ML040540674
| ML040540674 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 02/02/2004 |
| From: | Entergy Operations |
| To: | Document Control Desk, Office of Nuclear Reactor Regulation |
| References | |
| CNRO-2004-00008 M-EP-2004-001, Rev 0 | |
| Download: ML040540674 (113) | |
Text
Engineering Report M-EP-2004-001 Rev. 00 Page 26 of 54 The nodal stress data presented in the previous pages are the data imported into the respective Mathcad worksheet (discussed later) for further processing to obtain the pertinent stress distributions required for the fracture mechanics analysis.
The processing of the nodal stress data is described in Section 4.
3.0 Analytical Basis for Fracture Mechanics and Crack Growth Models Fracture Mechanics Models Surface Crack The mean radius-to-thickness ratio (Rm/t) for the CRDM nozzle is 2.739. The fracture mechanics equation used in the proposed revision to the ASME Code Section Xl is based on the solution from Reference 4. This solution is valid for an outside radius-to-thickness ("Rdt") ratio from 4.0 to 10.0. The CRDM nozzle uRo/tV ratio is lower (3.239), indicating that the CRDM nozzle is a thicker wall cylinder than those considered in Reference 4. Therefore, the fracture mechanics formulations presented in Reference 5 were chosen (the applicable URm/t" ratio is from 1.0 to 300.0).
The stress intensity factor (SIF) for the postulated crack under an arbitrary stress distribution was obtained from Reference 5. The model was for both an internal and external part through-wall surface crack subjected to an arbitrary stress distribution. This model is valid for a ratio of mean radius (Rmean)-tO-thickness (t) between 1.0 and 300.0. Since the ratio for the CRDM nozzle is 2.739, this model is considered applicable.
The equation for the SIF for the deepest point of the crack is given as [5]:
K =( a)fs * [ZaG ]
Q i=0 Where:
K, = SIF fksitin.J Q = Crack shape factor, defined as Q=l+1.464*(a)*-)65 when alc<1.O and, C
Q= 1+1.464*(c )165 when a/c > 1.0 a
a =Crack depth finch)
Engineering Report M-EP-2004-001 Rev. 00 Page 27 of 54 ai = Coefficients of the stress polynomial describing the hoop stress variation through the crack depth. Describes the power loading on crack face.
GC = Stress Intensity Correction Factors (SICF), which are provided in tables in Reference 5.
In Reference 5, SICF is presented for both the depth point of the crack ("a-tip")
and for the surface point of the crack ("c-tip"). Separate tables are provided for the internal (ID) and external (OD) surface cracks. In addition the values are provided in association with the Rm/t ratio, a/c ratio (crack aspect ratio), and alt ratio (normalized crack depth). The SICF tables are large and a suitable interpolation scheme is necessary to obtain proper coefficients dependent on crack size and shape for a given cylindrical geometry. Selected SICF from the tables for internal cracks for two different Rm/t ratios and a/c ratios are presented in Figure 18 below.
,2.73,9 2
X -
D 4
aI I
E m0
.1 003 0
0.2 A
a R/t - 2 & a/c = 0.2 R/t2&a/c =0.4 RA = 2 & a/c = 1.0 Rt-4&a/c=0.2 R/t=4&a/c=0.4 R/t = 4 & a/c = 1.0 04 0.6 0.8 X
L alt ratio
,0, R/T =2 & a/c =.2 R/t=2&a/c=.4 Rt=2&a/c= I
=4 & a/c =.2 R/t=4&ac=.4 R/t=4&a/c I
X a/t ratio Figure 18: SICF shown as a function of normalized crack depth for the "a-tip" (left figure) and the "c-tip" right figure. These figures show that simple linear interpolation would not provide accurate coefficients. These figures also show that a proper R,/t is essential to provide a reasonably accurate estimate of the SIF.
c 4
Engineering Report M-EP-2004-001 Rev. 00 Page 28 of 54 The figure above shows two features that are significant;
- 1) The interpolation used to obtain the SICF must be carefully performed such that the value accurately represents the crack geometry. This is accommodated by selecting a suitable order for the polynomial prior to performing an interpolation to obtain the specific value. This aspect is discussed in further detail in the section describing the analysis method.
- 2) The correct Rm/t ratio is essential for obtaining a reasonably accurate estimate of the SIF. Using a higher ratio will tend to underestimate the SIF and hence under predict the crack growth.
Both these features have been considered in the development of the analysis model such that a reasonable, yet conservative, estimate of the SIF is obtained.
Through-Wall Axial Crack The analysis for a through-wall axial crack was evaluated using the formulation of Reference 6. This formulation was chosen since the underlying analysis was performed considering thick-wall cylinders that had a "Rdt" ratio in the range of the application herein. The analysis used the outside surface (OD) as the reference surface and, hence, the same notation is used here.
It was noted in Reference 6 that the formulations based on thin shell theory do not consider the complete three-dimensional nature of the highly localized stress distribution. This would be the case for the residual stress distribution from welding.
The nonlinear three-dimensional stress distribution coupled with shell curvature must be properly addressed to account for the material behavior at the crack tip, which controls the SIF, such that the SIF is not underestimated. The information presented in Reference 8 compared the results from formulations derived using thin shell theory and those derived using thick shell formulation, these results highlighted the need to use thick shell based formulation for situations such as the current application to CRDM nozzle through-wall axial cracks.
The formulation provides the correction factors, which account for the "R0It" ratio and crack geometry (X), that are used to correct the SIF for a flat plate solution subjected to similar loadings. The correction factors were given for both "extension" and 'bending" components. The flat plate solutions for both membrane and bending loads were to be used to obtain the applied SIF. The formulations for SIF were given as [6]:
K (,,er
{ Ae + Ab}
- K P for the OD surface;
- and,
Engineering Report M-EP-2004-001 Rev. 00 Page 29 of 54 Kln,,er = {Ae - Ah}
- K. for the ID surface; where:
Ae and Ab are the "extension' and "bending' components; and, Kp is the SIF for a cracked Flat Plate subject to the same boundary condition and loading as the cracked cylinder.
The flat plate SIF solutions are written as:
Kp Afembrane =(Jh
- V; for membrane loading, and Kp-fendsing = or* b7 for bending loading.
Where:
ch and ab are the membrane and bending stresses and or is one-half the crack length.
The reference surface used in the evaluation was the OD surface. The stresses at the ID and OD at the axial elevation of interest were decomposed into membrane and bending components as follows:
a, =res-Ol) + ares-D) for membrane loading; and 2
=res
- ares-l) for bending loading.
2 where:
Ures-OD is the stress (residual+operating) on the OD surface; and, ares-ID is the stress (residual+operating) on the ID surface.
The data presented in the tables in Reference 6 for determining the Ae and Ab components were curve fit using a fifth order polynomial such that they could be calculated knowing the parameter X, which is defined as [6]:
A = [12 *(I
)]0
- (R *1)0.5 where v is Poisson's ratio and R is the mean radius.
Engineering Report M-EP-2004-001 Rev. 00 Page 30 of 54 The data obtained from the tables in Reference 6 were curve fit using a fifth order polynomial. The curve fitting was accomplished using Axum 7 [7]. The curve fit results for the components are presented in Figure 19 below.
Extension and Bending Constants for Throughwall Axial Flaws R/t = 3.0 (ASME PMIP 350 1997; pp 143)
AeM:- 1.0090 + 0.3621Vx + 0.0565*x 2 - 0.0082x 3 + 0.0004*x 4 - 8.3264E-006'x 5
Wn 4-U)a) 0 to a)
E r-0 0 - AbB:-
AbM:- -0.0063 + 0.0919x - 0.01 68x 2 - 0.0052-x3 + 0.0008'x4 - 2.9701 E-005-x5 0
2 4
6 8
Parameter Lambda {dimensionless}
10 i
1 2 Figure 19: Curve fit equations for the "extension and "bending" components in Reference 6. Tables ic and Id for membrane loading and Tables ig and lh for bending loading of Reference 6 were used.
Crack Growth Model To evaluate the potential for crack growth due to PWSCC, the crack growth rate equation from EPRI-MRP 55 [8] was used. The crack growth rate as a function of the SIF with a correction for temperature effects is given as [8]:
-~=exp[-
-g ( ---
)]az(K - K/h)"8 dt R TITret Where:
da/dt = crack growth rate at temperature T {m/s)
C1m
Engineering Report M-EP-2004-001 Rev. 00 Page 31 of 54 Qg = thermal activation energy for crack growth (31.0 kcal/molej R = universal gas constant {1. 103x 10f3 kcal/mole-0RJ T = absolute operating temperature at crack tip (0RJ T = absolute reference temperature for data normalization (1076.67 0R) a = crack growth amplitude (2.67x1ef'2)
K = crack tip SIF {Mpa-lm]
Kth = threshold SIF for crack growth (MPaIm)
,/ = exponent (1.16]
The above equation represents the seventy-fifth percentile curve. Since the PWSCC crack growth of interest is in the primary water, this model would provide a reasonably conservative crack growth. The operating temperature of 600 'F was verified to be a conservative upper bound based on the design input information documented in Appendix "A"..
4.0 Method of Analysis Mathcad Worksheet Format The analytical scheme was developed using Mathcad [9] which facilitates calculations (including recursive) in a logical manner. Appendix B provides annotated versions of the three sets of worksheets used in the current analysis. The three sets are for the ID surface crack, the OD surface crack and for the through-wall crack. In the paragraphs below the general approach used to develop the worksheet is presented.
The first part of the worksheet is common to all three sets and requires the proper identification for the analysis being performed. In this region the component and the reference location in that component are identified. Immediately below the identification entry are the geometric landmark entries. For the surface cracks three entries are required and these are:
- 1)
The length of the minimum freespan from the NDE data analysis
{FSnde.data.sheet}-
- 2)
The location of the crack with respect to the reference line (Upper crack tip at the reference line, center of crack at the reference line or lower crack tip at the reference line) {Val};
- 3)
The location of the bottom of the weld measured upwards from the nozzle bottom {ULstrs.Dist}.
For the through-wall crack the location of the crack upper tip is always at the reference line, while the two other landmark entries (freespan and bottom of weld) are similar to that for the surface crack. This completes the entries on the first page of the worksheet.
Engineering Report M-EP-2004-001 Rev. 00 Page 32 of 54 The second page of each Mathcad worksheet contains the inputs for crack dimensions, tube geometry, internal pressure, years of operation, iteration limit, operating temperature, and the constants for the PWSCC crack growth parameters. It should be noted that the crack growth is performed using metric units; hence, those constants are required to be in metric units. The remainder of this sheet does not require user input. The calculation shown is simple arithmetic to determine the values necessary for the analysis.
The third page of each worksheet is designed to import the required nodal stress data from the Excel spreadsheet provided by Dominion Engineering (described earlier). After the required data has been imported, the graph below the data table depicts the ID and OD stress distributions along the axial length of the nozzle. This graph is needed to aid in the selection of the nodal stress data to be used in the subsequent analysis. Once the data needed for the evaluation has been selected, it is pasted onto the third sheet at a variable defined as "Data". No further user input is required. The worksheets presented in Appendix C reflect this design.
Determination of Stress Field (Distributions)
The first step in the analysis is to develop the appropriate stress distribution to be used in the determination of the SIF. This is needed because the SIF formulation is based on use of a uniform stress distribution along the length of the tube. However, the stress field at the bottom portion of the nozzle, starting from the nozzle bottom, increases in magnitude as the bottom of the weld is approached. Consequently, if an assumed crack located in the vicinity of the reference line were to grow by PWSCC, it would be subjected to an increasing stress field. Thus, to use the stress distribution at the initial crack location would lead to an underestimate of the SIF since the SIF is directly proportional to the applied stress. In order to obtain a reasonably representative SIF under the prevailing stress field variation, a moving average scheme was developed. This scheme is as follows:
- 1) For the initial crack location the stress distribution at the two crack tips (lower and upper) and the crack center are averaged to produce an average stress field that is applied to the crack. It is this stress distribution that is used to ascertain whether there exists a potential for PWSCC crack growth.
This method is considered reasonable since it is similar to the superposition principle used in finite element based SICF determination.
- 2) The remaining portion of the nozzle extending from the upper crack tip to the bottom of the weld is divided into twenty (20) equal segments.
- 3) The stress distribution in the first segment, above the upper crack tip, is an arithmetic average of the first three initial crack region distributions (Lower tip, center of crack and the upper tip) plus the distribution in the first segment. Thus, when the crack enters the first segment the magnitude of the stress distribution is appropriately increased to account for the increased applied stress. Similarly, as the crack progresses upward to the weld bottom through the various segments, the applied stress distribution is adjusted accordingly. The small extent of the length between the reference
Engineering Report M-EP-2004-001 Rev. 00 Page 33 of 54 line and the bottom of the weld can be sufficiently accommodated by the twenty-segment characterization.
To accomplish this averaging scheme, the nodal stresses at the five (5) nodal locations through the tube thickness and its variation along the length of the nozzle are individually regressed with a third order polynomial. Hence, it is important to ensure that the axial distribution can be described by a third-order polynomial. The regression is performed along the nozzle axis at each of the five (5) locations individually. The result of the regression provides the spatial coefficients required to describe the stress distribution. The nodal stress data representing the region of interest, from the nozzle bottom to an elevation just above the bottom of the weld, is selected. In this manner, it is expected that proper representation of the stress distribution, pertinent to crack initiation and growth, can be accurately described.
An example of this approach is presented in Figure 20 below. In this example, the stress at the ID and the OD locations were selected from a typical set of nodal stress data. The graphs immediately below show the individual stress distribution and the result from the third-order polynomial fit. In the first set, the entire data set from the bottom of the nozzle to the top of the J-weld was used. The regression curve shows that the general trend is captured; however, the fit in localized regions are not accurate representation of the original data. Significant variation that might cause errors in the determination of the SIF could occur, which in turn could lead to an inaccurate estimate in crack growth.
The two lower plots follow the scheme utilized in the current analysis. In this process the nodal stress data from the bottom of the nozzle to an elevation just above the bottom of the J-weld is selected. In this manner the stress distribution in the region of interest is chosen for the regressed curve fitting.
This is necessary since the stresses in the weld region show significant variation (top plot) and cannot be adequately represented by a third-order polynomial. Limiting the stress distribution data to the region of interest would limit the variation and results in a more accurate fit. The plots in the lowest row, in Figure 20, show the improvement in the accuracy of fitting. The regression fit does provide an accurate representation of the stress distribution of the region. Therefore, the stress distribution used in the fracture mechanics analysis would be a reasonably accurate representation of the actual stress distribution in the region where the initial crack and subsequent crack growth are of interest.
This example and the associated plots in Figure 20 show that the regression method, as developed for the current analyses, provides an adequate representation of the stress distribution.
The analysis worksheets (Appendix C) contain a cautionary statement such that inaccurate regression is avoided. The Mathcad worksheet used to develop this example is presented in Appendix D, Attachment 1. However, it should be
Engineering Report M-EP-2004-001 Rev. 00 Page 34 of 54 noted that this attachment is not annotated but does follow the method used in the analysis worksheets.
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dii Strtss I)aLIt SO 6(4)
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- 1) i WRci resson I sin2 AiI data
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Nodal Data
< )1 - S lected Data SNt 111)
-7 G-I ()1 l
(
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1 1
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l ctjiIOll ITa h)io Iolrro-il
'i dl,
- 11) IRcurcssio1 uISItmn SclCcled llta
- 11) Sclcteod Nodal Data
}
l 2
4ic atiori 1--il I1 (t-, ni ai-lil
( )I ) R resslhI
'm
-c sc Icctd datta Sac
( A1) Sclictcd I Iata Sct Figure 20: Plots showing effect of nodal data selection on the accuracy of polynomial regression fit.
The first plot represents all nodal stress data from the nozzle bottom to the top of the J-weld.
The two plots, in the middle row, are the comparison of regression fit with nodal stress data; the full data set of nodal data for the ID and OD distribution was used.
The two plots, in the lower row, use a limited data set comprising the axial length to the bottom of the weld. The regression curve shows a significantly improved fit to the data.
Engineering Report M-EP-2004-001 Rev. 00 Page 35 of 54 Once the five polynomial equations for the axial distribution are established, the through-wall stress distribution for the three locations defined by the crack and the twenty segments are established. The distributions at the twenty-three locations are subjected to a third order polynomial regression to obtain the coefficients describing the through-wall distributions. These coefficients are used within the recursive loop to assign the coefficients based on the current crack location. The five axial distributions are used for the surface cracks (ID and OD) whereas only two are required for the through-wall crack (ID and OD distributions).
Iterative Analysis to Determine SICF For the surface cracks (ID and OD) the SICF coefficients were incorporated in two data tables. The first table contains the geometry data (Rm/t, a/c and alt) and the second table consists of the SICF data for the appropriate cylinder and crack geometry. The values for the data were obtained from Reference 5. The data contained in the two tables were regressed into function statements with an appropriate polynomial order. The data for cylinder geometries from Rm/t ranging from one (1) to four (4) were regressed with a third-order polynomial, and for those above four, a second-order polynomial was used. The selection of the polynomial order was based on matching the value in the table given, for a selected set of independent variables, with that obtained from the interpolation performed using the regressed coefficients. In this manner the accuracy of the regression-interpolation method was established. The interpolation equation was defined outside the recursive loop and function call was made inside the loop using the pertinent variables at the time of the call.
