GRAPHITE DESIGN HANDBOOK - UNT Digital Library/67531/metadc708244/m2/1/high_re… · Material constants for H-451 graphite thermal conductivity ..... 4-17 during neutron irradiation

DOE-HTGR-88111 Revision 0 AUG 0 5 1991

. _ I . .....~ .. . . . . . - . . . . . .

GRAPHITE DESIGN HANDBOOK

AUTHORSICONTRACTORS

GENERAL ATOMICS

BUnON OF THIS DOCUMENT IS UNLlMmD

ISSUED BY GENERAL ATOMICS FOR THE DEPARTMEW OF ENERGY

CONTRACT DE-AC03-88SF17367

SEPTEMBER 1988

D 0 E- H TG R- 8 8 1 1 1 Revision 0 909597/0

p b 7 ~ rJ T shall be made of c ~ c A R G D DOE Patent Coun

7 - 4 - S (

GRAPHITE DESIGN HANDBOOK

DtSPRIBUflON OF THIS DOCUMENP IS UNLlMm

Thle daoument is

Issued By General Atomics P.O. Box 85608

San Diego, California 92138-5608

DOE CONTRACT DE-AC03-88SF17367

GA Project 6300

SEPTEMBER 1988

RoU 2\66 GA 1485 (REV 4/88) GENERAL ATOMICS

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908438 DOE-HTGR-86035

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LIST OF EFFECTIVE PAGES

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CONTENTS

LIST OF ILLUSTRATIONS . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . SYMBOLS. ACRONYMS. AND ABBREVIATIONS . . . . . . . . . . . . . . . 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . .

1.1. Objective . . . . . . . . . . . . . . . . . . . . . . . 1.2. Scope . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Applicability . . . . . . . . . . . . . . . . . . . . . 1.4. Organization of this Handbook . . . . . . . . . . . . . 1.5. Definition of Symbols and Acronyms . . . . . . . . . . . 1.6. References . . . . . . . . . . . . . . . . . . . . . . .

2 . RESPONSIBILITY AND AUTHORITY . . . . . . . . . . . . . . . . . 2.1. Responsibility . . . . . . . . . . . . . . . . . . . . . 2.2. Quality Assurance . . . . . . . . . . . . . . . . . . . 2.3. Reference . . . . . . . . . . . . . . . . . . . . . . .

3 . NUCLEAR GRADE 2020 GRAPHITE . . . . . . . . . . . . . . . . . 3.1. Description of Grade . . . . . . . . . . . . . . . . . . 3.2. Application . . . . . . . . . . . . . . . . . . . . . . 3.3. Cylindrical Nuclear Grade 2020 Graphite . . . . . . . .

3.3.1. Introduction . . . . . . . . . . . . . . . . . . 3.3.2. Physical and Chemical Properties . . . . . . . . 3.3.3. Thermal Properties . . . . . . . . . . . . . . . 3.3.4. Mechanical Properties . . . . . . . . . . . . . 3.3.5. References . . . . . . . . . . . . . . . . . . . Large Rectangular Nuclear Grade 2020 Graphite . . . . . . 3.4.1. Introduction . . . . . . . . . . . . . . . . . . 3.4.2. Physical and Chemical Properties . . . . . . . . 3.4.3. Thermal Properties . . . . . . . . . . . . . . . 3.4.4. Mechanical Properties . . . . . . . . . . . . . 3.4.5. References . . . . . . . . . . . . . . . . . . .

3.4.

V

vii

ix

1-1

1-1

1-1

1-2

1-2

1-2

1-2

2-1

2-1

2-1

2-1

3-1

3-1

3-2

3-2 3-2

3-3

3-8

3-14

3-27

3-30

3-30

3-30

3-36

3-42

3-54

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4 . GRADE H-451 GRAPHITE . . . . . . . . . . . . . . . . . . . . . 4 . 1 . Description of Grade . . . . . . . . . . . . . . . . . . 4.2 . Application . . . . . . . . . . . . . . . . . . . . . . 4.3 . Physical and Chemical Properties . . . . . . . . . . . .

4.3 .1 . Density . . . . . . . . . . . . . . . . . . . . 4.3.2. Transport and Reaction Rates . . . . . . . . . .

4.4. Thermal Properties . . . . . . . . . . . . . . . . . . . 4.4 .1 . Specific Heat . . . . . . . . . . . . . . . . . 4.4.2. Thermal Expansivity . . . . . . . . . . . . . . 4.4 .3 . Thermal Conductivity . . . . . . . . . . . . . . 4.4.4. Emissivity . . . . . . . . . . . . . . . . . . .

4 . 5 . Mechanical Properties . . . . . . . . . . . . . . . . . 4.5 .1 . Transversely Isotropic Linear Elastic

Constants . . . . . . . . . . . . . . . . . . . 4 . 5 . 2 . Stress-Strain Curve . . . . . . . . . . . . . . 4.5 .3 . Strength . . . . . . . . . . . . . . . . . . . . 4.5 .4 . Fracture Toughness and the Critical Defect

Size . . . . . . . . . . . . . . . . . . . . . .

4 - 1

4-1

4 - 1

4-2

4-2

4-2

4-8

4-8

4-8

4-14

4-19

4-19

4-19

4-24

4-24

4-33

4 . 5 . 5 . Effect of Oxidation on Mechanical Properties . . 4-33

4 . 6 . Neutron Irradiation Effects on Dimensions . . . . . . . 4-34

4 . 6 . 1 . Irradiation-Induced Dimensional Change . . . . . 4-34

4.6.2. Irradiation-Induced Creep . . . . . . . . . . . 4-40

4 . 7 . References . . . . . . . . . . . . . . . . . . . . . . . 4-47

LIST OF ILLUSTRATIONS

Figure Page

3.3-1 . Specific heat of graphite as a function of

3.3-2. Design curves for change in room temperature thermal resistivity of 2020 graphite as a function of irradiation conditions . . . . . . . . . . . . . . . . . 3-13

3 .3-3 . Design curves for change in elastic modulus of 2020 graphite as a function of irradiation conditions . . . . 3-17

3.3-4 . Tensile stress-strain curve fo r 2020 graphite . . . . . . 3-19

3 .3-5 . Compressive stress-strain curve f o r 2020 graphite . . . . 3-20

temperature . . . . . . . . . . . . . . . . . . . . . . . 3-9

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LIST OF ILLUSTRATIONS (Continued)

3.3-6. Spec i f i ed minimum b i a x i a l f a i l u r e s u r f a c e f o r 2020

3.3-7. Design f a t i g u e diagram of nuc lea r grade 2020 g r a p h i t e

g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . . 3-23

a t 99% s u r v i v a l p r o b a b i l i t y w i t h 95% confidence l e v e l . . 3-26

temperature . . . . . . . . . . . . . . . . . . . . . . . 3-37

3.4-2. Design curves f o r change i n room temperature thermal r e s i s t i v i t y of 2020 g r a p h i t e as a f u n c t i o n of i r r a d i a t i o n cond i t ions . . . . . . . . . . . . . . . . . 3-41

3.4-1. S p e c i f i c hea t of g r a p h i t e as a func t ion of

3.4-3. Design curves f o r change i n e l a s t i c modulus of 2020 g r a p h i t e as a f u n c t i o n of i r r a d i a t i o n cond i t ions . . . . 3-44

3.4-4. T e n s i l e s t r e s s - s t r a i n curve f o r 2020 g r a p h i t e . . . . . . 3-46

3.4-5. Comprehensive s t r e s s - s t r a i n curve f o r 2020 g r a p h i t e . . . 3-47

3.4-6. S p e c i f i e d minimum b i a x i a l s t r e n g t h s u r f a c e for 2020 g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . 3-51

3.4-7. Design f a t i g u e diagram of nuc lear grade 2020 g r a p h i t e a t 99% s u r v i v a l p r o b a b i l i t y w i t h 95% confidence l e v e l . . 3-53

4.4-1. S p e c i f i c hea t of g r a p h i t e a s a func t ion of tempera ture . . . . . . . . . . . . . . . . . . . . . . . 4-9

4.4-2. Thermal expansion of H-451 g r a p h i t e . . . . . . . . . . . 4-11

4.4-3. Change i n mean CTE of H-451 g r a p h i t e as a f u n c t i o n of i r r a d i a t i o n cond i t ions (865 t o 1205 K ) , a x i a l and r a d i a l dimensions . . . . . . . . . . . . . . . . . . . . 4-12

4.4-4. Change i n mean CTE of H-451 g r a p h i t e as a f u n c t i o n of i r r a d i a t i o n cond i t ions (1250 t o 1705 K ) , a x i a l and r a d i a l d i r e c t i o n s . . . . . . . . . . . . . . . . . . . . 4 - 1 3

4.4-5. Thermal conduc t iv i ty of H-451 g r a p h i t e as a f u n c t i o n

4.5-1. F r a c t i o n a l change i n e las t ic modulus of H-451 g r a p h i t e

of neut ron i r r a d i a t i o n . . . . . . . . . . . . . . . . . 4-20

as a func t ion of i r r a d i a t i o n cond i t ions . . . . . . . . . 4-23

4.5.2a. T e n s i l e s t r e s s - s t r a i n curve f o r H-451 g r a p h i t e , a x i a l o r i e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . 4-25

4.5.2b. T e n s i l e s t r e s s - s t r a i n curve f o r H-451 g r a p h i t e , r a d i a l o r i e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . 4-26

4.5.3a. Compressive s t r e s s - s t r a i n curve f o r H-451 g r a p h i t e , a x i a l o r i e n t a t i o n . . . . . . . . . . . . . . . . . . . . 4-27

4.5.3b. Compressive s t r e s s - s t r a i n curve f o r H-451 g r a p h i t e ,

4.5-4a. T e n s i l e s t r e s s - s t r a i n curve f o r i r r a d i a t e d H-451

r a d i a l o r i e n t a t i o n . . . . . . . . . . . . . . . . . . . 4-28

g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . 4-29

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LIST OF ILLUSTRATIONS (Continued)

4.5-4b. Compressive stress-strain curve for irradiated H-451 graphite . . . . . . . . . . . . . . . . . . . . . . . . 4-30

4.6-1. Design curves for dimensional change of H-451 graphite, axial orientation. as a function of irradiation conditions . . . . . . . . . . . . . . . . . . . . . . . 4-36

4.6-2. Design curves for dimensional change of H-451 graphite. radial orientation. as a function of irradiation conditions . . . . . . . . . . . . . . . . . . . . . . . 4-37

4.6-3. Maximum densification point and crossover point for irradiated H-451 graphite as a function of irradiation temperature . . . . . . . . . . . . . . . . . . . . . . . 4-39

LIST OF TABLES

Table

3.3-1.

3.3-2.

3.3-3.

3.3-4.

3.3-5.

3.3-6.

3.4-1.

3.4-2.

3.4-3.

3.4-4.

3.4-5.

3.4-6.

4.3-1.

4.3-2.

4.4-1. 4.4-2.

Summary of oxidation kinetic constants for nuclear 2020graphite . . . . . . . . . . . . . . . . . . . . . . Air-graphite reaction rate coefficients . . . . . . . . . Thermal conductivity of 2020 graphite . . . . . . . . . . Thermal resistivity constant F. used in Eq . 3.3-7 . . . . Percent increase (P) in elastic modulus as a function of fluence and temperature . . . . . . . . . . . . . . . . . Uniaxial fatigue strength limits for 2020 graphite . . . . Summary of oxidation kinetic constants for nuclear 2020graphite . . . . . . . . . . . . . . . . . . . . . . Air-graphite reaction rate coefficients . . . . . . . . . Thermal conductivity of 2020 graphite . . . . . . . . . . Thermal resistivity constant F. used in Eq . 3.4-8 . . . . Percent increase (P) in elastic modulus as a function of fluence and temperature . . . . . . . . . . . . . . . . . Uniaxial fatigue strength limits for 2020 graphite . . . . Constants for H-451 graphite oxidation rate equation . . . Air-graphite reaction rate coefficients . . . . . . . . . Thermal expansion of H-451 graphite . . . . . . . . . . . Temperature-dependent conductivity components of H-451graphite . . . . . . . . . . . . . . . . . . . . . .

Page

3-4

3-6

3-11

3-12

3-16

3-24

3-32

3-34

3-38

3-40

3-45

3-52

4-4 4-5

4-10

4-16

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LIST OF TABLES (Continued)

4.4-3 . Material constants for H-451 graphite thermal conductivity . . . . . . . . . . . . . . . . . . . . . . . 4-17

during neutron irradiation . . . . . . . . . . . . . . . . 4-22 equations: H-451 graphite . . . . . . . . . . . . . . . . 4-35

4.5-1. Percentage change in elastic modulus of H-451 graphite

4.6-1. Polynomial coefficients for dimensional change design

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SYMBOLS, ACRONYMS, AND ABBREVIATIONS

A a x i a l d i r e c t i o n

b

b

CR

cP CTE

pe rcen t g r a p h i t e burnoff

i n v e r s e of t h e c r y s t a l l i t e boundary spac ing (Eq. 4 - 6 )

c e n t r a l r e f l e c t o r

s p e c i f i c heat a t cons t an t p r e s s u r e

c o e f f i c i e n t of thermal expansion

DH20 DCO e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of carbon monoxide i n

e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of steam i n g r a p h i t e

g r a p h i t e

DH2 e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of hydrogen i n g r a p h i t e

e f f e c t i v e d i f f u s i o n c o e f f i c i e n t of oxygen i n g r a p h i t e Do2 d i r r a d i a t i o n damage parameter (Eq. 4 - 6 )

E elastic modulus ( s e e s e c t i o n s on mechanical proper- t i e s ) , may have s u b s c r i p t x, 2 , 1, o r 3

E J , j = 1, 2 , 3

E energy l e v e l (of neut ron)

Ac t iva t ion energy (see s e c t i o n s on o x i d a t i o n rates)

F f r a c t i o n a l i n c r e a s e i n thermal r e s i s t i v i t y due t o neut ron i r r a d i a t i o n

Fb* Fc modifying f a c t o r s f o r e f f e c t s of burnoffs and c a t a - l y s t s on ox ida t ion rates

G

GA

shea r modulus (see s e c t i o n s on mechanical p r o p e r t i e s ) , may have s u b s c r i p t x , 2 , 1, o r 3

General Atomics

i x DOE-HTGR-88111/Rev. 0

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K

Kb

Kd

KU

thermal conductivity

effect of the grain boundary scattering (Eq. 4 - 6 )

effect of the irradiation damage (Eq. 4 - 6 )

crystallite conductivity with Umklapp processing dominating

KIC fracture toughness

Kj, j = 1, 2, 3

kj, j = 1, 2, 3

chemical rate constant (see sections on oxidation rates)

Arrhenius frequency factor (see sections on oxidation rates)

MS steady-state mobility coefficient, also called steady- state creep coefficient

n exponent in the oxidation rate equation

ORNL Oak Ridge National Laboratory

P pressure

'H29 'H20

PSR permanent side reflector

local partial pressures of hydrogen and steam, respectively

QA quality assurance

R radial direction

R omax1 omin RT room temperature

r radial distance from the axis of a billet

S

STP

SU

suc

sut

mean strength

standard temperature and pressure

specified minimum ultimate strength

compressive Su

tensile Su

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T

ucs UTS

X

Z

z Y

Q

urnax, umin

r

temperature

irradiation temperature

ultimate compressive strength

ultimate tensile strength

fractional weight loss from oxidation (burnoff)

axial distance from midlength of a billet

thermal expansivity

strain, may have subscript x, y, or z

irradiation-induced creep strain

elastic strain

irradiation-induced dimensional change (stress-free)

steady state part of eC transient part of eC thermal strain

shear strain, may have subscript xy, yz, or zx

internal damping factor (see Section 3 . 3 . 4 . 6 )

Poisson’s ratio (see sections on mechanical properties), may have subscript 12 or 13

applied normal stress, may have subscript x, y, or z maximum and minimum applied stresses, respectively, during a cycle in fatigue tests

exponential relaxation time in units of neutron f luence

shear stress, may have subscript xy, yz, or zx

fast neutron fluence expressed as equivalent HTGS fast fluence, E > 29 fJ or equivalently E > 0.18 MeV relaxation time (Eq. 4 - 3 2 )

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1. INTRODUCTION

1.1. OBJECTIVE

The objectives of the Graphite Design Handbook (GDH) are (1) to

provide and maintain a single source of graphite properties and phenom-

enological model of mechanical behavior to be used for design of MHTGR

graphite components of the Reactor System, namely, core support, per-

manent side reflector, hexagonal reflector elements, and prismatic fuel

elements; ( 2 ) to provide a single source of data and material models for

use in MHTGR graphite component design, performance, and safety anal-

yses; ( 3 ) to present properties and equations representing material

models in a form which can be directly used by the designer o r analyst

without the need for interpretation and i s compatible with analytical

methods and structural criteria used in the MHTGR project; and ( 4 ) to

control the properties and material models used in the MHTGR design and

analysis to proper Quality Assurance standards and project requirements.

