1 dresden, august 30 - september 03, 2010 a. pineau local approach to fracture (laf) as a...

1

Dresden, August 30 - September 03, 2010 A. Pineau

Local Approach to Fracture (LAF) as a Metallurgical and Mechanical Tool to Model Brittle Fracture and Ductile-to-Brittle Transition (DBT) in Structural Steels

André PineauCentre des Matériaux, UMR CNRS 7633, Evry Cedex, France

[email protected]

I. INTRODUCTION

II. BRITTLE CLEAVAGE FRACTURE : Main Characteristics

III. THEORY OF BRITTLE FRACTUREIII – 1. Weakest Link TheoryIII – 2. Effect of InhomogeneitiesIII – 3. Further Developments

IV. DUCTILE FRACTURE : Micromechanisms & Modeling Ductile Crack Growth

V. DUCTILE TO BRITTLE TRANSITION

VI. CONCLUSIONS

2


SCOPE

• MATERIALS - (Essentially) Ferritic Steels -- Pressure Vessel Steels : 16MND5 (B), 22NiMoCr37 (B), 21/4Cr 1Mo (M) -- Offshore Structural Steels : E 450, E 36

• LENGTH SCALE EFFECT

• SIZE EFFECT ON FRACTURE TOUGHNESS

• SCATTER IN RELATION WITH METALLURGICAL INHOMOGENEITIES

• FRACTURE MECHANICS SPECIMENS & CHARPY TESTS

• 2D / 3D ASPECTS

• ISOTHERMAL & NON ISOTHERMAL TESTS

See T. Yuritzinn et al. « Warm pre-stressing tests on specimens with semi-elliptical cracks and analysis of the results » EFM,(2010), vol.77,pp.71-83

3




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I. INTRODUCTION





VI. CONCLUSIONS

4

DUCTILE –TO - BRITTLE TRANSITION - DEFINITION

●●

●

mma

J(KJ/m2)K(MPa m1/2)L(KN)


T2

T3 > T2 > T1

OR DECREASING STRAIN RATE

OR DECREASING SPECIMEN SIZE

T1●

5

Crack x

Field+

1981ICF5

1986

1st Sem.1992AIME

Sem.

19962nd Sem.

20063st Sem.


GLOBAL APPROACH

FieldSingle parameterK, J, CTOD

K-T; J-QTwo parameters

LOCAL APPROACH

Crack Tip Physically-basedFracture Criteria

COMPUTATIONAL FRACTURE MECHANICS

1960 1970 1980 1990 2000

LEFM

EPFM

2010

LAF

σYY

6


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

LAF was introduced to take into account fracture micromechanisms and to account for complex loading conditions, such as mixed mode or

non-isothermal loading

1nm – 1µm

1- 10 mm

10 cm – 1m

1- 10 mm

1 – 10 mm

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[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

8

BRITTLE CLEAVAGE FRACTURE - MAIN CHARACTERISTICS


• TEMPERATURE DEPENDENCE

• SCATTER

• SPECIMEN SIZE EFFECT

• GEOMETRICAL DEPENDENCE

• LOADING RATE EFFECT

• EFFECT OF METALLURGICAL VARIABLES & INHOMOGENEITIES

X

9

K. Wallin, EFM,2002, Vol.69, pp.451-481, +TC8 - ESIS

EURO FRACTURE TOUGHNESS DATA SET

TEMP. & SIZE EFFECT


10

J.Heerens, D.Hellmann, EFM, 2002,Vol.69, pp.441-449See also R.Moskovic, EFM, 2002, Vol.69, pp.511-530 B.K. Neale, EFM, 2002, Vol.69, pp.497-509



SCATTER & SPECIMEN SIZE EFFECT

11


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, 637-64- J. Sumpter, ASTM STP 1171,(1993),492-502

Transition Temperature Increases with Crack Depth or

Constraint Effect

12

Correspondingthermal cycles

CorrespondingHAZ microstructures

Welded Structures

Run #1

Run #2

Run #3

A

BC

D

Coarse gained HAZ (CG HAZ)

