Characterisation of dislocation behaviour in RPV steel
Results obtained in the framework of the European project PERFECT (FI60-CT-2003- 208840) are presented.
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irk-123456789-963462016-03-16T03:02:04Z Characterisation of dislocation behaviour in RPV steel Monnet, G. Domain, C. Bacon, D. Terentyev, D. Results obtained in the framework of the European project PERFECT (FI60-CT-2003- 208840) are presented. Наводяться результати, отримані у рамках Європейського проекту PERFECT (F160-CT- 2003-208840). Приводятся результаты, полученные в рамках Европейского проекта PERFECT (F160- CT-2003-208840). 2009 Article Characterisation of dislocation behaviour in RPV steel / G. Monnet, C. Domain, D. Bacon, D. Terentyev // Вопросы атомной науки и техники. — 2009. — № 4. — С. 42-51. — Бібліогр.: 14 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/96346 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Results obtained in the framework of the European project PERFECT (FI60-CT-2003-
208840) are presented. |
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Article |
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Monnet, G. Domain, C. Bacon, D. Terentyev, D. |
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Monnet, G. Domain, C. Bacon, D. Terentyev, D. Characterisation of dislocation behaviour in RPV steel Вопросы атомной науки и техники |
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Monnet, G. Domain, C. Bacon, D. Terentyev, D. |
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Monnet, G. |
| title |
Characterisation of dislocation behaviour in RPV steel |
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Characterisation of dislocation behaviour in RPV steel |
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Characterisation of dislocation behaviour in RPV steel |
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Characterisation of dislocation behaviour in RPV steel |
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Characterisation of dislocation behaviour in RPV steel |
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characterisation of dislocation behaviour in rpv steel |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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http://dspace.nbuv.gov.ua/handle/123456789/96346 |
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Characterisation of dislocation behaviour in RPV steel / G. Monnet, C. Domain, D. Bacon, D. Terentyev // Вопросы атомной науки и техники. — 2009. — № 4. — С. 42-51. — Бібліогр.: 14 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT monnetg characterisationofdislocationbehaviourinrpvsteel AT domainc characterisationofdislocationbehaviourinrpvsteel AT bacond characterisationofdislocationbehaviourinrpvsteel AT terentyevd characterisationofdislocationbehaviourinrpvsteel |
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2025-07-07T03:32:26Z |
| last_indexed |
2025-07-07T03:32:26Z |
| _version_ |
1836957456987586560 |
| fulltext |
CHARACTERISATION OF DISLOCATION BEHAVIOUR IN RPV STEEL
G. Monnet, C. Domain
EDF, France;
D. Bacon
University of Liverpool;
D. Terentyev
SCK CEN
Results obtained in the framework of the European project PERFECT (FI60-CT-2003-
208840) are presented.
1. MD SIMULATIONS OF SLIP
ON {112} PLANES
1.1. Atomic model of the edge dislocation
The simulation model developed by
Osetsky and Bacon [1] was employed to study
the edge dislocation in the (011) base plane
and also modified to create the edge
dislocation in the (112) plane. Both
dislocations are created with a Burgers vector
b = ½[111]. In the case of the (112)
dislocation, the principal axes x, y and z of the
simulated BCC crystal were oriented along the
[111], [11 0 ] and [112] directions,
respectively.
The straight edge dislocation with slip
plane x-y was created along the y direction and
had Burgers vector b = ½[111] parallel to the x
axis. Periodic boundary conditions were
applied along the x and y directions. The box
was divided into three parts along z. The upper
and lower parts consisted of several atomic
planes in which atoms were rigidly fixed in
their original positions (block F) or displaced
following the applied loading conditions
(block D). Atoms in the inner region were free
to move (block M). A glide force on the
dislocation was generated by the displacement
of the block D in the x direction (AD) or in the
–x direction (TD), which corresponds to
simple shear strain γ. The corresponding
resolved shear stress induced by the applied
deformation was calculated as τ = Fx/Axy,
where Fx is the total force projected in the x
direction and computed from all atoms in
block D and Axy is the xy cross-section area of
the box.