1.2. SCOPE

The Reactor System includes graphite parts in the reactor core,

reflector, and internals (Ref. 1-1). The reference graphite in the

reactor core and replaceable hexagonal reflector components is grade

H-451.

criteria for core graphite (Ref. 1-2).

These components are to be designed to meet the structural

The reference graphite in the reactor internals components is the

nuclear grade 2020. There are two subgrades of interest, the cylinder

nuclear grade and the large rectangular nuclear grade. The large rect-

angular nuclear grade is molded i n large rectangular blocks. It is the

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r e fe rence m a t e r i a l f o r t h e permanent s i d e r e f l e c t o r and the c e n t r a l co l -

umn suppor t s t r u c t u r e . The c y l i n d r i c a l nuc lea r grade i s i s o s t a t i c a l l y

pressed and is intended for use as t h e co re suppor t component. This

nuc lear grade is provided as c y l i n d r i c a l logs . Both components are

designed t o m e e t t h e s t r u c t u r a l c r i t e r i a f o r g r a p h i t e c o r e suppor t s

(Ref. 1 -3) . S ince t h e material p r o p e r t i e s of g r a p h i t e are dependent on

bo th p rocess and s i z e , the p r o p e r t i e s of t h e s e two subgrades are def ined

s e p a r a t e l y .

T h i s r e p o r t g ives the des ign p r o p e r t i e s for bo th H-451 and 2020

g r a p h i t e as they apply t o t h e i r r e s p e c t i v e c r i t e r i a . The p r o p e r t i e s

are p resen ted i n a form f o r design, performance, and s a f e t y c a l c u l a t i o n s

t ha t d e f i n e or v a l i d a t e t h e component design.

1.3. APPLICABILITY

The p r o p e r t i e s presented i n t h i s handbook are t h e r e fe rence proper-

t i e s t h a t are approved f o r use i n MHTGR des ign , performance, and s a f e t y

c a l c u l a t i o n s .

1.4. ORGANIZATION OF THIS HANDBOOK

( L a t e r )

1.5. DEFINITION OF SYMBOLS AND ACRONYMS

(Later)

1.6. REFERENCES

1-1. "Reactor System Design Desc r ip t ion , " DOE-HTGR-86035, Rev. 2 (GA

Document 908438/3) , A p r i l 1988.

1-2 DOE-HTGR-88111/Rev. 0

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1-2. "S tzuc tu ra l D e s i g n C r i t e r i a for R e p l a c e a b l e G r a p h i t e C o r e E l e -

m e n t s , " DOE-HTGR-88150 , R e v . 0 (GA D o c u m e n t 9 0 9 7 2 9 / 0 ) , A u g u s t

1988.

1-3. "Proposed Sec t ion 111, D i v i s i o n 2, ASME B o i l e r and Pressure V e s s e l

C o d e , Subsect ion C E , D e s i g n R e q u i r e m e n t s f o r G r a p h i t e Core Sup-

p o r t s , " A p r i l 1984.

1-3 D O E - H T G R - 8 8 1 1 1 / R e v . 0

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2.1.

2. RESPONSIBILITY AND AUTHORITY

RESPONSIBILITY

Responsibility for maintaining this document is vested in General

Atomics.

2.2. QUALITY ASSURANCE

All structures and components that are designated as "safety-

related" shall come under a Quality Assurance Program which fully

complies with the requirements of Title 10 of the Code of Federal Regu-

lations Part 50 (10CFR50), Appendix B. The basic requirements and sup-

plements of ANSI/ASME NQA-1 (as endorsed by USNRC Regulatory Guide 1.28,

Revision 3) shall be implemented for activities that affect the quality

of such items. The core supports, permanent side reflectors, hexagonal

reflector elements, and prismatic fuel elements are "safety-related"

structures and components (Ref. 2-1). Therefore, the graphite used

in these structures and components is "safety-related."

2.3. REFERENCE

2-1. "Equipment Classification List for the Modular High Tempera-

ture Gas-Cooled Reactor," DOE-HTGR-86032, Rev. 2 (GA Document

908792/2), July 1987.

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3 . NUCLEAR GRADE 2020 GRAPHITE

3 . 1 . DESCRIPTION OF GRADE

There are two subgrades of nuclear grade 2020 graphite used for the

reactor internals components, the large rectangular nuclear grade and

the cylindrical nuclear grade. The large rectangular grade 2020 graph-

ite is a fine-grained, molded artificial graphite produced in large

rectangular blocks. It is the reference material for permanent side reflectors and central reflector column support blocks. To date, the

largest log fabricated and tested was 1.067 m ( 4 2 in.) long x 0.914 m

( 3 6 in.) wide x 0.457 m (18 in.) thick. The log intended for use as

central reflector column support blocks and permanent side reflector

column supports at the entrance of the hot duct will be slightly larger

than the above. For preliminary design analysis, the properties of the

log tested are assumed to apply to the larger size (until such time as

the experimental data are available).

The cylindrical nuclear grade 2020 graphite is a fine-grained, iso-

statically molded artificial graphite produced in cylindrical logs. The nuclear grade differs from the off-the-shelf commercial grade only in

that the raw material has been carefully controlled in impurity content,

hence its oxidation characteristics improved. All other material prop-

erties are nearly identical to those of a commercial grade of the same

size log. Nuclear grade is the reference material for the core support

structure, including the post block, post and lower plenum floor block.

The log tested (except oxidation rate) was a commercial grade of 1.98 m

( 7 8 in.) long x 0.254 m (10 in.) in diameter. The properties of the

cylindrical log varied somewhat with axial position along the log

because one end has a higher density than the other.

3- 1 DOE-HTGR-881111Rev. 0

90959710

For t h e p r e s e n t , un le s s o therwise noted, des ign d a t a g iven he rea f -

t e r w e r e der ived from a 0.254 m (10 i n . ) diameter log .

3.2. APPLICATION

Appl i ca t ion of 2020 grade g r a p h i t e t o t h e r e a c t o r i n t e r n a l s

components is summarized below:

1. Large r ec t angu la r nuc lear grade: permanent s i d e r e f l e c t o r

(PSR), PSR suppor t b lock a t t h e en t r ance of t h e h o t duc t and

c e n t r a l r e f l e c t o r column suppor t s t r u c t u r e .

2. C y l i n d r i c a l nuc lea r grade: pos t b lock , T-post , and lower

plenum f l o o r block.

3.3. CYLINDRICAL NUCLEAR GRADE 2020 GRAPHITE

3.3.1. I n t r o d u c t i o n

The nuc lea r 2020 g r a p h i t e p r o p e r t i e s are c o n s i s t e n t w i t h t h e

s t r u c t u r a l c r i te r ia f o r g r a p h i t e c o r e suppor ts (Ref. 3 .3-1) . Unless

o therwise noted, t h e mater ia l p r o p e r t i e s g iven below f o r t h e nuc lear

grade 2020 are mean va lues .

The m a x i m u m p red ic t ed f a s t neut ron f luence t o t h e g r a p h i t e c o r e

suppor t s t r u c t u r e is 2 x 1023 n/m2 ( E > 29 f J , HTGR), which i s l e s s t han

1% of t h e maximum f luence accumulated by f u e l element g raph i t e . Experi-

ence w i t h f u e l element g r a p h i t e has shown t h a t on ly e l a s t i c modulus and

thermal conduc t iv i ty w i l l be no t i ceab ly a f f e c t e d by a t o t a l f a s t neut ron

f luence of 5 x n/m2. Therefore , i r r a d i a t i o n e f f e c t s on o t h e r

p r o p e r t i e s descr ibed below a r e i n s i g n i f i c a n t and not d i scussed .


90959710

3.3.2. Phys ica l and Chemical P r o p e r t i e s

3.3.2.1.

averaged over t h e log (Refs. 3.3-2 and 3.3-3) .

Densi ty . The bulk d e n s i t y of 2020 g r a p h i t e is 1.78 Mg/m3

3.3.2.2. Transpor t and React ion Rates .

3.3.2.2.1. Steam-Graphite Oxidat ion Rates . The Langmuir-

Hinshelwood equa t ion , E q . 3.3-1, is used t o p r e d i c t s team-graphi te

o x i d a t i o n r a t e s f o r nuc lear grade 2020 g r a p h i t e (Ref. 3 .3-4) :

(3 .3-1)

where Rate = l o c a l g r a p h i t e mass f r a c t i o n r e a c t i n g pe r second,

P H ~ , P H ~ O = l o c a l p a r t i a l p re s su res of hydrogen and steam,

r e s p e c t i v e l y ,

Fb = modif ie r f o r e f f e c t s of bu rnof f ,

n = exponent,

where j = 1, 2, or 3,

k j = Arrhenius frequency f a c t o r ,

E j = a c t i v a t i o n energy,

R = 8.314 J/mole*K.

The va lues of K 1 , K2, K3, and n given i n Table 3.3-1 a r e based on d a t a

f o r t h e tempera tures i n d i c a t e d . U n t i l d a t a a t o t h e r tempera tures are

a v a i l a b l e , it is assumed t h a t k j i n Table 3.3-1 can be e x t r a p o l a t e d t o

o t h e r temperatures .

For pre l imina ry des ign , Fb is t h e same as t h a t used t o p r e d i c t

burnoff e f f e c t s f o r steam ox ida t ion of H-451 g r a p h i t e ( u n t i l such t ime


909597 / O

TABLE 3.3-1 SUMMARY OF OXIDATION KINETIC CONSTANTS FOR

NUCLEAR 2020 GRAPHITE

980 1.3 8.7E-10 1.I.E-3 2.6 - 8.7E-4 7.2E-9 9.OE-3 8.J.E-2

930 1.3 3.8E-10 1.6E-3 3.8 - 16E-4 2.3E-9 9.5E-3 1.7E-1

900 1.3 2.OE-10 2.OE-3 2.0 - 4.OE-4

,


909597 / O

a s a d d i t i o n a l 2020 g r a p h i t e o x i d a t i o n d a t a a r e a v a i l a b l e ) . The oxida-

t i o n r a t e of t h e nuc lear grade 2020 g r a p h i t e i s about o n e - f i f t h t h a t of

H-451 g r a p h i t e .

3.3.2.2.2. Air-Graphi te React ion Rates . The r a t e of o x i d a t i o n of

g r a p h i t e by a i r is

Rate = K

where Rate = l o c a l

l o c a l

g iven by Eq. 3.3-2 (Ref. 3 .3-8) :

g r a p h i t e mass f r a c t i o n r e a c t i n g p e r second ( S I ) o r

g r a p h i t e m a s s f r a c t i o n r e a c t i n g p e r hour ( u n i t s

normally used i n OXIDE code c a l c u l a t i o n s ) ,

Po2 = l o c a l p a r t i a l p r e s s u r e of oxygen.

Table 3.3-2 g ives t h e system of u n i t s der ived from H-327 exper imenta l

da t a . I t is assumed t h a t t h e a i r - g r a p h i t e r e a c t i o n r a t e of H-451 i s

i d e n t i c a l t o t h a t of H-327.

S ince t h e r e a r e no experimental d a t a on a i r - g r a p h i t e r e a c t i o n

r a t e r epor t ed for t h e grade 2020 g r a p h i t e , Eq. 3.3-2, t o g e t h e r w i t h

Table 3.3-2, s h a l l be used.

t o be modif ied by a f a c t o r equal t o t h e r a t i o of t h e s team-graphi te

oxidation rate of nuclear grade 2020 graphite to that of H - 4 5 1 graphite

a t t h e environmental cond i t ions of i n t e r e s t .

The va lue of K g iven i n Table 3.3-2 needs

3.3.2.2.3. R a d i o l y t i c E f f e c t on Oxidat ion Rate. The a v a i l a b l e

exper imenta l d a t a show t h a t t h e r e is a s m a l l and n e g l i g i b l e r a d i o l y t i c

e f f e c t on o x i d a t i o n r a t e i n a i r ( s e e d i s c u s s i o n i n S e c t i o n 4 .3 .2 .3) .

3-5 DOE-HTGR-88111/Rev, 0

9 0 9 5 9 7 / 0

TABLE 3.3-2 AIR-GRAPHITE REACTION RATE COEFFICIENCTS (a)

Systems of Units K E T R

SI 0.79 1.7 105 K 8.314 ( s *pa) -1 J /mol K J /mo 1 * K

OXIDE code 2.88 x 1O1O 4.06 104 K 1.986 ( % h* atm) -1 cal/mol cal / mo 1 - K

(a)See text for the appropriate values to be used in Eq. 3.3-2 for nuclear grade 2020 graphite.


909597 / O

3.3.2.2.4. Transport of Steam in Helium by Diffusion. The effec-

tive diffusion coefficient of steam in graphite is given by Eq. 3.3-3

(Refs. 3.3-5 through 3.3-7):

(3.3-3)

where D H ~ O = effective diffusion coefficient through graphite,

T = temperature (K), P = pressure at STP" (pa),

PtOta1 = total pressure (Pa).

A parameter such as diffusion through graphite is recognized to

vary by as much as a factor of three from sample to sample or from

position to position in the graphite block. Equation 3.3-3 describes

the present best estimate for H20 diffusion in graphite having 1%

average oxidation burnoff.

Equation 3.3-3 was obtained by pooling all available experimental

data on steam diffusion through graphite in helium. No corrections were made for the differences in porosity and pore structure. Equation 3.3-3

is assumed to be applicable to all reference HTGR graphites.

The effective diffusion coefficients recommended for carbon monox-

ide, oxygen, and hydrogen are as follows (until such time as experimen-

tal data are available):

9

DH2 = 2DH20 (3.3-4)

~

"STP - standard temperature and pressure.


909597/0

3.3.2.2.5. Transport of Steam i n Helium by Convection. The t r a n s -

p o r t of steam by convect ion involves t h e permeation of g r a p h i t e .

pe rmeab i l i t y c o e f f i c i e n t s of g r a p h i t e (Ref. 3.3-29) are:

The

KI = 1.55E-13 m2 ,

Kp = 9.20E-14 m2 ,

where t h e s u b s c r i p t s r ep resen t t h e fo l lowing reg ions of t h e hexagonal

g r a p h i t e b locks :

I = i n t e r i o r r eg ion c o n s i s t i n g of a hexagonal b lock having an a r e a

i n the p lane of t h e hexagon one-seventh of t h e corresponding

a r e a of t h e e n t i r e block,

P = per iphe ry r eg ion c o n s i s t i n g of t h e e n t i r e hexagonal block

minus t h e i n t e r i o r region.

The va lues of KF and Kp are der ived from d a t a on H-327 g r a p h i t e ; t hey

are assumed t o apply t o 2020 g r a p h i t e ( u n t i l such t i m e as exper imenta l

d a t a are a v a i l a b l e ) .

3.3.3. Thermal P r o p e r t i e s

3.3.3.1.

a t u r e range 250 t o 3000 K is given by Eq. 3.3-5 (Ref. 3 .3-9) :

S p e c i f i c Heat. The s p e c i f i c hea t of g r a p h i t e over t h e temper-

Cp = (0.54212 - 2.42667 x T - 90.2725 T'l

- 4.34493 x l o 4 T'2 + 1.59309 x l o 7 T-3

- 1.43688 x l o 9 T-4) x 4184 ,

where Cp = s p e c i f i c hea t a t cons t an t p r e s s u r e (J /kg-K),

T = t empera ture ( K ) .

(3 .3-5)

Equation 3.3-5 is a l s o presented g r a p h i c a l l y i n Fig. 3.3-1.


W I u)

1 1 I I I I I I I I I 1 I I 1 I I

I I I 1 1 I I 1 I I I I I 1 I 1 I

I I i 300 400 600 600 700 8Bol 988 lBBB llBB 1200 1300 1400 1600 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000

T E M P E R A T U R E , T ( K )

Fig . 3.3-1 Spec i f ic H e a t of Graphite as a Funct ion of Tmperature

0 W ul W 4 \ 0

0

909597 / O

3.3.3.2. Thermal Expansivity. The thermal expansivity of 2020 graphite

is given below (Ref. 3.3-10):

a = A + B (AT) , (3.3-6)

where a = CTE (l/"C),

AT = temperature increase above room temperature (OC), A = 0.3075 x in the radial direction,

= 0.3225 x in the axial direction,

B = 1.078 x in the radial direction,

= 1.167 x 10-9 in the axial direction.

3.3.3.3. Thermal Conductivity. The thermal conductivity of unirradi-

ated 2020 graphite is given in Table 3.3-3 as a function of measurement

temperature (Ref. 3.3-3). The change in thermal conductivity of irradi-

ated 2020 graphite at irradiation temperature is given in Eq. 3.3-6

(Ref. 3.3-11).

1 1 F + - - - - Ki(T) Ko(T) K0(295 K) ' (3.3-7)

where Ki(T) = thermal conductivity of irradiated graphite at temper-

ature T (K),

Ko(T) = thermal conductivity of unirradiated graphite at tem-

perature T (K) (derived from Table 3.3-3),

K0(295 K) = thermal conductivity of unirradiated graphite at room

temperature,

F = fractional increase in thermal resistivity due to

neutron irradiation (fluence dependence is given in

Table 3.3-4 and Fig. 3.3-2).

