more clearly the effect of nickel content Fig. 10 was drawn. In this figure, the temperature at which the result of "Arrest" is obtained in the HAZ-SCA test under the applied stress of 400 MPa is taken as the critical temperature (i.e., SCA temperature) and is shown on the ordinate. This SCA temperature be- comes lower when the nickel content is raised, K-joint is changed to X-joint, or welding material is changed from the ferritic type to the austenitic sort which is free from brittle fracture.
It was also noticeable that the SCA temperatures were very high compared with the ordinary transition temperatures, such as the 48 J (35 ft-lb) transition temperature in the Charpy test, on the welded joints used. When one has to select a material for an L P G storage tank operated at - 4 5 ~ and when one takes a combination of such severe conditions as 400 MPa of applied stress and a K-joint configuration caused by some unexpected coincidence of vari- ous consequences, then one may have to choose the 31/2% nickel steel.
R e l a t i o n s h i p B e t w e e n H A Z - S C A a n d Charpy Test Results
Although it is well known that the Charpy test is not a fracture toughness test, it has been used as an industrial small-scale test for a long time. It may therefore be useful to correlate Charpy test results with HAZ-SCA test results.
For the correlation, K values applied to the HAZ-SCA tests were calculated by means of Irwin's tangent formula for a center cracked specimen together
+10
~ ~ - 1 0
L
~ - 3 0
- s o
| '~ - 7 0 o
- 9 0
S t r e s s : 4 0 0 M P a
Thickness : 26N30mm
C r a c k size : 120mm - [ 3 ~ 1 ~ , ~ K- joint (G-WM)
~ " 9 I-I,= X-joint (~-WM) - - A ~ ~ ~ X - j o i n t
~ [ - I ~ r - W M )
w ,0,o, \ o \
Heat input ;35"~40kJ/cm "~/~
I i I = J = f = I
0 1 2 3 4 5
Ni c o n t e n t of s t e e l m a t e r i a l , %
FIG. lO--Effects of nickel content in steel, joint types, and types of weld metal on SCA tem- perature of weld HAZ.
T A N A K A ET A L ON N E W W I D E P L A T E A R R E S T TEST 37
with the half crack length of 60 mm (i.e., the half of the length of the surface notch in the tests). Figure 11 shows the relationship between the HAZ-SCA and Charpy test results. The abscissa is the difference between the test tem- perature for the HAZ-SCA test and the fracture appearance transition tem- perature (FATT) in the Charpy test. In some ~treas in this figure, the results of
" G o " and "Arrest" are mixed. The line shown in the figure, however, sepa- rates the "Arrest" data from the " G o " data. This line therefore may show a lower bound relationship between the K , value and the Charpy test results for weld HAZs.
Modification of the SCA Test
Because the starter plate for the HAZ-SCA test can inject a brittle fracture into any part of a steel plate, it can be applied for other objectives. The base metal SCA (BM-SCA) test shown in Fig. 12 is one example of such a modified specimen. With this test method, fracture behavior of a welded plate having a brittle fracture initiation at the weld joint can be studied. The main points of this test method are (1) that the weld residual stress is incorporated in the same way as in the actual structures, and (2) that the method uses a center cracked and hence symmetrical specimen which eliminates the effect of bend- ing moment found in single edge cracked specimens used in existing wide plate arrest tests.
1~ 300
g.
o ~ 200
==,m 100
V P r o p a g a t e / k A r r e s t
Materials AI-killed mild steels, Low temperature steels, A-516, EH36 and 1~3.5% Ni steels.
Welding methods SMAW, GMA , SAW and Electro gas W.
A -
v v W V~v ~ ~ v ~
Y
9 . 2
/x &
~ j .__t
-20 0 20
0 ~ 0
-40 40 60
T - - F A T T ( C v ) , ~
6
4 7 E E Z 2 -~
FIG. 11-- Correlation between HAZ-SCA and V-Charpy test results f o r low temperature steels with thickness range of 25 to 30 mm.
Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:28:35 EST 2015
38 FRACTURE MECHANICS: SEVENTEENTH VOLUME
I- 1,000-
r=% /=
, c / ' ~ ( f ( ( (,
& : : : r
L A J
,Notch ~/ I Britt-le~ U repair
Section AA
F I G . 12--Base metal SCA (BM-SCA) test specimen.
One of the present authors together with co-authors reported results of the BM-SCA test on low-temperature steels [13] and those on 9% nickel steels as well as the K analysis method by L E F M [14]. The data obtained by the BM- SCA test are also included in the analysis shown in the next section.
Correlation of CCA Test to SCA and Wide Plate Tests
The compact crack arrest test and the wide plate test results were brought together and analyzed by means of LEFM. Besides the two types of SCA tests, the duplex ESSO test has been conducted on some materials. The data of the duplex ESSO test were also included in the analysis. The applied K values are calculated without considering the dynamic situation of the run-and-arrest phenomenon of the brittle fracture. The results are summarized in Fig. 13.
The ordinate is the applied K value in the wide plate arrest tests; the abscissa is the K , value obtained by the CCA tests. Because all the wide plate tests are the " G o " and "Arrest" type of test, it can be said that a good correlation exists between CCA and other tests when solid and blank marks are separated by a line. Figure 13 seems to show a considerably good relationship between the small-scale and large-scale tests. This is very encouraging, since all the calculations were made by static methods. We may conclude that the static calculation can be applied to the brittle fracture arrest phenomenon when the crack length is not large. The designed half crack lengths were 60 mm in the HAZ-SCA and 150 mm in the duplex ESSO test. The half crack sizes ob- served in the BM-SCA tests with the results of "Arrest" were approximately 50 to 65 mm. Therefore the above conclusion may be valid up to a half crack length of 150 mm.
Figure 13 suggests that the CCA test when applied with the modified calcu- lation is applicable for the evaluation of fracture arrest toughness of various steel plates and their weld joints.
T A N A K A E T A L O N N E W W I D E P L A T E A R R E S T T E S T 39
n
O o
= L d
Q. D . X
> - O
400 -
3OO
2OO
100
kN- mm -3/z
0 4 8 12
I I [ 1 I I ~ I
o
/ ~
r n
00 L J r I f I ] r J
100 200 300 400
Ka Value by CCA test (Modified calculation), M P a - ~
FIG. 13--Relationship between CCA and various wide plate arrest test results.
7 E E 12
8
4
Conclusions
1. It was found that welded joints of steel materials which have been ap- plied to actual important applications could show considerably low fracture initiation toughness when investigated with numerous CTOD or Kic speci- mens or examined by the fatigue CTOD test.
2. The material that showed a low fracture initiation toughness fin the small-scale test will show also a low stress brittle fracture in the notched wide plate test when a crack tip is located at the same microstructure found to be brittle in the small-scale tests.
3. The SCA concept, which aims at the immediate arrest of brittle fracture when it propagates either beyond the length of the pre-existing surface defect or into a tougher material, seems to be the most realistic criterion when appli- cation of an arrest concept is necessary.
4. The HAZ-SCA test is suitable for the investigation on the practical ar- rest capability of steel plates and their weld joints.
Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:28:35 EST 2015
40 FRACTURE MECHANICS: SEVENTEENTH VOLUME
5. The nickel content of the base plate, the joint geometry of the weld, and the type of the welding material applied affect the HAZ-SCA test results.
When severe conditions are expected in service a considerably high nickel content of the base plate is required.
6. From Ka values obtained by the CCA test, results in the HAZ-SCA or BM-SCA test can be estimated. The CCA test seems to be a promising test method for fracture arrest toughness evaluation.
7. There was comparatively good correlation between the results of the HAZ-SCA and Charpy tests on the same weld joints.
References
[ I] High Pressure Gas Safety Association, "Report of Investigation on Accidents Related with Fracture of Spherical Tanks," High Pressure, Vol. 7, No. 5, 1969, pp. 1-24 (in Japanese).
[2] Authors do not have direct information; see for general information: "Overseas Loss Infor- mation," No. 31, June 1977, Taisho Marine and Fire Insurance Co., Ltd. (in Japanese).
