Local approach to fracture based prediction of reactor pressure vessel lifetime
New version of the local approach to fracture is presented. Within the framework of this approach a new methodology is developed, which supposes prediction of radiation life time of a reactor pressure vessel not by ultimate shift of the Charpy critical temperature, ΔTк, or by reference temperature,...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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irk-123456789-484762013-08-20T07:29:42Z Local approach to fracture based prediction of reactor pressure vessel lifetime Kotrechko, S.A. Meshkov, Yu.Ya. Научно-технический раздел New version of the local approach to fracture is presented. Within the framework of this approach a new methodology is developed, which supposes prediction of radiation life time of a reactor pressure vessel not by ultimate shift of the Charpy critical temperature, ΔTк, or by reference temperature, ΔT0 but by the condition of brittle fracture initiation of irradiated metal ahead of a crack tip in reactor pressure vessels. Предложен новый вариант локального подхода к разрушению. В рамках данного подхода разработана методика, согласно которой долговечность реакторных сосудов давления при радиации оценивается не по предельному смещению критической или исходной температуры, а из условия начала хрупкого разрушения облученного металла впереди вершины трещины в реакторном сосуде давления. 2009 Article Local approach to fracture based prediction of reactor pressure vessel lifetime / S.A. Kotrechko, Yu.Ya. Meshkov // Проблемы прочности. — 2009. — № 1. — С. 53-60. — Бібліогр.: 5 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48476 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Kotrechko, S.A. Meshkov, Yu.Ya. Local approach to fracture based prediction of reactor pressure vessel lifetime Проблемы прочности |
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New version of the local approach to fracture is presented. Within the framework of this approach a new methodology is developed, which supposes prediction of radiation life time of a reactor pressure vessel not by ultimate shift of the Charpy critical temperature, ΔTк, or by reference temperature, ΔT0 but by the condition of brittle fracture initiation of irradiated metal ahead of a crack tip in reactor pressure vessels. |
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Kotrechko, S.A. Meshkov, Yu.Ya. |
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Kotrechko, S.A. Meshkov, Yu.Ya. |
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Kotrechko, S.A. |
| title |
Local approach to fracture based prediction of reactor pressure vessel lifetime |
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Local approach to fracture based prediction of reactor pressure vessel lifetime |
| title_full |
Local approach to fracture based prediction of reactor pressure vessel lifetime |
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Local approach to fracture based prediction of reactor pressure vessel lifetime |
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Local approach to fracture based prediction of reactor pressure vessel lifetime |
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local approach to fracture based prediction of reactor pressure vessel lifetime |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2009 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/48476 |
| citation_txt |
Local approach to fracture based prediction of reactor pressure vessel lifetime / S.A. Kotrechko, Yu.Ya. Meshkov // Проблемы прочности. — 2009. — № 1. — С. 53-60. — Бібліогр.: 5 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT kotrechkosa localapproachtofracturebasedpredictionofreactorpressurevessellifetime AT meshkovyuya localapproachtofracturebasedpredictionofreactorpressurevessellifetime |
| first_indexed |
2025-07-04T08:59:56Z |
| last_indexed |
2025-07-04T08:59:56Z |
| _version_ |
1836706270607835136 |
| fulltext |
UDC 539.4
Local Approach to Fracture Based Prediction of Reactor Pressure
Vessel Lifetime
S. A. K otrechko an d Yu. Y a. M eshkov
Kurdyumov Institute for Metal Physics, National Academy of Sciences of Ukraine, Kiev,
Ukraine
New version o f the local approach to fracture is presented. Within the framework o f this approach a
new methodology is developed, which supposes prediction o f radiation life time o f a reactor
pressure vessel not by ultimate shift o f the Charpy critical temperature, ATK, or by reference
temperature, AT> but by the condition o f brittle fracture initiation o f irradiated metal ahead o f a
crack tip in reactor pressure vessels.
K e y w o r d s : local approach, reactor pressure vessel (RPV) steels, RPV lifetime,
fracture toughness, local stress.
