−−−====

−−−−−−−−====>>>>

∫∫∫∫0

n

20

2u

21

decohR

n

0

u

VdV

/1

/1/1expexp1P

lll

explSizep

LawlExponentia

See also Kroon & Faleskog in Inter. Journal of Fract. Vol. 118, (2002), pp.99-118 & Eng. Fract. Mechanics,

Vol. 71, (2004), pp. 57-79.


29

BEREMIN MODEL (83) (S.S.Y.)

CRACK

HRR Field0

σ

( ) ( )02

0 /J/x;/K/x σσ

HRR ( )

σσ=

σσ=σ

002

00YY /J

xg

/K

xf

B : Specimen Thickness

Cm (n) : constant

σ

σ−−=

−

mu0

mCB4m

04IC

RV

Kexp1P

−= ν22IC

IC 1E

KJ

( )2 2 4

022

0

1 exp1

mIC m

Rmu

J E BCP

V

σν σ

− = − −

−

yyσ


30

A533 SteelServer & Wullaert

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300TEMPERATURE (K)

FR

AC

TU

RE

TO

UG

HN

ES

S, K

IC

(MP

am1/

2 )

Experimental Results 1T to 11T

Theory, ICF5, Cannes, 1981m = 21 ; σσσσu = 2530 MPa ; Vo = 60 µm 3

PR = 0.90

0.50

PR = 0.10


31

J∆ LARGE SCALE YIELDING

T1 T2 T3

2

Ln (J/σσσσ0)

Ln (

σσ σσ w/ σσ σσ

u)m

= L

n [L

n (1

/1-P

R)]

T1< T2< T3

SMALL SCALE YIELDING (SSY)


32

BEREMIN MODEL & MASTER CURVE


−−−−

muu

m4m4

ICR V

CBKexp1P

MODELBEREMIN

(((( )))) (((( ))))[[[[ ]]]](((( ))))

(((( ))))mm25Bfor

mMPa100medianKT

CinT;mMPainK

TT019.0exp7030mediumK

63.0PK

mMPa20minK

minKKminKK

BB

exp1P

CURVEMASTER

JCo

oJC

Ro

I

4

Io

IIC

oR

========→→→→

°°°°

−−−−++++====−−−−====⇒⇒⇒⇒−−−−

≈≈≈≈−−−−

−−−−−−−−−−−−−−−−====

(((( )))) (((( ))))(((( )))) CstT/mediumKwhen

minKK,Kif

DEPENDENCE ETEMPERATUR

SAME THE PREDICT MODELS BOTH

4/m1oJC

IJCIC

====σσσσ−−−−

>>>>>>>>−−−−

−−−−

A. Lambert-Perlade, PhD Thesis, 2001


33

COMPARISON OF BEREMIN ( ) & MASTER CURVE ( ) (PR = 0.10 - 0.90)

m = 27σσσσu = 2158 MPa





34

BEREMIN MODEL - LIMITATIONS

(1) � THRESHOLD WEIBULL STRESS ?

(2) � STRAIN and/or TEMPERATURE DEPENDENCE OF MODEL PARAMETERS

(3) � EXISTENCE OF DIFFERENT MICROSTRUCTURAL BARRIERS FOR A PROPAGATING CRACKMULTIPLE BARRIER MODELS

(((( ))))?andm uσσσσ

⇒⇒⇒⇒


35








V. CONCLUSIONS


36

MULTIPLE BARRIER MODELS

20 µm

53°40° 58°

18°23° 52°

A. Lambert-Perlade & A.-F. Gourgues


37

A DOUBLE BARRIER MODEL FOR CLEAVAGE FRACTURE

A. Martin-Meizoso et al., Acta Metall. Mater. (1994), Vol. 42, pp. 2057-2068.

• STEP 1 : Fracture Probability of a M-A constituent / Critical Stress Criterion.

• STEP 2 : Probability of propagating a crack at the MA/Matrix Interface.

