Thermal, irradiation and cyclic loading analysis for stress fatigue crack in reactor vessels

Int. J. Pres. Ves. & Piping 31 (1988) 83-104

Thermal, Irradiation and Cyclic Loading Analysis for Stress Fatigue Crack in Reactor Vessels

Benjamin M. Ma Department of Nuclear Engineering, Iowa State University, 261 Sweeney Hall, Ames, Iowa 50011, USA (Received 9 June 1987; accepted 2 July 1987)

ABSTRACT The thermal, irradiation and cyclic loading analysis for stress fatigue crack ( SFC ) of the base and weld materials of L M F B R (liquid metal fast breeder reactor) and L WR (light water reactor) pressure vessels is theoretically carried out based on experimental data. The power function and exponential .function crack (rate) laws and the SFC theory are introduced and postulated .for the stress intensity factor, K, or the effective stress intensity.factor, KeH, versus the fatigue crack growth rate in the vessel materials. Experimental data of austenitic stainless steels 304 and 316, nickel alloy Incone1600, and low-carbon alloy steels A516 and A533 of the L M F B R and L WR pressure vessels were respectively computedly measured, examined and analyzed, and then plotted for either power function crack rate and/or exponential function crack law. The theoretical prediction and the computerized experimental data are in excellent agreement. These results can be applied in the respective L M F B R and L WR pressure vessel design, construction, operation and lifetime prediction in a fast or thermal nuclear power reactor to generate electricity.

NOMENCLATURE a ao

H a l f c r a c k length Initial c r a c k length

83 Int. J. Pres. Ves. & Piping 0308-0161/88/$03"50 © Elsevier Applied-Science Publishers Ltd England, 1988. Printed in Great Britain

84

Benjamin M. M a

A,B C CE CM c ¢s

d h F,f J K K~ff

Kdyn

K

Sla

k m, F/

U, Uf n

S T T t U

W X, y O~ ~, £mn

F if' (~ij

Constants Combined material-environment constant Environment constant Material constant Conversion constant Sound speed or velocity Depth of crack Thickness of specimen Function symbols The J-integral Stress intensity factor Effective stress intensity factor Dynamic stress intensity factor Static stress intensity factor The Boltzmann constant Constants or parameters Number of cycles, cycles to failure Neutrons, unit normal vector Surface Temperature Traction vector Time Displacement vector Strain energy density Coordinates Alpha particle, helium atom Strain Contour of line or unit Stress, stress tensor

1 INTRODUCTION The pressure vessel is one of the primary components of a light water reactor (PWR or BWR) or a liquid-liquid fast breeder reactor (LMFBR or internal fast reactor, IFR). The pressure or reactor vessel is normally operating under the conditions of elevated temperature, thermal cycling, coolant pressure, and irradiation effects. To study the design and operating experience of the large primary reactor component, it is necessary and economical to test various specimens of feasible candidate materials of the reactor vessel in a laboratory, particularly, stress fatigue crack (SFC, or fatigue crack growth rate) and stress corrosion crack (SCC, or corrosion crack growth rate). The

Stress fatigue crack in reactor vessels

85

SFC or SCC could fail the component(s) and affect the reactor service lifetime. 1,2 In general, engineering design and nuclear power plant operation for thermal (LWR) and fast (LMFBR) reactors require profound knowledge of nuclear reactor material properties and operating experience during the change of reactor material properties in the environment of high temperature, cyclic loading and neutron irradiation. Nuclear reactor metallic structures are subjected to elevated temperature, thermal cycling, cyclic loading with variable frequencies and stress ratios, and intensive neutron irradiation. The primary components of these structures, such as pressure vessel, fuel cladding, reactor core fixture, and supports, etc., are essentially susceptible to thermal, irradiation, and stress fatigue crack and breach, in particular, pressure vessel of thermal or fast power reactor. The most commonly used vessel materials are austenitic stainless steels (SS) AISI types 304, 304L, 308, 316 and 316L (in which 304L, 308 and 316L (low carbon) are the weldment materials); some nickel alloys: Inconel 600, 718 and Incoloy 800; and carbon alloy steels ASTM A516, A533 and A508; depending on reactor type and size. In previous papers, 3-8 the heat generation, temperature distribution, elastic thermal and pressure stresses, plastic stress and strains, irradiation swelling, irradiation creep, thermal fatigue analysis and elevated temperature, cyclic loading and irradiation effects on fatigue crack of LMFBR pressure vessels were carried out. In this paper the stress intensity analysis of reactor vessel crack under thermal, irradiation and cyclic loading is presented. The primary objectives of this paper are: 1.

2.

3.

To analyze the effects of elevated (mean irradiation or test) temperature, cyclic loading, and cyclic frequencies, and irradiation swelling, creep, hardening and helium embrittlement on stress fatigue crack (SFC) of the vessel materials and to introduce the power function and exponential function laws of stress intensity factor range, AK, and effective stress intensity factor, K~fr, for predicting the fatigue crack growth rates in order to select reactor vessel material. To correlate cyclic frequency and cyclic (thermal and mechanical) loadings with fatigue crack propagation behavior of the vessel materials at given elevated (irradiation or test) temperature and neutron (fast or thermal) fluence (i.e. integrated neutron flux). To compare the environmental sensitivity of sodium, vacuum, and air or water to fatigue crack growth rate and to evaluate the irradiation effects on the base and weld materials of austenitic stainless steels for LMFBR reactor vessels and low-carbon alloy steels for LWR pressure vessels.

