NBSIR 84-3000

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TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES -VII

To

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

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Fracture and Deformation Division

National Bureau of Standards

Boulder, CO 80303

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NBSIR 84-3000

TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES

UC 20b, c

'NATIONAL BUREAU

OF f. LIBRARY

-VII

Edited By

R.P. Reed and N.J. Simon

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

May 1984

Sponsored By

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

CONTENTS

Page

SUMMARY v

ORGANIZATIONAL CONTACTS vi

PROGRAM DESCRIPTION vi

HIGHLIGHTS OF RESULTS 1

STRUCTURAL ALLOYS

STRUCTURAL ALLOYS PROGRAM 11

SUMMARY OF MECHANICAL PROPERTY MEASUREMENTS OF STRUCTURAL ALLOYS. . . 12

LOW TEMPERATURE STRENGTHENING OF AUSTENITIC

STAINLESS STEELS WITH NITROGEN AND CARBON 13

DILATION OF AN FCC Fe-Cr-Ni ALLOY BY INTERSTITIAL

CARBON AND NITROGEN 25

EFFECTS OF CARBON AND NITROGEN ON THE ELASTIC

CONSTANTS OF 304-TYPE STAINLESS STEEL 47

THE TEMPERATURE DEPENDENCE OF THE TENSILE YIELD

STRENGTH OF SELECTED AUSTENITIC STEELS 65

MAGNETIC SUSCEPTIBILITY AND STRAIN-INDUCED MARTENSITE

FORMATION AT 4 K IN TYPE 304 STAINLESS STEEL 75

FATIGUE CRACK GROWTH IN SENSITIZED Fe-18Cr-3Ni-13Mn-0.37N

AUSTENITIC STAINLESS STEEL: THE SIGNIFICANCE OF MICROMECHANISMS. . . 85

MIDRANGE FATIGUE CRACK GROWTH DATA CORRELATIONS FOR STRUCTURAL

ALLOYS AT ROOM AND CRYOGENIC TEMPERATURES 103

AN AUTOMATED FATIGUE CRACK GROWTH RATE TEST

SYSTEM 141

LOW TEMPERATURE MONOCRYSTAL ELASTIC CONSTANTS OF

Fe-19Cr-10Ni 157

A NUMERICAL AND EXPERIMENTAL V ERF I CAT I ON OF COMPLIANCE

FUNCTIONS FOR COMPACT SPECIMENS 181

DESIGN AND PERFORMANCE OF A RING-SHAPED CLIP GAGE

FOR FRACTURE MECHANICS TESTING 209

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF MECHANICAL

PROPERTY TEST STANDARDS TO LIQUID HELIUM TEMPERATURE (4 K) 227
CONTENTS (Cont'd)

Page

WELDMENTS AND CASTINGS

WELDMENTS AND CASTINGS PROGRAM 241

SUMMARY OF MECHANICAL PROPERTY MEASUREMENTS OF WELDS 242

FRACTURE TOUGHNESS OF 25 Mn AUSTENITIC STEEL

WELDMENTS AT 4 K 243

TENSILE PROPERTIES AND FRACTURE TOUGHNESS OF

320LR SMA WELD METAL AT 4 K 253

FATIGUE CRACK GROWTH OF DUPLEX STAINLESS STEEL

CASTINGS AT 4 K 263

NONMETALLICS

NONMETALLICS PROGRAM 287

CONTINUOUS DAMAGE MECHANICS MODEL OF FRACTURE

IN LAMINATED COMPOSITES 289

INFLUENCE OF DAMAGE ON MECHANICAL PROPERTIES OF

WOVEN COMPOSITES AT LOW TEMPERATURES 329

NONMETALLIC MATERIAL STANDARDIZATION - MATERIALS

AND TEST METHODS 347

MECHANICAL PROPERTIES OF CONCRETE MORTAR AT LOW

TEMPERATURES 357

TENSILE, COMPRESSIVE, AND SHEAR PROPERTIES OF A

64-kg/m 3 POLYURETHANE FOAM AT LOW TEMPERATURES 365

TENSILE, COMPRESSIVE, AND SHEAR PROPERTIES OF A

96-kg/m 3 POLYURETHANE FOAM AT LOW TEMPERATURES 397

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF MECHANICAL

PROPERTY DATA FOR TENSILE TESTING OF COMPOSITE

MATERIALS TO LIQUID HELIUM TEMPERATURE (4 K) 425

TECHNOLOGY TRANSFER

TECHNOLOGY TRANSFER PROGRAM 435

NBS-DoE WORKSHOP: MATERIALS AT LOW TEMPERATURES 437

ACKNOWLEDGMENT 447

IV
SUMMARY

This report contains results of a research program to produce material property data that will

facilitate design and development of cryogenic structures for the superconducting magnets of magnetic

fusion energy power plants and prototypes. The program was developed jointly by the staffs of the

National Bureau of Standards and the Office of Fusion Energy of the Department of Energy; it is managed by NBS and sponsored by DoE. Research is conducted at NBS and at various other laboratories

through subcontracts with NBS.

Research results for 1983 are summarized in an initial "Highlights of Results" section and

reported in detail in the 22 technical papers that form the main body of this report. The technical

papers are presented under four headings reflecting the main program areas: structural alloys,

weldments and castings, nonmetal 1 ics , and technology transfer. Objectives, approaches, and

achievements are summarized in an introduction to each program area.

Work leading toward development of strong, tough structural alloys for use in superconducting

magnets continued this year, with low temperature studies assessing the quantitative dependence of the yield strength, density, and elastic constants of AISI 304 stainless steels upon carbon and

nitrogen concentration. Tensile property measurements of developmental austenitic steels from the

U.S., Japan, and the U.S.S.R. confirmed a logarithmic dependence of yield strength upon temperature

between 4 K and room temperature. Evidence is presented to show that the flow strength and austenite

stability of stainless steels are not significantly affected by 8-T fields at 4 K. New instrumentation

developed for low-temperature testing included a computer-assisted apparatus that was used to measure

threshold fatigue. Low-temperature welding research involved an investigation of the weld reinforcement

effect on the weld joint strength and measurements of the 4-K fracture toughness of 25MN - 5Cr

steel weldments and 320LR electrodes. In the area of nonmetal 1 ics , a standardized test specimen

was devised for a screening program to develop radiation-resistant composites for magnet insulation,

and models to predict damage in woven glass/epoxy laminates were tested experimentally at low

temperatures. Mechanical properties of concrete mortar and polyurethane foam at 4 K are reported.

Note : Certain commercial equipment, instruments, or materials are identified in this paper to specify the experimental procedure adequately. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best available for the purpose. Papers by non-NBS authors have not been reviewed or edited by the NBS editors. Therefore, the National Bureau of Standards accepts no responsibility for the comments or recommendations contained

therein.

V
ORGANIZATIONAL CONTACTS

The people responsible for the various major aspects of the program are listed below so that specific technical questions may be directed to them.

Department of Energy, Office of Fusion Energy, Washington, D.C. 20545

Program Monitor D. Beard (301) 353-4958

(FTS) 233-4958

National Bureau of Standards, Boulder, Colorado 80303

Program Manager R. P. Reed (303)

(FTS)

497-3870

320-3870

Structural Alloys R. P. Reed (303) 497-3870

R. L. Tobler (303) 497-3421

J. M. Arvidson (303) 497-3424

R. P. Walsh (303) 497-3537

Elastic Properties H. M. Ledbetter (303) 497-3443

Welding and Casting T. A. Siewert (303) 497-3523

H. I. McHenry (303) 497-3268

P. Purtscher (303) 497-5789

Nonmetal 1 ics M. B. Kasen (303) 497-3558

H. M. Ledbetter (303) 497-3443

R. D. Kriz (303) 497-3547

Technology Transfer N. J. Simon (303) 497-3687

University of Colorado, Mechanical Engineering Department, Boulder,

Colorado 80309

S. K. Datta (303) 492-7750
PROGRAM DESCRIPTION

The overall objective of the program is to assist in the design,

construction, and safe operation of 1 ow-temperature magnetic fusion

energy (MFE) systems, especially syperconducting magnets, through effective materials research and materials technology transfer. The specific

steps taken to achieve this objective are: (1) evaluation of low-temperature materials research needs specific to MFE devices; (2) development and monitoring of a research program to acquire the necessary data;

and (3) rapid dissemination of the data to potential users through personal contacts, publications, and workshops.

Efforts directed at the first specific objective began with the

publication of the "Survey of Low Temperature Materials for Magnetic

Fusion Energy" in March 1977. A recent publication updating part of

this survey, "Structural Alloys for Superconducting Magnets in Fusion

Energy System," was included in volume IV (1981) of this series. In

volume VI (1983), reviews of the properties of austenitic stainless

steels and of austenitic-steel elastic constants also contributed to

this objective. Through interactions with 1 ow-temperature design, con- struction, and measurement programs, such as the Large Coil Project and

MFTF-B, we are aware of new problems as they arise. This year's

contribution to the second objective is described in Table 1 in the form

of an outline of the research projects. The results appear later in

this report. Again this year, increased emphasis has been placed upon

research oriented toward the establishment of test standards. The third

objective is satisfied, in part, by these annual reports and by the

series of NBS-DoE Workshops on Materials at Low Temperatures, which are

held in Vail, Colorado. Since 1982, handbook pages presenting the

available data for specific materials have been distributed to

interested members of the low-temperature materials community.

vn
Table 1. Outline of the NBS/DoE Program on Material Studies for

Magnetic Fusion Energy Applications at Low Temperatures.

Program Area Organization Program Description

A. Structural Alloys

1. Strong, tough alloys NBS

2. Strong, fatigue-resistant NBS

al 1 oys

3. Low-temperature codes NBS

and standards

4. Physical properties NBS

B. Weldments and

1. Austenitic-steel NBS

wel ds

Assessment of low-temperature properties of selected

austenitic alloys containing

varying concentrations of C,

N, and Mn with an Fe-Cr base.

Assessment of Japanese aus- tenitic alloys with an Fe-Mn

base.

Assessment of fatigue and

fatigue crack-growth rates

of candidate structural

alloys, including 300 series

steels, Fe-Mn base alloys,

and age-hardened alloys.

Research to establish lowtemperature mechanical test

standards, now emphasizing

tensile, fracture toughness,

and fatigue.

Measurement and theory of

properties, such as elastic

constants and volume;

especially, alloying

effects

Casti ngs

Evaluation of the strength

and toughness properties of

weldments at 4 K. Continuation of studies to understand the mechanisms by

which residual delta ferrite

affects the deformation and

fracture of stainless-steel

welds.
Program Area Organization Program Description

2. Testing program NBS Continuation of mechanical

property testing at 4 K of

welds and plate material in

support of superconducting

magnet design and construction.

C. Nonmetallics for Magnet Structures

1. Standardization NBS Continued cooperation with

industry to refine

cryogenic-grade specifications for commercial

nonmetal lie bulk insulating

1 ami nates

2. Characterization NBS Determination of the variability in cryogenic

mechanical properties of

G-10CR cryogenic-grade

industrial laminates

produced by five U.S.

manuf acturers

3. Research materials NBS Development of methods for

rapidly and inexpensively

producing highly characterized, small specimens for

use in screening the

significant parameters

influencing cryogenic

radiation resistance of

nonmetal lie composite

i nsul ators

4. International cooperation NBS,

Rutherf ord

Laboratory,

Osaka

University

Agreement to actively

cooperate in development of

specimens, materials selection, and test procedures

in developing radiationresistant insulating

material s

IX
Program Area Organization Program Description

5. Property determination NBS

and model i ng

For laminated composites,

experimental and theoretical

study of the physical - mechanical properties,

especially at low

temperatures . Study of

the local-stress distribution

in a glass-fiber/epoxy

composite "unit cell" using

finite-element methods.

D. Technology Transfer

1. NBS/DoE Workshop NBS Presentation of research

results to the fusion com- munity, discussion of new

problems, and interaction

between interested parties

during a workshop.

2. Handbook NBS Distribution (1983) of

preliminary handbook data

pages on mechanical and

physical properties of 210-

6Ni-9Mn stainless steel.

Distribution (1984) of

AISI 304N and 304LN

stainless steels data pages

and preliminary work on handbook pages for AISI 316L

and 304 weldments.

x
HIGHLIGHTS OF RESUL TS

1

HIGHLIGHTS OF RESULTS

STRUCTURAL ALLOYS:

Strong, Tough Alloys

The studies leading toward development of strong, tough structural alloys

for superconducting magnet use continued, resulting in the following major

accompl i shments

1. The functional dependence of the yield strength on carbon and nitrogen

concentration in austenitic stainless steel 304 was assessed using

regression analyses of all available data at 4, 77, and 295 K. This

study indicated that carbon and nitrogen contribute about equally at room temperature, but at 4 K nitrogen contributes about 3 times more

than carbon to yield strength. Both elements contribute substantially

to strength at low temperatures. No clear power dependence of strength

upon carbon and nitrogen content could be found.

2. Tensile measurements on two Japanese austenitic steels, one steel

from the USSR, and two U.S. austenitic stainless steels confirmed

that the log of the yield strength is linearly related to the test

temperature.

3. Further measurements of the effects of magnetic field on austenitic

stainless steels provided additional evidence that the flow strength

and austenite stability are not significantly affected by fields up

to 8 T at 4 K.

Strong, Fatigue-Resistant Alloys

An program to measure fatigue crack growth rates at low stress-intensity

factors was initiated. Highlights are:

3
1. A computer-assisted program to measure threshold fatigue at low

temperatures has been developed and is now being used for measurements .

2. Fatigue crack initiation measurements were begun.

Codes and Standards

A proposal to provide the information needed to extend tensile test

standards to very low temperatures has been prepared for the Metal Properties

Council (MPC). The program considers the effects of strain rate on specimen

heating (and, therefore, flow strength) and grain size (to establish minimum

specimen sizes). Cooperation is continuing between NBS, industry, and other

government laboratories in an established MPC Low Temperature Task Group to

develop this program.

Physical Properties

Programs to understand the alloying effects in austenitic steels were

continued. Such understanding is essential to the design and processing of

these steels to insure optimum strength and toughness.

1. Using ultrasonic methods (near 5 MHz), the monocrystal elastic

constants (C^, C^, C^) of a Fe-19Cr-10Ni alloy were determined . This information is essential to understanding the property changes

that occur in these alloys because of a magnetic phase transition

near 50 K.

2. By ultrasonic methods, the effect of interstitial atoms on the

polycrystalline elastic constants (B, E, G, v) of a typical

austenitic stainless steel (AISI 304) was examined.

3. By x-ray diffraction from bulk specimens, the effect of interstitial

atoms in expanding the f.c.c. austenitic-iron unit cell of AISI 304

was studied. Such information is essential to models of

solid-solution strengthening.

4
WELDMENTS AND CASTINGS:

Weldments

An investigation of the weld reinforcement effect on the weld joint

strength of the 304L base/E316L filler weldment system in the temperature

range of 4 to 295 K shows that there is no adverse effect of the reinforcement

on strength. The results also indicate that the tensile strengths obtained

2 from the large specimens (cross-sectional area of 258 mm ) agree well with

2 those obtained from the smaller specimens (cross-sectional area of 9.62 mm ).

The fracture toughness, Jj , of 25Mn-5Cr steel weldments was measured at

4 K. The highest Jj value obtained was from a GTA weld, followed by an SMA

weld; an SA weld had the lowest Jj value. Degradation of fracture toughness

of the HAZ was observed because of the excessive carbide precipitation along

the grain boundary. The present results compare favorably with those of

stainless steel weldments produced with the same welding processes.

The tensile properties and fracture toughness of the 320LR electrode were measured at 4 K. The results show that the 320LR electrode has slightly lower

yield and ultimate tensile strengths than the 316L electrode does. The fracture

toughnesses of the 320LR and 316L electrodes are comparable.

Castings

The fatigue crack growth rates of a series of CF8M stainless steel castings

with varying delta-ferrite content were measured at 4 K. The results show

that the range of fatigue crack growth rates in CF8M castings fall within the

scatter band of AISI 316 results and are not significantly affected by the

delta-ferrite content, which ranged from 0 to 29 percent. Tensile properties

and fracture toughness measurements of this series of CF8M castings are reported

in volume VI of these reports.

5
NONMETALLICS

Standardi zation

We continue to work with representati ves of the United States laminating

industry to provide magnet builders with commercial sources of standardized,

reliable, nonmetallic insulating materials. The original specifications for

the CR-grade products were found to be unnecessarily restrictive in component

selection and did not contain minimum performance criteria. The specification

for G-10CR was therefore modified with industry consultation and guidance.

Further development of the G- 1 ICR specification will take place when the extent

of its future use by industry is clarified.

Characterization

By mechanical testing at 77 K, we have shown that the differences in room temperature or cryogenic mechanical performance of G-10CR products produced by

five U.S. laminating firms are not statistically significant. The existing

specification for this material, therefore, appears capable of ensuring the

desired uniformity in material performance.

Controlled Test-Specimen Development

Recognizing the unique demands put on specimens to be used in radiation

research, we have begun development of methods to produce specimens combining

the attributes of low cost, a high degree of characterization, small size, and

flexibility in component selection and treatment. These specimens will be

used in a screening program to define the significant parameters influencing

cryogenic radiation degradation. This information will then be used to design

optimum types of insulating laminates for use in magnet systems.

International Cooperation

Agreement has been reached between representatives of NBS, the Rutherford

Laboratory (England) and the ISIR (Osaka, Japan) to work toward development of

a common type of test specimen to be used in evaluating the influence of

6
various parameters on cryogenic composite radiation property degradation. A common approach to a method of specimen production has been agreed upon, and

procedures have been worked out for cooperative assessment of this method.

Property Determination and Modeling

1 . Prediction of cumulative damage in graphite/epoxy laminates at low

temperatures . By Kachanov's cumulative damage model, the influence

of residual thermal stresses at 76 K on the growth of ply cracks in

load-bearing plies of graphite/epoxy laminates were predicted. The

model assumes a localization of fiber fractures ahead of a dominant

ply crack. The model predicts a latent phase of damage development

followed by a rapid and severe damage localization occurring just

prior to final fracture. The results verify the experimental results

of previous investigators. A decrease in ply crack growth caused by

residual stresses at 76 K is predicted. Absorbed moisture was observed

to increase the growth of the dominant ply crack.

2. Prediction of stress redistribution caused by damage development in

woven composites at 76 K. By finite-element analysis, the redistribution of localized stresses in the woven glass/epoxy unit cell was studied. Stress concentrations in the warp-fiber bundles are predicted

near damaged fill-fiber bundles. Increases in curvature and residual

stresses at low temperatures decreased the stress concentration near damaged fill-fiber bundles. Previous experiments verify this increase

in strength at low temperature.

TECHNOLOGY TRANSFER

An NBS/DoE Workshop on Materials at Low Temperatures was held in Vail,

Colorado on October 17-19, 1983. The workshop brought together representati ves

of the fusion energy materials and magnet design community and served as a focal point to identify and discuss structural materials problems in superconducting magnet design and construction. The workshop is informal and its

proceedings are not published. A copy of the program and highlights of the

discussions may be found in the Technology Transfer section of this repor*

7
Handbook and supporting documentation pages have been prepared for 21Cr6Ni-9Mn stainless steels and distributed in preliminary draft format. Properties covered include: tensile strength, yield strength, elongation, reduction

of area, stress-strain curves, elastic constants, impact energy, fracture

toughness, stress- and strain-controlled fatigue life, fatigue crack growth

rate, and electromagnetic and thermal properties. These pages were also submitted to the advisory committee of the "Materials Handbook for Fusion Energy

Systems" and are currently in the review process. Preliminary work on handbook

pages covering AISI 304N and 304LN is in progress.

8
STRUCTURAL ALLOYS

STRUCTURAL ALLOYS PROGRAM

LEADER: R. P. Reed, NBS

STAFF: J. M. Arvidson, H. M. Ledbetter, R. L. Tobler, R. P. Walsh, NBS

OBJECTIVES:

(1) Development of strong, tough structural alloys for use at 4 K

in superconducting magnets.

(2) Development of strong, fatigue-resistant structural alloys for

use at 4 K in pulsed superconducting magnets.

(3) Development of effective codes and standards related to lowtemperature property measurements and structural design.

RESEARCH PAST YEAR (1983):

(1) Analysis of C and N effects on low temperature tensile

properties of 304 austenitic stainless steel.

(2) Characteri zation of the tensile behavior of Japanese, Soviet

and U.S. austenitic steels.

(3) Examination of effects of magnetic fields on 1 ow-temperature

strength and phase stability of 304 and 310 austenitic

stainless steels.

(4) Determination of monocrystal elastic constants of an austenitic

stainless steel ( Fe-19Cr-10Ni ) at low temperatures.

Measurements of the effects of C and N on the elastic constants

and dilatation of an austenitic steel.

RESEARCH THIS YEAR (1984):

(1) Characterization of Japanese high-manganese and austenitic

stainless steels.

(2) Assessment of the use of the notch-tensile test to replace the

J-integral fracture toughness test for routine testing at 4 K. (3) Measurement of temperature-dependence of flow strength of OFHC

copper and 1100 aluminum.

(4) Initiation of a cooperative program with industry to develop a lower cost alloy than 304 LN, with equivalent strength and

toughness at 4 K. (5) Threshold fatigue testing of 304, 316, and 310 steels at 4, 76,

and 295 K. (6) Continued studies on low temperature elastic properties of

austenitic steels.

(7) Initiation of a program to measure the stacking-fault energy of

high-manganese austenitic steels.

(8) Continuation of efforts to establish a program to develop

low-temperature mechanical -property test standards.

11
SUMMARY OF MECHANICAL PROPERTY MEASUREMENTS OF STRUCTURAL ALLOYS

Country Fracture Fatigue Crack Fatigue

Alloy of Tensile Elastic Toughness Growth Rate S-N Report Volume*

(Designation) Suppl ier 295,4 K 295-4 K 295,76,4 K 295,76,4 K 4 K (page)

AUSTENITIC STEELS Fe-19Cr-9Ni U.S. I, II, III I, II, III 1,11,111, II, III, IV I 1(15,71,213),

(304) IV, VI IV, VI IV 11(79,149,175),

111(15,91,105,

117) , I V ( 37 , 101

,

203,215,227) ,V(71)

VI ( 73)

Fe-19Cr-9Ni U.S. II, III, 1,11. III, IV III, IV 1(213), 11(79, 123,

( 304L

)

IV IV 175) , 1 1 1( 15) , I V( 37

,

101,131,302,215)

Fe-19Cr-9Ni-N U.S. I.III, IV I, III, IV I, III, IV 1(93), 111(15), IV

( 304N) IV (37,101,203,215)

Fe- 19Cr-9Ni -N U.S. II, III, IV II, III, II, III, IV II 11(35, 79), 111(15),

(304LN) IV,V,VI IV I V ( 37 ,101 ,203) ,V(29)

VI ( 113)

Fe-19Cr-9Ni- U.S. IV,

V

V IV,

V

IV(77) ,V( 15,59 , 189)

1 to 8Mn (304LN)

Fe-17Cr-9Ni-8Mn U.S. III 111(91)

Fe-17Cr-13Ni-2Mo U.S. I, II, III VI I,II II I 1(15, 71), 11(79),

(316) IV, VI 111(49,105,117),

IV( 147) ,V( 185) ,VI (87)

,

VI (157)

Fe-17Cr-13Ni-2Mo U.S. II II II 11(79)

(316LN)

Fe-25Cr-21Ni U.S. V,V I III, VI V 111(105, 117), V( 71

,

(310) 145) , VI ( 73)

Fe-18Cr-3Ni-13Mn U.S. I.VI III I I,VI 1(93), 111(91), VI ( 53)

Fe-21Cr-6Ni -9Mn U.S. I III, VI I I 1(15, 71), 111(91), VI ( 157)

(21/6/9)

Fe-21Cr-12Ni -5Mn U.S. 1,11 III I,II I,II 1(93), 11(79),

111(91)

Fe-13Cr-19Mn USSR III VI 111(79), VI (41)

Fe-20Cr-16Ni-6Mn USSR V , VI V V(29,213) , V I (113)

Fe-19Ni-9Co

(200-300 grades)

U.S. IV I V ( 237

)

Fe-5Cr-26Mn Japan VI VI ( 181

)

Many alloys Review Review Revi ew Review Review I V( 17,257 ) , V( 171

)

IV ,V ,VI IV,V,VI IV,V,VI IV,V,VI IV, VI VI (11) ,VI ( 127) ,VI (157)

ALUMINUM ALLOYS Al-4Mg U.S. IV II 11(35), I V( 185)

(5083-0)

Al-6Cu-0.2Mn-0.1Fe U.S. II II II II 11(19)

(2219-T87) SUPERCONDUCTORS

Nb-45T

U.S. III 111(133)

*Materials Studies for Magnetic Fusion Energy Applications at Low Temperatures: NBS1R 78-884 (I); NBSIR 79-1609 (II); NBSIR 80-1627 (III); NBSIR 81-1645 (IV); NBSIR 82-1667 (V); NBSIR 83-1 690( VI

)

12
LOW TEMPERATURE STRENGTHENING OF AUSTENITIC

STAINLESS STEELS WITH NITROGEN AND CARBON*

R. P. Reed and N. J. Simon

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

The quantitative effects of N and C concentration upon the yield strength

of 18Cr-9Ni austenitic stainless steels (AISI 304 series) was determined at room temperature, 77 K, and 4 K, based upon data available in the literature.

Strengthening by N and C was found to be strongly dependent upon temperature,

with effects of N generally dominating those of C, except at room temperature.

Results are discussed with regard to solid-solution strengthening theories.

*Published in Advances in Cryogenic Engineering - Materials , vol. 30, Plenum

Press, New York (1984), pp. 127-136.

13

INTRODUCTION

Austenitic steels have been used extensively in the construction of superconducting magnets. To restrain high field forces in

the support structures, stronger alloys than the conventional AISI

300 series stainless steels must be developed and characterized for use at liquid helium temperatures. These stronger alloys must also

retain adequate low temperature toughness. In the past few years

there have been several studies of high-N 18Cr-9Ni austenitic stainless steels (AISI 304LN, 304N, and higher N alloys). They demonstrate that N and C additions significantly raise the strength of

the steels at low temperatures.

This paper examines quantitative effects of N and C on the

strength of 18Cr-9Ni austenitic stainless steels (304 base) at room temperature, 77 K, and 4 K. The dependence of tensile yield

strength (a ) on the at.% of N and C (designated as [N] and [ C ]

)

is analyzed^ The results are discussed with respect to current

solid-solution strengthening theories.

PROCEDURE

Data sets of most of the tensile yield-strength measurements

(0.2% offset) between 4 and 300 K on 18Cr-9Ni alloys for which both

[N] and [C] are specified were assembled. 1 23 The range of [N] was

from 0.12 to 1.0 (0.03 to 0.26 wt.%). An adequate number of data

points for model testing was available for only three temperatures:

4 K, 77 K, and room temperature (57, 36, and 166 points, respectively) . Data from laboratory and production heats of annealed bar

15
and plate stock greater than 6.4-mm thick were used. Grain sizes,

when specified, ranged from 55 to 180 ym; reported hardness varied

from 79 to 94 .

Preliminary analyses of these data at all temperatures indicated a high degree of correlation between a and [N], [C] , and ( [N

]

+ [ C ] ) . (Correlation coefficients ranged fr^m 0.42 to 0.91.). However, low temperature plots of o vs ([N] + [C]) showed an apparent

change of slope at approximately-^ [N] + [C]) = 0.6, as illustrated

by Figs. 1 and 2. The room temperature plot (Fig. 3) does not show

this break in slope, though it may be obscured by the scatter of the

data. A recent set of measurements showed similar trends. 3 In the

range ([N] + [ C ] ) < 0.6, austenite metastability may affect a ; in

the high ( [ N ] + [C]) range, the alloys were considered stable x£ith

respect to martensite transformation at 0.2% offset strain. Consequently, limited composition data sets were used to test the models

given in Table 1 as well as the complete data sets described above.

These limited data sets were restricted to ( [N ] + [C]) >_ 0.60 (approximately 0.15 wt.%).

A linear least squares computer program was used to fit sums of

the powers of [N] and [C] according to Eqs. 1, 2, 3, and 4 given in

Table 1 . These powers were suggested by previous characterization

of N and C dependence In austenitic stainless steels of power 1 and

by various solid solution strengthening theories predicting powers

of 1/2 and 2/3. To obtain an independent assessment of the optimum

exponent per temperature, Eq. 5 was used in an iterative, nonlinear

least squares program. Because the fitting of Eqs. 1 through 5 to

the data indicated that the [C] terms were smaller than the [N]

terms (at least at 4 and 77 K) , Eq. 6, which omits any [C] dependence, was also tested. Plotting the data from the only set of

yield-strength measurements in which [N] was held constant while [C] was varied 3 suggested Eq. 7. For completeness, Eq. 8 was included

to test the possibility that [N] and [C] acted additively to some power

A set of about 210 measurements of yield strength at 4 K and room temperature on 304LN production heats from one supplier was made available to the authors, 24 but was not used in the present

analysis. A separate, preliminary analysis of these data indicated that the observed coefficient of variation (S.D./mean yield

strength) of 7 to 14% in the measured yield strengths was not due to

the relatively narrow differences of about 0.1 in [N] and 0.3 for

[C] , but was probably caused by metallurgical factors, such as grain

size variations or crystalline anisotropy in large grain size specimens. The variances observed in these measurements are important to

designers and will be treated in separate reports

2

5

’ 2 ^ The agreement of these measurements with an equation fitted to the limited

data set is discussed below.
YIELD

STRENGTH,

MPa

Htj

YIELD

STRENGTH,

MPa

1300

Fig. 1. Yield strength measurements at 4 K

plotted against

[N] + [C] .

ig. 2. Yield strength mea- surements at 77 K

plotted against

[N] + [C] .

ELs

teQ

d

n r 1 1 1 1 1 1

900 77 K •

* -

800 -

• • -

• 700 ' ' * -

• • • 600 " * -

•

500 - -

400 - • -

300 J 1 1 1 1 _l 1 L_

-

0 03 0.6 0.9 1-2 15

ON] + [C]), at %

Fig. 3. Yield strength measurements at room temperature plotted

against [N] + [C]

17
Table 1. Equations Fitted to Yield Strength Data

(1) °y

* °o+ VNl + A

C

[C] (5)

bn

bc °y

‘ °o+ VN1 + VC1

(2) ° y

- %

+ vn]2/3 + a

c

[ C ] 2/3 (6)

bn °y

“ °o

+ VN1

(3) °y

" °o

+ VN ) 1/2 + vc]1/2 (7) b

n

bc °y %

+ AHC

[H 1 [C1

(4) °y - %

+ VN]1/3 +

(8) °y ' %

+ V([N1 +

RESULTS

At each temperature, only slight variation was found in the

standard deviation (S.D.) for the fit of the complete data set to

Eqs. 1 through 5, 7, and 8. However, the S.D. for the fit of Eq. 6 was always larger, by about 6 to 30%, indicating that inclusion of

the [C] term is preferable.

Results for the fit of the limited composition data sets to

Eqs. 1 through 4 are shown in Tables 2 through 4. Restricting the

data to the range ( [ C ] + [N]) >_ 0.6 did not significantly reduce the

S.D.’s. No significant differences were observed in the S.D.’s as the power of [N] and [C] varied from one to 1/3. Factors that make

the determination of the power difficult are (1) the relatively narrow range of [N] and [C] for which yield strength data are available, (2) possible systematic differences in the yield strength measurements, which were made by a number of different laboratories,

and (3) variation of metallurgical factors, such as grain size.

Although it is not possible to show that any of Eqs. 1 through

8 is clearly preferable, it is important to observe that all

the calculated S.D.’s are a small fraction of the mean o (o ) at

each temperature. The values of S.D./o vary from 3 to J 8%. these

values are smaller than the coef f icient^of variation found for the

210 production heat measurements 24 discussed earlier. Metallurgical

variability is thought to be the cause of the variation. Figures 4,

5, and 6 show the deviation of the observed yield strengths from

those calculated using Eq. 1, and the range of the data from these

production heat measurements is also shown on Figs. 4 and 6.

Figure 7 shows the relative contributions from the [N] and [C]

terms of Eq. 1 as a function of temperature for the hypothetical

case of [N] = [C] = 0.1 wt.%. It appears that [N] and [C] play a larger role at 4 K than they do at room temperature, and that [N] is

18
Table 2. Yield Strength Equations (4 K, 36 Data Points)

Equation S.D. of Contribution of term for m - rci - o..10 wtZ

o (MPa); Fit to a [N] term [C] term a [N],[C] (at.Z) Data (MPa) (MPa) (MPa) (MPa) (MPa)

(1) 0 - y 275 + 851 [N] 4- 379 [C] 54 275 340 170 785

(2) 0 -

y -35 + 1 105[N]

2/3

+ 348 [C] 2/3

56 - 35 599 204 768

(3) 0

y -344 + 1366[K]

1/2 4- 360[C]1/2

57 -344 863 242 761

(4) 0 *

y

1/3 -962 + 1895 TN]

7

4- 416[C] 1/3 58 -962 1397 319 754

Table 3. Yield Strength Equations (77 K, 27 Data Points)

Equation S.D. of Contribution of term for [N] = [C] = 0.10 wtZ

o (MPa); Fit to a [N] term [C] term O

[N] . [C] (at.Z) Data (MPa) (MPa) (MPa) (MPa) (MPa)

(1) o * 364 +

y 520[N] 4- 186 [C] 24 364 208 84 656

(2) o = 171 +

y 685 [N] 2/3 4- 173[C[ 2/3

25 171 371 102 644

(3) a * -23 + y 855 [N] 1/2 4- 180[C] 1/2

26 - 23 540 121 638

(4) o

= -412 + y

1/3 1200[N] 7

4- 209[C] 1/3 26 -412 884 160 632

Table 4. Yield Strength Equations (293- 300 K, 76 Data Points)

Equation S.D. of Contribution of term for [N] » [Cl - 0.10 wtZ

a (MPa);

y Fit to Oo [N] term [C] term o^ [N],[C] (at.Z) Data (MPa) (MPa) (MPa) (MPa) (MPa)

(i) a - y 194 131 [N] + 185 [C] 24 194 42 83 329

(2) a -

y 132 + 171 [N] 2/3

+ 169[C] 2/3

24 132 93 99 324

(3) a * y

71 + 212[N] 1/2

+ 174 [C] 1/2 24 71 134 117 322

(4) a - y -51 + 295[N] 1/3

+ 199 [C] 1/3 24 -51 217 152 318

19
PREDICTED YIELD STRENGTH, MPa Fig. 4. Experimentally determined yield strengths

at 4 K plotted against

yield strengths predicted from Eq. 1.

PREDICTED YIELD STRENGTH, MPa Fig. 5. Experimentally determined yield strengths

at 77 K plotted against

yield strengths predicted from Eq. 1.

Fig. 6. Experimentally determined yield strengths

at room temperatures

plotted against yield

strengths predicted

from Eq. 1.

Fig. 7. Contribution of [N] and

[C] terms in Eq. 1 as a function of temperature

for a hypothetical 304

alloy with [N] = [C] = 0.1 wt . %.

20
considerably more important than [C] at 4 K, but at room temperature

the contributions become approximately equal. Similar trends are found with Eqs . 2, 3, and 4 (Tables 2 through 4) but the magnitude

of the ratio of the [N] term to the [C] term is different, owing to

the change in sign and magnitude of the term.

DISCUSSION

From Tables 2 through 4 and Fig. 7 it is clear that N and C

strengthening is strongly temperature dependent. Both [N] and [C]

contributions increase considerably from room temperature to 4 K.

At low temperatures, the effect of [N], becomes more dominant, as shown in Fig. 7. Nitrogen contributes about 6 times more at 4 K

than at 295 K, while the carbon contribution is about twice as large

at 4 K.

Generally, three contributions to

strengthening are considered: (1) the

ally assessed by measuring the lattice

concentration (c)

a Ac

o (2) the shear modulus (G) effect:

1 AG

n G Ac

(9)

( 10 )

solid-solution interstitial

misfit in atom size (6) usu- parameter (a^) with alloy

and (3) a core interaction, usually considered in terms of electronic or dislocation-solute atom interactions. The first and

second contributions are considered to be long range and therefore

athermal ; the third contribution involves short-range force interactions that thermal fluctuations can overcome. Preliminary analysis of available data indicates that 6 and q for N and C additions

to Fe-Cr-Ni alloys are adequate to account for the strength increase

observed at room temperatures in these alloys. However, at low temperatures the shear modulus decreases slightly as N and C are

added. 27 The lattice parameters as a function of [N] and fC] have

not been measured at 4 K; however, it is very unlikely that the in- crease is sufficient to account for the 6- and 2-fold strength in- creases from N and C, respectively.

