FATIGUE USAGE LIFE AND GRADIENT FACTORS ASME …

© 2015 Electric Power Research Institute, Inc. All rights reserved.

Steve Gosselin, PEDirector LPI, Inc.

Nuclear Regulatory CommissionPublic Meeting

June 30, 2016

FATIGUE USAGE LIFE AND GRADIENT

FACTORS for

ASME CLASS 1 PIPING ANALYSES

2© 2015 Electric Power Research Institute, Inc. All rights reserved.

Summary

Introduction Fatigue Mechanism and Testing Life and Gradient Factors Stage I and Stage II Life Example Application 2016 Activities


INTRODUCTION


Introduction

ASME Section III Code procedures introduced design practices that, when coupled with inservice inspections, provide confidence that reactor coolant pressure boundary components provide reliable service– Excellent performance of our operating plants is a testimonial to

these procedures Challenges not anticipated in the late 1960’s

– Reactor water effects– Plant life extension to 60 and 80 years– Flexible Operations


Introduction

This work examined two aspects of ASME Code NB-3600 fatigue life (Usage) calculation procedures– Allowable fatigue life is based on fatigue testing small

diameter smooth test specimens and is subsequently applied to all Class 1 piping regardless of their actual thickness

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


Stress Distribution: ASME Code vs Actual Component


Test Specimen Load Drop Crack Size

R

Test Specimen

a

CrackArea


FATIGUE MECHANISM


Fatigue Mechanism

Fatigue is predominantly the process of propagating a crack.

Fatigue process:Stage I – Initiation of microcracks– Microcrack growth and coalescence to form mechanically small

(short) cracksStage II– Propagation of mechanically small cracks (MSC)

characterized by EPFM – Component failure/load drop


Fatigue Mechanism (ii)

Once a microcrack forms, it continues to grow along its primary slip plane as Mode II shear crack oriented 45 degrees to the stress axis.

At low strains, Stage I Mode II crack growth may extend across several grains

Increasing stress intensity promotes slip on systems and slip is no longer confined to planes at 45° to the stress axis

Crack begins to propagate as a Mode I (tensile) crack normal to the stress axis in Stage II growth. Cracking is governed by power laws of crack depth and plastic strain


Fatigue Mechanism (iii)

Stage I Crack Growth – initially grow by shear (Mode II)

loading along preferential slip planes

– coalesce and propagate at decreasing rates to an engineering crack size

Stage II Crack Growth– characterized by an accelerating

crack growth rates – growth predicted by continuum

fracture mechanics methods. Crack shape: “half-penny”

Dowling (1977)


Fatigue Mechanism (iv)

Stage I to Stage II transition crack depth is between150 m (0.006 in.) to 250 m (0.010 in.) Chopra and Shack (2001)

Depending on the nature of the loading, Stage I to Stage II transition can occur between 20% and 50% of specimen life


FATIGUE LIFE TESTING


Fatigue Strain-Life Testing (ii)

Chopra 1999


ASTM Standard E 606-04

ASTM Standard E 606-04 – Smooth push-pull specimens tested under fully reversed

through-thickness uniform (membrane) loading conditions

– Strain/displacement controlled loading– Determination of failure may vary with the use: Separation: total separation or fracture of the specimenModulus Method: ratio of unloading-to-loading modulus is 0.5Force (Load) Drop: decrease in maximum force; typically 25% or

50%– Recent data reported in NUREG/CR-6909 Rev 1 defines Nfailure

at 25% load drop


Fatigue Strain-Life Data

ASME Section III – Fig. I-9.1, I-9.2, or I-9.3 (tabularized in Table I-9.0) in the ASME

Section III Mandatory Appendices– Adjusted for maximum mean stress– Reduction factor of 2 on stress or factor of 20 on cycles– Life factor accounts for: 1) data scatter, 2) surface finish, and 3)

weak-link statistical size effects NUREG/CR-6909 Rev. 1

– S-N design curves based on best estimate fatigue statistical models

– Life was reduced by a factor of 2 on stress or 12 on cycles– Adjustments for size effects were limited to weak-link statistical

size effects


NUREG/CR-6909 Rev. 1

Significantly larger database than original PVRC data– Argonne National Laboratory and Japanese data Mixture of 25% and 50% load drop data Air test temperatures between 25°C and 290°C Test specimens gauge diameters 0.2 inch to 0.375 inch All data normalized to 25% load drop criteria 25% load drop criteria is generally associated and with an

average 3-mm (0.118-in.) deep crack (Chopra and Shack 2001)


