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1300 CS LAS SS LF-GF
	ML18267A088
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Life & Gradient Factors for ASME Class 1 Piping Component Analyses Steve Gosselin, PE, Fellow LPI, Inc.

Gary Stevens, PE EPRI Working Group Design Methodology August 2018

Summary Introduction Fatigue Life Test Data Life and Gradient Factors Stage I Life Stage II Life Life and Gradient Factor Regressions Example Problem Status 2 © 2015 Electric Power Research Institute, Inc. All rights reserved.

Introduction This work examined two aspects of ASME Code fatigue life (Usage) fatigue calculation procedures - e.g. NB-3222.4, NB-3650, or XIII 3222.4(e)(5)

- allowable fatigue life is based on fatigue testing small diameter test specimens that are subsequently applied to all piping regardless of the actual thickness, and

- all component cyclic stresses are treated as uniform through-thickness membrane stresses and do not consider the presence of actual through-thickness stress gradients.

Test Specimen 25% Load Drop Crack Size For constant displacement test: 25% load drop (F25%) occurs when crack area equals 25% of original test specimen area.

Fatigue Strain-Life Testing ASTM Standard E 606-04

- Smooth push-pull specimens tested under fully reversed through-thickness uniform (membrane) displacement controlled loading

- Determination of number of cycles to failure may vary. Current data based on force (load) drop of 25% or 50%.

NUREG/CR-6909 Rev. 1

- Argonne National Laboratory and Japanese data

- Mixture of 25% and 50% load drop data (all data normalized to 25% load drop criteria)

- Air test temperatures between 25°C and 290°C

- Gauge diameters 0.2 in. (5-mm) to 0.375 in. (9.5-mm)

Life and Gradient Factors U

air = U air LFair GFair LF accounts for increased Stage II life associated a with piping thicknesses greater than the 0.304 inch median gauge thickness associated with the NUREG/CR-6909 Rev. 1 room temperature air test data.

GF accounts for the increase in room temperature air Stage II life associated with through thickness stress gradients U water = U

air Fen Stage I and Stage II life calculations for carbon steel (CS), low alloy steel (LAS) and stainless steel (SS) materials were based on material properties at room temperature (25°C).

Life Factor, LF A life factor LF corrects fatigue usage estimates for increased Stage II life associated with component thicknesses greater than the 0.304 inch median gauge thickness associated with the NUREG/CR-6909 solid pin test specimens.

N3mm N I + N II (3mm )

LF = =

N 25% ( N I + N II (25%) )

N I = Stage 1 life in number of cycles between 10 m (0.0004 inch) and 200 m (0.008 inch) under uniform membrane cyclic strain N II (3mm) = Stage II life in number of cycles between 200 m (0.008 inch) and 3mm crack depth under uniform membrane cyclic strain N II (25%) = Stage II life in number of cycles between 200 m (0.008 inch) and 25% load drop crack depth under uniform membrane cyclic strain 9 © 2015 Electric Power Research Institute, Inc. All rights reserved.

Gradient Factor, GF GF accounts for the increase in Stage II life associated with through thickness stress gradients

( N I + N II ) Membrane GF =

( N I ) Membrane + ( N II )Gradient where:

N I = Stage 1 life between 10 m (0.0004 inch) and 200 m (0.008 inch)

N II = Stage II life between 200 m (0.008 inch) and crack depth associated with a 25% load drop for the actual component thickness 10 © 2015 Electric Power Research Institute, Inc. All rights reserved.

Stage I and Stage II Life Two stages of fatigue crack growth

- Stage I: Initiation and growth of microstructurally small cracks

Stage I Life (i)

N I = NTotal N II Assumption: Stage I initiation and growth occurs under uniform membrane loading regardless of the absence or presence of linear and non-linear through-wall stress gradients.

Test Specimen 25% load drop crack depths 25% load-drop crack depth of 0.118 in. (3-mm) is associated with a 0.304 in. (7.72 mm) specimen gauge diameter that represents the median NUREG/CR-6909 test specimen size 14 © 2015 Electric Power Research Institute, Inc. All rights reserved.

LAS Stage 1 Life: 1.150% Strain Range (ii)

Stage II Life (i)

Crack growth of a mechanically small crack (0.008 in.) to a crack depth associated with a 25% load drop Stage II deterministic crack growth calculations were performed using the NRC PRAISE computer code PRAISE was modified to include a best estimate (50/50) of the C/LAS crack relationship in ASME Section XI Non-Mandatory Appendix C The alternating stress intensity was corrected for elastic-plastic material response in the HIGH strain LOW cycle region.

