1

Ghiath MONNET

EDF - R&D

Dep. Materials and Mechanics of Components,

Moret-sur-Loing, France

Bridging atomic to mesoscopic scale: multiscale simulation of plastic deformation of iron

PERFECT (PERFORM): integrated European project for simulations of irradiation effects on materials

FP 7 P rojectFP 7 P roject

P E R FO R M 60P E R FO R M 60FP 7 P rojectFP 7 P roject

P E R FO R M 60P E R FO R M 60

2

Objective :

Case of void interaction with dislocations

Irradiation leads to material damages

• production of point defects

• acceleration of aging

• formation of clusters, diffuse precipitates

Consequences: modification of mechanical behavior

• strong strengthening

• deformation localization and embrittlement

Prediction of radiation effects on mechanical properties

3

Atomic and mesoscopic approaches

Interaction nature: atomic(atomic vibration, neighborhood)

• Smoothing atomic features into a continuum model

• No adjustable parameter !!

Strengthening scale: microstructure(temperature, disl. density, concentration)

4

In this talk ...

• Molecular Dynamics simulation of dislocation-void interactions

• Analysis of MD results on the mesoscopic scale

• Dislocation Dynamics prediction of void strengthening

5

S

h

]011[ny

]111[bx

]211[lz

motion attraction R Bowing-up unpinning

Atomic simulations

• Size dependent results

• Different interaction phases

• Analysis of pinning phase

• Reversible isothermal regime

-50

0

50

100

150

200

0.000 0.004 0.008 0.012

R

a b c ed f

MPa

p

E poteV

6

dise ddd

curvF

discurvdisFeapp dddVdW

Elastic workDissipated work Curvature work

RRapp dVdVW Ε::Σ

Mechanical analysis at 0K

7

Energetics decomposition at 0K E

nerg

ie (

eV)

-10

0

10

20

30

40

0.0 0.2 0.4 0.6 0.8

(a)

Ecurv

Upot

Eel

Eint

r

(%)

-20

0

20

40

60

80

100

120

0,000 0,004 0,008 0,012

Ecurv

Upot

Eel

Eint

r

(%)

(b)

20 nm Edge dislocation, 1 nm void 40 nm edge dislocation, 2 nm void

Analyses provide interaction energy and estimate of the line tension

8

Analyses of atomic simulations at 0 K

How to define an intrinsic strength of local obstacles ?

9

The maximum stress depends on

• void size

• dislocation length

• simulation box dimensions

Intrinsic strength of voids at 0K

10

Case of all local obstacles

)( feff w

l

• Can be obtained from MD

• No approximation

lw

eff

)( fmaxc w

l

is c a characteristic quantity ?

Intrinsic strength of voids at 0K

fappappeff w

l

[Monnet, Acta Mat, 2007]

11

w

lcfmax

• The intrinsic “strength” depends on obstacle nature, not size

• Strength of voids > strength of Cu precipitates

GPa25.4)( voidsc

GPa33.2prct)( Cuc0

50

100

150

200

0.00 0.01 0.02 0.03 0.04 0.05 0.06

(MPa)fmaxapp

l

w

Intrinsic strength of voids at 0K

12

Identification of thermal activation parameters

Analyses of atomic simulations at finite temperature

13

Temperature effect on interaction

(MPa)

(%)

• Decrease of the lattice friction stress

• Decrease of the interaction strength

• Decrease of the pinning time

Stochastic behavior (time, strength)

[Monnet et al., PhiMag, 2010]

MD simulation, Iron, 0K, 20 nm edge dislocation - 1 nm void

14

Survival probability

The rate function

(MPa)

(%)

T = 300 K

Interaction time t

Survival probability: Po(t)

dP(t) = Po(t) (t) dt

0

0 )(exp)( dttP

0

)(exp)()( dttp

Probability density: p()

kT

tGt

)(exp)(

dp = (t) dt

15

Analyses of thermal activation: activation energy

Case of constant stress = c

c

ccs d

1exp

0

sc kTG ln)(

Determination of the attack frequency

2ln)(

w

blkTG Dsc

w

Peierls Mechanism

w

bkTG Dsc ln)(

Local obstacles

16

For constant strain rate: eff varies during t

Can we find a constant stress (c) providing the same survival probability at s ?

