ON THE CHALLENGING FEM ON THE CHALLENGING FEM APPLICATION FIELDS IN THE APPLICATION FIELDS IN THE

FRACTURE MECHANICSFRACTURE MECHANICS

Institute of Physics of Institute of Physics of Materials, AS of CR, Materials, AS of CR, Brno, Czech RepublicBrno, Czech Republic

Vladislav KozákVladislav Kozák

OutlineOutline

1. 1. Introduction Introduction

2. Local approach -Beremin2. Local approach -Beremin

3. GTN model3. GTN model

4. Cohesive-zone modelling4. Cohesive-zone modelling

5. Summary 5. Summary

1.Introduction FTTD1.Introduction FTTDLower transitionLower transition

lower transition upper

lowerbound transition

upperbound

stress control fracture

deformationcontrolfracture

SSY

Three different approaches to the Three different approaches to the damage modellingdamage modelling

no damage evaluation, elasto-plastic no damage evaluation, elasto-plastic constitutive equation, process zone is small, K, constitutive equation, process zone is small, K, J, C*J, C*

separation of surfaces is admitted, material separation of surfaces is admitted, material outside is described conventionally, the outside is described conventionally, the process zone is some surface region, fracture process zone is some surface region, fracture criterion is cohesive lawcriterion is cohesive law

softening behaviour is introduced into the softening behaviour is introduced into the constitutive model, e.g. accumulation of constitutive model, e.g. accumulation of damage, described by additional internal damage, described by additional internal variables, GTNvariables, GTN

Plastic zone ahead the crack Plastic zone ahead the crack tiptip

conditioncondition SSYSSY

conditionconditionelasto-plasticelasto-plastic

conditionconditionLSYLSY

regionregion::

large deformationlarge deformationJ-J-integralintegral conception conception K faktor K faktor conception conceptionnon defined only by non defined only by one parameterone parameter

2. 2. Local approach - BereminLocal approach - Beremin

·    Beremin·    Beremin model model 1. averaging stresses over 1. averaging stresses over

FPZFPZ 2. probability of fracture2. probability of fracture

·    Extension to Fracture ·    Extension to Fracture MechanicsMechanics

1. direct toughness 1. direct toughness prediction for SSYprediction for SSY

2. TSM2. TSM, , MinamiMinami, , KoppenhoeferKoppenhoefer, , RuggieriRuggieri

m

ii

miW VV 01 /

muWfP /exp1

mu

mICmy

f V

BCK

P

0

44

1

1ln

Local parameters technique determination

.)}/({ /101 m

im

W VV

1600 1700 1800 1900 2000 w [M Pa ]

0.0

0.2

0.4

0 .6

0.8

1.0C

umul

ativ

e pr

obab

ility

= 4 00 m

C -M n cast s teel

= 2 00 m = 1 00 m

-0.2 -0.16 -0.12 -0.08 -0.04 0

contraction [mm]

0

10

20

30

40

50

load

[kN

]

0 0.04 0.08 0.12 0.16 0.2JC [M P am ] s ize and constra in t corrected

0

0.04

0.08

0.12

0.16

0.2J C

[MP

am]

size

cor

rect

ed

w correction

m

u

wJ)()(

3. 3. Gurson-Tvergaard modelGurson-Tvergaard model (GT)(GT) nucleationnucleation

ff00 = 0,005 = 0,005

ffCC = 0,035 = 0,035

qq11 = 1,5 = 1,5; ; qq22 = 1 = 1

D D == 0,2 mm 0,2 mm

ffNN = 0,004 = 0,004

NN = 0,3 = 0,3

SSNN = 0,1 = 0,1

HMHHMHplasticityplasticity

GTGTplast.plast.

ff00

ffCC

DD

012

3cosh2

3

2 2*3

2*12

fq

qfq

SS

YS

m

YS

ijij

2

2

1exp

2 N

Np

N

N

SS

fA

GT x GTN GT x GTN modelmodel

ccF

cuc ff

ff

fff

f

f

ff

ff

c

c

q1, q2, q3 are used to adjust the modelq1, q2, q3 are used to adjust the model mm is hydrostatic stress is hydrostatic stress