In tro d u c tio n . A critical-temperature-shift-based methodology is used for
assessment o f irradiation embrittlement o f pressure vessel steels. Conventionally,
the Charpy temperature shift m ethodology is utilized. Moreover, the attempts are
made to use the M aster curve technique [1] to solve this problem. Recently, the
local approach to fracture (LAF) has been developed [2], which can be used as a
powerful tool for solving this problem [3].
The aim o f this study is to present a new version o f the local approach to
fracture and to exhibit ability o f its application to predict pressure vessel lifetime.
Theory. In the general case, the statistical criterion o f brittle fracture o f a
specimen or a structural element w ith a crack m ay be presented as
M
F ^ = 1 - П (1 - F ), ( 1)
where F -2 is the value o f tolerance for the probability o f fracture o f the total
cracked body, F t is the probability o f fracture o f an elementary volume, and M
is the num ber o f such elementary volumes within the “process zone”, i.e., within
the region where the crack nuclei form.
The value o f F i is usually assessed on the base o f the w eakest link
principle, which gives the approximate equation:
F i « 1 - exp - p V i
O ' ~
° 1 - ° th
(2)
1
where p i is the rate o f the crack nuclei (CN) generation w ithin the volum e unit
o f m etal at given value o f plastic strain, V is the elementary volume, o 1 is the
© S. A. KOTRECHKO, Yu. Ya. MESHKOV, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 53
S. A. Kotrechko and Yu. Ya. Meshkov
m aximum tensile stress within ith elementary volume, and a th , a u , and m are
the parameters o f the W eibull distribution.
To ascertain relation between the value o f local stress a \ at the m om ent of
fracture and the macroscopic characteristic o f loading, for instance, K j c , a
nonlinear boundary value problem for a cracked body should be solved. The
finite element m ethod (FEM) enables one to find the value o f K j c w ith a priori
given probability o f fracture F 2 . Such approach is realized in physical (a b in itio )
version o f LAF presented in [3]. The difference is that probability o f fracture of
an elementary volume, F t , was determined not by the approximate formula (2)
but directly by computer simulation o f the crack nuclei (CN) formation and
instability.
However, analytical expression for the local fracture criterion is more
acceptable for engineering calculations. As known for a cracked body, stress and
strain distributions ahead o f a crack tip are scaled in units J j / a j , where J j is
the value o f J -integral, and a j is the yield strength. It m eans that at the fixed
value o f J i / a j , an unambiguous relation between the m aximum value o f the
local probability o f fracture initiation ahead o f a crack, F imax, and the total
probability o f fracture o f a cracked body F 2 , m ust exist. It enables one, using (2),
to obtain the expression for the value o f local strength o f metal, a j , at given
value o f general probability F 2 :
о f - о th + о u
"ll/m
i n ( i - f )
p V
Respectively, the criterion o f fracture initiation m ay be presented as
a f
(3)
о
< I (4)
1
In [4], it is shown that the value o f the above ratio excess over the unit
characterizes stability o f ductile state o f metal in the crack vicinity, i.e., its
remoteness from brittle fracture. Thus, a new characteristic - a param eter of
m echanical stability P ms - was proposed:
a f
P ms = ~ T . (5)о
A t P ms > 1 the metal is relatively stable to brittle fracture, whereas at P ms < 1
it is unstable (which means brittle fracture initiation).
As shown in [4], the value o f the m etal local strength, a j , can be expressed
via R mc - the m inimum value o f fracture stress o f a standard specimen under
uniaxial tension w ithin the ductile-to-brittle-transition temperature range:
54
0 f - k vR m c , (6 )
ISSN 0556-171X. Проблемы прочности, 2009, N2 1
Local Approach to Fracture Based Prediction
where coefficient k v is the measure o f the scale effect related to excess o f the
value o f fracture stress o f o f the local volume V over the m inimum stress of
brittle fracture o f standard tensile specimen (V0 ~ 1000 mm ), R mc. According to
(3), the expression for k v is
o
k v = —
v R
th
+
o
R m
ln(1 — F imax )
1/m
(7)
The tensile stress level ahead o f the crack tip, o j, m ay be presented as
follows:
o 1 = j o y
/ \n
‘ e f
\ e Y )
(8)
where j is the coefficient o f local overstress ( j = o j / o , where o is equivalent
stress), e f is the value o f local plastic strain within the local region where
F = F Jmax, e y is plastic strain at yield strength, and n is strain-hardening
exponent.
