Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects
We performed analysis of the basic mechanism of
 radiation embrittlement of steels and weld seams
 with account of the direct matrix fracture, precipitation
 and segregation of chemical elements. A
 model is proposed, which describes matrix fracture
 due to it...
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| Опубліковано в: : | Проблемы прочности |
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| Дата: | 2004 |
| Автори: | , , , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2004
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation
 Embrittlement of Model Alloys: Cu and P Effects / L. Debarberis, A. Kryukov, F. Gillemot, M. Valo, A. Morozov,
 M. Brumovsky, B. Acosta, F. Sevini // Проблемы прочности. — 2004. — № 3. — С. 65-71. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860133618868813824 |
|---|---|
| author | Debarberis, L. Kryukov, A. Gillemot, F. Valo, M. Morozov, A. Brumovsky, M. Acosta, B. Sevini, F. |
| author_facet | Debarberis, L. Kryukov, A. Gillemot, F. Valo, M. Morozov, A. Brumovsky, M. Acosta, B. Sevini, F. |
| citation_txt | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation
 Embrittlement of Model Alloys: Cu and P Effects / L. Debarberis, A. Kryukov, F. Gillemot, M. Valo, A. Morozov,
 M. Brumovsky, B. Acosta, F. Sevini // Проблемы прочности. — 2004. — № 3. — С. 65-71. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | We performed analysis of the basic mechanism of
radiation embrittlement of steels and weld seams
with account of the direct matrix fracture, precipitation
and segregation of chemical elements. A
model is proposed, which describes matrix fracture
due to its neutron bombardment and for 11
model alloys provides an accurate description of
the processes of primary embrittlement and
re-embrittlement after scheduled heat treatment
(annealing). The distinctive features of the proposed
model are a possibility of explaining the
embrittlement processes before and after annealing
for alloys with low (or zero) Ni content and
its applicability to the analysis of operational behavior
of WWER materials.
Выполнен анализ основного механизма радиационного охрупчивания сталей и сварных швов с
учетом разрушения матрицы материала, осаждения и выделения химических элементов.
Предложена модель разрушения матрицы вследствие нейтронной бомбардировки, что
позволяет достаточно точно описать для 11 модельных сплавов процессы первичного и
вторичного охрупчивания после плановой термообработки (отпуск). Особенностью модели
является возможность объяснения отличий между процессами охрупчивания до и после
отпуска сплавов с малым (или нулевым) содержанием никеля, что позоляет использовать ее
для анализа поведения материалов, используемых в реакторах ВВЭР, при эксплуатации.
Виконано аналіз механізму радіаційного окрихчення сталей та зварних швів
з урахуванням руйнування матриці матеріалу, осадження і виділення хімічних
елементів. Запропоновано модель руйнування матриці унаслідок нейтронного
бомбардування, що дозволяє достатньо точно описати для 11 модельних
сплавів процеси первинного і вторинного окрихчення після планової
термообробки (відпуск). Особливістю моделі є можливість пояснити
відмінності між процесами окрихчення до і після відпуску сплавів із малим
(або нульовим) вмістом нікелю, що дозволяє проводити аналіз поведінки
матеріалів для реакторів ВВЕР при експлуатації.
|
| first_indexed | 2025-12-07T17:46:28Z |
| format | Article |
| fulltext |
UDC 539.4
Use of a Semi-Mechanistic Analytical Model to Analyze Radiation
Embrittlement of Model Alloys: Cu and P Effects
L. Debarberis,a A. Kryukov,b F. Gillemot,c M. Valo,d A. Morozov,e
M. Brumovsky,f B. Acosta,a and F. Sevinia
a Joint Research Center of the European Commission, Institute for Energy (JRC-IE),
Petten, the Netherlands
b Russian Research Center, Kurchatov Institute, Moscow, Russia
c AEKI, Budapest, Hungary
d VTT, Espoo, Finland
e PROMETEY, St. Petersburg, Russia
f Nuclear Research Institute (NRI), Rzez, Czechia
УДК 539.4
Применение полумеханистической аналитической модели для
анализа радиационного охрупчивания модельных сплавов.
Влияние содержания меди и фосфора
Л. Дебарбериса, А. Крюков6, Ф. Жиллемов, М. Валог, А. Морозовд,
М. Брумовские, Б. Акостаа, Ф. Севиниа
а Объединенный исследовательский центр Европейской комиссии, Энергетический
институт, Петтен, Нидерланды
б Российский исследовательский центр, Институт атомной энергии им. И. В. Курча
това, Москва, Россия
в АЕКИ, Будапешт, Венгрия
г ВТТ, Эспо, Финляндия
д ЦНИИ КМ “Прометей”, Санкт-Петербург, Россия
е Институт ядерных исследований, Ржеж, Чехия
Выполнен анализ основного механизма радиационного охрупчивания сталей и сварных швов с
учетом разрушения матрицы материала, осаждения и выделения химических элементов.