The through-wall crack SICF was obtained using the fifth-order polynomial equation presented earlier. These equations were provided inside of the recursive loop.
The recursive loop starts the calculation scheme to determine the crack growth for a specified time period under the prevailing conditions of applied stress. The first few statements are the initialization parameters. The calculation algorithm begins with the assignment of the through-wall stress coefficients based on the current crack location. Once the four coefficients (uniform, linear, quadratic and cubic) are assigned, the through-wall stress distribution is used as the basis to establish the stress distribution along the crack face in the crack depth direction. That is, the stresses through the thickness are used to determine the stress along the crack face for application in the determination of the SIF in accordance with Reference 5. Once again, five locations along the crack depth were used to define the crack face distribution. The stresses representing the crack face values were regressed with a third-order polynomial to obtain the stress coefficients that would be used in the determination. At this point, the internal pressure is added to the stress coefficient (SICF) for the uniform term. Therefore, the crack face is subjected to an additional stress representing the internal pressure.
Engineering Report M-EP-2004-001 Rev. 00 Page 36 of 54 Following the determination of the stress coefficients, the function call to obtain the four SICF coefficients is made. In this case the two function calls were necessary to account for the "a-tip" and the "c-tip". The crack shape factor ("Q") was then computed using the appropriate crack dimensions. The SIF is calculated separately for the "a-tip" and the "c-tip" using the stress coefficients, appropriate SICFs and crack dimensions.
In the through-wall crack solution; the fifth-order polynomial equations were solved using the current crack dimensions. The SIFs were computed for both the ID and OD locations and were then averaged. This averaged SIF was used for crack growth calculation. The crack growth calculation and the remainder of the program for both the surface cracks (ID and OD) and through-wall crack are identical.
The calculated SlFs were converted to metric unit for the computation of crack growth. The crack growth rate, based on the prevailing SIF was computed in metric units. Once this was done, a conditional branch statement was used to calculate the crack growth within the prescribed time increment. The crack growth was computed in English units by converting the calculated crack growth rate in meters-per-second to inches-per-hour. Thus, the crack growth extent was obtained in inches for the specified time period. Since the operating time was selected to be two years and the number of iterations chosen at one thousand five hundred (1500), the time increment for each crack growth block was about twelve (12) hours. After the calculations were performed, all necessary information (crack growth, SlFs etc.) was assigned to an output variable such that it is stored in an array. The last step of the recursive loop consisted of updating the essential parameters (namely, the index, crack length, time increment etc.).
Graphical displays of the results using both Mathcad and Axum plots complete the work sheet. The Mathcad plots are used to determine whether or not the crack reached the bottom of the weld in one operating fuel cycle and the Axum plots were generated for incorporation into this report.
The three attachments in Appendix B are sufficiently annotated to provide summary details for each major step in the program.
5.0 Discussion and Results Discussion The goal of the inspection program designed for the reactor vessel head penetrations is to ensure that the postulated crack in the vicinity of the blind zone does not reach the weld during the upcoming operating cycle following the refueling outage when the inspections are performed. Safety analyses performed by the MRP have demonstrated that axial cracks in the nozzle tube material do not pose a challenge to the structural integrity of the nozzle. Axial cracks, if allowed to exist undetected for sufficient periods of time can produce a primary boundary leak that can cause
Engineering Report M-EP-2004-001 Rev. 00 Page 37 of 54 damage to the reactor vessel head (carbon steel) and create a conducive environment for initiating and propagating OD circumferential cracks. These conditions challenge the pressure boundary; hence, critical importance is paid to proper periodic inspection and to the disposition of cracks that may be discovered. Therefore, proper analyses are essential to ascertain the nature of axial crack growth such that appropriate determination can be accomplished.
The analyses performed in this report were designed to capture the behavior of postulated cracks that might exist in the blind zone of the CRDM nozzle. The growth region for the postulated cracks (available propagation length) was to the bottom of the weld along the tube OD.
The design review of the RVH construction, the detailed residual stress analyses, the selection of representative nozzle locations, selection of representative fracture mechanics models, and the application of a suitable crack growth law have provided the bases for arriving at a comprehensive and prudent decision.
The axial crack geometry is selected for evaluation because this crack has the potential for propagation into the pressure boundary weld (the J-groove weld).
Because circumferentially oriented cracks will not propagate towards the pressure boundary weld, this crack type is not evaluated. The hoop stress distribution at the downhill location (00), at the mid-plane location (900 rotated from the downhill), and at the uphill (1800) location were chosen for evaluation. The axial distribution of the hoop stress magnitude for both the ID and OD surfaces shows that at an axial location below the evaluated elevation, the stresses drop off significantly and become compressive except for the specific group of nozzles identified earlier. In nozzles where a compression zone exists or where localized low tensile stress exists at the nozzle bottom, the potential for PWSCC crack growth would be significantly low to non-existent in these locations. For the isolated location (38.50 nozzle at mid-plane) where the tensile stress on the ID surface was 10.954 ksi, an additional fracture mechanics analysis was performed. The analysis and the results are presented in the following section.
The fracture mechanics evaluation considered the crack face to be subjected to the operating reactor coolant system (RCS) pressure. This is accomplished by arithmetically adding the RCS pressure to the uniform stress coefficient in the surface crack analysis and to the membrane stress for the through-wall crack analysis. In this manner, the stress imposed on the crack is accurately and conservatively modeled.
In order to ensure that the moving average technique did not create numerical errors, a Mathcad worksheet was created by using the stress averaging portion of the regular analysis worksheet. In this worksheet, the data table, which is used to import data from an Excel spreadsheet, was entirely populated with a linear through-wall stress distribution. The axial distribution of the stresses along the axis was kept constant. In this manner, the moving average method should provide results that have the same distribution at all locations along the tube axis. This implies the through-wall distribution is invariant along the length of the tube. The example and
Engineering Report M-EP-2004-001 Rev. 00 Page 38 of 54 the associated worksheets are provided in Appendix D, Attachment 2. The results of the experiment show that the stress distribution across the wall remained unchanged along the axis of the tube. Therefore the moving stress averaging method is validated.
The through-wall axial crack could have been considered as a single edge crack in a plate [10]. For this model to work properly, it is essential that the plate geometry be described accurately. The CRDM nozzle is welded to the head; hence the nozzle OD surface is clamped at the bottom of the weld. Therefore, the plate height would be equal to the length of the nozzle from the bottom of the nozzle to the bottom of the J-weld. When this plate height is assumed and the length of the through-wall axial crack is taken to be the length (height) of the blind zone, then the ratio of crack length to the plate height (assumed) may violate the pre-requisite for the SICF of 0.6. It is possible to assume the plate height to be equal to the nozzle height or some lower elevation (e.g. length equal to top of the J-weld). These assumptions tend to keep the crack-to-plate height ratio within the limit; however, the resulting SICF is lower than the membrane SICF from the model used in this analysis. A Mathcad worksheet showing the comparison is presented in Appendix D, Attachment 3. The results presented in this attachment demonstrate that the SICF for the model used in the current analysis is higher than the SICF produced by an edge crack model with longer plate lengths. In addition, the bottom zone of the CRDM nozzle is in compression, as shown in Figures 8-16, which further argues against postulating an edge crack for evaluating a through-wall crack. Therefore, for the two reasons cited herein the model developed for through-wall crack is considered valid and provides an accurate (but conservative) estimate of the SIF. The SICF comparison is presented in Figure 21 below.
Engineering Report M-EP-2004-001 Rev. 00 Page 39 of 54 Comparison of Magnification Factors 20 I
a F bsl
~1 Q F bs2,
-L A M, C
J 2 A C
0 Ai
-,_==
I _ -
503592 0.12 0.24 0.36 0.48 0.6 0.72 0.84 0.96
,31592 xl 0 aj Flaw length finch)
Edge Crack Panel Height upto Bottom of fillet weld Edge Crack Panel Height upto Top of J-weld Edge Crack Panel Height equal Full Nozzle Length )20 inches)
Entergy Model Membrane 1.08 1.2 1.32 1.43 1.55 1.67 1 79 1.792, Figure 21: Comparison of SICF for the edge crack configurations with the membrane SICF for current model. The current model results in a higher SICF value for the application considered.
The models used in the analysis presented here were compared with the conventional approach used by the industry. The OD surface crack evaluated shows that the model used provides similar SIF and, but, has the capability of separately evaluating the SIF at the two crack locations (the "a-tip" and the "c-tip"). The SIF comparison for a sample case from Appendix D, Attachment 4 is shown in Figure 22.
Engineering Report M-EP-2004-001 Rev. 00 Page 40 of 54 22 -
20 -
Ir___
Currentmodel(Entergy)
I ConventionalModel(industry) I m
.S
.i 18 -
16 -
14 -
12 1
t i
0.0 0.5 1.0 1.5 2.0 Operating Time (years)
Figure 22: Comparison of SIF for the current model and conventional model.
The conventional approach for the through-wall axial crack is the Center Cracked Panel (CCP) with an SICF of one (SICF = 1.0). This conventional model is compared to the current model used within this analysis. The Mathcad worksheet for this comparison is presented in Appendix D, Attachment 5. The results presented in this attachment clearly demonstrate that the SIF obtained by the current model is significantly higher than that from the conventional approach. Therefore, the estimated crack growth would be higher for the current model than that estimated using the conventional approach. This would lead to an underestimate of the crack growth, by the conventional model, leading to a non-conservative propagation length estimate. Figure 23 shows a comparison between the conventional and current models.
45 -
40 -
VP 35 -
At 3 0-(a 2 5-230 15 -
Current Model (Entergy)
Convention a /I Model (Indus try) 0.0 0.5 1.0 O perating Tim e (years}
1.5 2.0 Figure 23: SIF comparison between current model and conventional model.
Cab
Engineering Report M-EP-2004-001 Rev. 00 Page 41 of 54 A comparison of the fracture mechanics models for the current analyses and the conventional method are summarized in Table 11. The comparison shows that the models used in the current analyses would provide a higher estimate for the SIF.
The net result would be a higher crack growth rate and hence a larger crack propagation length for one (1) cycle of operation. These improvements in analysis methods are believed to more accurately predict crack behavior in the CRDM configuration and may be conservative compared to the conventional approach.
Table 12 Comparison of Fracture Mechanics Models Flaw Type Feature Conventional Approach Entergy Approach Surface Flaws Stress Distribution Fixed a Initial flaw Variable Distribution along Length (ID & OD)
Location of Tube & Flaw face Pressurized Part Throughwall Cylinder Fixed 'R/t' ratio of 4.0 Variable "R/ts ratio from 1 to 300 PartThrughall Geometry Flaw Geometry Fixed Aspect Ratio; "a/c' = 0.33 Variable Aspect Ratio; 'a/c" from 0.2 to 1.0 Flaw Growth Only Growth in Depth direction Growth both in the Depth and Evaluated Length directions evaluated Independently Throughwall Stress Uniform Tension @ Initial flaw Variable along Length; Both Axial Flaws Location Membrane and Bending components considered; Flaw face Pressurized Model Center Cracked Panel without Thick Cylinder with correction for Correction Factors Flaw/Tube geometry Results Analysis for the As-Built Condition The first set of analyses was performed using the as-built dimensions for the welds which were estimated from the review of the UT data from the inspection performed during the previous refueling outage. These analyses were performed at three azimuthal locations on the nozzle (downhill, mid-plane, and uphill). At each location, three crack geometries (ID surface, OD surface and through-wall) were evaluated. The extent of the compression zone in each nozzle group at the three locations was obtained from the stress distributions presented in Figures 8-17. From these figures, the compression zone at the three azimuthal locations is presented in Table 13, below. In these regions of compression, no PWSCC-assisted crack growth is possible; therefore, these zones can be excluded from consideration for inspection.
For those nozzle groups with tensile stress below 10 ksi the possibility for PWSCC crack initiation is extremely low. The region showing a high hoop tensile stress, (38.50 nozzle at mid-plane), was selected for additional fracture mechanics analysis.
Engineering Report M-EP-2004-001 Rev. 00 Page 42 of 54 Table 13: Results for Compression Zone Nozzle Group Azimuthal Location Height of Compression Zone (inch)Comment Head Angle (Measured from Nozzle (Degrees)
Bottom) 0 All (360O) 0.48 Downhill 0.4 18.2 Uphill 0.8 Mid-Plane 0.72 Downhill 0.357 26.2 Uphill 0.953 Mid-Plane 0.856 Downhill 0.5 38.5 Uphill 1.0 Mid-Plane 0
ID Tension {10.954 ksi}
All nozzles, with the exception of nozzle number 26 and the eight (8) previously repaired nozzles, at the three principal locations (downhill, uphill and mid-plane) showed a measurable freespan length to exist. For nozzle 26, since no UT measurements were provided, this nozzle was not considered in the evaluation presented herein. For the nozzles that had sufficient freespan length the three crack configurations; ID and OD surface and through-wall axial cracks were evaluated.
Thirty (30) analyses cases were performed. The worksheets representing these evaluations are presented in Appendix C, Attachments 1 - 30. The results from this set of analyses are summarized in Table 14. Table 14 provides the "Propagation Dimension" which represents the available freespan for the limiting nozzle within the specific nozzle group. For the surface crack type, the length dimension excludes the 0.175 inch that was assumed for the portion of the crack that extends into the freespan.
Table 14 also provides "Growth/Cycle" dimensions. This is the calculated crack growth for one cycle of operation and is used to evaluate the available propagation dimension of each individual nozzle (as determined from the UT data). This is done by comparing the available nozzle propagation dimension to the "Growth/Cycle" dimension. Where the available propagation dimension is larger, adequate margin for flaw growth is available without compromising the weld. When comparing the ID and the OD surface crack, 0.175 inch is subtracted from the available propagation dimension to account for the portion of the assumed crack that extends into the freespan.
Where the analysis results indicate that the surface and the through-wall axial crack configurations are not susceptible to crack growth by PWSCC (zero
Engineering Report M-EP-2004-001 Rev. 00 Page 43 of 54 growth). The analyses show that the prevailing stresses at the crack location produce a SIF that is below the threshold value. Hence, the potential for crack growth due to PWSCC does not exist.
None of the postulated ID part through-wall cracks came close to reaching the bottom of the weld or penetrating through the wall to meet the weld in one cycle of operation. Only in three of the cases evaluated (18.20 nozzle at the downhill and uphill location, and 26.20 nozzle at the downhill location) did the analysis indicate potential for PWSCC crack growth. In all three cases the estimated growth for one cycle of operation was well within the acceptable limits. Hence, there is no evidence to support that an ID initiated part through-wall crack would provide a leak path or reach the weld within one operating cycle.
In all thirty (30) cases evaluated for cracks postulated at the blind zone, the results demonstrate that a postulated flaw in the blind zone region will not challenge the weld in one cycle of operation. The analysis further demonstrates that a larger margin exists (longer than one fuel cycle) at all the plausible locations evaluated.
One nozzle location (38.50 nozzle at mid-plane) showed tensile stress of 10.954 ksi to exist on the ID surface at the nozzle bottom (Figure 17 and Table 11). The nozzle at this location was analyzed to ascertain the behavior of a postulated crack in this region. The analysis performed and the results obtained are discussed in the following subsection (Additional Analysis) for the 38.50 nozzle.
Engineering Report M-EP-2004-001 Rev. 00 Page 44 of 54 Table 14: ANO-1 Estimated As-Built Analyses Results Summary Fracture Mechanics Results Propagation Growth I Cycle Attachment Nozzle Angle Azimuth Crack Type Dmnin(inch)
I (Recto Location (L= length; In (Reactor Apni Vessel Head)
D= depth)
Appendix C (inch)
All ID 0.865U0.617D 0 U1 D*
I 0 Degree OD 0.865 0
2 1W 1.044 0
3 ID 0.255U0.617D 0.065J.111D0 4
Downhill OD 0.255 0.062 5
TW 0.430 0.313 6
18.2 Degree ID 1.275U0.617D 0.032 L0/.088 D^
7 Uphill OD 1.275 0
8 TW 1.45 0
9 ID 0.96U0.617D 0L0D*
10 Mid-Plane OD 0.96 0
11 TW 1.135 0
12 ID 0.405U0.617D
.041 U.092 D ^
13 Downhill OD 0.405 0
14 1W 0.58 0.047 15 ID 2.665510.617D OUOD
- 16 26.2 Degree Uphill OD 2.665 0
17 1W 2.84 0
18 ID 1.645U0.617D 0100D
- 19 Mid-Plane OD 1.645 0
20 1W 1.82 0
21 ID 0.265LJ0.617D 0 100D 22 Downhill OD 0.265 0.010 23 TW 0.44 0
24 38.5 Degree ID 2.9057LJ0.617D 0100 D' 25 Uphill OD 2.905 0
26 TW 3.08 0
27 ID 1.805L10.617D 0 110 D '
28 Mid-Plane OD 1.805 0
29 TW 1.98 0
30 For Surface Crack on the ID surface the dimensions for both in Length (L) and Depth (D) are provided. The limiting condition is reached when both the postulated flaw becomes through-wall crack and the upper tip reaches the bottom of the weld.