[3] Cuperus, N. J., "Cryogenic Storage Facilities for LNG and NGL," in Proceedings, 10th World Petroleum Congress, Panel Discussion 17, Paper 3, Heyden & Son, London, 1979.
[4] Tanaka, K., Sato, M., and Ishikawa, T., "Fatigue COD and Short Crack Arrest Tests," in Proceedings, International Conference on Fracture Toughness Testing: Method, Interpre- tation, and Application, Paper 18, London, March 1982.
[5] Ishikawa, T. and Tanaka, K., "Development of Fatigue CTOD Test for Investigation on Brittle Regions in Welded Joints," in Proceedings, Sixth International Conference on Frac- ture, New Delhi, Dec. 1984.
[6] Nibbering, J. J. W, and Lalleman, A. W., "Strength of EG Welded 34 mm Plate of Nb St.
52," SSL Report 143, Dee. 1969 (in Dutch) or IIW Doc. X-593-70, May 1970.
[ 7] Yokobori, T. and Aizawa, T., "A Proposal for the Concept of Fatigue Fracture Tough- ness," Journal of the Japanese Society for Strength and Fracture of Materials, Vol. 5, No.
2, 1970, pp. 54-58 (in Japanese).
[8] ASTM Committee on Fracture Testing of High-Strength Sheet Materials, ASTMBulletin, No. 243, Jan. 1960, pp. 29-40.
[9] Irwin, G. R., Welding Journal (Research Supplement), Vol. 41, Nov. 1962, pp. 519s-528s.
[10] Ripling, E. J. and Crosley, P. B., Welding Journal (Research Supplement), Vol. 61, No. 3, 1982, pp. 65-74.
[11] Merkle, J. G. and Corten, H. T., Journal of Pressure Vessel Technology, Transactions of ASME, Vol. 96, No. 4, 1974, pp. 286-298.
[12] Crosley, P. B. and Ripling, E. J. in Crack Arrest Methodology and Applications, ASTM STP 711, American Society for Testing and Materials, Philadelphia, 1980, pp. 211-227.
[13] Tanaka, K., Ohno, Y., and Yamada, N., "Selection of Steel Materials for LPG Storage Tanks," in Proceedings, International Conference on Transport and Storage of LPG &
LNG, Bruges, Vol. 2, 1984, pp. 9-16.
[14] Ishikura, N., Kohno, T., Maeda, H., Arimochi, K., and Tanaka, K., "Recent Develop- ment in Research on 9% Ni Steel and Its Weldments," in Proceedings, International Con- ference on Transport and Storage of LPG & LNG, Bruges, Vol. 1, 1984, pp. 1-11.
C. Y. Yang I and W. H. Bamford 1
Variable Flaw Shape Analysis for a Reactor Vessel under Pressurized Thermal Shock Loading
REFERENCE: Yang, C. Y. and Bamford, W. H., "Variable Flaw Shape Analysis for a Reactor Vessel under Pressurized Thermal Shock Loading," Fracture Mechanics: Seven- teenth Volume, A S T M S T P 905, J. H. Underwood, R. Chait, C. W. Smith, D. P.
Wilhem, W. A. Andrews, and J. C. Newman, Eds., American Society for Testing and Materials, Philadelphia, 1986, pp. 41-58.
ABSTRACT: A study has been conducted to characterize the response of semi-elliptic surface flaws to thermal shock conditions which can result from safety injection actuation in nuclear reactor vessels. A methodology was developed to predict the behavior of a flaw during sample pressurized thermal shock events. The effects of a number of key variables on the f/aw propagation were studied, including (1) fracture toughness of the material and its gradient through the thickness, (2) irradiation effects, (3) effects of warm prestressing, and (4) effects of the stainless steel cladding.
The results of these studies show that under thermal shock loading conditions the flaw always tends to elongate along the vessel inside surface from the initial aspect ratio. How- ever, the flaw shape always remains finite rather than becoming continuously long, as has often been assumed in earlier analyses. The final shape and size of the flaws were found to be rather strongly dependent on the effects of warm prestressing and the distribution of neutron flux.