Several theories predict a concentration dependence to the 2/3

power at 0 K. Asimov2 ® considered the interaction of double-kinked

dislocations with solute atoms that are present in sufficient con- centration to promote larger elastic distortions. Nabarro,^ 9 clarifying earlier treatments, also considers the breaking away and interaction of segments from numerous obstacles. Although these models

21
produce a 2/3 power dependence of concentration at 0 K, their temperature dependence has not been clarified. The uniform temperature

dependence of the flow strength31- of austenitic steels implies the

predominance of one rate-limiting deformation mechanism. The present study found that the power of concentration dependence of [N]

and [C] could not be rigorously determined. As listed in Tables 2 through 4, the variation of standard deviation is negligible between

power 1 and order 1/3 (Eqs . 1 through 4). The variation of a also can not be used to assess the power dependence of [N] and [C]

The

low magnitude of a at 4 and 77 K reflects the instability of the

austenite with respect to martensitic transformation01 of 18Cr-8Ni

steels; at low [N] + [C] contents the steel is very metastable,

tends to transform during straining, and the flow strength is

lower

3 3

The S.D.'s of all fits obtained at each temperature (Tables 2 through 4) are about 5 to 10% of the yield strengths. This uncertainty is comparable to the metallurgical and measurement variabilities. For example, the coefficient of variation of 210 measurements on 304LN production heats z_ with [N] and [C] held rather con- stant is 7 to 14%. This suggests that the N and C alloying elements

are primarily responsible for the low-temperature strength of the

Fe-18Cr-9Ni alloys.

To develop stronger austenitic stainless steels at low temperatures, N additions are essential. Carbon should be kept reasonably

low, to enhance weldability and to reduce carbide formation. Nitrogen is also expected to contribute greater strengthening in high-Mn

austenitic alloys and in higher Cr or Ni austenitic stainless

steels

CONCLUSIONS

In austenitic stainless steels, N and C concentrations strongly

influence the low-temperature flow strength. Nitrogen contributes

significantly more to strengthening than C in austenitic Fe-Cr-Ni

alloys at low temperature; at room temperature the contributions are essentially equal. The power dependence of [C] and [N] terms cannot

be determined from the data available.

ACKNOWLEDGMENT

This research was supported by the Department of Energy, Office

of Fusion Energy; Donald Beard, coordinator.

22
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2. K.

3. R.

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12. Y.

13. T.

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16. Y.

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N. Tada, T. Mori, and K. Yasukochi, Memo 9224, Japan Atomic

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Japan (1980).

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of Standards, Boulder, Colorado (1980), p. 17.

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(1981)

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(1979)

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Standards, Boulder, Colorado (1978), p. 91.

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of Standards, Boulder, Colorado (1979), p. 81.

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National Bureau of Standards, Boulder, Colorado (1982),

p. 29.

L. Tobler and R. P. Reed, in: NBSIR 81-1645, National Bureau

of Standards, Boulder, Colorado (1981), p. 77.

Tone, M. Ogawa, M. Yamaga, H. Kaji, T. Horiuchi,

Y. Kasamatsu, H. Nakajima, K. Yoshida, Y. Takahasbi, and

M. Shimada, in: "Austenitic Steels at Low Temperatures,"

R. P. Reed and T. Horiuchi, eds.. Plenum Press, New York

(1983), p. 263.

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"Advances in Cryogenic Engineering - Materials," Vol. 28,

R. P. Reed and A. F. Clark, eds.. Plenum Press, New York

(1982), p. 73.

Horiuchi, R. Ogawa, M. Shimada, S.Tone, M. Yamaga, and

Y. Kasamatsu, in: "Advances in Cryogenic Engineering - Materials," Vol. 28, R. P. Reed and A. F. Clark, eds.,

Plenum Press, New York (1982), p. 93.

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Pennsylvania (1969), 30 pp.

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Vol. 11, K. D. Timmerhaus, ed . , Plenum Press, New York

(1966), p. 447.

Takahasbi, Japan Atomic Energy Research Institute,

Iharaki-ken, Japan, private communication.

23
17.

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19. P.

o •

CNJ K.

21. R.

22. C.

23. F.

24. E.

25. Ha

26. R.

27. H.

CN OO R.

29. F.

30. R.

31. R.

"Austenitic Stainless Steels for Use at Cryogenic

Temperatures," Nippon Steel Corporation, Kawasaki, Japan

(1983) , 10 pp.

Randak, W. Wessling, H. E. Bock, H. Steinmaurer, and

L. Faust, Stahl Eisen 91:1255 (1971).

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England (1967), p. 505.

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Steel Inst., London 199:153 (1961).

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Containment Plant," The Welding Institute, Abington Hall,

Cambridge, England (1973), p. 130.

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Lawrence Livermore National Laboratory, Livermore,

California, private communication (1982).

iford Engineering Development Lab., Richland, Washington,

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of Energy, D0E/TIC-10122

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Boulder, Colorado, unpublished data (1983).

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Colorado, unpublished data (1983).

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Microstructure," D. C. Brandon and A. Rosen, eds., Israel

University Press, Haifa (1969), p. 69.

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Society for Metals, Metals Park, Ohio (1983), pp. 295-342.

24
DILATION OF AN FCC Fe-Cr-Ni ALLOY BY INTERSTITIAL CARBON AND NITROGEN*

H. M. Ledbetter and M. W. Austin

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

Boulder, Colorado 80303

Abstract

We studied the volume change arising from introducing interstitial carbon and

nitrogen into an fee Fe-Cr-Ni alloy, an alloy corresponding to AI S

- 304

stainless steel, Fe-18Cr-10Ni-2Mn. Carbon-plus-nitrogen content varied from

0.3 to 1.3 atomic percent. To complement these studies, we also examined

Fe-18Cr-14Ni-4Mn alloys with low, constant carbon content and with nitrogen

content varying from 0.04 to 0.91 atomic percent. We determined volume using

el ectropol i shed bulk polycrystall ine specimens and x-ray diffraction, which

yielded the fee unit-cell dimension. We find that an atom of carbon or nitrogen increases volume by approximately three times its own interstitial

atom volume and approximately 70 percent of iron's atomic volume. Contrary to some studies, we find that nitrogen exceeds carbon in dilating the fcc-iron

lattice. This occurs despite carbon's atomic volume exceeding nitrogen's. We

ascribe this to electronic effects, to carbon-iron bonds stronger than nitrogeniron bonds. For the dilation, we give a model calculation. Concerning

interstitial -iron interatomic bonds, we give some elementary discussion based

on quantum-mechanical wave functions.

Key Words: alloying effects; austenite; face-centered-cubic alloy;

interstitial; iron alloy; lattice parameter; stainless steel;

vol ume.

*Intended for publication in Acta Metal 1 urqica.

25

INTRODUCTION

This study sought to determine how carbon and nitrogen interstitial

alloying additions affect the volume of 304-type stainless-steel alloys.

Especially, we wondered whether carbon or nitrogen causes larger effects.

Such questions arise during various researches: for example, solid-solution

strengthening, nature of interatomic bonding, and interstitial -dislocation

interactions

Both carbon and nitrogen increase the strength of austenitic Fe-Cr-Ni

alloys. Nitrogen stabilizes the austenite, reducing the tendency at low

temperatures toward martensitic transf ormations . Carbon functions similarly,

but higher concentrations cause welding sensitization (chromium-carbide

precipitation)

Being a physical property, volume (or mass density) is insensitive to

details of internal structure related to thermomechanical treatment. However,

when determined with sufficient sensitivity, it provides an important parameter

for indicating interatomic-force changes, which may occur during alloying.

Indeed, small changes in volume may indicate large changes in the nature of

the interatomic bonding.

Commercial austenitic stainless steels always contain some carbon and

nitrogen, in amounts up to a few atomic percent. These small foreign atoms

enter the octahedral hole of the face-centered-cubi c (fee) lattice. This

largest fee interstice provides a space up to (/2 - l)r = 0.41 r , where r

a a a denotes the radius of the host atom on the fee sites. Based on a rigid-sphere

model, atoms larger than the interstice must expand the fee lattice. As shown

in Fig. 1, carbon and nitrogen atoms exceed the octahedral -hoi e size:

r

c /r

pe

= 0.890/1.271 = 0.700; r

N /r

pe

= 0.855/1.271 = 0.672. (The nitrogenatom radius poses some uncertainty. Here, as for carbon, we use the Pauling

27
tetrahedral -coval ent radius, corrected for co-ordination number, as described

below.) The lattice expansion caused by carbon and nitrogen does not remove

the usual metallic properties of ductility and conductivity. They are reduced.

Consistent with a trend toward coval ent-rnaterial properties, strength increases.

EXPERIMENT

Material s

Nine stainless-steel plates were purchased from the research laboratory

of a U.S. steel manufacturer. All plates had nearly the same base composition,

which fell within the limits of ASTM specification A240 for AI S

I - 304 stainless

steel, nominally Fe-18Cr-10Ni-l.5Mn-0.01P-0.02S-0.55Si-0.2Mo-0.2Cu weight

percent. The carbon and nitrogen contents varied as shown in the mill chemical

analyses in Table 1. The nine plates were produced from three 136- k g vacuuminduction-melted heats, split with respect to carbon level, and teemed into

7.6-cm x 20-cm x 36-cm hot-topped cast-iron ingot molds. The ingots were

reheated and soaked at 1561 K (2350°F), hot-rolled into 2.54-cm plates, and

air cooled. The plates were finally annealed at 1332 ± 7 K (1937 ± 13°F) for

1 h and water quenched. Hardness and grain size are also listed in Table 1.

Eight stainless-steel plates were obtained from the Soviet Union.

Considering their carbon and nitrogen contents, we selected five of these for

study. Chemical analyses appear in Table 1. All these plates were hot-rolled

to 2.4-cm thickness, annealed at 1450 K (2150°F) for 1 h, and fast waterquenched .

Methods

Samples were ground flat within ± 0.005 mm and were el ectropol ished in a

solution of H^PO^ to remove the surface damage. Specimens were measured in a

commercial manual diffractometer whose movement and electronics were modified

28
for computer control. A copper target at 34 kV and 20 mA irradiated the

steels through 3-degree Soller slits. The diffracted beam then passed a

0.2-degree slit and graphite monochromator. Profiles of (111), (200), (220),

(311), (222), (400), (331), and (420) lines were automatically recorded at

0.05- degree 2-theta intervals with 60-s exposures. Peak positions determined

2 by a parabolic fit were plotted against cos 0/sine. Repeatability of the

lower-index lines was such that we considered it more accurate to determine

the lattice parameter by averaging the four (331) and (420) and

values, which were well defined.

RESULTS

Figure 2 shows the variation of fee unit-cell dimension with carbonpi us-ni trogen content. Figure 3 shows the mass density determined two ways:

from x-ray diffraction using average atomic weights and by Archimedes's

method. We attribute the approximately 0.7-percent-higher x-ray density to

the occurrence of defects not detected by x-rays. These defects include grain

boundaries, voids, cracks, and lower-density inclusions.

Linear least-squares analysis of the results gives, when carbon and

nitrogen are not distinguished

a(8) = 3.586 + 0.00854 xc+N (1)

When carbon and nitrogen effects are separated, one obtains

a(8) = 3.5866 + 0.00783 x

c + 0.00861 xN (2)

where a is in angstroms and x denotes atomic percent. For the Soviet steels

with nearly constant, low-carbon content, one obtains

a(ft) = 3.5869 + 0.00761 x Q+N (3)

29
Table 2 contains the above results expressed as the percentage latticeparameter change per atomic percent solute. This table also contains results

from twelve other sources.

MODEL PREDICTIONS

Here we consider the predicted unit-cell dimension change due to interstitial atoms in the fee octahedral hole. We use two models: a rigid-sphere

lattice model and an elastic-continuum model. The first assumes incompressible

atoms; the second allows for elastic deformation by introducing the elastic

constants. Essential input to these calculations are the atomic sizes. For

iron, we use an atomic radius of rp

e

= 1.271 8. We obtained this by correcting

Pearson's [13] fcc-Fe lattice parameter, a^ = 3.6468 K at 916°C, for thermal

expansion and using the nearest-neighbor (nn) relationship

r c = r = /2a /4 (4) Fe nn y

x '

For carbon and nitrogen, we start with Pauling's [14] tetrahedral -coval ent

radii: r^ = 0.771 $ and r^ = 0.740 $. But these must be corrected from

cn = 4 to cn = 6 (cn = co-ordination number = number of nearest-neighbor

atoms). Pauling gave equations for this correction. Here, we take another

approach and consider the atomic radius from Eq. (4) compared with the

nearest-neighbor-atom spacing. The ratio of these varies with crystal

structure (co-ordination number). For the diamond-cubic lattice (cn = 4), we

find

r (4)

_ ( 3/32n) 1/3

a _ , 73(1718 lA33 ( 5 )

and for a simple-cubic lattice (cn = 6) —J6) ,1/3,

= ( 3/47T F a

= 1.241

r a/2

nn

( 6 )

30
Thus

,

,( 6 ) /r ( 4 ) = 2 //3 = 1.155 (7)

which leads to r = 0.890 R and rM = 0.854 R. Higher cn means that fewer

valence electrons contribute to binding, thus less-tight binding between

adjacent atom pairs. Pauling argued that higher cn means less-tight binding

( cn

)

reflected in a larger atomic radius. Zachariasen [15] pointed out that r

lc

varies with crystal structure simply because of energy requirements; energy

alone requires r^ cn ^ to decrease with decreasing cn.

Simple lattice model

Here we assume incompressible spherical atoms and consider what happens

locally to the fee unit-cell dimension, a, when we insert an interstitial atom

into the octahedral hole. This hole-site possesses full cubic symmetry, even

though the overall unit-cell symmetry reduces from Fm3m to P43m. Thus, the

interstitial behaves as a pressure center and produces isotropic effects.

From Fig. 1, we can write

Aa

a

r + r - /2r 1-/2 + r /r

a x a x a 72

£

77 ( 8 )

where subscript a denotes host atom (in this case, iron) and subscript x

denotes interstitial atom (in this case, carbon or nitrogen). Table 2 gives

the results of the calculation. For comparisons made below, we also compute

that the total volume change associated with a single interstitial:

= (1 + M) . 1 (9)

which yields 0.74 for carbon in fee iron. Thus, aV = (aV/V) 7/ 4 ) = 8.58 £

'.

Continuum model

Here we approach the problem differently, from the viewpoint of a

homogeneous, isotropic elastic continuum. For point defects, one sometimes

31
calls this a sphere-in-hole model. Several authors, notably Eshelby [16],

considered this model. Considering image forces and the elastic constants, in

this model the total volume change caused by an interstitial is:

( 10 )

where c denotes the singularity "strength," r

Q ^ the octahedral -hole radius, e

the strain at r

Q ^, and y an elastic-constant function

where B denotes bulk modulus, 6 shear modulus, and v Poisson's ratio. For

typical metals, v = 1/3 and y s 3/2. (For 304-type stainless steel, v = 0.290

and y

= 1.653.) In Eq. (10) it is difficult to estimate either c or e(r

Q ^).

We can use the above AV estimate to infer these. To do this, we invoke an

idea from Eshelby: the volume change contains two parts

AV = AV°° + AV

1 = yAV°° (12)

where AV°° arises from the classical elastic-displacement solution for a center

of dilation in an infinite medium (Love [17]) and AV* arises from image forces

necessary to ensure vanishing stress at the surface of a finite-size specimen.

Thus, for most cases AV°° and AV* are approximately the same size. Leibfried

and Breuer [18] described how to obtain a crude estimate of local displacements from AV? That is, AV°° gives information concerning local changes near

the defect. Following them, we confine the volume change to the first-neighbor

displacements, r 7 U. . Then 1 n n

AV“ = AV/ y = 4,r^

n u”nn

(13)

The strain at the Inn distance is:

E lnn

= 2u lnn/a =

2

(14)

32
For carbon in gamma iron (cn = 6) this predicts e lnn = 0.018, or approximately

two percent strain at the Inn distance.

DISCUSSION

This study contains two principal results. First, both carbon and

nitrogen interstitial atoms in fee iron increase volume approximately 0 . 7 Vp e or approximately three times the volume of the interstitial atom. Second,

despite carbon's larger atomic size, carbon dilates less than nitrogen.

The first result was explained above by a simple lattice-model calculation.

The interstitial occupies the center of an octahedron of iron atoms. It acts

effectively as a point pressure and pushes away all six Inn iron atoms. It

remains to see whether a complete continuum model would also predict the large

volume increase.

We now consider the second result: the smaller effect of carbon. In

this we can profit from recognizing the equivalence of Fe^X to a local fcciron unit cell containing one octahedral -si te interstitial atom, denoted X.

This permits us to infer properties of the alloy from those of the interstitial

compound. Viewed another way, Fe^X corresponds to fee iron with one-fourth of

the octahedral sites occupied in an ordered way by carbon. If all octahedral

interstices (see Fig. 4) are occupied, then the interstitial compound FeX

arises. This compound possesses a symmetry: Fm3m.

Nitrogen's extra electron probably produces a weaker metal -nonmetal

bonding. To complete its octet, carbon can share four electrons with its six

nearest-nei ghbor metal atoms, but nitrogen only three. Lower melting points

of nitrides relative to carbides supports the idea of weaker bonding.

Hume-Rothery [19] pointed out that "unless charges are to be built up...bondinn

in nitrides will be weaker than in carbides."

33
We believe that stronger bonding in Fe-C than in Fe-N accounts for

nitrogen expanding y-Fe more than carbon does, even though carbon is a larger

atom than nitrogen. Carbon produces stronger bonding, higher melting point,

higher elastic stiffness, and lower volume. The inverse relationship between

stiffness (and bonding strength) and volume is well known.

For models of solid-solution strengthening, and realizing that nitrogen

strengthens y-iron more than carbon does [20], the present results produce an

interesting conclusion. Strengthening may not arise from simple carbondislocation and nitrogen-dislocation interactions. Perhaps it arises from a

complex-defect/dislocation interaction. This complex defect could be an

interstitial pair, an interstitial host-atom pair, or an interstitial/selfinterstitial pair, but, in any case, one involving nitrogen interstitials.

Indeed, Igata et al . [21] suggested that a complex defect pins dislocations

more effectively than either carbon or nitrogen atoms alone. Igata and

coworkers' internal -friction studies on mechanically deformed 304-type stainless

steel showed three peaks versus temperature. They ascribed the lowest peak to

unpinning from carbon, the middle peak to unpinning from nitrogen, and the

highest peak to unpinning from a carbon-nitrogen/self-interstitial complex.

We can understand the stronger bonding in Fe-C compared with that in Fe-N

by considering the simplest quantum theory of atomic bonding, especially

2 2 2 electron-pair bonds. Carbon's normal electron configuration. Is 2s 2p ,

implies a valence of 2 corresponding to two unpaired electrons. But organic2 13 chemistry facts show that carbon's actual configuration is Is 2s 2p , a

low-lying excited state with four unpaired electrons and a valence of 4.

Indeed, carbon's four tetrahedral orthogonal, normalized s-p hybrid wave

functions are well known [22]:

34
T ( 15 ) el

= (s + p

x + py

+ p

z )/2

T

e2

= (s + Px - Py ' p

z )/2

T e3

= (s ' p

x + p «

' p - )/2

y

T

e4

= (s - p

x

- py

+ p

z )/2

The strengths of an s bond and a p bond are 1 and /3, respectively [23]. On

this scale, these tetrahedral orbitals have bond energies of 2, the highest

possible for 2s-2p hybrids, corresponding to the maximum possible number of

unpaired s-p electrons (four). Nitrogen's extra electron suggests a normal

2 2 3

electron configuration of Is 2s 2p or, more probably, the excited configura2 14

tion Is 2s 2p . In either case, nitrogen has only three unpaired electrons.

Thus, compared with carbon, it offers one-fourth fewer electrons for covalentionic bonding with iron. We note also that carbon's four wave functions fit

well into the octahedral symmetry of the interstitial sites in fee iron.

There are three bonds at right angles formed by dumbbel 1 -shaped p orbitals,

and a fourth bond, the s orbital, having spherical symmetry and, therefore, no

special direction. Following Hund, Dehlinger [24] emphasized the importance

of wave-function direction for bonding: "binding energy is a maximum if the

number of valence electrons per atom equals the number of degenerate functions...

and if the neighboring atoms lie in the direction of the preferred wave-function

directions, and in these directions only."

We can carry these elementary quantum-mechanical considerations one step

farther and consider the detailed wave functions that may occur between carbon

and its six octahedral -symmetry neighboring iron atoms. One can construct

equivalent octahedral orbitals by suitable hybridization of two d orbitals,

3 2 one s orbital, and three p orbitals, and thus obtain a sp d hybridization [25].

The maximum s-p-d bond strength is 3. This hybrid possesses nearly a maximum

strength, 2.923. From symmetry, only two d orbitals, d, 2 and d 2 2, combine

x x +y

35
with s and p:

d = f ,(r)(2x^ - y^ - z~) xx d

v J '

d

yy

= f

d(

r ^‘ x2 + 2y2 " ( 16 )

d zz

= Vr ^ _)(2 y

c + 2z2 )

with the constraint

3 2 This sp d hybrid bond requires six bonding electrons; carbon possesses only

four. Thus, carbon may capture two electrons from iron's metallic electron

gas and acquire a negative charge. Band-structure calculations [26] predict a

negative charge on carbon in the NaC^-crystal -structure compound NbC. Above,

we described the similarity between the compounds FeX and Fe^X and the y-Fe

solid solution containing interstitial X.

CONCLUSIONS

Both carbon and nitrogen interstitial atoms increase the volume of an

Fe-Cr-Ni-al 1 oy with composition near 304-type stainless steel. Even though

nitrogen is a smaller atom than carbon, it dilates more. Fe-C bonds stronger

than Fe-N bonds may explain this. Compared with their own atomic volumes, the

interstitials produce a surprisingly large dilation. A simple local lattice

model explains this.

ACKNOWLEDGMENT

Some support for this study came from the US DoE Office of Fusion Energy.

R. P. Reed of NBS provided encouragement. R. E. Schramm contributed to the

early x-ray-diffraction studies.

36
REFERENCES

1. V. G. Paranjpe, M. Cohen, M. B. Bever, and C. F. Floe, J. Met. 2, 261

(1950).

2. C. S. Roberts, Trans. AIME 197, 203 (1953).

3. W. B. Pearson, Lattice Spacinqs and Structures of Metals and Alloys , Volume 1, p. 921. Pergamon, New York (1958).

4. K. J. Irvine, D. T. Llewellyn, and F. B. Pickering, J. Iron Steel Inst.

199, 153-175 (1961).

5. L. Zwell, E. J. Fasiska, Y. Nakada, and A. S. Keh, Trans. Met. Soc, AIME

242, 765-766 (1968).

6. N. Ridley, H. Stuart, and L. Zwell, Trans. Met. Soc. AIME 245, 1834-1836

(1969).

7. N. Ridley and H. Stuart, Met. Sci. J. 4, 219-222 (1970).

8. D. J. Dyson and B. Holmes, J. Iron Steel Inst. 208, 469-414 (1970).

9. D. E. Diesburg, Ph.D. Thesis, Iowa State University, Ames, Iowa (1971).

10. M. Kikuchi, T. Tanaka, K. Hamagami , Y. Ogura, and R. Tanaka, Met. Trans.

A 7, 906-908 (1976).

11. J. Charles, Ph.D. Thesis, Universite Catholique de Louvain, Malonne,

Belgium (1982).

12. T. Sakamoto, Y. Nakagawa, I. Yamauchi , T. Zaizen, H. Nakajima, and S.

Shimamoto, in Advances in Cryogenic Engineering, Volume 30, p. 137.

Plenum, New York (1984).

13. W. B. Pearson, Lattice Spacinqs and Structures of Metals and Alloys , Volume 2, p. 82. Pergamon, New York (1967).

14. L. Pauling, The Nature of the Chemical Bond , p. 246. Cornell University

Press, Ithaca, New York (1960).

15. W. H. Zachariasen, Z. Kristallogr. 80, 137 (1931).

16. J. D. Eshelby, J. Appl . Phys. 25, 255-261 (1954).

17. A. E. H. Love, Mathematical Theory of Elasticity , p. 142. Cambridge

University Press, New York (1927).

18. G. Leibfried and N. Breuer, Point Defects in Metals I , p. 150. SpringerVerlag, Berlin (1978).

19. W. Hume-Rothery , Philos. Mag. 44, 1154-1160 (1953).

37
20 . R. P. Reed and N. J. Simon, in Advances in Cryogenic Engineering, Volume

30, p. 127. Plenum, New York ( 1984)

21. N. Iqata, H. B. Chen, K. Miyahara, and T. Uba, J. Phys. 42, C5193-C5198

(1981).

22. R. Dandel , R. Lefebvre, and C. Moser, Quantum Chemistry , p. 158.

Interscience, New York (1959).

23. Ref. 14, p. 119f

24. U. Dehlinqer, Theoretische Metallkunde, p. 66. Sprinqer-Verlaq, Berlin

(1955).

25. Ref. 14, p. 149.

26. W. Weber, Phys. Rev. B 8, 5082-5092 '(1973).

38
Table

1.

Chemical

composition

(weight

percent),

hardness,

and

grain

size.

cuN

•r— coc E mcooio LD CO CO CM O •*— d (X) I'". CT) O 00 cn co cn

03 v r—

S- CD

CQ

to

to | CL) | 1—

uo oo uo CM co 0 uo c QJ O S- CO co <—

CO i-". co co

co CO CO 00 co CO O

rn o

QC

co r-^ C'- 0 1-^ uo rH rH uo

CO cn CM uo CO r-H C" cn CM rH uo uo + O 0 H »—1 r-H CM CM CM CO 0 rH 1—

CM CM O O 000 0 0 0 O O 0 0 0 O O

cn cn cn 0 0 O O O O co

CO CO CO CM CM CM *3

- 0 cn CM CM CO 0 0 0 1—

r-H r-H CM CM CM 0 0 rH CM CM 0 000 0 0 0 O O 0 0 0 O O

X co cn ic 0 r'- UO CO r-H rH UO CM LD CO CO co cn CO UO CO CO CM CM CO CM

l_> O 000 0 0 0 O 0 0 O O O O

O 0 0 0 000 O 0 0 O O O O

O 0 r-H cn 0

CM rH CM o • • • O 0 0

uo uo O 0 cn o CM CM rH

2: • • • O O 0

O uo 0 CO rH CM OO

•

1— uo uo uo CM CM CM CM CM

oo • • • 0 0 0 O O O O O

CT) i-"- CO CO r-^ CO CO

rH r-H rH 0 0 0 0 O

00 0 0 0 0 0 0 0 O • • • 0 0 0 0 0 0 0 O

rH CM 00 uo 00 CM

CM CM CM 0 O 0 O rH

Q_ O O O 000 O 0 • • • O O O 0 0 0 O 0

C- O CM CO CO uo c ld UO 0 rH 0 cn cn

s: • • • r-H 1—

r-H M- co CO

r-H I-"- r-H cn cn cn CO CM co 0 •r— • • •

-2. 0 cn cn co CM LD rH CO rH rH rH rH rH

S- CO 0 co rH cn U) CO

CD • • • CO co 0 co co co co

r-H »—

CM r-H rH rH rH rH

rH CM CO LD rH CM 3 4 uo CO 7 8 cn 00 CO CO CO CO

39
Table 2. Effects of interstitial carbon and nitrogen on the lattice

parameter of fee Fe-Cr-Ni alloys; expressed as 100 (1/x) (Aa/a ) where x denotes atomic percent.

Alloy C N Source

Fe 0.211

Fe 0.267

Fe 0.275

Fe-18Cr-10Ni 0.167 0.234

Ni 0.210

Fe 0.199

Fe 0.190

Fe-18Cr-16Ni 0.182 0.157

Fe- 14-29Ni 0.210

Fe-25Cr-28Ni 0.201

Fe-25Cr-28Ni -2Mo 0.200

Fe-10Cr-5A2, 0.221

Fe-23Mn-5Aj> 0.160

Fe-30Mn-5At 0.160

Fe-30Mn-8At 0.157

Fe-17-25Cr-8-13Ni 0.203

Fe-18Cr-10Ni-2Mn 0.218 0.240

Fe-18Cr-14Ni -4Mn 0.212

0.202 0.182

Paranjpe et al . [1]

Roberts [2]

Pearson [3]

Irvi ne et al . [4]

Zwel 1 et al . [5]

Ridley et al . [6]

Ridley, Stuart [7]

Dyson, Holmes [8]

Diesburg [9]

Ki kuchi et al . [10]

Charles [11]

Sakamoto et al . [12]

Present study, measured

Present study, measured

Present study, rigid-inclusion,

lattice model

40
List of Figures

Fig. 1. Schematic representation of a face-centered-cubic unit cell.

Partly-covered circles represent corner atoms. Full circles represent

face-centered atoms. Shaded circle represents maximum diameter of

octahedral hole. Dashed circle represents relative size of carbon

atom in iron. Cube axes lie along [100]-type directions and closepacking occurs along [ 1 10] -type directions.

Fig. 2. Unit-cell dimension versus combined carbon-plus-nitrogen interstitial

atom content.

Fig. 3. Mass density versus combined carbon-pl us-ni trogen interstitial -atom

contents

Fig. 4. Face-centered-cubic unit cell. Open circles denote fee atoms.

Filled circles denote equivalent octahedral -hoi e interstitial atoms.

Lines define octahedron with interstitial atom at center with six

near-nei ghbor host-lattice atoms.

41
110 010 T10

Fig. 1. Schematic representation of a face-centered-cubic unit cell.

Partly-covered circles represent corner atoms. Full circles represent

face-centered atoms. Shaded circle represents maximum diameter of

octahedral hole. Dashed circle represents relative size of carbon

atom in iron. Cube axes lie along [100]-type directions and closepacking occurs along [110]-type directions.

42
3.63

43

Fig.

2.

Unit-cell

dimension

versus

combined

carbon-plus-nitrogen

interstitialatom

content.
oo

CD

44

Mass

density

versus

combined

carbon-plus-nitrogen

interstitial-atom

contents.
Fig. 4. Face-centered-cubic unit cell. Open circles denote fee atoms.

Filled circles denote equivalent octahedral -hoi e interstitial atoms.

Lines define octahedron with interstitial atom at center with six

near-neighbor host-lattice atoms.

45

EFFECTS OF CARBON AND NITROGEN ON THE ELASTIC CONSTANTS

OF 304-TYPE STAINLESS STEEL*

H. M. Ledbetter and M. W. Austin

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

Nine 304-type stainless-steel alloys were studied at room temperature.

Carbon-pl us-ni trogen contents of these alloys ranged from 0.067 to 0.325

weight percent (0.3 to 1.3 atomic percent). Five elastic constants--

longitudinal modulus, Young's modulus, shear modulus, bulk modulus, and

Poisson's ratio--were determined by a pulse-echo ultrasonic method. All the

elastic stiffnesses decrease 0.5 to 0.9 percent per atomic percent solute.

Poisson's ratio remains unaffected by carbon-nitrogen alloying. Existing

theory predicts decreases in elastic stiffness. A model by Eshelby relates

the elastic-stiffness decrease to the volume increase.

Note: A previous report in this series contained a manuscript on this

subject. Subsequent study showed that those specimen numbers were scrambled.

The present manuscript contains corrected results and conclusions.

Key words: bulk modulus; elastic constants; physical property; Poisson's

ratio; pulse-echo method; shear modulus; stainless steels; Young's modulus;

ul trasoni cs

*Intended for publication in Materials Science and Engineering .

47

INTRODUCTION

’his study sought to determine how carbon and nitrogen alloying add"'c'c r s

affect the elastic constants of 304-type stainless-steel alloys.

Both carbon and nitrogen increase strength of austenitic Fe-Cr-Ni alleys.

Nitrogen stabilizes the austenite, reducing the tendency at low temperatures

toward martensitic transformations. Carbon functions similarly, but higher

concentrations cause sensitization during welding. The increasing uses of

these a'loys, together with a dearth of reliable physical -property measurements, prompted the present study.

Being physical properties, elastic constants are relatively insensitive

to details of internal structure related to thermomechanical treat;~e r t.

However, when determined with sufficient sensitivity, they provide important

parameters for indicating interatomic-force changes, which may occu r during

alloying. Indeed, small changes in elastic corstants may ircicate 'a^ce

changes in the nature of the interatomic bonding.

Commercial austenitic stainless steels always contain some carbor a

r d

nitrogen, in amounts up to a few atomic percent. These sma" *ore'g r aters

occupy the octahedral hole of the face-centered-cubi c (fee' lattice. _r is

largest fee interstice provides a space up to (/2 - l)r = 0.41 r , where r

a a a denotes the radius of the host atom on the fee sites. Larger interstitial

atoms must expand the fee lattice. Both carbor and nitroger aters exceed the

octahedral -hoi e size: r^/rp = 0.890/1.271 = C.7C; r^/rp = 0.855/1.271 = 0.67.

(The nitrogen-atom radius poses some uncertainty. Here, as ^or ca r do r

, we ,se

the Pauling tetrahedral -coval ent radius corrected for co-ordi nation r .,~oe'\'

The lattice expansion caused by carbon ard nitrogen does not remove phe ust?'

metallic properties of ductility and conductivi ty . ’hey are -'educed. I*--?- ?-

tent with a trend toward covalent-material properties, screngt n ire-ease?.

49
EXPERIMENT

Materi al s

Nine stainless-steel plates were purchased from the research laboratory

of a U.S. steel manuf acturer. All plates had nearly the same base composition,

which fell within the limits of ASTM specification A240 for AI S 1-304 stainless

steel, nominally Fe-18Cr-10Ni-l.5Mn-0.20P-0.20S-0.55Si-0.2Mo-0.2Cu weight

percent. The carbon and nitrogen contents varied as shown in the mill chemical

analyses in Table I. The nine plates were produced from three 136-kg vacuuminduction-melted heats, split with respect to carbon level, and teemed into

7.6-cm x 20-cm x 36-cm hot-topped cast-iron ingot molds. The ingots were

reheated and soaked at 1561 K (2350°F), hot-rolled into 2.54-cm plates, and

air cooled. The plates were finally annealed at 1332 ± 7 K (1937 ± 13°F) for

1 h and water quenched. Hardness and grain size are also listed in Table I,

and mass densities are given in Table II.

Methods

Room-temperature sound velocities were determined by a pulse-echo-overlap

technique [1]. Quartz piezoelectric crystals with fundamental resonances

between 4 and 7 MHz were cemented with phenyl salicylate to one end of a

specimen with flat and parallel surfaces. An x-cut transducer was used for

longitudinal waves and an ac-cut for transverse waves. The specimen in this

case was a 1.59-cm x 1.59-cm x 1.27-cm parallelepiped with opposite faces

ground flat and parallel within 2.5 ym. Ultrasonic pulses 1 to 2 cycles long

were launched into the specimen by electrically exciting the transducer. The

pulses propagated through the specimen, reflected from the opposite face, and

propagated back and forth. The pulse echoes were detected by the transducer

and displayed on an oscilloscope equipped with a time delay and a microprocessor for time-interval measurements. The sound velocity was computed by

50
V = Zi/t ( 1 )

where i denotes specimen length, and t, the round-trip transit time. On the

oscilloscope, t was the time between adjacent echoes, the first and second

echoes usually being measured, and within these the time between leading

cycles. Elastic constants were computed from the general relationship

C = P v2 (2)

where p denotes mass density. The usual engineering elastic constants are

related to the longitudinal and transverse sound velocities, v^ and v^, by

longitudinal modulus = = pv^ (3)

shear modulus = G = pv| (4)

bulk modulus = B

= - ( 4/3 )

G

(5)

Young's modulus = E = 3GB/ ( - G) (6)

Poisson's ratio = v = (E/2G) - 1

= (1/2) (C

£

- 2G)/(C

£

- G) (7)

We measured mass density both by an Archimedes method and by x-ray diffraction. We used the latter values because they scattered less from a linear

fit.

RESULTS

Table II gives the principal results of the study: sound velocities and

elastic constants for nine type-304 stainless-steel alloys with different

carbon and nitrogen contents. Table III shows for one case, alloy 1, the

directional variation of the ultrasonic wave velocities. Table III implies

also that ultrasonic velocities can be measured in these alloys with an

uncertainty of 0.05 percent or less. Figure 1 shows these results graphi51
cally. Table IV contains the linear-least-squares parameters for the various

elastic constants. The last column in Table IV gives the percent elasticconstant change per atomic percent interstitial.

DISCUSSION

Results in Table II and Fig. 1 lead to the following conclusion:

although the effects are small, carbon and nitrogen additions reduce the

elastic stiffnesses--^, G, B, E--of 304-type stainless steel. By small, we

mean less than one percent stiffness reduction per atomic percent solute.

Poisson's ratio remains unaffected.

Present results contrast sharply with observations reported for ferritic

iron. Speich, Schwoeble, and Leslie [2] reported that carbon added to alpha

iron reduces elastic stiffnesses, such as E and G, by about five percent per

atomic percent carbon. Indeed, carbon is the most effective known alloying

element in altering alpha iron's elastic constants. Quantitative results for

nitrogen remain unreported, but one would expect nitrogen to behave like

carbon because their atomic diameters are similar. The essential distinction

between the ferritic and austenitic cases is the crystal structure. Bodycentered-cubic crystals are less accommodating to interstitials than are

f ace-centered-cubic crystals. Carbon alloyed into bcc iron occupies a distortedoctahedral interstice that has tetragonal symmetry, which produces a strong

tetragonal distortion; no similar distortion occurs in fee iron, where carbon

occupies larger octahedral interstices and the lattice distortion is isotropic.

This distortion reflects also in the much higher solubility of carbon and

nitrogen in fee iron compared with bcc iron.