3-10 DOE-HTGR-88111/Rev. 0

90959710

TABLE 3.3-3 THERMAL CONDUCTIVITY OF 2020 GRAPHITE

Conductivity at Measurement Temperature (W/m*K)

Orientation 295 K 473 K 673 K 873 K 1073 K

Radial 62.4 67.2 57.2 49.8 43.9

Axial 63.0 63.7 53.7 45.2 40.8

3-11 DOE-HTGR-88111/Rev, 0

9 0 9 5 9 7 / 0

TABLE 3.3-4 THERMAL RESISTIVITY CONSTANT F, USED IN EQ. 3.3-7

Irradiation Temperature (K) Fast Neutron Fluence

(1022 n/rn2) 673 873 1073

0.4

1

4

10

20

~ ~~

0.075 0.0885 0.0215

0.125 0.063 0.036

0.27 0.138 0.078

0.445 0.225 0.124

0.665 0.33 0.185

3-12 DOE-HTGR-881111Rev. 0

909597 /O al U

d c a

m

&

M

0

N

0

N

rcl

0

x

U

d

> r(

U

rn r( rn aJ &

rl

Ll aJ c

aJ Ll 3

U

a

kr

n

aJ

c

a0

Ed

a

Ju

Ud

00

o

v

Ll C

c

o

rld

U

aJ

a

Md

ea

a

a

S&

VL

l

d

!-I o

lu

wo

rn

c

aJ

0

>?

I

Llu

3

u

vc

2

clu

M

+

a

rn aJrn

U

E2

na

CJ I W

r)

M

9-l kl

3 'AlIA

IlSfS

3tl lVW

tf3H13tlrllV

tl3dW31 W

OOtl NI 3SV3tl3N

I 1VN

0113VtlJ

3- 13 DOE-HTGR-88111/Rev.

0

909597 / O

The t a b u l a t e d d a t a on F were e s t a b l i s h e d from a n a l y s i s of expe r i -

mental d a t a measured on misce l laneous g r a p h i t e s . U n t i l such t i m e a s

2020 g r a p h i t e thermal conduc t iv i ty d a t a under low i r r a d i a t i o n l e v e l

are a v a i l a b l e , it i s assumed t h a t Table 3.3-4 i s a p p l i c a b l e t o 2020

g raph i t e .

For o t h e r f a s t f l uences , a l i n e a r r e l a t i o n s h i p may be used between

logar i thms of F and f a s t f luence . An approximately l i n e a r r e l a t i o n s h i p

a l s o ex is t s between T and logar i thm of F.

Thermal annea l ing on thermal conduc t iv i ty appears t o begin a t

1273 K and is completed by 1573 K (Refs . 3.3-12 and 3.3-13). I n t h i s

tempera ture range t h e f r a c t i o n a l change i n conduc t iv i ty is c l o s e t o

l i n e a r l y p r o p o r t i o n a l t o temperature . The f r a c t i o n a l i n c r e a s e i n

thermal r e s i s t i v i t y , F , i n E q . 3.3-7 i s assumed t o l i n e a r l y dec rease

t o ze ro over t h e above temperature range.

3.3.3.4. Emiss iv i ty . The e m i s s i v i t y of 2020 g r a p h i t e f o r machined

s u r f a c e i s 0.85 (Refs . 3.3-14 through 3.3-16).

3.3.4. Mechanical P r o p e r t i e s

3 . 3 . 4 . 1 . Transverse ly I so t rop ic Linear E l a s t i c Constants . The

mechanical p r o p e r t i e s of 2020 g r a p h i t e can be modeled as t r a n s v e r s e l y

i s o t r o p i c . The i s o t r o p i c p l ane is i n t h e a c r o s s g r a i n d i r e c t i o n of an

i s o s t a t i c a l l y molded c y l i n d r i c a l g r a p h i t e log . The wi th -g ra in d i r e c t i o n

i s t h e a x i a l d i r e c t i o n , and is l a b e l l e d as t h e 3-ax is . The f i v e inde-

pendent parameters i n t h e t r a n s v e r s e l y i s o t r o p i c l i n e a r e l a s t i c m a t e r i a l

are two e l a s t i c moduli , E 1 and E3; shea r modulus, G I ; and two Poisson ' s

r a t i o s , ~ 1 2 and "13.

3- 14 DOE-HTGR-88111/Rev. 0

909597 / O

The properties given below are the average of the combined tensile

and compressive moduli at room temperature. The difference between two

moduli is less than 10% (Refs. 3.3-2, 3.3-3 and 3.3-17 through 3.3-19):

E1 = 9.5 GPa,

E3 = 8.9 GPa,

GI = 4 .1 GPa,

"12 = "13 = 0.15.

The elastic moduli given above are the secant moduli of the second

loading curve between 0 and 6.9 MPa.

The following modulus/temperature relationship applies to El, E3, and GI, but not 2/12 and "13 (Ref. 3.3-20):

C(T) = cRT - 9.94 x 10-4 (T - 21) + 3.09 x (T - 21)2 , (3 -3-8)

where CRT = El, Eg, or GI at room temperature (GPa),

T = temperature ("C),

C(T) = El, E3, or GI at temperature T (GPa).

T h e relationship is valid up to 1100°C.

The moduli increase with fast neutron irradiation. The percent

increase (P) is given in Table 3.3-5 as well as plotted in Fig. 3.3-3 as a function of neutron fluence and irradiation temperature (Ref. 3.3-21).

To calculate modulus (Ei) at any point during neutron irradiation, the

following equation applies:

Ei = Eo (1 + P/100) ,

3-15

(3.3-9)


909597 / O

TABLE 3.3-5 PERCENT INCREASE (P) IN ELASTIC MODULUS AS

A FUNCTION OF FLUENCE AND TEMPERATURE

Irradiation Temperature Fast Neutron Fluence (K)

(1022 n/m2) 6 73 873 1173

1 4.3 3.1 2.3

4 13.3 9.8 7.4

10 24.0 18.3 13.9

3-16 DOE-HTGR-88111/Rev. 0

0

52

N 0

c

c

3-17 DOE-HTGR-8811l/Rev.

0

9 0 9 5 9 7 / 0

where Eo = elastic modulus of unirradiated graphite at room

temperature,

P =(; - 1) x 100,

Ei = elastic modulus of irradiated graphite measured at room

temperature.

For P at irradiation temperature and fast neutron fluence other than that given in Table 3 . 3 - 5 , the following relationship applies:

1.

2 . Logarithm of P is a quadratic function of temperature ("C). Logarithm of P is a quadratic function of logarithm of $.

3 . 3 . 4 . 2 . Stress-Strain Curve. Typical room temperature (RT) tensile and compressive stress-strain curves for 2020 graphite are shown in

Figs. 3 . 3 - 4 and 3 . 3 - 5 , respectively (Refs. 3 . 4 - 2 , 3 . 4 - 3 , and 3 . 4 - 2 2 ) .

The curves are applicable to a nonlinear design analysis.

Typical RT tensile and compressive stress strain curves when com- pared in the stress range below the specified minimum ultimate tensile strength (Sut in Section 3 . 3 . 4 . 3 ) are slightly deviated from each other

by less than one "within log" standard deviation. For practical purpose

in the design analysis, the typical RT compressive stress strain curve can be considered as the same as the tensile curve when the maximum

stress is expected to be lower than Sut. The above assumption is not

valid for test evaluation'on component failure.

3 - 18 DOE-HTGR-88111/Rev. 0

909597/0

0 0.1 0.2

STRAIN (%)

0.3

Fig. 3.3-4 T e n s i l e stress-strain curve for 2020 graphite

3-19 DOE-HTGR-8811l/Rev. 0

909597/0

80

60

40

20

0 0 1 2 3

STRAIN (%)

Fig. 3.3-5 Cmpressive stress-strain curve for 2020 graphite

3-20 DoE-11ER- 8 8 11 1 /Rev. 0

909597 / 0

3.3.4.3. Strength.

Specified Minimum Ultimate Strength (Su). Specified minimum ulti-

mate strength is the uniaxial strength along a principal stress direc-

tion which is used in design analysis to measure the structural integ-

rity of a given core support graphite component against the design and

accident condition stresses. Per ASME Code Subsection CE (Ref. 3.3-l),

specified minimum strength is established from statistical treatment of

graphite strength data such that the survival probability is 99% with a

confidence level of 95%.

For unirradiated 2020 graphite at room temperature along the mate-

rial axes the specified minimum tensile strength (Sut) (Refs. 3.3-2,

3.3-3, and 3.3-17 through 3.3-19):

Sut = 14.7 MPa in the axial direction , ,16.1 MPa in the radial direction .

The specified minimum compressive strength (Suc) is

Suc = 51.0 MPa in the axial direction , 52.5 MPa in the radial direction .

In the off-axis case, the following Hankinson’s formula is

recommended for use:

14.7 x 16.1 S,t(d> = MPa , (3.3-10)

14.7 sin2 e + 16.1 e

where 8 is the angle between the direction of the principal stress and the axial (material) axis.

Both SUt and Suc may be assumed to increase with temperature and

neutron fluence identical to that for UTS (until such time as the

3-21 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

experimental data are available). The relationship is (Refs. 3.3-20 and

3.3-21)

Su(T) = [(S,)RT + 0.00392 (T - 2 9 4 ) ] (Ei/EO)lI2 7 (3.3-11)

where (S,)RT = room temperature unirradiated Sut (MPa),

T = temperature (K),

Ei = modulus of irradiated graphite at room temperature

(GPa) ,

Eo = modulus of unirradiated graphite at room temperature

(GPa) 9

S,(T) = S, of unirradiated 2020 at temperature T (MPa).

Specified Minimum Biaxial Strength. In the biaxial stress state,

the Coulomb-Mohr theory, modified to include a maximum tensile strength

cutoff, is the failure theory currently recommended for graphite

(Ref. 3.3-23). This theory defines that the maximum principal stress

governs failure in the first and third stress quadrants. In the second and fourth quadrants, the maximum principal stress or the Coulomb-Mohr

theory, whichever is more restrictive, is applied.

The specified minimum biaxial strength surface is established sim-

ilar to that of the above failure surface. The surface is given in

Fig. 3.3-6. Caution is required when using the biaxial strength in the

third quadrant. Early failure may occur in other modes prior to biaxial

compressive failure. Minimum values are determined by the ASME rules of

Ref. 3.3-1.

Fatigue Strength. The normalized fatigue strength (normalized with

respect to mean strength) is defined in Table 3.3-6 (Ref. 3.3-24) as a


909597/0

A X I A L Su. MPa

(-52.5, 0.)

20 (-37.8, 14.7)

8 / 10

-50 -40 -30 -20 -1 0 0

-10

-20

-30

-40

-5n

(-52.5, -51.0)

- (16.1, 14.7)

I 10

/ (0, -51 -0)

I 20

R A D I A L Su, MPa

(1 6.1, -34.9)

Fig. 3.3-6 Specified Minimum Biaxial S t r e n g t h Surface for 2020 Graphite

3-23 DOE-HTGR-88111/Rev. 0

909597 / O

TABLE 3.3-6 UNIAXIAL FATIGUE STRENGTH LIMITS FOR 2020 GRAPHITE

~ ~~ ~ ~~

Fatigue Strength Limits, Peak Stress/Mean Strength

R Number of 99/95 Lower Orientation (amin/gmax) Cycles 50% Survival Tolerance Limit

Axial 0

Radial

-1

-2

0

-1

-2

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100 1,000

10,000

100,000

100

1,000

10,000

100,000

0.87

0.83

0.80

0.76

0.84

0.79

0.74

0.70

0.85

0.80

0.75

0.71

0.86

0.81

0.77

0.73

0.79 0.73

0.68

0.63

0.81

0.76

0.71

0.66

0.69

0.66

0.63

0.60

0.66

0.62

0.58

0.54

0.66

0.62

0.58

0.55

0.71

0.67

0.64

0.60

0.61

0.56

0.52

0.48

0.66

0.61

0.57

0.53

3-24 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 1 0

function of stress ratio (R) and number of cycles. Survival is shown up

to l o5 cycles under uniaxial cyclic loading in air at ambient tempera-

ture. Mean strength of graphite, as well as fatigue strength, increases

with fast fluence and temperature in the range of interest. However, it

is assumed that normalized fatigue strength remains constant for the

design use.

The design fatigue diagram can be used to interpolate the fatigue

strength at other R ratios (Fig. 3 . 3 - 7 ) .

3 . 3 . 4 . 4 . Fracture Toughness and the Critical Defect Size. Fracture

toughness of unirradiated 2020 graphite at room temperature is

(Ref. 3 . 3 - 2 5 ) :

KIC = 1.25 MPa 6 .

The calculated critical defect size is 0.6 mm.

The reduction of KIC with oxidation follows the relationship

where x = fractional weight loss due to oxidation and the subscript "0"

represents the unoxidized state.

remains unchanged with oxidation.

The calculated critical defect size

3 . 3 . 4 . 5 . Effect of Oxidation on Mechanical Properties. The reduction

in tensile strength (S) and elastic modulus (E) is assumed to be the same for the commercial and the nuclear 2020 grades, which may be

represented by the following relationship (Refs. 3.3-26 and 3 . 3 - 2 7 ) :

E - = exp (-lox) , S - - - so Eo

3-25

( 3 . 3 - 1 3 )


90959710

Fig. 3.3-7. Design fatigue diagram of nuclear grade 2020 graphite at 99% survival probability with 95% confidence level


909597/0

where x = fractional weight loss due to oxidation and the subscript "0"


For the preliminary calculation on the component subjected to

external loads, it may be conservatively assumed that any portion of

graphite that oxidized to 20.1% loses its entire strength.

3.3.4.6. Material Internal Damping Factor. The internal damping factor

c, defined as the ratio of actual damping to critical damping is dependent on the stress amplitude. At a stress amplitude of 7.35 MPa, c is equal to 0.596% (Ref. 3.3-28). This i s for 0.5 Sut, approximately the

99/95 endurance limit.

c decreases only by 12%. When the stress amplitude is reduced to half,

3.3.5. References

3.3-1.

3.3-2.

3.3-3.

3.3-4.

3.3-5.

3.3-6.

"Proposed Section 111, Division 2, ASME Boiler and Pressure

Vessel Code, Subsection CE, Design Requirements for Graphite

Core Supports," April 1984.

Engle, G. B., "Properties of Unirradiated HTGR Core Support and

Permanent Side Reflector Graphites: PGX, HLM, 2020, and H-440N," ERDA Report GA-A14328, May 1977. Engle, G. B., and L. A. Beavan, "Properties of Unirradiated Graphites PGX, HLM, and 2020 for Support and Permanent Side Reflector LHTGR Components," DOE Report GA-A14646, June 1978.

Burnette, R. D., and G. R. Hightower, "Oxidation Kinetics of SC 2020 Graphite Nuclear Grade, Lot 1," GA Document 908038/0,

May 31, 1985.

Peroomian, M. B., A. W. Barsell, and J. C. Seager, "OXIDE-3: A

Computer Code for Analysis of HTGR Steam or Air Ingress Acci-

dents," GA Report GA-A12493 (GA-LTR-7), January 15, 1974.

Burnette, R. D., et al., "Studies of the Rate of Oxidation of ATJ Graphite by Steam," in Proceedings of 13th Biennial Confer-

ence on Carbon at Irvine, California, July 13-22, 1977.

3-27 DOE-HTGR-88111/Rev. 0

909597 / O

3.3-7.

3.3-8.

3.3-9.

3-3-10.

3 3-11.

3-3-12,

3.3-13.

3-3-14.

3.3-15.

3.3-16.

3-3-17.

3-3-18,

"HTGR Fuels and Core Development Program, Quarterly Progress

Report for the Period Ending August 31, 1977," ERDA Report GA-A14479, September 1977, p. 11-16.

Jensen, D., M. Tagami, and C. Velasquez, "Air/H-327 Graphite

Reaction Rate as a Function of Temperature and Irradiation," GA

Report Gulf-GA-A12647, September 24, 1973.

Butland, A. T. D., and R. J. Maddison, "The Specific Heat of Graphite: An Evaluation of Measurements," Journal of Nuclear

Material, - 49, 45 (1973-1974).

"Graphite Data Manual," DOE-HTGR [LATER], to be issued. Price, R. J., "Review of the Thermal Conductivity of Nuclear

Graphite under HTGR Conditions," GA Report Gulf-GA-A12615,

September 1973.

Engle, G. B., and K. Koyama, "Dimensional and Property Changes of Graphites Irradiated at High Temperatures," Carbon, - 6,

p. 455, 1968. Kelly, B. T., et al., "The annealing of Irradiation Damage in Graphite," Journal Nuclear Materials, 20, p. 195, 1966.