The improved methodology results in a more accurate and more realistic treatment of flaw shape changes during thermal shock events and provides the potential for quantify- ing additional margins for reactor vessel integrity analyses.
KEY WORDS: flaw shape, stress intensity factor, fracture toughness, crack initiation, crack arrest, thermal shock loading, warm prestressing, virtual crack extension (VCE) method
T h e m o s t s e r i o u s c h a l l e n g e t o t h e i n t e g r i t y o f a r e a c t o r p r e s s u r e vessel c o m e s f r o m t h e r m a l s h o c k l o a d i n g s t h a t c a n r e s u l t w h e n t h e s a f e t y i n j e c t i o n s y s t e m i n j e c t s c o l d w a t e r i n t o t h e n o r m a l l y h o t ( 2 9 0 ~ r e a c t o r vessel. T h i s i n j e c t i o n s y s t e m is d e s i g n e d t o c o o l t h e r e a c t o r c o r e t o p r e v e n t its o v e r h e a t i n g
~Westinghouse Electric Corporation, Nuclear Energy Systems, Pittsburgh, PA 15230.
41 Copyright 1986 byASTM International 9 www.astm.org Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:28:35 EST 2015
42 FRACTURE MECHANICS: SEVENTEENTH VOLUME
in the event of a loss of water pressure in the system. This thermal shock can produce high stresses as well as lowering the temperature and therefore the material toughness of the vessel itself.
During the thermal shock, a flaw, if it exists, will be driven to elongate, since the highest stresses and lowest temperature occur near the vessel sur- face. The elongation of the flaw is resisted by the combined effect of the de- creasing stress intensity factor at the surface as the crack lengthens and better material properties due to lower constraint and often more effective heat treatment of the plate or forging in that area. Elongation is also resisted by the presence of the stainless steel cladding.
The behavior of postulated flaws in the reactor vessel during a thermal shock has long been a subject of active investigation. Early procedures in- volved the use of simplified flaw shapes and approximations for calculating stress intensity factors. Analytical procedures have continually advanced to better deal with the complex interactions which occur between a flaw and the thermal shock loading. Several approaches are presently recommended for this assessment.
Section XI of the ASME Boiler and Pressure Vessel Code [1] provides a detailed procedure for fracture assessment of nuclear vessels. It is suggested that the flaw shape be assumed to retain its original aspect ratio after crack propagation has started. The Section XI guidelines state that crack initiation occurs when the maximum Mode I stress intensity factor, (KI) . . . . along the crack front exceeds the "K~c" value, which is the lower bound of the static crack initiation toughness, with a reference toughness curve for reactor vessel steels provided. Moreover, the Section XI guidelines also state that crack ar- rest will occur if (K~)max falls below the "Kla" value, which is the lower bound of the dynamic crack initiation and arrest toughness, with another reference toughness curve also provided.
Another treatment of the flaw shape is the NRC recommendation [13] in which the initial flaw shape is assumed to be semi-elliptical with an aspect ratio of 6:1; the flaw is then assumed to become continuous (i.e., infinitely long) after crack initiation has started. Apparently, both the ASME Section XI guidelines and the NRC assumption are not realistic, because the final flaw shape in the reactor vessel beltline region is dependent on the type of load, the material properties, and other factors. The NRC assumption will normally lead to much more conservative results than those which are based on the ASME guidelines. A more realistic flaw shape would fall between these two bounds. This has been demonstrated in a series of thermal shock tests conducted at Oak Ridge National Laboratory (ORNL) on scale-model ves- sels, in which a thick-walled cylinder with a 19 mm (0.75 in.) deep semi-circu- lar axial flaw on the inside surface was exposed to a severe thermal shock load. The results of the experiment showed that the crack propagated only axially and extended only to a finite length [2]. It should be mentioned that this experimental cylinder was not clad, and so the results do not reflect the complete set of interactions involved.