Intercritically reheated CG HAZ

Supercritically reheated CG 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


13

E 450

30 µmtransverse direction

short transversedirection

BASE METAL ( ferrite-Pearlite)

10µm

ICCGHAZ-25 ( Bainite)

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

Arrows indicate the presence of martensite- austenite (MA)constituents


14

ductile stable crack propagation over > 0.2 mm

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

0

50

100

150

200

250

300

-200 -150 -100 -50

Base metal

KJc (MPa.m1/2)

T (°C)

base metal

T0 = - 130°C

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

T0 = - 12°C


15




[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

16

0PZR

2c

00l000

V

dVpexp1P:V

lGriffith

dllppdllp:Vc

0 0

1

0

1/

10

/

1 exp

1 exp ;

2 2

m

R PZu

m m

mwR w PZ

u

Power Law

p l l

dVP

V

dVP

V

m

WEIBULL

0

2 21

20 0

exp

1/ 1/1 exp exp

1/

n

u

n

uR decoh

Exponential Law

l lp Size l

l

dVP

V

GUMBLE

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

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


WEAKEST LINK THEORY - BEREMIN MODEL

V0

17

BEREMIN MODEL (1983) (S.S.Y.)

HRR

002

00YY /J

xg

/K

xf

B : Specimen Thickness Cm (n) : constant

mu0

mCB4m

04IC

RV

Kexp1P

22IC

IC 1E

KJ

2 2 4

022

0

1 exp1

mIC m

Rmu

J E BCP

V

02

0 /J/x;/K/x

HRR Field

CRACK

0

yy


18

J LARGE SCALE YIELDING (LSY)

NUMERICAL

T1 T2 T3

2

Ln (J/0)

Ln

( w

/u)

m =

Ln

[Ln

(1/

1-P

R)]

T1< T2< T3

SMALL SCALE YIELDING (SSY)

ANALYTICAL


Beremin Theory can also be used for predicting directional effects (See e.g. T.L. Becker et al. (2002), EFM, Vol. 69, pp. 1521-1555; B. Bezensek, J.W. Hancock, (2007), EFM, Vol. 74, pp. 2395-2419)

Gradient Materials & Thermal Gradients

19

BEREMIN MODEL & MASTER CURVE

muu

m4m4

ICR V

CBKexp1P

MODELBEREMIN

mm25Bfor

mMPa100medianKT

CinT;mMPainK

TT019.0exp7030mediumK

63.0PK

mMPa20minK

minKK

minKK

B

Bexp1P

CURVEMASTER

JCo

oJC

Ro

I

4

Io

IIC

oR

CstT/mediumKwhen

minKK,Kif

DEPENDENCE ETEMPERATUR

SAME THE PREDICT MODELS BOTH

4/m1oJC

IJCIC

A. Lambert-Perlade, PhD Thesis, 2001


20

m = 22

2550u MPa 61.5 10mC

J.Heerens, D.Hellmann, EFM, 2002, Vol.69, pp.421-449


0.2a mm


497 / 757 #

CT12.5 N = 190

Only 1 init. site in small specimens

A. Andrieu, July 2010

21

m = 22

2550u MPa 61.5 10mC

J.Heerens, D.Hellmann, EFM, 2002, Vol.69, pp.421-449

0.2a mm


CT25 N = 136

497 / 757 #



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EURO FRACTURE TOUGHNESS DATA SETJ.Heerens, D.Hellmann, EFM, 2002, Vol.69, pp.421-449


Several (2-3) initiation sites in big specimensInhomogeneities Effect ?


m = 22

2550u MPa 61.5 10mC 0.2a mm CT100 N = 34

497 / 757 #

Several Initiation Sites (>2 or 3) on the fracture surfaces

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EURO FRACTURE TOUGHNESS DATA SETJ.Heerens, D.Hellmann, EFM, 2002, Vol.69, pp.421-449