Grenis, A. F., and A. P. Levilt, "The Spectral Emissivity and Total Normal Emissivity of Commercial Graphites at Elevated Temperatures,' Proceedings of Fifth Conference on Carbon,

p. 639, 1961.

Plunkett, J. D., and W. D. Kingery, "The Spectral and Inte- grated Emissivity of Carbon and Graphite," Proceedings of

Fourth Carbon Conference, p. 457, 1960.

Autio, G. W., and E. Scula, "The Normal Spectral Emissivity of

Isotropic and Anisotropic Materials," Carbon, 6, pp. 13-28, 1966.

"HTGR Fuels and Core Development Program. Quarterly Progress

Report for the Period Ending February 28, 1977," ERDA Report

GA-A14298, March 1977.

"HTGR Generic Technology Program, Semiannual Report for the

Period Ending September 30, 1979," DOE Report GA-A15606,

November 1979.

3-28 DOE-HTGR-88111/Rev. 0

909597 / O

3-3-19.

3.3-20.

3-3-21.

3.3-22.

3 3-23

3-3-24.

3 3-25

3.3-26.

3-3-27.

3.3-28.

3 3-29

"HTGR Generic Technology Program, Semiannual Report f o r t h e

Per iod Ending September 30, 1980," DOE Report GA-A16127,

November 1980.

H o , F. H . , and E. Chin, " T e s t Evalua t ion Report of t h e Ther-

m a l S t r e s s (TIS) Test f o r Core Support Graphi te , " Document

904445/B, August 12, 1980.

P r i c e , R. J . , "Mechanical P r o p e r t i e s of Graphi te of High-

Temperature Gas-Cooled Reactors : 19 Review," ERDA Report

GA-A13524, September 22, 1975.

P r i c e , R. J . , "Test Report: Instrumented B e a m T e s t s on 2020

Graph i t e , " GA Document 906550, I s s u e 1, June 1982.

H o , F. H . , e t a l . , "B iax ia l F a i l u r e Sur faces of 2020 and PGX

Graph i t e s , " Paper No. L4/6, P. 127, T ransac t ions of t h e 7 t h

I n t e r n a t i o n a l Conference on S t r u c t i i r a l Mechanics i n Reactor

Technology, Chicago, I L , August 22 , 1983.

P r i c e , R. J. , " T e s t Report: Fa t igue T e s t s on 2020 Graph i t e , " GA

Document 906202/1, September 1981.

Ea the r ly , W. P., and C. R. Kennedy, ORNL 1982 HTGR Program

Review, ORNL Progress Report , ORNL GCR/B-87/11, December 1987.

Beavan, L. A. , "Test Report: S t r e n g t h of Oxidized F i n e Gra in

Graphi te , 'I GA Document 906249, I s s u e 1, September 1981.

"Core Support Pos t and S e a t Graphi tes : Grades 2020 and A T J , "

i n "HTGR Generic Technology Program: Fuels and C o r e

Development, Quar t e r ly Progress Report for the Per iod Ending

August 31, 1978," DOE Report GA-A15093 ( S e c t i o n 3.6.3.1) ,

September 1978, p. 3-36.

H o , F. H. , and R. Sa l ava tc iog lu , " I n t e r n a l Damping Fac to r f o r

HTGR Core Support Pos t Materials," GA Document 90436511,

November 1979.

"Fuel Design Data Manual," GA Document 901866/F, A p r i l 1987.

3-29 DOE-HTGR-88111 /Rev . 0

909597 / 0

3.4. LARGE RECTANGULAR NUCLEAR GRADE 2020 IGRAPHITE

3.4.1. I n t r o d u c t i o n

The l a r g e r ec t angu la r nuc lea r grade 2020 g r a p h i t e i s re ferenced f o r

t h e permanent s i d e r e f l e c t o r (PSR) and c e n t r a l r e f l e c t o r ( C R ) column

suppor t s t r u c t u r e . The p r o p e r t i e s g iven i n t h i s s e c t i o n are p resen ted

t o be c o n s i s t e n t w i t h t h e s t r u c t u r a l cr i ter :La f o r g r a p h i t e c o r e suppor t s

(Ref. 3.4-1). Unless o therwise noted, t h e material p r o p e r t i e s g iven

below f o r t h i s nuc lea r grade 2020 g r a p h i t e are mean va lues .

T h e m a x i m u m p r e d i c t e d f a s t neut ron f luence t o t h e PSR and t h e CR

column suppor t s t r u c t u r e i s 1.2 x

only 3% of t h e maximum f luence accumulated by f u e l element g r a p h i t e .

Experience w i t h f u e l element g r a p h i t e has shown t h a t on ly e l a s t i c

modulus and thermal conduc t iv i ty w i l l be not. iceably a f f e c t e d by a t o t a l

f a s t neu t ron f luence of 2 x 1024 n/m2.

on o t h e r p r o p e r t i e s descr ibed below are i n s i g n i f i c a n t and no t d i scussed .

n/m2 ( E > 29 f J , H T G R ) , which i s

Therefore , i r r a d i a t i o n e f f e c t s

3.4.2. Phys ica l and Chemical P r o p e r t i e s

3.4.2.1.

averaged over t h e log (Refs . 3.4-2 and 3.4-3).

Densi ty . The bulk d e n s i t y of 2020 g r a p h i t e is 1.78 Mg/m3

3.4.2.2. Transpor t and React ion Rates.

3.4.2.2.1. Steam-Graphite Oxidat ion Rates . The Langmuir-

Hinshelwood equat ion , Eq. 3.4-1, is used t o p r e d i c t s team-graphi te

o x i d a t i o n rates f o r nuc lea r grade 2020 g r a p h i t e (Ref. 3.4-4):

(3.4-1)

3-30 DOE-HTGR-88111/Rev. 0

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where Rate = l o c a l g r a p h i t e mass f r a c t i o n r e a c t i n g p e r second,

P H ~ , P H ~ O = l o c a l p a r t i a l p re s su res of hydrogen and steam,

r e s p e c t i v e l y ,

Fb = modi f i e r f o r e f f e c t s of bu rnof f ,

n = exponent,

K j = kj exp(Ej/RT) ,

where j = 1, 2 , o r 3 ,

k j = Arrhenius frequency f a c t o r ,

E . = a c t i v a t i o n energy, 3 R = 8.314 J/mole*K.

The va lues of Kl, K 2 , K 3 , and n given i n Table 3.4-1 a r e based on d a t a

f o r t h e tempera tures ind ica t ed . Before a d d i t i o n a l d a t a a t o t h e r t e m p e r -

a t u r e s w i l l be genera ted t o a l low K j t o be determined, it i s assumed

t h a t k j i n Table 3.4-1 can be e x t r a p o l a t e d t o o t h e r tempera tures .

For p re l imina ry des ign , Fb is t h e same a s t h a t used t o p r e d i c t

burnoff e f f e c t s f o r steam o x i d a t i o n of H-451 g r a p h i t e ( u n t i l such t ime

as a d d i t i o n a l 2020 g r a p h i t e o x i d a t i o n d a t a a r e a v a i l a b l e ) . The oxida-

t i o n r a t e s of t h e nuc lea r grade 2020 g r a p h i t e i s about o n e - f i f t h t h a t of

H-451 g r a p h i t e .

3.4 .2 .2 .2 . Air-Graphi te React ion Rates_. The r a t e of o x i d a t i o n of

g r a p h i t e by a i r is g iven by Eq. 3.4-2 (Ref. 3 . 4 - 8 ) :

Rate = K exp(-E/RT) Po2 , ( 3 . 4 - 2 )

where Rate = l o c a l g r a p h i t e m a s s f r a c t i o n r e a c t i n g p e r second ( S I ) o r

l o c a l g r a p h i t e mass f r a c t i o n r e a c t i n g p e r hour ( u n i t s


Po2 = l o c a l p a r t i a l p r e s s u r e of oxygen.

3 - 3 1 DOE-HTGR-88111/Rev. 0

909597 / O

TABLE 3.4-1 SUMMARY OF OXIDATION KINETIC CONSTANTS FOR

NUCLEAR 2020 GRAPHITE

High Water >lo0 Pa H7O Low Water <lo0 Pa H7O

980 1.3 8.7E-10 l.lE-3 2.6 - 8.7E-4 7.2E-9 9.OE-3 8.1E-2

930 1.3 3.8E-10 1.6E-3 3.8 - 16E-4 2.3E-9 9.5E-3 1.7E-1

900 1.3 2.OE-10 2.OE-3 2.0 - 4.OE-4


90959 7 10

Table 3.4-2 g ives t h e system of u n i t s der ived from H-327 experimental

da t a . I t is assumed t h a t t h e a i r - g r a p h i t e r e a c t i o n r a t e of H-451 is


S ince there are no experimental d a t a o:n a i r - g r a p h i t e r e a c t i o n

r a t e r epor t ed f o r t h e grade 2020 g r a p h i t e , Eq. 3.4-2, t o g e t h e r w i t h

Table 3.4-2, s h a l l be used. With t h e except ion t h a t t h e K appeared i n

E q . 3.4-2 and va lue g iven i n Table 3.4-2 needs t o be modif ied by a

f a c t o r equa l t o t h e r a t i o of t h e ox ida t ion r a t e of nuc lea r grade 2020

g r a p h i t e t o t ha t of H-451 g r a p h i t e a t t h e environmental cond i t ions of

i n t e r e s t .

3.4.2.2.3. Rad io ly t i c E f f e c t on Oxidat ion Rate. The a v a i l a b l e

exper imenta l d a t a show t h a t t h e r e is a s m a l . 1 and n e g l i g i b l e r a d i o l y t i c

e f f e c t on o x i d a t i o n ra te i n a i r (see d i scuss ion i n S e c t i o n 4 .3 .2 .3) .

3.4.2.2.4. Transport of Steam i n Heliim by Di f fus ion . The e f f e c -

t i v e d i f f u s i o n c o e f f i c i e n t of s t e a m ' i n g r a p h i t e i s g iven by Eq. 3.4-3

(Refs . 3.4-5 through 3.4-7):

1.0 x x T1*58 x P ( m : 2 / s ) ,

P t o t a l DH20 = (3 .4-3)

where D H ~ O = e f f e c t i v e d i f f u s i o n c o e f f i c i e n t through g r a p h i t e ,

T = t empera ture ( K ) ,

P = p r e s s u r e a t STP* ( P a ) ,

Ptotal = t o t a l p re s su re ( P a ) .

A parameter such as d i f f u s i o n through g r a p h i t e is recognized t o

vary by as much as a f a c t o r of three from sample t o sample or from

p o s i t i o n t o p o s i t i o n i n t h e g r a p h i t e block. Equat ion 3.4-3 d e s c r i b e s

t h e p r e s e n t b e s t estimate for H20 d i f f u s i o n i n g r a p h i t e having 1%

average o x i d a t i o n burnoff .

"STP - s t anda rd temperature and p res su re .

3-33 DOE-HTGR-88111/Rev. 0

909597/0

TABLE 3.4-2 AIR-GRAPHITE REACTION RATE COEFFICIENTS (a)

Systems of Unir-s K E T R

SI

OXIDE code

0.79 1.7 105 K 8.314 (sepal -1 J /mo 1 K J/mol.K

2.88 x 101o 4.06 104 K 1.986 ( % ha atm) c a1 I no 1 cal /mo 1 K

~~

(a)See text for the appropriate values to be used in Eq. 3.3-2 for nuclear grade 2020 graphite.

3-34 DOE-HTGR-88111/Rev. 0

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Equation 3 . 4 - 3 was obtained by pooling all available experimental

data on steam diffusion through graphite in helium. No corrections were

made for the differences in porosity and pore structure. Equation 3 . 4 - 3

is assumed to be applicable to all reference HTGR graphites.

The effective diffusion coefficients recommended for carbon monox-

ide, oxygen, and hydrogen are as follows (until such time as experimen-

tal data are available):

DH2 = 2DH20 ( 3 . 4 - 4 )

3 . 4 . 2 . 2 . 5 . Transport of Steam in Helium by Convection. The trans-

port of steam by convection involves the permeation of graphite. The

permeability coefficients of graphite Ref. .3 .4-29 are:

KI = 1 .55E-13 m2 ,

Kp = 9 . 2 0 E - 1 4 m2 ,

where the subscripts represent the following regions of the hexagonal

graphite blocks :

I = interior region consisting of a hexagonal block having an area

in the plane of the hexagon one-seventh of the corresponding

area of the entire block,

P = periphery region consisting of the entire hexagonal block

minus the interior region.

3-35 DOE-HTGR-88111/Rev. 0

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The values of KF and Kp are derived from data on H-327 graphite; they are assumed to apply to 2020 graphite (until such time as experimental

data are available).

3.4.3. Thermal Properties

3.4.3.1. Specific Heat. The specific heat of graphite over the temper-

ature range 250 to 3000 K is given by Eq. 3.4-6 (Ref. 3.4-9):

Cp = (0.54212 - 2.42667 x T - 90.2725 T-I - 4.34493 x lo4 T-2 + 1.59309 x lo7 T-3

- 1.43688 x lo9 T-4) x 4184 , (3.4-6)

where C = specific heat at constant pressure (J/kg-K), P T = temperature (K).

Equation 3.4-6 is also presented graphically in Fig. 3.4-1.

3.4.3.2. Thermal Expansivity. The thermal expansivity of 2020 graphite

is given below (Ref. 3.4-10) :

a = A + B (AT) , (3.4-7)

where a = CTE (l/"C), AT = temperature increase above room temperature ("C),

A = 0.3075 x in the radial direction,

0.3225 x in the axial direction,

B = 1.078 x in the radial direction,

1.167 x 10-9 in the axial direction.

3.4.3.3. Thermal Conductivity. The thermal conductivity of unirradi-

ated 2020 graphite is given in Table 3.4-3 as a function of measurement

temperature (Ref. 3.4-3). The change in thermal conductivity of irradi-

ated 2020 graphite at irradiation temperature is given in Eq. 3.4-8

(Ref. 3.4-11).

3-36 DOE-HTGR-88111/Rev. 0

90959 7/0

-4

-4

J

Y

-2

I- .

rd

3-37 DOE-HTGR-88111/Rev.

0

909597/0

TABLE 3.4-3 THERMAL CONDUCTIVITY OF 2020 GRAPHITE

Conductivity at Measurement Temperature W l m . K)

Orientation 295 K 473 K 673 K 873 K 1073 K

Radial 62.4 67.2 57.2 49.8 43.9

Axial 63.0 63.7 53.7 45.2 40.8

,

3-38 DOE-HTGR-88111/Rev. 0

909597 / O

1 F + - - - - 1 K i ( T ) Ko(T) K0(295 K) ’ (3 .4-8)

where K i ( T ) = thermal conduc t iv i ty of i r r a d i a t e d g r a p h i t e a t temper-

a t u r e T ( K ) ,

K o ( T ) = thermal conduc t iv i ty of u n i r r a d i a t e d g r a p h i t e a t tem-

p e r a t u r e T ( K ) ( de r ived from Table 3 .4-3) ,

K0(295 K ) = thermal conduc t iv i ty of u n i r r a d i a t e d g r a p h i t e a t room

tempera ture ,

F = f r a c t i o n a l i n c r e a s e i n thermal r e s i s t i v i t y due t o

neut ron i r r a d i a t i o n ( f l u e n c e dependence is g iven i n

Table 3.4-4 and Fig. 3 .4-2) .

The t a b u l a t e d d a t a on F were e s t a b l i s h e d from a n a l y s i s of expe r i -

mental d a t a measured on miscel laneous g r a p h i t e s . U n t i l such t i m e as

2020 g r a p h i t e thermal conduc t iv i ty d a t a under low i r r a d i a t i o n l e v e l

a r e a v a i l a b l e , it is assumed t h a t Table 3.4-4 i s a p p l i c a b l e t o 2020

g r a p h i t e e

For other fast fluences, a linear relationship may be used between

logar i thms of F and f a s t f luence . An approximately l i n e a r r e l a t i o n s h i p

a l s o e x i s t s between T and logar i thm of F.

Thermal annea l ing on thermal conduc t iv i ty appears t o begin a t

1273 K and is completed by 1573 K (Refs . 3.4-12 and 3.4-13). I n t h i s

tempera ture range t h e f r a c t i o n a l change i n conduc t iv i ty is c l o s e t o

l i n e a r l y p r o p o r t i o n a l t o temperature . The f r a c t i o n a l i n c r e a s e i n

thermal r e s i s t i v i t y , F, i n Eq. 3.4-8 is assumed t o l i n e a r l y dec rease

t o zero over t h e above temperature range.


