ML20008F759
| ML20008F759 | |
| Person / Time | |
|---|---|
| Issue date: | 04/30/1981 |
| From: | Anderson W, Johns E C, Weidenhamer G NRC OFFICE OF STANDARDS DEVELOPMENT |
| To: | |
| References | |
| NUREG-0726, NUREG-726, NUDOCS 8105110046 | |
| Download: ML20008F759 (42) | |
Text
._.
l NUREG-0726 Preliminary Analysis of the Effect of Fatigue Loading and Crack Propagation on Crack Acceptance Criteria for Nuclear Power Plant Components U.S. Nuclear Regulatory Commission Office of Standards Development W. F. Anderson G. H. Weidenhamer E. C. Johns m
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NUREG-0726 Preliminary Analysis of the Effect of Fatigue Loading and Crack Propagation on Crack Acceptance Criteria for Nuclear Power Plant Components l
ateYu shed r 19 1 W. F. Anderson, G. H. Weidenhamer, E. C. Johns Division of Engineering Standards Office of Standards Development U.S. Nuclear Regulatory Commission Washington, D.C. 20555 l
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ABSTRACT The staff of the Division of Engineering Standards of the U.S. Nuclear R:gulatory Commission (NRC) initiated a preliminary stud'; to evaluate the con-servatism of existing design methods regarding cyclic loadings and crack growth in nuclear power plant components.
The study was based on the assumption that the application of the ASME Boiler and Pressure Vessel Code should be consistent throughout the design, operation, and inspection phases.
Specifically, any undetectable or allowable crack subjected to fatigue stress levels permitted by Section III of the Code should not be expected to grow larger than the size permitted by Section XI inservice inspection criteria.
The objective of this preliminary analysis was to calculate the magnitude of acceptable crack sizes consistent with the maximum fatigue usage allowed by the Code and to identify some important parameters that may be useful in the dsvelopment of crack acceptance standards.
The results reported are for Class 1 components only.
The results are not intended to be rigorous or comprehensive, but to show general trends from the effect of various parameters on crack size consistent with appropriate sections of the ASME Boiler and Pressure Vessel Code.
The results indicate that, if a component experiences a high level of cyclic stress that corresponds to a usage factor of 1.0, very small cracks can propagate to sizes that exceed code-specified limits.
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CONTENTS EBL*
iii ARSTRACT..............................................................
vii LIST OF FIGURES.......................................................
viii LIST OF TABLES........................................................
ix ACKNOWLEDGMENTS.......................................................
1 1.
INTRODUCTION.....................................................
3 2.
DISCUSSION.......................................................
6 3.
RESULTS..........................................................
7 3.1 Cyclic Stress...............................................
8 3.2 Wall Thickness..............................................
3.3 Crack Geometry ( Aspect Rati o)...............................
9 9
3.4 Usage Factor................................................
10 3.5 Environment.................................................
3.6 Threshold Stress Intensity Correlations.....................
10 3.7 Final Crack Size........................
'll 4.
CONCLUSIONS AND RECOMMENDATIONS..................................
12 23 REFERENCES............................................................
APPENDICES A-1 A.
Crack Propagation Analysis......................................
B-1 B.
Sample Calculations.............................................
l C.
Numerical Resul ts i n Tabul ar Form...............................
C-1 T
V
LIST OF FIGURES Figure Page 1
Initial Crack Size for Through-Wall Growth and Growth to Satisfy Section XI Criteria for a Typical Usage Factor.......
14 2
Initial Crack Size for Growth to Section XI Criteria with a Usage Factor of 0ne..................................
15 3
Initial Crack Size Plotted Against Alternating Stress.......
16 4
Effect of Aspect Ratio on Initial Crack Length in an Air Environment.................................................
17 5
Effect of Aspect Ratio on Initial Crack Half-Depth in an Air Environment.......................................
18 6
Effect of Aspect Ratio on Initial Crack Length in a Water Environment...........................................
19 7
Effect of Aspect Ratio on Initial Crack Depth in a Water Environment...........................................
20 8
Effect of Usage Factor on Initial Crack Size in an Air Environment..................................
21 vii
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LIST OF TABLES Table PaSe I
Matrix Identifying Parameters that Are Varied in Figure 1-8..
22 C-I Initial Size of Surface Flaw with a Usage Factor of 0.05 and an Aspect Ratio of 0.1 for Through-Wall Growth and Growth to Satisfy Section XI Criteria in a Water Environment........
C-1 C-II Effect of Aspect Ratio on Initial Size of Embedded Flaw with a Usage Factor of 1.0 in an Air Environment..................