Static simulations were performed in order
to compute the structure, the elastic energy and
the Peierls barrier of the edge dislocation. The
relaxation of the atomic motion has been
performed using a combination of conjugate
gradient algorithm followed by quasidynamic
relaxation (quenching). The strain increment
was 10-6 which provides sufficient accuracy of
the estimation of the stress [1]. The size of the
crystallite used for static simulations was
140√3/2×60√2×24√6 (lattice units), the
amount of freely mobile atoms was ~1.3 M.
MD simulations were performed to
obtained stress-strain curves corresponding to
the shear deformation under constant strain
rate applied in two opposite [111] directions at
different temperatures (from 10 up to 200 K).
The size of the crystallite used for MD
simulations was the same as for static
simulations along y and z axes and 50√3/2
along x direction and the amount of freely
mobile atoms was ~450000.
The interatomic potential for bcc Fe
developed by Ackland et al. [2] was used. The
integration of Newton's equations was
performed using a constant time step equal to
5 and 1 fs for simulations at low (1-50 K) and
high (above 50 K) temperatures, respectively.
1.2. Dislocation core structure and the
Peierls model
Inspired from the dislocation Peierls model
[3], a convenient way to represent the core
structure of the edge dislocation (ED) is to
build the distribution of displacements in the
atomic planes on both sides of the slip plane.
However, in the case of the (112) dislocation,
the BCC lattice implies to remove or add three
(111) half planes on one side of the slip plane
in order to create the edge dislocation.
The periodicity in the [111] is different
from that in the [112] direction. In addition,
the (111) is not a mirror plane. This suggests
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2009. №4-1.
42 Серия: Физика радиационных повреждений и радиационное материаловедение (94), с. 42-51.
that the (112) dislocation has an asymmetrical
core structure. The Generalised Stacking Fault
Energy (GSFE) is responsible for the decrease
of the dislocation core size. It can be obtained
from ab-initio (first-principles) calculation.
The comparison between the case of the (110)
and the (112) SFE can be found in Fig. 1.
The comparison shows that when the GSFE
is asymmetrical, the dislocation core structure
is also asymmetrical.
Consequently, the connection between the
different physical features of the dislocation
core structure, i.e. the displacements in the
upper and lower layers, the local equilibrium
condition and the GSFE cannot be established
through the PN model.
0.00
0.02
0.04
0.06
0.08
0.0 0.2 0.4 0.6 0.8 1.0
γ(eV/A2)
t(b)
(110)
(112)
0
0.04
0.08
0.12
0.16
-10 -5 0 5 10(b)
x(b)
(112)
(110)
ΔΦ(b)
Fig.1. Effect of the asymmetry of GSFE of the core structure: energy of staking fault in the (110)
and (112) planes (а) and the differential disregistery in the (110) and (112) dislocation core
structures (b)
b a
1.3. Effect of temperature on the
stress-strain curves
MD simulations of plastic shear in the TD
and AD senses were performed at different
temperatures at fixed strain rate (107 s-1), using
the same MD box (50√3/2×60√6×24√2) and
adjusting the equilibrium lattice unit and MD
time step. It is important to note here that,
given the large dislocation density in the MD
simulation box, the dislocation velocity
amounts only to some m/s, which is quite
usual in mechanical tests. The large strain rate
does not lead, in our simulations, to large
dislocation velocities observed in shock wave
propagation. Stress-strain curves extracted
from the simulations are presented in Fig. 2 for
the two directions of load. The critical stress
needed for the dislocation motion decreases
drastically with temperature; it reaches half
Peierls stress already at 10 K. At T =200 K, the
maximum stress measured over the whole
simulation period did not exceed 15 MPa for
both directions of load, as shown in Fig. 2.