STRESS GRADIENT AND SIZE EFFECTS


Peak Stress

o o ip ab a a b b

P D MS K C K C K C E | T T |t Z

K E | T | E | T

1 1 2 2 3 3

3 1 2

21 1

2 1 1

o o1 1 m

P DK C2t

Membrane Term:

( )

i2 2 m b

MK CZ

Global Bending Term:

( )

3 3 ab a a b b b

3 1 b

2 g

K C E | T T |1 K E | T |

2 11 E | T

1

Thermal Gradient Terms:( )

( )

( )


Through-wall Stress Distribution

20 m b g 1 b g 2 g

2 2m b g b g g

where: A A (2 3 ) / t A 1.5 / t

and:

(z) ( ) (2 3 ) / t) z 1.5 / t z

20 1 2(z) A A z A z


Through-wall Stress Distribution (ii)

The nonlinear gradient stresses result from transient temperature changes at the inside surface of the pipe.

The through-thickness thermal stress (g) of an insulated cylinder with wall thickness t, subjected to a ramp/step temperature change at the inside surface (z = 0), can be expressed by [NUREG/CR-6674]:

2

g Gz z(z) 1 3 1.5t t

In the case G is the maximum radial gradient thermal stress at the inside surface


Through-wall Stress Distribution (iii)

The through-wall axial stress thermal gradient predicted by NUREG/CR-6674 is compared against the prediction from the Tiffany finite difference code


Stress Gradient Effect

Code fatigue usage calculations apply peak stresses uniformly across the thickness.

Fatigue usage in the high strain-low cycle region are primarily driven by high peak thermal transient stresses at the inside surfaces and significant through thickness stress gradients

Crack tip stress intensities will decrease as the crack grows through the pipe wall.

Longer Stage II fatigue life results when the gradient stress is used rather than when the peak stress is applied uniformly across the thickness.


Gradient Factor, GF

( )( ) ( )

I II Membrane

I Membrane II Gradient

N NGFN N

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

where:

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

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


Size Effects

Weak link statistical size effects – In this case a larger size is expected to have an increased

probability of a weak region or flaw of a given severity being present, and hence a lowered average fatigue strength.

– Accounted for in both ASME and NUREG/CR-6909 design curves Size effects related to crack growth in larger test

specimens (Dowling 1977)– Larger specimens of identical material and applied cyclic strain tend

to have longer fatigue lives due to the increased number of cycles required to propagate a crack across the specimen.

Any improved methods of predicting size effects should address both effects


Size Effects (ii)

Strength of material calculations were performed to estimate equivalent 25% load drop crack depths in thicker push-pull test specimens

2 1 21 1 1

2 1 22 2 2

sin ( )( )2

sin ( )( )2

YCrack Area R s s Y s RR

Ya s s Y s aa

1

2

2 2 2

22

22

1 4

Y Rs

Y as

Y a R aR


Size Effects (iii)


Life Factor, LF

(3 )3

25% (25%)

I II mmmm

I II

N NNLFN N N

A life factor LF corrects fatigue usage estimates for increased Stage II life associated with piping thicknesses greater than the 0.304 inch median gauge thickness associated with the NUREG/CR-6909 air test data.

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

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


Stage I Life

I Total IIN 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.