86

Bet!jamin M. Ma

2 HEAT GENERATION, T E M P E R A T U R E DISTRIBUTION AND PEAK T E M P E R A T U R E Heat generation and temperature distribution with peak or maximum temperature in the inner wall of LWR or LMFBR reactor vessels originate from the attenuation of primary and secondary gamma rays and absorption of fast and thermal neutrons from the reactor core. 3 The heat generation rate depends on the gamma dose rate intensity and the neutron flux distribution, which, in turn, are related to the material (nuclear) properties and geometrical arrangement of the pressure vessel. In other words, the heat generation rate can be evaluated from the radiation energy flux, energy attenuation or absorption coefficient, buildup factor and exponential law of radiation attenuation. The difference between the heat generation rate and the heat removal rate from the wall determines the pressure vessel's level of elevated temperature at a quasiequilibrium state. The elevated temperature distribution and peak temperature in the wall resulting from gamma ray and neutron radiation of the reactor core are referred to as the mean irradiation or the test temperature developed in the vessel materials or specimens under experimental consideration. This irradiation or test temperature is also equivalent to the elevated temperature of a specimen irradiated in a fast or thermal research reactor, such as the Experimental Breeder Reactor, EBRII; the Ames Laboratory Research Reactor, ALRR; or the Advanced Test Reactor, ATR. 9

3 REACTOR DYNAMICS, T H E R M A L CYCLING AND CYCLIC LOADING Thermal cycling is induced by the inherent character of reactor dynamics. The period of thermal cycling induced by the reactor dynamics is called the reactor period. The reciprocal of the reactor period, by definition, is the cyclic frequency of the thermal cycling in each primary component, such as pressure vessel or fuel elements, of the reactor. This cyclic frequency of the reactor corresponds to the cyclic fluctuation of the radiation energy flux, neutron flux or reactor power. Thus, the effect of the cyclic frequency or thermal cycles of reactor power oscillation can directly transmit to the pressure vessel. The changes of the cyclic loadings and stress ratios can either be in both magnitude and direction, for example, from compression to tension and vice versa to induce shearing stresses. This corresponds to the cyclic loadings of each test specimen.

Stress fatigue crack in reactor vessels

87

4 I R R A D I A T I O N EFFECTS Pressure vessel or structural materials irradiated in a radiation environment of a nuclear reactor can induce various irradiation effects. The primary irradiation effects on a stress fatigue crack (SFC) of an L M F B R or LWR pressure vessel are irradiation swelling, irradiation creep, irradiation hardening and helium embrittlement. Irradiation swelling is closely associated with helium embrittlement and helium production because of the (n,~) reactions with elements present in the vessel material. 8-1° The reactions of neutron bombardment and nuclear transmutations with the elements, for instance 58Ni(n, 7)sgNi(n,~)56Fe, 5°Cr(n,7)SXCr(n,~)48Ti, 54Fe(n, 7)55Fe(n, ~)52Cr etc., can result in helium (alpha particle) production, helium content, helium embrittlement, and irradiation swelling in the vessel materials of stainless steels, nickel alloys and low-carbon alloy steels. Irradiation creep is induced in the radiation environment by a continuous deformation in the vessel material at a constant irradiation temperature and cyclic loading. The rate of irradiation creep is enhanced in comparison with that of conventional thermal creep. Irradiation hardening and helium embrittlement can increase mechanical strength but can reduce ductility of the vessel material. Therefore, the interactions of the irradiation swelling, irradiation creep, irradiation hardening and helium embrittlement can greatly enhance fatigue crack growth rate of the vessel material.

5 T H E R M A L , I R R A D I A T I O N C Y C L I N G A N D STRESS F A T I G U E CRACK, THE C R A C K T H E O R Y In the intensive radiation environment of the nuclear power reactor, L M F B R or LWR, the combination and interactions of elevated (irradiation) temperature, thermal and irradiation cycling, cyclic loadings (cyclic stresses or strains), and the irradiation effects can cause incipient thermal, irradiation and stress fatigue cracks in the reactor vessel materials. A stress fatigue crack usually occurs when a specimen undergoes cyclic thermal, irradiation and/or mechanical loadings. Thermal, irradiation and/ or mechanical fatigue is often produced by cyclic temperature loading and/ or cyclic mechanical (stress or strain) loading. In the presence of irradiation swelling, irradiation creep, irradiation hardening and helium embrittlement, the thermal, irradiation and stress fatigue crack (especially at low cycles) may be defined as a process whereby cracks (intergranular or structural) originate and propagate in vessel materials under the cyclic thermal, irradiation and mechanical loadings (during reactor operation or specimen test).

88

Be&.min M. Ma

As postulated earlier, the initiation of crack nucleation and the direction of crack propagation in multiaxial thermal, irradiation and mechanical (stress) fatigue of ductile material (e.g. L M F B R or LWR vessel materials) can be interpreted by the distortion energy theory. 6'9 Under the yield condition of the distortion energy theory the shearing stress nucleates cracks and the maximum principal stress propagates and extends cracks along the failure plane normal to the principal stress. This basic crack theory can adequately interpret the crack mechanisms and can equally apply to the thermal, irradiation and mechanical (stress) crack in the vessel materials.