Предложена модель разрушения матрицы вследствие нейтронной бомбардировки, что
позволяет достаточно точно описать для 11 модельных сплавов процессы первичного и
вторичного охрупчивания после плановой термообработки (отпуск). Особенностью модели
является возможность объяснения отличий меж ду процессами охрупчивания до и после
отпуска сплавов с малым (или нулевым) содержанием никеля, что позоляет использовать ее
для анализа поведения материалов, используемых в реакторах ВВЭР, при эксплуатации.
Ключевые слова: радиационное охрупчивание, полумеханистическая анали
тическая модель, отпуск.
© L. DEBARBERIS, A. KRYUKOV, F. GILLEMOT, M. VALO, A. MOROZOV, M. BRUMOVSKY,
B. ACOSTA, F. SEVINI, 2004
ISSN 0556-171X. Проблемы прочности, 2004, № 3 65
L. Debarberis, A. Kryukov, F. Gillemot, et al.
Background. General agreement on basic mechanism of radiation
embrittlement exists for primary embrittlement of steels and welds based on three
major contributions to damage: direct matrix damage, precipitation (mainly Cu)
and element segregation (mainly P). In spite of this fact, available models for
analysis of radiation data are mainly based on statistical correlation of large sets
of data. In this paper, a semi-mechanistic model based on key mechanisms is
proposed, which allows improved fitting of data and permits the visualization of
the relative contribution of the various damage components.
A set of model alloys with parametric variation of Cu, P, and Ni content have
been irradiated in High Flux Reactor (HFR) Petten and tested [1-4]. A second set
of such model alloys has been irradiated in Kola NPP, Russia
The low Ni model alloys results are studied in detail and demonstrate the
applicability of the proposed model to commercial steels and welds, in particular,
to WWER-440 type materials.
Key Embrittlement Mechanisms. The key embrittlement mechanisms
taking place during irradiation of RPV steels and welds are summarized in Table 1
[5].
T a b l e 1
Embrittlement Mechanisms Considered
Embrittlement mechanism Intrinsic features
Direct matrix damage Due to neutron bombardment
Matrix precipitation hardening Cu is the leading element
Segregation P is a recognized segregating element
Direct matrix damage due to neutron bombardment can be assumed to be
simply root square dependent on fluence for the particular material and
temperature. At higher irradiation temperatures the rate of damage is considered
to be decreasing due to increased atoms mobility.
During direct matrix damage formation, Cu, among with other elements, is
known to lead precipitation mechanism of nano-precipitates also inducing matrix
hardening and embrittlement. Such mechanism occurs until saturation depending
on available amount of precipitants, Cu concentration in particular.
In addition to matrix damage, other elements, like P, can segregate in grains
(and/or through diffusion processes at grain boundaries) or get attracted into the
Cu-type precipitates. Diffusion of segregants also takes place making this
mechanism rather difficult to understand in detail.
The analytical model based on the above-mentioned key mechanisms is
proposed and reviewed below.
Semi-Mechanistic Model. The effect of the various embrittlement
parameters is considered to be additive to the total damage expressed in terms of
ATshift ■ Matrix damage contribution, assumed to be square root dependent on
fluence, is then described as follows:
ATshift(matrix) _ [^ ^ ],
66 ISSN 0556-171X. npoôëeMbi npounocmu, 2004, N 3
Use o f a Semi-Mechanistic Analytical Model
where ATshift is the transition temperature shift component, O is the neutron
fluence, a is model fitting parameter, and n is the exponent (normally n = 1/ 2).
The parameter a is constant value for a given material and a given
irradiation temperature, which value decreases with incresing irradiation
temperature.
The contribution of Cu precipitation to the total transition temperature
shift can be described as
ATshift(Cu precipitation) _ b1[1 — e ̂ sa‘ ],
where b1 is a model fitting parameter, representing the maximum saturation
value of the shift due to precipitation, and O sat is a model fitting parameter,
representing the fluence at which saturation effects begin.