Stage II Life (ii)

PRAISE was modified to include a best estimate version of the C, LAS and SS crack growth relationships in room temperature air The elastic alternating stress intensity, KI, is subsequently adjusted for elastic-plastic material response in the high-strain low-cycle region at the crack a-tip and b-tip.

Elastic J-integral range, Jelastic, was obtained from linear elastic finite element analyses, and the elastic-plastic J-integral range, Jelastic-plastic, was computed by performing elastic-plastic finite element analyses 20 © 2015 Electric Power Research Institute, Inc. All rights reserved.

SS Stage II Life Stainless Steel Plastic Correction Factors (DKJ/DKI)

Strain A-TIP B-TIP Range K J K J

= 0.0478 ( a/t ) + 0.0023 ( a/t ) + 0.6072 2

0.48% = 0.0564(a/t)2 - 0.0025(a/t) + 0.7253 K I K I K J K J

= 0.0642 ( a/t ) - 0.0040 ( a/t ) +0.5305 2

0.80% = 0.0734(a/t)2 - 0.0089(a/t) + 0.6542 K I K I K J K J

= 0.083 ( a/t ) - 0.0093 ( a/t ) + 0.6068 = 0.0707 ( a/t ) - 0.0091( a/t ) + 0.4768 2 2 1.15%

K I K I K J K J

= 0.0702 ( a / t ) +0.0004 ( a / t ) + 0.5697 = 0.0086 ( a/t ) + 0.0191( a/t ) + 0.4302 2 2 1.50%

K I K I K J K J

= 0.0660 ( a/t ) + 0.0002 ( a/t ) +0.5376 = 0.0085 ( a/t ) + 0.0161( a/t ) + 0.3848 2 2 2.00%

K I K I K J K J

= 0.0629 ( a/t ) + 0.0009 ( a/t ) + 0.5138 = 0.0251( a/t ) + 0.0027 ( a/t ) + 0.3468 2 2 2.50%

Life & Gradient Factor Data Carbon/Low Alloy Steel and Stainless Steel

- Room temperature air environment Cyclic Loads:

- % Strain Range (e) = 0.48, 0.8, 1.15, 1.5, 2, 2.5 Nominal Pipe Sizes:

- NPS 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 14, 16,18, 20, 22, and 24 Pipe Schedules:

- 80 and 160 Pipe Thickness Range:

- 0.154 in. to 2.344 in.

Data

- 3780 Life Factors

C/LAS Life & Gradient Factor Data* (ii)

Carbon steel data shown N3mm N I + N II (3mm ) ( N I + N II ) Membrane LF = = GF =

SS Life & Gradient Factor Data* (ii)

Stainless steel data shown N3mm N I + N II (3mm ) ( N I + N II ) Membrane LF = = GF =

C/LAS Life Factor Regression Models

( ) ( ) / 1000 2 3 LF = A + B t * + C t * + D t

Carbon Steel where:

t * = ln ( t )

( ) 11.250 (e )

2 3 A = 52.295 590.26 e 139.14 e e * = ln ( e range )

B = 77.704 + 75.874 e * + 10.331 ( e * )

2 t = Thickness (in.)

C = 37.423 + 5.2371 e

D = 0.74926 Low Alloy Steel A = 180.96 545.24 e 138.58 e

( ) 11.933 (e )

2

3

+ 17.919 ( e )

2 B = 220.80 + 142.17 e *

C = 35.254 + 4.8640 e

D = 1.5080 27 © 2015 Electric Power Research Institute, Inc. All rights reserved.

SS Life Factor Regression Models

( ) ( ) / 1000 2 3 LF = A + B t * + C t * + D t

Stainless Steel where:

( ) ( ) t * = ln ( t )

2 3 A = 600.28 303.60 e

84.289 e

7.3023 e

e * = ln ( e range )

B = 195.04 + 103.10 e + 11.053 ( e )

2 t = Thickness (in.)

C = 4.2302 2.0595 e

D = 0.87079 28 © 2015 Electric Power Research Institute, Inc. All rights reserved.