C-1 C-III Effect of Aspect Ratio on Initial Size of Surface Flaw with a Usage Factor of 1. 0 in a Water Envi ronment.................
C-2 C-IV Effect of Usage Factor on Initial Size of Embedded Flaw with an Aspect Ratio of 0.1 in an Air Environment.................
C-2 viii
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i
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ACKNOWLEDGMENTS The authors thank the members of the Structures and Components Standards Branch, Office of Standards Development, who assisted with the development of this report, in particular, Dr. P. N. Randall and Mr. W. E. Norris.
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l 1.
INTRODUCTION The ASME Boiler and Pressure Vessel Code provides acceptance standards.
for flaws found by nondestructive examination (NDE).
Section III of the Code (Ref. 1) provides acceptance standards for materials and fabrication of nuclear components.
Section XI (Ref. 2) provides acceptance standards for preservice examinations and inservice examinations.
Some inconsistency appears between the acceptance standards of these two sections.
The Subcommittee on Section III formed an Ad Hoc Task Group on Nondestructive Examination Acceptance Standards in 1976 and charged this group with developing rational and reasonable NDE acceptance standards for welds in Section III Construction (Ref. 3).
This is in addition to a Main Commictee Ad Hoc Task Group on Examination and Acceptance Standards organized in 1974.
Some changes resulting from the efforts of the Main Committee Task Group have already been made in the Code.
Section III of the Code provides a basis for design to avoid fsilure by fatigue.
This is niven in the form of design fatigue curves that were developed using fatigue data from polished specimens.
These curves were developed before the study of crack propagation had progressed sufficiently to contribute to r
their basis.
1 In discussions during the development of acceptance standards for flaws found in the preservice examination of nuclear power plant companents, ques-tions were raised regarding the relationship of the acceptance standards to lin this report, the terms " flaw" and " crack" are used interchangeably.
1
other permissible design parameters.
Responses to those questions indicated that no effort had been made to quantify the effect of the initially proposed standards relative to allowable cyclic stresses for design.
Part of the basis for the proposed standards had included consideration of the cyclic loadings anticipated in service for some components rather than the maximum allowable cyclic loadings from the fatigue curves, i.e., a usage factor of 1.0.
The allowable numbers of cyclic loadings is usually an order of magnitude greater than that anticipated in service.
Therefore, this study was undertaken to obtain information on the relationship between allowable cyclic stresses and acceptable crack sizes for construction.
This work represents a preliminary step toward evaluating the conservatism of current design procedures and is not intended to be a rigorous or comprehen-sive attempt to form either a basis for design acceptance criteria or a basis for accepting or rejecting flaws found in service.
Futhermore, it is not intended to be a contribution to the field of crack growth research but is intended to explain a potential application of the results of such research to those involved in the development and application of general design rules.
Two parameters that are likely to be considered in the development of future standards for initial flaw size are workmanship standards and flaw detection capabilities, but no attempt was made in this study to relate acceptable initial crack size to these parameters.
The objective of this study was to estimate the size of acceptable cracks consistent with maximum fatigue usage allowed by the Code and to investigate some important parameters that may be useful in the development of crack : ept-l ance standards for nuclear power plant components.
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2.
DISCUSSION This preliminary study includes calculations of the magnitude of accept-able initial crack sizes for a variety of fatigue loadings to which cracks could be subjected.
The materials considered in this study are those for which both allowable cyclic stresses and crack growth data are available. This includes the pressure vessel steels.2 i
Because of varying characteristics during crack growth, the following simplifying assumptions were made in this study:
1.
Instead of taking a spectrum of cyclic loads, as would be done for an actual design analysis, a single value of cyclic stress and its associated number of stress cycles were used to calculate each data point for initial crack size.
The magnitude of the applied alternating stress intensity, 5,
3 and the associated number of stress cycles, N, are those given in Table I-9.1 (for pressure vessel steels) in Section III of the ASME Boiler and Pressure Vessel Code (Ref. 1).
t 2.
The membrane and bending stress correction factors, M, and M, are b
fixed at 1.0.
The flaw shape parameter, Q, is selected as 1.0 for flaws with l
aspect ratios of 0 and 0.1 and as 2.1 for flaws with aspect ratios of 0.5.
Because of the limited scope of this effort, variations of these three factors and the resulting effects on crack size, which could be either additive or com-pensatory, were not considered.
zThe term " pressure vessel steels" in this study refers to the low alloy steels, ASME SA-508, Classes 2 and 3, and ASME SA-533, Grade B, Class 1.
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3.
Cracks grow in a self-similar manner; i.e., the aspect ratio 3 remains constant.