909597 / O

TABLE 3.4-4 THERMAL RESISTIVITY CONSTANT F, USED IN EQ. 3.4-8

Irradiation Temperature (K) Fast Neutron Fluence

(1022 n/m2) 673 873 1073

0.4 0.075 0.0885 0.0215

1 0.125 0.063 0.036

0.27 0.138 0.078 4

10 0.445 0.225 0.124

20 0.665 0.33 0.185

3-40 DOE-HTGR-88111/Rev. 0

LL 10 >- t L: I- 2 v) w U -I a I

l - 1

U w I

W IT 3 I- s 3 w a

t- 2 0 0 U

0.1 w v)

W

u

a a

5 a 0 L 2

-I

2

0.01

-

-

- - - -

-

I R RAD I AT10 N TEMPE R ATU R E

1021 1 022 1 o~~ 1024 1025 1 026 'I - 05 (x, t-

t- FAST NEUTRON FLUENCE, S(N/M2) (E >29 fJ) HTGR ul 0 ul VI ul v \

\ r 4

F i g . 3 . 4 - 2 . Design curves for change in room temperature thermal resistivity of 2020 graphite 0 as a function of irradiation conditions 0

909597 / O

3.4.3.4. Emissivity. The emissivity of 2020 graphite f o r machined

surface is 0.85 (Refs. 3.4-14 through 3.4-16).

3.4.4. Mechanical Properties

3.4.4.1. Transversely Isotropic Linear Elastic Constants. The

mechanical properties of commercial 2020 graphite can be modeled as

transversely isotropic. The isotropic plane is in the direction

perpendicular to molding pressure (with-grain) for rectangular graphite

logs. The axes in this plane are designated 1-axis and 2-axis. The

across-grain direction is the axial direction, and is labelled as the

3-axis. The five independent unknowns in the transversely isotropic

linear elastic material are two elastic moduli, E1 and E3; shear

modulus, GI; and two Poisson's ratios, V 1 2 and "13.

The properties given below are the average of the combined tensile

and compressive moduli at room temperature, The difference between two

moduli is less than 10% (Refs. 3.4-17 through 3.4-19):

E1 = [later] GPa,

E3 = [later] GPa,

GI = [later] GPa, "12 = Vi3 = 0.15.

The elastic modulus given above is the tangent elastic modulus at the

origin of the stress-strain curve.

The following modulus/temperature relationship applies to all El,

E3, and GI, but not "12 and Vi3 (Ref. 3.4-20):

C(T) = cRT - 9.94 x 10-4 (T - 21)

+ 3.09 x (T - 21)2 , (3.4-9)

3-42 DOE-HTGR-88111/Rev. 0

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where CRT = El, E3, or G1 at room temperature (GPa),

T = temperature ("C),

C(T) = El, E3, or G1 at temperature T (GPa).

The relationship is valid up to 1100°C.

The moduli increase with fast neutron irradiation. The percent

increase (P) is given in Table 3.4-5, as well as plotted in Fig. 3.4-3, as a function of neutron fluence and irradiation temperature

(Ref. 3.4-21). To calculate modulus (Ei) at any point during neutron irradiation, the following equation applies:

Ei = Eo (1 + P/lOO) , (3 -4-10)

where Eo = elastic modulus of unirradiated graphite at room

temperature,

P = (t - 1) x loo ;

Ei = elastic modulus of irradiated graphite measured at room

temp era t ur e.

For P at irradiation temperature and fast neutron fluence other than that given in Table 3.4-5, the following relationship shall be used:

1.

2.

Logarithm of P is a quadratic function of logarithm of 4 . Logarithm of P is a quadratic function of temperature ("C).

3.4.4.2. Stress-Strain Curve. Typical room temperature (RT) tensile and compressive stress-strain curves for 2020 graphite are shown in

Figs. 3.4-4 and 3.4-5, respectively (Ref. 3.4-22). The curves are

applicable to a nonlinear design analysis when nonlinear analysis.


909597 / O

Fig. 3 . 4 - 3 . Design curves fo r change i n e l a s t i c modulus of 2020 g r a p h i t e as a func t ion of i r r a d i a t i o n cond i t ions

3 - 4 4 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

TABLE 3.4-5 PERCENT INCREASE (P) IN ELASTIC MODULUS AS

A FUNCTION OF FLUENCE AND TEMPERATURE

Irradiation Temperature ( K ) Fast Neutron Fluence

(1022 n/m2) 673 873 1173

1

4

10

4.3 3 . 1 2.3

13.3 9.8 7 . 4

24 .0 18.3 13.9

3-45 DOE-HTGR-88111/Rev. 0

909597 / O

20

15

10

5

0 0 0.1 0.2

STRAIN (%)

0.3

Fig . 3 . 4 - 4 . T e n s i l e s t r e s s - s t r a i n curve f o r 2020 g r a p h i t e


909597 / O

ao

60

40

20

0 0 1 2

STRAIN (%)

3

Fig. 3 . 4 - 5 . Comprehensive stress-strain curve for 2020 graphite

3-47 DOE-HTGR-88111/Rev. 0

909597 / O

Typical RT tensile and compressive stress strain curves when com- pared in the stress range below the specified minimum ultimate tensile

strength (Sut in Section 3 . 4 . 4 . 3 ) are slightly deviated from each other

by less than one "within-log" standard deviation. For practical purpose

in the design analysis, the typical RT compressive stress strain curve can be considered as the same as the tensile curve when the maximum

stress is expected to be lower than Sut.

valid for test evaluation on component failure.

The above assumption is not

3 . 4 . 4 . 3 . Strength.

Specified Minimum Ultimate Strength (Su). Specified minimum ulti-

mate strength is the uniaxial strength along a principal stress direc-

tion which is used in design analysis to measure the structural integ-

rity of a given core support graphite component against the design and

accident condition stresses. Per ASME Code Subsection CE (Ref. 3 . 4 - l ) ,

specified minimum strength is established from statistical treatment of

graphite strength data such that the survival probability is 99% with a

confidence level of 95%.

Since the specified minimum compressive strength (Suc) of 2020

graphite is about three to four times its specified minimum tensile strength (Sut), only Sut is needed in the uniaxial stress analysis.

For unirradiated 2020 graphite at room temperature along the

material axes, the specified minimum tensile strength (Sut) is

(Refs. [LATER] ) :

Sut(z) = [LATER] MPa in the axial direction , Sut(r) = [LATER] MPa in the radial direction .

3-48 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

The specified minimum compressive strength (Sue) is

Su,(z) = [LATER] MPa in the axial direction , Suc(r) = [LATER] MPa in the radial direction .

In the off-axis case, the following Hankinson’s formula is

recommended for use:

where 8 is the angle between the direction of the principal stress and the axial (material) axis.

Both Sut and S,, may be assumed to increase with temperature and

neutron fluence identical to that for UTS (until such time as the experimental data are available). The relationship is (Refs. 3.4-20 and

3.4-21)

Su(T) = [(Su)~~ + 0.00392 (T - 294)] (Ei/EO)ll2 9 ( 3 . 4 - 1 2 )

where (S,)RT = room temperature unirradiated S, (MPa),

T = temperature (K),

Ei = modulus of irradiated graphite at room temperature

(GPa) ,

Eo = modulus of unirradiated graphite at room temperature

(GPa) ,

Su(T) = S, of unirradiated 2020 at temperature T (MPa).

Specified Minimum Biaxial Strength. In the biaxial stress state,

the Coulomb-Mohr theory, modified to include a maximum tensile strength


9 0 9 5 9 7 / 0


(Ref. 3.4-23). This theory defines that the maximum principal stress

governs failure in the first and third stress quadrants. In the second

and fourth quadrants, the maximum principal stress or the Coulomb-Mohr

theory, whichever is more restrictive, is applied.

The specified minimum biaxial strength surface is established sim-

ilar to that of the above failure surface. The surface is given in

Fig. 3.4-6. Caution is required when using the biaxial strength in the

third quadrant. Early failure may occur in other modes prior to biaxial

compressive failure. Minimum values are determined by the ASME rules of

Ref. 3.4-1.

Fatigue Strength. The normalized fatigue strength (normalized with

respect to mean strength) is defined in Table 3.4-6 (Ref. 3.4-24) as a

function of stress ratio (R) and number of cycles. Mean strength of

graphite, as well as .fatigue strength, increases with fast fluence and

temperature in the range of interest. However, it is assumed that

normalized fatigue strength remains constant for the design use.

The design fatigue diagram can be used to interpolate the fatigue

strength at other R ratios (Fig. 3.4-7).

3.4.4.4. Fracture Toughness and the Critical Defect Size. Fracture

toughness of unirradiated 2020 graphite at room temperature is

(Ref. 3.4-25):

KIC = 1.25 MPa 6 .

The calculated critical defect size is 0.6 mm.

The reduction of KIC with oxidation .follows the relationship

(3.4-13)


9 0 9 5 9 7 / 0

Fig. 3 . 4 - 6 . Specified minimum b i a x i a l strength surface for 2020 graphite


909597 l o

TABLE 3.4-6 UNIAXIAL FATIGUE STRENGTH LIMITS FOR 2020 GRAPHITE

Fatigue Strength Limits, Peak Stress/Mean Strength ~~~ ~

R Number of 99/95 Lower Orientation (amin/amax) Cycles 50% Survival Tolerance Limit

Axial 0

Radial

-1

-2

0

-1

-2

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

100

1,000

10,000

100,000

0.87

0.83

0.80

0.76

0.84

0.79

0.74

0.70

0.85

0.80

0.75

0.71

0.86 0.81

0.77 0.73

0.79

0.73

0.68

0.63

0.81

0.76

0.71

0.66

0.69

0.66

0.63

0.60

0.66

0.62

0.58

0.54

0.66

0.62

0.58

0.55

0.71

0.67

0.64

0 . 6 0

0.61

0.56

0.52

0.48

0.66

0.61

0.57

0.53

3-52 DOE-HTGR-881111Rev. 0

909597 / O

Fig. 3 . 4 - 7 . Design f a t i g u e diagram of nuc lea r grade 2020 g r a p h i t e a t 99% s u r v i v a l p r o b a b i l i t y w i t h 95% conf idence l e v e l

3-53 DOE-HTGR-88111/Rev. 0

909597 /O

where x = fractional weight loss due to oxidation and the subscript o

represent the unoxidized state. The calculated critical defect size

remains unchanged with oxidation.

3.4.4.5. Effect of Oxidation on Mechanical Properties. The reduction

in tensile strength (S) and elastic modulus (E) is assumed to be the same f o r the commercial and the nuclear 2020 grades which may be

represented by the following relationship (Refs. 3.4-26 and 3.4-27):

S E exp (-lox) , - = - =

so Eo (3.4-14)

where x = fractional weight loss due to oxidation, and the subscript "0"


For the preliminary calculation on the component subjected to

external loads, it may be conservatively assumed that any portion of

graphite that oxidized to 20.1% and beyond loses its entire strength.

3.4.4.6. Material Internal Damping Factor. The internal damping factor

$, defined as the ratio of actual damping to critical damping, is dependent on the stress amplitude. At a stress amplitude of 7.35 MPa, $ is

equal to 0.596% (Ref. 3.4-28). This is for 0.5 Sut, approximately the 9 9 / 9 5 endurance limit). When the stress amplitude is reduced to half,

$ decreases only by 12%.

3.4.5. References

3.4-1. "Proposed Section 111, Division 2, ASME Boiler and Pressure

Vessel Code, Subsection CE, Design Requirements for Graphite

Core Supports," April 1984.

3.4-2. Engle, G. B., "Properties of Unirradiated HTGR Core Support and

Permanent Side Reflector Graphites: PGX, HLM, 2020, and H-440N, 'I ERDA Report GA-A14328, May 1977.

3-54 DOE-HTGR-88111/Rev. 0

909597 / O

3.4-3.

3.4-4.

3.4-5.

3.4-6.

3.4-7.

3.4-8.

3.4-9.

3.4-10.

3.4-11.

3.4-12.

3 -4-13.

3 4-14.

Engle, G. B., and L. A. Beavan, "Properties of Unirradiated Graphites PGX, HLM, and 2020 for Support and Permanent Side Reflector LHTGR Components," DOE Report GA-A14646, June 1978.

Burnette, R. D., and G. R. Hightower, "Oxidation Kinetics of SC 2020 Nuclear Grade, Lot 1," GA Document 908038/0, May 31, 1985.

Peroomian, M. B., A. W. Barsell, and J. C. Seager, "OXIDE-3: A



Burnette, R. D., et al., "Studies of the Rate of Oxidation of ATJ Graphite by Steam," in Proceedings of 13th Biennial Confer- ence on Carbon at Irvine, California, July 13-22, 1977.

"HTGR Fuels and Core Development Program, Quarterly Progress

Report for the Period Ending August 31, 1977," ERDA Report

GA-A14479, September 1977, p. 11-16.

Jensen, D., M. Tagami, and C. Velasquez, "Air/H-327 Graphite Reaction Rate as a Function of Temperature and Irradiation," GA

Report Gulf-GA-A12647, September 24, 1973. Butland, A. T. D., and R. J. Maddison, "The Specific Heat of Graphite: An Evaluation of Measurements," Journal of Nuclear

Material, 2, 45 (1973-1974). "Graphite Data Manual," DOE-HTGR [LATER], to be issued.

Price, R. J., "Review of the Thermal Conductivity of Nuclear Graphite under HTGR Conditions," GA Report Gulf-GA-A12615,

September 1973.

Engle, G. B., and K. Koyama, "Dimensional and Property Changes of Graphites Irradiated at High Temperatures," Carbon, 6, p . 455, 1968.

Kelly, B. T., et al., "The annealing of Irradiation Damage in Graphite," Journal Nuclear Materials, 20, p. 195, 1966.

Grenis, A. F., and A. P. Levilt, "The Spectral Emissivity and Total Normal Emissivity of Commercial Graphites at Elevated

Temperatures," Proceedings of Fifth Conference on Carbon,

p . 639, 1961.

3-55 DOE-HTGR-88111/Rev. 0

90959710

3 -4-15

3-4-16.

3.4-17.

3-4-18.

3.4-19.

3-4-20.

3-4-21.

3.4-22.

3.4-23.

3.4-24.

3-4-25.

3 4-26.

3.4-27.

3.4-28.

3-4-29.

P l u n k e t t , J. D . , and W. D . Kingery, "The S p e c t r a l and I n t e -

g ra t ed Emiss iv i ty of Carbon and Graph i t e , " Proceedings of

Fourth Carbon Conference, p . 457, 1960.

Aut io , G. W . , and E. Scula , "The Normal S p e c t r a l Emiss iv i ty of

I s o t r o p i c and Aniso t ropic Materials," Carbon, 4, pp. 13-28,

1966.

[LATER]

[LATER]

[LATER]

Ho, F. H . , and E. Chin, " T e s t Evalua t ion Report of t h e Ther-

m a l S t r e s s (TIS) T e s t f o r Core Support Graphi te , " GA Document

904445/B, August 12, 1980.

P r i c e , R. J., "Mechanical P r o p e r t i e s of Graphi te of High-

Temperature Gas-Cooled Reactors : A Review," ERDA Report

GA-A13524, September 22, 1975.

[LATER]

H o , F. H . , e t a l . , "B iax ia l F a i l u r e Sur faces of 2020 and PGX

Graph i t e s , " Paper No. L4/6, P. 127, Transac t ions of t h e 7 t h

I n t e r n a t i o n a l Conference on S t r u c t u r a l Mechanics i n Reactor

T e c h n o l o u , Chicago, I L , August 22, 1983.

Price, R. J. , " T e s t Report: Fa t igue Tests on 2020 Graphi te , " GA

Document 906202/1, September 1981.

Ea the r ly , W. P . , and C . R. Kennedy ORNL 1982 HTGR Program

Review, ORNL Progress Report , ORNL G C R / B - 8 7 / 1 1 , December 1987.

Beavan, L. A. , " T e s t Report: S t r eng th of Oxidized Fine Grain

Graphi te , " GA Document 906249, I s s u e 1, September 1981.

"Core Support Post and Sea t Graphi tes : Grades 2020 and A T J , "

i n "HTGR Generic Technology Program: Fuels and Core Develop-

ment, Quar t e r ly Progress Report f o r t h e Per iod Ending

August 31, 1978," DOE Report GA-A15093 ( S e c t i o n 3.6.3.1) ,

September 1978, p . 3-36.

Ho, F. H . , and R. Sa l ava tc iog lu , " I n t e r n a l Damping Fac to r for

HTGR Core Support Post Materials," GA Document 904365/1,

November 1979.

"Fuel Design Data Manual," GA Document 901866/F, A p r i l 1987.

3-56 DOE-HTGR-88111/Rev. 0

909597/0

4. GRADE H-451 GRAPHITE

4.1. DESCRIPTION OF GRADE

Grade H-451 graphite is a near-isotopic, petroleum-coke-based,

artificial graphite developed specifically for HTGR fuel element and

reflector application by Great Lakes Carbon Company. The graphite is

extruded into right-circular or oblong cylinders. The logs used for

HTGR application are 0.863 m (34 in.) long by 0.457 m (18 in.) in

diameter.

The design data presented herein have been derived from character-

ization tests of H-451 preproduction lot 426 and from strength testing

of production lot No. 440, 472, 478, and 482. Several hundred prepro-

duction logs of H-451 graphite were produced for qualification tests.

Three production grade lots, totaling over 300 logs, have been produced

for use in FSV reload segments.