Present results dispute those of a previous study. Laddach and

Schuler [3] studied the influence of nitrogen on the elastic properties of an

Fe-21Cr-20Ni alloy containing 0.02 and 0.29 weight percent nitrogen. They

52
concluded that "nitrogen raises the modulus of elasticity as well as the

modulus of rigidity, regardless of the nitrogen being either in interstitial

solution or precipitated in the form of nitrides." No reconciliation of this

conclusion and that of the present study seems apparent.

A related study by Diesburg [4] tends to support our findings. Diesburg

measured the single-crystal elastic constants of several fee Fe-Ni-C alloys

containing 11.3 to 33.3 atomic percent Ni and 0.0 to 4.5 atomic percent

carbon. All the elastic constants softened with increasing carbon content.

Of course, Diesburg's alloys differ distinctly from ours: they contained no

chromium; they contained no trace elements; they were studied below the Curie

temperature (in the ferromagnetic state); and they contained no grain

boundaries. Thus, any comparison must be cautious.

Because the effects are small and difficult to measure, one can usefully

consider the view of theory. Most existing theory applies to self-interstitials,

thus to atoms larger than most foreign interstials and with the same electronic

structure as the host-lattice atoms.

Simple theory fails to predict the effect of interstitials on elastic

constants. This failure arises from three factors: (1) the geometricalmechanical misfit, which causes changes in volume and sometimes shape; (2) the

electric-field misfit, which causes charge redi stribution , atomic-bond change,

and changes in interatomic potential and force constants; (3) the coupling of

these two types of misfit. The usual interstitial effects are to increase

volume (which reduces the elastic stiffness) and to increase the elastic

spring constants (which increases elastic stiffness).

A simple model by Dienes [5] predicted for copper that S e (1/x) (aC/C) =

10 percent; here x denotes interstitial concentration and C denotes elastic

stiffness. The Dienes model considers only the elastic-spring-constant

53
changes; neglecting volume, it represents an upper limit. Nabarro [6] criticized

this model and gave an alternative elastic-continuum calculation that predicted

S = 4 percent. Eshelby [7] pointed out two features of Dienes's calculations.

First, Dienes neglected image forces that are large and might even reverse the

sign of S. Second, Dienes's calculations should apply in the immediate

vicinity of the interstitial, predicting an elastic stiffening near the

interstitial, but an overall macroscopic elastic softening.

Experiment on unalloyed fee metals shows that S is larger than these

estimates, and is negative! Thus, one requires a more detailed model that

considers the above-mentioned coupling.

Apparently, Ludwig [8] first gave a detailed model based on energy

methods, but he considered only a vacancy defect in an fee lattice.

Pistorius [9] extended Ludwig's method to interstitials and predicted S = ±5

percent.

Perhaps Mel n ga i 1 is [10] provided the first successful calculation for

interstitial-atom effects on S. From elastic-energy methods, he predicted

that S = -18 percent. By assuming that the interstitial-atom elastic field

extended out to two unit-cell dimensions, he accounted for the 1 ow-temperature

radiation-induced elastic-constant change in copper.

Subsequent calculations predict similar effects. Dederichs et al . [11],

using Ludwig's energy method and the t-matrix method of Elliot et al . [12],

gave predictions for the individual C^: S

= -10 percent for + 2C^» -19

percent for - C^, -37 percent for C^. These predictions depend sensitively

on both the interatomic repulsive potential and the defect geometry. The

principal prediction is that S is large and negative. Leibfried and Breuer [13]

review the theory of point defects in metals, but give no detailed calculations

for S for interstitials. They emphasize that smaller interatomic distances

54
induce negative transverse-spring constants. For certain atomic motions, this

causes small restoring forces. Regions near interstitials become soft (almost

unstable). Local static and dynamic response to stress deviates considerably

from the average-medium response.

Thus, theory, both lattice-dynamic and elastic-continuum, predicts that

interstitials reduce elastic stiffness. This agrees with our present experimental findings for 304-type stainless steels alloyed with interstitial carbon

and nitrogen.

Using ideas by Eshelby [7], we can invoke theory more quantitatively and

examine the effects of volume change on changes in bulk and shear moduli.

(Recall that these two elastic moduli correspond to the two extreme forms of

mechanical deformation: volume change without shape change and shape change

without volume change.)

Eshelby pointed out that in a correct elastic-continuum calculation for

defects two forces arise:

00 I p . . = p . . + p . . H iJ

The first arises from the classical elastic solution for a dilatation

( 8 )

center in an infinite medium. The second, image stress, arises to ensure zero

stress at the body's surface. Although many models neglect image forces, they

are large, they sometimes dominate, and they sometimes reverse the effect of

00 _ p... Eshelby described essential differences in these two forces in terms of

the displacement field:

00 I u = M M

The displacement ^ with pure shear. But ^

I

(9)

fluctuates rapidly with position and is associated

varies smoothly, except near the surface, and is

55
oo associated mainly with hydrostatic stress. Thus, in alloying, jj produces

changes in the shear modulus while changes the bulk modulus.

Eshelby suggested, a bulk-modulus and volume relationship:

AB _ d£nB AV

! _ d£nB dV y - 1 B d£nV V d£nV V y

,1

( 10 )

where B denotes bulk modulus; V, volume; V , the volume change arising from

image forces; and y, an elastic-constant function.

3B + 4G _ 3

1 - v (ID

T 3B " 1 + v

where G denotes shear modulus and v, Poisson's ratio. Because d£nB/d£nV is

always negative, this relationship predicts that aB/B has an sign opposite to

that of the volume change dV/V. Slater [14] showed that

-d£nB/d£nV = 2r + 4/3 (12)

where the Gruneisen constant, r, is approximately two for most materials.

Taking v = 1/3, Eq. (10) becomes

(AB/B) = - (16/9) (dV/V) (13)

Ledbetter and Austin [15] found for these alloys that (1/x) (dV/V) = 0.0072,

which predicts (1/x) (aB/B) = - 0.0128 compared with the observed value,

-0.0085.

Considering now the shear modulus, G, by analogy with Eq. (10), we write

AG

G

dftnG A

V

d£nV V d£nG dV _1 d£nV V y

(14)

where V denotes the volume change arising from a point defect in an infinite

medium. For d&nG/dtnV, no relationship exists analogous to Eq. (12). Thus,

we use the thermodynamic relationship

d£nG

d£nV

dG B dP G

(15)

56
where P denotes pressure. We intend to obtain dG/dP from measurement. Since

this measurement does not yet exist for either an austenitic steel or fee

iron, we use the values reported for fcc-copper monocrystals: dC'/dP = 0.375

and dC^/dP = 2.63 [16]. (Of the 3d-electron transition metals, copper is the

fee nonmagnetic element closest to iron.) We convert these to the isotropic

(polycrystal) value by computing the Voigt and Reuss bounds and taking the

Hill arithmetic average. We obtain (dG/dP)y

o

. ^

= 1.73, (dG/dP)^

euss

= 0.92,

and (dG/dP) u

. 11 = 1.32. From Eqs. (11), (14), and (15), we obtain AG/G = -0.0118.

Compared with observation, -0.0052, this is too high by a factor of

approximately 2.

Thus, Eshelby's model, based on continuum elasticity and including the

image force accounts quite well for the present results. Model -measurement

disagreement for the shear modulus suggests that factors other than elastic

misfit enter the problem. Carbon-iron and nitrogen-iron electronic interactions

are a possibility [17].

CONCLUSION

In the studied composition range, elastic constants are determined mainly

by interactions among atoms occupying lattice sites; carbon and nitrogen

interstitial atoms lower elastic stiffness by approximately 0.5 percent per

atomic percent solute. Since elastic constants are determined by the interatomic force constants, these also must be nearly independent of carbon and

nitrogen content. Thus, the present results relate also to other force-constantdetermined physical properties, such as thermal expansivity and specific heat.

Eshelby's model accounts rather well for our observations, relating the

elastic-stiffness decrease to volume increase. Whether electronic interactions

affect the shear modulus requires further study.

57
ACKNOWLEDGMENTS

The U.S. DoE Office of Fusion Energy supported part of this study. R. L.

Tobler of NBS contributed the materials and grain-size measurements.

J. Dahnke of NBS assisted in measurements.

58
REFERENCES

1. H. M. Ledbetter, N. V. Frederick, and M. W. Austin, J. Appl . Phys. 51 , 305-309 (1980).

2. G. R. Speich, A. J. Schwoeble, and W. C. Leslie, Metal! . Trans. _3

,

2031-2037 (1972).

3. H. Laddach and P. Schuler, DEW-Tech. Ber. JJ3, 85-88 (1973).

4. D. E. Diesburg, The Elastic Constants of Fe-Ni-C Alloys . Ph.D. Thesis,

Iowa State University, Ames, Iowa (1971).

5. G. J. Dienes, Phys. Rev. 86, 228-234 (1952).

6. F. R. N. Nabarro, Phys. Rev. 87, 665-666 (1952).

7. J. D. Eshelby, J. Appl. Phys. 25^, 255-261 (1954).

8. W. Ludwig, in Calculations of the Properties of Vacancies and

Interstitial

s

, pp. 151-159. Misc. Pub! . 207, National Bureau of

Standards, Boulder, Colorado (1967).

9. M. Pistorius, Z. Angew. Phys. 29_, 145 (1970).

10. J. Melngailis, Phys. Status Sol i d i lj5, 247-252 ( 1966).

11. P. H. Dederichs, C. Lehmann, and A. Scholz, Z. Phys. B 20, 155-163

(1975).

12. R. J. Elliot, J. A. Krumhansl , and T. H. Merrett, in Local i zed

Excitations in Solids . Plenum, New York (1968).

13. G. Leibfried and N. Breuer, Point Defects in Metals I, Introduction to

the Theory . Springer-Verlag, Berlin (1978).

14. J. C. Slater, Introduction to Chemical Physics, p. 239. McGraw-Hill, New

York (1939).

15. H. M. Ledbetter and M. W. Austin, to be submitted to Acta Metal 1.

16. Y. Hiki and A. V. Granato, Phys. Rev. 144, 411-419 (1966).

17.

W. Hume-Rothery , Philos. Mag. 44, 1154-1160 (1953).

59
Table

I.

Chemical

composition

(weight

percent),

hardness,

and

grain

size.

a>M

tn ^E LD CO O LT) Lf) OO 00 CM o C a. CO r» Oi O 00 N CD CD r—

«&u

CJ

„ v CO m

IS) »—

<D r- r— id cti in CM co o in C OJ •o X co 00 r- CO *3* CO oo

&- rv OO 00 CO CO 00 00

*53 u Z O

cc

oo *3- O in z VO CD cm in oo »— CD CM o o r— r— CM CM CM CO o o o o o o o o o o

CT> CD O'* O o o o o o co CO CO CM CM CM *3- *3* z o o O f— f— CM CM CM o o o o o o o o o

CD CO oi r-^ *3- O in CM m 00 CO vO CD CO in CD CJ o o o o o o o o O

o o o o o o o o O

o o

r— CD o

13 CM r— CM

<_> • • • o o o

in in o o cn o CM CM r— 2:

• • • o o o

o in LO in in

</) • • o o o

CD VO r— p—

r— U1 o o o

o o o

r— CM

CM CM CM a. o o o

o o o

r>w o CM c LT> in

s: • • •

y— CD

•r— • • • z o CTv CD

co o CO

L- • • • O 00 00 oCM

f— CM 3 4 n vO oo CD

60
Table II. Mass density, sound velocities, and elastic constants of nine

carbon-plus-nitrogen-alloyed 304-type stainless-steel alloys.

Densi ty v

t

c

*

E G B V

(g/cm 3

) (cm/ys) (cm/ys) (GPa) (GPa) (GPa) (GPa)

1 7.967 0.5751 0.3140 263.5 202.3 78.5 158.8 0.288

2 7.966 0.5766 0.3146 264.9 203.1 78.8 159.7 0.288

3 7.962 0.5751 0.3142 263.3 202.4 78.6 158.5 0.287

4 7.950 0.5769 0.3141 264.6 202.2 78.4 160.0 0.289

5 7.948 0.5747 0.3150 262.5 202.7 78.9 157.4 0.285

6 7.945 0.5748 0.3144 262.5 201.1 78.5 157.8 0.287

7 7.933 0.5757 0.3139 262.9 201.4 78.2 158.7 0.288

8 7.923 0.5743 0.3155 261.3 202.5 78.9 156.2 0.284

9 7.914 0.5764 0.3135 262.9 200.7 77.8 159.2 0.290

Mean 7.945 0.5755 0.3144 262.2 202.2 78.5 158.5 0.287

Std

dev.

0.019 0.0009 0.0006 1.1 0.7 0.4 1.2 0.002

Pet.

std. error0.2 0.2 0.2 0.4 0.4 0.5 0.8 0.7

61
TABLE III. Directional variation of ultrasonic wave velocities in specimen 1 where the z direction is perpendicular to the rolling plane.

Propagati on

Di recti on

Pol arization

Di rection

V

£

(cm/us)

v

t (cm/ps)

X X 0.5746

X y 0.3140

X z 0.3143

y y 0.5753

y X 0.3139

y z 0.3138

z z 0.5753

z X 0.3143

z y 0.3140

Mean 0.5751 0.3141

Std. Dev. 0.0004 0.0002

Pet. std. error 0.07 0.07

62
Table IV. Least-square parameters for various elastic constants;

c C

0

(GPa)

a

(GPa)

l°°a/ C ox c+N

B 159.6 -1.349 -0.85

G 78.8 -0.410 -0.52

E 203.2 -1.314 -0.65

c

* 264.8 -2.040 -0.77

v (dimensionless) 0.288 -0.00049 -0.15

63
270 SO

Cl

E

o

<

QC

5°z

o

COCOo

CL

0.31

1 1

0.30 -

0.29 —

o

a < c o ° o 0.28 -

1 1 0 0.6 1.0 1.6

CAN CONTENT Cst. pet.)

Fig. 1. For 304-type stainless steel, variation of elastic constants with

interstitial carbon-plus-nitrogen content. B = bulk modulus,

C = longitudinal modulus, E = Young's modulus, G = shear modulus,

v - Poisson's ratio. Except for the dimensionless Poisson's ratio, all

units are GPa.

64
THE TEMPERATURE DEPENDENCE OF THE TENSILE YIELD STRENGTH OF

SELECTED AUSTENITIC STEELS*

R. P. Reed and J. M. Arvidson

National Bureau of Standards

Fracture and Deformation Division

Boulder, Colorado 80303

ABSTRACT

The temperature dependence of tensile yield strength has been measured

for five austenitic steels from 4 to 295 K. Two alloys (25Mn-5Cr-0 . 2C , 22Mn- 1 3Cr-0 . 2N) have been supplied by Japanese companies, one alloy (19Mn-13Cr) was supplied by a USSR institute, and two alloys were supplied by U.S. suppliers

( 18Mn- 1 7Cr-0 . 5N , AISI 310). All exhibit logarithmic dependence of yield

strength versus temperature.

*Published in Advances in Cryogenic Engineering - Materials , vol. 30,

Plenum Press, New York (1984), pr» . 263-270.

65

INTRODUCTION

The trend toward the use of higher field superconducting magnets

is creating the need for strong, tough structural materials to re- strain the high magnetic forces. Austenitic and high-N-austenitic

stainless steels are considered for such uses because of their high

strength and good toughness, combined with high Young’s modulus and

low thermal conductivity. Study of the temperature dependence of

tensile flow strength leads to better understanding of deformation

mechanisms in these face-centered cubic, polycrystalline alloys.

The tensile properties of five austenitic Fe-Cr-Ni and Fe-Cr-Mn

steels were measured. In these steels the Cr contents varied from

4.67 to 24.8 wt.%, the Ni from 0.8 to 20.8 wt.%, and the Mn from 1.7

to 21.79 wt.%. Yet it has been demonstrated that steels obtain their

low temperature yield strength primarily from C and N.

Previously, we have identified that, in general, there is a linear dependence of the log of the tensile yield strength (a ) on temperature (T) for Fe-Cr-Ni base austenitic steels at low^temperatures. i,z In these austenitic stainless steels changes (3%) of

Young’s modulus (E) as a function of temperature are observed through

the low-temperature magnetic transformation (beginning at the Ndel

temperature). However, in the Fe-Cr-Mn austenitic steels changes of

elastic properties are greater (^4-5%) at the Ndel temperature; also,

the magnetic transitions occur at higher temperatures (200-330 K)

In this paper, sensitive flow strength measurements indicate that a better linear fit is obtained when the flow strength is "normalized"

and In (a / G) is plotted versus T (G is the shear modulus)

67
The logarithmic dependence of flow strength on temperature suggests a common and singular deformation process. This paper presents

the suggestion that the limiting deformation process of polycrystalline austenitic steels at low temperatures may be overcoming obstacles or cross-slip.

TEST PROCEDURES

Tensile measurements were performed using a commercial 89-kN

(20,000-lbf) tensile/compression machine equipped with a calibrated

load cell accurate to ±0.5%. All specimens were 0.5 cm in diameter

in the reduced sections, subsize according to ASTM standard E-8/81. 3 The strain rate was 5 x 10 3 min 1

. Tensile measurements were con- ducted to failure at 295 K (air), 76 K (liquid nitrogen), and 4 K

(liquid helium). The cryostat 1 ’ 2 incorporates a universal joint for

the upper pull-rod and a spherical nut seating arrangement at the

lower end to ensure good axial alignment. Strain was measured using

Ni-Chrome low-temperature strain gages that have a sensitivity of

about 10 5 at 4 K. The strain-gage-to-specimen bonded joint usually

broke at a specimen strain of about 10 2 at 4 K. Intermediate temperatures were achieved by means of controlled thermal conduction

from the fluid reservoir below the specimen and resistive heaters on both specimen grips. The specimen temperature, measured using a type

"E" thermocouple bonded to the center of the specimen, was automatically regulated to within ±0.2 K with estimated uncertainty of ±1 K. 1 The procedure for conducting variable temperature tests on single

specimens has been previously discussed. 1

MATERIALS

The chemical composition, hardness, and grain size for each of

these five austenitic steels are listed in Table 1. The 17Cr-18Mn

alloy was received as annealed flat plate (2.86 x 8.28 cm) rolled

from electroslag remelted ingots. The 14Cr-17Mn alloy was obtained

as annealed, forged plate (2.5-cm thick). The 5Cr-26Mn alloy, solution treated at 1323 K for one hour and water quenched, was received

as plates (2.7 cm x 50 cm x 50 cm). The 25Cr-21Ni alloy (AISI 310) was received as 1 . 9-cm-diameter annealed bar. Tensile specimens of

the 13Cr-5Ni-22Mn alloy were supplied in the hot-rolled condition.

After machining to specimen form, all alloys were annealed at 1350 K

for 15 min.

EXPERIMENTAL RESULTS

The tensile properties of the five austenitic steels are listed

in Table 2. Notice that all alloys have good strength and that the

elongation tends to vary inversely as the yield strength. The

68
Table 1. Alloy Characterization

Alloy

Designation

Source Country Cr Composition

Ni Mn

(wt.

C percent)

N Hardness

Others (R ) B

Grain

Size

(pm)

18Cr-18Mn U.S. 17.44 0.40 17.70 0.11 0.48 0.48Si,0.013P,

0.002S,0.99Mo,

1 .01Cu,0.01Co

101 105

14Cr-17Mn USSR 13.9 0.8 17.0 .008 0.16 0.4Si,0. lCu,

0.02P.0.01S,

0. IV

86 320

5Cr-26Mn Japan 4.67 0.97 25.56 0.22 0.04 0.86S1.0.024P

O'. 00 IS, 0.009 A1 0.04Cu,0.04Nb

86 59

25Cr-2 INi U.S. 24.8 20.8 1.7 0.08 0.03 0.02P.0.02S

0. lMo,0.7Si

0. lCu

69 105

13Cr-5Ni-22Mn Japan 12.82 4.94 21.79 0.05 0.21 0.36S1.0.013P,

0.005S

93 51

Table 2. Tensile Properties at 4 K

Yield Tensile Reduction Young'

Strength Strength Elongation of Area Modulus

Alloy (MPa) (MPa) (percent) (percent) (GPa)

18Cr-18Mn 1780 2050 11 32 199

a 14Cr-17Mn 829 - - - 198 5Cr-26Mn 855 1500 39 62 191 25Cr-21Ni 765 1240 43 20 206

1 3Cr-5Ni-22Mn 1160 1580 22 44 196

a

a Estimated by H. M. Ledbetter®

fracture toughness of most austenitic steels was also found to vary

inversely as the yield strength. 4 Young’s modulus data are from

Ledbetter, 5 8 who used a pulse-echo measurement technique. Bodycentered cubic (a’) martensite was not detected in the tensile speci mens of any of the alloys after failure at 4 K (a bar-magnet torsion

balance with 0.04% sensitivity was used).

The log of the tensile yield strength is plotted versus tempera

ture in Figure 1. The data of Figure 1 and Table 2 represent the re suits from only one or two specimens per temperature per alloy. A

better fit is obtained if the flow strength is "normalized" by divid

ing by the shear modulus (G) . This normalization accounts for the

effects of the elastic modulus decreases (3% for Fe-Cr-Ni alloys,

4-5% for Fe-Cr-Mn alloys) at the Ndel temperatures 5-7 and for the

effects of the reduced moduli on flow strength. Thus, one obtains

69
( 1 )

a

_JL = G

a

o G

o

-AT

e

where a / G is the normalized yield strength at 0 K and A is a constant. °Va?ues of a and A from Equation 1 are listed in Table 3. The

shear moduli at 0 K (G ) from Ledbetter 5-9 are included in Table 3.

Table 3 also includes Hata of three other alloys ( 17Cr-12Ni-2Mo :AISI

316; 18Cr-10Ni: AISI 304LN; 20Cr-16Ni-6Mn) for which both temperaturedependent yield strength and shear moduli data are available

1 ’ 2 ’

DISCUSSION

Schwartz and co-workers (see, e.g., reference 11), studying the

observance of a maximum in the temperature dependence of dilute

alloys, have proposed that the flow strength varies as T

2 ^ 3 at low

temperatures in the absence of dislocation inertial effects. There

is a linear dependence of a /G as a function of T

2/

3

for austenitic

steels at low temperatures.^ However, this dependence deviates to

lower than predicted values at very low temperatures <20 K) for

the high-Mn austenitic steels. The linear dependence of ln(c /G) versus T is maintained at these low temperatures for all austenitic

steels included in Table 3. Although no decreases of flow strength

at low temperatures are observed in these austenitic steels, it may

be argued that the "softening" from a T

2 ^ 3 dependence at low temperatures is caused by reduced damping and dislocation overshoot. However, in lieu of more experimental clarification of the distinctions

Fig. 1. Tensile yield strength of austenitic alloys versus temperature

70
Table 3. Tensile Flow Characteristics

Equation (1) Alloy O

q (10 3

) Parameters A ( lO^/K)

Neel

Temperature

(K)

Shear Modulus

at 0 K (G ) (GPa)

°

18Cr-18Mn 23.0 4.3a 207 78.

0

b 14Cr-17Mn 10.7 4.8 274 78.5

5Cr-26Mn 11.7 5.3 330 74.5

25Cr-21Nl (310) 9.7 4.6 10 79.9

13Cr-5Ni-22Mn 15.0 4 .

a 231 77.

0

b 17Cr-12Ni-2Mn (316) 7.3 3.4 30 81.0

18Cr-10Ni (304LN) 8.9 3.2 50 82.1 20Cr-16Ni-6Mn 14.2 4.3 54 83.4

Q.Estimated; temperature-dependent shear modulus data not available.

Estimated by H. M. Ledbetter8

between these possible flow strength dependences, we assume that

equation 1 fits the experimental data best.

Characterization by plotting the log of the flow strength versus

temperature produces two regions of linear dependence. The transition temperature between the two regions varies from about 160 K

(5Cr-26Mn alloy) to 260 K (18Cr-18Mn alloy). However, there is no apparent correlation of the transition temperature with magnetic behavior (Ndel temperature) 6 ” 9 listed in Table 3 or with deformation

characteristics such as the stacking-fault energy. While the Neel

temperature has been measured for most of the alloys included in

Table 3 and is considered accurate, estimation of stacking-fault en- ergies for these austenitic steels is considered inaccurate. Schramm

and Reed 12 reported stacking-fault energies as a function of Cr, Ni,

Mn, and Mo concentration, obtained using regression analysis of x-ray

peak shift data of deformed Fe-Cr-Ni alloys and normalized to existing electron microscopy node data at the time of the study. Later,

Rhodes and Thompson 19 argued, on the basis of newer weak-beam electron microscopy data on Fe-Cr-Ni alloys, that the calculated values

of Schramm and Reed were too high and should be reduced some 30 %.

They presented a modified equation, but the form of their equation

places too great a dependence of Mn on stacking-fault energy to permit its use for high- Mn austenitic steels. Furthermore, Stolz and

VanderSande 1 ^ caution about the use of regression analyses for high-N

alloys

The constant a /G of Equation 1 represents the extrapolated

normalized yield strength at 0 K. This strength depends primarily

on C and N concentration. This is illustrated in Figure 2 which

illustrates that a /G is approximately linearly dependent on

C + 2N for the alloys listed in Table 3. More precise functional

71
relations between a and C and N content is discussed in another

paper. 15 The constant A of Equation 1 may be related to the

stacking-fault energy. Schoeck and Seeger 15 associated the onset

of stage 3 of f ace-centered-cubic (f.c.c.) single-crystal stressstrain curves with cross-slip. From their theory the log of the

associated stress (t ) should vary linearly with temperature.

CO

I

Fig. 2. Normalized tensile yield strength, o /G , as a function of

C and N content of the austenitic steels listed in Table 3.

5.4 €

“

5.0 o^ 4.8 (—5

4.6 S" 4.4 6

*" 42 f 4.0 o

lu 3 8 Q-3 3.6

C/D < 3.4

3 2

3.0 0 10 20 30 40 50 60 70 80 90 100 110 120 STACKING-fAULT ENERGY. mJ/m2

Fig. 3. Temperature dependence of normalized tensile yield strength

of 25Cr-21Ni, 17Cr-12Ni-2Mn, and 18Cr-10Ni alloys (Table 3) versus estimated stacking-fault energy.

1 1 1 1 1 11 1 1 ~r~

- /

- - « - _ / mm /

/

— /

—

- / - / _ /

*/ * m

L-/ * 1 1 1 1 l 1 l _i

72
1 7 This has been confirmed experimentally in single crystals. If

the early o-e region of f.c.c. polycrystalline metals is primarily

controlled by cross-slip, this same temperature dependence should be

expected. Unfortunately, as pointed out earlier, the stacking-fault

energies (y) of high-Mn austenitic steels are not accurately predictable yet. One can correlate d(a / G) / dT with the y’s of the

Fe-Cr-Ni steels; this correlation is^ shown in Figure 3. Here the

range of y is from the predictions of Schramm and Reed 12 (higher

values) and Rhodes and Thompson 13 (lower values). The slope of the

o -T relation decreases with increasing y._ However, the slope is

expected to be zero, when y is zero; since this is not the case, the

fit in Figure 3 of three data points may be fortuitous.

More recently, Escaig 18 has developed an alternative cross-slip

theory, and his model has been used to predict the stacking-fault

energy of polycrystalline Ag and Cu alloys by Beneteau and Coulomb. 18

The Escaig model, however, predicts a linear dependence of stress on temperature. It does appear that one rate process may control low

temperature polycrystalline deformation at low plastic strains; however, work remains to identify this process.

SUMMARY

The temperature dependence of the flow strength of five

austenitic steels, with varying Cr, Mn, Ni, C, and N contents,

has been measured at low temperatures (4-295 K) . A relation of

the form

oG

( 2 )

fits the experimental data best. The normalized strength at 0 K,

a /G , has been correlated with a function of C and N content. The

constant, A, has been correlated with the stacking-fault energy for

three Fe-Cr-Ni alloys.

ACKNOWLEDGMENTS

We thank Robert Walsh who carefully conducted many of the tensile tests. We are indebted to the suppliers of most of the steels

included in this study: K. Yushchenko, Raton Institute (14Cr-17Mn);

L. Meyers, Carpenter Technology Corporation (18Cr-18Mn); R. Ogawa,

Kobe Steel ( 13Cr-5Ni-22Mn) , and T. Inoue, Nippon Steel (5Cr-26Mn)

This project was partially supported by the Office of Fusion Energy

(DoE) , Donald Beard project monitor.

73
REFERENCES

1. R. P. Reed, R. L. Tobler, and J. W. Elmer, Proceedings of the

International Cryogenic Materials Conference , Kobe, Japan;

May 11-14, 1982, Butterworths , Guildford, Great Britain,

pp. 98-103.

2. R. L. Tobler, R. P. Reed, and D. S. Burkhalter, Advances in

Cryogenic Engineering - Materials , Vol. 26, Plenum Press, New

York (1980), pp. 107-119.

3. 1981 Annual Book of ASTM Standards , Part 10, Metals-Physical

,

Mechanical, Corrosion Testing, American Society for Testing

Materials, Philadelphia, Pennsylvania (1981), pp. 197-217.

4. R. L. Tobler and R. P. Reed, Advances in Cryogenic Engineering - Materials , Vol. 28., Plenum Press, New York (1982), pp. 83-92.

5. H. M. Ledbetter, Metall. Trans . llA:543-544 (1980).

6. H. M. Ledbetter, J. Appl. Phys . 52:1587-1589 (1981).

7. H. M. Ledbetter, accepted for publication in Physica (1983).

8. H. M. Ledbetter, private communication. National Bureau of

Standards, Boulder, Colorado (1983).

9. H. M. Ledbetter and M. W. Austin, Materials Studies for Magnetic

Fusion Energy - V , NBSIR 82-1667, report to Office of Fusion

Energy (DoE) , R. P. Reed and N. S. Simon, eds.. National

Bureau of Standards, Boulder, Colorado (1982), pp . 213-228.

10. R. L. Tobler, D. H. Beekman, and R. P. Reed, Austenitic Steels at

Low Temperatures , Plenum Press, New York (1983), pp. 135-160.

11. R. B. Schwartz, R. D. Isaac, A. V. Granato, Phys. Rev. Lett . 38:554-557 (1977).

12. R. E. Schramm and R. P. Reed, Metall. Trans . 6A: 1345-1351

(1975).

13. C. G. Rhodes and A. W. Thompson, Metall. Trans . 8A: 1901-1906

(1977).

14. R. E. Stolz and J. B. VanderSande, SAND 79-8735, Sandia

Laboratories, Albuquerque, New Mexico (1979).

15. R. P. Reed and N. S. Simon, Advances in Cryogenic

Engineering - Materials , Vol. 30, Plenum Press, New York

(1983)

16. G. Schoeck and Seeger, Defects in Crystalline Solids , The

Physical Society, London (1955), pp. 340-346.

17. S. Mader, Electron Microscopy and Strength of Crystals , Interscience, New York (1963), pp. 183-230.

18. B. Escaig, J . Phys 29:225-234 (1968).

19. A. Beneteau and P. Coulomb, Scr. Metall. 12:741-743 (1978).

74
MAGNETIC SUSCEPTIBILITY AND STRAIN- INDUCED MARTENSITE FORMATION

*+

AT 4 K IN TYPE 304 STAINLESS STEEL

R. B. Goldfarb, R. P. Reed, J. W. Ekin, and J. M. Arvidson

National Bureau of Standards

Boulder, Colorado

Abstract

Changes in magnetic susceptibility, x> as a function of strain- induced

structural transformations in AISI type 304-stainless steel at 4 K have been

observed using a mutual inductance technique with simultaneous measurement of

stress and strain. There is a small increase in x coincident with plastic

strain and a large increase in x with the load drops that occur during 'serrated

yielding. These are attributed to the formation of bcc martensite. The

increases in x are irreversible upon unloading. The application of a moderate

3-MA/m (37-kOe) dc field had no effect on the martensite formation.

* Sponsored, in part, by the Office of Fusion Energy, U.S. Department of

Energy.

+ # Published in Advances in Cryogenic Engineering - Materials , vol. 30, Plenum

Press, New York (1984), pp . 475-482.

75
1
INTRODUCTION

Plastic deformation of some metastable austenitic stainless

steels, such as AISI type 304, at cryogenic temperatures causes localized transformations to martensite. This phase is ferromagnetic, with a large coercivity at 4 K. These alloys are also

known to exhibit serrated yielding at liquid helium temperatures. 1 The first measurement of magnetic susceptibility during plastic

deformation was by Kelha and Niinikoski. 2 Bolshutkin et al.

investigated susceptibility correlated with martensite transformations at cryogenic temperatures. 3 In the present work,

quantitative measurements of susceptibility changes at 4 K during

martensite formation, with and without a background field, are reported. The results show that most of the martensite formation

occurs during the serrated yielding, and that the amount formed

increases with the magnitude of the load drops.

77
EXPERIMENT

Tensile specimens with about 6-mm gauge diameter and 4-cm

reduced-section length (cf: Ref 4) were machined from type 304

stainless steel rod stock. Composition (by weight) was nominally

73% Fe, 18% Cr, and 9% Ni. The specimens were annealed in helium

gas at 1066°C for 15 min, quenched in water, and electropolished

to remove 0.1 mm from the diameter. Tension was applied with the

specimen immersed in liquid helium within the bore of a 3-MA/m

(37-kOe) superconducting magnet. Magnetic ac susceptibility, x> could be measured with the dc field off. When the dc field was

on, it saturated the specimens and precluded measurement of x*

Fig. 1. Construction of susceptometer and demountable grips.

Reaction tube not shown.

78
The unfractured specimens could be unscrewed from the reaction

plate and, while still attached to the pull rod, withdrawn from

the Dewar. This allowed the samples to be changed without warming

the magnet and reaction-tube assembly. The construction of the

susceptometer is shown in Fig. 1. It was calibrated with a standard of dimensions similar to those of the specimens. The

calibration was verified by numerical methods. Note that the

entire specimen is well within the pick-up coil and remains so even after straining.

A mutual inductance technique was used to measure x* A

schematic of the electronics is shown in Fig. 2. An ac oscillator, in constant current mode, drives the field coil and provides

a reference for the lock-in amplifier, the phase-lock phase-shifter,

and the oscilloscope. When a magnetic transformation in the

specimen occurs, the mutual inductance between the field coil and

the pick-up coil increases. The constant ac current, I, ensures a constant field even when the self-inductance of the field coil

increases. The emf induced in the pick-up coil is input to a differential amplifier. The high input impedance of the amplifier

Fig. 2. Electronics schematic for susceptibility measurements.

79
ensures that substantially no current flows in the pick-up coil so that the emf is about equal to its open-circuit value. Also con- nected to the differential amplifier is a phase shifter. This

specially designed circuit locks onto the frequency of the driving

signal. Its output, variable in amplitude and phase, is set to

null the output of the differential amplifier, v, after the speci- men is inserted but before it is strained. The usual method of

compensation with an identical coaxial compensating (or "bucking")

coil was not chosen because of the limited space in the Dewar.

The output of the differential amplifier is connected to a lock-in

amplifier. The dc output of the lock-in was recorded vs. stroke

(strain). Load (stress) was also recorded vs. stroke.

The frequency selected for the ac x measurement was 100 Hz.

For the specimen geometry, permeability, and resistivity, this

frequency was not high enough to cause eddy-current problems. 5 The field coil was operated at 4 kA/m (50 Oe) rms . This relatively large ac field was needed because of the large coercivity

of martensite at 4 K.

RESULTS AND DISCUSSION

Figure 3 is a plot of x and load (stress) vs. stroke (strain).

Stroke was controlled at 0.1 mm/min. The specimen was unloaded at

various points on the curve to see whether the increased magnetic

signal was reversible. In the initial elastic and plastic regions

(a, b, and c in Fig. 3), there was a small, reversible increase in

X (d) . In the plastic region prior to each serrated yield (e)

,

there was a small irreversible increase in x (f ) • Coincident with

each of the serrated yields (i) , there was a large, irreversible

increase in x (j) caused by the formation of strain-induced bcc

martensite, which is ferromagnetic. Immediately following the

load drops, as reloading occurred (o) , the increase in x was once again reversible (p) . The slope of this increase became larger as the number of load drops increased. The reversible increases in x may be attributed to the inverse positive magnetostrictive effect:

an increase in x due to stress, predominantly of the already

transformed martensite.

The martensite formation at low temperature in metastable

austenitic stainless steels is strain induced. 7 The magnitude of

the increase in x» and therefore the amount of martensite formed,

correlates with the magnitude of the strain (load drops) . This

relationship is plotted in Fig. 4 for two specimens strained at

the usual rate of 0.1 mm/min. A third specimen was strained at

the rates of 0.2 mm/min and 1.2 mm/min. The increase in x depended

on the magnitude of the load drop but not on the strain rate.

Because of the adiabatic conditions at 4 K during the sudden load

drops, large localized rises in temperature occurred. It is likely

that the nonlinear relation between the magnitudes of the load

80
0.3

STROKE (eel)

Fig. 3. Load and increase in volume susceptibility vs. stroke:

(a) initial elastic region, (d) initial plastic region, (c)

unloading to zero and reloading, (d) reversible increase in x during a, b & c, (e) plastic region prior to load drop, (f)

irreversible increase in x during e, (g) unloading and reloading

prior to second load drop, (h) reversible decrease and increase in

X during g at higher level than d, (i) serrated yielding, (j)

irreversible increases in x during i, (k) unloading and reloading

prior to load drop, (1) reversible decrease and increase in x during k, (m) unloading and reloading immediately following load

drop, (n) reversible decrease and increase in x during m, (o)

elastic loading, unloading, and reloading following load drop, Cp'

reversible increase, decrease, and then increase in > during o.

