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1330 Simplified E-P Analysis
	ML18267A091
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Issue date:	09/24/2018
From:	Robert Tregoning; NRC/RES/DE
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Alternative Approaches for ASME Code Simplified Elastic-Plastic Analysis Sam Ranganath XGEN engineering Gary Stevens EPRI NRC Public Meeting on EAF Research and Related ASME Activities, Rockville, MD September 25, 2018

Background

NRC RG 1.207 requires the use of multipliers (Fen) on the cumulative usage factors (CUF) to account for the effects of environmentally assisted fatigue (EAF)

- Application of RG-1.207 can increase the calculated CUF significantly and can make it difficult to meet the CUF limits for new plants and plants with license renewal

- This can be exacerbated when higher number of cycles associated with Flexible Power Operation (load-following) are considered.

- In reality, there has been no field experience of cracking attributed to EAF; in the few cases where there has been cracking, it has been due to high cycle fatigue and EAF has not been a factor

- On the other hand, EAF test data show a strong environmental effect; this is not consistent with the good field performance. While the Fen factors in RG 1.207 are consistent with test data, they still do not reflect the good EAF field performance.

2

Background (cont.)

One way of addressing the EAF problem is to examine the original CUF (without Fen) which may be over-conservative

- Justify a lower CUF in the original analysis so that the fatigue usage multiplied by Fen is still acceptable.

The use of the ASME Code simplified elastic-plastic analysis (NB-3228.5 or NG-3228.5) is often the biggest source of conservatism in fatigue analysis.

- The focus of the EPRI project is to develop Alternative Approaches for ASME Code Simplified Elastic-Plastic Analysis There are two ways to update the high fatigue usage:

- Use new elastic-plastic (EP) analysis; an expensive option that requires new finite element analysis; difficult to apply for piping. Also, the Code does not provide explicit rules on how EP analysis is performed

- Propose a more realistic approach as an alternative to the NB-3228.5 rules for the Code simplified elastic plastic analysis.

3

Current Code Ke Equation

= 1 for Sn 3Sm 6

1

= 1+ 1 for 3Sm Sn 3Sm 1 3

= 1/ for Sn 3Sm 5 Carbon Steel Low Alloy Steel Stainless Steel/Ni-Cr-Fe 4

Ke 3 Comparison with the results from elastic 2 plastic analysis show the conservatism in the Code Ke value 1 A new approach that preserves the simplicity 0 0 1 2 3 4 5 6 7 8 9 10 of the Code approach, but results in a more Sn/Sm realistic CUF value is needed 4

Conservatism in the Code Ke -Analysis and Test Data Comparison of the Code Ke value with the results of elastic-plastic analysis show that the Code value is conservative by a factor of two or higher.

The higher Code Ke can result in an overestimate of 20-100 in fatigue usage.

More realistic Code Ke factors can be significant in addressing license renewal and RG 1.207 EAF challenges Tests1 have also been done on notched carbon steel and stainless steel specimens in air to compare the Code Ke with test data Results confirm that the Code Ke values are conservative by factors well in excess of 2 1TL Gerber, Effect of Constraint and Loading Mode on Low Cycle fatigue Crack Initiation - Comparison with Code Design Rules GEAP Report 20662, US AEC October 1974 Stainless Steel Carbon Steel 5

Ke Formulation in WRC-361 WRC-361 was one of the first efforts to examine the NB-3228.5 Code rules and offered alternate methods to determine Ke The Ke formulation in WRC-361 considers the following:

- Effect of Poissons ratio during plastic behavior. This is addressed by developing an equivalent

=0.5 0.5 and determining the ratio of stress intensity for elastic and elastic plastic behavior under strain controlled (e.g. thermal) loading. The stress intensity ratio is:

1

= = . For =0.3, the maximum value of =1.4 1

- Elastic follow-up during mechanical load cycling; this is evaluated using the present Code Ke equation.

- Notch strain redistribution based on Neuber analysis; the additional notch factor (over and above KT) is Kn = KT (1-n)/(1+n)

The effective Ke value for the first two factors is determined by a weighted average of and Ke. This is then multiplied by the notch factor Kn.

6

Other Available Options for Ke Analysis New elastic plastic analysis is an option There are Codes that reduce the conservatism in the ASME Code; some based on WRC-361 concepts

- French, British and Japanese Codes

- The RCC-M code includes the factor (Poissons ratio effect ). Kn (Neuber notch) is included in RCC-MR for high temperature reactors but not in RCC-M (for PWRs).