4.
The stress ratio, R, is taken as 0.
5.
Linear fracture mechanics and the data and methods of Appendix A to Section XI (Ref. 2) form a solid basis for calculating small crack sizes with stress values within the yield strength of the material.
6.
The acceptable crack sizes of the inservice crack acceptance standards of Section XI constitute a reasonable upper limit for crack growth.
Assumptions 2 and 3 imply that subsurface cracks are close to the center of the section with membrane stress only.
It should be noted that, for cases in which the yield strength of a mate-rial is exceeded, large plastic deformations may occur.
Since this analysis r
i is based on linear elastic fracture mechanics, Figures 1 through 8 are plotted with solid curves for a stress range below the yield strength of the material and with broken curves above.
No conclusions will be drawn from the data beyond yield.
l Using the preceding assumptions, the analysis is consistent with the ASME code procedures and data as follows:
3 Ratio of the minor half-diameter (half-depth) of an embedded flaw or the flaw depth of a surface flaw to the flaw length, i
4
1.
Section XI crack propagation techniques (Ref. 2),
2.
Section XI crack acceptance standards (Ref. 2),
3.
Section III allowable cyclic stress values (Ref. 1).
The assumptions implied by the application of the two sectiont, of the Code have raised concerns from some reviewers. One specific concern is the implied stress distribution associated with Assumption 1.
The basis for this concern is that a flaw can grow through the wall only if the stress at the tip of the crack remains large (at the level of the S-N data) across the thickness of the wall.
If the stress level decreases rapidly enough throughout the thickness, crack depth could be expected to stabilize.
In response to this concern, it should be pointed out that, since the crack depth permitted by the inservice inspection criteria is relatively small compared with the wall thickness, even stabilized cracks could be expected to exceed the criteria.
Reviewers also questioned the validity of using a single fatigue stress level from the S-N data as the magnitude of the applied fatigue loading (Assump-tion 1).
The basis for the concern is that loading at one stress level does not account for the variation in the loading as demonstrated by operating time histories.
However, by evaluating the acceptable initial crack size in this l
l way for a range of stress letels, one can observe the sensitivity of crack size to stress.
It has also been suggested that there are very few cases in which I
a component is subjected to stress levels having a usage factor of 1.0.
How-ever, since designers are allowed to design to a usage factor of 1.0, it is considered unduly optimistic to disregard the possibility of having components that are subjected to stress levels associated with a usage factor of 1.0.
5
Although the analysis was made in accordance with the Code, further ques-tions have been raised about using different parts of the Code thi.t are based on data from unrelated physical phenomena.
It is precisely the lack of rela-tionship between these phenomena that has prompted this study.
Attempts have been made to show that consideration should be given to the interrelationships between parameters involving crack growth, allowable cyclic stress, and accept-able crack sizes; failing to do so can lead to potentially serious inconsis-tencies.
Most of the calculations of initial crack size were made with the accept-able crack size criteria in Section XI of the ASME Code, but a through-wall crack was also used.
The through-wall criterion was included only for trends as some of the assumptions used in the derivation of the crack equation are violated as the crack becomes very large.
3.
RESULTS The results of the calculations are shown in Figures 1 through 8.
With the exception of the upper curve in Figure 1, the data show initial crack sizes that will not propagate to sizes larger than the acceptable crack sizes speci-fied in Section XI when the cracks c.re subjected tc cyclic stresses equal to the fatigue stress allowables given in Section III.
In addition, these calcula-tions were made for variations of the following parameters: wall thickness, crack geometry (aspect ratio), environment (air for embedded cracks or water for surface cracks), and usage factor.
Table I shows the combinations of specific parameters considered in the study.
It should be noted that the 1
6
abscissa of Figures 1 and 2 represents both the number of cycles and the alter-nating stress intensity acting in the area where the crack is located.
The stress values shown in brackets below the number of stress cycles are obtained from Table I-9.1 (for carbon, low alloy, and high tensile steels) in Section III of the Code (Ref. 1).
Although the same relationship would also apply in Fig-ures 3 through 8, only the stress values are shown in these six figures.
The equation used for calculating initial crack sizes is derived in Appen-dix A.
Appendix B presents sample calculations to demonstrate how this equation is used.
The results of the calculation for the initial crack size are very sensi-tive to the rounding off of the stress values.
The curves in Figures 1 through 8 were smoothed within a band that was based on the potential rounding-off error.
A reviewer should not expect to reproduce these curves exactly.
To facilitate the presentation of the results of this study the effect of each of the parameters (identified earlier) will be discussed separately.