• STEP 3 : Probability of crossing a packet boundary.

dVCCFxNDCCFxNexp1P*

ccv

**g

gvPZR

⟩+

⟨⟨∫−−=

Fg & F c Determined by Metallography2

1

g/cIa

21

2

g/c* K

1

EC

σβ=

σ

ν−

γπ=

2

1

g/gIa

21

2

g/g* K

1

ED

σβ=

σ

ν−

γπ=C D

2 31g/c

IaK

g/gIaK

σ


38


39

CRACKS AT GRAIN BOUNDARIES (1)

Qiao, Argon, Mat. Letters, vol.54, 2008, pp.3156-3160

See also Qiao , Argon, Mech. Materials, vol.35, 2003, pp.129-154 and pp.313-331


40


41


42

CRACKS AT GRAIN BOUNDARIES (2)Qiao, Argon, Mat.

Letters, vol.54, 2008,

pp.3156-3160


43








V. CONCLUSIONS


44

A SIMPLIFIED THEORY

BEREMIN MODEL (1983)+

S. BORDET (2005)

Second Order Approximation

• The cleavage stress depends on plastic strain

• This dependence remains deterministic


45

J.-J.Gilman, (1958)

ZINC SINGLE CRYSTALS


46


47

S. Kotrechko, Theoretical & Applied Fracture Mechanics, 40, (2003), 271-277


48

EFFECT OF PLASTIC STRAIN

• Strong Effect in Zn single crystals

• CLEAVAGE INITIATED FROM PARTICLESNucleation TiN in IN718 (F. Alexandre, 2005)

Bordet et al. (2005) (EFM, Part I, 435-452; Part II, 453-474)

( ) ( )1981min,Bereexp1P

Na

uN

0eq1nucl

σ

σ−σλ+σ−−=

( ) nuclt

0 propcleav PPtP δ= ∫

( )

εε

σσ−−=⇒εσ−=δ

0eq

eq

0Y

0nucleq0nucl0nucl exp1PdP1NP

[ ]

σσ−−=δ−−= ∫ ∫

m

*u

*w

PZ

t

0 nuclpropR exp1dVNPexp1P

( ) ( ) ( )( )u

PZ 00eq

eqnucl

mth

m1

0Y

0m*

w V

dVdtP1eq

∫ ∫

εε

−σ−σσσ=σ ε


49

A SOPHISTICATED THEORY TO BE DEVELOPED !

Third Order Approximation

• The local stresses are no longer uniform

- Random distribution due to elastic anisotropy(S. Kotrechko + S. Pommier)

- Crystalline plasticity(Ecole des Mines)

• "Self organisation" of the local stresses : Arching type effect(S. Pommier)


50

INHOMOGENEITY IN LOCAL STRESS DISTRIBUTION (EL ASTICITY )

• S. KOTRECHKO (Theoretical and Applied Fracture Mechanics, 47, (2007), 171-181)

• See also: S. POMMIER (Fatigue & Fracture of Engineering Materials & Structures, 25, (2002), 331-348.

( ) ( )[ ]( ) ( )[ ]( ) ( )[ ]21II2313I

221II

23I33

31II3212I2

31II22I22

32II3121I2

32II21I11

µµ2DDD

µµ2DDD

µµ2DDD

ΣΣ+ΣΣ+ΣΣ+Σ+Σ+Σ=σ



( )

[ ][ ]113322

1111

2IIII

2I

2I

IIIIII

ii

24.024.0and

40.160.0.dev.St3forTensionUniaxial

10x66.0µD;10x72.0µ;10x7.1D

grainsofondistributiRandomFe:Ex

anisotropyelastictheoffunctionstscoefficien:µ,µ,D,D

stresseslocaltheofVariance:D

Σ−Σ−σσΣ−Σσ

====

σ

−−−


51

Analogy with Granular Materials[Dantu, Radjai, Roux, Evesque …]

F

Distribution of maximum principal stress (FEM)