4.2. APPLICATION

Grade H-451 graphite is the reference material for both the fuel

elements and the replaceable hexagonal reflectors. The latter consists

of the upper and lower reflectors, central reflectors, and hexagonal

side reflectors. These components are to be designed to meet the

structural criteria for core graphite (Ref. 4-1). Unless otherwise

noted, the material properties given below are mean values.

4- 1 ’ DOE-HTGR-8811l/Rev. 0

9 0 9 5 9 7 / 0

4.3. PHYSICAL AND CHEMICAL PROPERTIES

4.3.1. Density

The density of H-451 graphite is 1.74 Mg/rn3 averaged over the log (Ref. 4-2).

4.3.2. Transport and Reaction Rates

4.3.2.1. Steam-Graphite Oxidation Rates. The Langmuir-Hinshelwood

equation, Eq. 4-1, is used to predict chemical kinetically limited steam-graphite oxidation rates for H-451 graphite (Refs. 4-3 and 4-4):

where Rate = local graphite mass fraction reacting per second (SI

units),

Rate = local graphite mass percent reacting per hour (former

units),

P H ~ , P H ~ O = local partial pressures of hydrogen and steam, respectively,

Fb, Fc = modifiers for effects of burnoff and presence of cat-

alysts, respectively,

n = 0.75,

Kj = kj exp(Ej /RT) ,

where j = 1, 2, or 3 ,

k. = Arrhenius frequency factor, J


90959710

E j = a c t i v a t i o n energy,

R = 8.314 j/mole*K.

Constants are g iven i n Table 4.3-1.

Fb = 0.447 + 0.8094 b - 0.3221 b2 + 0.0681 b3

- 0.00613 b4 + 12.32 x b5 + 2.89 x b6

- 1.15 x b7 , (4-2 1

w h e r e b is the pe rcen t g r a p h i t e burnoff and Fb is normalized t o 1% burn-

o f f ; i . e . , a t 1% burnoff Fb = 1.0. The above equat ion is r e s t r i c t e d t o

0 5 b 5 13; f o r h igher bu rnof f s , t h e va lue of Fb a t 13% burnoff should

be used.

Fc = 1 + ( C B ~ + 0.2 Csr) exp(12.153 - 4.264 x T ) , (4-3)

where C B ~ , C s r = concen t r a t ion of barium and s t ron t ium c a t a l y s t (mg/g

g raph i t e ) , ,

T = temperature ( K ) .

4.3.2.2. Air-Graphi te React ion Rates. The ra te of o x i d a t i o n of graph-

i t e by a i r is given by E q . 4-4 (Ref. 4-8):

(4-4 1 2 ' R a t e = K exp(-E/RT) Po

where R a t e = l o c a l g r a p h i t e m a s s f r a c t i o n r e a c t i n g pe r second ( S I ) o r

l o c a l g r a p h i t e m a s s f r a c t i o n r e a c t i n g pe r hour ( u n i t s


Po2 = l o c a l p a r t i a l p re s su re of oxygen.

Table 4.3-2 g ives t h e system of u n i t s der ived from H-327 experimental

da t a . I t is assumed t h a t t h e a i r - g r a p h i t e r e a c t i o n ra te of H-451 i s



TABLE 4.3-1 CONSTANTS FOR H-451 GRAPHITE OXIDATION RATE EQUATION

Units kl k2 k3 E1 E2 E3 R

SI 900 110 30 -274,000 -74,660 -95,850 8.314 pa-1 Jlmol Jlmol J/mol J /mol. K (s .pa)-l pa-0.75

OXIDE Code 3.28 x 1013 6.25 x lo5 3.04 x lo6 -65,460 -17,840 -22,900 1.986 F. ( 2 h-atm)-l a ~ n - 0 . ~ 5 atm-1 cal/mol cal/mol cal/mol cal/mol-K I c\

909597 / O

TABLE 4.3-2 AIR-GRAPHITE REACTION RATE COEFFICIENTS

Systems of Units K E T R

SI 0.79 1.7 105 K 8.314 (s.Pa)-l J/mol K J/mol-K

OXIDE code 2.88 x 1O1O 4.06 104 K 1.986 ( % h* atm) -1 cal / mo 1 cal /mol K


9 0 9 5 9 7 / 0

4.3.2.3. R a d i o l y t i c E f fec t on Oxidat ion Rate. I r r a d i a t i o n w a s shown t o

have no d i s c e r n i b l e e f f e c t on r e a c t i o n r a t e of H-327 g r a p h i t e i n t h e

temperature range of 385' t o 566OC (Ref. 4-9) . E t o , e t a l . (Ref. 4-10)

showed t h a t t h e c o n t r i b u t i o n of r a d i o l y t i c e f f e c t on t h e r e a c t i o n r a t e

w a s s m a l l enough t o neg lec t above 1050 K , and neut ron i r r a d i a t i o n d id

not a f f e c t t h e r e a c t i o n ra te un le s s t h e g r a p h i t e w a s a t t h e i n i t i a l

s t a g e of i r r a d i a t i o n . For des ign a n a l y s i s , t h e r a d i o l y t i c e f f e c t on

o x i d a t i o n r a t e s h a l l be d is regarded .

4.3.2.4. Transpor t of Steam i n Helium by Dif fus ion . The e f f e c t i v e d i f -

f u s i o n c o e f f i c i e n t of steam i n g r a p h i t e i s g iven by Eq. 4-5 (Refs . 4-5

through 4-7):

where D H ~ O = e f f e c t i v e d i f f u s i o n c o e f f i c i e n t through g r a p h i t e ,

T = temperature ( K ) ,

P = p r e s s u r e a t STP" ( p a ) ,

Ptotal = t o t a l p re s su re ( P a ) .

A parameter such as d i f f u s i o n through g r a p h i t e i s recognized t o

vary by as much as a f a c t o r of t h r e e from sample t o sample o r from

p o s i t i o n t o p o s i t i o n i n t h e g r a p h i t e block. Equation 4-5 d e s c r i b e s t h e

p r e s e n t b e s t estimate f o r H20 d i f f u s i o n i n g r a p h i t e having 1% average

o x i d a t i o n burnoff .

Equation 4-5 was obta ined by pool ing a l l a v a i l a b l e experimental

d a t a on s t e a m d i f f u s i o n through g r a p h i t e i n helium. N o c o r r e c t i o n s w e r e

made f o r t h e d i f f e r e n c e s i n p o r o s i t y and pore s t r u c t u r e . Equation 4-5

i s assumed t o be a p p l i c a b l e t o a l l r e fe rence HTGR g r a p h i t e s .

~

*STP - s t anda rd temperature and p res su re .


9 0 9 5 9 7 / 0

The effective diffusion coefficients recommended for carbon

monoxide, oxygen, and hydrogen are as follows:

4.3.2.5. Transport of Steam in Helium by Convection. The transport of

steam by convection involves the permeation of graphite. The permeabil-

ity coefficients of graphite (Ref. 4.4-42) are:

KI = 1.55E-13 m2 , Kp = 9.2OE-14 m2 ,

where the subscripts represent the following regions of the hexagonal

graphite blocks:

I = interior region consisting of a hexagonal block having an area

in the plane of the hexagon one-seventh of the corresponding

area of the entire block,

P = periphery region consisting of the entire hexagonal block

minus the interior region.

The values of KI and Kp are derived from data on H-327 graphite; they are assumed to apply to H-451 graphite.


909597 / O

4.4. THERMAL PROPERTIES

4.4.1. Specific Heat

The specific heat of H-451 graphite for temperatures from 250 to

3000 K is given below (Ref. 4-11):

Cp = (0.54212 - 2.42667 x T - 9.02725 x lo1 T-'

- 4.34493 x lo4 T'2 + 1.59309 x lo7 T-3

- 1.43688 x 109 T-4) x 4184 , (4-7)

where Cp = specific heat at constant pressure (J/kg-K),

T = temperature (K).

Equation 4-7 is also presented graphically in Fig. 4.4-1.

4.4.2. Thermal Expansivity

Mean Coefficient of Thermal Expansion. The mean CTE for unirradi-

ated H-451 graphite between room temperature and 5OO0C is 4.09 x 10-6/0C and 4.65 x 10-6/0C in the axial and radial directions, respectively

(Refs. 4-12 through 4-14). Its dependence on temperature can be calculated from the thermal strain given in Table 4.4-1 and Fig. 4.4-2.

The thermal expansivity of H-451 graphite changes during neutron

irradiation. The fractional change in thermal expansivity, (ai - ao)/ a,, is given in the following equation and Figs. 4.4-3 and 4.4-4 (Ref. 4-9):

(ai - a0)/a, = (0.27830 - 4.2734 x lom4 T + 1.7815 x T2) @ - 2.0664 x a2 + 1.3601 x 10-3 o3 , (4-8)


P I u)

I I I

I I I

I I 1 I I I I 1 I I 1 I I I I I I 1 I I I I

1 I 1 I 1 I I I

T E M P E R A T U R E I T ( K )

Fig. 4.4-1 Specific H e a t of G r a p h i t e as a Function of Tempratme

2000- S P E C 1 1800

. F I C

16oB H E A

1400 I

C

- 1200-

J

/ K G lBBB

K *

-

8 0 8

0

909597/0

TABLE 4.4-1 THERMAL EXPANSION OF H-451 GRAPHITE

Thermal Strain (10-3) Temperature ( O C ) Axial Radial

25 100 150 200 25 0 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600

0 0.26 0.42 0.60 0.80 1.00 1.20 1.42 1.65 1.88 2.12 2.35 2.60 2.83 3.10 3.35 3.58 3.84 4.10 4.33 4.60 4.88 5.14 5.42 5.70 6.00 6.30 6.60 6.90 7.24 7.55 7.90

0 0.32 0.52 0.74 0.95 1.20 1.43 1.68 1.93 2.19 2.46 2.75 3.03 3.32 3.58 3.88 4.16 4.41 4.73 5.06 5.32 5.62 5.91 6.23 6.53 6.85 7.16 7.50 7.85 8.20 8.52 8.90

4- 10 DOE-HTGR-881111Rev. 0

I a, a,

TEMPERATURE (OC)

0 200 400 600 800 1000 1200 1400 1600 1.0

0.8

E E a

0.6

LT I- In -1 a z a w I 0.4 t-

o. 2

TEMPERATURE (K)

F i g . 4.4-2 . Thermal expansion of li-451 g raph i t e

9 0 9 5 9 7 / 0

z < W E z

20

0

-20

- 2

4 0 Y c3 r- r-

I m Q) hl - w -60

I RRADlATl O N

DESIGN CURVE 923 K

I R RAOl ATlON TEMPERATU RE 865 - 1045 K

-20

4 0

TEMPERATURE 1080 - 1205 K

\ DESIGN \ C U R V E 1 1123K

-60 0 2 4 6 8 10

FAST NEUTRON FLUENCE, N/M2) (E >29 fJ) HTGR

Fig. 4 . 4 - 3 . Change in mean cte of H-451 graphite as a function of irradiation conditions (865-1205 K), axial and radial directions


9 0 9 5 9 7 / 0

I rn a¶ cy

2; - 6 0 . oc 20 z a w E z w

I R RAD I AT1 0 N TEMPER ATU RE 1250 - 1380 K

1323 K

I I I I I

IRRADIATION TEMPERATURE

1523 K

Fig. 4.4-4. Change in mean cte of H-451 graphite as a function of irradiation conditions (1250-1705 K), axial and radial directions

4- 13 DOE-HTGR-88111/Rev. 0

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where a, = a (5OOOC) unirradiated,

ai = a (5OOOC) irradiated, T = irradiation temperature (OC),

4 = neutron fluence (1025 n/m2, E > 29 fJ)HTGR.

The shifting rule for the mean CTE under nonisothermal irradiation

shall be performed at equal neutron damage as determined from the dimen-

sional change curve given in Section 4.6.1 (Rule 3 in Ref. 4 - 1 6 ) .

4 .4 .3 . Thermal Conductivity

The thermal conductivity of near-isotropic graphite is given by the

current models reviewed in Ref. 4-17. This model considers the depen-

dence of thermal conductivity (K) on the current measurement temperature (T,) and on the past history of irradiation temperature (TI) and fast neutron fluence ( 4 ) . The model is extended here to the case of a non-

isothermal irradiation.

The thermal conductivity as a function of current measurement tem-

perature can be considered as a superposition of three temperature-

dependent resistance mechanisms through Eq. 4-6 (Ref. 4 - 1 7 ) :

where a = porosity-tortuosity factor,

Ku(TC) = crystallite conductivity with Umklapp processing dominating,

b = inverse of the crystallite boundary spacing,

Kb(Tc) = effect of the grain boundary scattering,

d = irradiation damage parameter,

Kd(Tc) = effect of the irradiation damage.

4- 14 DOE-HTGR-88111/Rev. 0

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All of the above quantities are given as known input data in Tables 4.4-2 and 4.4-3 except for the irradiation damage parameter,

d. A s shown below, parameter d can be obtained by comparing con-

ductivities before and after irradiation.

4.4.3.1. Thermal Conductivity, Unirradiated. For unirradiated mate-

rial, the damage parameter d in Eq. 4-6 is zero. Equation 4-6 reduces

to

( 4 - 7 )

4 .4 .3 .2 . Thermal Conductivity, Isothermal Irradiation. The damage

parameter d in Eq. 4-6 can be found by comparing the unirradiated and

irradiated conductivities at one particular measurement temperature.

Room temperature (RT) is conveniently taken to be the reference temperature. Thus, Eqs. 4-6 and 4-7 combine to give the following:

where Ko(RT) = unirradiated room temperature conductivity, found by

evaluating Eq. 4-7 at T, = RT,

Ki(RT) = irradiated room temperature conductivity found by the procedure outlined below.

4.4 .3 .3 . Thermal Conductivity, Nonisothermal Irradiation. The proce-

dure to be used for calculating room temperature conductivity during a

nonisothermal irradiation is as follows:

1. Divide the irradiation period into n isothermal intervals.

The irradiation temperature during interval i is Ti. The

4-15 DOE-HTGR-881111Rev. 0

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TABLE 4.4-2 TEMPERATURE-DEPENDENT CONDUCTIVITY COMPONENTS OF H-45 1 GRAPHITE ( a)

Umklapp Grain Boundary Irradiation Damage Temperature KU(Tc) Kb(Tc) Kd (Tc)

(K) ( lo3 W/m*K) ( lo9 W/m*K) ( lo3 W/m.K)

100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700 1750 1800

39.12 20.42 5.36 2.67 2.00 1.49 1.21 1.07 0.929 0.864 0.799 0.743 0.686 0.653 0.619 0.590 0.561 0.538 0.515 0.487 0.460 0.441 0.423 0.408 0.393 0.381 0.368 0.360 0.352 0.343 0.335 0.328 0.320 0.315 0.310

1.20 2.49 4.02 5.54 6.97 8.19 9.41

10.36 11.30 11.99 12.68 13.18 13.68 14.10 14.52 14.69 14.85 14.96 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06 15.06

1.87 1.60 1.34 1.30 1.26 1.31 1.36 1.41 1.47 1.50 1.53 1.56 1.58 1.60 1.62 1.63 1.64 1.64 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65

(a)Refer to Eq. 4-6.

(b)The temperature points are equally spaced in order to facili- tate the linear interpolation.

4-16 DOE-HTGR-88111/Rev. 0

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TABLE 4.4-3 MATERIAL CONSTANTS FOR H-451 GRAPHITE THERMAL CONDUCTIVITY

Temperature Value Ref e r ence Range Symbol Equation (K) Axial Radial Units (a)

A 4- 10 4- 10

B 4- 10 4- 10

C 4-11

D 4-11

a 4-6 b 4-6

~~

573 to 873 873 to 1673

573 to 873 873 to 1673

573 to 1673

573 to 1673

573 to 1673

573 to 1673

0.2687 -0.5676

0 9.58 10-4

2.3897

1.207 x lom3 5.334

5.192 x LO6

~~

0.2687 -0 5676

0 9.58 10-4

1.222 10-3

2.2726

5.707

6.165 x lo6

-- n/m2*K

In (W/m*K)

K- 1

(a)Neutron -fluence units ( 1025 n/m2) are in terms of HTGR fast flUenCe, (E > 29 fJ)HTGR.

4-17 DOE-HTGR-88111/Rev. 0

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f luence a t t h e s t a r t of t h e i n t e r v a l i s (@)i - l , and t h e

f luence a t t h e end of t h e i n t e r v a l i s (@)i.

2. A t t h e s t a r t of t h e f i r s t i n t e r v a l , t h e room temperature

conduc t iv i ty is i n i t i a l i z e d t o Ko(RT) through E q . 4-7.

3 . A t the end of i n t e r v a l i, t h e room temperature i r r a d i a t e d

conduc t iv i ty i s given by t h e r e c u r s i v e formula, E q . 4-9:

where

r ( T i ) = A + BTi ,

and

K"' ( T ~ ) = exp(C + D T ~ ) , sa t

(4-10)

(4-11)

r = r e l a x a t i o n t i m e i n u n i t s of f l uence ,

= s a t u r a t i o n va lue of t h e room c o n d u c t i v i t y , RT Ksat

A , B , C , D = cons tan t s g iven i n Table 4.4-3.