Carbon Steel Pin KI*

* Forman and Shivakumar (ASTM STP 905)


Carbon Steel Pin KJ/KI Correction

∆J is calculated using the expression for cylindrical fatigue specimens obtained by Dowling [1977]

Modified to include a geometric shape factor developed by O’Donnell and O’Donnell as referenced by Park and Chopra [2000] for crack depth approaching 40% through-wall

23.2 5

2 ( 1)pJ a a

E S

2 30.6911 1.2685 5.6638 21.511S

a a aFD D D

∆K is calculated using the pin expression developed by Forman and Shivakumar [1986]


Carbon Steel Pin KJ/KI Correction (ii)


Stage I - Stage II Transition = 0.575%

Temperature (°C)

1219 36.5%

Room Temp

0.304

0.008

0.118

3342

2123

2

3.00E+04

20

172.527

0.575

Node 330 Stage 1 Life = 0.575%

Initial Flaw Depth, a (inch)

Initial Aspect Ratio, L/a

Pin Diameter (inch)

Elastic Modulus (ksi)

25% Load Drop Crack Depth (inch)

Salt (ksi)

alt (%)

NUREG 6909 R1 50|50 S-N Life

Stage 1 Membrane Life

Stage II Membrane Life at 3-mm Crack Depth (Calculated)


Stage I - Stage II Transition = 0.575% (ii)

N/Nf = 0.365

(Gavenda et al. 1997)


Stage II Life for Pipe Crack growth of a mechanically

small crack (0.008 in.) to a crack depth associated with a 25% load drop

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

The alternating stress intensity K corrected for elastic-plastic material response in the HIGH strain LOW cycle region.


EXAMPLE APPLICATIONBWR 4 Low Pressure Core Spray System

Reducing Elbow


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 ¾” 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 for the

component thickness and the presence of through-wall stress gradients.


Node 330 60-yr Air and Water Fatigue Usages


Node 330 Membrane-to-Gradient Ratios

Sp = 345.054 ksi– Sm = 61.406 ksi– Sb = 1.609 ksi– Sg = 80.161 ksi– Ke = 2.410


Node 330 Life and Gradient Factor Calculation

Membrane m/g = 0.751

0.594 0.594

0.008 0.008

0.243 0.243

2 2

3.00E+04 3.00E+04

20 20

172.527 172.527

0.575 0.575

3342 3342

1219 12194572 6057

4934 6960

1.000 0.752

0.941 0.9410.941 0.708

Node 330 Load Set 4-6 LF and GF

LF x GF

Gradient Factor, GF

Initial Flaw Depth, a (in.)

Initial Aspect Ratio, L/a

Thickness (inch)

Elastic Modulas (ksi)

25% Load Drop Crack Depth (in.)

Temperature (°C)

Salt (ksi)

alt (%)

NUREG 6909 R1 50|50 S-N Life

Stage 1 Membane Life

Membrane Life Factor, LF

Stage 2 Life N3mm

Stage 2 Life N25%


Node 330 Projected 60 and 80 Usage Factors

Load Set

Load Pair Fen 60-yr Air

Usage60-yr Envir

Usage 80-yr Envir

Usage LF x GFCorrected60-yr Air Usage

Corrected 60-yr Envir

Usage

Corrected 80-yr Envir

Usage1 4-6 5.972 0.1260 0.7525 1.0033 0.7080 0.0892 0.5328 0.7103

2 11-12 1.740 0.0050 0.0087 0.0116 1.0000 0.0050 0.0087 0.0116

3 11-14 1.740 0.0190 0.0331 0.0441 1.0000 0.0190 0.0331 0.0441

4 4-5 7.330 0.0010 0.0073 0.0098 1.0000 0.0010 0.0073 0.0098

5 5-14 1.740 0.0040 0.0070 0.0093 1.0000 0.0040 0.0040 0.0053

0.155 0.809 1.078 0.118 0.586 0.781CUF :


Conclusions

Revision 1 to NUREG/CR-6909 – Updated fatigue life solutions– Test specimen gauge diameters ranged from 5.1 mm to 9.5 mm (0.2

inch to 0.375 inch). – Specimens were subjected to constant displacement cyclic loading

and failure was defined by 25% load drop. – Chopra and Stevens observed that this load drop criterion was

associated with an average 3 mm (0.118 inch) deep crack. – Independent strength of material calculations reported in this paper,

confirmed their observation. Stage I life estimates were consistent with data Results suggest that these Life and Gradient factors can result in

measurable reductions in estimated fatigue usage (especially in thicker piping).


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FATIGUE USAGE LIFE AND GRADIENT FACTORS ASME …

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