Subsequently other segregants can be formed both proportionally to the
matrix damage and attracted into the Cu precipitates. Diffusion of segregants
plays also a role. To describe this additional contribution the following simple
model is proposed. It is based on a “logistic” shape type of function describing a
process of gradual increase followed by a rapid saturation:
AT = cshift(P segregation) c1
where c1 is a model-fitting parameter representing the maximum saturation value
of the shift due to segregation, O start is a model parameter representing the
fluence at which segregation starts, and c2 is a model parameter representing the
increase rate of the saturation effect.
Based on the above partial effects, the total effect in term of transition
temperature shift is
ATshifi = aO n + b j H - e - ° / ° sat ]+ c1
An example of primary radiation embrittlement calculated with the proposed
model is given in Fig. 1.
The relative contribution of the various damage components is also
visualized in Fig. 1. In total, a maximum of 6 parameters are required for the
prop°sed model: a , b^ O sat, c1, c 2 , and O start •
In order to simplify the fitting, some parameters (O sat , O start , and c2 ) can
be derived and fixed in first instance depending on the general behavior of the
analyzed data. The most important parameters are: a , b1, and c1. Provided the
model is correct, parameter b1 should depend mainly on Cu content, while c1
mainly on P content.
The proposed model is applicable for analyzing real surveillance data sets,
which can not be described by simple power-type functions.
start (1)
\
2 2 I c2
ISSN 0556-171X. npodxeMbi npounocmu, 2004, N 3 67
L. Debarberis, A. Kryukov, F. Gillemot, et al.
TO TAL
/ Pre i ip i ta t io n {Cu le ad)
ïeg regê tion (P lead)
Direc t matr ix lamage
1.0QE + 18 5.1 OE + 19 1.Q1E+20 151E+20 2.01E+20
F lu e n c e , n *c n r2
Fig. 1. Example of primary radiation embrittlement calculated with proposed model (Eq. 1).
In particular, the model accounts for the peculiar re-embrittlement behavior
after annealing of high P steels, like some WWER-440 high P welds. What is in
fact observed in the above steels [4] is that the embrittlement kinetics after
annealing is different than before annealing: re-embrittlement starts with a certain
delay and then rapidly increases. Such behavior is supported by microstructural
investigations indicating that during annealing P does massively re-solute back
and is almost fully available for the re-embrittlement, in contrast to Cu, which
would thus contribute marginally to re-embrittlement. The hypothesis that P is a
leading element of re-embrittlement after annealing is also supported by the
available data on WWER-440. In fact, the transition temperature shift is strongly
correlated with P content, but not with Cu content.
Application of the proposed model makes it possible to predict the specific
re-embrittlement behavior in comparison with the primary embrittlement. In fact,
assuming that P is the leading element of re-embrittlement and that Cu has
marginal effect, we can simply suppress the Cu term during the re-embrittlement
after annealing. The pattern obtained (see Fig. 2) reproduces qualitatively well the
behavior shown by WWER-440 high P welds.
2 .E + 19 4.E+19 6.E+19 8.E+19 10 .E +19
Fluence, n cnr2
Fig. 2. Example of primary radiation embrittlement and re-embrittlement calculated with proposed
model (Eq. 1).
68 ISSN 0556-171X. Проблемы прочности, 2004, № 3
Use o f a Semi-Mechanistic Analytical Model
Model Application to Model Alloys Data. The proposed model is tested on
available data of model alloys. A set of model alloys with parametric variation of
Cu, P and Ni content has been irradiated in HFR Petten and Kola NPP [6].
Both irradiations were executed at 270oC and at very similar fluence rate to
n ■
■>18
12 _2
minimize rate effects: — 2^10 n■cm . The obtained fluence at the HFR and
Kola were respectively ~ 6.9■ 1018 and — 7T1018 n■cm 2. The shifts obtained at
the HFR ranged from few degrees for very pure alloys to up to more than 2500C
for alloys with very high combined contents of Cu and P. The shifts obtained in
Kola, in spite of the much higher fluence, were just slightly higher than those
obtained at HFR.
The proposed semi-mechanistic model has been tested and refined using 22
data sets in total. First the data on alloys with low P contents have been analyzed,
in order to single out effect of Cu and related parameters; see for example Fig. 3.
Subsequently, the additional effect of P have been analyzed for the alloys
containing P at different Cu contents. The segregation parameters have been
optimized to fit the data (see Fig. 4).