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3.1 Cyclic Stress l
l Each point on the curves represents one alternating stress intensity, 5,
3 at a particular number of cycles taken from the S-N data.
The stress values j
were from just below the design stress parameter, S,(26.7 ksi), to a level much highrr than the maximum allowable design stress 35, (80 ksi). The results show tha' there is a characteristic combination of stress and number of stress i
a 7
cycles at which the initial crack size is a maximum.
For purposes of discus-sion, all crack sizes quoted from the figures are those near the maximum.
A more realistic spectrum of cyclic stress and corresponding number of cycles for the same usage factor would give initial crack sizes less than that maximum.
Figures 1 through 8 show that the alternating stress intensity, S,, at which the initial crack size becomes a maximum is approximately 29 ksi.
It should also be noted that in calculating usage factors from the S-N i
data, cyclic stresses that would not add to the usage factor but would contri-bute to crack propagation can be anticipated.
The Code does not require con-sideration of usage for cyclic stresses at values less than the minimum stress value of Table I.9-1.
3.2 Wall Thickness Wall thickness appears to have little effect on the calculated initial crack size.
The apparent reason for this is that, although the acceptable crack sizes given in Section XI vary linearly with thickness, the corresponding initial sizes do not vary significantly over a wide span of tnicknesses.
For example, the initial half-depth, a, for a subsurface flaw with On aspect ratio of 0.1 must not exceed 0.0278 inch for an 8-inch-thick wall, while that for a 5-inch-thick wall was calculated to be very similar at 0.0252 inch.
Although wall thicknesses other than 8 inches were considered in this study, only the results for the 8-inch-thick wall are shown (see Appendix B, Section 2).
8
3.3 Crack Geometry Crack geometry, which is measured in terms of aspect ratio, has a signifi-cant impact on calculated initial crack size.
Although Figures 4 and 6 indi-cate that the aspect ratio has little effect on acceptable initial crack length, the effect of the aspect ratio on initial crack depth is pronounced (see Fig-ures 5 and 7).
For example, Figure 4 shows that the initial lengths for cracks with aspect ratios of 0.5 and 0.1 in an air environment were of the same magni-tude at 25 ksi, having a differer.ce of only 0.04 inch or 17%.
However, Figure 5 shows the initial crack half-depth for an aspect ratio of 0.5 to be approxi-mately 4 times that for an aspect ratio of 0.1.
Figures 6 and 7 show the same general results for flaws in water environments.
This suggests that considera-tion of crack depth may be of less importance in establishing acceptance stand-ards.
This may be useful since measurements of crack depth by different flaw detection techniques can be expected to be inconsistent, while the measurements of crack lengths may be more consistent.
3.4 Usage Factor l
Urage factor is defined in Section III of the Code (Ref. 1).
As used herein, it is considered to be the ratio of the number af cycles experienced by a compo-nent at a specific value of alternating :; tress intensity to the number of cycles that the component is allowed from the S-N data for the same value of alternating stress intensity.
The results discussed thus far were determined for a usage factor of 1.0.
Figure 8 shows that, for a component that experiences fatigue loadings corresponding to usage factors of 1.0 and 0.1, the initial crack lengths of an embedded flaw with an aspect ratio of 0.1 are 0.28 inch and 1.3 inches, 9
l
respectively.
The figure also snows that, as the usage factor decreases to 0.01, the acceptable initial crack length increases to 2.0 inches.
e 3.5 Environment Of those parameters studied, the parameter that most significantly affects crack size is the environment.
Comparisons of the curves in Figures 4 and 5 with those in Figures 6 and 7 show that allowable initial crack sizes in a water environment are 15 to 20 times smaller than those in an air environment.
The growth relationships used to evaluate this parameter for ferritic steels were I
taken from Figure A-4300-1 in Appendix A to Section XI of the ASME Code (Ref. 2).
3.6 Threshold Stress Intensity Correlations Results indicate that, if a component experiences a cyclic stress level corresponding to a usage factor of 1.0, fatigue failure may occur even when only very small cracks are present initially.
However, very low stress inten-sities are associated with small crack sizes, and at low stress intensities, there may be a characteristic threshold value below which no cracks propagate.
Because of this, it is necessary to examine the results and compare the associ-ated stress intensities with threshold stress intensities.
In an air environment, the threshold stress intensity value for a stress ratio of zero is approximately 5 ksi/In (page J-13 of Ref. 4).
This compares with stress intensity values as low as about 5.6 ksilin obtained4 in this study 4See Appendix B for details on this calculation.
10
for the lowest stresses with small initial cracks.