81
drop and the increase in x reflects the isothermal nature of the

transformation of martensite in austenitic steels: larger temperature increases are associated with larger load drops, and larger

amounts of martensite form at higher cryogenic temperatures. 1

A 3-MA/m (37-kOe) dc field had no effect on the amount of

martensite formed. A comparison was made of four specimens, two

strained with the background dc field off and two with it on. The

ratio of x after straining divided by percent strain (about 6%) was virtually the same for all four specimens. Another specimen

was strained until it was in the serrated yielding region. After

each load drop, the specimen was unloaded, the field alternately

applied or removed, and the specimen reloaded until the next load

drop. The increase in x was recorded for 10 cycles and did not

depend on the presence or absence of' the field.

Although it does not apply to the above results, one possible

source of error in measuring the effects of magnetic fields on mechanical properties is that the application and removal of a dc

field may exert a force on the reaction tube or on the pull rod,

which results in changes in load. This could lead to spurious

w

co

w

3

w

PSo

2

w

>-

e-w

1-J w

P3

I—

E-* CUWU

CO2

CO

3

-

2 -

Strain Rate

o = Specimen 1, 0.1 mm/min

• = Specimen 2, 0.1 mm/min

a = Specimen 3, 0.2 mm/min

= Specimen 3, 1.2 mm/min

o

•o

o a

• A

O A o

A A< A

1 2 3

LOAD DROP (kN)

Fig. 4. Increase in volume susceptibility as a function of

magnitude of load drop.

82
conclusions regarding transient magnetic field effects in the

specimens. Figure 5 shows load and magnetic field vs. stroke

(controlled as a function of time) in the elastic region of a specimen (in this case austenitic type 310 stainless steel, nominal

composition: 54% Fe, 25% Cr, 21% Ni) . No changes in the stressstrain curve due to transient field conditions nor significant

magnetostriction would be expected in the elastic region of this

low-magnetization, stable alloy. However, as the field increased,

the load increased above its trendline. A reduction in field

caused the load to return to its trendline. The magnet was quenched after its final charge, causing a precipitous drop in

load. These apparently transient effects in the specimen were

actually due to the interaction of the magnetic field with the

weakly magnetic reaction tube and pull rod and local magnetic

fields caused by eddy currents. Such effects should be considered

in transient-field experiments (cf: Ref. 8).

CONCLUSIONS

AISI type 304 stainless steel, when plastically strained at

4 K, is known to undergo serrated yielding. This results in a pronounced increase in x» as measured at room temperature, which

has been attributed to the transformation of fee austenite (y phase)

<

Q

J

W

i-l

2

Jixi

3

O

Fig. 5. Artifacts in load-stroke curve caused by application and

removal of magnetic field.

83
to ferromagnetic bcc martensite (a' phase). In this work, the ac

X was measured at 4 K using a mutual inductance technique while

simultaneously measuring stress and strain. The following results

were obtained.

1. There was a small Increase in x in the initial elastic

and plastic regions, which was reversible upon unloading.

2. There was a small, irreversible increase in x with

plastic deformation prior to serrated yielding. This is attributed

to the formation of strain- induced martensite.

3. There were large, irreversible increases in x coincident

with the load drops associated with serrated yielding. These are

also attributed to the irreversible formation of strain-induced

martensite. The magnitude of the increases in susceptibility

correlated with the magnitude of the load drops.

4. Immediately following a load drop in the serrated yielding region, there was a reversible increase in x as elastic

reloading occurred. The slope of this increase became larger as the number of load drops increased. This may be attributed to the

inverse magnetostrictive effect. After reloading, further plastiq

strain prior to the next load drop caused a small, irreversible

increase in x*

5. The application of a moderate, 3-MA/m (37-kOe) dc field

at 4 K had no effect on the formation of martensite.

6. The application and removal of a dc magnetic field caused

changes in the stress-strain curve when measured as load vs. stroke. These changes were likely due to the magnetic force on the reaction tube and pull rod rather than transient magnetic

effects in the specimen.

REFERENCES

1. C. J. Guntner and R. P. Reed, ASM Trans . (). 55:399 (1962).

2. V. Kelha and T. Niinikoski, Acta Polytech . Scand . (Helsinki),

Phys . Incl . Nucleon . Ph 76:1 (1971).

3. D. N. Bolshutkin, V. A. Desnenko, and V. Ya. Ilichev, Phys . Met. Metallogr. 50:131 (1980) [Fiz. Met. Metalloved.

50:826 (1980)].

4. 1983 Annual Book of ASTM Standards, Vol. 03.01, A370-77,

Standard E6, ASTM, Philadelphia, 1983, pp . 41-42.

5. H. Zijlstra, "Experimental Methods in Magnetism," Vol. 2 North-Holland , Amsterdam (1976), pp. 72-79.

6. B. D. Cullity, "Introduction to Magnetic Materials," AddisonWesley, Reading, Massachusetts (1972), pp. 266-275.

7. R. P. Reed, Martensitic phase transformations, in: "Materials

at Low Temperatures," R. P. Reed and A. F. Clark, eds .

,

American Society for Metals, Metals Park, Ohio (1983), pp.

295-341.

8. D. N. Bolshutkin, V. A. Desnenko, and V. Ya. Ilichev, Cryogenics 19:231 (1979).

84
FATIGUE CRACK GROWTH IN SENSITIZED Fe-18Cr-3Ni-13Mn-0.37N

AUSTENITIC STAINLESS STEEL:

THE SIGNIFICANCE OF MICROMECHANISMS

R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A nitrogen-bearing austenitic stainless steel (Fe-18Cr-3Ni-13Mn-0.37N)

was fatigue tested in both the annealed and isothermally sensitized conditions

at 295 and 4 K. This temperature reduction caused fatigue and fracture

failure mode transitions in conjunction with a significant increase of

strength. Comparison of the sensitized versus annealed material at 295 K indicated no difference in the fatigue crack growth behavior at intermediate

aK. At 4 K, however, the fatigue resistance was degraded, with sensitized

material showing greater degradation than annealed material. These

differences were interpreted in terms of the operative failure

micromechanisms.

Key Words: Austenitic stainless steels; chromium carbo-nitride

precipitation; cryogenic properties of materials; fatigue;

fatigue crack growth; failure micromechanisms; sensitization.

Work supported by DoE, Office of Fusion Energy; not subject to copyright.

85

INTRODUCTION

The austenitic stainless steels are highly regarded as reliable cryogenic

alloys, but property degradations due to sensitization may limit their performance in some applications. Sensitization is a mi crostructural phenomenon

encountered when these steels are heated at temperatures from 700 to 1100 K.

After sufficient time at these temperatures , chromium carbo-ni trides begin to

precipitate at the grain boundaries.

Sensitization can be detrimental to corrosion resistance, as well as

1 2 cryogenic ductility and toughness, ’ but very little is known about the

effects of sensitization on fatigue properties. In a study of AISI 310S

3 stainless steel, Logsdon, Wells, and Kossowsky report that sensitization

produced no change at all in the 4 K fatigue crack growth rates (da/dN) at

intermediate stress-intensity factors (aK), whereas the 4 K fracture toughness

(Kj

c

) was reduced 36%. The present paper describes new data for a nitrogenstrengthened Fe-18Cr-3Ni-13Mn-0.37N steel, documents its failure mechanisms,

and contrasts its performance with that of AISI 310S.

EXPERIMENTAL MATERIAL AND PROCEDURE

The studied material is a commercial plate of Fe-18Cr-3Ni -13Mn-0. 37N

austenitic stainless steel, 25-mm thick and previously characterized by Read

4

and Reed. The composition in weight percent is: Fe-18.09Cr-3.26Ni-13.22Mn0.37N-0.038C-0. 12Mo-0.52Si-0.005S-0.028P. In the as-received condition the

material was annealed 1 h at 1353 K and water quenched. The nominal value of

grain size is ASTM No. 6, the Rockwell hardness is B93, and the tensile

properties are shown in Table 1.

The fatigue tests were performed on material in both the as-received

(i.e., annealed) and sensitized conditions. Representative mi crostructures

87
are shown in Fig. 1. The isothermal sensitization was induced by either of

two treatments designated as follows:

condition: 977 K, 0.75 h, water quench

S

2 condition: 977 K, 1.5 h, water quench

All tests used compact specimens 25-mm thick and 50.8-mm wide. The notch

was machined in the longitudinal plate direction and the load was applied

transversely (TL orientation). The specimen and cryogenic test apparatus are

5 described elsewhere.

The properties measured were the fatigue crack growth rates at 295 and

4 K and the 4-K fatigue fracture toughness (K^ ). All tests used sinusoidal

load control at a stress ratio of 0.1. The cycling rate was 20 Hz, except

near K

f when the frequency was reduced to values as low as 2 Hz. Cheng's"

7

computer-aided compliance method was used to record curves of crack length (a)

versus cycles (N), to plot da/dN-versus-AK, and to calculate the Paris equation

parameters C and n (i.e., da/dN= C(AK)

n

) on the basis of least-squares fits.

Calculations of were based on the maximum fatigue load and the crack

length at instability as the crack grew to critical size at progressively

increasing AK values.

RESULTS

Fatigue Crack Growth

The fatigue crack growth rate data are shown in Figs. 2 and 3. At 295 K,

the rates for both the S^ and S^ conditions were equivalent to rates for the

annealed condition^ (not shown). Figure 4 illustrates the micromechanism of

failure at room temperature. The distinguishing feature here is transgranul ar

striation formation owing to reversed plastic flow at the crack tip, and there

88
is no intergranular fracture. The same failure mode persisted for this steel

at 295 K in all three metallurgical conditions: annealed, S^, and S^. Thus,

the effect of grain-boundary precipitation on the fatigue crack growth rates

and failure mode at room temperature was negligible for the AK range studied.

The temperature reduction from 295 to 4 K greatly accelerated the crack

growth rates for Fe-18Cr-3Ni-13Mn-0.37N steel, both for the sensitized condi4

tions (Fig. 2) and for the annealed condition. The change from 295 to 4 K

also had remarkable effects on the Paris parameters: C decreased while n

increased strongly, as shown in Table 2. This behavior relates to some

striking transitions in the fatigue failure mechanisms, as shown in Fig. 4.

The ductile striation formations observed at 295 K were replaced at 4 K by

relatively brittle mechanisms promoting higher crack growth rates. Thre

brittle mechanisms at 4 K involved transgranul ar facet formation in the

annealed condition and intergranul ar failure in the sensitized conditions.

The fatigue crack growth rates at 4 K are compared in Fig. 3. At this

test temperature an effect of sensitization emerged: da/dN increased at 4 K

relative to the annealed condition, but the difference varied with aK as well

as the degree of sensitization. In particular, the rates for the S£ condition

accelerated well above the rates for both the and annealed conditions when

AK exceeded 30 MPa*m 2

.

Fatigue Fracture Toughness

The K

f

measurements showed that sensitization decreased the toughness

relative to the annealed condition if sufficient time was allowed at the

sensitizing temperature. Single specimen tests at 4 K yielded a value of

i i K^

c = 61 MPa*m 2 for the annealed condition and values of 61 and 41 MPa*mJ for

the and conditions, respectively. As shown in Fig. 5, the lower toughness

of the S

2 condition was associated with 100% intergranul ar failure, whereas

89
the annealed steel showed a mixed-mode mechanism consisting of transgranul ar

facets amidst dimpled failure zones. Intergranul ar failure was evidently a

consequence of the fact that carbide-matrix interfaces possess relatively low

cohesive strength. Carbide precipitation along the grain boundaries therefore

caused an overall reduction of the boundary cohesive strength owing to the

relative weakness of the carbide-matri x interface, and failure at the boundaries

became energetically favorable compared with the transgranul ar alternative.

The altered austenite stability and strength of the accompanying near-boundary

chromium-depleted zones may also have contributed to intergranular failure.

In any case, the consequences of such effects were obviously more severe in

the condition, which has more advanced carbide precipitation than .

DISCUSSION

The limited data available indicate that sensitization may significantly

reduce the fatigue crack growth resistance of stainless steels under certain

conditions, and in other cases there may be little or no effect. It is

suggested that the effect of sensitization on the alloy fatigue crack growth

behavior in the Paris range is a function of test temperature and alloy

composition, and can be qualitatively predicted from the effect of sensitization

on Kj

c> The suggested prediction scheme hinges on the relationship between n

and Kj

c

, as shown in Fig. 6. The data in this figure represent austenitic

steels with fracture toughness values covering a broad range, from 40 to 500

I MPa*m 2

. On this plot, two distinct regions are identified as follows:

In region I, the low toughness region, n depends on Kj

c

, increasing with

decreasing toughness and reaching values much greater than 4. Here, both the

fatigue and fracture mechanisms are essentially brittle, involving significant

portions of either transgranul ar faceting or intergranular failure.

90
In region II, the high toughness region, n is nearly constant at values

near 4, independent of Kj . Here the failure mechanisms are predominantly

ductile: striations form during fatigue, and dimples form during monotonic

loading to fracture.

Thus, it appears that the two-stage behavior of Fig. 6 is determined by

the operative failure mechanisms and that the transition between the toughnessdependent and toughness-independent fatigue regions can be gaged approximately

by the value of Kj . For the austenitic stainless steels of Fig. 6, this

1 transition occurs at K T = 150 to 200 MPa*m 2

. Ic

The contrasting behaviors of Fe-18Cr-3Ni-13Mn-0.37N and AISI 310S at 4 K

can now be explained as follows: The low toughness Fe-18Cr-3Ni-13Mn-0. 37N

steel at 4 K (Kj

c

= 71 MPa*m 2

) corresponds to region I. In this region n is

dependent on K^, and because sensitization decreases the toughness at 4 K,

there is a corresponding increase of n, which alters da/dN. In contrast, the

high toughness AISI 310S steel at 4 K (Kj

c = 282 MPa*m 2

) corresponds to region

II. In this case sensitization decreases the toughness to 181 MPa*m 2

, but n

remains unaffected in region II, and there is no effect of sensitization on

3

da/dN. Similarly, the fact that there exists an effect of sensitization on

the fatigue crack growth resistance of Fe-18Cr-3Ni -13Mn-0. 37N steel at 4 K but

not at 295 K is explained because at room temperature the toughness is quite

high and corresponds to region-II.

SUMMARY AND CONCLUSIONS

At 295 K, the Fe-18Cr-3Ni-13Mn-0.37N steel is characterized by high

toughness, and its fatigue and failure mechanisms are ductile. Precipitates

located at grain boundary sites owing to sensitization (1.5 h at 977 K) are

unable to alter da/dN since the fatigue mechanism at 295 K invariably is

91
transgranul ar striation formation.

At 4 K, the yield strength of this steel is more than triple its room

temperature value; consequently, the 4-K fracture toughness is relatively low

and the fatigue crack growth properties are degraded. At this low temperature,

extensive sensitization (1.5 h at 977 K) induces a transition in

micromechanisms from transgranul ar failure (annealed material) to

intergranul ar failure (sensitized material). Thereby, the 4-K fatigue crack

growth resistance and fracture toughness properties are measurably reduced.

It is concluded, in general, that the effects of sensitization on da/dN

at intermediate aK values appear to depend on the type of failure mechanisms

that operate at different material and temperature combinations, and on this

basis a predictive scheme is suggested.

ACKNOWLEDGMENT

The Department of Energy, Office of Magnetic Fusion Energy supported this

work. I am grateful to Mr. P. T. Purtscher of NBS who assisted in f ractographic

examinations.

92
REFERENCES

1. D. A. Wigley, "Heat Treatments to Desensitize and Remove Delta Ferrite

from a 21Cr-6Ni-9Mn Stainless Steel Intended for the Fabrication of

Aerofoil Models for Cryogenic Wind Tunnels," in: Austenitic Steels at Low

Temperatures , R. P. Reed and T. Horiuchi, eds., Plenum Press, New York

(1983), pp. 249-261.

2. S. Danyluk and J. Y. Park, "Low Temperature Intergranul ar Fracture and

Grain Boundary Chemistry of Sensitized Type 304 Stainless Steel," Seri pta

Metal 1 urgi ca , 16, (1982), pp. 769-774.

3. W. A. Logsdon, J. M. Wells, and R. Kossowsky, "Fracture Mechanics Properties

of Austenitic Stainless Steels for Advanced Cryogenic Applications," in:

Proceedings of the Second International Conference on Mechanical Behavior

of Materials, American Society for Metals, Metals Park, Ohio (1976),

pp. 1283-1289.

4. D. T. Read and R. P. Reed, "Toughness, Fatigue Crack Growth, and Tensile

Properties of Three Nitrogen-Strengthened Stainless Steels at Cryogenic

Temperatures," in: The Metal Science of Stainless Steel , E. W. Collings

and H. W. King, eds., Metallurgical Society of AIME, New York (1979),

pp. 92-121.

5. D. T. Read and R. L. Tobler, "Mechanical Property Measurements at Low

Temperatures," in: Advances in Cryogenic Engineering , vol . 28, Plenum

Press, New York (1982), pp. 17-28.

6. T. Yokobori and T. Aizawa, "Reports of the Research Institute for

Strength and Fracture of Materials," vol. 6, Tohoku University, Tohoku,

Japan (1970), p. 19.

7. Yi-W. Cheng, "A Computer-Interacti ve Fatigue Crack Growth Rate Test

Procedure," in: Materials Studies for Magnetic Fusion Energy Applications

At Low Temperatures-VI , NBSIR 83-1690, R. P. Reed and N. J. Simon, eds.

National Bureau of Standards, Boulder, Colorado (1983), pp. 41-52.

93
Table 1. Mechanical Properties for Annealed Fe-18Cr-3Ni-13Mn-0.37N

4

Stainl ess Steel

Temperature Yiel d U1 timate El ongati on Reduction

Strength

,

Strength

,

in 25 mm of Area

(K) 0 (MPa) a (MPa)

u <%) (%)

295 440 796 56 53

4 1540 1811 4 26

Table 2. Fatigue crack growth rate data for Fe-18Cr-3Ni-13Mn-0. 37N

and AISI 310S stainless steels.

Material, and Temperature No. of Paris equation parameters,

3 Condition (K) data pts. C n

Fe-18Cr-3Ni-13Mn-0.37N

4

Anneal ed 295 _ _ 0.97 X io

-10

-10

-10

1

0

-12

10

LC

-1

10U-15

10

3.82

Sensitized

,

S

1 S

?

295 24 2.10 X 3.63

Sensitized

,

295 21 1.35 X 3.70

Anneal ed

C. 4 41 1.09 X 5.73

Sensitized, S

1 s 4 28 1.29 X 5.18

Sen si ti zed

,

4 20 2.80 X 7.78

310S

3

Annealed, STQ^ 77, 4 -- 1.40 X 10-10

io10

3.75

Sensitized, STFC 77, 4 -- 1.40 X 3.75

cl — b

For metric units, with da/dN in mm/cycle and aK in MPa*m 2

.

£

Solution treated and water quenched.

Solution treated and furnace cooled.

94
LIST OF FIGURES

Fig. 1. Fe-18Cr-3Ni -13Mn-0. 37N steel microstructures.

Fig. 2. Fatigue crack growth rate data for sensitized Fe-18Cr-3Ni -13Mn-0 . 37N

steel at 295 and 4 K.

Fig. 3. Fatigue crack growth rate data for Fe-18Cr-3Ni -13Mn-0. 37N steel in

the annealed and sensitized conditions at 4 K.

Fig. 4. Fatigue failure mechanisms Fe-18Cr-3Ni-13Mn-0.37N steel: a) S,

condition at 295 K, b) annealed condition at 4 K, c) S, condition at

4 K, d) condition at 4 K.

Fig. 5. Fracture modes Fe-18Cr-3Ni-13Mn-0. 37N steel corresponding to

overload at 4 K.

Fig. 6. The n-^ersus-Kj correlation for selected austenitic stainless

steels . (The §rrows show the change in properties before and after

sensitization.

)

95
96

Fe-18Cr-3Ni-13Mn-0.37N

steel

microstructures.
FATIGUE

CRACK

GROWTH

RATE,

da/dN,

mm/cycle

STRESS INTENSITY FACTOR RANGE, AK, MPa-m1/2

_2 10 50

Fig. 2. Fatigue crack growth rate data for sensitized Fe-18Cr-3Ni -13Mn-0. 37N

steel at 295 and 4 K.

97

FATIGUE

CRACK

GROWTH

RATE,

da/dN,

in/cycle
FATIGUE

CRACK

GROWTH

RATE,

da/dN,

mm/cycle

STRESS INTENSITY FACTOR RANGE, AK, ksi-in1/2

_2 10 50

Fig. 3. Fatigue crack growth rate data for Fe-18Cr-3Ni-13Mn-0.37N steel in

the annealed and sensitized conditions at 4 K.

98

FATIGUE

CRACK

GROWTH

RATE,

da/dN,

in/cycle
99

100/xm s2,

4K

40/rm

Fatigue

failure

mechanisms

Fe-18Cr-3Ni-13Mn-0.37N

steel:

a)

S,

condition

at

295

K,

b)

annealed

condition

at 4

K,

c)

S,

condition

at 4

K,

d)S0

condition

at 4

K.
100

Fig.

5.

Fracture

modes

Fe-18Cr-3Ni-13Mn-0.37N

steel

corresponding

to

overload

at4

K.
c

LU

O

Q-X

LU

ho

0C0

*

O

<

QCO

LU

H

<

Fig. 6. The n-versus-K

T correlation for selected austenitic stainless

steels

4

. (The arrows show the change in properties before and after

sensitization.

101

Midrange Fatigue Crack Growth Data Correlations for Structural Alloys at Room

and Cryogenic Temperatures*t

R. L. Tobler and Y. W. Cheng

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Fatigue crack growth rate data for pure metals, structural alloys, and

welds at temperatures from 295 to 4 K are selectively reviewed. The data for more than 200 material and temperature combinations are discussed in terms of

the parameters C and n for the midrange of the da/dN-vs.-AK curve. Fatigue

resistance varies greatly among the differervt alloy classes and crystal

structure types, especially at extreme cryogenic temperatures where alternative failure mechanisms emerge. Good general correlations were achieved on the basis of Young's modulus, fracture toughness, and empirical equations

relating C and n for each alloy class.

Key words: austenitic stainless steels; cryogenic properties of metals;

fatigue; fatigue crack growth; fracture toughness; structural alloys; Young's

modul us

*Work supported by DoE, Office of Fusion

tTo be published by the American Society

Energy; not subject to copyright,

for Testing and Materials.

103

INTRODUCTION

To the surprise of many at the time, Paris and his colleagues [1,2]

correlated fatigue crack growth rates, da/dN, with the linear-elastic stressintensity factor range, aK. For the midrange of the da/dN-vs.-AK curve they

proposed the power-law equation:

da/dN = C(AK)

n (1)

where the parameters C and n were interpreted as material constants.

Subsequent studies have shown that the material behavior in this range is

governed by continuum mechanics and marked by a strong dependence on Young's

modulus, E. Often there is a relative insensitivity to metallurgical and

mi crostructural variables [3,4]. In theory, the conventional mechanical

properties, such as yield strength, a , and fracture toughness, l< T

, play

y ic

significant roles, but in practice their influence is difficult to predict.

For a number of alloy families at room temperature, it has been shown

that the coefficients and exponents of Eq (1) are related by the expression:

C = A(1/aK

0

)" (2)

or, equivalently,

log C = log A + n log (1 /aK ) (3)

Kitagawa and Misumi [5] first demonstrated these relationships for ferritic

steels. Subsequent correlations for austenitic steels, titanium alloys, and

aluminum alloys (all at room temperature) indicate that for each alloy systen

105
A and aK

q depend on the fatigue stress ratio, R, but are independent of

metallurgical and mi crostructural variations and environment to a considerable

1 extent [6-14]. The A (mm/cycle) and aK

q (MPa*m 2

) parameters correspond to the

coordinates of a pivot point where the da/dN-vs.-AK curves for a given alloy

system intersect one another [14].

The present paper surveys the available data for cryogenic structural

alloys, noting some simple correlations between fatigue crack growth rates and

conventional mechanical properties. In continuation of a previous study [15],

Eqs (2) and (3) are used to describe data at cryogenic temperatures where the

C and n parameters for materials show great variations. Pivot points for

various alloy families are calculated and compared, and the concepts of

structure-sensitive and structure-insensitive da/dN behavior are discussed.

MATERIALS AND PROCEDURES

The C and n parameters for a variety of materials [16-44] were collected

and reviewed for this paper. The alloys of interest are grouped as follows:

1. ferritic nickel steels (high-modulus bcc alloys)

2. austenitic stainless steels (high-modulus fee alloys, stable or metastable with respect to martensitic phase transformations at

cryogenic temperatures)

3. nickel-base superalloys (high-modulus fee alloys)

4. titanium-base alloys (intermediate-modulus hep or hep + bcc alloys)

5. aluminum-base alloys (low-modulus fee alloys)

Data for pure metals and for austenitic steel or nickel-base alloy welds

produced using various processes and filler metals are also briefly

considered.

The majority of the data were measured at NBS, using compliance methods

and compact or bend specimens with constant amplitude loading, typically at a

106
stress ratio of R = 0.1 and at frequencies of 20 ± 10 Hz. Additional relevant

data from other sources are included for comparison and confirmation, but an

exhaustive search was not attempted. Three temperatures and media are

emphasized: 296 ± 2 K ( room-temperature air), 76 or 77 K (liquid nitrogen),

and 4 or 4.2 K (liquid helium). At these temperatures, substantial tensile,

fracture, and elastic property data are available for correl ations . The Kj

c values referred to in the text are direct measurements or estimates from

J-integral tests. The E moduli are taken from original publications,

handbooks, or review papers [45-47]. For further details of metallurgical

characterization and test procedures, it is necessary to refer to the original

publications [16-44].

RESULTS

General data trends for alloy systems of major engineering significance

are represented in Fig. 1. Each alloy system shows greater property

variations at cryogenic than at room temperature. Three alloy systems were

considered: 1) ferritic steels containing up to 18% Ni (bcc structures),

2) austenitic stainless steels (fee, both stable and metastable alloys), and

3) austenitic nickel-base alloys (stable fee structure). The pivot points for

these data are discussed later in the text. The general behavior is

summarized here as follows:

At 295 K, the materials are ductile and tough, and fatigue crack growth

is produced by reversed plastic flow in the crack tip zones. The fatigue

exponents, n, typically range from 2 to 4. Striation formations, resolvable

by scanning electron microscopy at higher aK, are the principal failure

mechani sms

At 76 or 4 K, behavior is more diverse. Systematic compositional effects

emerge, such as the effect of nickel content in the ferritic steels at low

107
temperature. In many cases, the ductile striation mechanisms at 295 K are

replaced by brittle mechanisms at 76 or 4 K, and the fatigue exponents are

inflated to values greater than 4. Transgranul ar or i ntergranul ar fatigue

facets may be observed, even in some austenitic stainless steels. Extensive

martensitic phase transformations also occur in the metastable austenitic

stainless steels and may affect behavior at cryogenic temperatures.

Correlation of n with Yield Strength or Fracture Toughness

Figure 2 illustrates relationships between the fatigue exponents and the

conventional material properties for alloys having nearly equivalent values of

E. As shown, n tends to increase at high or at low Kj

c

. (In general, a

is inversely related to Kj

c

.) The sizable scatter here is due to the fact

that data for different steels and nickel-base alloys have been combined

with data for welds. The n-vs.-Kj

c plots for individual alloy families. Figs.

3 and 4, show more uniform trends. In these figures, two regions of behavior

can be clearly identified as follows:

1. Region I (the low-toughness region): The fatigue behavior depends on

K t , n increasing as K T decreases.

Ic 3 Ic

2. Region II (the high-toughness region): The fatigue behavior is

independent of K^, and n remains constant in the range 2 to 4.

This two-stage behavior appears to be a basic feature for all metals.

The point of transition from toughness-dependent to toughness-independent

behavior is material dependent and not yet predictable. We suggest that the

transition point hinges on the type of failure mechanisms operating, and that

these can be gaged approximately by the magnitude of Kj

c

. In region I,

brittle fatigue and fracture mechanisms are observed, whereas in region II,

ductile mechanisms are observed. The significance of the failure mechanisms

in affecting this two-stage behavior is taken up later in the discussion.

108
A correlation between n and Kj (region I) has significant implications.

Like o , K

Ic is dependent on metallurgical and mi crostructural variables and

temperature. Since regions of Kj

c -dependent and K^-i ndependent behavior

exist, a more general conclusion follows, namely that the fatigue crack growth

data of materials in general must exhibit two regimes of behavior: one is

sensitive to metallurgical variables and temperature, the other is not. The

following sections demonstrate some ramifications of this idea for lowtemperature fatigue.

Correlation of n and Temperature

In region I where n is inversely related to Kj

c

, a dependence of n on

test temperature is expected since temperature influences Kj

c

. This is shown

in Figs. 5 and 6 where n and Kj are plotted vs. temperature for 9% Ni

ferritic steel and a high-strength Fe-18Cr-3Ni-13Mn-0.37N austenitic steel.

In both cases, n eventually becomes inversely related to and increases to

values greater than 4 at extreme cryogenic temperatures, where Kj

c is reduced

sufficiently to reach region I.

As noted previously, there is no similar effect for the conventional AISI

300 series austenitic stainless steels [15]. The explanation for this relates

to the link between n and Kj

c

, as described above. High-strength alloys such

as ferritic steels, are subject to ductile-brittle transitions (DBT). AISI

300 series stainless steels, owing to their fee structure and relatively low

strength, do not exhibit DBT transitions, even at extreme cryogenic

temperatures. Thus, ferritic steels at cryogenic temperatures shift from

region II to region I behavior, whereas AISI 300 series steels always maintain

region II behavior.

Correlation of n and Composition

Nickel additions to ferritic steels will lower the DBT temperature while

increasing the Kj

c at sub-transition temperatures . Therefore, composition

109
becomes a crucial influence on the behavior of ferritic steels at low

temperatures . In Fig. 7, n for ferritic steels is plotted as a function of

nickel content at two temperatures, one ambient and one cryogenic. At 76 K, n

decreases as nickel increases from 0 to 5%, but at higher nickel contents n

remains at relatively low values, independent of composition. Again, this

relates to the interaction of n with Kj

c

; this time the behavior depends on

whether the composition establishes conditions corresponding to region I or

region II behavior. The Fe-Ni binary alloys behave similarly [48].

Correlation of log C and n

The purpose of this section is to apply Eqs. (2) and (3) to cryogenic

data. Accordingly, log C-vs.-n plots for various structural alloys are shown

in Figs. 8 and 9. The data demonstrate the C and n dependence expected from

Eq. (3), and this makes it possible to seek correlations with one parameter

(n) only.

Data for pure iron [16], titanium [39], and aluminum [40,41] are also

plotted on the appropriate graphs in Figs. 8 and 9. In comparison, data for

pure metals often do not fit the trends developed for their respective alloys.

For unalloyed iron and aluminum, the temperature reduction from 295 to 76 K

produces contrary effects: in the case of iron, log C decreases while n

decreases, whereas for aluminum, log C decreases while n is constant. In

contrast, however, Eq. (3) indicates that log C should decrease as n

i ncreases

Least-squares regression analyses for the log C-vs.-n plots, excluding

the nonconforming data for pure metals, are summarized in Table 1. Fairly

good fits are obtained, some of which may be improved by distinguishing

temperature effects or differences in failure mechanisms. As listed in Table

1, the correlation coefficients range from 0.92 to 0.99 (1.0 implies a perfect

110
correlation). Characteristics of the alloys' distinctive fatigue behavior

are:

Ferritic Steels : The spread of n increases at 4 K, reaching values up to

8. A single log C-vs.-n regression apparently fits the majority of data from

295 to 4 K. The scatter increases, however, when cryogenic data are admitted

to the correlation, and it is appropriate to exclude data for extraordi nari ly

brittle steels from the correlation [14].

AISI 300 Austenitic Stainless Series : The log C-vs.-n plot appears to be

temperature independent from 295 to 4 K, and n does not increase significantly

at 4 K, in contrast to the behavior of ferritic steels.

Other Austenitic Stainless Steels : In this group are the Fe-Cr-Mn,

Fe-Ni-Cr, and Fe-Cr-Ni-Mn-N steels that were not included in the AISI 300

series. Owing to exceptional strength in some grades, a behavior similar to

ferritic steels is observed at 4 K: high n values (up to 8) are obtained and

the scatter in log C-vs.-n plot increases.

Nickel Alloys : The available data are for superalloys having E moduli

only slightly higher than steels. For these alloys the correlations slightly

improve if temperature effects are separated; the log C-vs.-n plots then give

a slightly lower pivot point value at 76 and 4 K than at 295 K.

Titanium Alloys : The data are limited to measurements for the

T i - 5A1 - 2 . 5Sn and Ti-6A1-4V alloys for which the log C-vs.-n plot shows a high

correlation with absolutely no temperature dependence.

A1 umi num A1 1 oys : Again, cryogenic data are limited, but the correlation

coefficients for log C vs. n improve significantly if temperature effects are

distinguished. The pivot point and log C-vs.-n trend at 76 and 4 K is clearly

lower than at 295 K. This is similar to the effect observed in the nickel

alloys, but stronger. The 295- K data derive largely from tests of a 3003-0

111
alloy in various environments, but there is no discernable environmental

effect on log C vs. n.

Pivot Points

The pivot points corresponding to each of the alloy families discussed

above are listed in Table 2. Approximate agreement among different alloy

systems is found after normalization. Two normalizing parameters were

considered: aK

q /E and aK /(E/b) [13], where b is the equivalent of the

Burgers vector and is taken from Cullity's list [49] of the distances of

closest atomic approach for unalloyed metals. The correlations based on aK

q /E

and on AK

Q

/(E/b) are equally effective.

DISCUSSION

Log C-vs.-n Correlations

In principle, Eq. (2) predicts that all da/dN curves must intersect at a

single point (A,aK ) and fan out as a function of n [14]. In fact, there are

numerous materials with da/dN-vs.-AK trends that fail to intersect at the

calculated "pivot points." In practice, therefore, Eq. (2) serves to

approximate the entire data base, which includes nonconforming material

behaviors. Under these circumstances, the calculated pivot points for various

material classes are a measure of the center of gravity for the data in a

statistical sense.

One limitation of representing fatigue crack growth results in terms of

log C-vs.-n plots and pivot points is that the AK ranges for the associated

da/dN are not conveyed. Therefore, interpretations concerning individual

alloy behavior must be guarded in view of the unspecified information and the

approximate nature of such data representations.

Although the log C-vs.-n correlations are approximate, their usefulness

for certain purposes cannot be denied. In this paper, the format suggested by

112
Eq. (3) provided a concise basis for data presentation, summary, and

comparison. The trends of Figs. 8 and 9 help to distinguish the exceptional

behavior of pure metals. Similarly, some errors in the published C and n data

for structural alloys were identified, since they disagreed with the general

data trends. Finally, the pivot point normalizations conclusively demonstrate

the strong effect of Young's modulus on da/dN.

Significance of Young's Modulus

Fatigue is the result of plastic deformation processes, but under the

assumption of small-scale yielding, the plastic deformation is limited and

localized at the crack tip so it is possible to correlate da/dN with elastic

parameters: for midrange behavior, da/dN is directly proportional to AK (an

elastic stress-intensi ty factor) and 1/E (reciprocal of the elastic modulus).

As a fundamental physical property relating to atomic binding forces, Young's

modulus figures prominently in dislocation theory as well as continuum

mechanics. A dependence of da/dN on 1/E is explicit in some analytical models

of fatigue crack growth [3], The significance of the modulus in fatigue crack

growth is likewise evident from experimental correlations. The normalizing

parameter, AK/E, was first proposed by Anderson [2] and later used to

correlate striation spacings [50], pivot points [13], and macroscopic fatigue

crack growth rates [4]. The data demonstrate that a strong influence of

Young's modulus persists in both region I and region II.

From a materials viewpoint, E is fixed mainly by the primary alloy

elements and is only weakly dependent on secondary alloy elements,

microstructure, and related variables, including cold work, heat treatment, or

phase transformations [45]. Therefore, alloys of a given base metal system

are closely grouped with respect to elastic properties. It follows that if

da/dN is strongly influenced by E and weakly dependent on the conventional

113
mechanical properties as postulated for region II, then a structureinsensitive behavior is expected since E itself is structure insensitive.

Typically, Young's moduli for metals at low temperature show "regular"

behavior [45]: a nearly linear increase below 295 K, a plateau near 76 K, and

little or no change between 76 K and absolute zero. For the alloys of this

survey, the overall increase of E between 295 and 4 K never exceeds 11

percent. Such small changes are consistent with a temperature-insensitive

behavior in region II.

Maraging steels seem to provide an excellent example of the structure and

temperature-insensitive behavior just described. Data for 18% Ni maraging

steel at 295 K show no change in da/dN for the aged and unaged conditions [51],

while for the unaged condition there is no difference in da/dN at 295 and 76

K [22]. In contrast, strong effects on o and 1C are induced by aging or y c test-temperature reduction. The observations are plausible, assuming that we

are dealing with region II behavior, and realizing that the aging step and

test-temperature reduction to 76 K will increase E by only 9 and 5%, respectively.