6 CYCLIC T H E R M A L , I R R A D I A T I O N A N D M E C H A N I C A L LOADINGS, I R R A D I A T I O N EFFECTS ON W E L D M E N T S Metallic pressure vessels of L M F B R and LWR are made by welding the base and weld materials: particularly, 316/316L or 304/308 SS for L M F B R pressure vessels and A516/A508 or A533/A508 for LWR pressure vessels. The main concerns of welding the base and weld materials are (1) to prevent cracking in and near the weldments; (2) to maintain stress corrosion resistance at and near the welded area, i.e. free from the stress corrosion crack, SCC; (3) to control chemical composition and ferrite content of the welded joint; (4) to adjust and make uniform ferrite distribution at the welded area possible; and (5) to control the thermal and irradiation effects on the base and weld materials during and after welding. Cracks that were developed in the weld or heat-affected zone after the welding process are often related to the operating conditions of temperature, cyclic loadings and irradiation circumstance of the reactor vessel. In general, high temperature, low cyclic loadings and irradiation effects can cause leaks in the pressure vessels of the reactors.

7 CYCLIC T E M P E R A T U R E , M E C H A N I C A L LOADINGS, I R R A D I A T I O N A N D E N V I R O N M E N T EFFECTS OF SFC PROPAGATION CRITERION To analyze the behavior of stress fatigue crack, SFC, for a given materialenvironment combination, the growth rate of SFC propagation, da/dN, as defined, is considered as a unique function of the stress intensity factor, K, or effective stress intensity factor, K~fr, where a is the half crack length and N is the number of cycles of the cyclic loading. The values of K and Keff are independent of any geometry of test specimen predicting the crack behavior

Stress fatigue crack in reactor vessels

89

of the structural component to which the test data are measured, collected and then applied in design. A pressure vessel is a complex component in the nuclear reactor system. The stress intensity factor, K, or effective stress intensity factor, Keff, has the powerful ability to analyze and predict the behavior of SFC propagation of the large, complex component by utilizing experimental data obtained from selected small and simple specimens (e.g. reactor pressure vessel materials) tested in a laboratory. Many specimens of the base and weld materials of L M F B R and LWR pressure vessels have been tested in the EBR-II A L R R and ATR, respectively. The stress intensity factor range, AK, which corresponds to the strain range of SFC behavior, can consist of the principal thermal, irradiation and mechanical stresses of the pressure vessel. High temperature, irradiation swelling and irradiation creep can only produce principal thermal and irradiation stresses in the vessel wall. The stress fatigue crack (SFC) propagation criterion of any reactor primary component, such as reactor pressure vessel, piping system, or fuel elements, can be expressed in terms of fatigue crack propagation or growth rate, da/dN, as a single function of stress range, a, initial stress range, ao, half crack length, a, initial crack length, a 0, and combined material-environment constant, C. da

dN - f ( a , a, C) = f (a/ao, a/ao, C)

(1)

where C = CM + CE + " " for material constant, CM, and environment constant, CE, including stress corrosion crack and so on, of a nuclear reactor operating condition or specimen test conditions in a laboratory. This fatigue crack criterion may meet most material and environment combinations in engineering applications. All the primary components of a nuclear power reactor system experience the cyclic temperature, mechanical loadings, irradiation and environment effects related to the component materials. In such cases, the stress intensity factor, K, consists of thermal cycling factor, KT, cyclic mechanical loading factor, KM, cyclic irradiation factor, K~ and cyclic environment factor, K E. Hence, the stress intensity factor of the reactor component or test specimen is

K = KT + KM + Kt + KE

(2)

In terms of the thermal stress range, aT, mechanical stress range, aM, irradiation stress range, a~, environment stress range, aE and the geometric function of a plate test specimen of thickness, h, half crack length, a, crack

Benjamin M. Ma

90

depth, d and initial crack length, ao, the components of the stress intensity factor are expressed, respectively, by Kv

==-

O'T./T(a,d, h) = ffTfT(a/ao, d/h)

KM =--aMfM(a, d, h) = aMfM(a/a o, d/h)

(3) (4)

K 1==-a,.~(a, d, h) --- a,j~(a/ao, d/h)

(5)

KE ==-aEfE(a, d, h) = aEfE(a/ao, d/h)

(6)

in which the geometric function of thermal, mechanical loading, irradiation and environment cyclings includes enhancement factors for the effects of the irradiation temperature, creep and corrosion in the specimen. The range of the enhancement factor, e.g. irradiation creep rate, varies from 10 up to 100 from one case to another in the intensive irradiation environment imposed in the steady state of the reactor operation or specimen experiment in the laboratory. During startup and shutdown (or power up and power down), the nuclear reactor is at the transient state. At the transient state both reactor temperature and neutron flux oscillate irregularly to follow the pattern of reactor dynamics. If the specimens are tested in the static state and the static stress intensity factor is K sta, then the specimen test performed at the dynamic state is denoted by K ay". The relationship between static and dynamic stress intensity factors of the stress fatigue crack propagation criterion can be expressed as K = K ay"=-K "'aF(cs, t) = F c't

(7)

ao

where cs is the sound wave speed of dynamic impact, and t is the time. The sound speed is a function of material density of the specimen or primary reactor component. This equation actually represents the dynamic fatigue crack stability criterion. Equations (1) through (7) are basic equations that deal with the fatigue crack propagation or SFC of the combined cyclic temperature, mechanical loading, irradiation and environment effects in the steady or static state and at the unsteady or dynamic state of the test specimens or the reactor pressure vessel of L M F B R or LWR.