For a water environment, initial crack sizes that would give stress intensities as low as 1.3 ksi/IE were calculated. This compares to a threshold stress intensity in water of approximately 2.6 ksi/In (page 5-40 of Ref. 5).
Threshold stress intensities could be a factor in the development of crack acceptance standards.
Unfortunately, these stress intensities are not completely understood, and the preliminary comparison contained herein does not provide a basis for conclusions.
3.7 Final Crack Size One of the most surprising results of this study was that final crack size does not necessarily have a large impact on the calculated initial crack sizes.
Stated differently, cracks having very similar initial sizes can have final sizes that differ greatly.
Figure 1 shows that the initial crack size at beginning of life is essentially the same whether the crack propagates to Section XI criteria or whether the crack propagates through the wall.
This implies that a substan-j tial portion of usage is needed to propagate an initial crack to Section XI cri-teria and then only a small amount of usage is needed to propagate a crack from the Section XI size to a through-wall crack.
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It is emphasized that, although the results imply that it is possible for a flaw to grow to a through-wall size from the allowable size, only the trend is meaningful because the equation for predicting initial flaw size is invalid for through-wall cracks.
Specifically, as the flaw depth approaches the size of the wall thickness, the assumption that the membrane stress and bending stress 11
correction factors are both unity becomes invalid.
Results showing initial crack sizes are given in Figure 1, and sample calculations in Appendix B demonstrate how similar results were obtained for a subsurface flaw (air environment).
4.
CONCLUSIONS AND RECOMMENDATIONS The results of this study present an additional basis for determining acceptable flaw sizes.
Although no specific acceptance standards can be recom-mended owing to the simplified nature of this analysis, it is concluded that the effects of allowable cyclic loading should be considered with the potential for crack propagation in establishing acceptance standards.
In addition, it is concluded that, of the parameters evaluated in this study, usage factor and service environment have the most influence on crack growth.
As stated previously in Section 2, there are concerns and questions regard-ing the application of fatigue stresses allowed by the Code.
The comment most frequently made is that evaluation on the basis of a usage factor of 1.0 is unrealistically conservative.
This is principally because normal operating conditions rarely include such high levels of fatigue usage and, even when they do, declining stress gradients would limit crack growth.
These concerns and others are i.?portant and must be considered when specific acceptance standards are developed.
It is also concluded that, because of the limited scope of this study, a complete understanding of the significance of these results is not possible l
without extensive additional effort.
Therefore, it is premature either ta l
12 I
define the extent of any immediate problem or to prepose specific solutions.
Further study considering realistic component design and service conditions is needed in order to provide more specific conclusions.
The Code bodies should provide practical limits on usage factor.
For Sec-tion III of the Code, development of these limits should include consideration of many factors, including workmanship standards, flaw detection capability, threshold stress intensities, and service environment.
Similarly, for Sec-tion XI of the Code, limits on usage factor should be included in the basis for the present acceptance standards.
Also, consideration should be given to requiring special design acceptance standards and special inspection require-ments for components that can be expected to experience either high usage factors or severe environmental conditions.
In addition, it may be necessary to review the limits of the S-N data or require a crack propagation analysis or both if a component is subjected to a large number of cycles of stress below the apparent endurance limit.
Whether the results of this study have identified a potential practical l
shortcoming in core design procedures or whether occasions when components are l
l subjected to high levels of alternating stress are unrealistically rare, the i
development of flaw acceptance standards should be consistent throughout the design, construction, and inspection phases of the Code.
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100 101 8
8 6
6 Surfacs Crack 4
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4 Stresses exceed yield Stresses below yield
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Factor, 0.05 2
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Figure 1. Initial Crack Size for Through-Wall Growth and Growth to Satisfy Section XI Criteria for a Typical Ussge Factor
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a Figure 2. Initial Crack Gize for Growth to Section XI Criteria With a Usage Factor of One
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Figure 3. Initial Crack Size Plotted Against Attemating Stress 16
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Figure 6. Effect of Aspect Ratio on initial Crack Length in a Water Environment 19
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Table I.
MATRIX IDENTIFYING PARAMETERS THAT ARE VARIED IN FIGURES 1-8 Figure No.
Parameter 1
2 3
4 5
6 7
8 Final Crack Size Section XI Crii.eria X
X X
X X
X X
X Through-Wall
- X Environment (da/dN from Section XI)
I Embedded flaw (air environment)
X X
X Surface flaw (water environment)
X X
X X
X Aspect Ratio 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.5 0.5 0.5 0.5 0**
0 Usage Factor 0.05 1.0
- 1. 0 1.0 1.0 1.0 1.0 0.01 0.1 0.2 0.3 0.4 l
- 1. 0 i
"A through-wall crack is a mathematical exercise for representing the upper 2
limit of crack size.