Additional evidence for the role of Young's modulus derives from Fig. 1.

If the 295- K data presented there are superimposed, the bands for the three

material classes nearly overlap, despite significant differences in

composition ( i ron-vs . -nickel base) and crystal structure (bcc vs. fee, stable

or metastable). This explanation is offered: these alloys have nearly

equivalent moduli, and at 295 K all undergo fatigue by relatively ductile

mechanisms involving reversed plastic flow in region II where rather wide

variations of a and 1C are of minor consequence to fatigue crack growth,

y c Temperature Dependence

Some alloys show improved fatigue resistance at cryogenic temperatures,

whereas others are degraded.

114
An improved performance cannot be attributed to favorable temperature

effects on E, since any increase between 300 and 4 K is too small to account

for measurable improvements in fatigue crack growth rates. Instead, we assume

that significant temperature effects on the fatigue resistance at cryogenic

temperatures are induced when the plastic work for fatigue crack propagation

is altered. This may occur in conjunction with failure mode transitions, the

effects combining competitively or synergi stical ly to account for the

diversity of behaviors observed at 76 or 4 K compared with those at 295 K.

Plastic Work

Fine and Davidson [52] reviewed the measurements of plastic work.

Although few data are available at present, it is clear that temperature

reductions can improve the fatigue crack growth resistance of some metals at

cryogenic temperatures by increasing the plastic work for fatigue failure.

For example, pure aluminum exhibits a 100-fold decrease of rates as

temperature drops from 295 to 77 K, and the associated increase of energy

required for unit fatigue crack extension at 77 K has been measured [41]. For

an identical temperature reduction, the rates for the solid-solution alloy

5083-0 decrease 3 or 4 times [42]. Thus, a similar but less powerful effect

may operate in alloys. This may explain the improved fatigue crack growth

resistance of the aluminum-base, nickel-base, and stable iron-base alloy

families at cryogenic temperatures [25], but confirmation is needed.

Failure Micromechanisms

Temperature-induced transitions in microfailure mechanisms may introduce

either beneficial or detrimental effects, since the amount of plastic work

required for fatigue crack extension may then be increased or decreased.

Transitions from ductile to brittle mechanisms cause the shift from region II

115
to region I behavior as described in the text. In Fe-18Cr-3Ni -13Mn-0. 37N

steel, for example, the incidence of brittle mechanisms at 4 K drastically

increased n (Fig. 5), eclipsing any favorable trend that may have been

expected from a temperature effect on plastic work without a transition in

failure mode.

The explanation offered for high n in low-toughness alloys is that

brittle-failure mechanisms associated with monotonic loading begin to operate

concurrently with the cyclic mechanisms of crack growth [53-55]. This was

proposed in a study of ferritic steels at room temperature where the brittle

mechanism was intergranular fracture [54]. Another brittle mechanism

common in ferritic steels at low temperature is transgranul ar cleavage. Both

mechanisms generate brittle facets and both are sensitive to the maximum

applied K level because they are subject to a critical tensile-stress failure

cri teri on

Inflated fatigue exponents and degraded fracture toughness are common at

cryogenic temperatures owing to the increased probability of brittle-failure

mechanisms relative to room temperature. In fact, this phenomenon is

virtually universal at extreme cryogenic temperatures, having now been

observed in some austenitic steels, as well as ferritic steels, and

nickel-base, magnesium-base, and titanium-base alloys [56-58]. Our 4 K data

for austenitic stainless steels indicate that the high-strength Fe-Cr-Ni -Mn-N

steels are susceptible, whereas the relatively low strength Fe-Cr-Ni (AISI 300

series) steels are not.

The occurrence of high exponents associated with toughness degradation in

austenitic stainless steels at 4 K may seem surprising since these materials

are generally reputed to be ductile and tough at all temperatures . The

newly developed Fe-Cr-Ni-Mn-N steels, however, contain up to 0.4 percent

116
nitrogen, high enough to elevate a and reduce K

y sufficiently to attain

region I behavior.

The brittle mechanisms associated with high exponents in cryogenic

structural alloys may include transgranul ar crystallographic faceting,

slip-band decohesion, twin-boundary parting, and intergranul ar fracture. Some

representati ve fractographs are shown in Figs. 10 and 11. The brittle

mechanisms at 4 K are quite distinct from the striation mechanisms operating

at 295 K (Fig. 10). For example, a pronounced transgranul ar faceting occurs

in annealed Fe-18Cr-3Ni-13Mn-0.37N austen'itic stainless steel at 4 K (Fig.

1 1 A ) . Intergranul ar failure in this steel at 4 K is also induced after

sensitization treatments, owing to the embrittling effects of chromium

carbonitride precipitation along the grain boundaries (Figs. 11B, 11C).

In contrast to the adverse effects of transitions to brittle-failure

mechanisms described above, favorable transitions in fatigue failure

mechanisms are also possible, although less commonly encountered. An

outstanding example of a favorable transition occurs in metastable AISI 304L

stainless steel. In this steel, the usual transgranul ar crystal! ographic

mechanism at 295 K (Fig. 12) is replaced at 76 K by a unique transgranul ar

mechanism involving very fine, nondistinct features producing a very smooth

macroscopic failure surface (Fig. 13). This transition is associated with

extensive martensitic phase transformations, and a significant reduction of

da/dN occur between 295 and 76 K [28]. The austenitic instability may be

directly responsible for the improved fatigue resistance, for a variety of

reasons, as discussed by Schuster and Altstetter [59].

117
SUMMARY AND CONCLUSIONS

The midrange fatigue crack growth rate data for a variety of structural

alloys at room and cryogenic temperatures are selectively reviewed. The data

presentation follows a format suggested by the Ki tagawa-Mi sumi equation, where

log C is plotted versus n. Pivot points are calculated for cryogenic alloys,

regions of structure-sensi ti ve and structure-insensitive behavior are

identified, and the significance of some factors influencing the temperature

dependence of fatigue crack growth are briefly discussed.

The variability in da/dN is greater at 76 and 4 K than at 295 K. On the

basis of pivot point calculations, Young's modulus exerts a dominant effect in

that aK

q /E approximately normalizes the data for different alloy families.

Within each family the behavior is strongly influenced by failure mechanisms.

Plastic work and cyclic stress-strain properties are highly relevant to the

determination of fatigue property correlations, but such data are not

generally available for cryogenic alloys. In the absence of such data,

correlations were sought using conventional mechanical properties. Those

correlations indicate that two regions of behavior can be identified for

structural alloys:

1 .

2 .

In region I, da/dN is temperature and mi crostructure sensitive: E,

a , and K T influence the results,

y ic

In region II, da/dN is temperature and mi crostructure insensitive: E influences the results, whereas a and K T are irrelevant.

y Ic

118
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38. McHenry, H. I. and Schramm, R. E., Adv. Cryoq. Eng., Vol. 24, 1978,

pp. 161-165.

39. Thompson, A. W., Frandsen, J. D., and Williams, J. C., Met. Sci . , Vol. 9,

1975, pp. 46-48.

40. Ogura, T., Karashima, S., and Tsurukame, K. , Trans. Jap. Inst. Met., Vol.

16, 1975, pp. 43-48.

41. Liaw, P. K. , Fine, M. E., Kiritani, M. , and Ono, S., Scripta Metal 1.,

Vol. 11, 1977, pp. 1151-1155.

42. Tobler, R. L. and Reed, R. P., J. Eng. Mater. Technol., Vol. 100, 1977,

pp. 306-312.

43. McHenry, H. I., Naranjo, S. E., Read, D. T., and Reed, R. P., Adv. Cryog.

Eng . , Vol. 24, 1978, pp. 519-527.

44. Roberts, R., Wnek, K. , and Taf uri , J. C., Adv. Cryog. Eng. Vol. 24, 1978,

pp. 187-196.

45. Ledbetter, H. M., Elastic Properties, in: Materials at Low Temperatures , R. P. Reed and A. F. Clark, Eds ., American Society for Metals, Metals

Park, Ohio, 1983, pp. 1-45.

46. Ledbetter, H. M., Cryogenics . , Vol. 22, 12, 1982, pp. 653-656.

47. Naimon, E. R., Weston, W. F., and Ledbetter, H. M., Cryogenics, Vol. 14,

1974, pp. 246-249.

48. Gerberich, W. W. and Moody, N. R., in: Fatigue Mechanisms , ASTM STP 675,

American Society for Testing and Materials, Philadelphia, 1979,

pp. 292-341.

49. Cullity, B. D., Elements of X-Ray Diffraction, Addi son-Wesl ey Inc.,

Reading, Massachusetts, 1956, pp. 482-484.

50. Bates, R. C. and Clark, W. G., Jr., Trans. Am. Soc. Met., Vol. 62, 1969,

p. 380.

121
51 . Bathias, C. and Pelloux, R. M., Metal 1. Trans., Vol . 4, 1973,

pp. 1265-1273.

52. Fine, M. E. and Davidson, D. L., in: Fatigue Mechanisms: Advances in

Quantitative Measurement of Physical Damage , ASTM STP 811, J. Lankford,

D. L. Davidson, W. L. Morris, and R. P. Wei, Eds., American Society for

Testing and Materials, Philadelphia, 1983, pp. 350-370.

53. Ri tchie, R. 0. and Knott

,

J

F. , Mater. Sci

Eng. , Vol

14, 1974,

54. Ri tchi e

,

R. 0. and Knott

,

J. F . , Acta Metal 1 ., Vol. 21, 1973, pp.

639-648.

55. Richards, C. E. and Lindley, T. C., Eng. Fract. Mech., Vol. 4, 1972,

pp. 951-978.

56. Katz, Y., Bussiba, A., and Matthias, H., "The Reflection of Warm

Pre-Stressi ng on the Low-Temperature Fatigue Crack Growth Curve,"

submitted for publication.

57. Ryder, J. T. and Witzell, W. E., Effect of Low Temperature on Fatigue and

Fracture Properties of T i - 5A1 -2 . 5Sn (ELI) For Use in Engine Components,

submitted for publication.

58. Verkin, B. I., Grinberg, N. I., and Serdyuk, V. A., Correlation of the

Parameters of Fatigue Crack Growth With the Depth of Plastic Zone and

Fracture Micromechanisms In Vacuum and at Low Temperatures, submitted for

pub! ication.

59. Schuster, G., and Altstetter, C., in: Fatigue Mechanisms: Advances in

Quantitative Measurement of Physical Damage , ASTM STP 811, J. Lankford,

D. L. Davidson, W. L. Morris, and R. P. Wei, Eds., American Society for

Testing and Materials, Philadelphia, 1983, pp. 445-463.

122
LIST OF TABLES

Table 1.

Table 2.

Pivot point calculations for structural alloy families.

Pivot point normalizations for structural alloy families.

123
Table

1.

Pivot

point

calculations

for

structural

alloy

families.

qj i u

>>u 1—

cn CO CO cn CO CO c C\J 1—

rH cn r-H CO cn i-H LO

II t i rH o o i—

o i—8 *3 o LO i—8 CO

cj* OJ oi—

"—

d 4-> o d

•1

QJ LO CXI CO cn cn cn cn o CO cn

+-> •1 CTl cn cn cn cn cn cn O’! cn cn cn cn

fD

u • • • • • • • • • • • • i

•t

o cd CD o o o CD o o o CD o QJ 4- 1 1 i 1 1 1 1 1 1 1 1 1 s- 4- d CD o O

CD o

cn OJ CO cn CO LO LO r-H r—

cn CO CXJ LO cn i—

OJ 00 co cn r>* T3 i-H o o r-H o CO LO o CD i-H cn LO * d • • • • • • • • • • • o ro o o o o o o CD o o o o CD

“Od < d o

fD •i

CO CXI CO o 00 to o LO cn cn

i-H +-> +-> to cn CO CO LO LO r—

CO i—8 to fD *3* cn LO <3- LO CXI i—8 CO OJ

cn “O > 1—

1 1 i—l «—

i—

i-H i—

i—8 i—8 i—

CD i-H

O

d OJ 1 1 1 i 1 1 i 1 1 | 1 1 _J fD Q

CO CO cn *3* OJ cn CO CD CO ,

CO CO LO cn cn ^3 i—8 i—8 LO co CO LO OJ OJ OJ i-H LO CO

TDd

d T3O o CO o o CD o o o o o o CD

fD s- •r— fD +-> < “O fD CT) CO cn LO *3 LO OJ LO to d •i

LO CO CO CO (X) LO o CO LO

cn fD > CO »—

cn o cn CO o OJ cn o 4-J OJ • • • • • • • • • • • • _J oo o ro cn1 i 1 CO1 1 CO1 OJ1 1 CO1 CO1 CO1

CO

+-> d

4- •r— o o CO o i—

cn CO 00 o CO cn CO LO

Q_ r—

LO cn C\J OJ CJ !—

i—8 i-H i-H o fO

4-> fO Q

CD >1 >5 d 1

1 13 *3" •3* >> d xt- >> d

+-> o 1

o

fD o o o o o d o o o d d s +-> +-> +-> +-> +-> o *3- +-> 4-> 4-> o

QJ CZ CL v ^ LO LO LO LO LO LO LO LO LO LO ** £ cn cn cn cn cn cn LO cn cn cn cn LO

CL) CXI CXI C\J C\J OJ OJ OJ OJ OJ OJ

hto

to 1— 8 I OJ OJ d to QJ

CO r- QJ CD to QJ QJ CD CD at i

S_ +-> -M QJ +-> to to L0 to

OJ CD to to 1— to QJ QJ QJ CD to fD fD fD fD

QJ to DJ

C

u to to to to TD -ID -Q -Q JD

cn -d> to fD *r- • 1— to fD fD fD CO i

1 1 1 1 ,— o to O to fD 4-> to JD _Q JD -O CD E £ E £

fD • r—

O QJ U) +-> •1— QJ 1 1 1 i s 3 3 3 • r— TD +-> i

CO r— =3 tO tO

d 1— 1— to i— to .— to i— • 1- to

d toC to

d

s- QJ •iOJ

dO r— QJ

d to QJ >> QJ >> QJ >, Q> >, c >> •r- >> •1

>> •r—

CL) -M S- i—i -i

•r

U O) 4-> •r- T3 DZO o DZO Jd

O ro

O £ O £ a E

-t-> 00 s_

u CO fD

d -r- CD to fD i

U r—U f—

U r—

O r— +-> r- =3 i

3 — 3

(O (U 0J •1

M -M rO +-> +-> =3 -M QJ • r— |

•1

— 1

•i

— |

•i

— c

•1— 1

i— i

i

— i

s: h- Ll_

d

C i/> > * 1- to <w i :z: fD z: ru zC id -Z. fO 1— ro

C ro c fD c

124

alloys
Table

2.

Pivot

point

normalizations

for

structural

alloy

families.

JD c 0 0 CD LO

O r~-~ r-H

O r-H CO CO

LxJ • • • • • . • • • • • cn 0 CO CD r-H co r-H r^ cn O to o r-H r-H r-H r—H r-H <

CO LO r^ LU VIJ co CO r-H cn cn LO 0 E LO 0 LO 1—

r-H to LO r—H

O •cj- • • • • • * • • • • • i r-H r-H r-H r-H r-H 0 O CXI r-H O < O r-H

r-H ' "

^r LO CD CO 0 CXI

O CXI o E • • • • • ccj • • • • • cn «—

r-H CD LO LO CO CO < 03 CXI CO CXI CXI 00 CM co LO r-H r-H

Cl. 21 1 " ^ 

CD i—U

>>u 1

1 cn CO CO CD 00 CO CO i-H <c E CXI 1—

1—

cn r—H • CD • E • • • • • . • • • r-H

r-H r-H 0 0 r-H 0 r-H CXI

O LO ior-H

<u tO cn Z3

fO i— 03 CXI cn CO 00 CD cn CD LO LO CXI s- =3 Q- O CD CD cn O 0 1—

0 r-H

(i) TD CD CXI t—

r-H r-H CXI CM CXI CXI r-H > O —

< SI

<u >>

S-3 «=1- >> c 4-> 0 1

fO 0 O 0 O

O c 0 O 0 c

i- +-> +-> 4-> 4-> 0 xl" +-> -*-> +-> 0

o; ^—

CL LO LO LO LD LO tn LO LO LO LO E •—

cn cn cn cn CD cn LO CD CD CD CD

a; CXI CXI CXI CM CXI CM CXI CXI CXI CXI h—

to

to .

1 | CD CD C to CD

to •r- CD CD to CD CD CD CD 1— +-> +-> CD +-> to to to

CD CD to to 1— to CD (U CD CD to 03 03 03

<u to 13C 0 to to to to TD JD JD JD

(/> +-> to 03 *r- * r— to 03 (O 03 03 1— 1 1 1 i

u to O to ra +-> to _Q .a _Q _Q CD E E E_ ro "O •r— O CD to 4-> i

CD 1 1 1 1 £ 13 13 ZD

•r- CD H-> 1— CO r— ZD CO to

C 1— 1— to 1— to 1— to •1- toC toC 4-> •1— <D c 0 1— (D c to CD >•> a> >> CD >> CD >> C >> •r- O) LO S- H *1— •r- U CD +-> •r- -0 -x: 0 0 O -XC 0 03 O E O E +-> CD CJ Ul 03 -r- CD to ro I

O r— O r— U r— O r— +-> »— ZD ,

0

<o 1— CD • 1— *-H 4-> 03 4-> +-> 13 +-> O) •1

— 1— 1— ,

•1— r— •r— r— • 1—

r

1— ,1—

z; U. c <C to > -r- to < CO 5 2: 03 (O 21 03 ZI 03 1— 03 <C 03 <

125

Aluminum-base

76, 4

only

79

3.5

16.5

0.209

alloys
LIST OF FIGURES

Fatigue crack growth rate data trends for alloys at room and

cryogenic temperatures.

Figure 1. Fatigue crack growth rate data trends for alloys at room and

cryogenic temperatures.

Figure 2. Correlation of fatigue exponent n with the conventional yield

strength and fracture toughness.

Figure 3. Correlation of n and K T : various ferritic nickel steels.

lc

Figure 4. Correlation of n and Kj : various nitrogen-strengthened

Fe-Cr-Ni-Mn austenitic^tainless steels.

Figure 5. Effect of temperature on n and K^: 9 % Ni ferritic steel.

Figure 6. Effect of temperature on n and : nitrogen-strengthened

Fe-Cr-Ni-Mn austenitic stainless^teel

Figure 7. Effect of nickel content on fatigue exponent of ferritic steels

at 295 and 76 K.

Figure 8. Log C-vs.-n relationship for various steels (o 295 K, a 76 K,

4 K)

Figure 9. Log C-vs.-n relationship for three alloy systems having

different elastic moduli and comparison of several systems

(o 295 K, a 76 K, 4 K).

Figure 10. Fatigue failure mechanism in Fe-18Cr-3Ni-13Mn-0. 37N austenitic

stainless steel at 295 K.

Figure 11. Fatigue failure mechanisms in Fe-18Cr-3Ni-13Mn-0. 37N

austenitic stainless steel at 4 K.

Figure 12. Fatigue failure mechanism in AISI 304 L stainless steel at 295 K

Figure 13. Fatigue failure mechanism in AISI 304 L stainless steel at 4 K.

126
9|OAo/UJIU ‘NP/^P IJ1M0J9 >JOBJQ 0n6{lBJ

127

cryogenic

temperatures.
Fatigue

Crack

Growth

Exponent,

6

c 4

2

8

6

4

2

Figure 2.

o Ferritic Steel

A AISI 300 Series

V Austenitic Fe-Base

Austenitic Ni-Base

• Austenitic Welds

4 a A

rv&F o * A

o

A

\n 1=3

%

VZ VO

U

ad

V V

AO V

A A

| V V

icF

A

400 800 1200

Yield Strength, oy, MPa

1600

Fracture Toughness, K|c MPa-m 1/*

Correlation of fatigue exponent n with the conventional yield

strength and fracture toughness.

128
c

c

0

c

o

Q_

X

UJ

JZ

£

o

O

o

03

O

0

=3

O)

•+—1 0

LL

Figure 3. Correlation of n and Kj^: various ferritic nickel steels.

129
U ‘}U9U0dX3 L|}.MOJQ >)OBJQ 9n6nej

130

Figure

4.

Correlation

of

n

and K

T

:

various

nitrogen-strengthened
c

c

CD

c

o

Q_

X

LU

sz

£

o

0

o

26

<D

=3

D)

-*—

ctf LL

Figure 5. Effect of temperature on n and Kj

c

: 9% Ni ferritic steel.

131

Fracture

Toughness,

K|

Ci

MPam

1

/*
132

Fracture

Toughness,

K|

C

MPa-m

1

/*
Nickel Content, wt. %

Figure 7. Effect of nickel content on fatigue exponent of ferritic steels

at 295 and 76 K.

133
Logarithm

of

Fatigue

Crack

Growth

Coefficient,

log

C

Fatigue Crack Growth Exponent, n

Figure 8. Log C-vs.-n relationship for various steels (o 295 K, a 76

4 K).

134
Logarithm

of

Fatigue

Crack

Growth

Coefficient,

log

C

Fatigue Crack Growth Exponent, n

Figure 9. Log C-vs.-n relationship for three alloy systems having

different elastic moduli and comparison of several systems

(o 295 K, A 76 K, 4 K).

135
B

> , . i 30 /xm

Figure 10. Fatigue failure mechanism in Fe-18Cr-3Ni-13Mn-0.37N austenitic

stainless steel at 295 K.

136
Figure 11. Fatigue failure mechanisms in Fe-18Cr-3Ni -13Mn-0. 37N

austenitic stainless steel at 4 K.

137
L 1 250 fim

i 1 50 /xm

Figure 12. Fatigue failure mechanism in AISI 304 L stainless steel at 295 K.

138
A

I I 250 fJLtr\

B

i 50

j

Figure 13. Fatigue failure mechanism in AISI 304 L stainless steel at 4 K.

139
%
AN AUTOMATED FATIGUE CRACK GROWTH RATE TEST SYSTEM*+

Yi-Wen Cheng

David T. Read

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

An automated fatigue crack growth rate (FCGR) test system has been

developed that can be used for tests of constant-load-amplitude FCGR above

10~° m/cycle (ASTM E647-83) at normal (~10 Hz) or low (~0.1Hz) cyclic frequencies and for tests of near-threshol d and variable-load-amplitude FCGR.

The test system consists of a minicomputer, a programmable arbitrary waveform

generator, a servohydraul ic test frame, and a programmable digital oscilloscope. The crack length is measured using the compliance technique; the FCGR

and the stress intensity range are calculated and plotted automatically during

the test.

Key Words: automated test system; compliance technique; fatigue crack growth

rate; fatigue of materials; near-threshol d fatigue test; variable-load-amplitude

fatigue test.

Contribution of NBS; not subject to copyright.

Submitted for inclusion in the Proceedings of Symposium on Automated Test

Methods for Fracture and Fatigue Crack Growth, November 7-8, 1983, Pittsburgh,

Pennsylvania.

141

INTRODUCTION

Fatigue crack growth rate (FCGR) data can be used for material characterization and for fracture mechanics reliability analysis of structures subjected

-8

to cyclic loading. A standard test method for measuring FCGR above 10

m/cycle under constant amplitude loading has been developed and published in

the 1983 Annual Book of ASTM Standards under the designation ASTM E647-83.*

2 3

With the increased interest in the near-threshold FCGR ’ and FCGR under

4

environmental influence at low cyclic frequencies, more FCGR measurements are

being made, and they can be tedious and time-consuming. An automated FCGR

test system, such as that described in this paper, allows testing to proceed,

data to be taken, and load range to be altered in the absence of an operator.

There are four advantages of using an automated test system to measure

5 FCGR. First, it minimizes the testing time and operator attention. Second,

it reduces the data scatter. Third, because the testing is interactive and

automatic in nature, its procedure is relatively easy to follow and it requires

minimal operator training. Fourth, it eliminates subjective interpretation

and influence of the experimenter.

THE FCGR TEST METHOD

The sequence of the FCGR test is: first, obtain the raw data, namely,

fatigue crack length, a, versus elapsed fatigue cycles, N; then, reduce a and

N data to a plot of da/dN versus AK, where da/dN is the FCGR in mm/cycle and

AK is the crack-tip stress-intensity range in MPa*m

1//2

. Typical outputs are

presented in Figure 1.

The number of elapsed fatigue cycles can be obtained from counters

(electronic or mechanical) or conversion from time elapsed at the given

frequency. The methods of crack length measurement are complicated and have

7 been a subject of extensive study. * Although several methods of crack

143
length measurement have been developed, some require specialized equipment not

commonly available in mechanical testing laboratories. The compliance technique,

however, requires only monitoring of the load cell and the clip gage outputs,

which is routinely achieved in mechanical testing. Compliance is defined as

the specimen deflection per unit load, which is a function of crack length.

The load and deflection signals (voltages) can be interfaced to a computer.

Because of the simple instrumentation and the need in our laboratory for

environmental chambers for cryogenic temperature and saltwater corrosion-f atigue

tests, the compliance technique was chosen to measure the crack length.

EQUIPMENT OF THE AUTOMATED FCGR TEST SYSTEM

A schematic of the automated FCGR test system is shown in Figure 2.

Figure 2 also shows the sequence of operation and interaction between various

components. The test system consists of a closed-loop servo-controlled

hydraulic mechanical testing machine, a programmable digital oscilloscope, a

programmable arbitrary waveform generator, and a minicomputer.

The machine control unit, which is included in the hydraulic mechanical

test machine, includes a servo-control system, a feedback system, two dc

conditioners, and a valve drive. A nonprogrammable function generator with an

electronic pulse counter is usually built into the machine control unit of a

commercially available mechanical testing machine. Signal amplifiers and a

load cell are also included in the mechanical testing machine.

The programmable digital oscilloscope contains two 15-bit 100-kHz digitizers

and it serves as an analog-to-digital (A/D) converter. In addition to its

high speed A/D conversion rate, this oscilloscope features the ability to

instantaneously freeze and hold data in memory. The problems encountered with

5 slower A/D converters, such as interruptions during the test and low test

g frequencies are eliminated because of the high A/D conversion rate and the

144
f reeze-and-hol d ability of this oscilloscope. For the near-threshol d and the

variable-load-amplitude FCGR tests, load levels vary with time and a programmable function generator is needed. For these tests, the programmable arbitrary

waveform generator is used. The present programmable waveform generator is

not connected to any cycle-counting device and the fatigue cycle counts are

inferred from the cyclic frequency and the time elapsed, as given by the

computer. For the constant-load-amplitude FCGR test, the built-in function

generator is used.

Included in the minicomputer are a cathode-ray-tube (CRT) terminal, a

line printer, a dual floppy disk storage unit, and a digital plotter. The

minicomputer uses the 16-bit word and has 128K words of memory. The minicomputer

also contains an internal clock that reads to 1/60 s. The I EEE-488/GPIB is

used for the interface between the computer and the programmable digital

oscilloscope and between the computer and the programmable arbitrary waveform

generator.

APPLICATIONS

In the following discussion, attention is focused on how the test system

described above is used to conduct the FCGR tests. Requirements on grips,

fixtures, specimen design, and specimen preparation are detailed in various

14 9 standards ’ * and are not discussed in this paper.

Constant-Load-Amplitude FCGR Test

The test system described in the previous section can be programmed to

run the constant-load-amplitude FCGR test. The operational details, implementing

the procedures set forth by ASTM E647-83,^ are described in this section.

As shown in Figure 3, the input parameters are fed into the computer

through the CRT terminal using an interactive operation between the operator

and the computer. The input parameters include specimen identification,

145
specimen dimensions, Young's modulus, selected time interval for measuring

crack length, minimum load level for compliance measurement, load levels, and

test frequency. The time interval for measuring crack length must be kept to

a value small enough that every increment of crack growth will not exceed the

recommended value as prescribed in the standards.'*' The minimum load level for

compliance measurement is used to eliminate the possible crack closure

effects,^ which have a significant effect on the accuracy of crack length

measurement.

The precracked specimen is fatigue cycled under the prescribed loading

conditions and cyclic frequency. The typical frequency is 10 Hz. When the

preselected time interval for crack length measurement is reached, the computer

requests the 1 oad-versus-def lection data from the programmable digital ^oscilloscope, which freezes the load-deflection data in the memory instantaneously,

and correlates the data to a straight line using a linear least-squares fit.

The portion of the load-versus-deflection curve used for compliance calculation

is from the specified minimum load level to a value corresponding to 95

percent of the maximum load. The reason for excluding the upper 5 percent of

the load for calculation is that the clip gage tends to vibrate, and noise in

the clip-gage signal increases at the maximum load during the high-frequency

test. A linear correlation coefficient of 0.999 or better is usually obtained.

From the resulting compliance, the instantaneous crack length is computed

using the appropriate expression for the compliance calibration of the

specimen. ^ The precision of the crack length measurement is typically within

0.04 mm.

The increment of crack growth (the difference between the current measured

crack length and the last recorded crack length) is checked against the

recommended values.'* If the increment of crack growth is larger than the

minimum recommended values, the computer calculates N, £K, and da/dN; the

146
digital plotter plots the data points (a,N) and (da/dN,AK) on the a-versus-N

and on the da/dN-versus-AK graphs, such as shown in Figure 1; the line printer

prints the value of calculated compliance, the linear least-squares correlation

coefficient, a, N, da/dN, and AK results. All the resulting data are stored

on the floppy disk for the post-test analyses.

During the test, the point-to-point data reduction technique is used to

calculate AK and da/dN from a and N. Usually the results are consistent with

minimum scatter, as those shown in Figure 1. If the results of AK versus

da/dN scatter, the seven-point incremental polynomial method is used to smooth

the results after the test is completed.

The computer programs for post-test analyses include the following

capabilities:

1. Reducing a-versus-N data to AK-versus-da/dN by the seven-point

incremental polynomial method;

2. Converting units;

3. Plotting data in desired units;

4. Plotting data in desired coordinate ranges;

5. Plotting data of several different specimens on one graph (for

compari son)

1 ; 6. Calculating the materials constants C and n in the Paris equation,

da/dN=C( AK)

n

, and drawing the regression line through the data.

The computer programs, including the data acquisition routines, were

written in the PDP-11 Fortran language.

Near-Threshold FCGR Test

The computer programs used in the constant-load-amplitude FCGR test, with

some modifications, can be used for near-threshold FCGR tests. The major

difference in procedures between the two tests is that the load levels in the

near-threshold FCGR test decrease according to the initial AK value (in the

147
K-decreasing test technique). The load levels are calculated from the following

9 equations

AK

AP

AP

P

AK

q exp[C‘ (a - a Q

)]

, 1/2

max where Pmax

= BW AK/f ( a/W ) for compact-type specimen

= BAK/f ( a/ W ) for center-cracked-tensi on specimen

= Ap/(1 - R); P . = P R r min max

= maximum load

( 1 )

( 2 )

(3)

(4)

P . = minimum load

mi n

P . /P min 7 max

= specimen thickness

= specimen width

= the current crack length

= the crack length at the beginning of the test

f ( a/W ) = function of (a/W) dependent upon specimen geometry

AK = current crack-tip stress-intensity range

AK

q

= crack-tip stress-intensity range at the beginning of the test

C' = negative constant

The flow chart of the automated near-threshold FCGR test is summarized in

Figure 4. After each crack length measurement, the crack length is compared

with the last measured crack length to ensure that the minimum increment of

crack growth has occurred. If this is not done, then some unnecessary load

level adjustments will take place because of scatter in the crack length

measurement. AFter the crack length has increased a certain amount (for

example, 0.13 mm), the new AK is calculated according to equation (1). The

load levels are then adjusted using equations (2), (3), and (4).

In high-frequency fatigue testing, which is desirable in the near-threshold

FCGR test, hydraulic lag is a problem. This results in the specimen not being

148
actually subjected to the load range commanded by the computer (or waveform

generator). This problem is overcome by overprogrammi ng the load range

command using the trial -and-error method. During the overprogrammi ng process,

the computer monitors the values of P mQx

and P . through the programmable

digital oscilloscope and makes necessary changes to achieve the desired values

of P and P . . The overprogramming is done whenever there is a change in max min ran a

load range.

If the measured crack-growth increment, which is the difference between

the current measured crack length and the last recorded crack length, is

g larger than the minimum recommended values, the values of N, £K, and da/dN

are calculated and the results are printed, plotted, and stored. The previously

mentioned computer programs for post-test analyses are also applicable for

analyzing the data obtained in the near-threshol d FCGR test.

Variable-Load-Amplitude FCGR Test

The automated FCGR test system is also used in the variable-load-amplitude

FCGR test. The procedures used in this application are similar to those

described in the previous two sections.

The computer reads the prerecorded load-time history from the floppy

disks and controls the hydraulic machine through the programmable waveform

generator. At a preselected time interval, the crack length is measured. The

desired output in the variable-load-amplitude FCGR test is time versus crack

length. The results are printed, plotted, and stored for post-test analyses.

The present system has several limitations in the application of variableload-amplitude FCGR testing. The major one is that the waveform generator

needs about 0.1 s for changing one command to another, and this limits the

average frequency to about 1 Hz.

149
SUMMARY

An automated FCGR test system has been developed that can be used for

tests of constant-load-amplitude FCGR above 10"^ m/ cycle (ASTM E647-83),

near-threshold FCGR, and variable-load-amplitude FCGR. The test system offers

considerable time savings in data acquisition and in data reduction. The test

procedure is relatively easy to follow and enables technicians to produce data

with less scatter (with respect to the non-computer-aided technique), because

no manual data interpretation or data fitting is done.

ACKNOWLEDGMENTS

Mr. J. C. Moulder of NBS is acknowledged for helpful discussions on the

interface between the computer and the instruments. The work is supported by

the Department of Interior, Minerals Management Service, and the Department of

Energy, Office of Fusion Energy.

REFERENCES

1. "Standard Test Method for Constant-Load-Amplitude Fatigue Crack Growth

Rates above 10"° m/cycle" (Designation E647-83), i n

1 983 Annual Book of

ASTM Standards , section 3, Vol . 03.01, American Society for Testing and

Materials, Philadelphia, Pennsylvania (1983), pp. 710-730.

2. Fatigue Thresholds: Fundamentals and Engineering Applications , J.

Backlund, A. F. Blour, and C. J. Beevers, eds.. Engineering Materials

Advisory Services, Chameleon Press, London, United Kingdom (1982).

3. R. J. Bucci, "Development of a Proposed ASTM Standard Test Method for

Near-Threshold Fatigue Crack Growth Rate Measurement," in: Fatigue Crack

Growth Measurement and Data Analysis , ASTM STP 738, S. J. Hudak, Jr. and

R. J. Bucci, eds., American Society for Testing and Materials, Philadelphia,

Pennsylvania (1981), pp. 5-28.

4. T. W. Crooker, F. D. Bogar, and G. R. Yoder, "Standard Method of Test for

Constant-Load-Amplitude Fatigue Crack Growth Rates in Marine Environments,"

NRL Memorandum Report 4594 (August 6, 1981).

5. Y.-W. Cheng, "A Computer-Interacti ve Fatigue Crack Growth Rate Test

Procedure," in: Materials Studies for Magnetic Fusion Energy Applications

at Low Temperatures-VI , R. P. Reed and N. J. Simon, eds., NBS I R 83-1690,

National Bureau of Standards, Boulder, Colorado (1983), pp. 41-51.

150
6 . The Measurement of Crack Length and Shape During Fracture and Fatigue , C.

J. Beevers, ed.. Engineering Materials Advisory Services, Chameleon

Press, London, United Kingdom (1980).

7. Advances in Crack Length Measurement , C. J. Beevers, ed., Engineering

Materials Advisory Services, Chameleon Press, London, United Kingdom (1981).

8. J. J. Ruschau, "Fatigue Crack Growth Rate Data Acquisition System for

Linear and Nonlinear Fracture Mechanics Applications," Journal of Testing

and Evaluation , Vol . 9, No. 6 (Nov. 1981), pp. 317-323.

9. "Proposed ASTM Test Method for Measurement of Fatigue Crack Growth

Rates," in: Fatigue Crack Growth Measurement and Data Analysis , ASTM STP

738, S. J. Hudak, Jr. and R. J. Bucci , eds., American Society for Testing

and Materials, Philadelphia, Pennsylvania (1981), pp. 340-356.

10. W. Elber, "The Significance of Fatigue Crack Closure," in: Damage

Tolerance in Aircraft Structures , ASTM STP 486, M. S. Rosenfeld, ed.,

American Society for Testing and Materials, Philadelphia, Pennsylvania

(1971), pp. 230-242.

11. S. J. Hudak, Jr., A. Saxena, R. J. Bucci, and R. C. Malcolm, "Development

of Standards of Testing and Analyzing Fatigue Crack Growth Rate Data,"

AFML-TR-78-40, Air Force Materials Laboratory, Wright-Patterson Air Force

Base, Ohio (May 1978).

12. P. C. Paris and F. Erdogan, "A Critical Analysis of Crack Propagation

Laws," Transactions of ASME, Journal of Basic Engineering, series D, vol.

85, No. 3 (1963), pp. 528-534.