- ASME Code Case N-779 Some disadvantages: CC N-779

- and are new stress terms that need new stress analysis

- Ke correction even below 3Sm

- Potential Discontinuity in Ke at 3Sm

- N-779 difficult to apply, especially for piping components Need for simple model that does not require new stress analysis and retains the simplicity of the current code but without the excessive conservatism.

7

Proposed New Ke Formulation (NB-3200 and NG-3200)

Follows the WRC-361 method of using a weighted average approach for the thermal and mechanical load stresses

- = +

= Mechanical load: P+Q-Thermal Bending

= Thermal Load: Thermal Bending (TB)

Kn = Neuber notch factor = KT (1-n)/(1+n)

- is conservatively assumed to be 1.4 (corresponding to =0.3)

+

- = 1.4 1 + for 3 + 3 ; = , but not higher than Ke.

- Eliminates potential for a discontinuity at Sn = 3Sm The earlier proposal was to exclude the Neuber notch factor, Kn = KT (1-n)/(1+n)

- Exclusion of Kn could be justified but Code members felt that this would result in too much reduction in conservatism. The proposal was revised to include the Neuber notch factor Vessels and Core Support structures (NB-3200 and NG-3200) are considered separately from Piping (NB-3600) 8

Proposed Ke* Factors for SS, CS and LAS (Kt=1)

Ke* for Stainless Steel Ke* for Carbon Steel Ke* for Low Alloy Steel 3.5 6 6 ASME Code P+Q-TB=1 Sm ASME Code ASME Code 3 P+Q-TB=2 Sm P+Q-TB=1Sm P+Q-TB=1Sm P+Q-TB= 3Sm 5 P+Q-TB=2Sm 5 P+Q-TB=2Sm P+Q-TB =0 (i.e. all TB) P+Q-TB=3Sm P+Q-TB=3Sm P+Q-TB=0 (i.e. all TB) P+Q-TB=0 (i.e. all TB) 2.5 4 4 2

Ke*

Ke* 3 Ke* 3 1.5 2 2 1

0.5 1 1 0

1 2 3 4 5 6 7 0 0 Sn/Sm 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 Sn/Sm Sn/Sm 9

Consideration of Notch Effects WRC-361 recognizes Poissons ratio effects and elastic follow-up effects by using a weighted approach of thermal and mechanical stresses and multiplies it by a notch factor based on Neuber analysis.

WRC-361 specifies a Notch factor (over and above the standard Kt factor used in elastic analysis)

- The notch factor is given by:

- Depends on the strain hardening exponent n (equal to 0.3 for stainless steel and 0.2 for carbon and low alloy steel)

Since many Codes (e.g. RCC-M code) do not explicitly include the notch factor, example EP analysis is performed to determine the effect of the Neuber notch factor Kn.

10

Verification Problems for the Proposed Ke*

The objective of the verification problems was twofold:

- Compare the prediction of the Ke* equation with the results of elastic plastic analysis for unnotched geometry

- Determine the effect of additional notch factor Kn for the evaluation of components with stress concentration factor (SCF), Kt Kn is the additional factor over and above the Kt and accounts for local yielding in the SCF region Examples include notched and unnotched locations with a combined of mechanical (P+Q-TB) and thermal bending (TB)

- Bettis stepped pipe test (no notch)

- Notched (Kt=2.9) beam (both notch and unnotched locations) evaluated by Adams at KAPL

- Axial groove in a pipe (Kt=3) with mechanical and thermal loading

- Taper location in a pipe (Kt= 1.6) with mechanical and thermal loading 11

Example Problem: Bettis Stepped Pipe Test (SS)

Test performed by Bettis to evaluate Environmental Fatigue effects in Piping

Cycling from 100° to 650° F every four minutes; pressure held constant at 2500 psi

Thermal analysis and elastic plastic stress analysis results published by Jones et al at Bettis (ASME PVP 2004-2748)

Ke based on Thickness, Elastic Strain E-P analysis Elastic Plastic inch P+Q, ksi Amplitude, % strain amplitude % analysis (E=27E6 psi) 0.6 147 0.54 0.815 1.50 0.46 137 0.51 0.735 1.45 0.32 120 0.44 0.675 1.52 0.179 79.8 0.30 0.37 1.25 12