The results are interpreted for trends only.
- An aspect ratio of U is a mathematical exercise for representing the upper limit for a long flaw.
The results are interpreted for trends c.".ly.
22
l REFERENCES 1.
American Society of Mechanical Engineers, " Rules for Construction of Nuclear Power Plant Components," ASME Boiler and Pressure Vessel Code,Section III, Division 1 and Appendices, Winter 1979 Addenda.
2.
American Society of Mechanical Engineers, " Rules for Inservice Inspection of Nuclear Power Plant Components," ASME Boiler and Pressure Vessel Code,Section XI, Division 1 and Appendices, 1977 Edition, Winter 1979 Addenda.
3.
Doty, W. D., "Section III Ad Hoc Task Group on Nondestructive Examination Acceptance Standards," Text of Address, Proceedings, Forty-eighth General Meeting, National bcard of Boiler and Pressure Vessel Inspectors, April 30-May 4, 1979.
4.
American Society of Mechanical Engineers - Section XI Task Group on Flaw Evaluation, " Flaw Evaluation Procedures:
ASME Section XI," Edited by T. V. Marston, Nuclear Power Division, Electric Power Research Institute, i
EPRI NP-719-SR, August 1978.
5.
Mayfield, M. E.,
Forte, T. P., Rodabaugh, E. C.,
Leis, B.
N., Eiber, R.
J.,
" Cold Leg Integrity Evaluation," NUREG/CR-1319, Prepared by Battelle Columbus Laboratories for the U.S. Nuclear Regulatory Commission, February 1980.
Available for purchase from the NRC/GP0 Sales Program, U.S. Nuclear Regulatory Commission, Washington, DC 20555, and/or the National Technical Information Service, Springfield, VA 22161.
1 l
22
APPENDIX A CRACK PROPAGATION ANALYSIS The American Society of Mechanical Engineers (ASME) Code gives a stand-ardized procedure for performing crack propagation analyses.
In the ASME pro-cedure, a method for approximating crack shapes is coupled with crack growth equations to determine the final size of the flaw after being subjected to operational loads. The cracks are approximated by ellipses of the same general size and shape.
Two equations for crack propagation are given in Appendix A to ASME Sec-tion XI.
The first gives the stress intensity variation, AK, as y
AKy = (M,60, + M O"b)
(IA) b where Aa,, dab = variation of membrane and bending stresses (ksi)
= membrane stress and bending stress correction factors M,, Mb Q
= flaw shape parameter a
= minor half-diameter (half-depth) for embedded flaw or flaw depth for surface flaw (in) l 2
= crack longth (in) i l
The second equation relates the crack growth rate, da/dN (in/ cycle), to the stress intensity variation, AKy (ksi/Iii),
da/dN=CAKf (2A)
A-1
_,.,,__.___,_______,,_9
r where C is an empirically derived coefficient.
For a crack in an air environ-
-11 ment, C is given as 2.67 x 10 For a crack in a water environment, C is
-11 given as 37.95 x 10 To proceed with the derivation of the desired relationships, it is neces-sary to first employ the assumption that M, and M are unity.
Also, using the b
assumption that the sum of the variations of membrane stress and bending stress d
i is equivalent to twice the alternating stress intensity, S,,
given in the Appendices to Section III of the cnde, Equation lA can be rewritten as:
i
)
AK7 = 25,M.
(3A) l Employing the third assumption that cracks grow in a self-similar manner and separating variables in Equation 2A, integrating, and then substituting Equa-l tion 3A, one obtains:
-0.863 + 0.863CN(2S,Jn/Q)3.726 -1.159 g = [a7 3
(4A) a i
l where g = initial value of a (in) a f = final value of a (in) a N = number of stress cycles i
S, = alternating stress intensity from Table I-9.1 of ASME Section III (ksi) i A similar equation can be found on page F-73 of Reference 4. The results from Equation 4A and the equation in Reference 4 were compared, and adequate correla-i tion was obtained.
4 A-2 1
,m.-,
.,-,,e s-ue----~+,---_------------=w-
One additional item of information that can be obtained from Equation 4A is for the case in which a is allowed to become very large, i.e., grow through f
the wall.
For the cases considered in this study, the first term in the brac-kets in Equation 4A becomes negligible and Equation 4A reduces to:
g=[0.863CN(25,fi7Q)3.726-1.159 (SA) 3 a
Although a crack can become very large and grow through a wall, some of the assumptions that were employed in deriving Equation 4A are violated; hence, Equation 5A is not valid.