0.2a mm


m = 22

2550u MPa 61.5 10mC CT50 N = 137

497 / 757 #


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[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

25

C. Naudin, PhD Thesis, 1999

Plan RC Plan RA

A = AxialR = RadialC = Circumferential


16MND5 PWR STEEL - SEGREGATED ZONES

RADIAL

TANGENTIAL

INTERNAL INTERNAL

MID -THICKNESS

RADIAL

TANGENTIAL

Mic

roh

ard

ne

ss (

HV

0.1

)

Ph

os

ph

oru

s (W

t %

)

200 ppm

X 1.39

26

16MND5 PWR STEEL - SEGREGATED ZONES C. Naudin, PhD Thesis, 1999

Plate RC

Crack front

C

R

A = AxialC = CircumferentialR = Radial

Pro

bab

ilit

y

Nb of SZ intersecting Crack front (100 mm)

Large SZ (> 1 mm)

CT 100 (4T)3.64 + 2.31N

Pro

bab

ilit

y


Small SZ (< 1 mm)

CT 100 (4T)4 + 2.55N

Pro

bab

ilit

y


Large SZ (> 1 mm)

CT 25 (1T)1.10 + 0.69N

Pro

bab

ilit

y


Small SZ (< 1 mm)

CT 25 (1T)2.91 + 1.85N


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C = Cleavage

I = Intergranular

EDF

C.Naudin ,PhD, 1999


■■

■

■

■

■

■

■

■

■

■


RCCM Code

28

C. Naudin,PhD, 1999



C

R Fatigue crack frontCrack propagation direction 200 µm

mMPaK IC 74

CT Specimen - Number PU5Intergranular intiation sitesTemperature = - 60°C

MnS inclusions

Intergranular Fracture

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A T=-100°C

E (GPa) (MPa) B1 Q1 B2 Q2

MB 200 539.6 12.16 324.3 0.422 296

MI 240 750 12.16 434 0.422 450

2.0R

u 30 menV T = -100°C (MPa) m

MI 3700 15 50

MB 2710 22 50

/ 1.39SZ BMY Y

Double Isotropic Hardening For Both Materials

Constitutive Equations

Fracture Properties

CT Specimen W = 20 mm FE Calculations


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K = 45 MPa.m^0.5

K = 60 MPa.m^0.5

K = 75 MPa.m^0.5

CRACK TIP

MATRIX – Soft & Tough Material

SEGREGATED Material Strong & Brittle

Pf

Segregated Zone Thickness

Base MetalSegreg

ated Z

one

(e/B)trans

1 2 2 12 21 2 02 01 2 1 1 2( / ) / . / . / . /m m m m

trans Y Y u u m me B V V C C

CTOD

31



1/ 2

b l

ll b

b

CTOD CTOD l segregated zone

K K

int

int

2 2

' : exp!

2.66 10

15

n

P n Probability that n SZ intersect the crack front

B lPoisson s Law P n Bl

n

Area fraction of SZ mm

l platelets mean length mm

1 2

44 2

20

int

1 1 1

exp 1

2

b l b

b b l

f f f

Base SZ

m b m m lIC eff b m eff eff l ub m

effm m m bu b ul m

eff

P P P

K B C e e CB B

V B B C

e P n e

e mean platelet thickness mm

Crack Front

32


Plastic Zone Limitation

Large S.Y. Conditions

BeffB

Ln B , Ln Beff

Ln KLn KJ

(Pf = fixed)

4;f ICP fixed K B cst at a given temperature

4

1

Material Size Requirements for Applying SSY Solution to Macroscopically Inhomogeneous Materials

33


Material Size Requirements for Applying SSY Solution to Macroscopically Inhomogeneous Materials