8 THE J-INTEGRAL, POWER FUNCTION AND EXPONENTIAL F U N C T I O N C R A C K LAWS The path-independent integral or the J-integral can be considered as a parameter of the fatigue crack propagation criterion. The J-integral is an

Stress fatigue crack in reactor vessels

91

average measure of the crack tip elastic-plastic field that can be evaluated analytically and experimentally and is equivalent to the stress intensity factor, K. On the basis of linear elastic fracture mechanics (LEFM), the elastic-plastic analysis of the crack tip region provides a unique stress-strain field for a singularity at the crack tip. The strength of the crack tip irregularity is the stress intensity factor, K. Therefore, the crack tip region can be characterized by the unique parameter, K. Fracture must take place at a critical value of K resulting from the J-integral of strain energy. The energy line integral J near the crack tip of an elastic-plastic material with strain energy density, W, displacement vector, u, traction vector, T ( --- trijni) , prescribed by the outward normal, n, along a contour, F, is defined by the equation

J : ;r[wdy_T c xJ°l ds

(8)

where W = W(~.mn) =

~

mVl

(Tij dc, ij

(9)

e,,,, eij and o-ij are strain and stress tensors near the crack tip o f the elasticplastic material along the contour, F, of any closed curve, s.

8.1 Power function fatigue crack law The fatigue crack propagation or growth rate is commonly expressed in terms of the power function law of crack rate at a relatively low irradiation temperature and high cyclic frequency. 1~- 21 do d-N = A(AK)"

(10)

in which A K = Kmax --Kmln, Kmax,Kmin are maximum and minimum stress intensity factors. A and n are constants for a given material-environment combination or material component-operation condition. Alternatively, the fatigue crack growth rate in the power function is da d N = A[Kma~(1 - R)]"

(11)

where m is another parameter, and R = Kmax/Kmtn, the ratio of stress intensity factor or the ratio of minimum stress to m a x i m u m stress (in the inverse proportion to KmJKmi,O. By taking account of the effective stress

Beniamin M. Ma

92

ratio, the stress intensity factor range is replaced by the effective stress intensity factor, Kefr. Keff = Kmax(1 - R)m

(12)

Introducing this into eqn (10), the fatigue crack growth rate becomes da d N = A(Keff)"

(13)

The values o f m in the range of 0.40, 0-50-0.75 for various cases of types 304, 308, 316 SS and Inconel 600 have been found experimentally over a wide range of stress ratio R for L M F B R vessel materials. The values of R in the range from 0-30 to 0.80 for alloy steels A516, A508 and A533 of the LWR vessel materials were also found. 7'22 From the power function law of the stress intensity factor range AK or effective stress intensity factor Keff, various empirical equations for different material-environment combinations to predict crack growth rate, da/dN, have been proposed. 17- 20

8.2 Exponential function crack law At a relatively high temperature, high cyclic stress and low frequency, the irradiation swelling and creep predominate. The fatigue crack growth rate can be represented by the exponential function law that has a solid theoretical b a c k g r o u n d / 7 - 1 9 Thus

da

= Bexp

and/or -

da _ B exp -

_

dU

[

[

c AK 1 kT ]

kT ]

(14)

(15)

where B is a constant depending mainly on cyclic life Nf, stress intensity, and material-environment combination; c is the conversion constant; c AK and cKeff are the apparent activation energy (negative sign refers to energy lost due to cyclic loading); k is the Boltzmann constant, and T is the mean irradiation or test temperature. The factor c AK/kT or cKeff/kT represents the combination of elevated temperature, cyclic loadings and irradiation effects of the L M F B R or L W R pressure vessel. In general, the fatigue crack growth rate of the exponential function law is greater than that of the power function law.