Engineering Report M-EP-2004-001 Rev. 00 Page 45 of 54 The graphical presentation of results for those nozzle groups which showed some PWSCC crack propagation are discussed below, by nozzle group. In the graphs, a vertical blue line represents one fuel cycle and a horizontal red line represents available propagation dimension. When the curve is below the intersection point of these two lines, the analysis indicates that the postulated crack will not reach the weld in one operating cycle.
18.20 Nozzle Group Downhill In this nozzle the ID and the OD surface crack showed potential for PWSCC assisted crack growth. The crack growth and the corresponding SIF are presented in Figures 24 and 25. The plots show that the crack growth is very small and significantly lower than the limiting condition that would compromise the weld. The graph for the through-wall crack, Figure 26, shows that a through-wall crack postulated at the blind zone demonstrates crack growth that is within the allowable freespan length.
I 00 0 6-
'04 i-02 00 S
(9 04-0.3-0 2-0.1 00 I
00 0O5 1.0 1.5 2.0 OperatmngTi-e (yers)
{Length Direction) 00 05 1 0 Operating Te (y-ears) 15 2.0
{Depth Direction)
Figure 24: ID surface crack for nozzle group
- 18. 2° at downhill location. Crack growth in both the depth and length are shown. In both cases the crack growth is well below the intersection of the red and blue lines indicating sufficient margin. The SIF plot shows the SI at both the depth (a-tip) and surface (c-tip) points. The surface point SIF (red) is higher than the depth point SIF (blue) indicating that the crack growth would be more pronounced along the surface.
22 -
V 21 -
I 1 20 -
Xi 1Y -
j 18 -
I 17I 16
-=
S:F DePIPoint
_, ~f-Pn 0.0 0.5 1.0 Op ra.ng Timo.. yan-)
1.5 2.0 (SIF)
Engineering Report M-EP-2004-001 Rev. 00 Page 46 of 54 0.25 -
I 020-r'i 015 -
0IC1 F0 05 -
COO0 25 -
UrB X 20 010 I ~e__oii.11c-trpi:
0.0 0.5 1.0 Op-Mtig Time (years) 1.5 2.0 00 05 1.0 OprrOgTrre (year) 15 20 (SIF)
{Length Direction)
Figure 25: OD surface crack for nozzle group 18.20 at downhill location. Crack growth in the length is shown. The crack growth is well below the intersection of the red and blue lines indicating sufficient margin. The SIF plot shows the Si at both the depth (a-tip) and surface (c-tip) points. The surface point SIF (red) is lower than the depth point SIF (blue) indicating that the crack growth would be more pronounced in the depth direction.
110-
90-F 50 30 ID Sf.0ce SIF I Aveage SIF 0C0 5
1,0 1.5 20 Opor.0ng T-se (yebn) 0.0 0.5 1.0 1.5 2.0 Op~r.hng Ti.. (Ye-r.
{Crack Growth)
{SIF}
Figure 26: Through-wall crack for nozzle group 18.20 at downhill location. Crack growth is shown to be less than the freespan length.
18.20 Nozzle Group at Uphill In this nozzle, the ID surface crack showed potential for PWSCC assisted crack growth. The crack growth and the corresponding SIF are presented in Figures 27.
The plots show that the crack growth is very small and does not reach the bottom of the J-groove weld.
Engineering Report M-EP-2004-001 Rev. 00 Page 47 of 54 02 -
00I 5
r 0S 0 0 r__________________I I
0 0s I.
I, 0
s 0,.-an Time {y.....)
20~
0 0 05 s I
Op... Mg Tim (y...)
S 20.
(Depth Direction)
Figure 27: ID surface crack for nozzle group 18.20 at uphill location. Crack growth in both the depth and length are shown. In both cases the crack growth is well below the intersection of the red and blue lines indicating sufficient margin. The SIF plot shows the SI at both the depth (a-tip) and surface (c-tip) points. The surface point SIF (red) is higher than the depth point SIF (blue) indicating that the crack growth would be more pronounced along the surface.
(Length Direction)
Is -
t1 0 12 I =-
SI De
'II Point l
I I 0.0 a's I.O 0p,-atin Time{. as
,.5 2.0
{SIF) 26.20 Nozzle Group Downhill The results for this nozzle group showed potential for PWSCC crack growth for the ID surface crack and the through-wall crack. The graphical results for these cases are presented in Figures 28 and 29 respectively, which show that the crack growth to be within the acceptable limits. The crack growth was extremely small and the postulated cracks did not reach the bottom of the J-groove weld. Hence, the primary pressure boundary would not be affected.
Engineering Report M-EP-2004-001 Rev. 00 Page 48 of 54 0~0^
00 0.5 1.0 15 2.0 O nrasion Time bOyns)
(Length Direction}
00
- p.
.0 Op.-r.gmTime (y...)
1AS 2.0 (Depth Direction)
Figure 28: ID surface crack for nozzle group
- 26. 2° at downhill location. Crack growth in both the depth and length are shown. In both cases the crack growth is well below the intersection of the red and blue lines indicating sufficient margin.
The SIF plot shows the SI at both the depth (a-tip) and surface (c-tip) points. The surface point SIF (red) is higher than the depth point SIF (blue) indicating that the crack growth would be more pronounced along the surface
,..1 II' 1,-
ids Lo l
SsF D.plh port l
l _
S1F Surface Point l By 1
0 A:
0 a.
I 10IIo opeSIOQ Ton Wreas}
"I52.
(SIF) 05 05 W04
,T ° 3 a 0 2 O.1 00 25 2t x06 10 I
t I
30 0
1 1 0 Op.-!.in Time(eas 1.5 2.
G0 0.5
- 1.
1.S p0-50g T01 (e.
2.0
{Crack Growth)
(SIF)
Figure 29: Through-wall crack for nozzle group 26.2° at downhill location. Crack growth is shown to be less than the freespan length.
38.50 Nozzle Group Downhill Only the OD surface crack showed the potential for PWSCC crack growth.
However, the crack growth was very small and is shown in Figure 30. The postulated crack does not grow to the bottom of the J-groove weld.
A
Engineering Report M-EP-2004-001 Rev. 00 2.E iI YI 0.30 025 020-0 15 0 10 0005-0 00 00 05 1.0 1.5 Operating Time (year)
(Length Direction)
Figure 30: OD surface crack for nozzle group 38.50 a significantly less than the freespan length. The SIF fo value and that for the depth point is lower.
Additional Analysis In nozzle group 38.50 at the mid-planE stress at the nozzle bottom was 10.954 ksi.
immediately above the nozzle bottom up to t presents the stress distribution in this region OD surface. These distributions were obtair presented in Attachment 6 of Appendix D. T stress on the ID surface is rapidly decaying I mid-wall and OD surface show compressive Therefore it is unlikely that a through-wall ed prevailing stress distribution. However, the necessitates a fracture mechanics analysis t addition to the ID surface crack evaluation.
evaluated for this location (ID surface crack analysis results for these cases are presentE C, a graphical display of the results are pres pages.
Page 49 of 54
-D~ptt Point ('..'-tip)
Surf_.P.i.t tipj 0.1
- 0.
1.1 I.6 Op..ting Time (ye-a.)
{SIF}
it downhill location. Crack growth is shown to be
,r the surface point is higher than the threshold location, it was determined that the ID The stress distribution in the region he weld bottom was reviewed. Figure 31 for the ID surface, the mid-wall, and the ied from the regression analyses
'he stress distribution shows that the hoop
- o zero and that the distributions at the stresses in the immediate vicinity.
ge crack can be supported by the
,lose proximity of the nozzle bottom ising an edge crack formulation in Therefore, two crack configurations were and a through-wall edge crack). The
%d in Attachments 31 and 32 of Appendix ented and discussed in the following A.
Engineering Report M-EP-2004-001 Rev. 00 Page 50 of 54 ID Distribution 15 Mid-Wall Distribution 15 1010 5 \\\\O-10 00 l
Nodal DR j-512 0
1 2
3 0
1 2
3 A.Wo Dit.-0 fron. Nodolo Botloo j-h) ftioo Di.tanoe fron Nozzle BSoto nom
.h)o Figure 31: Nozzle group 38.50 at mid-plane location. Hoop stress distribution near nozzle OD Distrbution bottom at the ID surface, mid-wall, and OD 50 surface. The vertical red line is set at 0.50 inch from the nozzle bottom. Though the ID surface at the nozzle bottom has a tensile stress of 10.954 ksi, the stress decays rapidly to zero within a short A
distance. Whereas the stresses at the mid-wall 10-and OD surface are compressive in this region.
.10 D.1a 0
1 2
3 Di0nce Son Nozzl. ofto (oth)
The ID surface crack was postulated close to the nozzle bottom. The crack, with similar dimensions to those considered here, was located close (crack center 0.5 inch above nozzle bottom) to the nozzle bottom. The fracture mechanics evaluation (Mathcad worksheet) is presented in Attachment 31 of Appendix C. The graphical results from this analysis are presented in Figure 32. These results show that the postulated crack will not grow by PWSCC. Since the location of the postulated crack was so close to the free end of the nozzle and the fracture mechanics models were for cracks removed from the edge, an edge crack model was evaluated to ensure that the results from the ID surface analysis could be supported. The edge crack model was the same model used in the comparison study presented in Attachment 3 of Appendix D. The Mathcad formulation and the analysis are presented in Attachment 32 of Appendix C. The results from this analysis are presented in Figure 33. The initial flaw length was 0.5 inch (based on the stress distribution) and the plate height was set at 3.13 inches (bottom of weld), which was the distance from the bottom of the tube to the bottom of the J-groove weld. In this configuration the limiting flaw size, to maintain the validity of SICF (i.e. Crack Length/Plate Height < 0.6), was 1.878 inches. The results show that the postulated crack does not reach the weld in two (2) years of operation. Though the stress distribution does not favor a through-wall edge crack configuration, this crack configuration would provide the limiting case if the limit of the
Engineering Report M-EP-2004-001 Rev. 00 Page 51 of 54 crack length to plate height ratio remained below 0.6. In the analysis presented in 2 of Appendix C it is shown that there was no propensity for PWSCC crack growth.
The results presented in Figures 33 and 34 clearly demonstrate the placing a crack near the nozzle bottom, which had shown an ID surface tensile stress of 10.954 ksi, does not cause crack growth by a PWSCC mechanism. The SIF for the postulated flaw at this location, subject to the prevailing stress distribution, is below the threshold value for PWSCC crack growth. Therefore not inspecting this region will not (negatively) impact the level of quality or safety.
Oepth Grobkh Lo*
Gmvvth c
I0.0 0) 0.04-o 0.3 Eots T 4.1-e 04 0.02 0.0 0.5 1.0 OperahngT.W fye 1.5 2.0 Figure 32: Nozzle group 38. 5' at mid-plane location ID surface crack. The crack dimensions are similar to that used for the as-built analysis at the blind zone location. The crack was placed close to the nozzle bottom. The fracture mechanics results demonstrate that this ID surface crack will not grow by a PWSCC mechanism.
00 05 1.0 1.5 20 Cpffmm Thne teat1 23 21-19:
1.7 I.5 00 05 1.0 4haftTkr 6-1.5 20 (SIF}
C!
1'2-5
......-11,11,111,
Engineering Report M-EP-2004-001 Rev. 00 Page 52 of 54 0.5 9
0.3 C
7 0.1
'I
-0.33
-0.51 0.3 09 1.3 1.8 0.3 0.8 1.3 1.8 Opw9*lgLnews O
Cpeong T-6ne )a
{Crack Growth)
(SIF)
Figure 33: Nozzle group 38.50 at mid-plane location with an edge crack. There is no potential for PWSCC crack growth. The SIF at the crack tip is well below the threshold value.
6.0 Conclusions The evaluation performed and presented in the preceding sections supports the following conclusions:
- 1) The detailed deterministic analyses incorporating the as-built dimensions for the weld and nozzle length were used to accurately define the inspection zones for the CRDM nozzle groups. Nozzle number 26 (26.20 nozzle group), which did not have proper UT data recorded, is not addressed by this engineering report.
- 2) The developed models, incorporating a method to account for applied stress distribution variation along the nozzle length, have been shown to be a reasonably realistic but conservative representation of the expected phenomenon. The models are generalized and have the potential to be used at other locations of the nozzles.
- 3) The fracture mechanics models were shown to be representative of the expected crack and nozzle configurations. A review of the current model results and that from the conventional approach showed that the current model produced higher SIF than the conventional model. Therefore, the current model provides a more accurate and conservative estimate of crack growth.
- 4) The analyses demonstrate that the UT inspection above the normal blind zone will provide an adequate assurance that the J-groove weld will not be compromised in one operating cycle.
Engineering Report M-EP-2004-001 Rev. 00 Page 53 of 54
- 5) The work plan presented herein, defined additional evaluations that would be needed for the determination of an augmented inspection region.
However, the deterministic fracture mechanics analyses demonstrated that augmented inspection was not required.
- 6) The additional analysis performed for one location in one nozzle group (38.50 nozzle at the mid-plane location) where the ID surface stress was tensile showed that the postulated cracks at this location will not compromise the weld, since the results of the analyses showed no potential for PWSCC induced crack growth.
- 7) The regions below the lowest inspection elevation, at other locations, experience lower stresses or have a compression zone. Hence, at elevations below the lowest inspection elevation, a significantly lower potential for crack growth by PWNSCC exists. Thus, at these lower locations PWSCC, crack growth is not expected.
- 8) The ID surface cracks either did not show any potential for crack growth, or the crack growth was well within acceptable limits. Hence, ID surface cracks in a region below the weld are not expected to compromise the weld.
- 9) The deterministic fracture mechanics analysis demonstrates that the proposed changes to the inspection requirements specified in the NRC Order will still provide an acceptable level of safety and quality commensurate with the NRC Order.
Engineering Report M-EP-2004-001 Rev. 00 Page 54 of 54 References
- 1) NRC Order; Issued by letter EA-03-009 addressed to "Holders of Licenses for Operating Pressurized Water Reactors"; dated February 11, 2003.
- 2) "Materials Reliability Program: Demonstration of Vendor Equipment Procedures for the Inspection of Control Rod Drive Mechanism Head Penetrations (MRP-89"; Electric Power Research Institute; Technical Report TR-1007831; September 2003.
- 3) a: "PWSCC of Alloy 600 Materials in PWR Primary System Penetrations";
EPRI TR-103696; Electric Power Research Institute, Palo Alto, CA; July 1994.
b: DEI E-Mail containing the Nodal Stress Data for ANO-1 CRDM Analysis; J.
Broussard (DEl) to J. S. Brihmadesam (Entergy); E-4142-00-2, Dated 11/24/2003.
c: "BWR Vessel and Internals Project - Evaluation of crack growth in BWR Stainless Steel RPV Internals (BWRVIP-14)"; EPRI TR-105873; Electric Power Research Institute, Palo Alto, CA; March 1996.
d: "BWR Vessel and Internals Project - Evaluation of crack growth in BWR Nickel Base Austenitic Alloys in RPV Internals (BWRVIP-59)"; EPRI TR-108710; Electric Power Research Institute, Palo Alto, CA; December 1998.
- 4) "Stress Intensity Factor Influence Coefficients for Internal and External Surface Cracks in Cylindrical Vessels"; I. S. Raju and J. C. Newman, Jr.; ASME PVP Volume 58 "Aspects of Fracture Mechanics in Pressure Vessels and Piping";
1982.
- 5) "Stress Intensity Factors for Part-Through Surface Cracks in Hollow Cylinders":
S. R. Mettu etal; NASA TM-111707; Prepared by Lockheed Engineering &
Science Services; Houston, Texas; July 1992.
- 6)
"New Stress Intensity factor and Crack Opening Area Solutions for Through Wall Cracks in Pipes and cylinders": Christine C. France, etal.; ASME PVP Volume 350 "Fatigue and Fracture"; 1997.
- 7) Axum 7; Data Analysis Products Division, Mathsoft Inc., Seattle, WA; February 1999.
- 8)
"Materials Reliability Program (MRP) Crack Growth Rates for Evaluating Primary Water Stress Corrosion cracking (PWSCC) of Thick Wall Alloy 600 Material": MRP-55 Revision 1; Electric Power Research Institute; May 2002.
- 9)
Mathcad - 11; Data Analysis Products Division; Mathsoft Inc.; Seattle WA; November 2002.
- 10) "Stress Intensity Factors Handbook Volume 1"; Y. Murakami, Editor-in-Chief; Pergamon Press; 1986; Section 1.3.
Engineering Report M-EP-2004-001 Rev. 00 Appendix A Appendix A This Appendix contains design information and UT analysis data.
This Appendix has tw o (2) Attachments.
Engineering Report M-EP-2004-001 Rev. 00 Appendix "A; Attachment 1 Page I of I Design Data Iunuy for ANO-1 CRDNI Ana1viis Nnoz.le Tube:
Nozzlc OD: 4.0 inchiei Nozzc ID: 2.765 inches Material Yicld STrenglh: Low 32.7 ksi; I ligh 48.5 ksi RPV IHead:
RPV I lead Inner Radius (to basc metal): 87.25 inchcs RP V llead Thickness (excluding clad): 6.625 inches Operating Cnnditions:
Opcrating Pressure: 2.235 psig Operatimg Temperature: 600 DF Notc - Since lhe operating prcssurc anrd temperature valucs are variable (reFerence C.ALC-8S-E-0100-30), the operating conditions specified %were selected to provide a nominal vaiuc Ifr normal operation that is appropriatc tor the alalasis.