LIST OF FIGURES

1. Data outputs from the automated FCGR test.

2. Schematic of the automated FCGR test system.

3. Summary flow chart of the automated constant-load-amplitude FCGR test.

4. Summary flow chart of the automated near-threshol d FCGR test.

151
o

o

oo.

lO

1 o

LO

CO Q_

*

o <

CM

00

U_

O)

c

4—

C0CO O

a3o

CO

epAo/wuj ‘NP/^P

O w

co0

_C

CO +-CO

LOCO

°°OOoof Oq,

o

co

iq

CM

o

o

lOo

X

CM

CO0

O

>

o

o

CM

LO

LUO ‘B

152

Figure

1.

Data

outputs

from

the

automated

FCGR

test.
Figure 2. Schematic of the automated FCGR test system.

153
Figure 3. Summary flow chart of the automated constant-load-amplitude FCGR

test.

1 54
Figure 4. Summary flow chart of the automated near-threshold FCGR test.

155

Low-temperature monocrystal elastic constants

of Fe-19Cr-10Ni

H. M. Ledbetter

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

Boulder, Colorado 80303 USA

By a pulse-echo-overlap ultrasonic method, we determined the monocrystal

elastic constants (C^, C

12 , C 44 ) of an Fe-19Cr-10Ni alloy between 295 and

4 K. In composition this laboratory alloy approximates a technological

austenitic stainless steel: AISI 304. Many previous studies on polycrystalline steels found a low-temperature magnetic phase transition that

affects physical properties, including elastic constants. At the transition,

anomalies occur in all polycrystal elastic constants: Young's modulus, shear

modulus, bulk modulus, and Poisson's ratio. The present study found that the

transition, near 50 K, does not affect one monocrystal elastic constant: C 44 ,

the resistance to shear on a (100) plane in a [100]-type direction. We

interpret this new observation from the viewpoint of a Born-type lattice

model. Also, we comment about the relationship between the elastic-constant

changes and the 1 ow-temperature magnetic state.

Key Words: austenite; bulk modulus; elastic constants; low temperatures;

magnetic phase transition; monocrystal; phase transition; physical properties;

Poisson's ratio; shear modulus; sound velocities; stainless steels; Voigt

elastic stiffnesses; Young's modulus.

Intended for publication in Journal of Physics and Chemistry of Solids.

157

INTRODUCTION

Austenitic stainless steels rank high among existing technological

materials. They enter many varied applications, often in large quantities.

Probably best known among these steels is AISI 304, nominally Fe-18Cr10Ni-2Mn. Currently, much research effort focuses on improving the properties

of these steels. Much remains not understood. A principal obstacle to

understanding is the nature of the ingredient elements: Fe, Cr, N i , Mn , C, N.

All four metals exhibit either ferromagneti sm or anti ferromagneti sm; the

magnetic state affects physical properties. Among all common elements, the

anti ferromagneti c ones present the most formidable resistance to theoretical

understanding. Mainly this resistance arises from the d-shell electrons that

determine bonding and magnetic state. Present theory of metals deals cautiously with d-shell electrons. The two interstitial elements, C and N,

present another set of problems. What are their in-alloy atomic volumes and

electron states? Are they dispersed or clustered? Do they bond preferentially with one element?

Because these steels retain their ductility and toughness, they find

widespread low-temperature applications. Changing temperature alters their

properties, especially their magnetic state, which relates fundamentally to

many other properties.

For the 304-type steel , Ledbetter [1] recently reported the polycrystal

elastic constants between 293 and 4 K. Those results comprise the following

features: (1) From 293 to approximately 100 K, all elastic constants behave

regularly. (2) Below this, centered near 50 K, the alloy undergoes a phase

transition that magnetic-susceptibility measurements reveal to be magnetic:

high-temperature paramagnetic to 1 ow-temperature antiferromagnetic or to

low-temperature spin glass [2], (3) Cooling through the transition softens

159
all the elastic stiffnesses: bulk modulus, shear modulus. Young's modulus.

(4) At the same time, Poisson's ratio increases. (5) Below the transition,

further cooling restores the regular temperature behavior of all the elastic

constants, except Poisson's ratio, which either remains constant or increases,

contrary to the regular behavior of decreasing continuously during cooling.

(6) Above the transition temperature, the bulk modulus shows "premonitory"

softening. Studies on many other similar alloys show qualitatively the same

behavior [3,4]. The main difference in these alloys is that their transition

temperature depends on chemical composition, especially Mn, which raises the

transition temperature. Some hi gh-Mn-content alloys exhibit a transition

above ambient temperature [5,6].

Magnetic-susceptibi 1 i ty-versus-temperature measurements [3,7] on the

polycrystal alloys reveal that a magnetic phase transition always accompanies

the elastic-constant discontinuities. Susceptibility, x> shows a sharp

upward-pointing cusp. The curve shape corresponds to that of a classical

paramagneti c-anti ferromagneti c transition [8], but also to that of a spin

glass condensation [9]. Thus, simple x(J) measurements fail to distinguish

between the two possibilities: antiferromagnetic and spin glass. Above the

transition temperature, x fits a modified Curie-Weiss law:

x(T) = x

0 + C/(T - 0 ) (1)

where x

0

> C, and 0 are adjustable parameters. Various alloys yielded a nearly

alloy-independent background paramagnetic susceptibility, x

0

> of 13.5 emu/g.

In these alloys, 0 tends to be small, either positive or negative, and a

fraction of the transition temperature, T^. Kittel [10] lists properties of

many anti ferromagnets ; in all cases, 0 is negative and the absolute value

160
almost always exceeds by a factor up to 5.

The present research sought a better understanding of these lowtemperature elastic-constant phenomena by studying them in a monocrystal

laboratory alloy, which eliminates many extraneous variables, such as interstitial C and N atoms, substitutional Mn atoms, and possible grain-boundary

and grain-size effects. At the same time, one obtains more information

because an fee crystal has three independent elastic constants (C^, C^» C 44

in Voigt notation), whereas a quasi -i sotropi c polycrystalline aggregate has

only two independent elastic constants. The relate directly to interatomic forces and to well-defined deformation modes. From reported lowtemperature anomalies [1] in the polycrystal shear modulus, G, we do not know

which of the two principal cubic-symmetry shear moduli, or (C^ - C^)/2,

or both, shows anomalies. As described below, knowing this helps elucidate

the magnetic transition.

EXPERIMENT

Material

An alloy of nominal weight-percent composition Fe-19Cr-10Ni was vacuum

melted and vacuum cast from high-purity metals. Single crystals were grown by

a Bridgman technique, homogenized at 1350°C for 20 h, cut to shape and size

with a spark cutter, and annealed at 1100°C for 20 h. Back-reflection Laue

x-ray diffraction was used to establish the crystal orientation, which was

2.5° from a [110] axis. Specimen dimensions were 1.5 cm x 1.5 cm x 0.7 cm.

Mass density measured by Archimedes's method was 7.937 g/cm .

Method

For brevity we omit the measurement-method description, which we gave

elsewhere [11], including 1 ow-temperature procedures [12]. Particular details

161
that differ here include: 5 to 10 MHz measurement frequency, commercial

adhesive transducer-specimen bond.

RESULTS

Figure 1 gives relative measured values between 293 and 4 K for three

elastic constants: = (C^ + + 2C^)/2, C^, and C' = (C^ - C^)/2,

from which one calculates, for T = 293 K, = 205, = 126, C

1 = 33.4, and

C ^2

= 138 GPa. Figure 2 shows, versus temperature, some derived monocrystal

elastic constants: C^, B = (C^ + 20^)73, and the Zener elastic anisotropy

[see Eq. (2)]. In Fig. 3, we give the quasi-isotropic (polycrystal) elastic

constants derived from the C.. by Kroner's method [131. At 293 K, these are:

i J bulk modulus, B, = 160; shear modulus, G, = 75.6; Young's modulus, E, = 196

GPa; and Poisson's ratio, v, = 0.296.

DISCUSSION

The 1 ow-temperature anomaly

The study's most remarkable result is that near 50 K all . behave

anomalously, except C^. Although upon cooling through the transition the

lattice softens its resistance to ( 1 10 ) [ 1 10] , C'-type, shear, it retains its

resistance to ( 100 ) [ 100 3 , C^-type, shear. Thus, the Zener anisotropy factor

^ = ^ ^44/ (

C

1

“ (2)

increases abruptly during cooling through the transition.

Because we know from magnetic-susceptibi 1 i ty-versus-temperature measurements that the transition involves a change from paramagnetic to antiferromagnetic or spin glass, and because antiferromagnetic phases involve spin

162
ordering on lattices or sublattices, we consider the contributions to the

elastic constants from f i rst-nearest and second-nearest neighboring atoms. We

assume a central -force pair interaction. (This is not exact. One requirement

of a central potential is the Cauchy condition, = C^. As shown above,

this condition holds within 10 percent for this alloy.) It makes sense to

neglect volume-dependent, structure-independent energy terms because they

affect all the C^. Also, this approach agrees with a conclusion of Alers,

Neighbours, and Sato [14], They considered the magnetic-exchange interaction

in an experimental study of Fe-30Ni elastic constants and concluded that "the

effects of a noncentral interaction were ... too small to be observed."

If the interatomic potential is denoted $(r), then, following Born's

classical studies, the Brugger elastic constants, which are fourth-rank

tensors, are given at T = 0 K by:

C. .. , i jkl

2 ru

5n • -drii i ij kl 2 V Z)D

2 $(jc)r?

where D$(jc) denotes ( l/jc)[S$(jc)/5r] . The

obtained by a sum over two-body atom-atom

energy density, U, of the crystal

interaction energies:

i s

u = (i/2v°)it(r) (4)

where V° is the undeformed atomic volume. The n-- are components of the

Lagrangean elastic strain matrix

n = (1/2)1^ - 4) (5)

where X is the 3x3 identity matrix, t denotes transposition, and the deformation matrix, J,,is defined by

163
JC = ilc' ( 6 )

where £° and £ are the interatomic spacings in the initial state and in the

deformed state, respectively.

Face-centered cubic crystals have twelve nearest neighbors at

<±1, ±1, 0 > a/2 and six next-nearest neighbors at <±1, 0, 0 > a, where a is

the unit-cell dimension. In this case one obtains from Eq. (3):

C 44 ^ C 2323

2V

4(-|) D

2 $(y|) + 0 +, (7)

where ... indicates contributions from pairs beyond second-nearest neighbors.

Similarly, one obtains

C - (C n - C

12 )/2 - (C 1U1 - Cj 122 )/2

= —J2(4) 4

D

2 4(4) + a 4

D

2

*(a) +...]

2 V

L

( 8 )

We find an important difference. First and second neighbors contribute to C'

only first neighbors contribute to C 44 . (In bcc crystal structures, the

situation reverses: second neighbors contribute to but not to C' [15].)

Thus, the second-neighbor interaction can change dramatically without

affecting C^.

Now we consider--how can second-neighbor interactions affect the elastic

constants while first-neighbor interactions do not? The answer lies in two

factors: the electron-spin structure and the Bethe-Slater curve Figs. 4 and

5). This electron-spin structure is based on 4-K neutron-diffraction studies

of y-Fe by Abrahams et al . [16] and of Fe- 1 5C r- 1 5N i by Ishikawa et al. [17],

These studies found Neel temperatures of 8 K and 21 K, respectively. The

164
structure consists of (200)-plane sheets of parallel spin with alternate

sheets being anti paral 1 el . The magnetic moments align nearly parallel and

antiparallel with a cube axis, a [100]-type direction. (We neglect the angle

between the spin vectors and the cube axes, which tends to make the crystal

structure monoclinic. We consider the spins either up or down.) Examination

of Fig. 4 reveals that all six second-neighbor spins are parallel to the

reference spin. However, for the twelve f i rst-nei ghbors , eight are antiparallel ( antiferromagnetic array) but four are parallel (ferromagnetic

array). Thus, if we write an expression for the exchange energy [18]:

U e = -2 Z J (r) VS

j

(9)

i>j

where J(r) is the exchange integral shown in Fig. 5 and £. is the spin on atom

i ; through second neighbors this becomes (taking S = 1)

U

e

= 8J(r

1

) - 12J(r

2

) (10)

Thus, second neighbors dominate the exchange energy because approximately

J(r

2

) = -7J(r

1

) (11)

Thus, in this case, second neighbors (at r^) contribute approximately twelve

times as much to exchange energy as do first neighbors (at r^).

For elastic-stiffness constants, which relate to J(r)'s second spatial

derivative, the second-neighbors also dominate. Consider, for example, the

bulk modulus:

165
( 12 )

B

= (C u

+ 2C

(1/2 V°)

12 )/ 3 ( c im

(16/3) (a/2)

4

+ 2C 1122^ 3

D

2 $(a//2) + (2/3)aVo(a) + ...

Written out in terms of first and second derivatives of J(r), this becomes

( 1/3V°

)

2r

1 J"(r1

) - 4r

1 J'(r1

) + r^ J"(r

2 )-2r2

J ' (r

2

) (13)

where primes denote derivatives with respect to r. For the present case,

Fig. 5 shows that J ' (

2

) and J"(r^) practically vanish. Thus,

B e

« ( 1/3V°

)

-4r

1 J

l (r

x

) + r

2 J"(r2

)

(l/3V°)B

e (r

1

) + B

e (r

2

) (14)

Because J'(r^) is positive and J"(r

2

) is negative (indeed near its maximum

negative value), both f i rst-neighbor and second-neighbor exchange-energy

interactions reduce the bulk modulus. But to see their relative contributions, B

g

( r

2

) /^

e

( r

l) ’ we neec* a re 3 ationshi p between J'(r^) and J"(r

2

). To do

this we approximate J(r) with the function

J(r) = ar

^ - br

n (15)

After some algebra, recognizing that r

2

= r (J max) and taking n = 10 (higher n

raises the ratio), we find the ratio

B e (r

2 )/B

e (r

l

) s 4 (16)

Thus, this confirms that second neighbors dominate the exchange contributions

166
to the elastic constants. Taking n = 10 corresponds to a high positive slope

at low r/d, as suggested in Fig. 5. The exact shape of the J(r) curve remains

unknown. With some success, several studies [20,21] attempted to relate

elastic constants to the J(r) curve. Unlike the present study, they focused

mainly on f i rst-nei ghbor interactions.

The above considerations are consistent with an anti ferromagneti c lowtemperature phase where the main exchange-energy contributions to the elastic

constants originate in the first-neighbor and second-neighbor interactions.

Indeed, Fig. 5 shows that Heisenberg exchange forces are short-range.

These same considerations are not consistent with the ideal spin glass.

This magnetic state envisages "negligible effect of directly coupled pairs"

and "results from a random distribution ... of the interactions between

neighboring moments" [22]. That is, forces are long-range as provided, for

example, by an RKKY coupling [23]. Spin glasses provide no distinction in

magnetic moment at f i rst-nei ghbor and second-neighbor positions. Both sets of

atoms exhibit randomly oriented moments frozen in time. Concerning concentration, Hurd [22] points out that "the spin glass ... exists only within a

limited range of concentration of magnetic solute. The concentration must be

high enough to give interactions via RKKY coupling yet low enough to avoid

clusters or linkages of directly coupled moments ... the 'dilute' and 'percolation' limits, respectively ... occur in an fee alloy at about 0.01 and 20

atomic percent ... direct exchange dominates above the percolation limit,

leading to ferromagneti sm or anti ferromagneti sm. " Thus, in the present case,

by this reasoning, concentration also excludes the spin glass possibility. It

remains unclear whether mi ctomagneti sm or cluster magnetism [24] provide

possible 1 ow-temperature magnetic states in these Fe-Cr-Ni alloys.

167
Another factor favors a low-temperature anti ferromagneti c phase over spin

glass: the shear-modulus softening. Eshelby's elastic-continuum studies [25]

show that a shear-modulus change arises from local short-range changes in the

immediate neighborhood of the imperfection, usually within the second-neighbor

distance. (Here we take imperfection to mean a departure from the nonmagnetic

paramagnetic state, a spin arrangement that exerts an internal pressure,

analogous to a point defect. This pressure alters volume and elastic stiffness [26].) Anti ferromagneti sm can alter G because it involves short-range

forces that arise from wave-function overlap. As Fig. 5 shows, antiferromagnetism vanishes for large interatomic spacings. On the other hand, the

spin glass state depends on indirect exchange, such as RKKY, and, therefore,

on long-range forces. Thus, we can exclude spin glass forces from those

affecting the shear modulus.

Monocrystal -poly crystal relationship

Now we consider how the present measured monocrystal elastic constants

measured here compare with those for a similar-composition polycrystal reported

previously [11]. This may represent the first such comparison for a concentrated ternary alloy. This comparison requires "averaging" the monocrystal

constants to obtain the effective polycrystal constants. Landau and Lifshitz

[27] remind us that "there is ... no general relation between the moduli of

elasticity of a polycrystal and those of a single crystal of the same substance." Ledbetter [28,29] showed recently for Cu that the best averaging

method, among eight considered, is Kroner's [13]. Table I gives the comparison. The one-to-two percent disagreement probably arises from the monocrystal

polycrystal chemical -composi tion difference.

Elastic anisotropy

During cooling from ambient temperature to the anti ferromagnetic transi168
tion, the Zener elastic anisotropy, A, Eq. (2) behaves regularly. It

decreases slightly as for other fee metals such as A!, Cu, and Ni and for bcc

Fe. At the transition, A rises abruptly and exceeds its ambient-temperature

value. This occurs because C' softens whereas does not. Many

authors (e.g., Ref. 30) associate high A with incipient lattice instability.

This suggests that the 1 ow-temperature magnetic phase offers less resistance

than the hi gh-temperature nonmagnetic phase to crystal -structure change to a

bcc or eph crystal structure. However, magnetic energy may offset this.

Other matters

It should not escape attention that behaves anomalously in the

paramagnetic region. Whereas dC/dT is negative for all the other monocrystal

elastic constants, dC^/dT is practically zero and very slightly positive, as

shown in Fig. 2. Negative dC/dT is the usual, normal behavior for all the

C^. For this particular anomaly we offer no explanation. is difficult

to consider theoretically because, unlike most other C.., it is nonphysical.

In a crystal, no elastic wave exists correspondi ng to C^. The anomaly

suggests some materi al -state change that offsets the expected temperature

change of C^. Perhaps a magnetic change occurs. One useful view of is

in terms of Poisson's ratio:

v100

h_2 =

C 12

S 11

C 11

+ C 12

(17)

where denote the elastic compliances. With dC

12

/dT s 0, then

dv100^ v 100

s " d Cn/(C n

+C

12 ) (18)

and Poisson's ratio decreases more rapidly with decreasing temperature.

Figure 3 shows that Av/v = -4.0 percent between T = 293 and 0 K. For Cu, an

169
elastically softer material where one expects larger changes with temperature,

one finds Av/v = -2.0 percent. This small difference is important because, as

Koster and Franz [31] pointed out, "Poisson's ratio depends to a much greater

extent on the conditions of bonding than do the other elastic coefficients."

Small anomalous Poisson' s-ratio changes signal a significant change in the

nature of the interatomic bonding. In usual materials, a reduction in C^/C-q

indicates a move from metallic bonding toward covalent or ionic bonding [32].

But, in magnetic materials, reduced C^/C^ perhaps signifies something quite

different, related to electron-spin rearrangements . The drastically different

temperature behavior of and C^ suggests strong noncentral force interactions. Such forces arise, for example, in many-body interactions, which may

enter the description of magnetic clusters.

Neither can one neglect the softening of all elastic stiffnesses except

C' and (the shear moduli) at temperatures above the magnetic transition.

This softening of all dilation-related elastic stiffnesses occurs upon cooling

below approximately 100 K. We will call this premonitory dilation softening.

Probably it arises from some magnetic interaction that expands the lattice and

reduces the bulk modulus. As Eshelby [25] pointed out, pure bulk-modulus

changes tend to be associated not with rapidly fluctuating forces (such as

arise from the exchange interaction), but with long-range, smoothly varying

forces. Upon cooling, one would expect long-range, indirect interactions to

emerge before the direct-exchange interactions that depend on d-shell overlap.

CONCLUSION

The first measurements of austeni tic-steel -1 i ke monocrystal elastic

constants at low temperatures show an interesting result: C^ behaves regularly

170
while all other behave anomalously at the magnetic transition. We interpret this to mean that only second-neighbor interatomic interactions change

during the transition. A possible model puts both antiparallel and parallel

electrons on first-neighbor sites and parallel-spin electrons on secondneighbor sites. Because of the behavior, because a softened shear modulus

implies short-range interatomic-force changes, and because of high concentrations of magnetic species, we conclude that the 1 ow-temperature phase is

anti ferromagneti c rather than spin glass. Other peculiarities include a

nearly temperature-independent C^ and premonitory softening of bulk-modulusrelated elastic constants.

ACKNOWLEDGEMENTS

The U. S. DoE Office of Fusion Energy supported this study. Dr. N. F.

Fiori of Cabot Corporation loaned the monocrystals. Mr. J. Ward assisted with

measurements, and Mr. M. W. Austin with many miscellaneous contributions.

171
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s

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172
22. C. M. Hurd, Contemp. Phys. 23^, 469-493 (1982).

23. D. C. Mattis, The Theory of Magnetism I ( Spri nger-Verl ag , Berlin, 1981),

p. 229 ff.

24. P. A. Beck, in Progress in Materials Science, Volume 23 (Pergamon,

Elmsford, New York , 1978) , pp. 1-49.

25. J. D. Eshelby, J. Appl . Phys. 25, 255-261 (1954).

26. J. F. Janak and A. R. Williams, Phys. Rev. B 14, 4199-4204 (1976).

27. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon,

Elmsford, New York, 1959), p. 40.

28. H. M. Ledbetter, J. Phys. D: Appl. Phys. 13_, 1879-1884 (1980).

29. H. M. Ledbetter, Phys. Status Solidi (a) 66_, 477-484 (1981).

30. C. Zener, Elasticity and Anelasticity of Metals (U. of Chicago Pr.

,

Chicago, 1948), p. 32 ff.

31. W. Koster and H. Franz, Metal 1. Rev. 6_, 1-55 (1961).

32. H. M. Ledbetter, to be published.

173
TABLE I. Calculated and measured polycrystal elastic constants. Units are

GPa, except v, which is dimensionless.

B E G V

Cal cul ated 160 196 75.6 0.296

Measured3 158 200 77.4 0.290

a Ref. 11.

174
Fig. la. From 4 to 293 K, relative measured elastic constants C. = (C n + C

12 + 2C44 )/2, C* = (C n - C 12 )/2, and C44 .

Fig. 2 From 4 to 293 K, derived monocrystal elastic constants and B,

and Zener elastic anisotropy, A.

Fig. 3. From 4 to 293 K, quasi -.isotropic (polycrystal) elastic constants

computed from C.. by Kroner's method. B denotes bulk modulus, E,

Young's modulus, G, shear modulus; and \), Poisson's ratio.

Fig. 4. Suggested electron-spin structure of y-Fe and Fe-15Cr-15Ni . Adapted

from references 16 and 17.

Fig. 5. Bethe-Slater curve of magnetic exchange energy versus r/d, where r denotes interatomic spacing and d, diameter of 3d-electron shell.

Adapted from reference 19. For fee Fe, the second-neighbor distance,

r

2 = *^ r i’

"' les on ^ slightly to the left of the Co point.

175
(

293 )

Fig. la. From 4 to 293 K, relative measured elastic constants C.

( Ci i + C-^2 + 2C^)/2, C

1 = (C n

- C^2 ^ ^

anc* ^44*

176
ANISOTROPY

C

12

(GPa)

142

TEMPERATURE (K)

Fig. 2 From 4 to 293 K, derived monocrystal elastic constants C,o and B,

and Zener elastic anisotropy, A.

177

BULK

MODULUS

(GPa)
POISSON’S

RATIO

CD

TEMPERATURE, (K)

Fig. 3. From 4 to 293 K, quasi-.tsotropic (polycrystal) elastic constants

computed from C.. by Kroner's method. B denotes bulk modulus, E,

Young's modulus] J G, shear modulus; and v, Poisson's ratio.

178

SHEAR

MODULUS

(GPa)

BULK

MODULUS

(GPa)
Fig. 4

i

% ref. atom in (111) plane

©6 nn in (111) plane

© 3 nn above (111) plane

© 3 nn below (111) plane

O 6 nn

Suggested electron-spin structure of y-Fe and Fe-15Cr-15Ni . Adapted

from references 16 and 17.

179
J(r)

Fig. 5. Bethe-Slater curve of magnetic exchange energy versus r/d, where r denotes interatomic spacing and d, diameter of 3d-electron shell.

Adapted from reference 19. For fee Fe, the second-neighbor distance,

r

2 = y/^ r i’

^ 1es on ^y slightly to the left of the Co point.

180
A Numerical and Experimental Verification of Compliance Functions for Compact

*+

Specimens

Carpenter* R. L. Tobler and W. C. **

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A two-dimensional finite-element study of the compact specimen was performed in verification of its elastic compliance calibration functions.

The finite-element results confirm Newman's boundary collocation solutions

within 2 %. Empirical calibrations were also obtained using alloys with

well-known elastic moduli. The numerical and empirical agreement depends on the state of stress assumed in the model, with better agreement for plane

stress than for plane strain. Assuming plane stress and a Poisson's ratio of

0.3, numerical solutions predict the true crack lengths within 4% or better

for relative crack lengths, a/W, greater than 0.35.

Key Words: Compact tension specimen; compliance; crack-mouth-opening

displacement; elastic modulus; finite elements; numerical

analysi s

*Work supported by Office of Fusion Energy, U.S. Department of Energy; not

subject to copyright.

To be published in Engineering Fracture Mechanics .

**National Bureau of Standards Guest Worker, on leave from Department of Civil

Engineering and Mechanics, University of South Florida, Tampa, Florida.

181

INTRODUCTION

Crack-opening-displacement measurements have been used in a wide variety

of experimental fracture mechanics studies [1-5]. Such measurements provide a

method of detecting crack initiation and growth, based on the fact that the

specimen compliance, V, increases with increasing crack length, a. In this

paper, compliance is defined simply as the ratio between the elastic-crackopening displacement, 6, measured between two reference points spanning the

crack surfaces, and the load, P.

The advantages and limitations of compliance techniques are reviewed

elsewhere [6-12]. The accuracy of crack length predictions clearly depends on

the validity of both the expression used to correlate 6/P and a, and the

experimental uncertainties of the relevant physical measurements and material

elastic properties [13-17]. To obtain accurate correlations, experimentalists

sometimes develop their own empirical calibration curves. This tedious

procedure is necessary for some less-common specimen configurations [6], but

in general, it is far more efficient to employ the published analytical

expressions that are available for standard specimens. In the latter case,

slight adjustments may be desirable for reasons described in the text.

A number of analytical calibrations have been published for compact

specimens [18-30]. The elastic compliance calibration functions are usually

given in normalized form by polynomial expressions as follows:

EBV = f (a/W) (1)

where E is Young's modulus, B is specimen thickness, W is specimen width, and

V- = 6../P . In this notation, i = 0 designates measurements at the specimen

edge, and i = L, the load line. Earlier solutions to obtain the calibration

183
functions employed boundary collocation techniques because of the difficulty

at the time of characterizing the crack-tip singularity with finite elements

[24]. These functions so derived have been incorporated into standard

fracture mechanics test procedures. This paper examines the reliability of

the existing collocation solutions based on a combination of some new finiteelement calculations and physical measurements. Calibration functions for

standard and modified compact specimens are considered.

EXPERIMENTAL PROCEDURE

Numerical Calculations by Finite Elements

Two compact tension specimen configurations were analyzed using the

POLO-FINITE program [31]. These two specimens are recommended in the ASTM

standards for and Jj

c testing [32,33]. Typical finite-element

idealizations of these configurations, shown in Figs. 1 and 2, consisted of

8-node quadrilateral isoparametric finite elements [34]. The crack-tip

idealization shown in Fig. 3 illustrates how the quadrilateral elements

adjacent to the crack were collapsed to zero length with the midside nodes of

adjacent faces at quarterpoints to exactly model the elastic l//r strain

singularity [31,35,36]. Figure 4 illustrates the three types of pinhole

loadings investigated.

The numerical results depend on assumptions about the stress state and

elastic properties. Plane strain was assumed, and because of symmetry, only

one-half of each specimen was idealized. The plane stress displacements and

compliance functions were obtained by conversion from the plane strain

results [24].

Specimen Designs

Compact specimens having either the standard Kj

c configuration or that

shown in Fig. 5 were machined from the AISI 316 stainless steel and 2024-T351

184
aluminum alloys described in Table 1. These served as calibration specimens

to confirm the analytical results. The configuration of Fig. 5 is the

J-integral specimen often used at NBS; it specifies cutouts for knife-edge

positioning at the load line, and to facilitate this modification the pinhole

centers are shifted slightly to 0.3W from the notch plane centerline. The

standard Kj

c specimen is diagramed in ASTM E 399-83 and it specifies pinhole

centers at 0.275W [32]. All specimens were of the TL orientation with B

=

25 mm and W/B = 2. Razor-blade knife edges were spot-welded to the edge or

load line positions and ASTM E399-83 clevises were used.

Elastic Properties

Young's modulus, E, and Poisson's ratio, v, of the calibration materials

were measured ul trasonical ly at 295 K using cubic specimens (1.95 cm 3 ).

Results are listed in Table 1. The ultrasonic technique [37-39] gives dynamic

moduli (E^) with uncertainties of ±1%, whereas conventional tensile tests give

static moduli (E

s

) with uncertainties of ±5 - 10%. For this reason,

ultrasonic data are preferable.

The elastic moduli at 76 K were not measured directly but were estimated

as follows:

76

~ E 295 ( E 76/E 295^ ( 2 )

Here E^ is the measured value at 295 K for the present alloys; E^ and E^

are ultrasonic data for other heats [38-39].

Physical Crack-Length-Compliance Measurements

Displacements were measured with a clip-gage meeting the requirements of

section 6.3 of ASTM E 399-83. Using an extensometer micrometer, calibrations

with a repeatability ±0.5% were performed at each temperature, 295 and 76 K.

185
To obtain EBV, specimens were fatigue tested at 20 Hz with periodic

interruptions for single-cycle loading at 0.02 Hz. At this lower rate, the

load cell and clip-gage outputs were put into a minicomputer after

analog-digital conversion, and V

q or for each crack length was calculated

by the method of least squares. Typically, 180 readings were input from the

upper half of the 6 vs P records but data from the lower half were excluded to

avoid crack-closure effects.

To correlate EBV with a/W, crack-front markings were created on the

failure surface byJ alteringa the stress ratio, R = P . /P , between 0.1 and min max’

0.5 with P held constant. The physical crack lenqths were then measured

from the failure surfaces after testing, taking the average of five readings

(2 at the specimen edges, 2 at the quarter points of thickness, and 1 at the

midthickness). This method of crack-front marking simulates actual fatigue

tests and is preferable to saw-cutting or machining successively deeper

notches, since those procedures would reduce the specimen stiffness by

removing material.

The precision of both the load cell and gage output was ±0.01 mV as read

from a digital voltmeter. The linear correlation coefficients for V were

0.999 or better, and the repeatability of individual crack length determinations was ±0.025 mm. The specimen dimensions were measured to the nearest

0.025 mm, and the physical crack length was measured to the nearest 0.5%.

RESULTS

Numerical Calculations

For the standard Kj specimen of ASTM E 399-83 [32], Fig. 6 compares the

present finite-element results with the results of Newman [23-25], who used

boundary collocation to obtain his solutions. Shown are results for plane

186
strain with v = 0, 0.3, and 0.5. The finite-element solution blows up at

v = 0.5, so only results at v = 0 and v = 0.3 are given. The finite-element

idealization modeled the machined notch tip, whereas the collocation procedure

did not. This is a minor distinction, however, and the two compliances for V Q

agree within 1%. The present results, therefore, confirm Newman's solutions.

For the recommended Jj

c specimen of ASTM E 813-81 [33], it was of

interest to determine whether the modifications made to allow load-line

displacement measurements would significantly affect V^. In Fig. 7 finiteelement calculations for this specimen are compared with the collocation

results [24] for the standard Kj

c specimen without modifications. In this

case, the agreement is typically better than 1% and never exceeds 2%,

indicating that the effect of notch modifications on load-line displacements

for the Jj

c specimen can, indeed, be ignored.

Three different assumptions about loading conditions were modeled

for both the standard Kj

c and Jjc specimen configurations, as illustrated in

Fig. 4, but the effects of these variations on V and V, were found to be

o L negligible (less than 0.5%), once again confirming Newman [24].

Empirical Observations

The experimentally measured compliances are listed in Tables 2 and 3,

while comparisons between the numerical results of Newman [24,27] and

experimental data are shown in Figs. 8 and 9 for edge and load-line

di spl acements

As shown in Tables 4 and 5, the experimental calibrations agree best with

the numerical solutions assuming plane stress, while the agreement assuming

plane strain is relatively poor. An apparent agreement is achieved assuming

plane strain with v = 0, but this is fortuitous, since v is nearly 0.3 for the

materials tested. As shown in Fig. 7, v has a strong effect in plane strain;

187
the percent difference between EBV^ for v = 0 and v = 0.5 is on the order

of 20%, depending on a/W. Therefore, when plane strain is assumed with v

=

0.3 instead of v = 0.0, the calibration function is altered so that

experimental agreement is poor.

However, reasonable agreement is achieved with models assuming plane

stress, in which case Poisson's ratio has negligible effect on the numerical

results. Assuming plane stress with v = 0.3, the disparity between the

measured and calculated V and V, is not more than 4% at a/W = 0.35, and

o L it decreases to less than 2% for longer cracks, a/W _> 0.5. Since an error of

2% or less borders on experimental uncertainty, the calibrations are in

virtual agreement at a/W = 0.5. At the lower a/W ratios where the errors are

measurable, the numerical results slightly underestimate V q and slightly

overestimate V^.

The experimental data were fitted with curves similar to those used for

the numerical solutions so that quantitative comparisons in Tables 4 and 5

could be made at convenient a/W ratios.

DISCUSSION

The main contributions of the present study are: First, the

two-dimensional finite-element analysis undertaken shows that it is possible

to apply the finite-element method to the compact specimen with results

equivalent to a boundary collocation method. Second, the question of the

uncertainty of Young's modulus on the normalization parameter, EBV, is

addressed experimentally by using calibration materials with ul trasonical ly

measured elastic constants. Hence, the numerical and empirical calibration

functions can be more accurately compared. Finally, the experimental results

also confirm that E is truly a linear scaling factor and normalizing

188
parameter. In this study E was varied experimentally by altering the alloy

composition or the test temperature. Temperature has no inherent effect on

the calibration curves if the appropriate values of E and displacement gage

calibrations are used.

In general, the calculated and experimental displacement calibration

functions must inevitably show some disagreement. Fundamental errors may

arise from failure of the model to replicate the specimen in full detail or

from assumptions about the stress state and elastic properties, as discussed

below. Uncertainty also attends physical measurements, with possible errors

arising from instrumentation, mi smachining , or friction in the clevis grips.

These errors would tend to alter the calibration functions by introducing

nonlinear effects; such effects are thought to be minor for the compact

specimens and modifications studied here, but perhaps they contribute to the

results in Fig. 9.

Overall, the finite-element results of this study confirmed the results

of Newman in several respects, including his finding that the empirical data

agree better with numerical solutions for plane stress than for plane strain.

We think this is fortuitous to some extent, since the analytic models assume a

two-dimensional problem with conditions of either plane strain or plane

stress, whereas the specimens actually have three dimensions, and the stress

state varies with thickness, approaching plane stress only at the surfaces.

In any case, the relative success of the plane stress solution justifies its

practical use and incorporation into standard procedures (e.g.. Table Al.l of

ASTM E 813-81 [33]).

Using the analytical solution of Saxena and Hud&k [217 ] for plane stress

to predict the specimen behavior, several authors cite Young's modulus as the

major source of systematic error in determining the normalizing parameter.

189
EBV [2,12]. Usually E is not precisely known for the alloy being tested, so

it must be estimated. Some recent publications are helpful in these estimations. For example, Young's moduli for forty engineering alloys between 590

and 0 K are now available from a single source [37]. Yet, sizable error

remains since heat-to-heat uncertainties can amount to 5% [37] or, in extreme

cases, 15% [12]. For this reason, the use of handbook values or other

estimates of E limits accuracy, and most experimentalists employ correction

factors to the published numerical solutions to obtain more accurate

calibration curves for physical crack length predictions.

Since E is considered to be the major source of uncertainty, an

"effective modulus" correction is often adopted. According to this method, an

effective modulus, E is deduced from the calculated and measured EBV data.

First, E is estimated for the test material, and then a comparison in terms of

the ratio of the measured-to-predicted EBV reveals a mismatch. This ratio

multiplied times E is taken as E ^

and is substituted back into the

calculations to correct for the mismatch.

Then

E eff

BV = f (a/W) (3)

Usually, E ^

is deduced from one well-defined crack front (perhaps the

final fatigue crack length) that is visible on the post-test failure surface.

This factor to linearly shifts the analytical curve, which then predicts the

physical crack lengths over the entire range of a/W.

Actually, the effective modulus is a simplified correction factor that

compensates for all errors regardless of source. It approximately accounts

for the linear errors in E, as well as any nonlinear errors from other sources,

190
including any error in the analytical approach that uses a two-dimensional

model for a three-dimensional specimen. In the present paper, the uncertainty

normally associated with E was minimized by employing ultrasonic measurements

at 295 K. Consequently, E was known with good accuracy (1%), and the

remaining disparity between numerical and empirical calibrations (Fig. 9) was

attributable to other sources.