Stress fatigue crack in reaetor vessels

93

9 E X P E R I M E N T A L RESULTS OF R E A C T O R VESSEL MATERIALS The experimental results of the reactor vessel materials such as austenitic stainless steels, nickel alloys or low carbon steels are equally applicable to the piping systems of L M F B R S or LWRs. Fatigue crack specimens were tested in the EBR-II, A L R R or A T R for Type 304 and 316 stainless steels, nickel alloy Inconel 600 and alloy steels A516 and A533 at different combinations of temperature cyclic frequency, stress ratio, neutron fluence and heat treatment. The data were measured, calibrated, and analyzed from various sources v'8'l°'z° and are shown in Figs 1-14. The relatively complete data have been plotted through a tedious process of examination, selection, analysis and careful evaluation on the basis of eqns (10)-(13) for the power function law (Figs 1-8) and eqns (14) and (15) for the exponential function law (Figs 9-14). These curves or scatter bands show the general trend of the experimental results (both irradiated and unirradiated) as illustrated in Figs 1-8 for use in an engineering design of the L M F B R pressure vessel. Figures 9-14 can be used for the engineering design of either L M F B R or LWR pressure vessels, respectively. For given vessel materials operating at designed ranges of elevated temperature, cyclic frequency and neutron fluence, the lifetime of an L M F B R or LWR pressure vessel can be predicted from a prescribed fatigue crack rate or SFC propagation rate of the vessel. The fatigue crack growth rates of irradiated specimens are greater by orders of 10 or more than those of the unirradiated specimens. In previous papers, 1'2'v'8'~°'2° the crack theory for the thermal and irradiation fatigue crack rate in a cylindrical-controlled thermonuclear reactor first wall, reactor fuel elements and in L M F B R pressure vessels was respectively postulated and experimentally verified. Therefore, the crack theory applied to the fatigue crack growth rate has a firm foundation. The influence of the elevated temperature, cyclic loadings, irradiation and environment effects on fatigue crack growth rate of the base and weld materials for the L M F B R or LWR pressure vessel on the basis of the experimental data obtained, examined, analyzed and evaluated were preliminarily given, z° 1.

2.

Elevated temperature, thermal cycling and cyclic loading have a great effect on fatigue crack growth rate. For given values of AK or Keff, the fatigue crack growth rates of austenitic stainless steels 304 (especially cold-worked 20%), 316, and 316L and Ni alloy 600 increase with temperature. For a given temperature and neutron fluence, high cyclic loadings at

tO-5

10 -4

I

I

I

I

IOT

I

I

I

I

I

I

I

I

102

STRESS INTENSITYFACTORRANGE, AK, MN/(m)3/2

I

ANNEALEDTYPE-304 STAINLESS STEEL TESTEDAT 430 °C f = 40 cpm, R = 0.05

o

Fig. 1. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 304 at temperature 430~C.

i

~

g

~ 10-3

tO-2

UNIRRADIATED AGED I150 h AT 475 °C PRIOR TO TESTING EBR-II IRRADIATED ].3xlO21n/cm2, E • O.l Mev

102

STRESS INTENSITY FACTORRANGE, AK, kg/(mm)3/2

i0-3-

i

.

.

.

i

102 '

UNIRRADIATED AGED ]150 h AT 475 °C PRIOR TO TESTING

.

'

1.3xlO21n/cm2, E > O.l Mev

o EBR-II IRRADIATED

.

i i I lOI

,

i

i

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102

t I I

/.,,,c,SV" "-SCATTERBANDFOR /~ UNIRRADIATED, UNAGED /A;J SPECIMENS TESTEDUNDER /Z~o~ SIMILAR CONDITIONS

f = 40 cpm, R = 0.05

TESTEDAT 430 °C

ANNEALED TYPE-304 STAINLESS STEEL

//°

.

Fig. 2. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 304 al temperature 430C.

STRESS INTENSITY FACTORRANGE, &K, MN/(m)3/2

10-5

~10 -4

"-.

tO-2

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STRESS INTENSITY FACTORRANGE, AK, kg/(mm)312

2

z

lO-5

lO-4

w

!

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i

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--

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l

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i

TESTED AT 430 °C f = 40 cpm, R = 0.05

20% COLD-WORKEDTYPE-316 STAINLESSSTEEL

1 . 5 x l 021 n/cm 2,

o EBR-II IRRADIATED

UNIRRADIATED AGED 1150 h AT 475 °C PRIOR TO TESTING

I

Fig. 3. Variation of stress intensity factor range with fatigue crack growth rate of 20% cold-worked stainless steel 316 at temperature 430°C.

i---

N

i

~

~ 10_3

lO-2

l

STRESS INTENSITY FACTORRANGE, z~K, kg/(mm)3/2 102 I '

/~

0 C

0 Q o A

f f f f

= = : =

40 cpm, R = 0.05 40 cpm, R = 0.05 400 cpm, R = 0.05 400 cpm, R = 0.50

f = 40 cpm, R = 0.05

0

/ ~"

_ __A~ ENVIRON_~NT ~ * f : I0 cpm, R : 0

/

i

lO
TESTEDAT 430

ANNEALEDTYPE 304 STAINLESSSTEEL

i

/r/

/L"/

/(~/

~ /~

12o , , J r

I01 102 EFFECTIVE STRESS INTENSITY FACTOR, Kmax [l-R] 0"6, MN/(m)3/2

10-6--

I°-5

i0-4

'

1.3(i021) n/cm2

'

i

Fig. 4. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 316 in air environment at temperature 430°C.

u.

~T

~

'

max

EFFECTIVE STRESS INTENSITY FACTOR, K [l-R] 0"6, kg/(mm)3/2

2"

q

=

i

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=

I

~

I01

t

1

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v

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0.05

0.50

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|

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• R= 0.50

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OR = o R:

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LOW OXYGENSODIUM ~ R = 0.05

0.05 < R < 0.50

I

1o 2

~

I

~ R : 0.50 HIGH-OXYGENSODIUM

I

I

S.S

.STED AT ,30 oc

TYPE 304

//

i

EFFECTIVE STRESSINTENSITY FACTOR, Kmax[l - R]0.6, kg/(mm)3/2

I

fi,J

X~'

/~

I

/

v

~//ANNEALED

...,

)4// ~/

(~

I

102

//

/

v

t~///180 < f < 400 cpm

~

E • 0.1 MeV

1.3(1o2) ./~m2

I

Fig. 5. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 304 in sodium and vacuum environments at temperature 430°C.