However, Equation SA represents an upper limit for crack growth, and the results can be interpreted for trends.
A-3
APPEhDIX B SAMPLE CALCULATIONS 1.
CALCULATION OF INITIAL CRACK SIZES OF EMBEDDED FLAW 1.1 Section XI Criteria In order to use Section XI criteria, the wall thickness and the crack aspect ratio must be known.
For this example, a wall thickness of 8 inches and an aspect ratio of 0.1 (subsurface flaw) are chosen.
With these parameters, the final crack size, a, as determined from Table IWB-3510-1 in Section XI must not f
exceed 2.6% of the wall thickness.
Therefore, f = 0.208 inch.
a t
Equation 4A may then be used to calculate the initial crack size:
-0.863+0.863(2.67x10'II)N(2SdEIN)'
3 a; = [af a
where a
is the initial value of a g
a is the final value of a f
5,N are the alternating stress intensity and number of stress 3
cycles, respectively, from the S-N data Q
is the flaw shape factor.
i B-1
i The values for S, and N are determined from Table I-9.1 in the Appendices to Section III of the code.
They will be taken as S, = 20 ksi with the corres-5 ponding value for N = 10 cycles.
The specified minimum yield strength for ferritic steels of the type considered is 50 ksi; therefore, the value of (o,+ o )
is 0.4.
For an aspect ratio (a/2) of 0.i and a stress ratio of b
ys 0.4, the value of the flaw shape factor (Q) from Figure A-3300-1 of Section XI t
is approxirrately 1.0.
On substituting the appropriate values into Equation 4A, the initial value of a (a ) is found to be:
9 j = [0.208-0.863 + 0.863(2.67 x 10 ' )(10 )
5
~
a (2 x 20/n/1.0)3.726 -1.159.
3
-2 g = 2.782 x 10 inch.
a 1.2 Through-Wall Crack To determine the size of an initial crack that might be expected to propa-gate through the wall, Equation 5A is used.
On substituting the values for S,,
N, and Q that were used in the previous calculation, the initial crack size for this case is found to be:
-2 g = 3.483 x 10 inch.
a 4
- o represents the minimum yield strength for the material considered in this 3
example.
i B-2
It is clear that the difference between the initial crack size for the 1
through-wall crack and the initial crack size based on the Section XI criteria is 0.007 inch.
Since the aspect ratio is 0.1, the difference between the lengths of the initial cracks is 0.070 inch.
2.
EFFECT OF WALL THICKNESS ON INITIAL CRACK SIZE CALCULATIONS Although there is some effect of wall thickness on the calculated initial crack size, this effect is not as significant as one might expect.
This is shown by the following calculation:
Using Table IWB-3514-2 for an embedded flaw in a 5-inch-thick wall, the final flaw size can be calculated to be:
f = 5 x 0.026 = 0.130 inch.
a Using Equation 4A, the initial flaw size can then be calculated:
-2 g = 2.52 x 10 inch.
a This result is not drastically different from the value obtained for a
-2 wall thickness of 8 inches (2.782 x 10 inch).
3.
CALCULATION OF STRESS INTENSITY VARIATION Employing the assumptions stated in Appendix A, the stress intensity varia-tion is given as:
B-3
d j
1' l
AKy = 25, M i
Using values determined previously, the initial stress intensity varia-tion may be determined as:
4 t
y=2x12.5/n(0.016)/1 ksi[G l
AK I
g=5.6ksi/G j
AK I
i
(
i i
1 6
i i
l l
i
}
i f
i t
i l
i B-4 1
i h
t nn---.-
n-
,,,,.n,
-.--n e
-r-s
--~e n,, - - -,--. - - - - ---
l APPENDIX C NUMERICAL RESULTS IN TABULAR FORM TABLE C-I Initial Size of Surface Flaw with a Usage Factor of 0.05 and an Aspect Ratio of 0.1 for Through-Wall Growth and Growth to Satisfy Section XI Criteria in a Water Environment (See Figure 1)
Initial Crack Depth (in)
N S,(ksi)
Section XI Through-Wall Criteria Growth 2
10 205 6.3E-3 6.7E-3 3
10 83 1.9E-2 2.3E-2 4
10 38 3.4E-2 4.7E-2 5
10 20 3.7E-2 5.2E-2 6
10 12.5 2.2E-2 2.7E-2 TABLE C-II Effect of Aspect Ratio on Initial Size of Embedded Flaw with a Usage Factor of 1.0 in an Air Environment (See Figure 5)