0.0 0.5 1.0 1.5 2.0
0
100
200
300
400
St
re
ss
(M
P
a)
Strain (%)
10 K
25 K
50 K
77 K
100 K
200 K
Anti-Twinning load
0.0 0.5 1.0 1.5 2.0
0
100
200
300
400
S
tre
ss
(M
P
a)
Strain (%)
10 K
25 K
50 K
77 K
100 K
200 K
Twinning load
Fig. 2. Loading curves of the (112) dislocation in the twinning and antitwinning directions as a
function of temperature
At low T (10 & 25 K), however, there is a
remarkable difference in the stress-strain
curves obtained for TD and AD loads. In
particular, applying AD deformation, the
43
critical stress is clearly higher and the
frequency of drops is lower, than in the case of
TD load. The larger drop in the stress suggest
that the length of a dislocation jump, while
moving from Peierls valley to another one, is
different in these two cases.
Using visualisation tools we have looked at
the motion of the dislocation core in detail.
The location of the dislocation core and
identification of atoms belonging to it was
realised as described above. Following the
motion of the dislocation core is has been
revealed that dislocation may move via
different mechanisms depending on
temperature. At T=0 K, the {112} edge
dislocation experiences a rigid motion of its
entire length over the Peierls valley.
In the absence of thermal activation, the
rigid motion in the both loading directions
requires a large quantity of mechanical work.
The stress level is of the same order of
magnitude, as that needed for the motion of
the ½<111> screw dislocation [6].
At finite temperature, the dislocation is
found to move with the help of the nucleation
and propagation of double-kinks alone its line.
Every stress drop corresponds to a jump over
several Peierls valley. In other terms, although
the stress is decreasing during the drop,
double-kinks continue to nucleate on the
dislocation line.
On the other hand, since the motion of the
(112) edge dislocation is controlled at low
temperature by the nucleation of the double-
kinks, one expects the mobility to follow the
same law as that of screw dislocation, i.e.
proportionality to the dislocation length
weighted the Boltzmann factor. One can thus
apply the same treatment proposed by Domain
et al. [6] in which the following equation was
proposed to deduce the value of critical stress
from the stress-strain curve:
kT
V
V
kT
c
ττ expln= ,
where V is the activation volume, k the
Boltzmann constant. Here we note that the
value of the τc is slightly dependent on the
activation volume. An approximate value of V
is therefore enough to obtain an approximate
value of the critical stress. In order to have a
rough approximation of V, we performed MD
simulation at T = 77 K and used different
strain rates [4]. Assuming the maximum stress
as proportional to the critical stress, the
activation volume was estimated close to 4b3.
Assuming that this value of V slightly varies at
different temperature, the critical stress as a
function temperature can be evaluated.
1.4. Conclusion
The Peierls stress for the motion of the
(112) dislocation in both senses is very large
compared to that of the (110) dislocation. This
suggests that the <111>(112) slip systems is
little active at low temperature. But this strong
Peierls resistance is shown to decrease
strongly with temperature thanks to thermal
activation. Edge dislocations can therefore
move in both senses at almost the same stress
as those in the (110) slip planes.
2. DATABASE OF INTERACTION
FORCES FOR EDGE DISLOCATIONS
AND RADIATION DEFECTS USING
DIFFERENT POTENTIALS
The aim of this research is to compare the
results of earlier computer simulations of the
interaction between edge dislocations and
defect clusters created by radiation damage in
α-iron (Fe) with similar studies using a more
recent interatomic potential. Two types of
cluster have been treated, namely self-
interstitial atom (SIA) loops and voids.
The earlier research used the interatomic
potential for α-Fe developed in 1997 by
Ackland et al. [2], but recent simulation
studies indicate that the potential derived by
Ackland, Mendelev and co-workers in 2004
[5] provides a more realistic model for point
defects, their clusters and screw dislocations
[6-8]. Thus, it was planned that some of the
previous work on the interaction of edge
dislocations with intrinsic defects such as
voids and SIA loops would be repeated with
the new potential in order to check the validity
of the atomic mechanisms and values of
critical stress, τc, found earlier. This was
considered necessary because some defect
clusters have been shown to provide
sufficiently high obstacle strength that the
branches of the dislocation at the cluster are
pulled into a screw-dipole configuration at
τc, and it is the behaviour of the screw that
44
distinguishes the two potentials. We have
examined the core structure of the infinitely
long, straight, ½<111>{1 1 0} edge
dislocation in the two models. There is no
significant difference. However, the critical
resolved shear stress for dislocation glide at
T = 0 K (the Peierls stress) for the two
models is distinctly different, i.e. about
83 MPa with the 2004 potential compared
with just under 25 MPa with the older one.