~i0_6

=

i

10-5

"m~ ~0_4

z

10" 3 -

I

EFFECTIVE STRESSINTENSITY FACTOR, Kmax [I - R]0"6, MN/(m)3/2

,

i

"

102

'

101

' , , ~J

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7,X,~ TESTS~ONDUCIED ~IN 24 vC 7 AIR ENVIRONMENT ANNEALED TYPE 30, STAINLESS STEEL TESTEDAT 430 °C

/.i

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Kmax [I-R] 0"5, MN/(m)3/2

102

a ! , ,J

E > 0.1 MeV

1.3(tO21) n/cm2

LOW OXYGENSODIUM 0 R = 0.05 R = 0.50 VACUUM • R = O.OB6 • R = 0.50 • R = 0.50

,

Fig. 6. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 304 in sodium and vacuum environment at 430~C (eqn (6)).

10-7

,

- ~ / 7 SCATTERBANDFOR

~

330
CONDUCTEDIN 430°C AIR ENVIRON~-Ni

//

!1/i

fl

EFFECTIVE STRESSINTENSITY FACTOR,

tO_5

10-4

~10-6

.

!

10-3----SCATTER BANDFOR TESTS

i

Kmax El-R] 0"5, kg/(mm) 3/2

EFFECTIVE STRESSINTENSITY FACTOR,

i

i

ii

I

102 i

TESTED AT 540 °C

STAINLESS STEEL

ANNEALED TYPE 304

~. //

//

///

i

!

i

R : 0.05 R = 0.50 R = 0.086

R : 0.50 R = 0.50

•

•

•

VACUUM

0 ~

LOW OXYGEN SO6IUM

330
CONDUCTEDIN 540Uc AIR ENVIRONFENT

i

1.3(1021 ) n/cm 2 E > 0.1 MeV 10-7 , , , ,l i i I I i , , ,i i01 102 EFFECTIVE STRESS INTENSITY FACTOR, Kmax [ I - R ] 0"5, MN/(m) 3/2

-6

I

_--SCATTER BAND FOR_TESTS

i

,

Fig. 7. Variation of stress intensity factor range with fatigue crack growth rate of solution-annealed stainless steel 304 in sodium and vacuum environments at temperature 540°C.

~D

~i0

~ I 0 -5

~J

-m

10"3

i

EFFECTIVE STRESS INTENSIoTY5FACTOR, Kmax [ l - R ] " , kg/(mm)3/2

10 -6

10-5

10-4

I

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/

,

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J

1

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102

I

f = 400 cpm, 0.05
I01 EFFECTIVE STRESS INTENSITY FACTOR

I

~:)/

/v/

~o/

j

102

TESTEDAT430°C)

,

I~

,

ANNEALEDINCONEL 600

i

/r~/

1.3(20211 n/cm 2 E>O.l

o R = 0.600

A R = 0.333

~

growth rate of Inconel 600 at temperature 430°C.

Fig. 8. Variation of effective stress intensity factor with fatigue crack

u_

=

u

10 -3

o R = 0.050

I

EFFECTIVE STRESS INTENSITY FACTOR

m~

2"

P~

i0 -(

10-5

I o

0.333 0.500

R R

R = 0.050

f

l

20

I 30

EFFECTIVE STRESS INTENSITY FACTOR

i0

l

f = 400 cpm, 0.05
TESTED AT 540 °C

ANNEALED TYPE 316 STAINLESS STEEL

P/z

f

Fig. 9. Variation of effective stress intensity factor with fatigue crack growth rate of annealed stainless steel 316 at temperature 540~C.

,,<

I'-"

I

t,~l

10 -4

10-3

I

o R = 0.600

R = 0.333

R = 0.050

I

1 30 EFFECTIVE STRESS INTENSITY FACTOR

L 20

I ]0

f = 400 cpm, 0.05
TESTED AT 540°C

ANNEALED TYPE 316 STAINLESS STEEL

E > 0 . I MeV

1.3(1021) n/cm2

I

Fig. 10. Variation of effective stress intensity factor with [~tiguc crack growth rate ofannealed stainless steel 316 al temperature 540'~C.

u_ 10_6

~ i 0 -5 me

~3

10 -4

10-3

5

~C

10-6

10-5

t

20

-

I

30

f = 400 cpm, 0.05
TESTED AT 540°C

ANNEALED INCONEL 600

1.3(1021 ) n/cm2

EFFECTIVE STRESS INTENSITY FACTOR

I

10

/~l~r'/

/o~ /

o R : 0.500

I

Fig. 11. Variation of effective stress intensity factor with fatigue crack growth rate of lnconel 600 at temperature 540°C.

i

m-

10-4

10-3

/

1

R = 0.333

o R = 0.050

1

Fig.

u

12.

u_

I

I

1

540°c TESTEO

L

3,°C

1

LOW CARBON ALLOY STEEL A533

i0 20 30 40 50 60 STRESS INTENSITY FACTORRANGE AK MN/(mm)3/2

//

f /

THERMAL ENERGY

1.2(1021 ) n/cm2

THERMAL REACTOR (ATR) IRRADIATED AT R = 0.40, 0.33, 0.30

Variation of stress intensity factor range with fatigue crack growth rate of low-carbon alloy steel A516.