s

dttsc

0

)(expexpkT

G cc

)(exp

s

s

tdtts

c

)()(1

0

Development of G = A - V*eff teffc V

V )exp(ln

1 **

c little sensitive to V*

Analyses of thermal activation: critical stress

17

The critical and the maximum stresses

• Always c < max

• When T tends to 0K, c tends to max

• At high T, c is 30% lower than max

Critical stress for voids

0

100

200

300

400

0 200 400 600

max

(GPa)

c

T (K)

18

0.0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800

G (eV)

T (K)

C = 8.1

• t varies slowly with T

• t varies with strain rate MD simulations (t 1 ns): C = 8

Experiment (t 1 s): C = 25

Activation energy = f (stress, temperature)

Experimental evidence G(c) = CKT

kTCw

btkTG D

c

2ln)(

0.0

0.1

0.2

0.3

0.4

0.5

2.5 3.0 3.5 4.0 4.5c(GPa)

G (eV)

Activation energy

19

Dislocation Dynamics simulations of void strengthening

Using of atomic simulation results in DD

• validation of DD simulations• determination of void strengthening

20

Validation of dislocation dynamics code

0

0,5

1

1,5

2

1 10 100 1000

Example of the Orowan mechanism

B

r

D

L

bA

pc

0

ln

[Bacon et al. PhilMag 1973]

)( pc Lb

bD

Screw

Edge

Simulation of the Orowan mechanism

21

Comparison of dislocation shape

Edge dislocation - void interaction

GPa25.4)( voidsc

22

Thermal activation simulations in DD

Edge dislocation - void interaction

150

200

250

0 200 400 600

DD

MD

Comparison between DD and MD results

eff

Activation path in DD

• Computation of eff

• Calculation of G(eff)

• Estimation of dp =(t)dt

• Selection of a random number x

• jump if x > dp

23

DD prediction of void strengthening

• Average dislocation velocity : 5 m/s

• Number of voids : 12500

0

50

100

150

200

250

0.0 0.5 1.0 1.5

Prediction of the critical stress

T° K Periodic row Random distribution

0 K 245 MPa 200 MPa

600 K 165 MPa 140 MPa

24

Conclusions

• Atomic simulations are necessary when elasticity is invalid

• Obstacle resistance must be expressed in stress and not in force

• Void resistance = 4.2 GPa to be compared to Cu prct of 4.3 GPa

• Despite the high rate: MD are in good agreement with experiment

• Activation path in DD simulations is coherent with MD results

• DD simulations are necessary to predict strengthening of realistic microstructures

25

Collaborators

• Christophe Domain, MMC, EDF-R&D, 77818 Moret sur loing, France

• Dmitry Terentyev, SCK-CEN, Boeretang 200, B-2400, Mol, Belgium

• Benoit Devincre, Laboratoire d’Etude des Microstructures, CNRS-ONERA, 92430 Chatillons, France

• Yuri Osetsky, Computer Sciences and Mathematics Division, ORNL

• David Bacon, Department of Engineering, The University of Liverpool

• Patrick Franciosi, LMPTM, University Paris 13, France

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Any problem?

• Segment configuration (in DD) influence the critical stress

• Given MD conditions, thermal activation can not be large

• How to “explore” phase space where eff is small (construct the whole G (eff))

• Accounting for obstacle modification after shearing

• Develop transition methods for obstacles with large interaction range

• Give a direct estimation for the attack frequency

• What elastic modulus should be considered in DD

• How to model interaction with thermally activated raondomly distributed obstacles?

27

Screw dislocation in first principals simulations

Ab initio simulation

EAM potential, Mendelev et al. 2003EAM potential,Ackland et al. 1997