Furthermore, the steady-state dislocation
velocity under the same applied resolved
shear stress and temperature is significantly
lower with the 2004 potential, as shown in
Fig. 3. We have not found an explanation for
these differences in dislocation behaviour in
the two models.
Fig. 3. Velocity vs temperature for edge
dislocations in models of Fe under constant
applied resolved shear stress of 50 MPa
2.1. Dislocation-SIA loop interaction
The atomic-scale dynamics of an edge
dislocation interacting with self-interstitial
atom (SIA) loops was described in the report
for month 24 [9]. The effects analysed and
modelled involve either (a) loop drag by a
gliding dislocation when the loop Burgers
vector b is parallel to the glide plane, or (b)
intersection when b is inclined to the glide
plane, resulting in either absorption for small
loops or dislocation pinning before
breakaway for large loops. Papers on this
research have been published [10].
The simulations treated an edge
dislocation with b = ½[111] interacting with
SIA loops with b = ½[1 1 1], which is
inclined to the dislocation glide plane (1 1 0),
and containing either 37 or 331 interstitials.
Such a loop is attracted to the dislocation in
both cases. Small loops are easily absorbed
as jogs on the dislocation at all T by rotation
of their Burgers vector to ½[111] and are
relatively weak obstacles to dislocation
glide, whereas large loops react to form
segments with b = [010] and are strong
obstacles. The mechanisms observed are
broadly consistent with those for the large
loops, but τc at low T (i.e. 0 or 1 K) is high
(~530 MPa). The results are published in
[11].
We have now carried out simulations of
loops with 169 SIAs using the 1997 potential
in order to compare results for loops of the
same size. The τc values obtained to date are
summarised in Fig. 4,a. It is seen that
although the critical stress at low T is much
higher (by a factor of two) with the 2004
potential, there is little difference in the
critical stress between the two models at
300 K. The data in Fig. 4,a also show that
the applied strain rate (‘sr’) has little effect
on τc.
On the basis of these results, we conclude
that differences between dislocation-loop
interactions are probably not significant for
temperature conditions of interest
(T ≥300 K), but to confirm this completely
we are now determining τc at 600 K with the
1997 potential. Fig. 4,b contains the data of
Fig. 4,a together with τc for 37-SIA and 331-
SIA loops. It is clear that there is a marked
transition in obstacle strength between loops
with 37 SIAs and those with 169.
Furthermore, the effect of loop size is small
for loops that form <010> segments on
reacting with the gliding dislocation.
Finally, we are also simulating loops with
b = <100> using the two potential models
and will present the results in the next report.
45
a b
Fig. 4. Comparison of τc for an edge dislocation with b = ½<111> breaking away from a row of
interstitial loops with b = ½[1-11] for the 1997 and 2004 interatomic potentials. Applied strain
rate is in units of 106 s-1. Loops containing 169 SIAs (a); As (a) plus data from [10] for loops
containing either 37 or 331 SIAs (b)
2.2. Dislocation-void interaction
This difference in behaviour seen above for
loops at low temperature (T ~ 0 K) is also
apparent in the interaction between an edge
dislocation and a periodic row of voids. Fig. 5
shows dislocation line shape at the maximum
(critical) stress, τc, for the two potentials. The
void diameter is 2 nm. It is seen that the line
on one side of the void in the model based on
the 2004 potential (Fig. 5,b) is strongly aligned
with the [11 1 ] direction at 70° to b, which is
horizontal in these figures. Estimates of the
elastic line tension indicate that this alignment
effect is not due to elastic anisotropy: it is
assumed to arise from trapping of the
dislocation core in this orientation. On the
other hand, although no voids do not form at
0 K, it is important theoretically to investigate
the response of the material at 0 K with pre-
existing obstacles as voids. In fact, at finite
temperature, thermal activation can only
decrease the obstacle strength. The response
obtained at 0 K represents therefore the
maximum strength of the defect.