~10 -6

~=

~ I 0 -5 m

10-4

m~

e~

P~

¢b

mb

I

20

I

30

I

40

I

50

STRESS INTENSITY FACTOR K MN/(mm)3/2

I

10

ADING COMBINEDLOADING o TRANSVERSELOADING

1.5(104 ) n/cm2 E > 0.i mev 20% COLD-WORKEDINCONEL600 TESTEDAT 540o C

EBR-II IRRADIATED AT R = 0.05, 0.250, 0.600

60

Fig. 13. Variation of stress intensity factor range withfatigue crack growth rate of 20% cold-worked lnconel 600 at temperature 54ff'C.

10-5

10.4

10-3

Fig. 14.

n/cm2

!

20

I

30

I

40

/ /

I

50

60 STRESS INTENSITY FACTORRANGE, AK MN/(mm)3/2

I

i0

/7

//

ASTM A533 GRADE B VESSELSTEEL TESTEDAT 540o C / /

THERMAL ENERGY

1.2(1021 )

THERMAL REACTOR (ATR) IRRADIATED AT STRESS RATIO R = 0.15, 0.25

Variation of stress intensity ~cIor range with ~tigue crack growth rate of A533 vessel steel lested at 540°C.

~ lO-6

N

10_5

10-4

3

Stress fatigue crack in reactor vessels

3.

4.

101

a low cyclic temperature can induce a high fatigue crack growth rate in the vessel material. For a given value of AK or Keff, the fatigue crack growth rate at 540°C increases with decreasing cyclic frequency. At fast neutron fluence of 1.3-1.5 × 1021n cm -2 (neutron energy E > 0.1 MeV) in the temperature range of 430-540°C the neutron fluence produces little effect on the fatigue crack propagation behavior for cold-worked and annealed stainless steels. Higher neutron fluence, however, can produce marked effects on the properties of vessel materials by enhancing the crack rates. The fatigue crack growth rate increases monotonously with AK or Keff. The crack growth rate in sodium and a (partial) vacuum show little differences, but these rates were much less than those in air at 430 ° and 540°C. The influence of elevated temperature, cyclic loadings, irradiation and environment effects on the weldments of the L M F B R and LWR pressure vessels are also found from the experimental experience and results: (a) weld-deposited metals (SS 308, 316L and 304L, 308 with almost the same properties) can have high-yield strength and low ductility compared to the wrought-base metals (SS 304 and 316). Stress relief near 900°C for a short period of aging can reduce the yield stress and recover the ductility of the vessel materials. This behavior results from the thermal recovery of residual stress and weld-reduced prestrain of the matrix austenite and the transformation of delta phase to sigma phase ferrite; (b) irradiation effects in weld materials are generally similar to the trends established for wrought-base materials. The largest proportionate property changes occur in the solution-annealed weld metal. Residual stress and weld-reduced prestrain in the weld metal require higher temperature to anneal and remove irradiation effects. (c) Adequate weldability and good service performance of austenitic stainless steels and Ni alloys require control of the weld-deposit chemical composition, ferrite content, and microstructure in order to prevent hot-cracks or fatigue cracks in the presence of elevated temperature, cyclic loadings, irradiation and environment effects for the L M F B R pressure vessel weldments, especially at vessel nozzle corner. 24

A similar summary can be drawn for weld and base metals of alloy steels A516, A508 and A533 that are used for the LWR pressure vessel weldments.22 - 24.

102

Benjamin M. Ma

10 M A I N C O N C L U S I O N S F r o m the preceding analysis, the following main conclusions are made.

1.

.

.

Under the cyclic thermal, mechanical loadings, and irradiation conditions, elevated temperature, low thermal cycling and cyclic loadings have a great effect on the fatigue crack growth rate or SFC propagation behavior. For a given value of stress intensity factor, AK, or effective stress intensity factor, Keff, the fatigue crack growth rate of austenitic stainless steels 304 and 316, nickel alloy Incone1600, and low-carbon alloy steels A516, A508 and A533 can be adequately predicted for the L M F B R or LWR pressure vessel respectively. The fatigue crack growth rate, da/dN, increases with AK or Kerr. At a given temperature and neutron fluence, a low cyclic frequency or high cyclic loading can cause high fatigue crack growth rate in the base and weld materials of the L M F B R or L W R pressure vessel. For a given value of A'K or Keff at 540°C or 595°C, the exponential function crack (rate) law follows the fatigue crack growth rate by increasing with decreasing cyclic frequency. At a relatively low temperature (430°C or 380°C), however, the fatigue crack growth rate obeys the power function crack (rate) law. The fatigue crack growth rate of austenitic stainless steels 304 and 316 in the environment of sodium and a vacuum are much less than that in air or water at 430°C. This would be of great importance for structural components (such as pressure vessel, fuel elements, etc.) of L M F B R or L W R in order to operate safely in a sodium or vacuum environment. A fast or thermal neutron fluence of 1"2-1.5 x 1021 n c m -2 litre, at a relatively low temperature of 430°C or less, produces little difference in fatigue crack growth rate. The irradiation effects produced by the thermal neutrons, however, are more pronounced thatn those of the fast neutrons. In connection with the magnitude of the fatigue crack growth rate, on one hand the neutron fluence can increase the irradiation hardening and helium embrittlemerit in structural or vessel materials to retard the crack rate, while on the other hand it can increase irradiation creep rate. As a result, the fatigue crack rate in the vessel material is enhanced by an order of 10 or more. REFERENCES

1. Ma, B, M., Transient pellet-cladding interaction of LWR fuel elements-Computer Code ISUNE-4, Nucl. Engng Design, 58 (1980), pp. 303-38.