Initial Crack Half-Depth (in)
N S,(ksi) a/E = 0 & 0.1 a/E = 0.5 10 580 7.2E-4 4.5E-2 3
10 83 1.4E-2 6.3E-2 4
10 38 2.6E-2 1.1E-1 5
10 20 2.8E-2 1.2E-1 6
10 12.5 1.6E-2 5.7E-2 C-1
TABLE C-III Effect of Aspect Ratio on Initial Size of Surface Flaw with a Usage Factor of 1.0 in a Water Environment (See Figure 7)
Initial Crack Depth (in)
S (ksi)
N a
a/2 = 0 & 0.1 a/A = 0.5 10 580 3.4E-5
?.4E-3 3
10 83 7.1E-4 3.5E-3 4
10 38 1.4E-3 6.9E-3 5
10 20 1.6E-3 7.6E-3 6
10 12.5 8.4E-4 4.1E-3 TABLE C-IV
^
Effect of Usage Factor
- on Initial Size of Embedded Flaw with an Aspect Ratio of 0.1 in an Air Environment (See Figure 8)
Initial Crack Half-Depth (in) b (ksi)
N a
U=0.01 U=0.1 U=0.2 U=0.3 U=0.4 U=1. 0 10 580 9.7E-3 4.5E-3 2.9E-3 2.1E-3 7.2E-4 1
3 10 83 1.9E-1 9.7E-2 6.1E-2 4.4E-2 3.4E-2 1.4E-2 4
10 38 2.0E-1 1.3E-1 9.2E-2 7.1E-2 5.7E-2 2.6E-2 5
10 20 2.0E-1 1.3E-1 9.7E-2 7.5E-2 6.1E-2 2.8E-2 6
10 12.5 1.9E-1 1.1E-1 6.8E-2 5.0E-2 3.9E-2 1.6E-2 Usage factor is defined as the ratio of the number of cycles experienced by a component at a specific value of alternating stress intensity to the number of cycles that the component is capable of withstanding (from the S-N data) for the same value of alternating stress intensity.
C-2
U i
'J.S. NUCLEAR REGULATORY COMMISSION
,7 BIBLIOGRAPHIC DATA SHEET NUREG-0726 4, TITLE AND SU81sTLE (Add vokme Na.sf apprepnanel
- 2. (Leave blmk)
Preliminary Analysis of the Effect of Fatigue Loading and Crack Propagation on Crack Acceptance Criteria for Nuclear
- 3. RECIPIENT 15 ACCESSION NO.
Power Plant Components
- 7. AUTHORISI
- 5. DA1E REPORT COMPLETED "Te'ptember I'f9}0 W. F. Anderson, G. H. Weidenhamer, Earl R. C. Johns
- 9. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS tractudr lia Codel DATE REPORT ISSUED Office of Standards Development l "1981
^"
Aun U.S. Nuclear Regulatory Commission 8*"""*"*'
Washington. D. C.
20555
- 8. floave Wank}
l
- 12. SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (includr Isa Codr1 Office of Standards Development U.S. Nuclear Regulatory Commission
- 11. CONTRACT NO.
Washington, D. C.
20555
- 13. TYPE OF REPORT PE RIOD COVE RED //nclusive daars)
Technical Report
- 15. SUPPLEMENTARY NOTES
- 14. (Leave Nek)
"d ;Ir#YiErNaEy""s#tudy was initiated to evaluate the conservatism of existing
^'
e design methods regarding cyclic loadings and crack growth in nuclear power plant components. The study was based on the assumption that the application of the ASME Boiler and Pressure Vessel Code (the Code) should be consistent throughout the design, operation, and inspection phases. Specifically, any undetectable or allow-able crack subjected to fatigue stress levels permitted by Secticn III of the Code should not be expected to grow larger than the size permitted by Section XI in-service inspection criteria.
The objective of this analysis was to estimate the magnitude of acceptable initial crack sizes under various conditions and to identify some important param-I eters that may be used in the development of crack acceptance standards. The results are intended not to be rigorous but to show general trends from the effect of various l
parameters on crack size consistent with appropriate sections of the Code.
The results indicate chat very small cracks can propagate to sizes larger than postulated Code limits if they experience the total number of cycles of stress that are allowed by the Code (a usage factor of one). The two parameters that have the most effect on crack propagation are found to be usage factor and environment.
- 17. KEY WORDS AND DOCUMENT ANALYSIS 17a. DESCRIPTORS 17b. IDENTIFIERS /OPEN-ENDED TERMS
- 18. AVAILABILITY STATEMENT
- 19. SECUhiTY CLASS (TAs report)
- 21. NO. OF PAGES Unclassified Unlimited UYcYaYsifDe)$
I"'#
~#
NRC FORM 335 (7-77)
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