T i = i r r a d i a t i o n temperature dur ing i n t e r v a l

( K )

. 4-18 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

4. C a l c u l a t e t h e conduc t iv i ty a t t h e assumed c u r r e n t tempera ture

Tc by apply ing Eqs. 4-6 and 4-8.

4.4.3.4. Thermal Conduct iv i ty Input Data for Near - I so t rop ic Graphi te .

The i n p u t d a t a r equ i r ed t o c a l c u l a t e t h e thermal c o n d u c t i v i t y of near-

i s o t r o p i c g r a p h i t e i n W/m*K i n t h e a x i a l and r a d i a l d i r e c t i o n s are

g iven i n Tables 4.4-2 and 4.4-3. The c a l c u l a t e d curves are shown i n

F ig . 4.4-5.

4.4.3.5. E f f e c t of Thermal Annealing. Thermal annea l ing on thermal

c o n d u c t i v i t y appears t o begin a t 1273 K and is completed by 1573 K

(Refs . 4-18 and 4-19). The f r a c t i o n a l change dec reases a lmost l i n e a r l y

w i t h i n c r e a s i n g temperature . The i r r a d i a t i o n damage parameter , d i n

Eq. 4-6, is assumed t o decrease l i n e a r l y t o ze ro over t h e above

tempera ture range.

4.4.4 Emiss iv i ty

No e m i s s i v i t y d a t a f o r H-451 g r a p h i t e have been r epor t ed . However,

e m i s s i v i t y does no t vary much between g r a p h i t e grades , and e m i s s i v i t y

of 0.85 f o r a machined g r a p h i t e s u r f a c e s h a l l be used (Refs . 4-20

through 4-22).

4.5. MECHANICAL PROPERTIES

4.5.1. Transverse ly I s o t r o p i c Linear E la s t i c Cons tan ts

The f i v e independent l i n e a r e l a s t i c c o n s t a n t s i n the t r a n s v e r s e l y

i s o t r o p i c mater ia l are two e las t ic moduli , E 1 and E3; s h e a r modulus, GI;

and two Poisson ' s r a t i o s , ~ 1 2 and "13.

are des igna ted 1-axis and 2-axis . The a x i s normal t o t h e i s o t r o p i c

p l ane i s l a b e l e d as t h e 3-axis .

The axes i n t h e i s o t r o p i c p l ane

4- 19 DOE-HTGR-8811l/Rev. 0

909597 / O

- (1025N/M2, E > 29 fJ HTGR)

I R RAD I AT1 ON TEMPERATURE ('C) 600 7 00 800 900 1000 1100

100

75

50

25

t I I L 3

100 0 u

I I I I I I

H-451, RADIAL

7 5.

50

25

I n c -

800 900 1000 1100 1200 1300 1400

IRRADIATION TEMPERATURE (K)

Fig. 4.4-5. Thermal conductivity of H-451 graphite as a function of neutron irradiation

4-20 DOE-HTGR-88111/Rev. 0

909597 / O

The mean values of these elastic constants at room temperature,

including the effect of spatial distribution, are (Ref. 4-23):

E1 = 7.35 + 1.11 x * r2 + 2.95 x z2

- 3.8 x r2z2 ,

E3 = 8.31 + 1.76 x loe2 r2 + 1.53 x z2

- 2.7 x 10-5 r2z2 , (4-12)

G1 = E1/2(l+V) ,

all Y = 0.12 ,

where El, E3, and G1 are in GPa, r = radial distance from the axis of the billet, 58.5 in. ( i n . ) ,

z = axial distance from midlength of the billet, 5-16 in. (in.).

The elastic moduli given above are the secant moduli of the second load-

ing curve between 0 and 6.9 MPa.

The following modulus/temperature relationship applies to all E and

G's, except Y (Ref. 4-24):

(4-13)

where CRT = E or G at room temperature (21OC) (GPa), T = temperature -21'C ("C).

The fractional change in elastic modulus of H-451 graphite due to

isothermal neutron irradiation is given in Table 4.5-1, which i s also

presented graphically in Fig. 4.5-1 (Ref. 4-25). The elastic modulus

due to nonisothermal neutron irradiation shall be evaluated using the

shifting rule identical to that f o r the dimensional change

(Section 4.6.2).

4-21 DOE-HTGR-88111/Rev. 0

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TABLE 4.5-1 PERCENTAGE CHANGE IN ELASTIC MODULUS OF H-451 GRAPHITE

DURING NEUTRON IRRADIATION

~ ~~~

Change in Elastic Modulus at Irradiation Temperature Fast Neutron Fluence, @

(1025 n/m2) ( % I (E > 29 ~J)HTGR 673 K 873 K 1173 K 1473 K

0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00

0 83.0 90.5 95.0 98.1 100.8 102.8 104.8 106.5 108.0 109.8 111.3 113.0 114.5 116.3 117.4 119.3 121.0 122.8 124.3 126.0 127.4 129.0 130.6 132.2

135.4 137.0 138.6 140.2 141.8 143.4 145.2

133. a

0 68.0 76.8 81.6 85.3 88.0 90.4 92.0 93.5 94.8 95.5 96.5 97.5 98.4 99.0 100.0 100.8 101.2 102.0

103.4 104.0 104.7 105.3 105.9 106.5 107.1 107.8 108.4 109.0 109.6 110.2 110.6

102.8

0 54.0 63.8 68.6 71.4 73.2 75.0 75.7 76.7 77.0 77.3 78.0 78.7 79.3 80.8 82.3 85.2 90.6 95.9 101.0 106.0 111.3 116.8 122.0 127.2 132.4 137.6 142.8 148.0 153.2 158.4 163.6 169.0

0 52.0 62.0 66.6 68.5 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.2 70.0 70.5 71.0 71.5 72.7 73.2 74.3 75.2 76.7 78.1 79.8

83.4 85.9 88.5 91.2 94.8 98.4 103.0

81.5

4-22 DOE-HTGR-88111/Rev. 0

909597 / O

I I I I I I l

I I I I I I I

-

Fig. 4.5-1. F r a c t i o n a l change i n e l a s t i c modulus of H-451 g r a p h i t e as a f u n c t i o n of i r r a d i a t i o a n cond i t ions

4 - 2 3 DOE-HTGR-88111/Rev. 0

909597 / O

The Poisson's ratios, ~ 1 2 and "13, are assumed to remain constant

with respect to temperature and neutron irradiation.

4.5.2. Stress-Strain Curve

A typical room temperature tensile and compressive stress-strain

curve found for the axial direction of unirradiated H-451 graphite are

presented in Figs. 4.5-2 and 4.5-3, respectively (Ref. 4-26). A typical

tensile stress-strain curve in the radial direction can be constructed

by increasing the axial strain at a given stress by 15%. This factor

was obtained form the mean ratio of axial elastic modulus to radial

elastic modulus. The mean failure point has a fracture strain of 8%

higher in the axial direction than in the radial direction.

The irradiated tensile stress strain curve [LATER] Fig. 4.5-4 (Ref. 4 - 2 7 ) .

4.5.3. StrenFth

4.5.3.1. Ultimate Tensile and Compressive Strenpth (UTS and UCS).

Per Core Graphite Structural Design Criteria (Ref. 4-1), mean ultimate

strength is used in stress analyses to evaluate the structural integrity of a given core graphite component against the design and accident

condition stresses.

the axial and radial directions in a log may be considered.

Spatial distribution of ultimate strength in both

Since UCS of H-451 is almost four times its UTS, only UTS is needed

in the stress analysis.

The spatial distribution of room temperature mean UTS in the unir-

radiated reference H-451 log is presented by (Ref. 4-17):

UTS = a + br2 + Cz2 + dr2z2 ,

4-24

(4-14)

DOE-HTGR-8811l/Rev. 0

909597/0

15

10

5

0 0 0.1 0.2

STRAIN (%)

0.3

Fig. 4.5-2(a) T e n s i l e stress-strain curve for H-451 graphite, axial orientation

4-25 DOE-TIER-8 8 11 1 /Rev. 0

909597/0

15

10

5

0 0

I I 0.1 0.2

STRAIN (%)

0.3

Fig. 4.5-2(b) T e n s i l e stress-strain curve for H-451 graphite, radial orientation

4 - 2 6 DoE-IlTGR-88111/Re~. 0

909597/0

60

50

40

30

20

10

0 0 1 2

STRAIN (%)

3

Fig. 4.5-3(a) Ccanpressive stres-strain cuwe for H-451 graphite, axial orientation

4-27 DOE-HTGR-88111/Rev. 0

909597/0

60

50

40

30

20

10

0 0

I I 1 2 3

STRAIN (%)

Fig. 4.5-3(b) Ccarrpressive stress-strain curve for H-451 graphite, radial orientation

4-28 DOE-H'IGR-~~~~~/R~V. 0

9 0 9 5 9 7 / 0

Fig. 4.5-4a. Tensile stress-strain curve for irradiated H-451 graphite

4-29 DOE-HTGR-88111/Rev. 0

90959 7 / 0

Fig. 4.5-4b. Compressive stress-strain curve for irradiated H-451 graphite

4-30 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

where UTS = mean ultimate tensile strength along either axial or radial

direction (MPa),

r = radial distance from the axis of the billet, 1*8.5 in.

(in. 1,

z = axial distance from midlength of the billet, <*16 in. (in.)

a = 12.406 MPa for UTS(r),

= 10.712 MPa for UTS(z),

b = 0.0977 MPa/in.2 for UTS(r),

= 0.0636 MPa/in.2 for UTS(z),

c = 0.0113 MPa/in.2 for UTS(r),

= 0.0310 MPa/in.2 for UTS(z),

d = 0.000312 MPa/in.4 for UTS(r),

= 0.000365 MPa/in.4 for UTS(z),

and the origin (r = 0 and z = 0) is at the center of the log.

In the off-axis case the following Hankinson’s formula is recommended for use:

UTS(z) x UTS(r) UTS(6) =

UTS(Z) sin2 e + UTS(r) cos2 e 1 (4-15)

where e is the angle between the direction of the principal stress and the axial axis. UTS(z) and UTS(r) are the UTS in the axial and radial

directions, respectively.

The UTS increases with temperature. At the present, the percentage incrase is assumed to be similar to that of 2020 graphite (the first

factor on the right hand size of Eq. 3.3-11 in Section 3.3.4.3).

4-3 1 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

The change in UTS due to neutron irradiation is related to the

irradiation-induced change in modulus by (Ref. 4-15):

0.64 si

SO 9 (4-16)

where So = UTS of unirradiated H-451,

Si = UTS of irradiated H-451,

Eo = elastic modulus of unirradiated H-451,

Ei = elastic modulus of irradiated H-451.

The fractional changes in modulus during irradiation are given in

Table 4.5-1.

4.5.3.2. Biaxial Strength. In the biaxial stress state, the

Coulomb-Mohr theory, modified to include a maximum tensile strength


(Ref. 4-21).8 To construct a'failure surface, the UTS at any generic

point of interest including the environmental effects governs the

failure in the first tension/tension quadrant. In the third

compression/compression quadrant, a constant ultimate compressive

strength (UCS) of 51 MPa (7400 psi) is used for both the axial ( A )

and radial (R) directions. In the remaining two quadrants, the

modified Coulomb-Mohr theory as defined by

OA = -51.0 + 2 x OR MPa in the Fourth quadrant ,

OR = -51.00 + 2 x OA MPa in the Second quadrant , (4-17)

and the maximum principal stress theory, whichever is more restrictive,

applies.

The effects of environment, such as temperature and neutron irradi-

ation, are assumed to be identical to that of UTS (Section 4.5.3.1).

4-32 DOE-HTGR-88111/Rev. 0

90959710

4.5.4. F rac tu re Toughness and t h e C r i t i c a l Defect S i z e

Room temperature f r a c t u r e toughness of u n i r r a d i a t e d H-451 g r a p h i t e

is (Ref. 4-28):

KIC = 1.54 MPa 6 (1400 p s i a) 1.40 MPa 6 (1270 p s i a)

AR o r i e n t a t i o n

RR o r i e n t a t i o n

The f i r s t l e t t e r i n t h e o r i e n t a t i o n i n d i c a t e s t h e d i r e c t i o n normal t o

t h e c rack and t h e second l e t t e r t h e d i r e c t i o n of propagat ion.

s t and f o r the a x i a l and r a d i a l d i r e c t i o n s , r e s p e c t i v e l y .

A and R

The c a l c u l a t e d c r i t i c a l de fec t s i z e is 1.5 mm (0.06 i n . ) .

The r educ t ion of KIC w i t h ox ida t ion fol lows t h e r e l a t i o n s h i p

(Ref. 4-22)

where x = f r a c t i o n a l weight l o s s due t o ox ida t ion . The c a l c u l a t e d

c r i t i c a l d e f e c t s i z e i nc reases w i t h oxida t ion .

KIC i n c r e a s e s s l i g h t l y w i t h neutron i r r a d i a t i o n (Ref. 4-29). For

des ign use , KIC is assumed t o remain cons t an t .

4.5.5. E f f e c t of Oxidat ion on Mechanical P rope r t i e s

The r educ t ion i n t e n s i l e s t r e n g t h ( S ) and e l a s t i c modulus ( E ) of

uniformly oxid ized H-451 g r a p h i t e is represented by t h e fo l lowing

r e l a t i o n s h i p (Ref. 4 - 3 0 ) :

S/So = exp(-5x) ,

E / E o = exp(-6x) ,

4-33

(4-19)


909597 / O

where x = fractional weight loss due to oxidation,

subscript "0" = the unoxidized state.

The relationship is valid for uniformly oxidized H-451 graphite with

burnoff up to 20%.

4.6. NEUTRON IRRADIATION EFFECTS ON DIMENSIONS

4.6.1. Irradiation-Induced Dimensional Change (Refs. 4-15 4-25, 4-31, 4-32, and 4-33)

The permanent dimensional change (e1) due to fast neutron damage has been expressed in terms of average irradiation temperature (T ) and

fast neutron fluence (Q) for H-451 graphite. The irradiation-induced

dimensional change (e1) is expressed by the polynomial in Eq. 4-20, which is valid for irradiation between 623 and 1573 K and to fast neutron fluences of 10 x 1025 n/m2 (E > 29 fJ)HTGR:

0

(4-20)

where EI = irradiation-induced dimensional change, A&/& ( % ) ,

4 = fast neutron fluence (E > 29 fJ)HTGR (1025 n/m2), T$ = average irradiation temperature - 273 (K), Ci = coefficients determined for each orientation of H-451 graph-

ite (coefficients are listed in Table 4.6-1).

The design curves described by the polynomial (Eq. 4-20) are presented

graphically in Figs. 4.6-1 and 4.6-2.


9 0 9 5 9 7 / 0

TABLE 4.6-1 POLYNOMIAL COEFFICIENTS FOR DIMENSIONAL CHANGE

DESIGN EQUATIONS: H-451 GRAPHITE

Coefficient Axial Radial

C1

c2

c3

c4 c5

c7

C9

c10

c11 c12

c6

c8

c13

c14 15

c16

c17

c18

1.11617

-0.92197 x +0.20463 x

-0.16458 x

+0.40809 x +O. 64947 -0.56929 x +0.18972 x

-0.29277 x

+0.20435 x -0.59274 x

-0.65404 x

+0.32751 x

-0.13449 x +0.22245 x

-0.51973 x -0.16038 x +0.41756 x

1.15132

-0.82968 x

+0.17060 x

-0.12645 x

+0.27657 x

+O .39 177 -0.36540 x +O. 12750 x -0.20230 x 10-7

+0.14233 x 10-lo

+0.13110 x 10-1

-0.18768 x

+o. 10199 x 10-5 -0.27004 x +0.36498 x

-0.35768 x -0.23579 x

+0.57329 x

4-35 DOE-HTGR-88111/Rev. 0

9 0 9 5 9 7 / 0

0

-1

-2

-3

0

H-451 AXIAL

2 4 6

FAST NEUTRON FLUENCE, CP N/M2) (E X . 1 8 MeV) HTGR

Fig. 4 . 6 - 1 . Design curves for dimensional change of H-451 g r a p h i t e , a x i a l o r i e n t a t i o n , as a func t ion of i r r a d i a t i o n condi t ions

4 - 3 6 DOE-HTGR-88111/Rev. 0

a

909597 / O

1

0

- 1

H-451 RADIAL

0 2 4 6 8

FAST NEUTRON F L U E N C E , @ ( 1 0 2 ' N/M2) (E >0.18 MeV)HTGR

Fig. 4 . 6 - 2 . Design curves for dimensional change of H-451 graphite, radial orientation, as a function of irradiation conditions

4 - 3 7 DOE-HTGR-8811l/Rev. 0

9 0 9 5 9 7 / 0

The maximum densification point and crossover point [LATER] are

shown in Fig. 4 . 6 - 3 (Ref. 4 - 3 4 ) .