4;f ICP fixed K B cst at a given temperature

Ln B , Ln Beff

Ln KLn KJ

(Pf = fixed)4

1

Kth

Pf

Apparent Reduction of Size Effect & Scatter

BeffBMesoscopic Size Effect

Microscopic Size EffectLarge S.Y. Conditions

34

C. Naudin,PhD thesis, 1999


3

0

3

0

539.6 , 2710 , 22, 50

750 , 3700 , 15, 50

Y u

Y u

BM MPa MPa m V µm

SZ MPa MPa m V µm

Base Metal

SZ; e = 2 mm

Prob

abil

ity

to F

ailu

re

Fracture Toughness, MPa m1/2

CT 25 B.Metal

CT 25 1 S.Z(2 mm)

CT 100 B; Metal

CT 100 1 S.Z (2mm)

CT 25 2 S.Z(2mm)

35

C. Naudin, 1999


Fra

ctur

e T

ough

ness

, MP

a m

1/2

Fra

ctur

e T

ough

ness

, MP

a m

1/2

Fra

ctur

e T

ough

ness

, MP

a m

1/2

Assuming no SZ

36

BEREMIN MODEL – LIMITATIONS - FURTHER DEVELOPMENTS

(1) THRESHOLD WEIBULL STRESS ?

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

(3) EXISTENCE OF DIFFERENT MICROSTRUCTURAL BARRIERS FOR A PROPAGATING CRACK MULTIPLE BARRIER MODELS

?andm u


37




[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

38


FURTHER DEVELOPMENTS

• Tables for Cm Coefficient in Beremin Expression

• eff >> s ( X 1000 – 10 000)

- Grain boundary crossing in particuliar twist grain boundaries

- Cleavage microcrack percolation in a damaged zone at crack tip

- Multiple barrier models : Sequential micromechanisms and conditionnal statistics

• Another source of scatter : Stress distribution in polycrytals

- Polycrystalline Plasticity

39

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 & Fc Determined by Metallography 2

1

g/cIa

21

2

g/c* K

1

EC

2

1

g/gIa

21

2

g/g* K

1

ED

C D

2 31g/c

IaK

g/gIaK


+ Conditionnal Probability

1 µm

40

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


41


CRACKS AT GRAIN BOUNDARIES (2) & MIXED FRACTURE MODES

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

BOTH EFFECTS CONTRIBUTE TO THE INCREASE OF

EFFECTIVE SURFACE ENERGY

CLEAVAGE CRACK PERCOLATION BY DUCTILE FRACTURE

42

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


43

locP

if

ifp

i = 1 i = 2

loc

1

0

ifApplied local stress ; Local fracture stress

Pro

bab

ilit

y D

ensi

ty

ifp

Cu

mu l

a tiv

e P

rob

a bi l

ity,

locP

N. Osipov

G. Cailletaud

A.F. Gourguesloc

if

dpPP if

ifo locR


44




[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

45

L. Devillers-Guerville, 1998DUPLEX STAINLESS STEEL

Cavity nucleation & growth from embrittled ferrite

DUCTILE FRACTURE MICROMECHANISMS


46


DUCTILE FRACTURE (MICROMECHANISMS)

• NUCLEATION: Still poorly understood

Very much material dependent

Link with Gurson model

• CAVITY GROWTH: Large Research Effort since Gurson (1977) Model

See e.g. G.T.N. (1972, 1984); G.L.D (1997, 1994, 2001); Benzerga, Besson (2004);Pardoen Hutchinson (2000); Pardoen (2006) Single crystals (J.Kyzar, 2005, 2008)

• CAVITY COALESCENCE: Partly understood

Thomason Model (1985, 1990) Very much remains to be done Strongly Material dependent

nuclp

ii fff 1

47

Void coalescence – experimental

Courtesy of Arnaud Weck, (Ph.D.) with Dave Wilkinson

48


DUCTILE FRACTURE (MODELING)

• STRATEGY 1: Neglect coupling effects between mechanical fields & damage (See e.g. D’Escatha & Devaux, (1979))

• STRATEGY 2: Explicit modeling of cavities ahead of crack tip using refined finite element meshes (See e.g. Aravas, Mc Meeking (1985); Tvergaard, Hutchinson (2002))

• STRATEGY 3: Introduction of cohesive zone model (See e.g. Tvergaard, Hutchinson (1992); Brocks et al.,(2003))

• STRATEGY 4: Computational cells Pursued mainly by groups in France, Germany, U.K., U.S.

