1 ghiath monnet edf - r&d dep. materials and mechanics of components, moret-sur-loing, france...
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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
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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]
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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?
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Screw dislocation in first principals simulations
Ab initio simulation
EAM potential, Mendelev et al. 2003EAM potential,Ackland et al. 1997
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