A COMPOSITE MODEL
OF
MICROSTRUCTURAL EVOLUTION
IN
AUSTENITIC STAINLESS
STEEL UNDER FAST NEUTRON IRRADIATION*
R.
E.
Stoller
Metals
and
Ceramics Division
Oak Ridge National Laboratory
Oak Ridge,
TN
37331
and
CONF-860605—28
G.
R.
Odette
University
of.
California
DE87
000018
Santa Barbara,
CA
ABSTRACT
A rate-theory-based model
has
been developed which includes
the
simultaneous evolution
of the
dislocation
and
cavity components
of the
microstructure
of
irradiated austenitic stainless steels. Previous work
has generally focused
on
developing models
for
void swelling while
neglecting the time dependence
of
the dislocation structure. These models
have broadened
our
understanding
of
the physical processes that give rise
to swelling, e.g.,
the
role
of
helium
and
void formation from critically-
sized bubbles. That work
has
also demonstrated some predictive capability
by successful calibration
to fit the
results
of
fast reactor swelling data.
However, considerable uncertainty about the values
of
key
parameters
in
these models limits their usefulness
as
predictive tools. Hence the use
of
such models
to
extrapolate fission reactor swelling data
to
fusion reactor
conditions
is
compromised.
The present work represents
an
effort
to
remove some
of
these uncer-
tainties
by
self-consistently generating the time dependence
of
the dislo-
*Research sponsored
by
the Division
of
Materials Sciences, U.S.
Department
of
Energy, under contract DE-AC05-840R21400 with Martin Marietta
Energy Systems, Inc.
and
the Office
of
Fusion Energy, U.S. Department
of
Energy, under contract AM03-765F00034 with the University
of
California
at
Santa Barbara. Partial support
for
one
of
the authors (Stoller)
was
pro-
vided
by
the U.S. DOE Magnetic Fusion Energy Technology Fellowship Program
administered
by
the Oak
Ridge Associated Universities.
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of
this article,
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the
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ratlin
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in and to any
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covering
the
article.
cation structure, both faulted loops and network dislocations. The model's
predictions reveal the closely coupled nature of the evolution of the
various microstructural components and generally track the available fast
reactor data in the temperature range of 350-700°C for doses up to 100 dpa.
As the theoretical model has become more complex, parameter choices were
constrained to a more limited range of values in order to obtain this
agreement between theory and experiment. While the model remains approxi-
mate in many respects, it should ultimately provide a more useful tool for
understanding microstructural evolution under irradiation and permit more
confident predictions of void swelling in future fusion reactors.
INTRODUCTION
The task of predicting the observable effects of neutron irradiation
of stainless steel is hindered by the complex interactions of numerous
microscopic phenomena
(1,2).
A rigorous treatment requires that one con-
sider the simultaneous evolution of the various microstructural features
and microchemical effects such as solute segregation and irradiation
induced phase instabilities. Parameters such as effective point defect
biases are difficult to quantify precisely, yet they play a major role in
determining the nucleation and growth rates of the various extended
defects.
Development of theoretical models is further hindered by an incomplete
data base and large heat-to-heat variations in microstructural data. Such
variations may in part be related to effects such as reactor duty differen-
ces during various experiments or uncertainties in the temperature, flux,
and fluence at which the experiment was conducted. However, type 316
stainless steel has also shown a significant sensitivity to subtle changes
in minor alloying elements (e.g. carbon, titanium, and silicon) (3) and
details of thermo-mechanical treatment. Such sensitivity increases the
uncertainty in determining values for certain critical physical parameters,
such as "effective" diffusion coefficients and the recombination coeffi-
cient. Further, model predictions are not unique in that various combina-
tions of mechanisms and parameters can result in "reasonable" agreement
with the data. This is particularly a problem if interpretation of limited
data sets, containing intrinsic uncertainties, are interpreted in terms of
single or few mechanisms. Unfortunately such interpretations are often
further compromised by only qualitatively considering the underlying mecha-
nisms and by failing to consider the statistical significance of so-called
data trends. Single mechanism models can be very important in developing
an understanding of individual processes; however, they can justifiably be
applied in quantitative analysis only if both rigorous control over experi-
mental variables is maintained and if it can be shown that the interaction
of multiple mechanisms is not important. This is not often the case in
practice. However, empirical approaches may still provide an engineering
expedient for data correlation and some limited extrapolation of data.
More complex quantitative models allow for competition and interaction
of mechanisms which have been identified, but they suffer from the proli-
feration of non-unique parameters as noted above. Hence, they are most
effective as analytical tools only if the possible ranges of parameter com-
binations are identified and considered in any extrapolation. Two impor-
tant components of any data analysis effort are the explicit recognition of
the likely non-uniqueness of any single calibration and a quantitative
effort to ascertain the consequences of this in extrapolated predictions.
This general problem has been discussed in some detail previously (1).
The model described below is part of an overall effort to develop a
quantitative understanding of microstructural evolution in irradiated
alloys.
The model focuses on the coupled evolution of the major
microstructural features observed in irradiated austenitic stainless
steels;
bubbles, voids, faulted dislocation loops and network dislocations.
The effects of second phase precipitate particles are included to a limited
degree.
The effects of microchemical evolution, which is knov/n to occur
and is likely to be of importance, are not explicitly treated. However,
the influence of microchemical evolution is approximately accounted for in
the various rate theory parameters. The major approximation here is in the
use of material parameters (e.g. biases and diffusivities) which are not
altered to reflect either spatial or temporal fluctuations in the alloy
composition.
DESCRIPTION OF THE MODEL
The model developed here is an extension of previous work which exa-
mined primarily the evolution of the cavity component of the irradiated
microstructure
(4—8).
That work helped to establish the generally accepted
sequence of events which lead to void swelling; viz., that bubbles nucleate
and slowly grow by accumulating both vacancies and helium until they reach
a critical size, r*, which is determined by the vacancy supersaturation, S,
the material parameters y, the surface energy and ft, the atomic volume and
temperature, T.
r* = f(£n S)
The function f(£n S) is a non-ideal gas correction factor (8); for an ideal
gas f = 4/3 and k is Boltzman's constant. After reaching this critical
size the bubbles are converted to voids and begin to grow primarily by
vacancy accumulation. Similar theoretical work by others has also con-
firmed this general scenario
(9-11).
Since references 6 and 7 describe the
cavity evolution model in detail, it will not be discussed further here.
Calculation of Point Defects Concentrations
The approach used to calculate the point defect concentrations
follows the familiar rate theory
(7,12).
The conventional rate equations
which describe the vacancy and interstitial concentrations are slightly
modified due to the dislocation evolution models. The following assump-
tions are implicit in the mathematical description:
1. The concentrations of vacancies and mono-, di-, tri-, and tetra-
interstitials are calculated as if they were at steady state during a
given time step.
2.
Only the mono-defects are mobile. Mobility of small clusters has been
shown to have no significant effect on the point defect calculations
(13).
A relatively high interstitial migration energy (0.85 eV) is