Accounting for (6) and (8), the expression for P ms is
K ,
(9)
where K ms is the coefficient o f m echanical stability o f metal under uniaxial
tension:
R
js _____ R mc____
K ms = , , . n , ( 10)
0 Y ( e c I e Y )
cr
q cr is the force equivalent o f the em brittlement effect due to both triaxial tension
and localization o f fracture initiation ahead o f the crack tip,
i \n
j ( e f
( 11)
K ms characterizes the level o f stability o f the m etal plastic state under uniaxial
tension, and is unambiguously determined by the m echanical properties obtained
under uniaxial tension: R mc, o y , and n. Parameter q cr shows how will this
initial level o f stability decrease if this metal is placed at the macrocrack tip [4].
For typical pressure vessel steels o y = o 0.2 (ey = 0.002), and critical strain is
ec ~ 0.02 , therefore, K m s = Rmc I (o 0.2 ‘ ^ )■
According to (10), radiation-enhanced hardening o f pressure vessel steel
m ust result in the reduction o f it m echanical stability level, K ms. Using Eqs. (9)
and (10) and well-known dependence yield strength increm ent A o ys vs. fluence
q cr
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1 55
S. A. Kotrechko and Yu. Ya. Meshkov
value O ( A o ^ B h ( o / 1 0 2 2 ) m° , where 0.33-0.51 [5]), and the expression
for the param eter o f m echanical stability o f irradiated steel, P ^ ., can be obtained
C . = ■ ( 12)
E m
w here E m is the general force equivalen t o f the em brittlem ent w hich
characterizes the total embrittlement due to both stress-strain field ahead o f a
crack tip and radiation-enhanced hardening o f metal:
E ms q crq i r , (13)
where coefficient q ir characterizes the degree o f radiation em brittlement o f steel
due to it radiation-enhanced hardening [4]:
B h I O ) m°
q r ~ 1 + r ^ 1 ^ 2 2 . (14)O y \ 1022 /
Dependences (12) and (14) enable one to predict the value o f critical fluence
O c , at which the cracked pressure vessel fails (P ^ s = 1) at the given value o f load
J i / O Y ■
W hen solving this problem, the scale effect is critical. According to (11) and
(7), this effect governs the embrittling force value o f a crack (parameter q cr)■
in the first approximation, the value o f an elementary volume V { can be
expressed as
Vi = B h i , (15)
where B is the crack front length and h i is param eter characterizing the width o f
an elementary volume, for w hich O f is determined. The upper lim it o f h t is
determined from the condition that stress and strain variations within h i limits
m ay be neglected. The lower lim it o f h i characterizes the minimum size o f the
region required for the CN formation. In the first approximation, this size m ust be
o f the true grain size order.
Accounting for (15) and (7), the expression (11) for q cr will be the
following:
q cr
j ( e f l e c ) n
O th
+
Rm
ln(1—f m
p i h i B
1/ m (16)
)
According to (16), susceptibility o f the value o f embrittling force o f a crack
q cr to change in the crack front length B, depends on the value o f param eter m.
For typical pressure vessel steels, m is determined, above all, by the
inhomogeneity o f distribution o f carbide sizes.
56 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1
Local Approach to Fracture Based Prediction
Technique fo r P red iction o f C ritical F luence O c. The essence o f technique
proposed is to obtain the dependence o f the param eter o f m echanical stability P ms
on the fluence value O , and to find critical value O c, at which P ms = 1 (i.e.,
brittle fracture is initiated ahead o f a crack-like defect tip in a pressure vessel)
grounded on the findings o f tests o f surveillance specimens. According to (12), it
is necessary to know the value o f K ms for steel in the initial (non-irradiated) state
and then to estimate the degree o f irradiation em brittlement o f steel ( q ir)
grounded on the findings o f tests o f surveillance specimens under uniaxial tension
as well as to find the value o f q cr for a cracked non-irradiated metal.