Verification Arkansas Nluclear One, Design Enginceriua Jkpartmenit r
(Jamie N. Gobell)
(JDate)
Engineering Report M-EP-2004-001-00 ; Page I of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length ANO UNIT I Low Hill Side odCROM Hia Nil Side odCRDM Data Axial position:
- ]-Calculsed Oimerwoon:
Data Axial Position:
Csckull Oimension:
NozzleAzimuth Dead zonal Bdttom of fillet Top of JSweild 8dtom of fillet I Tp of J4M I AzimutI Dead zoMa Bottm of filtlITop of J-wld IBaotlm of flile Top of J-el I
I I
1.00 1 52 T
f1 4.0B0 I'
1.04 I
181.00 1AI 2.520 1
3.9 1 1.04 1
W0 M
E I
Engineering Report M-EP-2004-001-00 ; Page 2 of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length ANO UNIT 1 291 1 358.001 0.560 1 1.570 I
2Z850 1 01j10 1 2.290 1172.00 0.520 3780 5440 3.240 4920 36 0.00 0.10 1.490 l
850 O80 21040 18000 0810 3.810 5.530 3.000 4.720 37 11650 0.690 1530 Z90 l 0.40 12000 284.50 0,60 3810 5.410 13120 4.720 36 360.00 1.640 3.180 4.080 1 20 2Z440 21800 1720 5.400 7.200 3.6t 5480 40 1.50 0.730 1.610 3.050 OI0 1 320 181.50 0730 3.930 5.970 3.200 5.240 41 1.00 09061 2.02 3.438 11120 1
.532 17100 0906 4734 6482 3
3 0.00 0.730 170 Z810 1240 LOtO 180.00 0.650 4.290 5.850 3.640 5.200 44 10.00 0.30 1.060 1I90 0.760 z2eo 193.00 0.20 3.530 5.770 3.240 5.4tO 45 18250 0.330 1.210 Z490 O0880 2.180 250 0330 3.410 5.130 3.0t0 4100 46 168.001.530 1 1370 Z930 108 0 l
400 68.00 0.530 4530 6.650 4.000 6.120 47 0.00 0.650 J 1.10 r 2.770 017 OO120 180.00J 0.610 4.490 6.570 3580 5.960 48 10.00 0.330 1 1.730 2850 J 1400 Z520 218.501 0.330 4.610 1
6.450 4.2tO 6.120 3.00 010 11320 Z760 O
0J40 Z2t0 183.001 048O 4.400 6200 3.920 5.720 50 210.00 06114 1840 3.480 1.160 ZO00 24.001 0.680 5.040 j
7.080 4360 6.400 51 240.00 0.760 1.880 2 880 1120 120 66.00 O0.4 4.960 7.160 4.120 6.320 52 253.00 0790 2000 1 3.040 1,240 1 2t0 81.00 0.760 5.080 7.160 4.320 6.400 53 No dead zne visibbb, minium free span length Is 1.040" 54 0.00 i 0.10 i 1090 i
Z530 i
0.0 I
2g240 1180.00 020 1 4.610 6.490 1
4.320 6.200 55 66.0 0.650 1.410 2.410 0.760 1.6J0 1281.501 050 1 4.650 6.490 1
4.000 5140 56 Canlgurahon of repair area makes free span lent measurement rmietendsna for this peneration.
50 32 001 0.92l I 17760 3200 l
.40 l
280 1152.001 020 l 5280 I
7240 l
4.30 l
6A320
-ii 0000 0000 I1 0.000 0.000 59 354,00 0.690 1,730 1
3,370 1.040 2.68 117100j 0.690 j 5.050 1 7.130 4360 6.440 C-2 ~
Engineering Report M-EP-2004-001-00 ; Page 3 of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length ANO UNIT I 60 1 104.50 1 0.610 1 1530 1
2730 1
020 2.120 299.501 0.610 1 4.770 6
B770 I
.1bO I
6.160 61 0.00 1.50 2.570 3770 0920 2.120 17550 1650 5.90 8010 l 60360 2
1.50 0.660 1850 2810 0160 2.120 18150 0J0 4.970 7.090 t.210 6.00 63 359.00
.00 2040 3.320 100 2.30 18100 1
O 00 5.800 7.780 tUO o.leO 64 150 O.600 1730 3530 0
IN0 172.50 0130 4930 7.250 t.240 b.560 65 Do dead zone viaibl@, mninm free "mn leqHo is 0.1' b6 3.00 0440 1240 2840 I
Om O 2.200 177.00 040 4.800 7.180
.360 6.720 67 0.00 0.40 1.280 2720 OUO 128070
.440 4.720 8880 t.2tO 6A40 6
0.00 0.650 1 490 3090 01m 2.41 0
27.00 1.400
.220 8520 4J20 7.120 bi 95 50 OAOO 1240
- 2.
060 2.040 27850 0400 4.00 8680 4AO 61280 Notes 11 Data does not clearly show the 'dead zone' orbottom of fillet anphere bound the weld 21 "dead zone'not clearly defined around entre weld, position e-naed based on adacent data.
(3j Datadoesnolieaiyshowthedeadzone'anyrhen aroundte weld 41 "dead zone" and'bottom of fillef magesintersect, samn data loatbon recorded for both cumns tboon dofiltmay not be accurately ocatedl
( S ) Deta drop ov in area of interest CT
Engineering Report Al-EP-2004-001-00 ; Page 4 of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length Transmittal E-mail BRIHMADESAM, JAISHANKER S From:
SWAIN. RONALD VANCE Sent:
Friday. December 19. 2003 2:55 PM To:
BRIHMADESAM. JAISHANKER S: SIMS. WILLIAM D Cc:
LEWIS. RAYMOND S: JAMES. WILLIAM
Subject:
FW: ANO-1 CRDM Inspection Data -FANP Docu-nent 51-5038454-00 Here is the official documentation certifying the UT free span neasurements performed by Framatome. Bob Allen informed me that he plans to complete his verification of my free span measurements of the Westinghouse data by this evening. I will forward you an official e-mail slating this fact. when it is completed. Ilm on vacation alter today. but can be reached at 985-320-1583 if needed Ronnie
--- -Onginal FMessage-----
From: SON Steve [1]
Sent: Friday, December 19, 2003 2:52 PM To: SMITH, JAMES A; SWAIN, RONALD VANCE Cc: GRIGG David F; COLE Bob; RANSON Craig; LEWIS M rtt
Subject:
ANO-1 CRDM Inspection Data - FANP Document 51-5038454-00 Jim I Ronnie:
Attached please find the FANP document for the CRDM inspection data reviewed I provided with the Entergy spreadsheet.
Thanks Steve Son Project Manager Office. (434) 832-3767 Mobile (434) 841-3276 Email steve son@framatome-anp corn
Engineering Report NI-EP-2004-001-00 ; Page 5 of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length FTI Certification: Document 1 20440 0) (2'200~2)
A ENGINEERING INFORMATION RECORD FRAMATOME ANP Documet Iiepntifier 51 -
5038454 - 03 Tlile ANO Unit 1 CRDM Ddai Revieav PREPARED BY:
REVIEWED BY:
Name KC Grbetsberg.^r Name MCI ews Signatur Date Signature Teohnisal M3nager Stalenent. Initials 1254 Reviewer is Independent Remarks:
See attached page for details of the data supplied to Ertnrry Nuclear South I ANO Unit 1.
See also Excel sprcadsheet:
"ANO1 CRDM free span lengths R Swain B Flesner Rev.12-13-20031(51-5038454-OO).xIs'
Engineering Report MI-EI -200-001-00 ; Page 6 of 6 Appendix "A"; Attachment 2 NDE Data for Freespan Length FTI Certification: Document 2 A
FRAMATOME ANP I
To:
From:
Subject:
I Ronald V. Swain I NDE Lv. III Ertergye NucIal Scuth Kent C. Gebetsberger I Framatome ANP UT Level Ill ANO Unit 1 CRDM Data Review Customer Entergy Nuclear South Date:
December 19 2003 Dear Ronald.
Framatome ANP (FANP) per your request performed some additional CRDM data analysis checks on the UT data collected on Unit 1. This letter is to certify that only the following CRDM nozzle penetrations were reviewed, and that the technique utilized for this review was performed in accordance with standard FANP practices Obiective The objective of the UT data review was to deternire the amount of nozzle material that was actually inspected with the UT technique below the low-hill or downhill side of the J-groove weld. FANP personnel recalled the UT data from our copy of the data and performed physical measurements utilizing the Accusonex 'A' and "C' scan images The data supplied to you was designed to discount for the 'dead zone of the bottom portion of the nozzle penetration and supply you the amount of nozzle material from where good UT data began to both the low hill and high-hill portions of the J-groove weld.
These physical measurements were peifomned cn the following CRDM nozzle penetrations only; the information supplied was the 'Dead Zone". 'Bottom of fillet", and the 'Top of J-weld" dimensions on the Entergy supplied Excel spreadsheet.
All calculations associated with the Entergy supplied spreadsheet were produced by Entergy and were not reviewed for accuracy.
2 3
4 5
6 l
7 8
9 11 1
12
-13 14._
15 19 16 20 17 22 18 23 31 42 27 28 33 34 30 39 Bret Flesner FANP UT Level II Reviewer Initial ANO Reviewer Kent C. Gebetsberger FANP UT Level IlIl Reviewer
Engineering Report M-EP-2004-001 -00 Appendix B Appendix B Explanation of Mathcad i orkshect used in the deterministic Fracture Mechanics Analyses.
This Appendix has three (3) Attachments.
Engineering Report M-EP-2004-001-00 Appendix B; Attachment I Page I of 22 ID Surface Flaws Primary Water Stress Corrosion Crack Growth Analysis ID flaw-Developed by Central Engineering Programs, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: S. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"18.2" Degree Nozzle, "Downhill" Degree Azimuth, Calculation Basis: MRP 75 tih Percentile and Flaw Face Pressurized Mean Radius 4o-Thickness Ratio:- 'IL/r - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI URP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inchmhr.
ID Surface Flaw General information containing the Component Identification for analysis. Note the information for Nozzle group, Location, and Elevation at which the analysis is being performed. This information is not critical to the analyses; it is general information but it is important for cataloging the analyses files.
The fRrt Required mput is is the Fespan kngth obtained from the NAE data sheet (Excel spread sheet)
FSnde data.sheet := 0.43 To place the flow with Uepsect t the reference point, the flaw tips and center can be located as follows:
- 1) The Upper -C-tip" located at the refece point (Enter 1)
- 2) 7Th Center of the flaw at the,vfrivnce point (&nter 2)
- 3) 7Te lower 'C-tip located at the reerence point (Enter 3).
Val:= 2 The Input Below is the Upper Limit for the evclation, which is the bottom of the filet weld kg.
This is shomn on the Excel spread sheet as weld bottom. Enter this dimension (measurtd freon netk bottom) below.
1iLStrs.Dist := 1.712 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
RerPoint = L-Sirst.Dist - FSnde data sheet
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 2 of 22 Three critical information are required for the three on page one.
- 1) The first entry required {FSnde.data~sheet} is the "freespan length"; this entry defines the Freespan length obtained from the analysis of the NDE data. This entry is from the NDE data sheet
- 2) The second entry {Val} defines the location of the Crack. In the current analysis a value of two (2) is selected. This value locates the center of the flaw at the reference line described above.
- 3) The third required input is the upper limit, elevation above nozzle bottom, to be used for the stress distribution that will be used in the analyses. This location for the current analyses is chosen to be the bottom of the weld such that the appropriate stress profiles are incorporated into the analyses. This is obtained from the Stress analysis results data sheet (Excel Spread sheet).
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 1 Page 3 of 22 Input Data L :35 Initial Flaw Length a=
0.06787 Initial Flaw Depth od 4.00 Tube OD id:= 2.765 Tube ID Pint := 2.235 Design Operating Pressure (internal)
Years := 2 Number of Operating Years Jim = 1500 Iteration limit forCrackGrowth loop T := 600 Estimate of Operating Temperature aOc := 2.67 12 Constant in MRP PWSCC Model for 1-600 VWought p 617 deg. F Q
= 31.0 Thermal activation Energy for Crack Growth {MRP)
Tref := 617 Reference Temperature for normalizing Data deg. F
- 1) General Input data for tube and flaw geometry. In addition other parameters required for the analyses are defined. These inputs remain unchanged for this set of analyses.
- 2) The input for internal pressure Pint is used to add the internal pressure to the flaw face.
- 3) The operating time Years is set to two (2) such that proper analysis for one cycle of operation is obtained.
- 4) The iteration limit ILim is prescribed as a large number (1500) such that small time increments for crack growth are used in the crack growth analysis.
- 5) The remainder of the inputs are for crack growth model, which is based on MRP-55 at the seventy-fifth percentile.
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 1 Page 4 of 22 od Ro := 2 id Rid:7 t:= RO -Rid Rm:= Rid+ +
Timopr := Years 365-24 CFinhr := 1 417105 Timopr him Pmtbik 50 l L
co:
2 Rt Rt. -
F Q-F I__
X A
Co I Li 103-lo k
TT+45967 crf+459 67) a(
Temperature Correction for Coefficient Ala CO = CO]
75 th percentile MRP-55 Revision 1 General calculations to develop the constants needed for the analyses.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 5 of 22 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AVIII)atal :=_____
0
-32.98
-29 55
-27.62
-25.63
-23 66 0 46 4.42 1 43
-2.62
-5.98
-7 49 0 083 23.6 20 13 1747 13.58 8 56 113 39.38 3376 2859 2355 169 1 37 41.08 356 32.56 29.09 28 07 1 56 35.47 35 03 34.72 41.39 51 48 1 71 25.31 30,93 36.76 48.63 57 32 7
1 85 16B46 26 76 37.58 49.67 67 27 2 2 15.18 24 43 37.51 53.17 72,59 2 14 16,04 228 36 7 51,39 59 83 AXclie:= AlIlata)'
1DAs I := ; "[)ataih Strc-:,s D)iStlibUtiell
- )),1=
A11D)ata<
-SI)
-xrial Heixatioll ahom e tatolflinic I
- 11) D~iSt bL 6,t( 1
)I) IDistributioni Ret' Voilit =
282 1 ) the nodal stress data is imported from an Excel spread sheet provided by Dominion Engineering. The appropriate data set in the spread sheet is provided in the import command in Mathcad. It is important not to import the node number column.
- 2) The data imported is plotted for the ID and OD distribution along the length of the nozzle.
- 3) The plot presents all the nodal stress data imported. This plot is used to define the region of interest for analysis and to select the sub-set of stress distribution data pertinent to the analysis.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 6 of 22 Observing the stress distribution select the region in the table above labeled Data All that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight ihe entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
( 0
-32.98 -29.552 -27.619 -25.631 -23 659) 0.463 4 418 1 431 0.834 23.603 20.133 1.131 39.381 33.757 I)ata := 1 1.369 41.077 35.596
-2 622 17.472 28.588 32.564 34.721 36.756 37.578 37.506
-5.982 13.58 23.549 29.095 4 1.389 48 633 49 667 53.17
-7.485 8.558 16.901 28 069 51.476 57.324 67 274 72.592 )
1.56 35.472 35.035 1.712 25.309 31.93, 1.854 Is 476 26..75t
.1.9(6 15.182 24.435 Axl := D~ata<(o)
Nil) := I)ata(3)
I,) := I)ataO)
IQ := D~ata(4)
QT := IM);la2 01)):= D~ata(5)
Ry) := regrcs rAxI, I), 3)
ZQ Ir ::= rgres.
,eslAxI,Ql,3)
R(,) := regres.AAxI,01),3)
RtNll) := regres.S,(xI,.NlD,3)
R-rQ ::= regresAixl,TlQ,3) 1 ) Shows the incorporation of the selected data into a Data matrix that will be used in the analysis.
- 2) The definiton of the axial distribution at the five locations through the wall thickness are defined.
- 3) A third-order polynomial regression is performed at each of the five through-wall locations to define the curve used to develop the through-wall distributions.
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 1 Page 7 of 22 II1t l.',l.=
It lii o-. il, Val = I St i
i ; 1 \\!.11 = 2
,.c l-,,il + C(
i,.l I "I jp := I I..,,, + co Flaw center Location above Nozzle Bottom I ISir.lD)ist -
I lip It S
- 1) defines the upper tip of the flaw based on reference line and flaw location (Val) inputs provided in the first sheet.
- 2) Determination of segment length above the initial crack upper tip location.
Twenty (20) segments are used.
N :=2(1 Number of locations for stress profiles Lo.o
- = 1:1.(01,' -1.
i:= i..N +;
I Incri
=
C( i' i < 4 I,l1CSt1.1.1.%
L! other%% ise
.oci := I.oc-I + Incri
- 1) Setting of the iterative loop to develop the through-wall stress distribution.
- 2) Initialization of the loop to define axial elevation and segment length required to obtain the through-wall stress profiles at defined locations.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 8 of 22 SID := R1[) + R11) I
+/- + 1 [X1 ( l Loci) +/- 1(11) d LOCi)-
3D 1)I1 6
SQli RQ'
+ R
+RQ (L*ci)
+ RQ (Loc)
(33 SNII~i :=RM
+ ROA
[.oci + R MDr.( l-OCi} + RI (lci STQ:
RI7Q, + R-FQ l.j+
R§-r (loc)
+ Rl9I~-Q Li)
SODi := Raf + R [) Loci + R(D (Loc))
+ R01) (
i)
Determination of stresses at the five locations through the thickness and at defined elevations. This structure develops the matrix for the through-wall stress distributions for the defined locations that will be used in the moving average method for developing the stress profiles.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 9 of 22 j := I.. \\
Sj'Ij:=
=
rii S
-+
I)1~ + SII).J+2 is j = I 3
I.
