ML20206R879
| ML20206R879 | |
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|---|---|
| Issue date: | 05/10/1998 |
| From: | Simon Sheng NRC (Affiliation Not Assigned) |
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| NUDOCS 9905210007 | |
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.h4 6th intemational Conference on Nuclear Engineering ICONE-6 May 10-15,1998 Copyright C 1998 ASME i
AN ASSESSMENT OF THE STRESS INTENSITY FACTOR CAL'CULATION i METHODOLOGIES DUE TO RESIDUAL STRESSES IN FAVOR AND VISA-II.D CODES Simon C. F. Sheng, Material Engineer l
Materials and Chemical Engineering Branch ;
l U. S. Nuclear Regulatory Commission i Phone: (301) 415-2708 {'
L Fax: (301) 415-2444 l E-mail: SHENG @ NRC. GOV Address: 7D4, OWFN, USNRC, Washington D. C. 20555 l
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ABSTRACT -
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Although the two probabilistic fracture mechanics codes for nuclear vessel integrity evaluation: I FAVOR and VISA-II.D consider residual stresses across the vessel wall, their methodologies !
l are not identical. Hence, in either deterministic or probabilistic vessel analysis, they do not
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produce the same stress intensity factors (SIF) due to residual stresses, even though the same residual stress distribution has been prescribed by the user. This paper assesses the analytical l aspect of the SIF calculation due to residual stresses in these two codes and compares their l results. Some reported results in the literature have also been compared, so that a I comprehensive assessment can be made to all different results from different sources, and the l reasons for the discrepancies be given. The objective of this paper is to assist users of these two codes (1) to understand the approximation (s) made in the underlying methodology of each code regarding the SIF calculation due to residual stresses and (2) to better assess the relative I accuracy of their results when a particular code is used to perform vessel simulations.
INTRODUCTION l
Although the subject of residual stresses has been studied extensively as indicated by the report by ASME Section XI Task Group on Reactor Vessel Integrity Requirements (1993) and the review by Merkle (1997), a consensus has not been reached regarding the magnitude and '
shape of the residual stress distribution through the vessel wall and the necessity of including l them in various reactor pressure vessel (RPV) fracture analyses. Nonetheless, the two RPV fracture analysis codes that we considered here: FAVOR (1997) and VISA /II.D (1991), have the capability to include residual stresses in their vessel integrity simulations. Historically, the residual stresses have been assumed to be of a symmetric cosine distribution, which was first ;
introduced by Tuppeny et al. (1968). On the contrary, Appendix E of Section XI of the American Society of Mechanical Engineers (ASME) Code specified an asymmetric cosine i distribution for the residual stress, with +10 ksi at the inside surface and -10 ksi at the outside surface.
l The copyright law provides that no copyright exists in works prepared by an officer or employee of the U.S. Govemment as part of his or her official duties.
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2 Recently, FAVOR employed a more realistic representation based on a through-wall weld residual stress distribution developed by the heavy section steel technology (HSST) program.
The HSST program was sponsored by the United States Nuclear Regulatory Commission (USNRC).
This paper does not intend to settle the issue on the magnitude and shape of the residual stress distribution, nor does it intend to justify the inclusion of residual stresses in vessel fracture analyses. Instead, this paper evaluates the underlying methodologies in these two codes for determining the stress intensity factors (SIF) due to residual stresses (K.), explains the discrepancies among K results from using the two codes, and provides general guidelines in interpreting the K.results.
ANALYTICAL MODELS '
The analytical models for residual-stress SIF calculations in both codes are of the influence-coefficient type. A typical example is the method for Ki determination for surface flaws in !
Appendix A of Section XI of the 1995 Edition of the ASME Code. In that case, the coefficients G , G i, G 2, and G 3, which are needed for K, determination, are derived from numerous simulations of finite element models (FEM) with various crack geometries subjected to four basic loading conditions: uniform, linear, quadratic, and cubic. This paper refers to an approach using results from FEM simulations of certain basic cases, but not necessarily the same as in the Appendix A of the ASME Code. The difference in the influence-coefficient methods as defined by the two RPV fracture analysis codes will be discussed in detail when each K.
calculation methodolony is presented.
Model 1 - VISA /ll.D VISA /II.D provides two distributions for residual stresses across the vessel wall:
i o = (oo).cos (2n.x/t), (Eq.1) ;
and l c = (oo).cos ( n.x/t), (Eq. 2) where aois the maximum value of the residual stress, x is the distance from the inner vessel I wall, and t is the vessel wall thickness. The user can select either of these distributions and specify onto control the magnitude of the residual stresses.