a b
Fig. 5. Dislocation line shape in the glide plane at the critical stress for a periodic row of voids
(diameter = 2 nm and centre-to-centre spacing 41.4 nm) in α-Fe at T = 0 K. The Burgers vector
direction is horizontal in these visualizations. The 1997 interatomic potential (a);
the 2004 potential (b)
46
a b
Fig. 6. Comparison of the stress vs. strain plots for an edge dislocation cutting and breaking
away from the periodic row of voids in Fig. 1 at (a) low T and (b) 300 K. ‘Ackland’ and
‘Mendelev’ refer to the 1997 and 2004 interatomic potentials [2,12], respectively
It results in τc = 350 MPa compared with
just over 200 MPa found with the older
potential - see the stress-strain plots in Fig. 6,a.
However, the marked difference in critical
stress and line shape disappears as T is raised,
as illustrated by the stress-strain plots for
300 K in Fig. 6,b. This indicates that the
results for void strengthening obtained
previously using the 1997 potential would be
consistent with those from similar simulations
based on the 2004 potential. We are now
testing this conclusion by analysing results of
new simulations across a range of conditions
of void size, temperature and strain rate.
3. DD SIMULATIONS OF CARBIDE
STRENGTHENING AT LOW
TEMPERATURE
3.1. Introduction
The present work is dedicated to the
investigation by Dislocation Dynamics (DD)
simulation of the low temperature behaviour of
RPV steel.
The low temperature mechanical behaviour
of RPV steel is controlled by the thermally
activated motion of screw dislocations.
Concerning precipitation strengthening, most
of models and theoretical approaches are based
on the assumption of isotropic mobility of
dislocations independently of their character.
Even the well established model (called in the
following the BKS model) proposed by Bacon
et al. [13] does not allow to predict
precipitation strengthening in dynamical
conditions, i.e. when the motion of dislocation
is time dependent.
We use DD simulations to predict
strengthening due to carbides in RPV steel.
The mobility law already constructed for
dislocations is found to provide a good
description of dislocation behaviour at low
temperature. They are therefore used to
investigate the effect of carbide on the flow
stress.
In the following, we present the study of the
interaction of infinite dislocations with infinite
periodic row of carbides. The study
characterises the temperature and rate effects
on the interaction. Then we show the influence
of the carbide distribution on the flow stress.
3.2. Mobility laws of dislocations
In DD simulations, the mobility law that
allows to deduce the velocity of a screw
segment vvis as function of the effective stress
τ* was fitted on experimental results using the
Kocks formulas [14]. The result of fitting
provides the following equation:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ Δ
⎟
⎠
⎞
⎜
⎝
⎛ Δ
−=
0
*
00 sinh2exp
τ
τ
kT
H
kT
HLHvvis ,
where H and τo are constant, L the screw
segment length and ∆Ho the total activation
energy close to 0.84 eV. The value of is
363 MPa is not considered to be representative
to the Peierls stress at 0 temperature.
Concerning edge dislocations, we do not
have at our disposal any experimental
information about thier mobility at low
47
temperature. Characterisation using Molecular
Dynamics (MD) simulation was only
performed in pure iron and the corresponding
viscous drag coefficient is not appropriate in
our case of RPV steel. Therefore we make the
assumption that the mobility of edge
dislocation is proportional to that of screw
dislocations with a factor K much larger than
unity. Explicitly, the velocity of edge segment is
given by:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ Δ
⎟
⎠
⎞
⎜
⎝
⎛ Δ
−=
0
*
00
0 sinh2exp
τ
τ
kT
H
kT
HKvvedge ,
where vo is constant and taken equal to
105 µm/s. The factor K is a strongly decreasing
function of temperature. This ensures that the
difference in mobility between screw and non-
screw segments decreases with temperature,
which is in agreement with experience.
3.3. Infinite dislocation interacting with
periodic row of carbides
In order to bypass difficulties related to the
carbide distribution, we start first by
characterising using DD simulation
interactions with periodic rows of carbides.