CÛÛ
HFR data
I V K C u
Kola data
ж s '
H C u
I — ---------------------------- •
L C u ♦
J i-— ----------
4 0 .0 0
Fluence, 1018 n-cnr2
XCO
m
D
3 0 0
2 5 0
200
1 5 0
100
5 0
0
0.00
HFR data
I VH Cu & H P
Kola data
------ /
1 ■ /
VH Cu & M P
! A H Cu & H P •
i <S L Cu & H P — *--------
4 0 .0 0
Fluence. 101S n cm 2
Fig. 3 Fig. 4
Fig. 3. Model tuning on P free alloys (VH Cu —0.9 wt.%; H Cu —0.4 wt.%; L Cu —0.05 wt.%).
Fig. 4. Model tuning on P rich alloys; additional effect of P (H P —0.04 wt.%; M P —0.01 wt.%).
Ь term in model c1 term in model
Fig. 5. Model parameters linearly related to Cu and P contents.
The proposed model can be optimized to fit the complete data set of Ni-free
alloys at both fluences. The model parameters for precipitation and segregation,
as expected, are in direct relation with the Cu and P contents, respectively. The
ISSN 0556-171X. Проблемы прочности, 2004, N2 3 69
L. Debarberis, A. Kryukov, F. Gillemot, et al.
CQ T3
R 2 = 0.927
■
♦
♦
♦ HFR data
■ Kola data
DBTT SHIFT, °С
Measured
Fig. 6. Model prediction (Eq. 1) versus measured DBTT shifts (for all alloys and two fluences).
observed relationship is simply linear, which confirms validity of the proposed
model (see Fig. 5). The overall capability of the model to predict the behavior of
the 11 model alloys at the two fluences is summarized in Fig. 6 . The fitting could
be further improved by using weighting factors for a few data points with lower
probabilities than others, but for the scope of this work the results are considered
to be satisfactory, and real improvement can be achieved by producing new sets
of data at lower fluence, below the HFR fluence actual value [7].
Conclusions. The basic mechanisms of radiation primary embrittlement of
steels and welds are direct matrix damage, precipitation (mainly Cu) and element
segregation (mainly P). The effect of the various embrittlement parameters is
considered to be additive to the total damage expressed in terms of ATshij -t .
The proposed model has been tested on a large set of data on Ni-free model
alloys irradiated at the same temperature and at two very different fluences
obtained at the HFR Petten and Kola NPP.
The model was used to analyze the behavior of Ni-free alloys and fit the
qualified data sets qualitatively very similar to WWER-440 materials. The model
allowed to describe the re-embrittlement differences when compared to primary
embrittlement. It is recommended for application to commercial WWER steels and
welds [8-9].
Резюме
Виконано аналіз механізму радіаційного окрихчення сталей та зварних швів
з урахуванням руйнування матриці матеріалу, осадження і виділення хіміч
них елементів. Запропоновано модель руйнування матриці унаслідок нейт
ронного бомбардування, що дозволяє достатньо точно описати для 11 мо
дельних сплавів процеси первинного і вторинного окрихчення після плано
вої термообробки (відпуск). Особливістю моделі є можливість пояснити
відмінності між процесами окрихчення до і після відпуску сплавів із малим
(або нульовим) вмістом нікелю, що дозволяє проводити аналіз поведінки
матеріалів для реакторів ВВЕР при експлуатації.
1. High Flux Reactor (HFR) Petten, EUR 15151 EN.
70 ISSN 0556-171X. Проблеми прочности, 2004, № 3
Use o f a Semi-Mechanistic Analytical Model
2. L. Debarberis, F. Sevini, B. Acosta, et al., “Results of embrittlement studies
on model alloys, reference steels, and RPV materials at JRC-IE,” PLIM-
PLEX‘01 Conference, London, Nov. 28-30, 2001.
3. L. Debarberis, F. Sevini, B. Acosta, et al., “Results of embrittlement studies
on model alloys, reference steels, and RPV materials at JRC-IAM,” 7th Int.
Conf. on Materials Issues in Design, Manufacturing, and Operation o f NPP
Equipment (June 2002), St. Petersburg, Russia.
4. L. Debarberis, K. Torronen, F. Sevini, et al., “Experimental studies of
copper, phosphorus, and nickel effect on RPV model alloys at two different
fluences,” 6th Int. Conf. on Materials Issues in Design, Manufacturing, and
Operation o f NPP Equipment (June 19-23, 2000), St. Petersburg, Russia.
5. N. N. Alekseenko, A. Amaev, I. Goryn, V. A. Nikolaev, “Radiation damage
of nuclear power plant pressure vessel steels,” in: ANS Russian Materials
Monograph Series (1997), ISBN 0-89448-564-4.
6 . L. Debarberis, F. Sevini, B. Acosta, et al., “Comparison with irradiation
embrittlement of model alloys and commercial steels; analysis of similitude
behaviors,” in: International Journal Materials (in print).