The K. values for these distributions are from 6 ANSYS FEM simulations,3 for each distribution. The FEM model is a half-vessel model with the dimensions of a generic pressurized water reactor (PWR) vessel with R/t = 10, where R, is the inner radius of the
- ~~ ~m ,
vessel. For each distribution, three FEM models having crack depths alt of 0.25,0.5, and 0.75 are created, where the crack is modeled as an infinite long axial crack. Residual-stress distributions were imposed as surface tractions to the faces of the axial crack. Because of the large number of grid points along the crack face in the FEM model, the residual stress distribution can be modeled in great detail. Hence, VISA /II.D's influence-coefficient approach does not use loading type, i.e., uniform, linear, quadratic, and cubic, as variables.
To provide K values for alt other than 0.25, 0.5, and 0.75, a third order polynomial was fitted through the dimensionless K. values for each distribution, and the resulting equations were coded in VISA-II.D for calculating K.-
K (Eq. 3)
= [1.122 + 0.54733(alt) - 9.040(a/t)' + 7.9467(a/t)*].[co .(n.a)"]
for the stress distribution of Equation (1) and K = [1.122 + 0.32667(a/t) + 1.088(a/t)2 + 0.46933(/t)a*].[co .(n.a)"] (Eq.4) for the stress distribution of Equation (2).
It should be noted that VISA /ll.D does not include cladding in the wall thickness "t" that appeared in Equations (3) and (4). Further, although VJSA-II.D has inherited VISA.ll's (1986) special provisions for dealing with finite length axial flaws, the methodology is an approximate one, and is not based on FEM simulations of semi-elliptical cracks.
Model 2 - FAVOR FAVOR provides a non-sinusoidal residual stress distribution that can not be changed by the user. A plot of this distribution is shown in Figure 1. Unlike VISA-II.D, FAVOR does not calculate the K. values separately for the build-in residual stress distribution, nor does it calculate the SIFs for other stress components (i.e., due to pressure, thermal transient, and cladding). FAVOR sums up all these stress components and then calculates the SIF for this combined stress profile, in the SIF calculation, an influence-coefficient approach by Keeney et al. (1995) that resembles the above-mentioned ASME method was used. The number of FEM simulations performed to generate the influence coefficients in the FAVOR Code for K.
calculations is more than an order-of-magnitude larger than that of the VISA-II.D method. To be exact, the alt values being simulated are 0.01,0.0184,0.05,0.075,0.1,0.2,0.3, and 0.5; the aspect ratios are 2:1, 6:1, and 10:1; and the loading types are ur.iform, linear, quadratic, and cubic. Like VISA /II.D, R/t is set to be 10.
" PLACE FIG.1 HERE"
w- -w,Q-4 Although K is not an output parameter of FAVOR, we can still evaluate K. using the FAVOR code by setting all stress components, except the residual stress, to zero. This is how the author used the deterministic version of the FAVOR code to obtain the results directly for the built-in residual stress distribution. For each simulated crack depth, FAVOR approximated the specified residual stress distribution across the crack depth by a third order polynomial and calculated the coefficients for this polynomial. These calculated polynomial coefficients, plus the influence coefficients in the FAVOR code, determine the resulting K value. For other residual stress distributions, the K. calculations have to be performed outside the FAVOR -
code.
NUMERIC RESULTS, AND DISCUSSION To make a fair comparison, we selected the conventional symmetric cosine distribution as the residual stresses for all simulations performed using the two codes. The parameter oo is set to be 77.91 MPa (11.3 ksi). Although oowas 55.16 MPa (8.0 ksi) in the work by Tuppeny et al.,
the review by Merkle indicates that the peak residual stress magnitudes in vessel welds range from 48.27 MPa (7.0 ksi) to 89.64 MPa (13.0 ksi). Therefore, the current value of 77.91 MPa (11.3 kai) is in line with the recent study. The aspect ratio all for axial flaws, where "1" is the total crack length, is set to be 0.1 because both codes permit the use of this aspect ratio.
The numerical results are summarized in Table 1. Both the VISA /II.D results and the FAVOR results are obtained using the symmetric cosine distribution fe the residual stresses. The FAVOR results are from a third order polynomial fit to the residuai stress distribution across the crack depth. The VISA /II.D and FAVOR results in Table 1 are calculated i)y the author using the formulas in the codes because K is not an output parameter of either FAVOR or VISA-II.D. Further, FAVOR does not allow the user to specify the residual stress distribution.