The findings suggest that when using a correction factor, it may be

desirable to determine the effective modulus correction for relatively deep

cracks first, and then use a second correction factor determined from Fig. 9

to obtain better accuracy in predicting shorter crack lengths.

SUMMARY AND CONCLUSIONS

A finite-element modeling of the edge (V ) and load-line (V^) elastic

compliances for compact specimens is described. The finite-element solutions

are compared with existing boundary collocation solutions and with empirical

data for alloys of well-known elastic properties and a/W ratios from 0.3 to

0.7. Plane strain was assumed and the results were also converted to obtain

solutions in plane stress. The physical crack curvature was accounted for

using a five-point average experimental crack length measurement. Conclusions

are:

1) The present finite-element and published collocation solutions agree

within 2 % or less.

2) Assuming plane stress with v = 0.3, the numerical solutions are in

near agreement with experiment: V

Q

is slightly overpredicted , while

V

L is slightly underpredicted , but the differences do not exceed 4

at a/W = 0.35, and at higher a/W the differences are negligible.

3) Various assumptions about pin loading, a slight shift of the pinhole

location, and moderate notch modifications to locate knife edges at

191
the load-line in J-integral test specimens do not have significant

effects on the calibrations.

ACKNOWLEDGMENTS

The elastic constants were measured by Dr. H. M. Ledbetter with assistance

from M. W. Austin. Helpful discussions with them and with Drs. Y. W. Cheng,

D. T. Read, and R. H. Dodds are gratefully acknowledged.

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Iowa (1973) 76-95.

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London (1980) 1-27.

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192
12 . G. R. Yoder, L. A. Cooley, and T. W. Crooker, in Fatigue Crack Growth

Measurement and Data Analysis, ASTM STP 738, S. J. Hudak, Jr. and R. J.

Bucci, Eds., American Society for Testing and Materials, Philadelphia

(1981) 85-102.

13. D. L. Dull, J. D. Buch, and L. Raymond, Engineering Fracture Mechanics 4

(1972) 523-531.

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D.C. (1975) 1-31.

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Mechanics 9 (1977) 901-923.

16. T. Nicholas, N. E. Ashbaugh, and T. Weerasooriya , On the use of

compliance for determining crack length in the inelastic range, to be

publ ished.

17. R. L. Hewitt, Journal of Testing and Evaluation 11 (1983) 150-155.

18. B. Gross, E. Roberts, Jr., and J. E. Srawley, International Journal of

Fracture Mechanics 4 (1968) 267-276.

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20. W. K. Wilson, Engineering Fracture Mechanics 2 (1970) 169-171.

21. M. J. Orloski, Journal of Research 74C (1970) 21-27.

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587-589.

23. J. C. Newman, Jr., NASA Tech Note, NASA TN D 6736 (1971) 1-45.

24. J. C. Newman, Jr., in Fracture Analysis, ASTM STP 560, American Society

for Testing and Materials, Philadelphia (1974) 105-121.

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26. J. E. Srawley, International Journal of Fracture 12 (1976) 475-476.

27. A. Saxena and S. J. Hudak, Jr., International Journal of Fracture 14

(1978) 453-468.

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Fatigue 1 (1979) 37-47.

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of Civil Engineering and the Academic Computer Center, University of

Kansas, Lawrence, Kansas (1983).

193
32. Standard Test Method for Plane Strain Fracture Toughness of MetallicMaterials, ASTM Designation E 399-83, 1983 Annual Book of ASTM Standards,

American Society for Testing and Materials, Philadelphia (1983) 518-553.

33. Standard Test Method for J

T

, A Measure of Fracture Toughness, ASTM

Designation E 813-81, 1983 Annual Book of ASTM Standards, American

Society for Testing and Materials, Philadelphia (1983) 762-780.

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McGraw-Hill, New York (1971).

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Physics 46 (1975) 185-194.

LIST OF TABLES

1. Calibration specimen materials and their elastic properties at 295 K.

2. Crack length and edge compliance (V

q

) data tabulation.

3. Crack length and load-line compliance (V^) data tabulations.

4. Normalized compliance, EBV

q

, for displacements at the specimen edge.

5. Normalized compliance, EBV^, for displacements at the specimen load line.

LIST OF FIGURES

1. A finite-element idealization for the Kj

c compact specimen of Fig. 1.

2. A finite-element idealization for the Jj

c compact specimen of Fig. 2.

3. Finite-element crack-tip substructure.

4. Three possible assumptions about pinhole loading.

5. An alternative Jj

c compact specimen used at NBS.

6. Finite-element results for the K^

c compact specimen of Figure 1.

194
7 . Finite-element results for the recommended Jj specimen with load-line

modification.

8. Comparison of numerical and experimental elastic displacement

cal ibrations.

9. Relative agreement of numerical and experimental results.

195
Table 1. Calibration specimen materials and their elastic properties at 295 K.

Alloy

Desi gnation

Condition

and Form

Young's Modulus,

E (GPa)

Poisson's Ratio,

V

2024-T351 aluminum cold-worked 25.4-mm 73.45 0.343

bar

AISI 316 stainless annealed 50.8-mm 198.0 0.294

steel pi ate

196
Table 2. Crack length and edge compliance ( V ) data tabulation.

Crack Length, a Relative

A1 1 oy

( Measured

,

a m

mm)

Predicted

,

a

P

Absol ute

Difference,

a -a (mm) m p

Percent

Difference,

(a -a )/a xlOO

m p m

Crack

Length

,

a/W EBV

0

2024-T351 15.350 16.100 -0.750 -4.88 0.302 26.44

16.000 16.775 -0.775 -4.84 0.315 27.75

18.250 18.875 -0.625 -3.42 0.360 32.38

19.175 19.825 -0.650 -3.39 0.378 34.87

22.900 23.250 -0.350 -1.53 0.451 45.60

24.600 25.050 -0.450 -1.83 0.485 53.10

30.075 30.100 -0.025 -0.083 0.592 85.78

30.375 30.350 +0.025 +0.082 0.600 88.41

197
Table 3. Crack length and load-line compliance (V^) data tabulation.

Alloy

Crack Length, a (mm)

Measured, Predicted,

a a m p

Absol ute

Difference

a -a (mm) m p

Percent

Difference

(a -a )/a xlOO

m p m

Rel ati ve Crack

Length

,

a/W EBV

0

2024-T351 15.525 14.475 1.050 6.73 0.306 13.21

16.200 15.125 1.075 6.64 0.319 14.10

18.325 17.725 0.600 3.27 0.361 17.93

18.900 18.250 0.650 3.44 0.372 18.83

21.525 20.900 0.625 2.90 0.424 24.02

22.075 21.550 0.525 2.38 0.435 25.47

25.050 24.675 0.375 1.50 0.493 36.15

26.675 26.100 0.575 2.15 0.525 39.45

28.025 27.925 0.100 0.35 0.552 47.44

28.775 28.450 0.325 1.13 0.567 50.26

30.325 30.300 0.025 0.08 0.597 61.67

AISI 316 19.800 19.075 0.725 3.66 0.391 20.46

22.050 21.675 0.375 1.70 0.435 26.02

23.225 22.400 0.825 3.55 0.458 27.91

24.600 24.000 0.600 2.44 0.485 32.45

26.350 25.950 0.400 1.52 0.520 39.33

28.000 27.675 0.325 1.16 0.552 47.01

33.775 33.650 0.125 0.37 0.666 95.08

198
Table 4 Normalized compl iance, EBV , for displacements at the

o’ K specimen edge.

Boundary Collocation

( v=0. 3)

a/W Plane Strain Plane Stress

Finite-Element Solution

(v=0 .3)

Plane Strain Plane Stress

Experiment Results

(v=0.294 or 0.343)

0.3 22.54 24.90 - - 26

0.4 32.80 36.18 - - 37

0.45 40.24 44.23 35.1 38.5 45

0.5 49.72 54.76 49.6 54.5 56

0.6 80.90 89.02 80.6 88.6 89

0.7 152.46 165.48 149.3 164.1 -

0.75 223.3 245.4 221.1 243.0 _

Tabl e 5. Normalized compl i ance

,

EBV^, for displacements at the specimen load line.

a/W

Boundary Collocation

(v=0.3)

Plane Strain Plane Stress

Finite-Element Solution

(v=0. 3)

Plane Strain Plane Stress

Experiment Results

(v=0. 294 or 0.343)

0.3 12.98 14.26 - - 13

0.4 20.78 22.84 - - 21.5

0.45 26.35 28.96 25.7 28.24 27.5

0.5 33.65 36.99 33.0 36.27 36

0.6 57.02 63.32 56.1 61.65 62

0.7 114.24 125.55 110.1 121.0 123

0.75 168.7 185.4 166.2 182.65 .

199
Fig. 1. A finite-element idealization for the Kj compact specimen of Fig. 1.

200
Fig. 2. A finite-element idealization for the Jj

c compact specimen of Fig. 2.

201
T

Fig. 3. Finite-element crack-tip substructure.

202
Fig. 4. Three possible assumptions about pinhole loading.

203
Fig. 5. An alternative Jj compact specimen used at NBS.

204
RELATIVE CRACK LENGTH, a/W

Fig. 6. Finite-element results for the Kj compact specimen of Figure 1.

205
NORMALIZING

PARAMETER

EBV,

RELATIVE CRACK LENGTH, a/W

Fig. 7. Finite-element results for the recommended J T specimen with load-line modification. ic

206
RELATIVE

CRACK

LENGTH,

a/W

0.8

Fig. 8

0.6

0.4

0.2

-— Finite Element,

Collocation Solutions

Experimental Data

o Aluminum * 316 SS

100

NORMALIZED COMPLIANCE, EB8/P

Comparison of numerical and experimental elastic displacement

cal ibrations.

207
PREDICTED

vs.

MEASURED

CRACK

LENGTHS,

<

a

m-ap

)/amXlOO

RELATIVE CRACK LENGTH, a/W

Fig. 9. Relative agreement of numerical and experimental results.

208
Design and Performance of a Ring-Shaped Clip Gage for

Fracture Mechanics Testing

R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

and

J. Shepic

Martin Marietta Aerospace

Denver, Colorado

ABSTRACT

A ring-shaped clip-on displacement gage for fracture mechanics testing is

described. The novel design of this gage offers superior sensitivity and

operating conveniences compared with the conventional double-cantilever beam

type gage referenced in ASTM fracture test standards. The construction of

ring gages for room temperature and cryogenic applications is discussed.

Key Words: cryogenic instruments; displacement gages; fracture mechanics

testing; materials testing; strain gages.

*Sponsored in part by the Office of Fusion Energy, U.S. Department of Energy.

•f* To be published by ASTM Journal of Testing and Evaluation .

?09

INTRODUCTION

Clip-on displacement gages are utilized in all types of fracture

mechanics tests to obtain records of load versus displacement, which provide

the basic data from which resistance to crack extension is evaluated. In

standard tests of bend or compact specimens, for example, displacement is

measured between knife edges at reference points spanning the mouth of the

crack. 1 The clip gage is placed in position and held there by the spring

action of its beams. As the specimen deforms under load, the crack-opening

displacement increases, the gage flexes, the electrical signal is altered, and

the gage is released without damage if the maximum opening range is exceeded

or if the specimen fractures.

The widespread use of clip gages is due to their simplicity, convenience,

and reusability. Clip gages may be purchased or custom built to suit all

kinds of specimens, and they provide a linear output that is adaptable with

analog-digital conversion to computerized testing.

In 1966, Krafft 2 employed a dual-lobed clip-on gage for low-temperature

high-strain-rate tests. At about the same time, NASA researchers 3 "

6 developed

the double-cantilever beam type (DCB) gage. Today the DCB gage is recommended

in ASTM standards 1 for ambient temperature tests. Fowlkes 7 also succeeded in

constructing a DCB type gage for extreme cryogenic environments. The purpose

of this paper is to document the development of a new ring-shaped gage that

represents a departure from the conventional DCB design, with some improvements.

GAGE DESIGN

A 20-mm-diameter ring-shaped clip gage with 5.7-mm travel is shown in

Fig. 1. This new design calls for an aluminum alloy ring-shaped body that is

211
slotted to accept short beams of 17-7 PH stainless steel. The rear of the

aluminum ring is reduced in thickness and provides the bending element onto

which four 350-ft commercial electrical resistance strain gage films are

bonded. Two films are located on the inner diameter and two on the outer

diameter of the ring. The outer films are protected by a stainless steel

guard fixed to the ring with set screws.

In contrast, the conventional DCB gage design consists of a solid block

body that serves as a spacer between two titanium alloy cantilever beams. In

this case, the strain gage films are bonded to the upper and lower beam

surfaces. Thus, the principal differences in the two gage designs lie in the

geometry of the body and the location of the films.

The different designs account for some significant differences in

performance. The DCB gage has two bending elements, whereas the ring gage has

only one. In principle, this should result in superior linearity for the ring

gage, especially for large gages with wide travel. For most applications this

advantage may be academic, however, since moderately sized gages of both

designs are able to meet the linearity requirements of section 6.3.2 of the

ASTM E 399-83 standard. 1 A more obvious practical benefit derives from the

different handling characteristics of these gages, as described in the next

section.

GAGE INSTALLATION

For a conventional Kj

c test, the gage is mounted at the specimen edge,

since this is convenient and since any reference point for displacement

measurement is adequate. In a Jj

c test, however, it is necessary to measure

load-line displacements so that the work done on the specimen can be

calculated from the area under the 1 oad-versus-di spl acement record.

212
Therefore, it is common to recess the knife edges to a position on the load

line. A notch modification for this purpose is shown in Fig. 2.

Unfortunately, modifications such as those shown in Fig. 2 tend to hinder

the installation of conventional DCB gages. It is difficult to depress the

gage beams manually while attempting to attach the beam tips at the knife

edges. Therefore, forceps must be used to position the gages properly. Also,

the strain gage films on the top of DCB beam surfaces are exposed and can be

damaged by the forceps or the specimen.

By virtue of its relatively low spring constant, the ring gage can be

easily installed by squeezing the body of the ring between the thumb and index

finger of one hand. Unlike conventional DCB gages, the beams themselves are

not handled, fingers do not interfere as the beams contact the knife edges,

and there is no risk of damage to the strain gage films during mounting.

In cryogenic tests, operations are more complicated, and the ability to

rapidly mount or demount the clip gage greatly facilitates the transfer and

testing of specimens. Immediately after a J-integral test, the specimen is

still intact and access to the gage from either side is blocked by the clevis

grips (see Fig. 2). Typically the gage and specimen are too frigid to handle,

so the use of forceps is necessary. With ring gages, however, protective

gloves can be worn without compromising dexterity because only light pressure

needs to be applied to the gage body, which is freely accessible.

INSTRUMENTATION

Like the DCB gage, the ring gage employs four strain-gage films wired in

a conventional Wheatstone bridge arrangement. The excitation is provided by a

commerical power supply or by the modular circuitry built into the servo213
hydraulic test machine. The gage output is also conditioned using

conventional circuitry.

For room temperature service, the selection of strain gage films and

wiring techniques are the same as for conventional DCB gages. Cryogenic

applications require additional screening of strain gages and related

materials, as well as proper construction techniques and low-voltage signal

processing.

With ring gages operating in liquid helium at 4 K, a low excitation

voltage of 2.5 Vdc is preferred, because at higher excitation voltages the

noise at 4 K increases disproportionately to the signal output. In Fig. 3,

the degradation of the signal quality is reflected in terms of the correlation

coefficients for the compliance measurements of a cracked compact test

specimen. Compliance is defined as the slope of the elastic displacement

versus load plot. To obtain the data of Fig. 3, five loadings were taken for

a specimen with fixed crack length, and the data were averaged. A correlation

coefficient of 1.0 represents a perfectly linear fit. The data show that as

the excitation voltage exceeds 5 Vdc, the noise becomes especially marked and

unacceptable. This may be due to localized boiling of the helium at the gage

surfaces due to Joule heating.

CRYOGENIC APPLICATIONS

Tests in our laboratory are frequently performed with specimens submerged

in liquid nitrogen or helium. These media are chemically inert, but they

entail problems of thermal cycling, moisture condensation, and freeze-up.

Gage failures may take the form of excessive electrical noise, film debonding,

deterioration of solder joints, or electrical shorting. Excessive electrical

noise may arise from inadequate solder connections, conductive debris on gage

214
surfaces, or other sources, such as electromagnetic radiation. These problems

have been surmounted by proper techniques, so that the ring gages now in

operation have remained in service for more than two years, surviving millions

of fatigue cycles and hundreds of fracture toughness tests at 4 K.

MATERIALS AND CONSTRUCTION TECHNIQUES

Foil resistance strain gages are produced in a wide variety of sizes

and forms, with various active alloy elements. Options include protective

encapsulation, solder dots, integrated terminals, preattached leads, high

endurance leads, stripable backings, and self-temperature compensation. One

vendor boasts forty thousand variations, but not every kind is stocked and' not

every kind of wire element and backing combination works well at all

temperatures

Since strain-gage primers and reference books do not discuss cryogenic

applications, our selection of strain gages for cryogenic applications was

guided by the available 1 i terature 8 " 15 and manuf acturers ' recommendations.

For test temperatures ranging from 300 to 4 K, we selected a ni ckel -chromi urn

alloy having a sel f-temperature-compensated active element and a glass-fiberreinforced epoxy-phenolic resin with a fully encapsulated matrix.

Sel f-temperature-compensating gages were chosen to minimize the apparent

strain that is created when the gage films are bonded to substrates and

cooled. The residual apparent strain that remains after cooling is then

cancelled electrically.

Bondable terminals were used to create a stress-relief point between the

foils and the lead wires to prevent accidental damage when the lead wires are

yanked

215
Commercially available polytetraf 1 uoroethyl ene (PTFE) insulated lead

wires were used. All common insulating materials retain good insulating

properties at cryogenic temperatures . However, such materials are typically

brittle at cryogenic temperatures, and they eventually crack in response to

thermal cycling. Therefore, the greatest problem is mechanical failure

leading to electrical shorts. But PTFE is an exceptional polymer, retaining

several percent ductility at 4 K and offering superior cryogenic flexibility

compared with the polyethylene and polyvinyl chloride insulations, which are

commonly used at room temperature. 16 Noise from electromagnetic radiation was

reduced further by shielding the PTFE-insul ated lead wires with additional

commercial insulation containing a thin wrapping of conductive material.

The choice of solder for cryogenic service was based on composition. All

Pb-Sn solders are ductile at room temperature, but not all retain ductility at

cryogenic temperatures. 17 A small amount of tin is needed to promote wetting

and compatibility with rosin fluxes, but greater amounts cause brittleness at

cryogenic temperatures. The ductile solders for extreme cryogenic service are

the Pb-rich face-centered-cubic alloys. 17 Therefore, we used a 97.5% Pb - 1%

Sn - 1.5% Ag solder composition to connect leads, strain gages, and bondable

terminals. This solder shows improved strength and high ductility at

temperatures down to 77 K. 18

Appropriate adhesives for bonding the strain gages and terminals to the

gage body for cryogenic service are available from the gage manufacturers, as

are cleaners, solders, applicators, and hardware kits.

GAGE CALIBRATION

Calibrations at room and cryogenic temperatures are performed using a

vertical dial micrometer with the clip gage attached to knife edges at the

216
bottom of a rod-in-tube apparatus, as shown in Fig. 4. Calibrations at

cryogenic temperatures are performed after enclosing the gage in a Dewar

covered at the mouth with styrofoam.

Fixed-point calibrations are performed in room-temperature air or in

baths of liquid nitrogen or liquid helium. The corresponding cryogenic

temperatures are 76 and 4 K, respectively, at the atmospheric pressure and

elevation in Boulder, Colorado. Variable temperature calibrations are also

performed in nitrogen or helium vapor. In this case, a thermocouple is

attached to the gage, and calibrations are performed as the Dewar is gradually

warmed or cooled by periodic injections of gas.

Calibration data for a ring gage are shown in Fig. 5. The performance

is desirable in that the gage output is only weakly temperature dependent.

Between 295 and 4 K the calibration may vary by several percent, while the

reproducibi 1 i ty of calibrations at fixed points is typically within ±0.5%.

The calibrations are repeated regularly to check for small changes due to

extended periods of service.

SUMMARY AND CONCLUSION

A clip gage design incorporating a ring-shaped geometry is proposed.

The design is simple and functional and offers sensitivity and linearity

matching or exceeding the conventional double-cantilever-beam gage. Moreover,

the ring gage offers practical advantages for some tests owing to superior

handling characteristics as described in the text. Ring-gages have

demonstrated excellent service life for tests at ambient and cryogenic

temperatures. Cryogenic applications are facilitated by the fact that the

gage calibrations at 295 and 4 K are nearly equivalent.

217
REFERENCES

1. Standard Test Method for Plane-Strain Fracture Toughness of Metallic

Materials, ASTM Designation E 399-83, in: 1983 Annual Book of ASTM

Standards, Section 3, American Society for Testing and Materials,

Philadelphia, 1983, pp. 518-553.

2. Krafft, J. M., A Rate Spectrum of Strain Hardenabi 1 i ty and Fracture

Toughness, in: Report of NRL Progress, Naval Research Laboratory,

Washington, D.C., 1966, p. 6.

3. Fisher, D. M., Bubsey, R. T., and Srawley, J. E., NASA Tech Note D-3724,

1966.

4. Brown, W. F., Jr. and Srawley, J. E., Fracture Toughness Testing and Its

Applications, ASTM STP 381, American Society for Testing and Materials,

Philadelphia, 1965, pp. 133-196.

5. Brown, W. F., Jr. and Srawley, J. E., Plane Strain Crack Toughness

Testing of High Strength Metallic Materials, ASTM STP 410, American

Society for Testing and Materials, Philadelphia, 1966, pp. 1-129.

6. Bubsey, R. T., Fisher, D. M., Jones, M. H., and Srawley, J. E.,

Compliance Measurements, in: Experimental Techniques in Fracture

Mechanics, A. S. Kobayashi, Ed., Iowa State University Press, Ames, Iowa,

and Society For Experimental Stress Analysis, Westport, Connecticut,

1973, pp. 76-93.

7. Fowlkes, C. W. and Tobler, R. L., Fracture Testing and Results for a Ti-6A1-4V Alloy at Liquid Helium Temperature, Eng. Fract. Mech., 8^ 1976,

pp. 487-500.

8. Gillette, 0. L., Strain Gages at Cryogenic Temperatures , ISA Journal,

1964, pp. 51-54.

9. Wnuk, S. P., Jr., Strain Gages for Cryogenics, ISA J., 1964, pp. 67-71.

10. Kaufman, A, Investigation of strain Gages for Use at Cryogenic

Temperature, Exp. Mech., _3> No. 8, 1963, pp. 177-183.

11. Silbert, L., Meyer, H. E., and Van Beek, W. M., Strain Gage Development

Program, Test Report 826-2003 May 1976, Martin Marietta, Denver,

Colorado, pp. 131.

12. Telinde, J. C., Strain Gages in Cryogenic Environment, Exp. Mech., _10,

1970, p. 394.

13. Walstrom, P. L., Strain Gages for Superconducting Magnet Testing,

Cryogenics, 9_, 1980, p. 509.

14. Freynik, H. S., Jr., Roach, D. R., Deis, D. W., and Hirzel, D. G.,

Evaluation of Metal-Foil Strain Gages for Cryogenic Application in

Magnetic Fields, Adv. Cryog. Eng., 24-, 1978, p. 473.

218
15. Sparks, L. L., Temperature, Strain, and Magnetic Field Measurements,

Chapter 14, in: Materials at Low Temperatures, R. P. Reed and A. F. Clark, Eds., American Society for Metals, Metals Park, Ohio, 1983, pp.

515-571.

16. Mathes, K. N., Electrical and Mechanical Behavior of Polymers at Cryogenic Temperatures , SPE Journal, 20_, No. 7, 1964, pp. 643-637.

17. Kalish, H. S., and Dunkerley, K. J., The Low Temperature Properties of

Tin and Tin-Lead Alloys, Trans. AIME, 180 , 1949, pp. 637-656.

18. Kaufman, A. B., Selecting Solders for Low Temperature Service, Mater.

Des. Eng., 48, No. 6, 1958, pp. 114-115.

219
List of Figures

Figure 1

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Design of a ring-shaped clip gage.

A ring-shaped clip gage and compact specimen with recessed notch

used in J-integral fracture toughness testing.

Effect of excitation voltage on noise level at 4 K. (The noise

decreases the correlation coefficient of the di spl acement-versusload plot for a compact specimen with a stationary crack.)

Cryogenic gage calibration apparatus.

Temperature dependence of the calibration factor for a ring-shaped

clip gage.

220
Figure 1. Design of a ring-shaped clip gage.

221
Figure 2 A ring-shaped clip gage and compact specimen with recessed notch

used in J-integral fracture toughness testing.

222
SPECIMEN

COMPLIANCE

(S/P)

CORRELATION

COEFFICIENT

1.000

0.998

0.996

0.994

0.992

0.990

2 3 4 5 6

EXCITATION VOLTAGE, V

Figure 3. Effect of excitation voltage on noise level at 4 K. (The noise

decreases the correlation coefficient of the di spl acement-versusload plot for a compact specimen with a stationary crack.)

223
Figure 4. Cryogenic gage calibration apparatus.

224
CALIBRATION

FACTOR,

mm/V

TEMPERATURE, K

Figure 5. Temperature dependence of the calibration factor for a ring-shaped

clip gage.

225

PER

CENT

CHANGE

FROM

295

K

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF

MECHANICAL PROPERTY TEST STANDARDS

TO LIQUID HELIUM TEMPERATURE (4 K)*

Metal Properties Council

Low Temperature Task Group

Proposal Statement of Work

1 / 8/84

*This proposal was written and approved by the Low Temperature Task Group of

the Metal Properties Council. NBS guidelines for the use of SI units were

not followed.

227

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF

MECHANICAL PROPERTY TEST STANDARDS

TO LIQUID HELIUM TEMPERATURE (4 K)

Introduction

There has been recent emphasis on the use of superconducting magnets to

constrain and direct plasma flow in fusion and magneto hydrodynamic (MHD)

energy experiments. The high magnetic fields necessary for plasma confinement

create large forces that must be restrained by the magnet support structure.

This places emphasis on sound structural design and dependable material

properties at liquid helium temperature. Prototype magnet structures, ever

increasing in size, continue to be designed and built. Although most magnets

have operated successfully over their brief experimental lifetime, there has

recently been a structural failure reported at the Tullahoma, Tennessee MHD

magnet.

Currently, there are no standardized mechanical property test procedures

for use at liquid nitrogen (77 K, -320°F) temperatures or below. Mechanical

testing at liquid helium (4 K, -452°F) temperatures involves unique

conditions, compared to room temperature. At 4 K, the thermal conductivity of

metals and alloys is considerably reduced (usually several orders of

magnitude) and the specific heat is tending toward zero. Consequently, when

work is done on the specimen during testing, the resultant internal heat is

not easily removed from the specimens. Heating within the specimen tends to

be localized and heat transfer is difficult. This is commonly referred to as adiabatic heating. Serrated yielding is produced during tensile tests. Each

serration results from localized specimen yielding and temperature increases

greater than 50 K have been recorded. Typical stress-strain curves for an austenitic stainless steel at room temperature, 195, 76, and 4 K are shown in

Figure 1. Special attention must be paid to strain rates and the cooling

media, to ensure maintenance of test temperature in the specimen.

It is expensive to use liquid helium. The capital costs of an efficient

cryostat, the liquid costs, and the special handling, storage, and transfer

costs associated with liquid helium add complexity and expense. Additionally,

the strength of most metals and alloys increases at lower temperatures,

requiring the use of larger loading trains if the room temperature specimen

size is maintained. For strong alloys, load capacities of pull rods, grips.

229
and cryostat would have to exceed 100,000 lbs. It is not efficient and is

much too costly to design such large-capacity test systems and, to date, none

in the world exist. Instead, typically 20,000 - 50,000 pound capacity tensile

cryostats are used in testing at 4 K. Therefore, assessment is needed of the

consequences of using reduced specimen sizes when testing at low temperatures.

The research described in the following sections is necessary to produce

the information required to extend existing room temperature mechanical

property testing standards to low temperature (77 K) . Proposals are hereby

solicited, to perform the work described. Proposals which do not address all

the tasks will be given equal consideration and the work described here may be

divided among more than one contractor.

Task I. Internal Specimen Heating

A. Experimental: Strain Rate Effects

At ambient temperature, specimen heating induced during straining in a tensile test is relatively small, on the order of a few degrees at strain

rates normally used. As the test temperature decreases, in most materials,

the specific heat decreases, and the temperature rise will be greater than at room temperature for the same amount of work. Similarly, thermal conductivity

decreases in most materials and, therefore, any additional heating is slower

to dissipate. These effects become increasingly pronounced as the test

temperature is decreased until at 4 K (-452°F), if tensile tests are performed

at strain rates commonly used at room temperature, substantial temperature

increases are observed, possibly on the order of 50 K (100°F). The magnitude

of this effect varies from one type of material to another and may even vary

within materials of nominally the same composition. Temperature increases

during testing are believed to lower the measured yield and ultimate strength

and probably increase elongation and reduction in the area.

Notice, for example, the effect of strain rate on two austenitic

stainless steels^ at 4 K (-452°F), shown in Figures 2 and 3. The 304L alloy

is metastable and martensite forms during plastic deformation; the 310S alloy

‘'‘From the research of Dr. K. Ishikawa, National Research Institute for Metals,

Isukuba, Japan (1983).

230
is stable and no martensite forms during straining. Increasing the strain

-5 -1 -2 -1

rate from 3.3 x 10 s to 3.3x10 s reduces the amplitude of the discontinuous yields and increases the amount of internal specimen heating from periodic

jumps of 55 K to continuous increases of 150 K. The ultimate strength is

reduced almost 40 percent and the elongation increased about 20 percent as the

strain rate is increased. Clearly, the effect of strain rate is very significant.

It is necessary to assess the magnitude of strain rate effects at very

low temperatures in order to:

1. Determine a maximum strain rate 'for tensile tests which will produce

mechanical property data that accurately reflect reliable material

properties at the test temperature.

2. Assure that data generated in different laboratories is directly

comparabl e.

The materials of interest in this study are: 1) austenitic stainless

steels, 2) aluminum alloys, and 3) copper. Testing is to be performed at

4.2 K (-452°F), 77 K (-320°F) and 295 K (room temperature) . The test environments are liquid helium, liquid nitrogen, and air, respectively.

The magnitude of strain-induced heating in the candidate materials at the

temperatures of interest is to be assessed. Several materials including one stable and one metastable austenitic stainless steel, one austenitic stainless

steel weld, one aluminum and one copper alloy should be tested. A minimum of

three and preferably four strain rates, not exceeding those given in appropriate ASTM standards, are needed to clarify dynamic heating conditions. Each

specimen shall be instrumented to record internal specimen temperature con- tinuously during testing. Only two replicate specimens are required of each

test condition. See Table 1 for a list of test conditions. Although the

proposer is free to suggest modification to this schedule. Stress-strain

curves should be recorded and tensile properties should be measured as a function of strain rate. Standard low temperature cylindrical specimens

should be used.

231
The proposal should clearly state the intended strain rates, the method

of temperature measurement, the method of strain measurement, and the method

of obtaining and maintaining the proper test environment. The specimens to be

used in the investigation should be described in the proposal.

Materials used in this program should be adequately characteri zed prior

to the start of testing. This includes measurement of grain size, hardness

and chemistry. The proposer should indicate where and how the material for

testing will be obtained.

Post-test examinations should be used to correlate experimental results

with physical changes which may take place during testing. As a minimum, some metallography and fracture surface examinations should be conducted for this

purpose. The proposer should suggest the extent of post-test examinations to

be conducted.

B . Model Development: Effects of Strain Rate and Cooling Media

Cryogenic tensile tests carried out in a liquid media have the advantage

of relatively good heat transfer characteristics between the specimen and

liquid. Tests, which are conducted at temperatures other than those for which

a common cryogenic liquid is available, require a cold gas as the cooling

medium. Because of the relatively poor heat transfer of gases as opposed to

liquids, the internal heating effects in gaseous environments are magnified.

The heat transfer characteristics of the gases, thermal conductance of the

specimen, and heat capacity of both the specimen and gas change with temperature.

An experimental program to assess all of the variables could be very

large. Because the specimen geometry is simple and the physical properties of

the materials relatively well known, this task lends itself to analytical

modeling. A model should be developed or adopted to predict the internal

specimen heating in terms of gas, liquid, and alloy thermal conductivity;

alloy and cooling media heat capacity; specimen load and strain rate; and

temperature.

232
This model should be correlated with the strain rate experiments of Test

Program IA and predict the increase of internal specimen heating as a function

o< cooling media. A few measurements should be conducted in other media

(gaseous helium and nitrogen) to verify the model. The proposer should

suggest a verification test matrix. This model should then be used to suggest

a standard tensile test procedure for testing in gaseous environments.

Task II. Subsize Specimen Use: Effects of Grain Size

When testing polycrystalline metals and alloys at low temperatures, it is

advantageous to use reduced specimen sizes. Reduced specimen sizes are necessary to minimize coolant usage and to conserve loading capacity (since

material strengths are typically 2-3 times greater than at room temperature).

The major deterrent to the use of smaller specimens is the effect of grain

size, in relation to specimen size, on strength, ductility and other property

variability. Specimens must contain a representative number of grains per

cross-section to ensure the absence of anisotropic crystal 1 ographi c influence

on material strength and ductility. Therefore, research must be conducted to assess the influence of grain size on properties of common structural alloys

used in cryogenic service.

The research should characterize the effects of grain size on tensile

yield strength, ultimate strength, elongation, and reduction of area. The

standard ASTM E-8 tensile bar specimen and two reduced bar specimens (suggested

1/8 and 1/4 inch diameter) should be compared. Grain size should vary over at

least 1.5 orders of magnitude. Strain rate should be held constant (0.02

in/in/min is suggested). Test temperatures should include 4, 77, and 295 K. Alloys must include one austenitic stainless steel, one austenitic stainless

steel weld, one aluminum alloy and one copper alloy. Special attention must

be given to the method for obtaining grain size variation to ensure the same degree of prepared orientation for each grainsize. The proposal should state

how grain size and orientation will be achieved in each specimen.

As in IA of this request for proposal, the proposer should describe the

specimen to be used and the pre- and post-test material characteri zations

requi red

233
This model should be correlated with the strain rate experiments of Test

Program IA and predict the increase of internal specimen heating as a function

of cooling media. A few measurements should be conducted in other media

(gaseous helium and nitrogen) to verify the model. The proposer should

suggest a verification test matrix. This model should then be used to suggest

a standard tensile test procedure for testing in gaseous environments.

Task II. Subsize Specimen Use: Effects of Grain Size

When testing polycrystalline metals and alloys at low temperatures, it is

advantageous to use reduced specimen sizes. Reduced specimen sizes are necessary to minimize coolant usage and to conserve loading capacity (since

material strengths are typically 2-3 times greater than at room temperature).

The major deterrent to the use of smaller specimens is the effect of grain

size, in relation to specimen size, on strength, ductility and other property

variability. Specimens must contain a representati ve number of grains per

cross-section to ensure the absence of anisotropic crystal 1 ographic influence

on material strength and ductility. Therefore, research must be conducted to assess the influence of grain size on properties of common structural alloys

used in cryogenic service.

The research should characterize the effects of grain size on tensile

yield strength, ultimate strength, elongation, and reduction of area. The

standard ASTM E-8 tensile bar specimen and two reduced bar specimens (suggested

1/8 and 1/4 inch diameter) should be compared. Grain size should vary over at

least 1.5 orders of magnitude. Strain rate should be held constant (0.02

in/in/min is suggested). Test temperatures should include 4, 77, and 295 K. Alloys must include one austenitic stainless steel, one austenitic stainless

steel weld, one aluminum alloy and one copper alloy. Special attention must

be given to the method for obtaining grain size variation to ensure the same degree of prepared orientation for each grainsize. The proposal should state

how grain size and orientation will be achieved in each specimen.

As in IA of this request for proposal, the proposer should describe the

specimen to be used and the pre- and post-test material characterizations

requi red.

234
Table 1 Suggested Test Matrix for

Part IA

Material

s

Strain Rates Repl ications Temperatures

Stainless Steels 1.0x10”? in/s 2 4 K

a) Stable Austenitic 1 .0x10 4 in/s 77 K

b) Metastable Austenitic 1.0xl0”r in/s 295 K

Copper 1 . 0xl0”

D in/s

A 1 umi num

Total Number of Tests r 4 x 4 x 2 x 3 = 96

235
Stress,

cr

(GPa)

Figure 1. Typical stress-strain curves at low temperatures

of AIS I 300 series austenitic stainless steels.

236

Stress,

cr

(ksi)
T T T

150 - 310S

liq. He „ , 33 x 10 s

60

50

40

30

20

10

4

Figure 2. Stress-strain curves at liquid helium temperatures of

AISI 310 at three strain rates. Lower data, indicated

by T in lower figures, represents temperature rises

associated with the total drops.