Notched Beam Example (Adams - KAPL) 13

Axial Groove: Comparison with Elastic Plastic Analysis 3.5 Code Ke Factor 3 Ke by Elastic Plastic Analysis Proposed Ke* including notch factor 2.5 2

Ke Factor 1.5 Stainless Steel 1 Pipe (Kt= 3) 0.5 0

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 (P+Q)/Sm 14

Tapered Shoulder: Comparison with Elastic Plastic Analysis Ke by Stress, T Ke Elastic-Case R KT ksi °F P+Q/Sm Ke*

Code Plastic (MPa) (°C)

Analysis 12 450 Stainless Steel A 0.14 1.6 (82.7) (250) 4.99 3.21 2.00 1.17 Pipe (Kt= 1.6) 12 400 B 0.16 1.6 4.51 2.68 1.94 1.16 (82.7) (222.2) 12 350 C 0.18 1.6 4.04 2.15 1.86 1.12 (82.7) (194.4) 12 300 D 0.20 1.6 3.56 1.62 1.62 1.04 (82.7) (166.7)

Ti Net Delta T Stainless steel stepped pipe Cases Pressure Ti To Delta T psi Deg F Deg F Deg F A 12000 100 550 450 B 18000 100 550 450 C 18000 100 400 300 D 12000 100 100 0 15

Conclusions from the NB-3200 (Vessel) Analysis The existing ASME Code simplified procedures for elastic plastic analysis have been shown to be overly conservative The new proposal for Ke*:

- Reduces the conservatism in the existing ASME Code approach

- Considers Poissons ratio and elastic follow up ( and Ke) effects and includes Neuber notch factors over and above Kt

- Requires no new stress analysis

- Has the potential to significantly reduce CUF values

- Will in most cases, show that even with the inclusion of the Fen factors in RG 1.207, acceptable fatigue usage can be demonstrated 16

Piping Analysis (NB-3600)

The rules of NB-3200 can also be used for piping, but because of the large number of piping components and the high cost and time involved, this is not feasible.

The preferred alternative is to use the equation in NB-3650 which includes:

- Equation 9 of NB-3652 (primary stress limits),

- Equation 10 of NB-3653.1 (primary plus secondary stress limits)

- Equation 11 of NB-3653.2 (peak stress intensity range) for use in fatigue usage analysis

- Equation 12 of NB-3653.6 (limits on stress due to thermal expansion and anchor movement)

- Equation 13 of NB-3653.6 (limits on The primary plus secondary membrane plus bending stress intensity, excluding thermal bending and thermal expansion stresses

- Equation 14 (alternating stress for use in fatigue analysis)

- Thermal ratchet limit on T as given in NB-3653.7 A key difference between NB-3200 and NB-3600 is that the through thickness T stress is classified as a peak stress for piping whereas it is secondary for the vessel

- The T stress is not included in the P+Q calculation and does not affect the Code Ke value

- Consistent with this, the original proposal for Ke* did not include the peak stress, but many Code members felt that this would lead to a reduction in the overall conservatism

- As in the NB-3200 case, the members felt that the Neuber factor should also be included

- The revised approach in this presentation includes the T stress and the Neuber factor.

17

Proposed Ke* for Piping (NB-3600)

Starting with the WRC-361 equation:

Sn therm Sn mech Ke = K + Ke SnV SnV E T1 Sn therm = ST1 + C3 C3 STaTb ; ST1 =

2(1)

Sn mech = C1 SPr + C2 SMom + C3 STaTb = Eq. 13+Eq 12 Sn,v = Sn,piping + ST1 = Eq. 10 +

Expressing Ke* in terms of R and R1:

1

= 1.4 1 3 +

1+

.13+.12 +(.10(.13+.12)) 1 where = 1 = =

, + .10+ 2 1 E, and are the Youngs Modulus, thermal expansion coefficient and Poissons ratio respectively 18