" PLACE TABLE I HERE" Results in Table 1 are plotted in Figure 2. Figure 2 also contains (1) results from VISA /II.D without using the correction factor for all = 0.1, (2) results reported in Merkle's review using a thermal-analogy method reported in another paper by Merkle (1995), and (3) results directly from FAVOR. The VISA /II.D results for infinitely long axial cracks are obtained from applying Equations (3) and (4). The ORNL's thermal-analogy method is based on a direct FEM analysis where the residual stresses are created computationally by imposing a fictitious, symmetric, cosine temperature distribution through the vessel wall. Although it was shown by Merkle (1995) that the resulting circumferential stress from the temperature distribution is not precisely a symmetric cosine function, it is very close for the case of R/t = 10. Hence, ORNL's thermal-analogy method is almost exact, and provides accurate results for comparison. The results from ORNL's thermal-analogy method have been adjusted to reflect a ao value of 77.91 MPa (11.3 ksi). The results directly from the FAVOR printout are obtained by applying the FAVOR methodology internally in the code for FAVOR's built-in residual stress distribution.
5 H. ACE FIG. 2 HERE" Figure 2 reveals that the discrepancies among K. results from various sources using different codes are quite large. The results can be separated into three groups in the order of descending K,,,u The first group represents results from using the VISA /ll.D methodology with all = 0. The second group represents results from using the VISA /ll.D methodology with all
= 0.1, from using the ORNL's thermal-analogy method, and from using the FAVOR technology.
The third group represents results directly from the FAVOR output.
The results in the first group are for axial cracks of infinite length. They are included in Figure 2 ,
to demonstrate the irriportance of specifying the aspect ratio for semi-elliptical cracks in VISA /II.D simulations. Otherwise, VISA /II.D may over estimate the K,,,o value by more than 20%.
The results in the second group are the next highest. They are from three sources. The solid line represents results from applying the FAVOR procedure, in which a third order polynomial was used to fit the symmetric cosine distribution of residual stresses across the crack depth.
Depending on the crack depth, a fraction of the symmetric cosine function over a period of 2n was approximated by this polynomial. The dashed line represents results from the same residual stress distribution by applying the VISA /II.D procedure. The two crosses represent results from ORNL's thermal-analogy method. Figure 2 indicates that a good agreement exists among results in the second group for a/t less than 0.3. In fact, only these results are valid.
For a/t greater than 0.3, K,,,u values from VISA /II.D are significantly larger than the K,,,u values from using the FAVOR approach. The author believes that for alt greater than 0.3, VISA /II.D gives better results. This is because the FAVOR approach uses a third order polynomial to fit the residual stress distribution across the crack depth. For deep cracks, it is no longer appropriate to approximate a major portion of the symmetric cosine distribution of period 2n by a third order polynomial.
The results in the third group are the lowest. They are generated by the FAVOR code directly.
Figure 2 shows that the K,,,u values from FAVOR for the built-in residual stress distribution are generally lower than other results presented in Figure 2 for the symmetric cosine distribution of residual stresses with ooequal to 77.91 MPa (11.3 kai).
CONCLUSIONS The K,,, results from using VISA /ll.D and FAVOR indicate that the third order polynomial fit is appropriate for cracks with alt values less than 0.3, which correspond to less than one third of the whole period of the symmetric cosine distribution of residual stresses across the vessel wall. This conclusion is supported by results from ORNL's thermal-analogy method and the 3 FEM based method of VISA /II.D, in which sufficient details of the residual stresses have been j modeled in the FEM model. FAVOR's approach of approximating the symmetric cosine I i
l
_, ,_ ,e *++>+ 4e =w w em .., amee- - *- + amos= "
l distribution of residual stresses across the crack depth is consistent with the commonly used influence-coefficient methodology in predicting SIFs due to various types of loading.
Nevertheless, they are only good for aA less than 0.3. For alt larger than 0.3, the results can be off by more than 50%. This is because for deep cracks, it is no longer appropriate to approximate a major portion of the symmetric cosine distribution of residual stresses of period 2n by a third order polynomial.