Depending of the initial character of the
infinite dislocation, the nature and the force of
interaction is strongly modified as we will see
in the following.
3.3.1. Case of edge dislocation
Although the mobility is dependent on
temperature, the length of the segment is not
affecting the velocity. Also the other
characters are treated in the same way as edge
character. We expect the precipitation
hardening to be slightly dependent on
temperature.
L = 0.1 µm
L = 2 µm
L = 0.1 µm
L = 2 µm
0
50
100
150
200
0 0.5 1 1.5 2 2.5
T = 50 K
T = 250 K
( )MPaΔ cτ
(µm)L
0
50
100
150
200
0 0.5 1 1.5 2 2.5
T = 50 K
T = 250 K
( )MPaΔ cτ
(µm)L
a b
Fig. 7. Critical shape of the edge dislocation at 50 K with different carbide spacing (a) and the
Orowan strengthening as a function of carbide spacing for 50 and 250 K (b)
In Fig. 7 we can see that the critical shape
of the dislocation is similar to that achieved
with isotropic dislocation mobility,
independently of the carbide spacing. Fig. 1,b
shows that the associated strengthening is
almost independent of temperature and close
to that predicted by the BSK model [1].
The case of non-screw dislocations is then
easy to predict and similar to the interaction in
the athermal regime. This is du to the fact that
the screw dipole generated during the
bypassing process is of low mobility in
comparison with non-screw dislocations. The
stress increment is therefore needed to
generate the screw dipole and elongation of
the latter does not involve large increase in
the stress. When the screw dipole is long
enough the mobility of screw dislocation
increases sufficiently to enable bypassing of
carbides.
3.3.2. Case of screw dislocation
Unlike edge segment, the mobility of screw
segments is strongly dependent on stress and
temperature and is affected by the length of
the segment. DD results prove that by
decreasing temperature the strengthening
decreases also. It appears that strengthening
follows two regimes: (i) at large precipitate
spacing, the strengthening is small and
48
slightly dependent of the spacing and (ii) at
small spacing, the strengthening decreases
strongly with spacing, as shown in Fig. 2.
When the temperature rises, the strengthening
approaches that given in the BSK model [13]
but remains below it.
0
50
100
150
200
250
0 1 2 3 4 5
T = 50 K
T = 250 K
( )MPaΔ cτ
(µm)L
0
50
100
150
200
250
0 1 2 3 4 5
T = 50 K
T = 250 K
( )MPaΔ cτ
(µm)L
L = 0.1 µm
L = 2 µm
L = 0.1 µm
L = 2 µm
Fig. 8. Сritical shape of the screw dislocation at 50 K with different carbide spacing(a) and the
Orowan strengthening as a function of carbide spacing for 50 and 250 K (b)
а b
The figure shows that the mechanism is
dependent on the spacing of carbide. At large
spacing the dislocation is not curved while at
small spacing, it adopts a critical shape close
to that observed in the athermal regime. The
surprising feature is that the observed
strengthening is always less than theory.
3.3.3. Case of random character
An infinite dislocation of random character
behaves as mixture of a screw and edge
dislocation. However, the corresponding
interaction is rather complicated and not
introduced here for the sake of brevity. The
random behaviour is investigated in the
following study of the interaction with random
distribution of carbides.
3.4. Carbide-induced strengthening
in RPV steel
Carbides are introduced in the simulation
space following the same procedure used to
characterise the carbide strengthening in the
athermal regime (Fig. 8). For more
information about the characterisation of the
carbide population, readers are invited to
consult the latter report.
Here we recall only that dislocations mobility
is highly anisotropic which alters the
behaviour of the dislocation microstructure.
The effect of temperature on the evolution
of the microstructure is depicted in Fig. 9. The
difference in dislocation shape suggest large
differences in the mechanical response of the
system.
T = 50 Kb
0.5 µm
T = 50 Kb
0.5 µm0.5 µm
T = 250 K
b
0.5 µm
T = 250 K
b
T = 250 K
b
0.5 µm0.5 µm
Fig. 9. Сomparison between the dislocation microstructure
obtained at 50 and 250 K
49
Here we can state some remarks from a
qualitative point of view. On the one hand, at
high temperature the anisotropy in dislocation
mobility is small and the dislocation-line shape
looks like that obtained in the athermal regime.