Example Problem for Piping-1 BWR FW Piping Load Pair Eq 10 Sn Eq 11 Eq 12 Eq 13 Eq 14Salt Ke Code DT1 DT1 stress New R New R1 New Ke* New Ke*/Ke New cycles Code cycles 3 78 89 29.5 24.5 87 1.95 205 28.6 0.507 0.5 1.68 0.86 1325 878 4 63.8 80.5 17.7 19 56.8 1.41 244 34.0 0.375 0.6 1.40 0.99 2968 2916 5 68.3 78.4 27.9 21.9 62 1.58 178 24.8 0.535 0.5 1.50 0.95 2632 2208 6 54.3 73.2 30.7 10.4 43.4 1.05 157 21.9 0.54 0.5 1.05 1.00 9582 9582 7 56.3 70.8 31.6 19.5 41.7 1.13 95 13.2 0.735 0.3 1.13 1.00 8611 8611 8 54.5 66.6 38 18 38 1.06 49 6.8 0.913 0.1 1.06 1.00 12818 12818 9 60.2 63.1 32.4 20.6 40.3 1.28 57 8.0 0.778 0.2 1.28 1.00 8418 8418 10 56.8 63.1 18.6 21.6 36.1 1.15 126 17.6 0.54 0.5 1.15 1.00 11780 11780 19

Example Problem for Piping-2 CALCULATION NUMBER 101 CODE SECTION III CLASS 1 ASME-1989 REV A89 2013/05/16 09:57:30 [4533]

Feedwater B1 C1 K1 B2 C2 K2 C3 K3 C3PRIM C4 Z DIAM/TH MATERIAL E Alpha CARBON 0.071 1.247 1 2.287 3.43 1 1 1 0.5 1.1 8.82E+01 15.107 STEEL 2.95E+07 6.00E-06 Allow Cycles Allow Cycles % Reduction EQN.10 EQN.12 RANGE°F EQN.13 EQN.11 Code Ke EQN.14 T1 Stress R R1 Ke* Code Ke New Ke* in CUF 90284 78754 41.4 13196 97067 2.009 97526 5234 0.963 0.037 1.986 622 643 3.3 90284 78754 39.8 13196 97067 2.009 97526 5032 0.965 0.035 1.987 622 642 3.1 87896 76366 41 13196 94679 1.93 91359 5184 0.962 0.038 1.910 753 777 3.0 80749 79628 96.3 2787 96563 1.692 81675 12175 0.887 0.113 1.659 1043 1100 5.1 75846 65438 157.2 12075 102142 1.528 78048 19875 0.810 0.190 1.504 1179 1230 4.2 75846 65438 155.7 12075 102142 1.528 78048 19685 0.811 0.189 1.504 1179 1230 4.2 82426 79232 41.4 4859 89209 1.748 77947 5234 0.959 0.041 1.734 1181 1207 2.1 74695 64286 155.9 12075 100797 1.49 75086 19710 0.809 0.191 1.473 1306 1347 3.0 74695 64286 154.4 12075 100797 1.49 75086 19521 0.810 0.190 1.473 1306 1347 3.0

Extent of Benefit varies from case to case

Modest reduction in Ke with some reduction in fatigue usage (adding the T stress and the Neuber factor limits the potential benefit). The proposal is still conservative

All the information needed to calculate Ke* is available in piping stress reports; no new analysis is needed 20

Summary of Revised Code Case For Vessels and Core Support Structures

= 1 for 3 1

+1

= Smaller of Ke and 1.4(1 ) + for 3 < 3 1

= Smaller of 1 and 1.4(1 ) +1

+ for 3

=

alt = /2 For Piping Components

= 1 for 3 1

+1

= Smaller of Ke and 1.41 3 + for 3 < 3 1

= Smaller of 1 and 1.41 3 + for 3

+1 3 1

=

2 1

.13+.12

=

.10+

+.10(.13+.12) 1 =

.10+

alt = /2 21

Status of the Proposed Code Case The code case (especially the piping part) has been discussed extensively in several WG-Piping meetings and most of the important comments have been addressed Technical basis document and the revised Code Case have been completed. They will be uploaded to the ASME code web site with the expectation of a letter ballot by the November meeting at Atlanta

- Voting by WG-Piping, WG-Design Methodology and WG-Core Support Structures and subsequently by SG-Component Design and SG-Design Methodology 22

TogetherShaping the Future of Electricity 23

1330 Simplified E-P Analysis
Person / Time
ML18267A091
Issue date:	09/24/2018
From:	Robert Tregoning NRC/RES/DE
To:
Shared Package
ML18267A083	List: ML18267A084 ML18267A085 ML18267A086 ML18267A087 ML18267A088 ML18267A089 ML18267A090 ML18267A091 ML18267A092 ML18267A093 ML18267A094 ML18267A095 ML18267A096 ML18267A097 ML18267A098 ML18267A099 ML18284A024
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Download: ML18267A091 (23)
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ML18267A091

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