=
S
-L I1 '-
sidl -I-'
lI)+SI)j4' j + 2 tit Iier"x it'se SQl
+ OI + + SQlj.+:
j 3
il'j=
I S4t
- (j+ II+SQIJ+2
-I Tthr i isc
+ 2
+ I' Q i
+ SI 2
J -2
+ 2l ie is S\\NI)j + S\\ID)jt + S\\II)i+2 Siq
=
"I SI,,,]
0 + I I +S%),+
j+ 2 of1lien ise SiI :=
501)D + SO)I).i+l + SU)I).,+'
i~
.1 isod
.(j + I) + so),i+'
.1i
+ 2 (1111cm i>.
Loop structure to perform the calculations for stress profiles at the defined locations along the nozzle height.
- 1) All five locations through the thickness are similar.
- 2) The first conditional statement defines the average stress at the initial flaw location, which is the average of the stress at the lower tip, the flaw center, and the upper tip. These stresses are used to calculate the applied stress for the initial flaw.
- 3) The second conditional statement performs the moving average at each segment location. Thus the moving average accounts for the changing stress field as the crack progresses towards the bottom of the weld. In the current analyses the stress field increases in magnitude as the crack progresses towards the weld bottom.
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 1 Page 10 of 22 u :=
m100 UO = 0o00)
U 1 := 0.25 U2 := 0-50 U3 := 0.75 Y := stack(uo u u2 u3, u4 )
SIG: stack(Sjd1, ISqt I Smd I s tq1 Sod,)
SIG3 stack(Sid, Sqty Smd' Stq3 Sod3)
SIG5 stack( Sid, Sqt5 Smd5'Stq5 'Sod5)
SIG7 stack( id7, Sqy Smd7, Stq7 'Sod7 )
SIG9 stack( sid Sqt, Smd Stq9 Sod9)
SIGII :=stack(Sid Sqt1,Smd1,,Stq, 1 Sod,,)
SIG 13 stack(Sid13 Sqt3,Smd,3' Stq13,Sod B)
SIG, 5 stack (Sid Sqty'5smd sStq,5.Sod,,)
SIG1 7 stack( Sid 7Sq1,7' Smdl 7 stq 1 7 Sod7)
SIG 19 := stack (Sid,9' sqt] 9 Smdg9 tq' Sod19)
S'G2 =stack Sid,,Sqty Smd sStq, -Sod, )
SJG 4 stack(Sid,, 'qtmd 4'tq 4 S)od4)
SIG 6 stack( Sid6 S5qt 6' Smd6, Stq6
'Sod6)
SIG8 stack(Sid8 S5 qysmd8 ' S tq8 I Sod8)
S1GI 0 stack( Sid' 5qt10'S md,0'S tqjO Sod,0)
SIG 1 2 stack(Sid12
,Sqt12.Smd12*Stq,2 Sod 2)
SIG 14 stack (Sid14'Sqtl4,Smd 4 Stq14 Sod 14)
SIG16 stack(Sid Sqt16 Smd '5tq16 Sod,6)
SIG 18 stack(Sid,, Sqtl *Smd, *Stq, 'S od,)
SIG 20 stack( SidO, qt2O' md20 Stq, Sod20)
Setting of a column matrix for the stresses at each segment for the five through-wall location.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page II of 22 IDRG2 := regress(YSIG2,3)
IDRGI := regress(YY,SIGI,3)
IDRCG3 =
IDRG5 :=
IDRG 7 :=
IDRG 9 :=
IDRGII IDRG1 3 IDRG 15 regress( Y, SIG 3, 3) regress(Y.SIG 5,3)
IDRG4 := regress(Y,SIG 4,3)
= regress(Y, SIG 7, 3)
= regress(Y,SIG9,3)
- = regress( Y, SIG I I 3)
- = regress( YSIG13,3)
- = regress(YSIG 15,3)
IDRG 6 := regress(Y,SIG 6,3)
IDRG 8 := regress( YSIG.3)
IDRG1 o := regress(YSIGIO.3)
IDRG12 := regress(Y.SIGI 2.3)
IDRG14 := regress(YSIG14.3)
IDRG 1 6 := regress(YSIG16.3)
IDRG 17 := regress( YsIG17,3)
IDRG19 := regress(Y,SIG 19,3)
IDRG 18 := regress(YSIG18,3)
IDRG 2 0 := regress(Y.S1G 2 0,3)
Third-order polynomial regression to determine the coefficients that describe the stress distribution through the wall at the defined locations.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 12 of 22 SICF Coefficient Determination
.Ish :=
0 1
_2 0
1.000 0.200 0.000 1
1.000 0.200 0.200 2
1.000 0.200 0.500 3
1.000 0.200 0.800 4
1.000 0.200 1.000 5
1.000 0.400 0.000 6
1.000 0.400 0.200 7
1.000 0.400 0.500 8
1.000 0.400 0.800 9
1.000 0.400 1.000 10 1.000 1.000 0.000 11 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 14 1.000 1.000 1.000 15 2.000 0.200 0.000 16 2.000 0.200 0.200 17 2.000 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 20 2.000 0.400 0.000 21 2.000 0.400 0.200 22 2.000 0.400 0.500 Partial data table for the SICF determination.
- 1) Column 0 is the Rm/t ratio.
- 2) Column 1 is the a/c ratio (crack aspect ratio)
- 3) Column 2 is the aft ratio (normalized crack depth)
This table in conjunction with the table in the following page together is used to determine the particular SICF
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 1 Page 13 of 22
.0 1
13 4
.5 6
7 0
1 076 0 693 0 531 0 434 0 608 0.083 0 023 0.009 1
1 056 0 647 0 495 0 408 0 615 0.085 0 027 0.013 2
1 395 0 767 0 557 0 446 0 871 0.171 0 069 0.038 3
2 53 1 174 0 772 0.58 1.554 0.363 0 155 0.085 4
3 846 1.615 0 995 0 716 2.277 0.544 0 233 0.127 5
1 051 0 669 0 536 0 444 0.74 0.112 0 035 0.015 6
1 011 0.646 0 504 0 421 0.745 0119 0 041 0.02 7
1 149 0.694 0 529 0 435 0.916 0181 0 073 0 04 8
1.6 0.889 0 642 0.51 1.334 0 307 0 132 0 073 9
2 087 1.093 0 761 0 589 1.752 0 421 0183 0 101 10 0 992 0.704 0 534 0 506 1.044 0 169 0 064 0 032 11 0 987 0.701 0 554 0 491 1.08 0 182 0 067 0 034 12 1 01 0.709 0 577 0 493 1.116 0 2 0 078 0 041 13 1 07 0.73 0 623 0 523 1.132 0 218 0 095 0 051 14 1 128 0.75 0 675 0 556 1.131 0.229 0 11 0.06 5
1049 0.673 0 519 0 427 0 6 0 078 0 021 0 008 16 1091 0.661 0 502 0 413 0.614 0083 0 025 0 012 Partial table of the influence coefficients (SICF) as described below:
- 1) Column 0 is the uniform coefficient for the a-tip.
- 2) Column 1 is the linear coefficient for the a-tip.
- 3) Column 2 is the quadratic coefficient for the a-tip.
- 4) Column 3 is the cubic coefficient for the a-tip.
- 5) Column 4 is the uniform coefficient for the c-tip.
- 6) Column 5 is the linear coefficient for the c-tip.
- 7) Column 6 is the quadratic coefficient for the c-tip.
- 8) Column 7 is the cubic coefficient for the c-tip.
Both tables, (labeled Jsb and sambi), have the same number of rows.
Engineering Report M-EP-2004-001-00 Appendix B; Attachment I Page 14 of 22 W :=Ish)
X JsbhI)
Y := Jsbh-)
aU Sambi(O) aL Sambi'l) aQ Sambi(2) ac = Sambi(3)
CU Sambi(4)
CL Sambi(5)
CQ Sambi(6)
CC := Sambi(7) n :=13 if Rt < 40 2 otherwise "a-Tip" Uniform Term Matl := augment(W, X, Y)
VaU au Ratj regress(MaIJ.VatlJn) faJ(WX.Y) := inter RatJUMaUVaU{ XI1 YJ tat1 (4 4, 8) = 1424 Check Calulation Programming steps shown for determining the SICF.
- 1) First is the definition of the column matrix defined with respect to the tables above.
- 2) Second is the conditional statement that defines the polynomial order based on cylinder property (Rrt ratio). For thick cylinder the polynomial order is cubic (3) whereas for thin cylinder it is quadratic (2).
- 3) Third the Mau statement assembles the matrix required for regression and interpolation for the uniform a-tip SICF.
- 4) Fourth the Rau statement performs the nonlinear regression on the assembled matrix to determine the regression coefficients needed for the interpolation routine. This is for the uniform a-tip term.
- 5) Fifth the fau statement defines the interpolation function. This is for the uniform a-tip term.
- 6) Sixth the fau(4,.4,.8) statement is the check calculation for RmIt = 4, a/c =
0.4 and a/t = 0.8. The calculated value of 1.424 compares favorably with the text value of 1.443.
- 7) Similar structure is followed for all the other SICF entries.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 15 of 22 Recursive Loop for Calculation of PWSCC Crack Growth (IRtSallllbi
=
I gi s-Is C(g ~- C
- 1, I1 c'll Hill Start of the recursive loop showing the loop initialization.
- 1) Index "j" is set to zero (0).
- 2) Initial crack depth and half length are defined.
- 3) The Time for corrosion interval is initialized.
- 4) The internal loop for each corrosion time span is initiated.
ID) R ( -,1)
I)Rl(i l
-.)
I1)lR(i, IDRG5,A) 11DRG7 A
- lIDRG8i, I) SC7 I)DRGix A
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 16 of 22 i 'Ci
- Co(
i C' K Cj -
Co + I [zA(I'.S. aE "
i I' (3 + I 1 v4tl i.;lX "t <
Cv% "
Mo + '
lU1
.S1 I
i I ' 1+
I i 11.c'S
.S I
< C K Co + -;- I 11CS11,.11\\ "
N i
C Co + 3 I 1CSt.*.
i < C -
Co + 4 i
' Co+ 4 1lflCSS.Z.i O< Cj K Co +/-. 1 i
Co + ' I S.;11
< Cj
- Co +i 11 I' co3 + i6 I licsI.
- K 1
N i I'CO+ ('. nIcsII.S.;I\\ " < *i.1 i
ifI Co + 7-I11CSII.S.I\\
K C* K Co) + 7-(PCl.N;v<
Co) +
8 1 ]C4", J.;l I
I I1 I((I()
ii 1c + 8iICl1.itrs.a\\
Ad < Cj
- Co +') IPh1C#S.trS.a\\
Partial statement showing assignment of the uniform stress coefficient. The assignment considers all twenty (20) segments. Similar assignment statements cover the other three stress coefficients (viz. linear - a1, quadratic-G2, and cubic G3). The assignment is based on the current flaw upper c-tip location. The conditional statement is based on current location "cj" as compared to the upper and lower limit for each segment.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 17of22
'(1_ g
()
r_
)
( I).
+t
)
t2' (o)+
OI 5-jai I7.)
+ (-)2{
(
)5;)
+I I
I
)
CF 2{
0.75 -a1 I
)2 0 {.75 -a i -
)
t
+ G ~t
.0 a
(
I
)
'I
()Cy I (
I
)
-(
I t )
Using the stress coefficients for the through-wall stress distribution, this step determines the stress distribution across the crack face in the depth direction.
The crack depth is divided into five equal segments. The stress distribution across the crack face is calculated for each current crack location.
Xo <- (1i) x I-() 2 X.) <-.
X\\
3 <-- 0.7-5 X42-stack(x1.
xjx 2.x;x 4)
ST'- stack(
.W j I
RG i-- reatress(X.1.3)
Developing the appropriate matrix and performing a third-order polynomial regression to determine the stress coefficients for the stress distribution across the crack face. These stress coefficients are used in the SIF dteremination.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 18 of 22
()l G.(; + P'[ It G I() t-w (;I I (Y-)
R' i MA+
(TO '~- KU(i Assignment of the stress coefficients. The stress coefficient for the uniform term (O7 contains the coefficient for the uniform stress (operating+residual) and the addition of the internal pressure (Pint). This is the step where the internal pressure is added to the calculation. This step ensures that the crack faces are pressurized.
Lj A Rj C-t (llJ; R.t t.Atltj..-VIJ)
(Gal j'ill1.( Rt..R*.
'AI~ 'F'Ii)
.1
(
cIc(( l l.ARj.A'Ij)
G i-l
+
't(tt
\\tj
\\§i (iC.1 j; l
R;(
It.A Rtj *.A' F i)
(iG I' 1v(R(
ll.A,.lj-,A'l' i)
Step showing calculation of current crack aspect ratio (a/c), the current crack normalized depth (alt) and the function call (G,,; e.g.(
i )} for the eight SICF associated with the current crack dimensions.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 19of22 I
4 I+
14{
i Cj>4j
Ž CiI O5 I + 144 te\\
s 111
.4
{2
'ic~
'Sci Determination of the crack shape factor depending on the current crack aspect ratio.
K Gl;oLiafl
{,
.G II +
+(1
!ILI + oitj Ke,,
(Go6L + G. Ii o'S,(
Gictt
+ l('i+ Gm C'(LI + Gw(}(ii K0, K
9;j1./ 199 Q.
(.ij J
K 7-K
-II,)
Determination of the SIF at the two crack tips (a-tip and c-tip) in English units and conversion to metric units.
I (
M xI it' KR K
otlotr\\\\ ise
.1 Conditional statement to test for the threshold value for the SIF. This is needed for PWSCC crack growth analysis. Done for both the a-tip and c-tip. Only the a-tip is shown.
Calculation of the crack growth rate (da/dt} in metric units (m/sec). Shown for the a-tip but sthe same calculation is performed for the c-tip.
I.;
It)'
bi c
i(s
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 20 of 22 Calculation for crack growth in one time block. This block for the current analysis is about twenty-four hours (24 hrs.). The crack growth is in English units (inch) because the conversion factor {CFinhr} is used. The first statement is set when the SIF is below the upper asymptote and the second statement is used when the SIF is greater than the upper asymptote. When the SIF is greater than the upper asymptote, the SIF independent crack growth is about 0.5 inch per year.
O(LIl)L11( j.112)
Cj OLIlI)tl1(j
')LI 0tlIl[)ll1 j. I j - Ci OLtil1Uil i. '}-i 8
otLIIIILII j.,,-
lc C.,
OLt~lp11( 1 A..
O~t l l(. i.l;,,
30 -;-24 Typical output statements within the recursive loop showing the storing of variables that are required for loop operation and those of interest in displaying the time dependent trend.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 21 of 22 j e-j + I aj 4-Lj-I Ci' -- cj-I
+
1);J*
i-I
+ H a
I a v
I il a1 > t tIJ otlilcrv isc NClj i-NC'131.il + (y[lk output The recursive loop is incremented and the required variables (crack depth, crack length, and the time variable are updated for the start of the next recursive loop operation. The last statement is a dummy statement to terminate the recursive loop.
ProPLength= 0.255 Flaw Growth in Depth Direction 0.6
.f:
C-0.4.
I I
I I
I I
I I
I II I
I I
I I
I I
0.2.
U 0 0.2 0.4 0.6 0.8 1
1.2 Operating Timc )
X cars 1.4 1.6 1.8 Typical Mathcad graphical display used to evaluate the important parameters.
The PropLength in the upper left corner is used to ascertain the growth to the weld.
This number is calculated internally before the recursive loop is started. This is the difference between the weld bottom location (ULstrs.Dist) and the Crack Upper Tip location (UTip).
CGRsarnbi,; x) 1.02 1.019 1.019 1.019 1.019 1.019 1.019 1.019 1.018 1.018 1.018 1.018 1.018 1.018 1.018 1.018 CGRsarnbk 6) 18 514 18 526 18 528 18 529 18531 18 533 18 535 18 537 18 539 18541 18 543 18 545 18 546 18548 1i3.55 18 552 Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 1 Page 22 of 22 CGRsarnb k 5) 15.654 15.703 15.704 15.705 15.706 15.707 15.708 15.709 15.71 15.71 15.711 15.712 15.713 15.714 15.715 15.716 Typical numerical output in tabular form used to ensure proper functioning of the model.
0 6 -
0.5 -
-04 S
- 20.
0.2 -
0.1 0 0 - I 0.0 0.5 I 0 0 p era t~n g T in. e (y ears) 1.5 2 0 Typical Axum graphics for use in the report.
End of the Mathcad worksheet Description
Entergy Operations Inc Central Engineering Prograirts Appendix B; Attachment 2 Page 1 of 30 Engineering Report M-EP-2004-001-00 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"18.2" Degree Nozzle, "Downhill" Degree Azimuth, Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/1hr.