The corresponding strengthening is therefore
expected to be the same at room temperature.
One the other hand, since screw dislocation at
low temperature are almost not curved, we
suspect the microstructure not to be affected
by the carbide presence.
In order to have a more precise prediction
of carbide effect on the mechanical response, 4
similar DD simulations were carried out at
different temperatures, as seen in Fig. 10. The
athermal strengthening is added for
comparison.
0
5
10
15
20
25
30
35
40
0 100 200 300 400
(K)T
(MPa)Δ cτ
Athermal strengthening
0
5
10
15
20
25
30
35
40
0 100 200 300 400
(K)T
(MPa)Δ cτ
0
5
10
15
20
25
30
35
40
0 100 200 300 400
(K)T
(MPa)Δ cτ
Athermal strengthening
Fig. 10. Сarbide induced strengthening in
RPV in the athermal regime
We can see that carbide strengthening
decreases strongly at low temperature. It tends
to a threshold of almost 10 MPa at very low
temperature. The origin of this threshold is still
unknown by the author.
3.5. Conclusions
This deliverable reports DD simulation
results on carbide strengthening in RPV steel
at low temperature. We have shown that the
interaction between dislocations and carbides
depends on the local dislocation character. For
screw dislocation, the strengthening is strongly
dependent on the temperature, rate and carbide
spacing. The strengthening is a complex
function of these parameter but, in all cases, it
increases with temperature. However, no
significant temperature effect was observed in
the case of non-screw dislocations.
The behaviour of the dislocation
microstructure in the presence of random
distribution of carbides is rather complex. The
strengthening depends on temperature strain
rate. Whatever the simulation conditions, the
strengthening increases with temperature and
decreases with strain rate.
REFERENCES
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T. Harry // Phil Mag. A.1997, v. 75, p. 713.
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v. 52, p. 23.
4. G. Monnet, D. Terentyev // Acta Mater.
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Condens. Matter. 2004, v. 16, p. 2629.
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PERFECT WP IV.
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50
ХАРАКТЕРИСТИКА ПОВЕДЕНИЯ ДИСЛОКАЦИЙ В СТАЛИ ДПЛА
Дж. Монет, С. Домейн, Д. Бейкон, Д. Терентьев
Приводятся результаты, полученные в рамках Европейского проекта PERFECT (F160-
CT-2003-208840).
ХАРАКТЕРИСТИКА ПОВЕДІНКИ ДИСЛОКАЦІЙ В СТАЛІ ДПЛА
Дж. Монет, С. Домейн, Д. Бейкон, Д. Терентьєв
Наводяться результати, отримані у рамках Європейського проекту PERFECT (F160-CT-
2003-208840).
51
CHARACTERISATION OF DISLOCATION BEHAVIOUR IN RPV STEEL
1. MD SIMULATIONS OF SLIP
ON {112} PLANES
1.1. Atomic model of the edge dislocation
1.2. Dislocation core structure and the Peierls model
1.3. Effect of temperature on the
stress-strain curves
1.4. Conclusion
2. DATABASE OF INTERACTION FORCES FOR EDGE DISLOCATIONS AND RADIATION DEFECTS USING DIFFERENT POTENTIALS
2.1. Dislocation-SIA loop interaction
2.2. Dislocation-void interaction
3. DD SIMULATIONS OF CARBIDE STRENGTHENING AT LOW TEMPERATURE
3.1. Introduction
3.2. Mobility laws of dislocations
3.3. Infinite dislocation interacting with periodic row of carbides
3.3.1. Case of edge dislocation
3.3.2. Case of screw dislocation
3.3.3. Case of random character
3.4. Carbide-induced strengthening
in RPV steel
3.5. Conclusions
ХАРАКТЕРИСТИКА ПОВЕДЕНИЯ ДИСЛОКАЦИЙ В СТАЛИ ДПЛА
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