Stress fatigue crack in reactor vessels

103

2. Ma, B. M., Pellet-cladding interaction of LMFBR fuel elements at unsteady state--an introduction to Computer Code ISUNE-5, A S M E J. Engng Power, 103(4) (1981), pp. 627-36. 3. Ma, B. M., Heat generation and temperature distribution in cylindrical reactor pressure vessels, Int. J. Nucl. Engn Design, 11 (1970), 1-15. 4. Ma, B. M., Thermal and pressure stresses in cylindrical pressure vessels, Int. J. Nucl. Engng Design, 11 (1970), pp. 416-27. 5. Ma, B. M., Plastic stresses and strains in cylindrical reactor pressure vessels, Proc. 1st Inst. Conf. on Structural Mechanics in Reactor Technology ( S M i R T ), Paper No. G1/5, West Berlin, Germany, Sept. 19-24, 1972. 6. Ma, B. M., Irradiation swelling, creep and thermal fatigue analysis for cylindrical fusion vacuum wall, invited lecture, 2nd SMiRT, West Berlin, Germany, Sept. 10-14, 1973. 7. Ma, B. M., Irradiation swelling, creep and thermal fatigue analysis for LMFBR pressure vessels, A S M E Pressure Vessel and Piping Conf., Paper No. PVP-1, Miami Beach, Florida, June 24-28, 1974. 8. Ma, B. M., Irradiation effects on controlled thermonuclear reactor (CTR) first wall materials, Nucl. Engng Design, 39 (1976), pp. 203-13. 9. Ma, B. M., Nuclear Reactor Materials and Applications, Van Nostrand Reinhold, New York, 1982. 10. Ma, B. M., Irradiation swelling, creep, thermal shock and thermal cycling fatigue analysis of CTR first wall, Nucl. Engng Design, 28 (1974), pp. 1-30. 11. Roberts, R. and Erdogen, F., The effect of mean stress on fatigue crack propagation in plates under extension and bending, J. Basic Engng Trans. ASML, Series D, 89 (1967), p. 835. 12. Yang, C. T., A study of the law of crack propagation, J. Basic Engng Trans. ASME, Series D, 89 (1967), p. 453. 13. James, L. A. and Knecht, R. L., Fatigue crack propagation in fast-neutron irradiated Types-304 and -316 stainless steels, J. Nucl. Technol., 19 (1973), p. 148. 14. James, L. A. and Knecht, R. L., Fatigue crack propagation behavior of Type 304 stainless steel in a liquid sodium environment, Met. Trans., GA (1975), p. 109. 15. Melville, P. H., Crack propagation and crack arrest in stress gradients, Int. J. Fracture, 13 (1977), p. 165. 16. Ma, B. M., Irradiation swelling, creep, thermal shock and thermal cycling fatigue analysis of LWR fuel elements, Computer Code ISUNE-2, Proc. 3rd SMiRT, Paper D 1/3, London, England, Sept. 1-5, 1975; also Nucl. Engng Design, 34 (1975), p. 361. 17. Ma, B. M., A creep analysis of rotating solid disks, J. Franklin Inst., 267(2) (1959), pp. 149-65. 18. Ma, B. M., A further creep analysis for rotating solid disks of variable thickness, J. Franklin Inst., 269 (1980), p. 408. 19. Ma, B. M., Creep analysis of rotating solid disks with variable thickness and temperature, J. Franklin Inst., 271 (1961), p. 40, also 277 (1964), p. 363. 20. Ma, B. M., Elevated temperature, cyclic loadings and irradiation effects on fatigue crack of LMFBR pressure vessels, A S M E Pressure Vessel and Piping Conf. San Francisco, California, Paper No. 79-PVP-59, June 25-29, 1979. 21. Ellyin, F. and Li, H. P., Fatigue crack growth in large specimens with various stress ratios, J. Pres. Ves. Technol., Trans. ASME, 106 (1984), pp. 255-60. 22. Paris, P. C., Wessel, E. T. et al., Extensive Study of Low Fatigue Crack Growth

104

Benjamin M. Ma

Rates of A533 and A508 Steels, ASTM, Washington, DC, STP513, 1972, pp. 141-76. 23. James, L. A. and Carlson, K. W., The fatigue-crack growth and ductile fracture toughness of ASTM A387 Grade 91 Steel, J. Pres. Ves. Technol., Trans. A S M E , 107 (1985), pp. 272-8. 24. Kussmaul, K., Bund, D. and Junsky, J., Influence of repair welding on cyclic thermal shock behavior of an RPV nozzle corner, Int. J. Pres. Ves. & Piping, 25 (1986), pp. 89-109.