OD Surface Flaw Note :- The two differences between this model and the ID surface flaw model are:
- 1) Use of SICF tables from Referencel for External flaws (pages 9 - 12).
- 2) The stress distribution is from the OD to the ID (pages 6 - 8).
These differences are noted (in bold red print) at the appropriate locations.
The first Required input is the Freespan length from the NADE data sheet (Excel spread sheet)
FSnde data.sheet : 0.430 To p/ace the flow with repsect to the reference point, the flow tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower "c-tip" located at the reference point (Enter 3).
Val := 2 Enter the Upper extent of the Stress Distribution used for analysis (bottom of Fillet weld of the J-grrove weld)
ULStrs.Dist := 1.712 RefPoint := ULStrs.Dist - FSnde.data.sheet A_
&2L Developed by.
J. S Brihmadesam Verified by:
B. C. Gray
Eiitergy, Operations Inc Central Engineering Prograins IFnput uala Appendix B; Attachment 2 Page 2 of 30 Engineering Report M-EP-2004-001.00 L := 0.35 aO := 0.09872 od := 4.00 id := 2.765 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID phit := 2.235 Years := 2 Iiim = 1500 T := 604 aXoc := 2.67 10- 12 Q, := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R od R
- =-
R
- id Rid T=
t := Ro-Rid t
R I-l =R i+
riiopr := Years 365 24 CF inlir := 1.417 105 Tirnopr Chlk =
' = irn Prntblk l 5
Co :=I-Rm t
1 103.10-3 T+459.67 Tref+459.67 1 C01 := c r0U0c Temperature Correction for Coefficient Alpha Co = C 0 1 Stress Input Data 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 3 of 30 Engineering Report M-EP-2004-001-00 Input all available Nodal stress data in the table below. The column designations are as follows:
Column ""o = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData 0
-32.98
-29.55
-27.62
-25.63
-23.66 0.46 4.42 1.43
-2.62
-5.98
-7.49 0.83 23.6 20.13 17.47 13.58 8.56 1.13 39.38 33.76 28.59 23.55 16.9 1.37 41.08 35.6 32.56 29.09 28.07 1.56 35.47 35.03 34.72 41.39 51.48 1.71 25.31 30.93 36.76 48.63 57.32 1.85 18.48 26.76 37.58 49.67 67.27 2
15.18 24.43 37.51 53.17 72.59 2.14 16.04 22.8 36.7 51.39 59.83 AXLen := AllData(°)
IDA11 := A11Data(')
0DA11 := AlIData(5)
Stress Distribution 100 IDAII r
All sC-ODI v:
50 0
-50 _0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
RefPoint = 1.282 Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy, Operations Inc Central Engineering Programis Appendix B; Attachment 2 Page 4 of 30 Engineering Report M-EP-2004-001 -00 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(0
-32.98 -29.552
-27.619
-25.631
-23.659)
Data :=
0.463 4.418 0.834 23.603 1.131 39.381 1.369 41.077 1.56 35.472 1.712 25.309 1.854 18.476 1.43 1 20.133 17.472 13.58 8.558 33.757 28.588 23.549 16.901 35.596 32.564 29.095 28.069 35.035 34.721 41.389 51.476 30.935 36.756 48.633 57.324 26.759 37.578 49.667 67.274
-2.622
-5.982
-7.485 1.996 15.182 24.435 37.506 53.17 72.592 )
MxI := Data(0)
MD := Data(3)
I D := Data(l1)
TQ := Data(4)
QT = Data(2)
OD := Data(5)
RID := rc-ress(AxIjD,3)
RQT := rercss('Axi, QT, 3)
ROD := re-rcss(AxI1,OD,3)
RMD := rcrcss(AxI,MD,3)
R
- = regrcss(AxjTQ,3)
ULStrs.Dist := 1.786 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
FLCntr R=
ReCi'Pjilt -
if Val = I RelfPoint if Val = 2 Ref poilt + Co otherwise Flaw center Location Location above Nozzle Bottom UTip := FLCntr + co IfllStrs.ava `
ULStrs.Dist - UTip 20 Developed by:
J. S. Blihmadesam Veniled by:
- 8. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 5 of 30 Engineering Report M-EP-2004-001-00 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles in the Axial Direction for Fracture Mechanics Analysis N := 20 Loco := FLCntr L
i := I.. N + 3 Number of locations for stress profiles Incr :=
co if i < 4 llncStrs.avg otherwise Loc: Loci-, + Incri SlDi RID3 + RID4 Loci + RID (Loci) 2 + RID 1(Loci)3 SQTi RQT + RQT -Loci + RQT.(Loc1)2 + RQT.(Loci) 3 SMDi RMD3 + RMD4' Loci + RMD (Loc,) 2 + [ RMD6 (Loci)3]
STQi RTQ + RTQ -LoCi + RTQ (Loc;)2 + RTQ (Loci) 3 T3 5Q Q'Lc)
T6 SODi ROD + ROD Loci + ROD.(Loci) 2 + RoD.(Loci)3 3
4 56 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j := I.. N Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Eitergy/ Operations Inc Appeni Central Engincering Prograirs I
Sid SD+ SIDj+ + SIDj+2 itj Sid
- (j + I) + SIDj+2 JI otherwise j+2 jix B; Attachment 2 Page 13 of 30 5qt SQTj + SQTj+I + SQTj+2 5qt 0
) (i + I) + SQTr+ 2 j+ 2 Engineering Report M.EP-2004-001-00 if j= I otherwise SMlDj + SIDj+, + SMlDj+2
- f;
=,
Sind.:
j 3
Smdj (j + i) + SIDj+2 j+2
.. J 5 tqj.
STQj + S -Qj+1 + STQj+2 if j = 1 3
stq
- (j + I) + ST'Qj+2 I
2 otherwvise j +
otherwise SODj + SODj+. + SODj+2 C i = I Sod =
j Sod.( +
) + SODj+2 j+ 2
.. J otherwvise Note the Change here to develop stress distribution form OD to ID Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution) 1I0 := 0.000 LI I := 0.25 U
0:=050 Li' :=0.75 U4 := 1.00 Y :=stack L10,U I, LP),U 3,,
f SIG I := stack (Sod.Stq, Sind,9Sqt I ISid 1)
Developed by:
J. S. SBnhmadesam SIG, = stack(Sod 9Stq,,S1-d Sqt Sid Venfled by:
S. C. Gray
Entergy Operations Inc CentralI Engineering Prograits Appendix B; Attachment 2 Page 7 of 30 Engineering Report M-EP-2004-001-00 SIG3 = stack( Sod3 Stq3 S md)SqySd 3)
SIG5 := stack ( Sod S tqS5 9Smd5 9 Sqt 5 9 Sid5)
SIG 7 = stack ( Sod7 9 Stq7 9Smd 71 Sqt7 1 Sid7)
SIG9 := stack(Sod 9S 5tq9'Smd9'Sqt9'Sid 9)
SIG I I := stack (Sodl 119Stql
,Smdi 11'Sqti 1,9Sid 11)
SIG 13 := stack(Sod1 3 9 Stq13 9 Smd
' qt13 Sidl3)
SIG 15 := stack ( Sod 15 ' Stq smd15 Sqt15' Sid 15)
SIG 4 = stack(Sod4 ' Stq4 Smd 4 Sqt4 ' Sid 4)
SIG 6 := stack(Sod Stq6' Smd6, qt6 Sid6)
SIG 8 := stack(Sod 8 Stq 8. Smd Sqt Sid8 )
SIG 10 := stack(Sodlod Stq10, Smd10 Sqt1O Sid )
SIG12 := stack(Sod12,Stq12,Smd2' Sqt2 Sid12)
SIG 14 := stack(Sod 1, Stq14,Smd 1
qt14 'id 14)
SIG16 := stack(Sod16,Stq1 6,Smd 16' qt16 ' Sid 16 )
SIG 17 = stack(Sod 17 ' Stq17' Smd17' Sqt17'Sid 17)
SIG,8 := stack(Sod 18Stq, 5 Smd8' Sqt1 8 Sid18)
SIG I9 := stack (Sod19 Stq, Smd19 Sqt 19 'Sid 19)
SIG20 := stack(Sod 20, Stq20' Smd
' qt2 Sid20)
Regression of Throughwall Stress distribution to obtain Stress Coefficients throughwall using a Third Order polynomial ODRGI := regress(Y,SIG I,3)
ODRG2 := regress(Y,SIG2,3)
Developed by:
J. S. Btihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering P'rognams ODRG3 regress(Y,SIG3,3)
ODRG5 reuress(Y. SIG5,3)
ODRG7 regress(YSIG7,3)
ODRG9 regress(Y,SIG 9,3)
ODRG I regress( Y, SIGI ODRG13 regress(Y,SIG 3,3)
ODRG1
- regress(Y,SIGj 5,3)
ODRG17 regress(Y,SIG 1 7,3)
ODRG1 9 regress(Y,SIGi 9,3)
Appendix B; Attachment 2 Engineering Report Page 13 of 30 M-EP-2004-001-00
- ODRG, re=ress(Y,SIG4,3)
ODRG 6 r:= ress(YS1G 6,3)
ODRG8 regress(YSIG8 3)
ODRG 10 regress(Y,SIG10,3)
ODRG12: regress(YSIG12,3)
ODRG14 regress(YSIG 14,3)
ODRG 16 regress(Y SlG16,3)
ODRG 18 r:= ress
,(Y SIG18,3)
ODRG-,0 regress(YSIG)0,3)
Stress Distribution in the tube. Stress influence coefficients obtained from thrid order polynomial curve fit to the throughwall stress distribution I roPLength = ULStrs.Dist - FLCntr C0 ProPLelgtIh = 0.329 Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SCO4 Model)
{NO INPUT Required}
Developed by:
J. S. Bnhmradesam Verifed by:
B. C. Gray
Enitergy Operations inc Central Engineering Prograins Appendix B; Attachment 2 Page 9 of 30 Engineering Report M-EP-2004-001-00 Data Tables for External falws from Reference 1 Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
_0 1
2-0 1.000 0.200 0.000 1.000 0.200 0.200 2
1.000 0.200 0.500 3
1.000 0.200 0.800 4
1.000 0.200 1.000 5
1.000 0.400 0.000 6
1.000 0.400 0.200 1.000 0.400 0.500 8
1.000 0.400 0.800 9
1.000 0.400 1.000
-8 1.000 1.000 0.000 11 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 14 1.000 1.000 1.000 15 2.000 0.200 0.000 16 2.000 0.200 0.200 17 2.000 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 20 2.000 0.400 0.000 21 2.000 0.400 0.200 22 2.000 0.400 0.500 23 2.000 0.400 0.800 24 2.000 0.400 1.000 25 2.000 1.000 0.000 26 2.000 1.000 0.200 27 2.000 1.000 0.500 28 2.000 1.000 0.800 29 2.000 1.000 1.000 30 4.000 0.200 0.000 31 4.000 0.200 0.200 32 4.000 0.200 0.500 33 4.000 0.200 0.800 34 4.000 0.200 1.000 C AA
^
n Ann n
nn Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy, Operationis ilc Central Engineering Programnls Appendix B; Attachment 2 Page 10 of 30 Engineering Report M-EP-2004-001-00 t.uuut v.J+UU u.uuu 36 4.000 0.400 0.200 37 4.000 0.400 0.500 38 4.000 0.400 0.800 39 4.000 0.400 1.000 40 4.000 1.000 0.000 41 4.000 1.000 0.200 42 4.000 1.000 0.500 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 0.400 0.200 67 300.000 0.400 0.500 68 300.000 0.400 0.800 69 300.000 0.400 1.000 70 300.000 1.000 0.000 71 300.000 1.000 0.200 72 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.000 1.000 1.000 Developed by:
J. S. Brihmadesam Veri led by:
B. C. Gray
Eitergy Operations inc Central Engineering Programszs Appendix B; Attachment 2 Page 11 of 30 Engineering Report M-EP-2004-001 -00 Sambi :=
0 1
2
.3 4
5 6
.7 0
1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1
1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2
1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3
2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4
4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5
1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6
1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7
1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8
2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9
2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 35 1
0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 l 0.72 0.568 1.781 0.427 0.181 0.1 Developed by:
J. S Blihmadesam Verified by:
B. C. Gray
Eittergy Operations hic Central Engineering Programs Appendix B; Attachment 2 Page 12 of 30 Engineering Report M-EP-2004-001-00 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 048 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 042 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 NV' := Jsb(())
X := Jsb(l)
Y := Jsb(2) aU := Sambi(0) aL := Sambi(l)
.(2) aQ := Sambi CQ := Sambi(6) ac := Sambi(3)
CC := Sarnbi(7)
CU := Sambi(4)
CL := Sambi(5)
Developed by:
J. S. Bnhmnadesam Verified by:
S. C. Gray
Entergy Operations Inc Central Engineering Prograinis Appendix B; Attachment 2 Page 13 of 30 Engineering Report M-EP-2004-401-00 n :=
3 if Rt < 4.0 2 otherwise "a-Tip" Uniform Term MaU := aulgment(W, X, Y)
VaU :a= aU RaU := regress(Mau, VaU n) faU (W.' x, Y) := interp RaU, MaU VaU, X I faU(4,4,8) = 1.741 Check Calculation Linear Term MaL := augment(U',X,Y)
VaL := aL RaL := repress(MaL, VaL, n)
W{a{
faL(W, X, Y) := interp RaL, MaL, VaL, X I
-~Y
)-
faL(4,.4,.8) = 0.919 Check Calculation Quadratic Term Developed by.
J. S. Bnfhmadesam Verifed by:
B. C. Gray
EntergyB Operations Inc Central Engineering Prograism Appendix B; Attachment 2 Page 14 of 30 Engineering Report M-EP-2004-001-00 M/faQ := atgrnent(W, x, Y)
VaQ := aQ RaQ := regress(NaQ. VaQ, 1) i [Q)[
faQ(4,.4,.8) = 0.656 Check Calculation Cubic Term MaC := augment(W, X, Y)
VaC := aC taC := regress( 1aC. Vaat, 11) faC(\\\\W.XY) := inte faC(4,4,S8) = 0.524 (W)-
- I aC, VaC, X I Check Calculation Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 15 of 30 Engineering Report M-EP-2004-001-00 "C" Tip Coefficients Uniform Term Mcu := augment(WN,X,Y)
RCU := regress( Mcu, VcU, n) fcu(\\\\,X, Y) := interp RcUMcU, ~cCU' rXI fcu(4,.4,.8) = 1.371 Check Calculation Linear Term MCL := augment(W,X,Y)
VL := cL RcL := regress(McLVcLn) rW){
fcL( \\\\t,X, Y) := interp RcL RMcL MVcL, X I fcL(2,.4,.8) = 0.319 Deve/oped by:
J. S. Bnthmadesam Check Calculation Verified by:
B. C. Gray
Entergy Operations Inc Central Enginieering Prograns Appendix B; Attachment 2 Page 16 of 30 Engineering Report M-EP-2004-001-00 Quadratic Term NMcQ := au-imcnt(W,X,Y)
VcQ:
CQ RcQ := recgrcss(MCQvcQ~n)
W)-
, NM-CQ VcQ, X I
,y )-
Check Calculation fcQ(4,.4,.8) = 0.126 Cubic Term NICC := au-mnent(W,X,Y)
VCC := c R~c := rcgress( Nc, Vc* )
fcC(WXY) := intcrp RcCNIcCVcC, X L f c(4,.4,.8) = 0.068 Check Calculation Developed by:
J. S. Brihmadesam Verified by:
S. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 17 of 30 Engineering Report M-EP-2004-001.00 Calculations: Recursive calculations to estimate flaw growth.
Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi =
j*-0 aO <- aO CO *- CO NCBo0 - Cblk while j < 1lim (o0- ODRG3 if cj < co ODRG2 if co < cj < co + ncStrs.avg 3
ODRG3 if Co + Incstrs.avg < cj < co + 2 IncStrs.avg 3
ODRG4 if co + 2flncstrs avrg < cj < co + 3]flCStrs~avg ODRG5 if CO + 3 IncStrs avg < Cj S co + 4-1 ncStrs avg 3
ODRG6 if CO + 43InCStrs.avg < Cj < co + 4 IncStrs.aNPg 3
ODRG7 if Co + s lncstrsaavg < cj < co + 6 IncStrs.avg 3
ODRG8 if co + 6, ncstrs.avg < cj < Co + 7 1ncstrs.avg 3
ODRG9 if CO + 7 1ncstrs.avg < cj < co + 8 1nCStrs.avg 3
ODRGIO if co + 8, IncStrs avg < ci < co + 9 1ncStrs.avg ODRGI I if co + 9 Incstrs.avg < cj < co + 10 Incstrs.avg 3
ODRG10 if co + lo flcstrs~avg < Cj < co + 9iflCStrs.avg~
ODRG1 if co+ I-flncStrsavg < cj S co+ 12i nCStrs.avg i<3 ODRG 14 i f co+ 12liflcStrs.av~g < cj S co + 13 ]fIlCstrs.av~g 3
Developed by.