As it follows from (10), brittle strength o f metal, R mc, determined as the
m inim um fracture stress over the ductile-to-brittle-transition temperature region
under uniaxial tension [4] is the key characteristic for K ms determination.
Figure 1 presents the dependences o f K m and q ir on fluence for pressure
vessel steel 15Kh2NMFA (Table 1).
T a b l e 1
Mechanical Properties of Pressure Vessel Steel 15Kh2NMFA in the Initial
and Irradiated States
Steel RRmc •
MPa
Non-irradiated state Irradiated state
о 2
О
-
C)
MP P P n
(20о C)
T>. о C o0r2,MPa
(20о C)
n
(20о C)
CоT,0
15Kh2NMFA 1400 595 0.06 -167 663 0.05 -130
K„
Fig. 1. Effect of the fluence value $ on the coefficient of mechanical stability K ms (1) and the
parameter qir (2) of RPV steel 15Kh2NMFA.
The essence o f technique o f experimental determination o f q cr value for a
crack in non-irradiated steel is shown in Fig. 2. It consists in the ascertainment of
critical temperature Tc, at w hich fracture o f specimen occurs at specified value of
J i / o y . The point o f intersection o f the temperature dependences o f fracture
ISSN 0556-171X. Проблемы прочности, 2009, № 1 57
q
S. A. Kotrechko and Yu. Ya. Meshkov
toughness o f non-irradiated steel, K j c , and stress intensity coefficient K IL for
the given value J j / o y determines the above temperature. In this case:
I E o y
K IL = J~ Y2 b L , (17)
V1 — v
where L is the dimensionless loading parameter:
L = 1/M = J l l ( b o Y ), (18)
M is the dimensionless param eter in ASTM E1921, b is the ligam ent size, E is
the Young modulus, and v is Poisson’s ratio.
Kjç , MPa • m1/2
200
150
100
50
0
-200 -150 -100 -50 0
Temperature T , 0 C
Fig. 2. The temperature dependence of the coefficient of mechanical stability of pressure vessel
steel, K ms, and the value K Jc for proof crack in a reactor pressure vessel.
The value o f param eter q cr is quantitatively equal to the magnitude o f K ms
at this critical tem perature Tc. It follows from the dependence (9), according to
which condition q cr = K ms(T c) holds at the m om ent o f fracture ( J ms = 1). The
values o f q cr for fracture probabilities 0.05 and 0.95 are ascertained similarly.
Knowing the coefficient o f m echanical stability in the initial state, K ms, the
value o f parameter, q cr, and the relation between q ir and O , the dependence of
param eter o f m echanical stability o f irradiated steel, J ^ , on the fluence value
can be plotted (Fig. 3). The value o f fluence, at which J ^ = 1, is the critical value
o f O = O c.
R esults and Discussion. Pressure vessel steel 15Kh2NM FAin the irradiated
and initial states was employed as the subject o f study (Table 1).* Figure 1
presents dependences o f the coefficient o f m echanical stability K ^ and q ir on
* Mechanical tests were conducted by Senior Researcher, Ph.D. V. N. Revka.
58 ISSN 0556-171X. npoôneMbi npoHHoemu, 2009, № 1
Local Approach to Fracture Based Prediction
the value o f fluence at the tem perature 20° C. To approximate the experimental
data, the value m$ = 1/3 was used. Figure 2 demonstrates the technique of
determination o f the param eter q cr. Temperature dependence o f K j c was plotted
based on the test data on three-point bending o f precracked surveillance Charpy
specimens. The value o f K j c was adjusted to B = 150 mm by the M aster curve
technique (ASTM E1921 standard). This B value is approximately equal to the
front length o f a p roof elliptic crack o f depth a = 25 mm (0.1255, where S is a
thickness o f the reactor pressure vessel wall). To sim plify calculations,
curvilinearity o f the crack front was neglected. Calculations were executed for
l ° Y = mm.
p x ms
Fluence $-10 22, neutron/m2
Fig. 3. Effect of the fluence value, O, on the parameter of mechanical stability of steel, Pms, ahead
of a crack tip in a reactor pressure vessel wall.