Characteristic length > grain = arch dimension

sand = water + grains

S. Pommier, FFEMS, (2002), 25, 331


52

LOCAL STRESS HETEROGENEITY : 3D

Max. principalstress

Tensile loading Copper

S. Pommier


53

Distribution calculated from the results of 70 calculations

Zirconium Titanium Zinc Copper Iron Aluminum

Minimum value (MPa) Maximum value (MPa) Mean value (MPa)

926 1046 976

1058 1225 1141

792 1269 1036

679 1283 1018

1379 2107 1799

640 726 681

Standard Deviation (MPa) 27 35 123 121 144 16

3 times the standard deviation in percentage of the mean value

8.5% 9.25% 35% 35% 24% 7%

S. Pommier (FFEMS, 25, (2002, 331-348)


54

F. Barbe, S. Forest, G. Cailletaud, Int. J. Plasticity, 17, (2001), 537-563


55

F. Barbe, S. Forest, G. Cailletaud, Int. J. Plasticity, 17, (2001), 537-563


56

BAINITIC STEEL N. Osipov

G. Cailletaud

A.F. Gourgues


57

BAINITIC STEEL

N. Osipov

G. Cailletaud

A.F. Gourgues


58

( )σ>σlocP

( )if

ifp σ=σ

i = 1 i = 2

( )locσ

1

0


( )ifσApplied local stress ; Local fracture stress

Pro

babi

lity

Den

sity

( )ifp

Cum

ulat

ive

Pro

babi

lity,

( )σ>σlocP

N. Osipov

G. Cailletaud

A.F. Gourgueslocσ

ifσ

( ) ( ) σσσσσ dpPP if

ifo locR =×⟩= ∫

∞

59

STATISTICAL ASPECTS OF CLEAVAGE FRACTURE - CONCLUSIONS

• Various sources of scatter for cleavage fracture

• This scatter has strong practical implications. Threshold stress ? Size effect

• Modelling. Three approximations :

- Engineering purposes. 1st Order Approximation will remain largely usedHowever attempts made to consider that in the master curve approach, T0 is statistically distributed

- Most urgent problem : Strain and Temperature dependence of

• Many metallurgical means to develop microstructure with improved fracturetoughness

A 508 steel / 2 1/4 - 1 Mo steel

uσ


60








V. CONCLUSIONS


61

L. Devillers-Guerville, 1998DUPLEX STAINLESS STEEL

Cavity nucleation & growth from embrittled ferrite

DUCTILE FRACTURE MICROMECHANISMS


62

CAVITY COALESCENCE

DUCTILE FRACTURE MICROMECHANISMS

Steel C-Mn Aluminium 6156


63

GTN Model (Growth)

• Isotropic hardening + Elasticity

• Comparison with calculations on elementary cells (cavity + matrix)See Koplik & Needleman, 1988

• "New" Yield Surface

Most often :

But new calculations(Faleskog et al., 1998) showed thatq1 and q2 dependon and work hardening exponent, n

( )pyσ

221

y

kk212

y

2eq fq1

2

qcoshfq2 −−

σσ+

σσ

=φ

1q,2/3q 21 ==

E/yσ


64

GTN Model (Cavity Nucleation)

( ) ⋅⋅⋅ +ε−= pAtrf1f np

Growth Nucleation

• Phenomelogical Approach- Fitting of An on macroscopic tests- See e.g. (Chu & Needleman, 1980)

• Experimental Approach- See e.g. Duplex Stainless Steels (Devillers-Guerville et al., 1997)

( )

ε−−π

= 2n

2n

n

nn

s2

pexp

s2

fA


65

GTN Model (Coalescence)

Definition of an effective cavity volume fraction, f*

0fq12

qcosh*fq2 2*2

1y

kk212

y

2eq =−−

σσ+

σσ

=φ

=*fwhere ( ) ccc

c

ffiffff

ffiff

>−δ+<

δ*f

cf

Not necessary to introduce accelerating factor, when statistical cavity distribution is taken into account(Devillers-Guerville et al., 1997; Decamp et al., 1997)

δ

cf


66

GTN MODEL - EXTENSIONS

• Plastic Anisotropy (Bron - Besson, 2004)

• Cavity Shape (Gologanu - Leblond, 1993, 1997)