J. S. Brlhmadesam Verified by:
B. C. Gray
Entergy Operatioms iIc Appendix B; Attachment 2 Engineering Report Central Enginecring Programs Page 18 of 30 M-EP-2004-001-00 ODRGs if o 3ll~ra, < C' < C()+ 14 [InCStrs.avby ODRG1 5 if CO+
ilCStrj.av,( < Cj < C0+ 5 3
l ODRG16 if C(0+ 15 I4il-Crj,,
< Cj S Ca+ 6l flCStrsJav 16~G~3 i
+
Iltr-a, j
(+1 Ictsv ODRG 17 if C(+ 1i5.I1cStr:;aav,, < Cj < C0 + 16 Il cStrs.avo ODRG1 if C(
1 C'
C6n
+
17C 3
+
CStrs.avgl J
0
+
lCStrs.avg ODRG 19 if Co + 17 lCStr,;av}
< Cj < c( + 38-I CStrs.avo 3
ODRG5 3
+
otherwise a
ODRG4 if co
+
c<
ODRG7 if C( < cj C0, + lflcStrs avs
-4
- ODRG, if CO + InCstrs avg < Cj < C( + 2-IIlCStrs.av\\,
ODR 4 if c( + [-lcStrs avg <C 0+8llsr~v ODRG4 if C0 + 2 IlncStrs avU < Cj < Co + 3i-IIlCStrs.avo 4
L ODRG 5 if CO + 3-il cStrsav,, <
Cj S
C0 + 4ilC ncStrs.av 4
L ODRG6 if C(o+ 4IlcStrs.av,, < Cj
< CO + 5iI lCStrs.av(
ODRG 7 if co+ 5IflcStrsavit < cj < C0 + 6i IlCStrs.av(,
4 Z
0DRG84 if C0 + 6*IflncStrs.avg < Cj
- C0 + 7 1IflCSt rs~av(,
ODRG 9 if C0 + 7ifl CStrs~avg < Cj
- C( + 8ifl CStrs~av(,
4 L
ODRG1 4 if C( + 81f ncStrsav,, < cj < C( + 9.flncStrs.avo ODRG,1 4 if C, + 9]-lncStrs.av. < Cj < C, + 1tOilCStrs.avo ODRG 12 if C0 + l Oifl CStrs;av,(, < Cj
- C 0 +I h-l CStrs.avg
-4 ODG3 if C0 + I IilCStr;.;av(y 11j1 0 + ~fCStrs av~
4 ODRG 14 if CO + 12if11CStr:;.avg < Cj *~ C0 + 13-IlCStrS av1, 4
I ODRG 15 if Cfl+ 13if11CStr:;.avf
< Cj
- C0 + 14 I~
sa~
4 L
ODRG,<
i f Co + 1~f~4
,...I Mc
< C
- Cn + I5ifl nce,,
Developed by:
J. S. Brihmadesam Verifed by.
B. C. Gray
Entergy Operations Iric Central Engineering Programs I U4 ODRG 17 ODRG 18 4 ODRG19 ODRG2 0 4 ODRG 1 ODRG2 ODRG45 OR5 ODRG4 ODRG75 ODRG5 ODRGg5 ODRG6 5
ODRG7 ODRG1 0 5
ODRG95 ODRG1 O ODRG 13 5
ODRG1 2 ODRG1 5 ODRG 14 ODRG 17 Appendix B; Attachment 2 Page 19 of 30 Oub.avg J
v3tLI.avg if co+ 15flncStrs avg < cj < Co + 16f nCStrs.avg if co+ 16flncStrs avg < cj < co + 17f nCStrs.avg if co+ 17 lncstrs.avg < cj < co + 18f nCStrs.avg othenvise if cj < CO if co < cj < co + InCstrs.avg if co + Incstrs avg < cj S Co + 2 lnCStrs.avg if c0 + 2]flCstrs avg < Cj < co + 3-ncStrs.avg if co + 32 Incstrs.avg < cj < CO + 4. ICstrs.a3g if co + 4. Incstrs.avg < Cj < co+ 5f lCStrs.avg if co + 54 Incstrs.avg < cj < co + 6 IflCStrs.avg if co + 6 IlncStrs avg < cj < C0 + 7 IfnCStrs.avg if co + 7 lncstrs.avg < cj < co + 8 lncstrs.avg if co + 87 ncstrs.avg < cj < co + 9 IncStrs.avg if cO + 9 1ncstrs.avg < cj < CO + 90 inCStrs.avg if co + 910 ncstrs.avg < c 1 < co + I 1I nCStrs.avg if co+ I I lncstrs.avg < cj S co + 12I ncStrs.avg if Co + 12 lncStrsaavg < cj< co + 13. IncStrs.avg if co+ 13 lncstrs.avg < cj < co+ 14 Incstrs.axg if co+ 14.Incstrs.aNg < cj < co+ I5 nlCStrs.avg if CO + 15. ncstrs.a~lg < cj < Co + 16-ncStrs.avg Engineering Report M-EP-2004-01 -00 Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations hic Centra l Engincering Progrnims ODRG 1 85 ODRGl95 ODRG20 ODRGI6
-6 ODRGI6
- ODRG, ODRG 4 6
ODRG-ODRG 6 6 ODRG7 6 ODRG 8 6 ODRG 96 Appendix B; Attachment 2 Page 20 of 30 if co+ i6 1ncStr.;av,, < cj S co + 17 IflCStrs.avty if C0 + l7f lcStr.avo<ci cj Co + 1 8 IICStrs.avi, otherwvisc if cj S C0 if co < cj S co + IncStrs avg if co + IflCstrs.avg, < cj S CO + 2 I1CStrs.av(,
if co+ 2-11CStrsav\\,
< cj S co + 3 1nCStrs.avo if c0 + 3 llCStrs av, < cj S co + 4 1nCStrs.avr iif C0 + 4 Icstrs av} < cj S Co + 5 IflCStrs.avg ir C0 + 5-lCStrsav(, < Cj S c0 + 6-1cStrs.av.
if c( + 6 IfcStrs av" < cj S Co + 7 1 lcStrs.avt, if C0 + 7 I1CStrs av} < cj S co + 8] flCStrs.avg, if C0 + 8dflCSrs av" < cj S co + 9 1nCStrs.avx, if CO) +I9 IncStrs.av(, <cj*Sco + 110 llCStrsjvg if Co + I9-l"CStr.avi < Cj S C()+ I IIcstrs.avv if co + I-ilCStr3avfl < cj S co + I-llcstrs.avy if co +
l -I ncStrijava < Cj S CO + 13 InlCStrs.aivo if c 0 + 12lJncStrsav( < Cj S Co + 14 ilCStrs.avg if c0 + 13-11CStrsaav,, < Cj S co + 15 111CStrs.av, i f C0 + 14-1 CSj riav(y < Cj
- C0 + 17-1 1SIr~v if C0+ 17IsnCStr avo < Cj < Co+ 16 1llcStrs.avo if rC + 16-incStrs.av,. < Cj Co + 17 IilCStrs.alvu if C( + l7 Incstri av(-, < Cj S C() + i8-1ilcStrs.tlv, Engineering Report M-EP-2004-001-00 ODRGIO 6
ODRGI 16 6
ODRG1 2 ODRG1 366 ODRGI 4
.6 ODRG1 46 ODRG1 66 ODRG 18 6
ODRG18 6 ODRG 19,
Developed by:
J. S. Bnhmnadesam Venfied by.
B. C. Gray
Entergy Operations Inc Central Engineering Prograntts Appendix B; Attachment 2 Page 21 of 30 Engineering Report M-EP-2004-001-00 ODRG 20 otherwise 6
(oj 4 I-0
+ 0 (0. 5
) + 02{.
0.25.aj2 t
)
t.25-aj) 42
+
(
+
(o2-(. +03.-(.
<q
- 00 + I 1 (*
a +
F2{)
+ 03 0.5.aJ',I t )
3 (0.75-aj)h t
)
( ~oaj Io-j2 i.0 aj)3 t4< 0(tt)<~
(3t t
x0 <- 0.0 x <- 0.25 x2<- 0.5 x3 <- 0.75 x4 < X <- stack(x 0,xj,x 2,x-3,x4 )
ST <- stack(40,4 1,42,43 44)
RG <- regress(X,ST,3) 00 0<- RG3 + Pint (10<- RG4 C020 <- RG5 ARj<- -
Cj ATJ <- ajt C.-
<- f-..{R..AR;.AT:l Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Etitergy Operations Inc Central Engineering Progranis Appendix B; Attachment 2 Page 22 of 30 Engineering Report M-EP-2004-001-00
-au -
-auk--t, --,
J'
-JJ Gal < faQL(RtAXRjA'rj)
Gaqj <
aQ ( R ARj, ATJ)
G
<- 1 aC Rt'AlAti-)
GCUj < fcU(Rt, A[ZjATj)
Gcl <- rcL( Rt, Altj, A rj)
G i Gcqj < fCQ(RtARjATj)
G
<- fcC(RtARjA/T) ccqi I + 144 (cj)
I + 1.464-1.65 Ka&
~~~ijJ*S.(o O1I +Goa.+a)d~
il' cj > aj otherwise Kaj f
l
+<_
+ 6Y#0 Gcq + OxG
'(
"O ' aj.5I aja Kc; Qj )
(('00CL Gcu + (TI O <c'cl; + al 0 Ccqj +
30 Cj Ka c Kaj 1.099 K -
.. 9 KYj < Kcj 1.099 Ka 19.0 if Ka otherwise J
IK E-9.0 if K, < 9.0 K,
otherwise Da Co (Kaj 9.0)1.16 Da < I Da-'CFiilIir Cblk ii Ka < 80.0 Developed by:
J. S. Btihmadesam Verified by:
B. C. Gray
EDtergy Opera tions Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 23 of 30 M-EP-2004001-00
_J J
J 4-107
-CFinhr Cblk otherwvise D *- CO0 (Kyj 9.0)'1 6 DCS -
DC.-CFinhr-Cblk if K
< 80.0 4-lo-10 CFinhr-Cblk otherwvise output(j,o) <- j output(j, I) <- aj OUtpUt(j, 2) <- Cj - CO output(j, 3) E Dag output(j, 4) <- Dcg.
output(j, 5) -
Kaj oLutpUt(j, 6) <- KCj NCBj Oitput(j,7) 365-24 oUtpUt(j, 8) < Gau output(j,9)
- Gal.
output(j, 10) *- Gaq ouItput(j, 1) - Gac OUtPUt(j, 12) < Gc0 OLItpLIt(j, 13)
- Gcl oUtpLlt(j, 14) & Gcqj output(j
- 15) E Gcc0 J
i<-j+ I aj <- aj-, + Dag Developed by:
Verified by:
J. S. Slihmadesam B. C. Grav
- - -1
Entergy; Opera tions Inc Ceitnra I Engineeritg Programus Appendix B; Attachment 2 Page 24 of 30 Engineering Report M-EP.2004-001-00 cj <- cjjI + Dc-aj -
t if aj > t aj otherwise NCBj -
NCBj-i + Cbik output k := o.. 1lim Developed by:
J. S. Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Prograns Page 25 of 30 M-EP-2004-001-00 PrPLenth = 0.329 Flaw Growthl in Depth Direction I
I I
I I
I I
I I
0.6 c
0.4 2
0.2 0'
0 0.2 0.4 0.6 0.8 I
1.2 1.4 1.6 1.8 Operating Time {years}
Entergy-CEP Model 0.4
.329
'a 0.3 c
x 0.2 is 0.1 0 0 0.2 0.4 0.6 0.8 1
1.2 1.4 1.6 1.8 Operating Time {years}
Entergy-CEP Model Developed by:
Verified by:
J. S. Blihmadesam B. C. Gray
Entergy, Operations hlic Central Engineering Programs Appendix B; Attachment 2 Page 26 of 30 Engineering Report M-EP-2004-001 -00 Stress Intensity Factors C-,
C a'
V)
C I-so 60 I 40 r I
I I
I I
I I
I I
........................................................................................................................ I............
I I
I I
I I
I I
I 20 0 L 0
0.2 0.4 0.6 0.8 1
1.2 Operating Time lyears}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 1.4 1.6 1.8 Developed by.V J. S. Bnhmadesam Venried by.-
S. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 27of 30 Engineering Report M-EP.2004-001-00 v:
E Q
In iL)
Eo a) cU
.Q 0.8 Influence Coefficients - Flaw 0.7 0.6 0.5 0.4 l--------------
0.3 0.2 0.1
O-----.-- ------------ ----........................ -.-. ---- ------
0 0 0.2 0.4 0.6 0.8 1
1.2 1.4 1.6 1.8 Uperating time {years}
Iva" - Tip -- Uniform "a" - Tip -- Linear
-~-----
"a" - Tip -- Quadratic "a" - Tip -- Cubic
- "c" - Tip -- Uniform
-c' - Tip -- Linear
~-~--- I"c" - Tip -- Quadratic it"c" - Tip -- Cubic Developed by:
J. S. Srihmadesam Verified by:
S. C Gray
Entergy! Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 28 of 30 Engineering Report M-EP-2004-001-00 CGRsarbi 0.621 0.621 0.622 0.622 0.622 0.622 0.623 0.623 0.623 0.623 0.623 0.624 0.624 0.624 0.624 0.625 CGRsarnbi 13.791 14.951 14.954 14.957 14.959 14.962 14.965 14.968 14.97 14.973 14.976 14.978 14.981
-14.984 14.986 14.989 CGRsanibi k,5) 8.708 9.356 9.36 9.364 9.368 9.372 9.376 9.38 9.384 9.388 9.392 9.396 9.4 9.404 9.408 9.412 Developedby.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Opcrations Inc Central Engineering Programs 70 l
D Dz 70 I
- f 30 a
-10 8
.50 0.0 008 -
0 06 -
.9 0.02-6 i
0.00-
/
Appendix B; Attachment 2 Page 29 of 30 Engineering Report M-EP-2004-001.00 00 05 10 Operaning Time (years]
1.5 20 Developed by:e J. S. Brihmadesam Vernfed by:-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 30 of 30 Engineering Report M-EP-2004-001 -00 20 -
0 1-I1
-f i10 Surface Point ('Ctip)
I -
Depth Point ("a"- up) I 5-.-
0.0 0.5 1.0 Operating Tine (years) 1.5 2.0 Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray Coo
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page I of 11 Through-Wall Axial Crack Model Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs. Entergy Operations Inc bevelopedby: J. S. Brihmodesatm Verified by: B. C. Gray Note : Only for use when R., 11,.,/t Is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev 1 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"1 8.2"degree Nozzle, "Downhill" Degree Azimuth Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev.1.
Through Wall The correction is applied in the determination of the crack extension to 9
obtain the value in inch/hr.
Axial Flaw The same first part as the previous attachments. (see Attachment 1 of this Appendix)
The First Input is the Upper limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULSirs Dist := 1.712 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
The Second Input is is needed to locate the reference line (eg. Top of blind Zone).
The through-wall flaw "Upper tip" is located at the reference line. Enter the Length of the Freespan from NDE data sheet.
FXSde datashect := 0.430 BZ:= ULJStr,.Dist - I:Snda.data sbico Location of Blind Zone above nozzle bottom (inch)
Only two inputs one defining the location of the Bottom of the Weld { ULstrs.Dist }
and the other Freespan length {FSnde.data.sheet } are needed. The flaw description is not needed for this crack type, because the flaw upper tip is placed at the reference line (i.e. at the top of the blind zone)
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 2 of I I Input Data :
I.:= 0.25 od := 4.00 id := 2.765 PI nt := 2.235 Years:= 2 lim:= 150(1 1 := 604 v := 0.307 Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poisscns ratio @ 600 F Oc:= 2.67I0 12 Qg:= 31.0 Tref:= 6 17 Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F The input data is similar to that in Attachment 1, except that the crack (flaw) length is based on stress distribution consideration. The flaw length determination is made by locating the lower tip of the flaw at a location where the average stress ([ID + OD]/2} is about 10 ksi. In this manner the lower tip is at a location where no PWSCC growth towards the bottom of the nozzle is possible.
[I
- r I
I 6
'1 Co:
1 (,3. -, T 145967 T,,r+459.67)-
(
ijp =Ya-652 I'd blk :=
i Ihin id t :=.. - R.,
Rm := Ri + -
2
('I~ ih, := 1 4 7 1 (
M11blk := l50I 5 0i I:= 2 Determination of constants. Note the conversion for crack growth rate {da/dt}
from metric (m/sec) to English units (inch/hr) is obtained by the factor defined as CFinhr.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 3 of II Stress Distribution in the tube
. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn O" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1' = ID Stress data at each Elevation (ksi)
Column '5' = OD Stress data at each Elevation (ksi)
'All
-=,
-0 I
1 "I
.L.2j
-1
-3 0
0
-32.98
-29.55
-27.62
-25 63
-23 66 1
0.46 4 42 1.43
-2.62
-5 98
-7.49 2
0.83 23 6 20.13 17.47 13 58 8.56 3
1.13 39.38 33.76 28 59 23 55 16.9 4
1.37 41.08 35.6 32.56 29 09 28.07 5
1.56 35.47 35.03 34.72 41.39 51.48 6
1.71 25.31 30.93 36 76 48 63 57.32 7
1.85 18.48 26.76 37.58 49 67 67.27 8
2 15.18 24.43 37.51 53.17 72.59 9
2.14 16.04 22.8 36.7 51.39 59.83 AllAol:= DataAl (AIM:=
tsataAl) I A(sOI):= DataAl 5 The nodal stress information is fully imported from the appropriate Excel spread sheet provided by Dominion Engineering. However, only the ID and OD distributions are required for this analysis. The stress input for this calculation uses the applied stress as defined by Membrane and bending components.