49

SUMMARY ABOUT MECHANISMS

• Void coalescence is a second stage of void growth but with plastic flow localized in the intervoid ligament

• Void coalescence can take place (1) ± normal to the main loading direction « internal necking »(2) ± in the direction of maximum shear « coalescence in shear»(3) in columns (precursor of transverse delamination/splitting)

depending on the void arrangement, loading mode and strain hardening capacity

• Void coalescence can be accelerated by the presence of a second population of voids (in shear : « void sheeting »)

• Void coalescence should not be confused with plastic localization mechanisms resulting from the damage induced softening, involving effects of the structure and boundary conditions


50




[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

51

K. Wallin, EFM,(2002), Vol. 69, pp. 451-481

10.0P expf

90.0P expf

Cleavage Fracture

30M

)1(M/EbK2/12

YIc



52

WHY DOES A TRANSITION EXIST ?

1 - PROBABILISTIC ASPECT

Volume of sampled material increases with crack growth (See e.g. Brückner, Munz (1984); Wallin, (1993)) 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


53

PROPAGATING CRACK

CRACK CRACK


54

B. Tanguy, 2001

MAXIMUM STRESS AHEAD OF A PROPAGATING CRACK

CHARPY V SPECIMEN


55

Steel 16 MND5

J.C. Lautridou , 1980


56

Gao et al., 1999

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


WHAT ABOUT EURO FRACTURE TOUGHNESS DATA SET ?

57

MODELING OF CHARPY IMPACT TEST IN PWR STEEL

• 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.


58

CHARPY TEST SIMULATION B. Tanguy


59

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


See also :- Schmitt et al., IJPVP, 1994, Vol. 59, pp. 21-29- A.Rossoll, PhD Thesis, 1998

60

A 508 STEEL


TEMPERATURE

σu

A

B

• A regime: Cleavage without significant ductile crack growth

• B regime : Cleavage after large ductile crack growth: Influence of the damaged zone which reduces local stresses by

local crack « shielding » effect

61




[email protected]

I. INTRODUCTION





VI. CONCLUSIONS

62


CONCLUSIONS & PROSPECTS

• CLEAVAGE - eff >> S - Temperature dependence – Needs more detailed metallographical observations

- Microstructural barriers – Collective behaviour of cleavage microcracks - Polycrystalline plasticity

• INTERGRANULAR - int = f (impurity content). Threshold ? - Intergranular initiation in relation with intragranular inhomogeneities in plastic deformations within grains in a polycrystal - Competition between Cleavage & Intergranular in macroscopically inhomogeneous materials

• DUCTILE - Concentrate more on cavity nucleation & cavity coalescence - Orientation of fracture surfaces (flat vs slant fracture) - Microtomography,Laminography (See also : T. Morgeneyer et al.Acta Mater.,vol.56, 2008,p.1651)

• CRACK ARREST - Still poorly understood

• DEVELOPMENT of more sophisticated models but which should remain tractable

H:\ECF 18 DRESDE-Ao<FB>t 2010\2139_all_crop_bin_r_2fps_annotate.avi

63


THANK YOU FOR YOUR ATTENTION

[email protected]

ISO-27 306 (2009) Method of loss correction of CTOD fracture toughness assessment of steel components

64


65

With the exception of 100 mm specimens more than 50% of the specimens showed single initiation sites

531.6)95.01/1(Ln/)05.01/1(Ln 2/1

6.47

0.95

0.05


J. Heerens, 2002

1 dresden, august 30 - september 03, 2010 a. pineau local approach to fracture (laf) as a...

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