• Thomason, (1985, 1990)

• Pardoen and Hutchinson (2000)

• Benzerga (2000)

COALESCENCE THOMASON MODEL


67








V. CONCLUSIONS


68

COMPUTATIONAL STRATEGIES TO SIMULATE DUCTILE CRACK GROWTH

STRATEGY 1 • Use of the void Nucleation, Growth and Coalescence laws

• Integrate them using solutions of elastoplastic crack problems

• Neglect coupling effects between mechanical fields and DamageSee e.g. d'Escatha and Devaux, 1979


69


STRATEGY 2 • Explicit modeling of the cavities using refined finite element mesh

• Requires a criterion for void coalescence

• Limitation to small crack extension and simple void geometrySee e.g. Aravas, McMeeking, 1985. Tvergaard, Hutchinson, 2002


70


STRATEGY 2STRATEGY 2STRATEGY 2

STRATEGY 3 • Pursued mainly by groups in France, Germany, U.K. and U.S.

• Constitutive model (Gurson or Rousselier) with damage-induced softening

• Averaging over a critical distance

• Introduction of an internal length (e.g. Mudry et al., 1989. Rivalin et al., 2001)

COMPUTATIONAL CELLS


71


STRATEGY 2STRATEGY 2STRATEGY 2

STRATEGY 4 • Introduction of the Cohesive Zone Model

• CZM parameters depend on constraint effects

• Crack path must be prescribed in advanceSee e.g. Tvergaard and Hutchinson, 1992. Brocks et al., 2003


72

SIMULATION OF DUCTILE CRACK GROWTH RESISTANCE CURVES

• Considerable success of the so-called "local approach" (Pineau, CSI, 2003)or "top-down" approach to ductile fracture (Hutchinson and Evans, 2000)

• Assessment of the fracture integrity of structural components under large scale yielding conditions

• Main interest : microstructural parameters(void volume fraction, void spacing,etc…) must be set such that the model reproduces experiments on specific specimens

• 3D aspects of crack initiation and growth have been simulatedComparison with experiments scarce (Gao et al., 1998; Rivalin et al., 2001)

Very much remains to be done : flat/slant fracture in these sheets

SUMMARY


73








V. CONCLUSIONS


74

WHY DOES A TRANSITION EXIST ?

1 - PROBABILISTIC ASPECT

Volume of sampled material increases with crack growth

Sketch

2 - MESO-MECHANICAL ASPECT

Maximum stress increases with crack growth

B. Tanguy

3 - MICRO-MECHANICAL ASPECT

Local stresses amplified by cavity growth

(Petti & Dodds, IJSS (2005), p. 3655) J.C. Lautridou


75

PROPAGATING CRACK

CRACK CRACK


76




Sketch



B. Tanguy





77

B. Tanguy, 2001

MAXIMUM STRESS AHEAD OF A PROPAGATING CRACK

CHARPY V SPECIMEN


78




Sketch



B. Tanguy





79

Steel 16 MND5

J.C. Lautridou , 1980


80

SAMPLING EFFECT DUE TO CRACK GROWTH

( )22IK

• WALLIN (1989)- Assumes that the "effective" volume continues to grow as

( )( ) ( )( )

( )thicknessspecimenB;stresscleavage

SSYundercalculatedeasilyKforvaluegnormalizinK;afK

daafBK

2

K

af

P1

1Ln

f

0I

a

0

240

2f

40

4

R

==σ=∆=

∆σ+∆=− ∫

∆

• BRUCKNER & MUNZ (1984)- Assumes that the size of the active volume is constant during crack extension