These components are dependent on the stresses at the ID and OD surface.
The model used uses the OD surface as the reference surface and the same method is followed in the calculation for this model.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 4 of II 1.282 1.712 75 25 1(1()
_5 A
In
)
05 I
1.5 2
2.5 3
Axial l)istance aLi)ov iBottom linchl
- 11) I)islribution 0----
- 01) distribution BIZ= 1.282 The ID and OD distribution are plotted. The blind zone is located. The upper flaw tip is at the blind zone location and the lower flaw tip is located close to the region where the average stress (membrane) is about 10 ksi.
Observing the stress distribution select the region in the table above labeled Data All that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-32.98 --29.552 -27 619 -25 631 -23.659) 0.463 4.418 1.4:; 1
-2 622
-5.982
-7.485 0.834 23.603 20.133 17.472 13.58 8.558 1.131 39.381 33.757 28.588 23.549 16.901 I)ata:=
1.369 41.077 35.596 32.564 29 095 28.0)69 1.56 35.472 35.035 34.721 41.389 51.476 1.712 25.309 30.935 36.756 48633 57.324 I 854 18.476 26.759 37.578 49 667 67.274 1.996 15.182 24.435 37.506 53.17 72.592 )
A\\I:= Data
- 1) : ID;ital I 0I):= [)ata 5 IZI):= regress(Axl. II).3)
R([):= regress (Axl.01).3)
The Data matrix is obtained in a similar manner as described in Attachment 1 of this appendix. The regression is only performed on the ID and OD distributions as these are the only distributions required for the computation.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page5of II Flaw Center above Nozzle Bottom FLCntr:= BZ - I UL~trs.Dist - BZ Ifcstrs.avg :=20 Location of the crack center and the segment height are defined. Once again twenty (20) segments are utilized.
Calculation to develop Stress Profiles for Analysis Hoop Stress Profile In the axial direction of the tube for ID and OD locations N := 20 Number of locations for stress profiles Loco:= FLCntr-L i:= I. N + 3 Incri:= II if i<4 Inc Sr5 avg otherwisc Loc. := Loc; t + Incr; SlD.:= RID3 + RID4-Loc. + RID',(L
+ RID6 (LC SOD i:= ROD3 + ROD L O(Lc) + ROD6.(LOC1)
In a similar manner to Attachment 1 of this appendix, the ID and OD stress profiles along the nozzle length are determined.
Development of Elevation-Averaged stresses at 20 elevations along the tube for use In Fracture Mechanics Model j:= I.. N SID. + SID.
+ SID.
Sid :=
if j= I J
3 Sid (j + I) + SiDj+2 j+2 ISOD + SODj+I + SODj 2
..,._+2 SodJ :=
3
-- I, Sod (j + I) + SODE+2 I
Io2heise j+2 Sod + Sid a j:=
J J+ Pint Sod - Sid Gb :
j 2
Engineering Report M-EP-2004-001-00 Appendix B; Attachment 3 Page 6 of II The moving average stress, the membrane (am) containing the internal pressure (Plnt) and the bending component (Gb) are computed.
Membrane Bending OD Stress ID Stress Stress Stress 0
o a
0 0
0 0
0 0
1 31.422 1 -6.992
.1 22.195 1
36.179 2
32.651 2
-6.232 2
24.184 2 36.649 3 33.514 3
-5.656 3
25.623 3
36.935 4
34.19 4
-5.165 4
26.79
'4 37.12 5 34.757 5
-4.719 5
27.803 5 37.241 6
35.253 6
-4.297 6
28.721 6 37.315 m 7 35.7 Ob= 7 -3.888 Sod = 7 29.577 Sid = i7 37.353 8
36.11 8 -3.485 8
30.391 8
37.36 9
36.493 9 -3.083 9 31.175 9
37.34 10 36.852 10 -2.679 10 31.938 10 37.296 11 37.192 11 -2.272 11 32.685 11 37.228 12 37.515 12 -1.859 12 33.421 12 37.139 13 37.824 13
-1.44 13 34.149 13 37.029 14 38.119 14 -1.014 14 34.871 14 36.898 15 38.403 15
-0.58 15 35.588 15 36.747 Tabular display of the various stress components are printed to ensure that the regression and the moving average methods are functioning properly.
PropLength:= ULStrs.Dist - (FLCntr + I)
PrOPLength = 0.43 Allowable Propagation Length {PropLength}is defined as the difference between the bottom of weld elevation and the blind zone (upper flaw tip location) elevation. Since the Flaw Center {FLcntr} is located at half flaw length below the blind zone the second term within the parenthesis is the location of the blind zone.
NCI10 I
Cblk
((
hile i 5 flin I(Ti appId I I 1 if 1i 10 Start and initialization of the recursive loop. The crack dimension used in the analysis is the half crack length defined as (I. Therefore the initial crack size is set to the initial crack half length {1o).
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 7ofI I Cniiappld v-Gil if I; < l G2 if I0< I;*10 + lnCStrs.avg mw if 10 + lncStrs ag <
< 10 + 2dfnCStrs.a%.g a114 if 10 + 2]lncStrs.avg < I; < 10 + 3 ]fnCStrs.av%
Gil 5 if 10 + 3 'lnCStrs.avg < I; < 10 + 4]fnCStrs.a%,g sII16 if I + 4 1ncStrs.avg < I; < 10 + 51nCStrs.avg Gll7 if 10 + 5 IncStrs avg < 1i 5 10 + 6 -lncStrs.avg 0Gil8 if l0 + 6 IlncStrs avg < I < 10 + 7 IfnCStrs.avg 119 iif 10 + 7 ]fnCStrs.avg < 1; < 10 + 8 lnCStrs.avg I 0 if 10 + 8Ifncstrs avg < I; c 10 + 9dfnCStrs.avg Gil 11if 10 + 9 1nCStrs.avv < Ii < I0 + llflncStrs.avg Assignment of the applied stress component. This example shows the membrane component {Oml for eleven segments. In the model all twenty (20) segments are considered and similar assignment is made for the bending component {fb). The assignments are based on the current flaw location and the boundaries for the segment. This assignment is similar to the assignments described in Attachment 1 of this appendix.
0 v2)]0 L
Definition of the Crack parameter with respect to cylinder geometry (mean radius and thickness). This parameter accommodates the effect of cylinder geometry on the SIF.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 8 of II t -
1.0090 + 0.3621-).i + 0,0'65. (Xi)
- 0.00o2-(.i)
+ O.OOO4.(Xi)' -
.326.0l 6 (i)5 tAbmi. - -0.0063 + 0.0919-?*i - 0.0168.(?,i)
- 0.005'2(x)
+ 0.0008.(in)
- 2.9701-10 Ati., 4- 0.0029 + 0.0707-ki - 0.0197-(ki)' + 0.o0o34.(xj) 3 0.0003.(xi)' + 8.80s (o 6_(k)
Abb. 4-- 0.9961 - 0.3806.Xi + 0.1239.(fl)
- 0.1)2 11(Xi) + 0.0017-(ki)' - 4.9939-1C' (b)
Determination of the SICF for the two component stress loadings based on current crack half length and cylinder geometry (using the non dimensional flaw length X.
0.5 lKP,,,j =.
ntlappld' 'T-l1 lKpbj <-- Gb.applld' (' xli).
Calculation of SIF for an equivalent flat plate geometry for the two applied stress conditions (membrane and bending).
Knilenibnl)nlD v- (ACel11i + Al),,, J) -KPI11 Knienlmll) nDi 4- (Aellu tAbin). Kp,,ll KbenldOD)
(Aebi + Abbj)-Kpb Kbenldl )
(Aeb, - Abbi).Kpb, Calculation of the SIF at the ID and OD for the two component stresses. Note the SICF factors are used as multipliers to the equivalent plate solutions determined above in calculating the SIF for the cylinder geometry.
KAp,,ODi v-Kl11embililoDi + KbenIdODl lKf~l)l)D4 <
Knieniml)r
+ KIbenld)D
.1 The applied SIF at the ID and OD are determined by the sum of the sub-component SIF for the two conditions (membrane and bending).
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 9 of I1 KAppODl
+ KAppIDl Ka
- KApp. 1.099 Ka.
9.0 if K}a 59.0 Ka othernise The applied SIF used for determining the crack growth is taken as the arithmetic average of the ID and OD SIF. The second statement converts the SIF from English units to metric units. The third statement ensures that the threshold criterion is appropriately satisfied. This conditional statement is used to prevent obtaining an imaginary value for the crack growth rate {da/dt} by a negative value for the (SIF-SIFThreshold) term. Therefore this conditional statement ensures that the difference is zero (0) when the applied SIF is below the threshold value.
Die,,
CO.(Ka - 9.0)1.16 Dienprtih l-Dien Cl inhrCbk if Kac < 80.0 4-10
- CICFinlhrCblk othenvise Calculation of crack growth rate {daldt} and the crack growth within a time block.
The crack growth rate is calculated in metric units (m/sec) and the crack growth in English units by use of the conversion factor {CFinhrl output( 1o) v-i NCB.
OUtput 4
,(itu(,
- 1) v365-24 nh ntnht..
4-
);
Output statements to store variables required for loop operation and those for evaluation of time dependent crack growth. This part is similar to the same step described in Attachment 1 of this appendix.
Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 10 of II i-i+
I I
i -Ij + )Ienit lf hll NC1B r NCB H1 + CbIk Loop increment and redefinition of parameters for the next recursive loop calculation.
1'RopI
- 1.tjj ~=
0.43 Flaw Length s. hime I. U 0. .Do
- r Ii 1
5 I I- ____ -7 -A____ __ V o _-llf -WV 0 0.2 0.1 06 0.8 I 1.2 LI. 1.6 1.8 TC li11 Oper.tiliii Time ICelts Enterg Mllode Typical Mathcad graphics used to compute the impact of crack growth. Note the allowable propagation length information in the top left corner. In this example the crack growth in one cycle exceeds the allowable propagation length, therefore the postulated flaw would reach the bottom of the weld within one operating cycle (1.5 years).
17 668 18.971 18,979 18 986 18 993 19 19 008 19015 19 022 1903 19,037 19045 19 052 19059 19 067 19 074 25.186 25.598 25.606 25.615 25.623 25.632 25.64 25.649 25.657 25.666 25.675 25.683 25.692 25.7 25.709 25.717 Engineering Report M-EP-2004-001 -00 Appendix B; Attachment 3 Page 11 of 11 I C ,,= 47 253 47 279 47.304 4733 47 355 47 381 47 407 47 432 47 458 47 484 47 509 47 535 47 561 47 586 47612 47 638 of the model. Typical tabular output to ensure proper functioning So0 -. I D s u I
- S I
f A -e 4 e S IF I130 - I 20 - =~ 0 0 1 0 O v a fine ITlm
- y-.
I.5 2.0 Typical Axum plot for use in the report. This is similar to Attachment 1 of this appendix.
Engineering Report M-EP-2004-001 -00 Appendix C Appendix C Mathcad vorkshect for CEDM Deterministic Fracture Mechanics Analyses This Appendix has 32 Attachments. Attachments 31 and 32 contain the additional evaluations for the 38.50 nozzle at the nozzle bottom.
Entergy Operations Inc. Central Engineering Programs Appendix C; Attachment I Page 1 of 11 Engineering Report M-EP-2004-001 -00 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Programs, Entergy Operations Inc. Developed by: J. S. Brihmadesam Verified by: B. C. Gray
References:
- 1) "Stress Intensity factors for Part-through Surface Cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 1 Component: Reactor Vessel CRDM -"0" Degree Nozzle, "All" Degree Azimuth Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr. ID Surface Flaw Developed by. J. 5. Bnhmadesam Verified by: B. C. Gray
Entergy Operations Inc. Centra I Engineering Programs Appendix C; Attachment I Page 2 of 11 Engineering Report M-EP-2004-001-00 i E M od
- 0.
2 id Rid -= t:= Ro - Rid Rm :=Rid + Timopr := Years-365*24 CFinhr := 1.417-105 Timopr Cblk: rimn PMtblk = 50 L Co := 2 Rm Rt -= 1103lo 3T+45.67Tref+459.67)_ co, := e [ 7 (4c Temperature Correction for Coefficient Alpha Co:= Co1 75 th percentile MRP-55 Revision 1 Developed by: J. S. Bnhmadesam Verified by: B. C. Gray
Entergy Operations Inc. Central Engineering Programs Appendix C; Attachment I Page 3 of 11 Engineering Report M-EP-2004-001 -00 AllData 0 -30.99 -30.92 -31.72 -35.43 -35.97 0.44 -2.37 -4.15 -6.02 -7.41 -9 0.79 27.86 23.57 19.7 18 12.78 1.08 42.8 38.7 32.04 24.15 15.99 1.3 47.38 40.95 35.62 31.78 29.73 1.48 48.17 40.84 37.03 40.9 48.51 1.63 43.48 39.76 38.46 47.75 56 1.79 35.07 35.43 38.78 48.73 61.47 1.96 25.7 30.81 38.83 51.73 66.52 2.12 19.18 27.11 38.58 52.69 65.89 AXLen := AllData(O) IDAll := AlIDataP') ODAlI:= AllData(5) Refpoint = 0.589 Developed by: J. S. Blihmadesam Verified by: B. C. Gray C `X7
Entergy Operations Inc. Centra I Engineering Programs Appendix C; Attachment 1 Page 4 of 11 Engineering Report M-EP-2004-001 -00 Data := 0 -30.99 -30.92 -31.719 0.441 -2.37 -4.15 -6.024 0.793 27.862 23.567 19.705 1.076 42.802 38.705 32.039 1.303 47.376 40.949 35.624 1.484 48.173 40.841 37.026 1.629 43.475 39.757 38.459 1.794 35.074 35.427 38.776 1.959 25.697 30.809 38.834 2.124 19.183 27.111 38.578 -35.433 -7.411 17.995 24.149 31.779 40.902 47.748 48.731 51.732 52.687 -35.967 ) -9.003 12.782 15.988 29.726 48.506 55.999 61.472 66.515 65.89 ) AxI := Data(°) MD:= Data(3) ID:= Data(l) TQ := Data(4) QT := Data(2) OD := Data(5) RID := regress(Axl, ID,3) RQT := regress(Axl,QT,3) ROD := regress(Axl, OD,3) RMD := regress(Axl, MD,3) RTQ:= regress(Axl,TQ,3) Developed by. J S. B5ihmadesam Verified by.: B. C. Gray
Entergy Opera tions Inc. Central Engineering Programns Appendix C; Attachment I Page 5 of 11 Engineering Report M-EP-2004-001 -00 FLCntr = RefPfint - cO if Val = I RefPoint if Val = 2 RefPoint + cO otherwise Flaw center Location above Nozzle Bottom UTip FLCntr + cO IlnCstrs.av~g : ULStrs.Dist - UTip 20 31111000"WIRMS P71M M Sat Aug 09 10:59:39 AM 2003 ProPLength = 0.865 Developed by:V J. S. Blihmadesam Velified by B. C. Gray
Entergy Operations Inc. Central Engineering Programs Appendix C; Attachment I Page 6 of 11 Engineering Report M-EP-2004-001-00 0.6. U S 04 0.4 0. I- )0. CU 0La 2 Flaw Growth in Depth Direction I I I I II I I I I III I 0.5 I 1.5 2 2.5 Operating Time {years} 3 3.5 4 1.5 U C 0t C U 13 l 0.5 I II I I I I I I I I I I I I 0 -0.5 t _1 0 0.5 I 1.5 2 Operating Time 2.5 {years} 3 3.5 4 Developed by: J. S. Bnhmadesam Venfledby. B. C. Gray
Entergy Operations Inc. Central Engineering Programs Appendix C; Attachment I Page 7 of 11 Engineering Report M-EP-2004-001 -00 Developed by: J. S. Brihmadesam Verified by: B. C. Gray
Entergy Operations Inc. Appendix C; Attachment I Engineering Report Central Engineering Programs Page 8 of 11 M-EP-2004-001 -00 Developed by: J. S. Brihmadesam Verified by: B. C. Gray
Entergy Operations Inc. Central Engineering Programs CGRsambi (k, 8) 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 Appendix C; Attachment 1 Page 9 of 11 Engineering Report M-EP-2004-001 -00 CGRsambi(k 6) 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 7.164 CGRsambi sab(k, 5) 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 5.969 Developed by: J. S. Bflhmadesam Verified by: S. C. Gray
Entergy Operations hic. Central Engineering Progranms Appendix C; Attachment I Page 10 of 11 Engineering Report M-EP-2004-001-00 0.5 1.0 1.5 Axial Distance From Nozle Bottom (inch) 0.08 100 R 0.08 0.04 0 1 2 Operating Tire (years) 3 4 Developed by: J. S. Bnhmadesam Venfled by: S. C. Gray
Entergy Operations Inc. Central Engineering Programs 0.5 - c' 03 I I 0.1 ToI(43 Appendix C; Attachment 1 Page 11 of 11 Engineering Report M-EP-2004-001-00 45 Is 0 1 2 Operating Tine {years) 3 4 - 7.0 t 6.6 .2 5.8 1= SI el on l l _ F Su -c oinl 0 1 2 Operating Tine {ye=r) 3 4 Developed by. J. S. Brihmadesam Verified by. B. C. Gray cr}}