YSYS is yield stress is yield stress

f* is void fraction, ff* is void fraction, fc c is the critical void fraction for is the critical void fraction for

coalescencecoalescence ffF F is the final value of f, fis the final value of f, fuu*=1/q1.*=1/q1.

f *

fu *

fc

fc fF f

GTGTN

dfdfnucl.nucl.=Ad=Adpp

material parameters identificationmaterial parameters identification

500 m

f1=0.0073 f2=0.0073 f3=0.0083 f4=0.0126 f5=0.0131 f6=0.0349

void distribution in the neck area void distribution in the neck area of the round tensile barof the round tensile bar

void distribution in non-affected void distribution in non-affected areaarea

the influence of the mesh size on the curve the influence of the mesh size on the curve elongation-contractionelongation-contraction

0

2

4

6

8

L

[m

m]

0 0.5 1 1.5 2 2.5

d [m m ]

f0 = fN = 0

f0 = 0,001

f0 = 0,0001

fN = 0 ,04G T m odel

num ber of e lem ents: 10

0

2

4

6

8

L

[m

m]

0 0.5 1 1.5 2 2.5

d [m m ]

f0 = fN = 0

f0 = 0,001

f0 = 0,0001

fN = 0,04G T m odel

num ber of e lem ents: 14

varying values of fvarying values of f00 and f and fN N and determination of input dataand determination of input data

0 1 2 3

d [m m ]

0

2

4

6

8

10

L

[mm

]

EXPf0=fN =0

fN=0.004

fN=0.04

fN=0.06

f0 = 0.005

G T m odel

0 1 2 3

d [m m ]

0

2

4

6

8

10

L

[mm

]EXPf0=fN =0

f0=0.005

f0=0.001

f0=0.008

fN = 0.004

G T m odel

ff00 = 0.005, f = 0.005, fFF (f (fCC) = 0.035) = 0.035 q1 = 1.5, q2 = 1 (q3 = q1 q1 = 1.5, q2 = 1 (q3 = q122))

ffNN = 0.004 = 0.004 NN = 0.3, S = 0.3, SN N = 0.1= 0.1

3PB SE(B)3PB SE(B)

L/2

W

a

B/2

L = 250 mmL = 250 mm l = 200 mml = 200 mmW = 50 mmW = 50 mm B = 25 mmB = 25 mm a = 25,25 mma = 25,25 mm

mesh sizemesh size

0 1 2 3 40.5 1.5 2.5 3.5

C O D [m m ]

0

20

40

60

5

10

15

25

30

35

45

50

55

65

F [k

N]

EXPM KP (0 .1)M KP (0 .05)

2.5

mm D/2

0 0.5 1 1.5 2 2.5

a [m m ]

0

200

400

600

800

J [M

Pam

m]

EXPq 2=0.8

q 2=0.82 M KP

q 2=0.85

"construction line"ASTM 1820:J = 2Ya

J

J0.2BL

JI SZW

J0.2

JI

a0.2 mmaSZW

FEM J=1,39FEM J=1,39yyaa

The influence ofThe influence of q q22 on the values on the values

ofof J-integrálu J-integrálu at stable crack at stable crack initiationinitiation

The influence of the h parameter The influence of the h parameter (triaxiality parameter)(triaxiality parameter)

0.75 0.8 0.85 0.9 0.95 1q 2 [-]

40

60

80

100

120J i F

EM

[M

Pam

m]

0.9 1 1.1 1.20.95 1.05 1.15

h [-]

40

60

80

100

120

J i FE

M [M

Pam

m]

4. Cohesive-zone modelling4. Cohesive-zone modelling

ductileductile

crack pathcrack path

5. Summary5. Summary

The coincidence of the results of the numerical modelling and the The coincidence of the results of the numerical modelling and the experiment is generally the basic criterion.experiment is generally the basic criterion.