( )( )

volumeactivetheofsizethedescribingttancons:W;initiationcrackatKofvalueK

daafWK

1

K

K

P1

1Ln

ii

4a

0i40

4

0

i

R

=

∆+

=

− ∫∆

�� In both cases, or R curve must be known( )aK ∆

( ) sizezoneprocesscleavage/K/xwhereK

a21

K

K

P1

1Ln

)1993(WallinbyproposedcorrectionDCGtheofressionexpSimplified

2fi2

i

2f

0

i

4/1

R

σ≈β

βσ∆+=

−

⇒


81

ELIMINATION OF ELIGIBLE NUCLEATION SITES

( )( )

elementiththeofVvolumethein

particleafrommicrovoidanucleatetoobabilityPrP

V

VP1

i

ivoid

m/1

0

ini

Iivoid

n1iw

=

σ−Σ=σ =

See e.g. Koers et al. (1995)

• Very few results in the literature

• This effect is usually neglected


82

MnS

CLEAVAGE

A 508 Steel Notched Specimen T = - 150°C

CLEAVAGE INITIATED FROM MnS INCLUSIONSTanguy, 2007


83








V. CONCLUSIONS


84

A SIMPLIFIED APPROACH TO DB TRANSITION

• Based on the assumption that the stress-strain field is not modifiedby crack extension except the loading parameter, J

See e.g. Amar, Pineau, 1987; Koers et al., 1995

• Strong limitations to this approach

Does not account for modifications in the stress field of a propagating crack

Does not rely on a possible change in micromechanisms


85

Amar & Pineau, 1987

See also Koers et al., 1995. Fe 510 Nb


86

MORE ADVANCED MODELS FOR DB TRANSITION

OBJECTIVES

(i) • Stress Profiles ahead of a growing crack

Strongly dependent on geometry (bend vs tension)

(ii) • Introduction of damage ahead of the crack tip produces a macroscopic reduction

of the "local" stresses (GTN model). At metallurgical scales ductile damage

amplify local stress(See Petti & Dodds, 2005)

(iii) • Sampling effect due to crack growth

(iv) • Elimination of eligible particles (or nucleation sites)

(v) • Effect of plastic strain on cleavage stress

(See above, Beremin, 1983, Bordet et al., 2005)


87

Toyoda et al., 1991; Ruggieri & Dodds, 1996HSLA Steel


88

Ruggieri & Dodds, 1996HSLA Steel


89

Gao et al., 1999

GTN Model f0 = 0.0045, fc = 0.20, D = 0.30 mm, m = 11.86, MPa2490u =σ


90








V. CONCLUSIONS


91

APPLICATION OF THE LOCAL APPROACH TO DUCTILE-BRITTLE TRANSITION IN FERRITIC STEELS

MODELING OF CHARPY IMPACT TEST

• MATERIAL : PWR A 508 Steel

• NUMERICAL MODELING- 3D- Viscoplastic Constitutive Laws- GTN & ROUSSELIER Models for Ductile Fracture- BEREMIN Model for Cleavage Fracture

• COMPARISON EXPERIMENTS & NUMERICAL SIMULATIONS- Interrupted tests to measure ductile crack growth

See : B. Tanguy et al., Eng. Fracture Mechanics (2005), Vol. 72. Part I : pp. 49-72. Part II : pp. 413-434.


92

CHARPY TEST SIMULATIONB. Tanguy


93

Fracture at –60°C under dynamic

conditions :

a) Experimental fracture surface,

b) Simulation of ductile crack

propagation

(contour plots indicate )Iσ

A 508 Steel• No Inertial Effect

• Strain Rate Effect (Viscoplasticity)

• Ductile Damage (Rousselier & Gurson)

• Adiabatic Heating


94

A 508 STEEL


95

MODELING CHARPY-V TEST - CONCLUSIONS

1 - Accurate Description of Load-Displacement Curves

and Ductile Crack Growth Provided that 3D Modeling is Used

2 - Good Description of Tunnelling Effect for Ductile Crack Growth

3 - Necessity of Using a Viscoplastic Constitutive Equation and to account

for Adiabatic Heating

4 - Temperature Increase as Large as 150°C

5 - Easy Prediction of Index Temperatures TK28 and TK68

6 - Above 100 Joules, appears to be an Increasing Function of Temperatureuσ≈≈≈≈

CHARPY TESTS TUNING DAMAGE MODEL PARAME TERS FRACTURE TOUGHNESS PREDICTION


96

CONCLUSIONS and ADDITIONAL COMMENTS

• Illustration of the benefit of the micromechanical modeling of fracture

• More complex but rewarding : size effect; non-isothermal loading; mixed mode etc…

• Many research areas to be explored :

(1) Cleavage Stress or See Kotrechko et al.