C/LAS Gradient Factor Regression Models GF = 1 (1 ) A + B + C + D / 1000 where:

Carbon Steel m

=

A = 486.03 124.65 t * + 60.446 240.41 477.06 e

m + b + g

( ) b 2

B = 15.873 t * + 25.591 t * + 28.354 t

14.676 t

e * =

m + b + g C = 26.691 2 229.76 + 31.654 e

and

( )

2 D = 12.153 27.369 e 62.559 e 2 *

m = Uniform membrane stress b = Linear bending stress Low Alloy Steel g = Non-linear gradient stress

( )

A = 1254.3 131.44 t * + 42.095 ( ) 263.20 ( ) 831.82 e* ( ) (

t * = ln ( t ) e * = ln e range )

B = 15.484 ( t ) + 24.215 ( t ) ( ) + 28.095 ( t ) ( ) 16.569 ( t )( e )

2 C = 27.324 ( ) 221.22 ( )( ) + 27.642 ( ) ( e )

2

D = 10.828 ( ) 33.048 ( ) ( e ) 103.34 ( e )

2 2

SS Gradient Factor Regression Models GF = 1 (1 ) A + B + C + D / 1000 where:

Stainless Steel m

=

A = 914.68 45.507 t

155.40 40.507 559.38 e

m + b + g

( ) b 2

B = 19.835 t * + 33.757 t * + 33.359 t * + 6.1255 t

e * =

m + b + g C = 32.740 2 202.8 13.47 e

and

( )

2 D = 24.029 + 20.685 e 59.375 e 2 *

m = Uniform membrane stress b = Linear bending stress g = Non-linear gradient stress

(

t * = ln ( t ) e * = ln e range )

BWR 4 LPCS 10 x 12 Reducing Elbow 60 year design fatigue usage calculation at a Schedule 80 10 X 12 reducing elbow in a Low Pressure Core Spray (LPCS) system Original calculation performed according to stress analysis procedures specified in ASME III NB-3600 The highest fatigue usage was located at Node 330 where a 3/4 socket-welded elbolet is attached to Schedule 80 10 X 12 reducing elbow The reducing elbow thickness at the location is 0.594.

60 year fatigue usage estimates are corrected the component thickness and the presence of through-wall stress gradients.

Node 330: C/LAS/SS Life Factor

( ) ( ) / 1000 2 3 LF = A + B t * + C t * + D t

Carbon Steel Low Alloy Steel Stainless Steel where:

t * = ln ( t )

A = 915.309 A = 1732.397 A = 925.461 e * = ln ( e range )

B = 55.105 B = 35.2658 B = 44.948 t = Thickness (in.)

C = 14.037 C = 56.8178 C = 13.427 and, D = 0.74926 D = 1246.04 D = 0.871 t * = 0.5209 LF = 0.9440 LF = 0.9476 LF = 0.9526 e * = 4.4654 37 © 2015 Electric Power Research Institute, Inc. All rights reserved.

Node 330: C/LAS/SS Gradient Factor GF = 1 (1 ) A + B + C + D / 1000 Carbon Steel Low Alloy Steel Stainless Steel where:

= 0.4289 A = 1732.397 A = 2543.655 A = 1539.775

= 0.0112 B = 35.2658 B = 39.9132 B = 11.894 and C = 56.8178 C = 48.9774 C = 30.846 m = 61.406 ksi D = 1246.04 D = 2059.01 D = 1184.960 b = 1.609 ksi g = 80.161 ksi GF = 0.7634 GF = 0.7735 GF = 0.7730 t * = 0.5209 e * = 4.4654 38 © 2015 Electric Power Research Institute, Inc. All rights reserved.

CS/LAS/SS LF & GF Comparisons LF and GF Comparison for CS at 1.15% Strain Range pcPRAISE Regression % error Life Factor, LF 0.9430 0.9440 0.1060 Gradient Factor, GF 0.7635 0.7634 -0.0131 LF x GF 0.7200 0.7206 0.0929 Note: The CS LF and GF regressions agree with the pcPRAISE solution to within 0.11%.

LF and GF Comparison for LAS at 1.15% Strain Range pcPRAISE Regression % error Life Factor, LF 0.9471 0.9476 0.0528 Gradient Factor, GF 0.7732 0.7735 0.0388 LF x GF 0.7323 0.7330 0.0916 Note: The LAS LF and GF regressions agree with the pcPRAISE solution to within 0.10%.

LF and GF Comparison for SS at 1.15% Strain Range pcPRAISE Regression % error Life Factor, LF 0.9523 0.9526 0.0315 Gradient Factor, GF 0.7729 0.7730 0.0129 LF x GF 0.7360 0.7364 0.0444 Note: The SS LF and GF regressions agree with the pcPRAISE solution to within 0.05%.

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