The following horizontal shifting rule for the dimensional change

shall be used for the nonisothermal operating condition:

1.

2.

3 .

4 .

5.

Usable lifetime is conservatively defined as the fluence when

the graphite under irradiation returns to its original volume.

This fluence is represented by L(Ti) at temperature Ti.

The fraction of lifetime used by a fluence increment of A7(Ti)

is AUi = Ar(Ti)/L(Ti).

The cumulative usage fraction is AUi = Ui. i

A shift from the E1(Ti) curve to E1(Ti+l) curve under the non-

,isothermal condition is performed at equal Ui.

curve at Ui and beyond is horizontally shifted to the vertical

line (constant fluence) with the same Ui on the E1(Ti) curve.

The E1(Ti+l)

The vertical gap in EI [between the E1(Ti) and the shifted eI(Ti+l) at Vi] is assumed to be closed by the transient

ional chang

I Esh(Ti+l) = €I on the shifted E1(Ti+l) curve,

I ksh(Ti+l) = the vertical gap at Ar(Ti+l) = 0,

4 - 3 8 DOE-HTGR-881111Rev. 0

90959 7 / 0

Fig. 4 . 6 - 3 . Maximum densification point and crossover point for irradiated H-451 graphite as a function of irradiation temperature

4 - 3 9 DOE-HTGR-8811l/Rev. 0

909597 / O

A~(ti+l) = the fluence measured from the point with

Ui (the temperature change point),

r = a fluence constant, equal to 0.8 x

lo2' n/Cm2 (E > 29 fJ)HTGR.

4.6.2. Irradiation-Induced Creep

4.6.2.1. Rheological Model. Mechanical behavior of graphite under

irradiation has always been modeled for the HTGR as a standard linear

solid, as proposed by Head (Ref. 4-35). The one-dimensional standard

linear solid consists of a Kelvin element (spring and dashpot in paral-

lel) and a Maxwell element (spring and dashpot in series) in series.

The Kelvin element represents the transient response, and the Maxwell

element the steady-state response. Beside the above two elements, there

are two black box elements to represent the thermal strain and

irradiation strain components.

In the standard linear solid model, the total strain at any generic

point in an irradiated material body can be conveniently partitioned

into the following five components:

1. Thermal strain, E * .

2. Irradiation-induced dimensional change also called irradiation

strain, €1.

3 . Elastic strain, Ee.

4. Transient creep strain, ET.

5. Steady-state creep strain, eS.

E9 and E1 are the stress-free strain components. E e and Ee are

instantaneously recoverable, but the amount recovered may differ from

the initial strain imposed.

irrecoverable.

ET has delayed recovery. and E S are

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The thermal strain, E O , can be calculated for a given temperature distribution and thermal expansivity given in Section 4 . 4 . 2 .

irradiation-induced dimensional change, EI, can be obtained from Section 4.6 .2 . The remaining three strain components will be discussed

later.

The

Generalization of the one-dimensional creep model to multiaxial

case was reported in Ref. 4-36. The remaining three strain components

in the multiaxial case can be represented as a system of matrix differ-

ential equations. These are:

Elastic

g = !y ge .

Transient Cree2

*T E N

Steady Creep

* S E N

where the dot

,

( 4 - 2 2 )

( 4 - 2 3 )

represents differentiation with respect to fluence.

Equations 4-22 to 4-24 are coupled by the fact that the total

strain, $, is the sum of five components:

( 4 - 2 5 )

In the last four equations,

material properties ge, ET, Es, and ET are (6x6) matrices. and all g ’ s all (6x1) vectors, while the

Using the

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assumption of transverse isotropy and referring to a rectangular Carte-

sian coordinate system, typical vectors and matrices of these quantities

can be represented in component form as:

and

(ETy-1 =

1 T -

EX

1 - T EX

UT

Ez

ZX - - T 0

0 0

0 0

0 0 0 1 - T E,

2(l+vL ) 0 0 XY

Symmetric

1 - GT ZX

( 4 - 2 6 )

( 4 - 2 7 )

( 4 - 2 8 )

4-42 DOE-HTGR-88111/Rev. 0

S K

0 Y s Ms - Y s Ms 0 XY x zx 2

- Us Ms 0 0 zx z MS X

MS 0 0 2

2 ( l + v s )Ms 0 XY x

S yuunet r ic

2 XY

1 - U

Symmetric

0

MS ZX

0

0

0

0

s Gzx E,

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Y ( 4 - 2 9 )

9 ( 4 - 3 0 )

4 - 4 3 DOE-HTGR-g8111/Rev. 0

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E X

E2 where 7 = - ,

6 = vzx (1 + vxy) . ( 4 - 3 1 )

I t should be c l e a r t h a t t h e r e a r e f i v e independent m a t e r i a l parameters

conta ined i n each of t h e m a t e r i a l p rope r ty ma t r i ces as a d i r e c t con-

sequence of t h e t r a n s v e r s e i so t ropy assumption.

A f u r t h e r r educ t ion i n t h e number of p r i m i t i v e m a t e r i a l parameters

i s made by assuming:

( 4 - 3 2 )

where

t i m e . " With t h i s assumption, t h e system of ma t r ix E q . 4 - 2 3 becomes:

i s an i d e n t i t y ma t r ix and 4~ is a scalar c a l l e d t h e " r e l a x a t i o n

( 4 - 3 3 )

which is decoupled and, t h e r e f o r e , can be i n t e g r a t e d e a s i l y . The

p h y s i c a l i m p l i c a t i o n of t h e assumption ( 4 - 2 3 ) i s tha t t h e r e l a x a t i o n

t i m e cons t an t i s t h e s a m e i n a l l d i r e c t i o n s and t h a t t h e Po i s son ' s

r a t i o s a r e t h e same i n both t h e p a r a l l e l s p r i n g and t h e dashpot

mechanisms, ET and ET.

An i n t u i t i v e assumption i s in t roduced f o r GZx, Ms and G i x : zx'

1 - 2 Ex + E2

Gzx = 2 (1 + V Z X ) '

4 - 4 4 DOE-HTGR-88111/Rev. 0

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1 1 + - s 1 - - s 1 2 Mx Mz - - -

S Ms 2 1 + uzx 9

zx

( 4 - 3 4 )

1 ET + ET 2 x Z GT =

T 2 1 + uzx zx

After the last two assumptions, the independent material parameters

for the viscoelastic response of core graphite are:

Elastic

Steady Creep

Transient Creep

The linear elastic material properties are given in Section 4.5 .1 . The

remaining material properties will be specified in the next section.

4 . 6 . 2 . 2 . Irradiation Creep Parameter. A l l the Poisson’s ratios in

creep, namely, Vgy, Vgx, u&, and uTX are assumed to be constant. This

is due to two considerations. First, the creep data are not sufficient

and derive a set of values as a function of temperature and fluence.

Secondly, the more important one is that the stress results are not

4-45 DOE-HTGR-88111/Rev. 0

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sensitive to the creep Poisson's ratios. Based on the OC creep series,

the following value is recommended for use (Ref. 4-37):

us = u i x = 0.5 XY

The "relaxation time," @R, is best estimated to be 4 x n/cm2 (E > 0.18 MeV, HTGR) from pooled data of all available graphite experiments

(Ref. 4-38). This value is assumed to apply to H-451 graphite. The

relaxation time does not have significant.effect on the irradiation

stress at or beyond a fluence of, say, five times the "relaxation time."

The transient creep elastic moduli, E$ and ET, are taken to equal the respective elastic moduli at the "time" loading or unloading occurs

(Ref. 4-38).

The remaining last two material properties are the steady creep

mobility coefficients in two directions ( o r called steady-state creep

coefficients), M$ and Mg. specimens, it is reasonable to assume:

Due to small number of radial creep

Ms = Ms . X z

Reference 4-39 recommends the following expression for design use:

B B

E = - [l - exp (-25 4 ) ] + E (2.87128 @ + 0.14853 @T

- 2.48083 a2 + 0.25992 Q2T + 0.44420 a3 - 0.05671 a2T) , (4-35)

4-46 DOE-HTGR-88111/Rev. 0

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where 4 = f a s t neut ron f luence (n/cm2 x E > 29 f J > ,

T = i r r a d i a t i o n temperature ( O C / l O O ) ,

E = e la s t i c modulus a t t h e " t i m e " loading o r unloading occurs

(GPa),

U = app l i ed stress (MPa).

4.6.3.2. E f f e c t of Creep S t r a i n on Phys ica l P r o p e r t i e s . Creep s t r a i n

up t o 4.5% does not s i g n i f i c a n t l y a l t e r d e n s i t y , e l a s t i c modulus, d e f e c t

s i z e (hence s o n i c a t t e n u a t i o n ) and e lec t r ica l r e s i s t i v i t y (Refs . 4-40

and 4-41).

ab ly a f f e c t e d by a c reep s t r a i n component. The fo l lowing r e l a t i o n s h i p

is obta ined a t 8OO0C from a x i a l specimens i n a compression c reep s e r i e s

(Ref. 4-41):

Thermal expans iv i ty is t h e only p rope r ty known t o be no t i ce -

QC = Qo - 0.504 E C .

where Q, = c o e f f i c i e n t of thermal expansion ( t o 8000C) of a c reep

specimen w i t h c reep s t r a i n of tC ( 10-6/0C),

a, = c o e f f i c i e n t of thermal expansion ( t o 80OoC) of an uns t r e s sed

c o n t r o l specimen i r r a d i a t e d under t h e same c o n d i t i o n as t h e

c reep specimen ( 10-6/ O C ,

eC = c reep s t r a i n , nega t ive f o r compressive c reep s t r a i n ( % ) .

The r e l a t i o n s h i p is assumed t o be a p p l i c a b l e t o t e n s i l e c reep r eg ion as

w e l l as t o t h e r a d i a l d i r e c t i o n .

4.7. REFERENCES

4-1. "Core Graphi te Conceptual Design Cri ter ia ," Document 908950/0,

August 29, 1986.

4-2. Engle, G. B . , and R. J. Price, "St rength Tes t ing of Product ion

Grade H-451 Graphi te ; Lots 472, 478, and 482," ERDA Report

GA-A14269, March 1977.

4-47 DOE-HTGR-88111/Rev. 0

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4-3. "Coolant Impurity/Core Material Interaction," in "HTGR Fuels

and Core Development Program, Quarterly Progress Report for

the Period Ending August 31, 1976," ERDA Report GA-A14046,

September 24, p. 4-26 (1976).

4-4. Velasquez, C., G. Hightower, and R. Burnette, "The Oxidation of H-451 Graphite by Steam, Part 1: Reaction Kinetics," DOE

Report GA-A14951, August 1978.

4-5. Peroomian, M. B., A. W. Barsell, and J. C. Seager, "OXIDE-3: A



4-6. Burnette, R. D., et al., "Studies of the Rate of Oxidation of ATJ Graphite by Steam," in Proceedings of 13th Biennial Conference on

Carbon at Irvine, California, July 13-22, 1977.

4-7. "HTGR Fuels and Core Development Program, Quarterly Progress

Report for the Period Ending August 31, 1977," ERDA Report

GA-A14479, September 1977, p. 11-16.

4-8. Jensen, D., M. Tagami, and C. Velasquez, "Air/H-327 Graphite

Reaction Rate as a Function of Temperature and Irradiation," GA

Report Gulf-GA-A12647, September 24, 1973.

4-9. Jensen, D., et al., "Air/H-327 Graphite Reaction Rate as a Function of Temperature and Irradiation," Gulf-GA-A12647,

September 24, 1973.

4-10. Eto, M., et al., "Estimation of the Graphite Materials With Water Vapor," presented at IAEA Specialists Meeting on Graphite

Component Design, September 8, 1986, at JAERI, Japan. See also

JAERI-M8848 and 9166 (1980).

4-11. Butland, A. T. D., and R. J. Maddison, "The Specific Heat of Graphite: An Evaluation of Measurements," Journal of Nuclear

Material, 2, 45 (1973 to 1974). 4-12. Johnson, W. R., and G. B. Engle, "Properties of Unirradiated Fuel

Element Graphites H-451 and TS-1240," ERDA Report GA-A13752,

January 31, 1976.

4-13. Engle, G. B., and W. R. Johnson, "Properties of Unirradiated Fuel Element Graphites H-451 and S0818," ERDA Report GA-A14068,

October 1976.

4-48 DOE-HTGR-88111/Rev. 0

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4- 14.

4- 15.

4-16.

4-17.

4- 18.

4-19.

4-20.

4-21.

4-22.

4-23.

4-24.

4-25.

4-26.

4-27

Beavan, L. A., "Properties of Unirradiated Production Grade H-451, Lot 478," DOE Report GA-A15116, January 1979.

Price, R. J., and L. A. Beavan, "Final Report on Graphite Irradi-

ation Test OG-3," ERDA Report GA-A14211, January 1977.

Price, R. J., and G. Hagg, "Property Changes in Graphite Irradi- ated at Changing Irradiation Temperature," GA Report GA-A15270,

July 1979.

Price, R. J. , "Review of the Thermal Conductivity of Nuclear

Graphite Under HTGR Conditions," GA Report Gulf-GA-A12615,

September 1973.

Engle, G. B., and K. Koyama, "Dimensional and Property Changes of Graphites Irradiated at High Temperatures," Carbon 6, p. 455,

1968.

Kelly, B. T., et al., "The annealing of Irradiation Damage in Graphite," Journal of Nuclear Material, 20, p. 195, 1966. Grenis, A. F., and A. P. Levilt, "The Spectral Emissivity and Total Normal Emissivity of Commercial Graphites at Elevated Tem-

peratures," Proceedings of Fifth Conference on Carbon, p. 639

(1961).

Plunkett, J. D., and W. D. Kingery, "The Spectral and Integrated Emissivity of Carbon and Graphite," Proceedings of Fourth Carbon

Conference, p. 457 (1960). Autio, G. W., and E. Scula, "The Normal Spectral Emissivity of

Isotropic and Anisotropic Materials," Carbon 4, pp. 13-28 (1966). Ho, F. H., to be determined. Smith, M. C., "Effects of Temperature and Strain Rate on Transverse Tensile Properties of H4LM Graphite Tested in Helium

and in Vacuum," Carbon 1, 147 (1964).

Price, R. J., "Test Status Report: Graphite Irradiation Capsule

OG-5," GA Document 906247, Issue 1, October 20, 1981. Price, R. J. , "Test Status Report: Uniaxial Stress-Strain Tests

on H-451 Graphite," GA Document 906469, Issue 1, April 30, 1982.

[LATER]


909597/0

4-28. Ho, F. H., et al., "Biaxial Failure Surfaces of 2020 and PGX

Graphites," Paper No. L4/6, P. 127, Transactions of the 7th

International Conference on Structural Mechanics in Reactor

Technology, Chicago, IL, August 22, 1983. "High-Temperature Gas-Cooled Reactor Technology Development

Program, Annual Progress Report f o r Period Ending December 31,

4-28.

4-29.

4-30.

4-3 1.

4-32.

4-33.

4-34.

4-35.

4-36.

4-37.

4-39.

4-40.

4-41.

4-42.

1982," ORNL-5960, June 1983.

"HTGR Technology Development Program Annual Progress Report for

Period Ending December 31, 1983," ORNL-6053, June 1984.

Velasquez, C., et al., "The Effect of Steam Oxidation on the

Strength and Young's Modulus of Graphite H-451," DOE Report

GA-A14657, December 1977.

Price, R. J., and L. A. Beavan, "Final Report on Graphite Irradiation Test OG-1, "USAEC Report Ga-A13089, August 1, 1974.

Price, R. J., and L. A. Beavan, "Final Report on Graphite Irradiation Test OG-2," ERDA Report GA-A13556, December 15, 1975.

Price, R. J., "Design Polynomial for Irradiation Strain in H-327

and H-451 Graphite, Rev. 10/8/83," GA Document 907173, Issue 1,

October 28, 1983.

[LATER]

Head, J. L., "The Transient Creep of Graphite in a Reactor Environment," Proceedings 3rd SMIRT Conference, London, United

Kingdom, September 1-5, 1975, Paper C1/6. Tang, P., "Graphite Creep Subroutines i n the TWOD/THREED Codes,"

GA Document 906120/1, August 10, 1981.

"Monthly Progress Report for February 1982, HTR Technology

Program," ORNL/GCR/B-82/2, March 1982.

Ho, F. H., '"-451 Irradiation Creep Design Model"; DOE-HTGR-

88097/0, GA Document 909679/0, May 27, 1988.

"High-Temperature Gas-Cooled Reactor Technology Development

Program Annual Progress Report for Period Ending December 31,

1983," ORNL-6053, UC-77, June 1984.

"Graphite Data Manual," DOE-HTGR [LATER], to be issued. "Fuel Design Data Manual," GA Document 901866/F, April 1987.

4-50 DOE-HTGR-881111Rev. 0

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