VISNil D uses a methodology which represents the cosine distribution of residual stresses by an array of nodal forces in the FEM model, and hence, can give valid results for all crack depths. However, the methodology is only accurate for infinitely long axial cracks. For semi-elliptic flaws of certain aspect ratios, an approximate approach using a " correctional Factor" ,
documented in the VISNil manual is used. Although the VISNil manual contains information '
indicating that this approximate approach is appropriate for certain applications, the general applicability of this approximate approach has not been established. Nevertheless, Figure 2 indicates that the K. results from VISNil.D are always conservative.
REFERENCES ;
ASME Section XI Task Group on Reactor Vessel Integrity Requirements,1993, " White Paper on Reactor Vessel Integrity Requirements for Level A and B Conditions," EPRI TR-100251, Electric Power Research Institute, Palo Alto, Califomia.
FAVOR Manual,1997, " Fracture Analysis Vessels: Oak Ridge," Heavy-Section Steel Technology (HSST) Program, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Keeney, J.A. and Dickson, T.L.,1995, " Stress-Intensity-Factor influence Coefficients for Axially Oriented Semielliptical Inner-Surface Flaws in Clad Pressure Vessels (R/t=10)," Report ORNUNRC/LTR-93/33, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Merkle, J.G.,1997, " Appraisal of Data Conceming Residual Stresses in Main Pressure Vessel Welds," Heavy-Section Steel Technology (HSST) Program, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Merkle, J.G.,1995, " Closed-Form Stress intensity Factor Calculations for Reactor Pressure Vessels Under Constant-Rate Temperature Change Loading," NUREG/CR 4219, Vol.10(2),
Heavy-Section Steel Technology (HSST) Program, Oak Ridge National Laboratory, Oak Ridge, Tennessee.
Tuppeny, W.H., Siddall, W.F., and Hsu, L.C.,1968, " Thermal Shock Analysis on Reactor Vessels due to Emergency Core Cooling System Operation," A-68-0-1, Combustion Engineering, Inc., Windsor, Connecticut.
VISNil.D Manual,1991, Letter Report from Simonen, F.A. to Mayfield, M.E. (USNRC) including Articles on Residual Stress and input Description of the code, Pacific Northwest Laboratories, Richland, Washington.
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VISA /Il Manual,1986, " VISA-Il- A Computer Code for Predicting the Probability of Reactor i Pressure Vessel Failure," Pacific Northwest Laboratories, Richland, Washington.
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l Figure listing:
Figure 1 HSST derived through wall weld residual stress distribution Lsed in FAVOR code l Figure 2 K. results from using the VISA /II.D and FAVOR codes l l for semi-elliptical axial cracks with all = 0.1 ,
1 l
l l
1
, . ...ww -~ . , -
---_.e4,.- -- -
V l . .
~ . . .
l- Table 1. Numerical results from using the two codes for axial cracks of all = 0.1 with a symmetric cosine stress distribution with o = 11.3 kal l
l a alt VISA-II.D FAVOR v2 (inches) (ksi-in ) (ksi-inv2)
.065 .01 5.49 5.45
.325 .05 11.71 11.94
.650 .10 15.20 15.72 1,95 .30 13.07 12.59 3.25 .50 2.14 -5.66 I
(cm) 2.0 4.0 s.0 s.0 10.0 12.0 14.0 10 . . . . . . .
60 a
e -
50
.I V -.
e 6 - l 40 e
W -
30 4 -
W 20 2 -
E E 2 -
10 h 0
- 0 5
g -
-10 3 -2 -
2
-20
-4 -
-30
, , , , , i 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 RPV Through Wall Location (!nches)
Figure 1. HSST derived through wall weld residual stress distribution used in FAVOR code.
.. . .. - . - . . . . . . . _ . . . T= . - . :- =
. . (cm) . .
2.0 4.0 6.0 8.0 10.0 12.0 8 5 1 8 I I 20 -
1 20 11
+ '
10 -
lll ',
10 ,
s l e -
1 '
s T
.Y w
s
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J0 1: VISMI.D (a/1 =0)
II: Solid - FAVOR Dashed - VISMI.D .
-10
-10 -
Cross - ORNL Review 111: FAVOR - Build in Residual Stresses
- -20
-20 ''''l''''l''''i''''I''''
1 2 3 4 5 a (inches)
Figure 2. Kr iou results from using the VISA /II.D and FAVOR codes for semi-elliptical axial cracks with a/1 =0.1.
. . - - - - . . . . . - . - - - - .. _ _ --_ _ _ _