YANG AND BAMFORD ON VARIABLE FLAW SHAPE ANALYSIS 43
Many experimental programs were conducted in laboratories such as Fra- matome [14], Knolls Atomic Power Laboratory [20], and Oak Ridge Labora- tories [21-23] to study the effect of stainless steel cladding on failure load of carbon steel specimens. All test results showed that the unirradiated cladding did significantly improve the load carrying capacity of the specimens.
The purpose of this paper is to study the flaw behavior as a function of the toughness related parameters while the flaw shape is allowed to vary during the crack propagation.
Method of Flaw Shape Change Analysis
In evaluating fracture behavior of a structural component both the mate- rial properties and the crack driving forces should be considered. Assume that very little plastic deformation is involved in the fracture process. Based on linear elastic fracture mechanics (LEFM), only the fracture toughness and the stress intensity need to be considered for the analysis. Methods of deter- mination of material properties and the stress intensity factors are briefly de- scribed below.
Determination of Material Properties
Based on LEFM, Klc and Kin are the material properties that can be used to determine, respectively, whether crack initiation or arrest will or will not oc- cur. For conservatism, the Klc and Kla data to be used in the analysis are taken from the lower bounds of all tests.
Since the fracture toughness varies with temperature, for convenience, a temperature scale is defined relative to the reference nil-ductility transition temperature, R TND T. The R TND T is a nonphysical constant related to the brit- tle-to-ductile fracture transition temperature.
The reactor vessel steels (A-533 and A-S08) and the weld metal are suscep- tible to fast neutron fluence or irradiation damage. As a result of the irradia- tion damage the fracture toughness is decreased with the time of exposure.
The reduction in toughness due to irradiation damage is enhanced with the increasing content of copper and nickel. The degree of irradiation damage can be assessed by measuring or determining the shift to higher temperatures of the reference transition temperature, ARTNDT.
ARTND T is generally determined by so-called "trend curves", which corre- late the fluence and copper content to ARTNDT. Based on the initial RTNDT value of the material at a specific location, the RTNDT values at the end of the power plant design life can be determined from the trend curves. These final RTNDT values are used to calculate Kit and Kla.
Determination of Klfor Surface Flaws
The stress intensity factors for most of the two-dimensional problems under simple loading conditions can be found in handbooks [e.g., 3]. In the case Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 18:28:35 EST 2015
44 FRACTURE MECHANICS: SEVENTEENTH VOLUME
where the body is subjected to generally distributed symmetric loads, Kl may be computed by Bueckner's weight function method [4, 5]. For surface flaws, three-dimensional calculations are involved in determination of the Ki-distri- bution along a crack front. A brief review of the works on this subject is given in Refs 6 and 7. In general, numerical analysis is required to deal with this type of problem. Recently, Parks [10] developed the virtual crack extension (VCE) method to determine the Jrvalues for three-dimensional problems.
The VCE method is used in the present paper to determine the Ki-distribu- tion for semi-elliptical cracks in a reactor vessel.
In practice, direct fracture mechanics analysis for the entire transient his- tory experienced by a reactor vessel is prohibitively expensive because the load is time varying. More economic approaches have been developed by, for ex- ample, McGowan and Raymund [6], Heliot et al [7], and Raju and Newman [8], using the superposition technique. In the superposition technique, the stress intensity factors for a given crack are first computed for the uniform, linear, quadratic, and cubic (or higher order) loads which act on the crack surface. Then, in the actual evaluations, the stress (for example, the thermal stress due to a thermal transient) is given approximately by a polynomial function. The coefficients of the polynomial represent the weight of each load component that comprises the total load. Therefore the total stress intensity factor is determined by combining the contributions from each component load.
Assume that the normal stress distribution across a vessel section can be represented by a polynomial equation
(~ : ~ A j x J (j : O, 1, 2, .3) (1)
J
where x is measured from the inside surface of the cylinder (Fig. 1) and A j ' s are the coefficients of the stress distribution that can be determined by the least-square curve fitting technique.
Ri
FIG. 1--Schematic of a longitudinal semi-elliptical flaw on the inside surface of a cylinder.