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1300 CS LAS SS LF-GF
	ML18267A088
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Issue date:	09/24/2018
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Steve Gosselin, PE, Fellow LPI, Inc.

Gary Stevens, PE EPRI Life & Gradient Factors for ASME Class 1 Piping Component Analyses Working Group Design Methodology August 2018

2

Summary Introduction Fatigue Life Test Data Life and Gradient Factors Stage I Life Stage II Life Life and Gradient Factor Regressions Example Problem Status

3

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.

4

FATIGUE LIFE TEST DATA

5

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.

6

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)

Observation: 25% load drop criteria was associated with an average 3-mm deep crack (Chopra and Shack 2001)

7

LIFE & GRADIENT FACTORS

8

Life and Gradient Factors air air air air U

U LF GF

=

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

water air U

U 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).

9

Life Factor, LF

(

)

(3

)

3 25%

(25%)

+

=

+

I II mm mm I

II N

N N

LF N

N N

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.

I N = Stage 1 life in number of cycles between 10 m (0.0004 inch) and 200 m (0.008 inch) under uniform membrane cyclic strain (3

)

II mm N

= Stage II life in number of cycles between 200 m (0.008 inch) and 3mm crack depth under uniform membrane cyclic strain (25%)

II N

= Stage II life in number of cycles between 200 m (0.008 inch) and 25% load drop crack depth under uniform membrane cyclic strain

10

Gradient Factor, GF

(

)

(

)

(

)

I II Membrane I Membrane II Gradient N

N GF N

N

+

=

+

GF accounts for the increase in Stage II life associated with through thickness stress gradients where:

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

II N

= Stage II life between 200 m (0.008 inch) and crack depth associated with a 25% load drop for the actual component thickness

11

STAGE I LIFE

12

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

- Stage I: Initiation and growth of microstructurally small cracks

- Stage II: Growth of mechanically small cracks

13

Stage I Life (i)

I Total II N

N N

=

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.

14

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

15

CS, LAS, SS Stage I Life for 1.150% Strain

16

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

Strain Range Stage I (cycles) 0.48%

35,202 0.80%

3,797 1.15%

1,249 1.50%

627 2.00%

320 2.50%

197 Low Alloy Steel

17

Pin Crack Depth vs Life Fraction Comparison (Damiani and Smith)

18

STAGE II LIFE FOR A CYLINDER

19

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.

20

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

21

C/LAS Stage II Life

22

SS Stage II Life Strain Range A-TIP B-TIP 0.48%

0.80%

1.15%

1.50%

2.00%

2.50%

Stainless Steel Plastic Correction Factors (DKJ/DKI)

2

= 0.0564(a/t) - 0.0025(a/t) + 0.7253 J

I K

K

2

= 0.0734(a/t) - 0.0089(a/t) + 0.6542 J

I K

K

(

)

(

)

2 0.083 a/t

- 0.0093 a

=

/t

+ 0.6068 J

I K

K

(

)

(

)

+

2 0.0702

/

0.0004

/

0 9

=

6

.5 7

J I

K K

a t a t

(

)

(

)

2 0.0660 a/t

+ 0.0002 a/t +0

=

.5376 J

I K

K

(

)

(

)

2 0.0629 a/t

+ 0.0009 a/t + 0.513

=

8 J

I K

K

(

)

(

)

2 0.0478 a/t

+ 0.0023 a/t + 0.607

=

2 J

I K

K

(

)

(

)

2 0.0642 a/t

- 0.0040 a/t +0.5305

=

J I

K K

(

)

(

)

2 0.0707 a/t

- 0.0091 a/t

=

+ 0.4768 J

I K

K

(

)

(

)

2 0.0086 a/t

+ 0.0191 a/t

=

+ 0.4302 J

I K

K

(

)

(

)

2 +

= 0.0085 a/t 0.0161 a

/t

+ 0.3848 J

I K

K

(

)

(

)

2 0.0251 a/t

+ 0.0027 a/t

=

+ 0.3468 J

I K

K

23

LIFE & GRADIENT FACTOR REGRESSIONS

24

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

- 3780 Gradient Factors

25

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

Carbon steel data shown

(

)

(3

)

3 25%

(25%)

+

=

+

I II mm mm I

II N

N N

LF N

N N

(

)

(

)

(

)

I II Membrane I Membrane II Gradient N

N GF N

N

+

=

+

26

SS Life & Gradient Factor Data* (ii)