According to calculation results, at this loading level ( J j / o y = 0.13 mm) the
effect o f the crack em brittlem ent param eter for given values o f probabilities
0.05; 0.50, and 0.95 amounts to q ° r° 5 = 1.765, q ° r5° = 1.635, and q ° r95 = 1.550,
respectively. Data presented in Figs. 1 and 2 enable one to plot the dependence of
the m echanical stability param eter P ms on the fluence value and to ascertain the
critical magnitude o f the fluence (Fig. 3). Calculation results clearly m anifest the
essential effect o f the probability o f critical event under consideration on the
critical fluence value. Thus, at the probability o f unstable equilibrium o f a
crack-like defect in a pressure vessel p r = 0.5, the value o f critical fluence
22 2exceeds O c > 200 -10 neutron/m , and at p j = 0.05, the critical fluence value
22 2amounts to O c = 72-10 neutron/m , which is m uch closer to the standard
value o f 57 neutron/m for pressure vessels o f WW ER-1000 reactors. N otew orthy
is that option o f determination o f the critical fluence value with a priori
probability makes possible a quantitative prediction o f the reliability o f safe
operation o f a reactor pressure vessel.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N9 1 59
S. A. Kotrechko and Yu. Ya. Meshkov
C o n c l u s i o n s
1. A new approach to prediction o f reactor pressure vessel lifetime is
proposed; within the framework o f this approach, the critical value o f fluence is
determined not by the ultimate shift o f Charpy critical temperature, ДТК, or by
ДТ0 according to the M aster curve technique, but by the condition o f instability
o f the ductile state (initiation o f brittle fracture) o f irradiated m etal ahead o f a
crack tip in a reactor pressure vessel.
2. The condition o f ductility exhaustion (initiation o f brittle fracture) o f the
irradiated metal within the local region ahead o f a crack tip can be described by
two new m echanical characteristics, namely:
(i) the coefficient o f m echanical stability K ms, which characterizes ability of
metal to resist transition from ductile to brittle state in laboratory conditions of
uniaxial tension; it is determined unambiguously by such structure-sensitive
characteristics as brittle strength R mc, yield strength a 0 2 , and strain-hardening
exp °nent n ( K ms = R mc/ ( a 0.2 ‘ 1 0 ^
(ii) force equivalent o f embrittlement E m, which demonstrates how m uch is
this initial (laboratory) level o f m echanical stability, K ms, decreased by the effect
o f both radiation strengthening o f steel (param eter q ir) and inhomogeneous force
field ahead o f a crack tip (parameter q cr ) (E m = q irq cr).
1. W. Server, S. Rosinski, R. Lott, et al., “Application o f M aster Curve fracture
toughness for reactor pressure vessel integrity assessment in the U SA ,” Int.
J. P r e s s . V ess. P ip in g , 79, 701-713 (2002).
2. A. Pineau, “Development o f the local approach to fracture over the past 25
years: theory and applications,” Int. J . F r a c t. , 138, 139-166 (2006).
3. S. Kotrechko, “Physical fundamentals o f local approach to analysis of
cleavage fracture,” in: T ra n sfe ra b ility o f F ra c tu r e M e c h a n ic a l C h a ra c te r is t ic s ,
Kluwer Academic Publishers (2002), pp.135-150.
4. S. Kotrechko and Yu. M eshkov, “A new approach to estimate irradiation
embrittlement o f pressure vessel steels,” Int. J . P r e s s . V ess. P ip in g , 85,
336-343 (2008).
5. T. Byur and K. Farell, “Irradiation hardening behavior o f polycrystalline
metals after low temperature irradiation,” J. N u c l. M a te r . , 326, 86-96
(2004).
Received 11. 06. 2008
60 ISSN 0556-171X. Проблеми прочности, 2009, № 1
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