PERFO RM 6 0
F P 7 P r o je c t
PERFECT (PERFORM): integrated European project for
simulations of irradiation effects on materials
Bridging atomic to mesoscopic scale: multiscale
simulation of plastic deformation of iron
Ghiath MONNET
EDF - R&D
Dep. Materials and Mechanics of Components,
1
Moret-sur-Loing, France
Objective :
Prediction of radiation effects on mechanical properties
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
Case of void interaction with dislocations
2
Atomic and mesoscopic approaches
Interaction nature: atomic
(atomic vibration, neighborhood)
Strengthening scale: microstructure
(temperature, disl. density, concentration)
• Smoothing atomic features into a continuum model
3
• No adjustable parameter !!
In this talk ...
• Molecular Dynamics simulation of dislocation-void interactions
• Analysis of MD results on the mesoscopic scale
• Dislocation Dynamics prediction of void strengthening
4
Atomic simulations
 
y  n [1 1 0]
 MPa
200
S
g
R
150
h
 
x  b [111]
 
z  l [112]
E pot eV
100
50
a b
c
d
e
f
p
0
-50
0.000
0.004
0.008
• Size dependent results
motion
attraction
R
Bowing-up
unpinning
• Different interaction phases
• Analysis of pinning phase
5
• Reversible isothermal regime
g
0.012
Mechanical analysis at 0K
d
dg  dg e  dg dis
   F   curv


R
R
Wapp    V  Σ :: d Ε  V   dg
dWapp  V  dg e  F dg dis   curv dg dis 
Elastic work
Dissipated work
6
Curvature work
Energetics decomposition at 0K
20 nm Edge dislocation, 1 nm void
40
40 nm edge dislocation, 2 nm void
120
(a)
100
30
(b)
Upot
Upot
80
Energie (eV)
20
gr
60
Eel
gr
Eel
40
10
Ecurv
Ecurv
20
0
0
Eint
-10
0.0
0.2
0.4
g (%)
0.6
-20
0.8 0,000
Eint
0,004
0,008
0,012
g (%)
Analyses provide interaction energy and estimate of the line tension
7
Analyses of atomic simulations at 0 K
How to define an intrinsic strength of local obstacles ?
8
Intrinsic strength of voids at 0K
The maximum stress depends on
• void size
• dislocation length
• simulation box dimensions
9
Intrinsic strength of voids at 0K
[Monnet, Acta Mat, 2007]
 eff   app
 eff
l
  app   f 
w
 eff
Case of all local obstacles
l
 (   f )
w
w
• Can be obtained from MD
• No approximation
l
l
 c  ( max   f )
w
is c a characteristic quantity ?
10
Intrinsic strength of voids at 0K
200
 max
l
 f   c
w
max
 app
 f (MPa)
150
100
 c (voids)  4.25 GPa
50
w
l
 c (Cu prct) 2.33 GPa
0
0.00
0.01
0.02
0.03
0.04
• The intrinsic “strength” depends on obstacle nature, not size
• Strength of voids > strength of Cu precipitates
11
0.05
0.06
Analyses of atomic simulations at finite temperature
Identification of thermal activation parameters
12
Temperature effect on interaction
[Monnet et al., PhiMag, 2010]
MD simulation, Iron, 0K, 20 nm edge dislocation - 1 nm void
 (MPa)
g (%)
• Decrease of the lattice friction stress
• Decrease of the interaction strength
• Decrease of the pinning time
13
Stochastic behavior (time, strength)
Survival probability
The rate function w (t )   exp 
dp = w(t) dt
DG  (t ) 
kT
 (MPa)
T = 300 K
Survival probability: Po(t)
dP(t) = Po(t) w(t) dt
 

P0 ( )  exp  w (t ) dt
 0

Probability density: p()
g (%)
 

p ( )  w ( ) exp  w (t ) dt
 0

Interaction time Dt
14
Analyses of thermal activation: activation energy
Case of constant stress  = c

 s     wc exp wc  d 
0
1
wc
DG( c )  kT ln  s   
Determination of the attack frequency
Peierls Mechanism
Local obstacles
w
bl 

DG( c )  kT ln   s   D 2 
w 

15
b

DG( c )  kT ln   s   D 
w

Analyses of thermal activation: critical stress
For constant strain rate: eff varies during Dt
Can we find a constant stress (c) providing the same survival probability at s ?
DG ( c )
wc   exp 
kT
wc 
 s

exp wc s   exp  w (t ) dt
 0

1
s
s
 w (t ) dt 
w (t )
s
0
Development of DG = A - V*eff
1
*
c 
ln
exp(

V
 eff )
*
V
c little sensitive to V*
16
Dt
The critical and the maximum stresses
Critical stress for voids
400
(GPa)
300
max
200
• Always c < max
• When T tends to 0K, c tends to max
• At high T, c is 30% lower than max
c
100
T (K)
0
0
17
200
400
600
Activation energy = f (stress, temperature)
Experimental evidence DG(c) = CKT
Activation energy
0.5
0.5
DG (eV)
DG (eV)
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
C = 8.1
T (K)
0.0
2.5
3.0
3.5
c(GPa)
4.0
0.0
4.5
0
200
400
600
  b
DG( c )  kT ln Dt D   C kT
 2w 
• Dt varies slowly with T
• Dt varies with strain rate
18
MD simulations (Dt  1 ns): C = 8
Experiment (Dt  1 s): C = 25
800
Dislocation Dynamics simulations of void strengthening
Using of atomic simulation results in DD
• validation of DD simulations
• determination of void strengthening
19
Validation of dislocation dynamics code
Example of the Orowan mechanism
2
 c (b Lp )
Screw
1,5
1
Edge
0,5
D b
0
1
10
100

 c  A ln   B 
L p   r0 

1000
b   D 
20
[Bacon et al. PhilMag 1973]
Simulation of the Orowan mechanism
Comparison of dislocation shape
Edge dislocation - void interaction
 c (voids)  4.25 GPa
21
Thermal activation simulations in DD
Edge dislocation - void interaction
250
eff
DD
200
Activation path in DD
• Computation of eff
• Calculation of DG(eff)
• Estimation of dp =w(t)dt
MD
150
0
200
400
600
• Selection of a random number x
• jump if x > dp
22
Comparison between DD and MD results
DD prediction of void strengthening
Prediction of the critical stress
250
200
150
100
50
0
0.0
• Average dislocation velocity : 5 m/s
23
• Number of voids : 12500
0.5
1.0
1.5
T° K
Periodic row
Random distribution
0K
245 MPa
200 MPa
600 K
165 MPa
140 MPa
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
24
Collaborators
• Christophe Domain, MMC, EDF-R&D, 77818 Moret sur loing, France
• Dmitry Terentyev,
• Benoit Devincre,
SCK-CEN, Boeretang 200, B-2400, Mol, Belgium
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
25
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 DG (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?
26
Screw dislocation in first principals simulations
Ab initio simulation
EAM potential, Mendelev et al. 2003
27
EAM potential,Ackland et al. 1997