Stainless steel data shown

(

)

(3

)

3 25%

(25%)

+

=

+

I II mm mm I

II N

N N

LF N

N N

(

)

(

)

(

)

I II Membrane I Membrane II Gradient N

N GF N

N

+

=

+

27

C/LAS Life Factor Regression Models

( )

2 3

/1000

=

+

LF A

B t C

t D

t

( )

2 3

2 52.295 590.26 139.14 11.250 77.704 75.874 10.331 37.423 5.2371 0.74926 A

B C

D e

e e

e

=

+

=

+

=

( )

(

)

ln ln range where:

t t

t Thickness (in.)

e e

=

( )

2 3

2 180.96 545.24 138.58 11.933 220.80 142.17 17.919 35.254 4.8640 1.5080 A

B C

D e

e e

e

=

+

=

+

=

Carbon Steel Low Alloy Steel

28

SS Life Factor Regression Models

( )

2 3

/1000

=

+

LF A

B t C

t D

t

( )

2 3

2 600.28 303.60 84.289 7.3023 195.04 103.10 11.053 4.2302 2.0595 0.87079 A

B C

D e

e e

e

=

+

=

( )

(

)

ln ln range where:

t t

t Thickness (in.)

e e

=

Stainless Steel

29

C/LAS Gradient Factor Regression Models Carbon Steel Low Alloy Steel

(

)

1 1

1000

=

+

GF A

B C

D /

( )

2 2

486.03 124.65 60.446 240.41 477.06 15.873 25.591 28.354 14.676 26.691 229.76 31.654 12.153 27.369 62.559 A

t B

t t

C D

e e

e

=

+

=

+

=

+

=

( )

(

)

( )

( )(

)

( )( )

(

)

(

)( )

(

)( )

( )

( )( )

( )

2 2

1254.3 131.44 42.095 263.20 831.82 15.484 24.215 28.095 16.569 27.324 221.22 27.642 10.828 33.048 103.34 A

t B

t t

C D

=

+

e

=

+

e

=

+

e

=

e

m m

b g

b m

b g

where:

=

+

=

+

( )

(

)

Uniform membrane stress

= Linear bending stress

= Non-linear gradient stress ln ln m

b g

range and t

t

e e

=

30

SS Gradient Factor Regression Models Stainless Steel

(

)

1 1

1000

=

+

GF A

B C

D /

( )

(

)

2 2

914.68 45.507 155.40 40.507 559.38 19.835 33.757 33.359 6.1255 32.740 202.8 13.47 24.029 20.685 59.375 A

t B

t t

C D

e e

e

=

+

=

+

m m

b g

b m

b g

where:

=

+

=

+

( )

(

)

Uniform membrane stress

= Linear bending stress

= Non-linear gradient stress ln ln m

b g

range and t

t

e e

=

31

EXAMPLE NPS 10 Schedule 80 Reducing Elbow

32

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.

33

Node 330 60-yr Air and Water Fatigue Usages

34

Node 330 Membrane-to-Gradient Ratios

35

Node 330 Stage I Life

36

Node 330 LF and GF Calculation

37

Node 330: C/LAS/SS Life Factor

( )

2 3

/1000

=

+

LF A

B t C

t D

t

( )

(

)

ln ln range where:

t t

t Thickness (in.)

e e

=

Carbon Steel Low Alloy Steel 915.309 55.105 14.037 0.74926 A

B C

D

=

LF 0 9440 0.5209 4.4654

and, t

e

=

1732.397 35.2658 56.8178 1246.04 A

B C

D

=

LF 0 9476 Stainless Steel 925.461 44.948 13.427 0.871 A

B C

D

=

LF 0 9526

38

Node 330: C/LAS/SS Gradient Factor Carbon Steel Low Alloy Steel

=

GF 0 7634 1732.397 35.2658 56.8178 1246.04 A

B C

D

=

GF 0 7735 0.4289 0.0112 where:

=

61.406 ksi

= 1.609 ksi

= 80.161 ksi 0.5209 4.4654 m

b g

and t

e

=

(

)

1 1

1000

=

+

GF A

B C

D /

2543.655 39.9132 48.9774 2059.01 A

B C

D

=

Stainless Steel

=

GF 0 7730 1539.775 11.894 30.846 1184.960 A

B C

D

=

39

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%.

40

41

DISCUSSION

42

TogetherShaping the Future of Electricity

ML18267A088

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