(2) Ductile Fracture Models (too) sophisticated ?

(3) New experimental techniques (X-ray 3D Tomography) : Nucleation of cavities

(4) Existing models based on CSM. How far ? Crystallographic aspects

(5) Development of simulation tools : more complex situations (Welds etc…)

(6) Extension of ductile cracks over long distances remains a real challenge

( )?T,fu ε=σ


97








V. CONCLUSIONS


98


CONCLUSIONS

• Illustration of the benefit of micromechanical modelling of fracture

• LAF more complex but rewarding : size effect , non-isothermal loading , etc…

• Many research areas remain to be explored :

- Cleavage stress σu (temperature)

- Ductile fracture models ( too) sophisticated

- Shear dominated ductile fracture

- New experimental techniques ( Tomography )- Cavity nucleation

- Existing models based on C.M.- How far ? Crystallographic aspects?

- Development of simulation tools

- Extension of ductile cracks over long distances remainsa real challenge

99

THANK YOU FOR YOUR ATTENTION

For further information

[email protected]


100

LIMITATION (1) : THRESHOLD WEIBULL STRESS

Actually, existence of a threshold stress in Beremin model since plastic deformation over a critical distance (Xc) is a prerequisite to initiate cleavage fracture

cominI X3~K ππππσσσσ

Increasing Temperature

Ln

KIC

(MP

am1/

2 )

for

PR

= C

ons t

ant

(((( ))))TLn oσσσσ

Centre des Matériaux - Ecole des Mines de Paris ICF Moscow 7-12 July 2007 A. Pineau

101

Experimental Results (Soehmaker - Rolfe.1971)

(-177°)

(-144°)

(-196°)

(-128°)

(-137°)

(-196°)(-147°)

(- 84°)

(- 73°)

(-104°)

(- 36°)

(-125°)

(-116°)

(- 83°)

2.0

2.5

3.0

3.5

4.0

4.5

6 6.25 6.5 6.75 7Ln σσσσ0 (σσσσ0 in MPa)

Ln K

I C (

KI C

in M

Pa

m1/

2)

ABS - C Mild Steel(σσσσ y at R.T. = 280 MPa)

( )Cin °

−•

−−•

−−•

≈

≈

≈

θεεε

1

11

15

sec20

sec10

sec10.5


102

0

50

100

150

200

-200 -150 -100 -50 0 50

ICCGHAZ-25

Results of the “double barrier” model with TPB specimens.Open circles denote microcrack events, solid circles are for final fracture of the specimens.Solid (resp. dotted) lines represent 10%, 50% and 90% probabilities for the specimen to fracture (resp. for a cleavage microcrack to propagate across a particle/matrix boundary) as given by the DB model.

TEMPERATURE (°C)

TO

UG

HN

ESS

(M

Pa √√ √√

m)

( )

( )25CGHAZ

mMPa28K

25ICCGHAZ

mMPa18K

mMPa8.7K

MPa2112

g/gIC

g/gIC

g/cIC

CAM

−=

−=

=

=σ −

E 450


103


104

Standard Fracture Toughness specimens and wide plate components linked with the equivalent CTOD ratio β


2c

a

2a


t

ca

σσσσ∞∞∞∞c a

a

a


t



t

σσσσ∞∞∞∞σσσσ∞∞∞∞

t


Standard fracture toughness specimens

Equivalent CTOD ratio β

Surface crack

Surface crack



Center surface crack panel (CSCP) Center through-thickness crack panel (CTCP)

Edge surface crack panel (ESCP) Edge through-thickness crack panel (ETCP)

B = t

W a0= BH H

S = 4W

1.25W

0.6W

a0 = BW

B = t

0.6W

Structural components

(0.45 < a0 / W < 0.55)

3-point bendCompact

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