7. L. Debarberis, F. Sevini, B. Acosta, et al., “Irradiation embrittlement of
model alloys and commercial steels: analysis of similitude behavior,” Int. J.
Pres. Vessel & Piping, 79, 637-642 (2002).
8. A. Kryukov, D. Erak, Y. Shtrombakh, et al., “Advanced model for the
WWER RPV material re-embrittlement assessment,” IAEA Expert Meeting
on Irradiation Embrittlement, UK (2002).
9. A. Kryukov and L. Debarberis, “Achievements, open issues and developments
on WWER RPV irradiation embrittlement assessment & AMES European
Network Strategy,” IAEA Specialist Meeting on Irradiation Embrittlement,
Madrid (1999)
Received 05. 09. 2003
ISSN 0556-171X. npoôëeMbi npounocmu, 2004, N 3 71
|
| id | nasplib_isofts_kiev_ua-123456789-47089 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T17:46:28Z |
| publishDate | 2004 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Debarberis, L. Kryukov, A. Gillemot, F. Valo, M. Morozov, A. Brumovsky, M. Acosta, B. Sevini, F. 2013-07-09T17:34:13Z 2013-07-09T17:34:13Z 2004 Use of a Semi-Mechanistic Analytical Model to Analyze Radiation
 Embrittlement of Model Alloys: Cu and P Effects / L. Debarberis, A. Kryukov, F. Gillemot, M. Valo, A. Morozov,
 M. Brumovsky, B. Acosta, F. Sevini // Проблемы прочности. — 2004. — № 3. — С. 65-71. — Бібліогр.: 9 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/47089 539.4 We performed analysis of the basic mechanism of
 radiation embrittlement of steels and weld seams
 with account of the direct matrix fracture, precipitation
 and segregation of chemical elements. A
 model is proposed, which describes matrix fracture
 due to its neutron bombardment and for 11
 model alloys provides an accurate description of
 the processes of primary embrittlement and
 re-embrittlement after scheduled heat treatment
 (annealing). The distinctive features of the proposed
 model are a possibility of explaining the
 embrittlement processes before and after annealing
 for alloys with low (or zero) Ni content and
 its applicability to the analysis of operational behavior
 of WWER materials. Выполнен анализ основного механизма радиационного охрупчивания сталей и сварных швов с
 учетом разрушения матрицы материала, осаждения и выделения химических элементов.
 Предложена модель разрушения матрицы вследствие нейтронной бомбардировки, что
 позволяет достаточно точно описать для 11 модельных сплавов процессы первичного и
 вторичного охрупчивания после плановой термообработки (отпуск). Особенностью модели
 является возможность объяснения отличий между процессами охрупчивания до и после
 отпуска сплавов с малым (или нулевым) содержанием никеля, что позоляет использовать ее
 для анализа поведения материалов, используемых в реакторах ВВЭР, при эксплуатации. Виконано аналіз механізму радіаційного окрихчення сталей та зварних швів
 з урахуванням руйнування матриці матеріалу, осадження і виділення хімічних
 елементів. Запропоновано модель руйнування матриці унаслідок нейтронного
 бомбардування, що дозволяє достатньо точно описати для 11 модельних
 сплавів процеси первинного і вторинного окрихчення після планової
 термообробки (відпуск). Особливістю моделі є можливість пояснити
 відмінності між процесами окрихчення до і після відпуску сплавів із малим
 (або нульовим) вмістом нікелю, що дозволяє проводити аналіз поведінки
 матеріалів для реакторів ВВЕР при експлуатації. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects Применение полумеханистической аналитической модели для анализа радиационного охрупчивания модельных сплавов. Влияние содержания меди и фосфора Article published earlier |
| spellingShingle | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects Debarberis, L. Kryukov, A. Gillemot, F. Valo, M. Morozov, A. Brumovsky, M. Acosta, B. Sevini, F. Научно-технический раздел |
| title | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects |
| title_alt | Применение полумеханистической аналитической модели для анализа радиационного охрупчивания модельных сплавов. Влияние содержания меди и фосфора |
| title_full | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects |
| title_fullStr | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects |
| title_full_unstemmed | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects |
| title_short | Use of a Semi-Mechanistic Analytical Model to Analyze Radiation Embrittlement of Model Alloys: Cu and P Effects |
| title_sort | use of a semi-mechanistic analytical model to analyze radiation embrittlement of model alloys: cu and p effects |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/47089 |
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