237

Temperature

(K)
Stress

(kg/mm

CN]

150

100

50

4

OJ

5-4 D

4-1

<uQ.E

0) E-i

Figure 3. Stress-strain curves at liquid helium temperatures of

AISI 304L at three strain rates. Lower data, indicated

by T in lower figures, represents temperature rises

associated with the total drops.

70

- 60

- 50

. 40

- 30

. 20

• 10

- 4

238

Temperature

(K)
WELDMENTS AND CASTINGS

239
*
WELDMENTS AND CASTINGS PROGRAM

LEADER: T. A. Siewert (After April 1, 1984)

STAFF: H. I. McHenry, P. T. Purtscher, NBS

OBJECTIVES:

(1) To investigate the metallurgical factors that affect the mechanical

properties of stainless-steel weldments and castings at cryogenic

temperatures

(2) To contribute to the development of improved filler metals for

welding stainless steels for liquid-helium service.

(3) To evaluate the mechanical properties of weldments and castings at

4 K. (4) To develop methods of detecting defects and evaluating their

significance in stainless-steel weldments.

RESEARCH PAST YEAR (1983)

(1) The fracture toughness of 25Mn-5Cr weldments produced by three

different welding processes was measured at 4 K. (2) The tensile properties and fracture toughness of E320LR filler

metal were measured at 4 K. (3) Tensile tests were conducted on large-scale stainless steel

weldments with the weld reinforcement in place.

(4) Fatigue crack growth rates were measured at 4 K on CF8M castings

with varying ferrite content.

(5) Mechanical properties testing at 4 K in support of superconducting

magnet design and construction continued.

RESEARCH THIS YEAR (1984)

(1) The tensile properties and fracture toughness of weldments produced

by selected welding processes will be measured at 4 K. (2) An evaluation of fully austenitic weld metals with low sulfur and

phosphorus contents will be initiated.

(3) A series of stainless steel welds with varying oxygen contents will

be produced.

(4) Mechanical property testing at 4 K in support of superconducting

magnet design and construction will continue.

241
Summary

of

Mechanical

Property

Measurements

of

Welds o o 00 CO cn cn

00>1o o oI I CO CO

oo oo o o LO LO cE

13c c c Z Z o o

vo oo

LO 00 LO «—< LO LO

242

Properties

listed

by

year

in

this

table

may

be

located

in

"Materials

Studies

for

Magnetic

Fusion

Energy

Applications

at

Low

Temperatures"

as

follows:

1978,

Vol. I,

NBSIR

78-884;

1979,

Vol.

II,

NBSIR

79-1609;

1980,

Vol.

Ill,

NBSIR

80-1627;

1981,

Vol.

IV,

NBSIR

81-1645;

1982,

Vol. V,

NBSIR

82-1667;

1983,

Vol.

VI,

NBSIR

83-1690;

1984,

Vol.

VII,

NBSIR

84-3000.
FRACTURE TOUGHNESS OF 25MN AUSTENITIC STEEL WELDMENTS AT 4 K*

Y. W. Cheng, H. I. McHenry, and P. N. Li

National Bureau of Standards

Boulder, Colorado 80303

T. Inoue and T. Ogawa

Nippon Steel Corporation, Kawasaki, Japan

ABSTRACT

The fracture toughness of 25Mn steel weldments was measured at 4 K using

the single-specimen J-integral procedure. The highest J value obtained was

from the gas-tungsten-arc weld, followed by the shielded-metal-arc weld; the

submerged arc weld had the lowest J value. Degradation of fracture

toughness of the heat-affected zone was observed because of carbide

precipitation along the grain boundary.

*Published in Advances in Cryogenic Engineering - Materials , vol. 30, Plenum

Press, New York (1984), pp. 303-310.

^Guest Worker; on leave from East China Institute of Chemical Technology,

Shanghai, China.

243
/
INTRODUCTION

In recent years, there has been an increased interest in the

study of replacing nickel with manganese in steels for cryogenic

applications. 1 2 The driving force behind this interest stems

from the relative price of manganese and nickel. Nickel is an important element in steels for cryogenic applications, such as 5%

nickel steel, 9% nickel steel, and the AISI 300-series austenitic

stainless steels.

One of the high-manganese steels developed for cryogenic

applications is the 25Mn-5Cr-lNi steel. Previous studies indicate

that this steel has desirable cryogenic properties, i.e., high

strength and high toughness, 2 4 low thermal expansion coef f icient

,

b and stable austenitic microstructure. 2 4 Filler metal with nearly

matching composition has also been developed. 2 This paper presents

the results of a weldability study in which fracture toughness

measurements of the 25Mn-5Cr-lNi steel weldments were performed in

liquid helium at 4 K.

MATERIALS

The test weldments were 27-mm-thick plates welded by three

different welding processes in the flat position: shielded-metal

arc (SMA) , submerged arc (SA) , and gas-tungsten arc (GTA) welding

245
processes. The welding parameters and joint preparation are given

in Figure 1. For GTA and SA weldments, the joints were deep

U-grooves with a 30° included angle. The grooves were filled with

weld metals. The welds were then back-gouged right underneath the

previous welds to a depth of 15 mm and filled with weld metals.

So the weld contours outlined with solid and dashed lines (Figure 1) were on top of each other and overlapped at mid- thickness of the

plates. The welds were x-ray inspected and no detectable flaws were found. The chemical compositions and tensile properties at

4K4 of the weld metals are presented in Tables 1 and 2.

EXPERIMENTAL PROCEDURES

Fracture toughness of the 25 . 4-mm-thick compact tension (CT)

specimens was measured with the J-integral method. 6 Tests were conducted in liquid helium at 4 K using a cryostat described by

Fowlkes and Tobler. 7 The single-specimen unloading-compliance

technique 6 was used to measure J-Aa (crack extension) resistance

curves. The J-Aa curves were then used to determine J T . The

X c plane strain fracture toughness estimate, K (J) , was calculated

from J using the following relation: 6

K

Ic

(J) ( 1 )

At 4 K, Young's modulus, E, was taken to be 190 GPa, and Poisson's

ratio, v, was taken as 0.274. 6

For GTA and SA welds, the notches were at the center of the

weld metal. For SMA welds, the notches were at the fusion line,

in the heat-affected-zone (HAZ—2 mm from the fusion line) , and in

process

groove

current, voltage &

rate

150A-25V-8/10 cm/min.

4.0 0

DCRP

500A-34V-35cm/min.

4.0 0, coil

flux: Mg0-Si02-CaF2

250A-15V-10cm/min.

2.4 0

Ar shielding

Fig. 1. Welding parameters; dimensions are in millimeters.

246
Table 1. Chemical Composition of Weld Metals (wt.%)

C Si Mn P S Ni Cr Mo Fe

GTA 0.156 0.13 26.55 0.003 0.006 3.15 6 . 44 1.18 bal

SMA 0.224 0.54 26.68 0.006 0.002 3.02 7.24 1.11 bal

SA 0.19 0.46 25.86 0.008 0.004 2.94 7.19 1.05 bal.

Table 2. Tensile Properties of 25Mn Steel at 4K4

0 . 2%YS UTS %EL

MPa MPa

Base Metal 894 1525 49

Weld Metal (SMA) 962 1338 35

the weld metal (3 mm from the fusion line) . The specimen locations

and orientations are shown in Figure 2.

RESULTS AND DISCUSSION

The results of the fracture toughness tests at 4 K are summarized in Table 2. The materials tested were ranked in

descending order in terms of fradture toughness: GTA weld metal,

SMA fusion line, SMA weld metal, SMA HAZ , and SA weld metal. The

Jj value of the SMA weld metal in the present study was 86%

higher than that of a previous report (119 kJ/m2 vs. 221 kJ/m2 ).

4

Fig. 2. Specimen locations

and orientations:

left: GTA and SA;

right: SMA.

247
CRACK EXTENSION, Aa, in

crack extension, Aa, mm Fig. 3. J-Aa curves of weld metals.

Table 3. Fracture Toughness of 25Mn Steel Weldments at 4 K.

Type Crack Position J

T

* Ic

kJ/m2

Kt

’ Ic

MPa/m

GTA Weld Metal 258 230

SA Weld Metal 139 169

SMA Weld Metal 221 213

SMA Fusion Line 232 218

SMA HAZ 140 169

Base Metal T-L 280 242

The reason for the discrepancy is not clear. The fracture toughness

of the 25Mn steel weldments compared favorably with austenitic

stainless steel weld metals of the AISI 300 series (Fe-Cr-Ni

steels) .1® 12

Effects of Welding Process

As shown in Table 3 and Figure 3, the GTA weld metal not only

has the highest value, but its J-Aa curve has the steepest

slope. This is indicative of high resistance to both crack

initiation and ductile tearing. The SA weld metal has the poorest

248
. SA Weld Metal . 10^m

(a)

SA Weld Metal

(b)

Fig. 4 Typical fracture surface of weld metal fractured in a ductile manner.

resistance to crack initiation and ductile tearing. The variation

in fracture toughness among weld metals produced by different

welding processes has been attributed to the cleanliness of the

weld metal. 13 Of the welding processes studied, the GTA and the

SA processes are expected to produce the "cleanest" and the

"dirtiest" welds, respectively.

All the fracture surfaces of weld metals, as revealed by

scanning electron microscope, were typical of weld metal fractured

in a ductile manner. Dimples were the predominant feature on the

fracture surface, as shown in Figure 4. Small nonmetallic

inclusions, about 2ym or smaller, were usually present at the

centers of the dimples.

Effects of Crack Location in Weldment

In addition to weld metal, fracture toughness was also

measured at the fusion line and in the HAZ for the SMA weldment.

Table 2 and Figure 5 show that the fusion line and weld metal had

similar fracture properties. However, the fracture toughness,

Jj.^, of HAZ was degraded by 37%.

Metallographic examination showed excessive grain boundary

precipitation in HAZ, which were identified as niobium carbide.

The grain boundary precipitation caused the specimens to fracture

in an intergranular fracture mode, as shown in Figure 6. Fractographic examination also showed defect-like inclusions in the HAZ,

as shown in Figure 7.

249
CRACK EXTENSION, Aa, in

CRACK EXTENSION, Aa, mm

Fig. 5. J-Aa curves of SMA weldments.

It should be noted that the fracture surfaces of both the SMA

weld metal and SMA fusion line consisted of weld metal and base

metal because of the weld joint design. The major portion of the

fracture surface of weld metal specimens was weld metal. The reverse was true for fusion line specimens.

CONCLUSIONS

1. The J values of GTA, SMA, and SA welds are 258, 221, and

119 kJ/m2

, respectively. The higher fracture toughness of some welds tested is attributed to fewer nonmetallic inclusions.

2. For the SMA weldment, the J value of the material along the

fusion line is similar to that of the weld metal (221/kJ/m2 ).

However, the J T value of HAZ is much lower, only 140 kJ/m2

. 1 c The degradation of fracture toughness of the HAZ is due to

excessive carbide precipitations along the grain boundaries,

resulting in an intergranular fracture.

ACKNOWLEDGMENT

The Department of Energy, Office of Magnetic Fusion Energy

supported this study. P. Purtscher of NBS contributed the metallographic and f ractographic examinations.

250
. 25QHm 40/im

Fig. 6 Fracture surface of Fig. 7 Fracture surface

SMA HAZ. Intergranular of SMA HAZ . Defectfracture is evident. like inclusions are present in the HAZ.

REFERENCES

1. J. Charles, A. Berghezan and A. Lutts, High-manganese-aluminum

steels for cryogenic applications: The Fe-30Mn-8A£-(0-l)C

alloys, in: "Proceedings of the International Cryogenic

Materials Conference," Butterworths , London (1983),

pp. 360-363.

2. H. Yoshimura, M. Masumoto, and T. Inoue , Properties of lowcarbon 25Mn-5Cr-lNi austenitic steel for cryogenic use, in

"Advances in Cryogenic Engineering Materials," Vol. 28,

Plenum Press, New York (1982), pp. 115-125.

3. H. Yoshimura, T. Shimizu, H. Yada, and K. Kitajima, Toughness

of high manganese-chromium austenitic steels at liquid

helium temperature, Trans. Iron Steel Inst. Jap. 20:187

(1980)

4. H. I. McHenry, J. W. Elmer, and T. Inoue, Fracture properties

of a 25Mn austenitic steel and its welds at 4 K, in:

"Materials Studies for Magnetic Fusion Energy Applications

at Low Temperatures-V , " R. P. Reed and N. J. Simon, eds.,

NBSIR 82-1667, National Bureau of Standards, Boulder,

Colorado (1982), p. 245.

5. H. Yoshimura, N. Yamada, H. Honma, and T. Ito, Microstructures,

low temperature toughness and thermal expansion coefficients

of high manganese-chromium austenitic steels, Trans. Iron

Steel Inst. Jap . 16:98 (1976).

6. ASTM designation: E813-81, standard test for J , a measure of

fracture toughness, in: "Annual Book of ASTmS tandards

,

251
Part 10," American Society for Testing and Materials,

Philadelphia (1982), pp. 822-840.

7. C. W. Fowlkes and R. L. Tobler, Fracture testing and results

for a Ti-6A5,-4 alloy at liquid helium temperature, Eng . Fract. Mech . 8:487 (1976).

8. D. T. Read, The computer-aided J-integral test facility at

NBS , in: "Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures-III" , R. P. Reed, ed .

,

NBSIR 80-1627, National Bureau of Standards, Boulder,

Colorado (1980), p. 205.

9. H. M. Ledbetter and M. W. Austin, Elastic constants of an Fe-5Cr-26Mn austenitic steel, 76-400 K, in: "Materials

Studies for Magnetic Fusion Energy Applications at Low

Temperatures-VI , R. P. Reed and N. J. Simon, eds., NBSIR

83-1690, National Bureau of Standards, Boulder, Colorado

(1983), p. 181.

10. J. W. Elmer, H. I. McHenry, and T. A. Whipple, Strength and

toughness of fully austenitic stainless steel filler metals

at 4 K, in: "Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures-IV, " R. P. Reed and

N. J. Simon, eds., NBSIR 81-1645, National Bureau of

Standards, Boulder, Colorado (1981), p. 289.

11. D. T. Read, H. I. McHenry, P. A. Steinmeyer, and R. D. Thomas,

Jr., Metallurgical factors affecting the toughness of 316L

SMA weldments at cryogenic temperatures. Weld. J. Res . Suppl. 59:104s (1980)

12. T. A. Whipple, H. I. McHenry and D. T. Read, Fracture behavior

of ferrite-free stainless steel welds in liquid helium,

Weld. J. Res. Suppl. 60:72s (1981).

13. T. A. Whipple and D. J. Kotecki, Weld process study for 316L

stainless steel weld metal for liquid helium service, in:

"Materials Studies for Magnetic Fusion Energy Applications

at Low Temperatures-IV," R. P. Reed and N. J. Simon, eds.,

NBSIR 81-1645, National Bureau of Standards, Boulder,

Colorado 80303 (1981), p. 303.

252
TENSILE PROPERTIES AND FRACTURE TOUGHNESS OF

320LR SMA WELD METAL AT 4 K*

Y. W. Cheng

Fracture and Deformation Division

National Bureau Of Standards

Boulder, Colorado

T. A. Siewert

Alloy Rods, Inc.

Hanover, Pennsylvania

ABSTRACT

The tensile properties and fracture toughness of 320LR fully austenitic

stainless steel weld metal, produced by the shiel ded-metal -arc process, were measured in liquid helium at 4 K. The preliminary results showed that yield

strength and ultimate tensile strength of the 320LR weld metal are 8 and 12

percent lower, respectively, than the lower bound of the published data for

316L fully austenitic stainless steel weld metal, while values of fracture

toughness are similar for the two weld metals.

Key Words: Austenitic stainless steels; cryogenic properties of materials;

fracture toughness; J-integral; microfissures; tensile properties;

wel dments

Contribution of NBS; not subject to copyright.

253

INTRODUCTION

It is well known that microfissures are usually present in fully

austenitic stainless steel welds. To avoid microfissures, a small fraction of

ferrite is desirable in austenitic stainless steel welds [1]. However, there

are two properties of ferrite that are undesirable for applications in the

construction of superconducting magnets. First, ferrite is brittle at low

temperatures, which is one of the factors degrading the fracture toughness of

austenitic stainless steel welds [2]. Second, ferrite is f erromagnetic , which

enhances the forces in the magnetic field.

Therefore, superconducting magnet applications require ferrite-free

austenitic stainless steel welds. This is usually accomplished by choosing

chemical compositions for filler metals that will produce fully austenitic

stainless steel welds, according to the Delong diagram [3].

To reduce or eliminate microfissures in the welds, levels of residual

impurities, such as sulfur and phosphorus, are kept to a minimum. This is

based on the theory that microfissures occur as a result of the segregation of

residual impurities at the grain boundary during the solidification process [4].

The 320 electrode contains up to 32 to 36 weight percent nickel and will

produce fully austenitic stainless steel welds. The most common application

of this electrode is to weld alloys for use in highly corrosive environments.

To reduce the microf i ssuring tendency, the LR (low-residual) grade is

introduced. Because the 320LR electrodes produce welds that meet the

requirements for superconducting magnet applications in terms of being free of

ferrite and microfissures, the objective of this study was to measure their

tensile properties and fracture toughness at 4 K, values that are not

255
currently available. The results are compared with those of the more commonly

used 316L fully austenitic weld metal.

MATERIALS

The test weldment was a 25.4-mm-thick plate of 304L stainless steel

welded with a 320LR electrode. The welding was done by the manual shieldedmetal-arc (SMA) process in the flat position. The welding parameters and

joint design are given in Figure 1. The joint had a 12.7-mm root gap and a

45° bevel. It was filled with one full layer, three split layers, five triple

layers, and three quadruple layers, using 95 A and 21 V with reverse polarity.

The chemical compositions of 320 electrodes, as specified in AWS A5.4-78, and

320LR electrodes, as specified by the manufacturer, are summarized in Table 1.

EXPERIMENTAL PROCEDURES

Tensile properties were measured in the longitudinal weld direction (all

weld metal) using a 6.35-mm-diameter, 50.8-mm-gage-length specimen (one

specimen). The specimen was instrumented with electrical resistance strain

gages in the gage section for strain measurements. The test was conducted in

liquid helium at 4 K using a cryostat similar to that described by Reed [5],

-4

The strain rate was 4.2 x 10 /s in the low elongation range for determination

_3

of 0.2% offset yield strength (o^) and then was increased to 4.2 x 10 /s to

expedite the test. The increase in strain rate is not expected to affect the

test result because ultimate tensile strength (UTS) is insensitive to the

strain rate within the test range. Young's modulus (E) was determined from

the linear portion of the stress-strain curve of the tensile test. The

location of the weld tensile specimen within the fusion zone is shown in

Figure 1.

Fracture toughness of 25.4-mm-thick compact tension (CT) specimens (two

specimens) were measured with the J-integral method [6]. The location and

256
orientation of the specimens are shown in Figure 1. Tests were conducted in

liquid helium at 4 K using a cryostat described by Read and Tobler [7]. The

single-specimen unloading-compliance technique [8] was used to measure J-Aa

(crack extension) resistance curves. The J-Aa curves were then used to

determine J

T

. The plane strain fracture toughness estimate, K. (J), was

calculated from Jj

c using the following relation [6]:

Poisson's ratio, v, was taken to be 0.3, and Young's modulus, E, was

determined in the present study.

EXPERIMENTAL RESULTS AND DISCUSSION

Tensile properties and fracture toughness results at 4 K are summarized

in Table 2. For comparison, properties of the more commonly used fully

austenitic 316L weld metal [9] are also presented in Table 2. The 316L

electrode contains 11 to 14 weight percent nickel, and is produced by the SMA

process with welding conditions similar to those of the present study.

Fracture toughness of the 320LR weld metal is comparable to that of the fully

austenitic 316L weld metal. The results for elongation (EL) and reduction of

area (RA) also fall within the scatter band of the 316L weld metal data.

Visual examination of fracture surfaces revealed no indications of welding

flaws.

Young's modulus of the 320LR weld metal at 4 K is about 22% lower than

that of 316 stainless steel plates owing to a higher nickel content (Invar

effect) and texture in the weld [10,11]. The yield strength and ultimate

tensile strength of the 320LR weld metal are 8 and 12 percent lower,

respectively, than the lower bound of the published data for 316L weld metal.

( 1 )

257
Note that there was only one tensile test in this study because of material

unavailability. Based on analysis of the data in Reference 9, the data

scatter estimates for well -control 1 ed weldments (with respect to welding

parameters) and testing conditions are ±15 percent for yield strength and ±10

percent for ultimate tensile strength of the mean value. For a better

characterization and for confirmation of the observed lower strengths of the

320LR weld metal, additional tensile tests are desirable.

The 320LR electrode costs more than the 316L electrode, owing to a higher

nickel content and lower levels of residual elements. At 4 K, it has a

comparable fracture toughness, and possibly lower yield and ultimate tensile

strengths. Considering its higher cost and possibly lower strength, the 320LR

weld metal appears less attractive for use in superconducting magnet designs

than 316L.

SUMMARY

Tensile properties and fracture toughness of 320LR fully austenitic

stainless steel weld metal, produced by the shielded-metal-arc process, were

measured in liquid helium at 4 K. The preliminary results show that yield

strength and ultimate tensile strength of the 320LR weld metal are 8 and 12

percent lower, respectively, than the lower bound of the published data for

316L fully austenitic stainless steel weld metal, and values of fracture

toughness are similar for the two weld metals. Considering its higher cost

and possibly lower strength, the 320LR weld metal appears less attractive for

use in superconducting magnet designs than 316L.

ACKNOWLEDGMENTS

This study was supported by the Department of Energy, Office of Magnetic

Fusion Energy. R. P. Walsh of NBS conducted the tensile test.

258
REFERENCES

1. C. D. Lundin and D. F. Spond, "The Nature and Morphology of Fissures in

Austenitic Stainless Steel Weld Metals," Welding Journal, Welding

Research Supplement , 55, 356s-367s (1976).

2. D. T. Read, H. I. McHenry, P. A. Steinmeyer, and R. D. Thomas, Jr.,

"Metallurgical Factors Affecting the Toughness of 316L SMA Weldments at

Cryogenic Temperatures," in: Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures-II , ed. R. P. Reed, NBSIR 79-1609,

National Bureau of Standards, Boulder, Colorado (1979), pp. 313-351.

3. W. T. Delong, "Ferrite in Austenitic Stainless Steel Weld Metals,"

Welding Journal, Welding Research Supplement , 53, 273s-286s (1974).

4. J. A. Brooks and F. J. Lambert, Jr., "The Effects of Phosphorus, Sulfur

and Ferrite Content on Welding Cracking of Type 309 Stainless Steel,"

Welding Journal, Welding Research Supplement , 57, 139s- 143s (1978).

5. R. P. Reed, "A Cryostat for Tensile Tests in the Temperature Range 300 to

4 K," in: Advances in Cryogenic Engineering , vol.7, Plenum Press, New

York (1962), pp. 448-454.

6. "Standard Test for J

T

, a Measure of Fracture Toughness," ASTM

designation: E813-81,in: Annual Book of ASTM Standards , Part 10,

American Society for Testing and Materials, Philadelphia,

Pennsylvania (1982), pp. 822-840.

7. D.T. Read and R. L. Tobler, "Mechanical Property Measurements at Low

Temperatures," in: Advances in Cryogenic Engineering , vol . 28, Plenum

Press, New York (1982), pp. 17-28.

8. D. T. Read, "The Computer-Aided J-Integral Test Facility at NBS," in:

Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures-I II , ed. R. P. Reed, NBSIR 80-1627, National Bureau of

Standards, Boulder, Colorado (1980), pp. 205-216.

9. T. A. Whipple, H. I. McHenry, and D. T. Read, "Fracture Behavior of

Ferrite-Free Stainless Steel Welds in Liquid Helium," in: Material

s

Studies for Magnetic Fusion Energy Applications at Low Temperatures-I 1

, ed. R. P. Reed, NBSIR 80-1627, National Bureau of Standards, Boulder,

Colorado (1980), pp. 167-194.

10. H. M. Ledbetter and R. P. Reed, "Elastic Properties of Metals and Alloys,

I. Iron, Nickel, and Iron-Nickel Alloys," Journal of Physical and

Chemical Reference Data, vol. 2, 531-618(1974).

11. H. M. Ledbetter, "Texture in Stainless-Steel Welds: An Ultrasonic Study,"

in: Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures-VI , eds., R. P. Reed and N. J. Simon, NBSIR 83-1690,

National Bureau of Standards, Boulder, Colorado (1983), pp. 339-356.

259
LIST OF TABLES

1. Chemical compositions of 320 and 320LR electrodes

2. Tensile properties and fracture toughness of 320LR weld metal at 4 K

LIST OF FIGURES

1. Welding parameters and joint design of the test weldment; orientation and

location of the specimens.

260
Table 1. Chemical compositions of 320 and 320LR electrodes

Electrode C Cr Ni Mo Cb+Ta Mn Si P S

E320* 0.07 19-21 32-36 2-3 8xC min. 0.5-2.

5

0.60 0.04 0.03

1.0 max. E320LR 0.035 0.30 0.02 0.015

Note: Single values are maximums.

* Specification of AWS A5.4-78.

** Specification of manufacturer.

Table 2. Tensi 1

e

properties and fracture toughness of 320LR weld metal

K t ,*

Ic

E, a , yUTS, EL, RA,

MPa/m GPa MPa MPa % %

E320LR 163

149 ave 156

161.6 674 978 40 35.7

E316L** 95-200 729-882 1121-1300 25-48 23-44

* Estimated from J T . Ic ** Fully austenitic (0% ferrite); from Reference 9.

261
e

£

c

COc

o

toc

CD£

Q

<

ID

CD

>

00

Cl) OJz. k_ —

=3 O O >

CLcro

Q

Fig. 1. Welding parameters and joint design of the test weldment;

orientation and location of the specimens.

262
FATIGUE CRACK GROWTH OF DUPLEX STAINLESS

STEEL CASTINGS AT 4 K*

P. T. Purtscher, Y. W. Cheng, P. N. Li**

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Constant-load-amplitude stage II fatigue crack growth rates at 4 K were measured for duplex stainless steel castings. The results show that at a aK of

i -4

60 MPa*m , da/dN = 7.6 x 10 mm/cycle for an alloy with 1% ferrite. For an alloy with 8% ferrite, da/dN is 35% greater, and for an alloy with 29% ferrite,

da/dN is 260% greater than for the 1% ferrite alloy. However, the exponent in

the Paris equation does not change appreciably (less than 18%) as the ferrite

content changes from 1 to 29%.

Keywords: Austenitic stainless steel castings; cryogenic properties of

materials; delta ferrite; fatigue crack growth rate; stainless steel

* Contribution of NBS; not subject to copyright.

**Guest worker; on leave from East China Institute of Chemical Technology,

Shanghai , China.

263

INTRODUCTION

Stainless steel castings can facilitate fabrication of structural components

for 1 ow-temperature applications by eliminating the need for welding. The

deformation and fracture behavior of stainless steel castings at 4 K has been

12 3

reported previously. ’

’ However, fatigue design data for stainless steel

castings at low temperature are needed to ensure reliable performance.

CF8M stainless steel castings are roughly equivalent in composition to

wrought AISI 316. Conventionally processed AISI 316 is 100% austenite [facecentered cubic structure (fee)] at room temperature, but the cast structure

normally contains some delta ferrite [body-centered cubic (bcc)] within the

austenite matrix. The amount of bcc phase is determined by solidification and

chemical composition variables. Delta ferrite in the mi crostructure of

12 3

stainless steel castings reduces the toughness at 4 K.

’

’ For CF8M castings,

the 4-K toughness was 352 MPa*m 2 with 1% ferrite, 148 MPa*m 2 for 8% ferrite,

and approximately 110 MPa*m 2 for 17, 23, and 29% delta ferrite. Above 15%

ferrite, the bcc phase was present as a nearly continuous phase in three

dimensions and provided an easy path for crack propagation under monotonic

1 oadi ng.

The fatigue crack growth rate (FCGR) of stable fee alloys is usually less

at 4 K than at room temperature. For metastable fee alloys, the FCGR may or

may not increase as the test temperature drops from room temperature to 4 K,

depending on the specific composition. AISI 316 is metastable; it undergoes

some strain-induced martensitic transformation at 4 K, but the FCGR of AISI

316 does not change appreciably with temperature.^

The FCGR of bcc alloys normally shows a higher stress dependence than the

FCGR of fee alloys as the test temperature is decreased from room temperature

265
to 4 K. The increased stress dependence can be correlated with the occurrence

of brittle fracture modes (cleavage) on the surface rather than the fatigue

4 striations typically seen on the fatigue fracture surface of an fee alloy.

There are no fatigue crack growth data for austenitic stainless steel

4

castings at 4 K. The purpose of this study is to determine the effect of

delta ferrite on stage II FCGR of CF8M austenitic stainless steel castings at

4 K.

MATERIALS AND EXPERIMENTAL PROCEDURE

Three different alloys were fatigue tested at 4 K. The chemical composition, tensile properties at 4 K, and the fracture toughness at 4 K of each

alloy are shown in Table I. All three alloys fall within the compositional

limits for the CF8M grade. These three alloys solidify as primary delta-ferrite

alloys that intersect the eutectic triangle of the Fe-Cr-Ni phase diagram so

5 that austenite envelops the ferritic dendrites before complete solidification.

The delta ferrite in the room-temperature microstructure is located at the

spines of the dendrites.

A single compact tension specimen was tested for each of the alloys

containing 1 and 8% ferrite. Duplicate specimens were tested for the 29%

ferrite alloy. The test temperature was maintained at 4 K by submersing the

specimens in liquid helium. The cryostat system that was used for the fatigue

g testing was described previously.

The fatigue crack growth rate was determined by a computer-aided

procedure"

7 in accordance with ASTM E647-81 for constant-load-amplitude fatigue

-8

crack growth rates above 10" m/cycle. The crack growth was monitored by

measuring the change in compliance of the specimen. The R ratio (minimum

load/maximum load) used was 0.1, and the loading frequency was 20 Hz.

266
o "he Paris equation was used to characterize the fatigue crack growth:

da/dN = A( AK) m

(1)

where da/dN is the crack growth per cycle, aK is the stress intensity factor

range (K - K . ) , and A and m are the parameters in the Paris equation. y v max min' r

The fatigue fracture surface of each alloy was examined with a scanning

electron microscope.

RESULTS

Table II suimarizes the FCGR results. On the basis of previous experience

with the computer-aided FCGR procedure, the specimen to specimen variation in

the results from duplicate specimens is estimated to be ±20%. For a better

characterization and to confirm the results reported here, additional f atigue

tests are desirable.

Figures 1 through 3 show the log-log plots of da/dN vs. AK for each of

the three alloys. In figure 4 the three curves are superimposed on one plot

r~ with the reported literature value for AISI 316.° For the castings, there was

a general increase in FCGR with increasing delta ferrite, but the increase was

relatively small. The FCGR of the AISI 316 that did not contain any delta

ferrite was between the 1 and 8% ferrite alloys.

An interesting observation of the fatigue surfaces could be made with the

unaided eye. The fracture surfaces of all specimens were relatively rough and

appeared to follow the dendritic solidification structure (Figure 5); normally

the fatigue fracture surface of AISI 316 is normally smooth when observed with

the unaided eye.

Scanning electron microscopy (SEM) was used to study the microscopic

fracture features of each of the three alloys. For the alloy with 1 de'ta

267
ferrite, the surface was covered with poorly formed fatigue striations and a

fracture morphology that was related to the dendritic solidification pattern.

As AK increased, some secondary cracking was found on the fracture surface

(Figures 6 and 7)

For the alloy with 8% delta ferrite, the fracture surface showed essentially

the same topography, (Figure 6), but with some quasi-cleavage facets that

represent fracture through the delta ferrite. Secondary cracking was observed

on the fracture surface over the entire range of AK (Figure 8). Fracture

morphology due to the dendritic solidification pattern was still present on

that portion of the surface that corresponds to the austenite matrix.

When the delta ferrite content was increased to 29%, the fatigue fracture

surface showed more of the quasi-cl eavage facets with secondary cracking

(Figure 9). The fraction of the surface that was covered by the quasi-cleavage

facets increased by an amount that correlates qualitatively with the increase

in delta ferrite. The fracture morphology due to the dendritic solidification

was still present, but to a lesser degree.

DISCUSSION

The degree of influence of second phase volume fraction on the FCGR of

duplex mi crostructures is expected to depend on mechanical variables such as

the relative flow strength of the two phases, applied AK and ^mx - In the

case of CF8M castings with delta ferrite, the ferrite phase had higher strength,

lower ductility, and lower fracture toughness at 4 K than the austenite phase.

The FCGR of these alloys was divided into regions of low and high aK

behavior. At low AK values, the da/dN did not correlate with the delta

268
ferrite content, as evidenced by the crossover in Figure 4 for the 8 and 29%

ferrite alloys. At high AK values, increasing ferrite content correlated well

with the increase in da/dN.

SEM showed two distinct morphologies on the fracture surfaces of the

three alloys: A morphology with poorly formed striations and dendritic

features (referred to as striation morphology) and a quasi -cl eavage morphology

(referred to as cleavage morphology). For the sake of discussion, the measured

crack growth rate can be thought of as the sum of the crack growth of each of

the morphologies and can be expressed as:

(da/dN)

mea> = (da/dN) str _ (da/dN) cle _ (2)

where (da/dN) = crack growth rate measured in test

mea. (da/dN) ^

= crack growth rate (striation morphology)

(da/dN) .j = crack growth rate (cleavage morphology)

The striation morphology showed two microscopic features: the poorly

formed striations and the dendritic features. Fracture exhibiting this

striation morphology moved selectively through the austenite instead of

following the plane of maximum stress, indicating that the crack was propagating through relatively weak points in the structure. However, the (da/dN) mea

of the 1% alloy was lower than the reported value of da/dN for AISI 316 over

the range of AK reported (Figure 4). Therefore, this striation morphology is

not inherently weak, even though part of the fracture occurred through interdendritic regions of the austenite.

The delta ferrite in the microstructure fractures at 4 K with a quasicleavage morphology that is controlled by the applied stress in much

269
the same way that stress controls cleavage fracture. The stress at the

interface between ferrite and austenite must exceed a critical stress for

quasi -cl eavage fracture to occur. Once the critical stress is attained, the

crack propagates through the ferrite by the quasi-cl eavage mechanism. In

fracture toughness testing, the crack will exhibit a cleavage morphology

exclusively through the ferrite if the ferrite forms a nearly continuous path

1 2 in three dimensions. ’ However, in fatigue, the crack does not grow exclusively through the ferrite, even for the 29% ferrite alloy where the

ferrite was nearly continuous in three dimensions.

The correlation between (da/dN) and delta ferrite at high values of mea. s

aK and K can be explained by considering the fracture mechanisms. The high max r J 3 3

stress levels promote the cleavage fracture morphology at or ahead of the

crack front during the fatigue test. Therefore, (da/dN)

c ^ e exceeds (da/dN)^^ ,

which explains why (da/dN) of the 8% ferrite alloy exceeds (da/dN) of

the 1% ferrite alloy. Likewise, (da/dN) meaof the 29% ferrite alloy exceeds

(da/dN) of the 8% ferrite alloy, mea

Another factor to consider in examination of the results of the FCGR

tests is the change in the stress dependence as a function of delta ferrite

content (Table II). The results show that the m value in the Paris equation

does not increase uniformly along with the increase in ferrite content. When

the magnitude of the m values are compared with the m values at 4 K reported

4

tough austenitic stainless steels, there are no appreciable differences.

270
SUMMARY

The presence of delta ferrite in the mi crostructure of the CF8M castings

has a significant effect on stage II FCGR at 4 K. At a AK of 60 MPa*m 2, da/dN

4 -4

= 7.6 x 10 mm/cycle for the 1% ferrite alloy, 10.3 x 10 mm/cycle for the

8% ferrite alloy, and 19.7 x 10" 4

mm/cycle for the 29% ferrite alloy. The

increase in da/dN is correlated with the occurrence of a quasi -cl eavage

fracture morphology on the fatigue fracture surface of the f erri te-containing

alloys. The increase in da/dN with increasing ferrite content is large, but

the m value in the Paris equation does not change appreciably (less than 18%).

ACKNOWLEDGMENT

This work was supported by the Department of Energy, Office of Fusion

Energy.

REFERENCES

1. E. L. Brown, T. A. Whipple, and R. L. Tobler, "Fracture Toughness of CF8

Castings at Four Kelvin," Met. Trans. Vol . 14A, No. 8 (1983),

pp. 1179-1188.

2. T. A. Whipple and E. L. Brown, "Deformation and Fracture of Stainless

Steel Castings and Weldments at 4 K," in Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures - VI , NBSIR 81-1645, R. P. Reed and N. J. Simon, eds., National Bureau of Standards, Boulder,

Colorado (1981), pp. 213-233.

3. T. A. Whipple and H. I. McHenry, "Mechanical Properties of Stainless

Steel Castings at 4 K," in Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures - VI , NBSIR 81-1645, R. P. Reed and

N. J. Simon, eds., National Bureau of Standards, Boulder, Colorado

(1981), pp. 235-241.

4. R. L. Tobler and R. P. Reed, "Fatigue Crack Growth Resistance of Structural

Alloys at Cryogenic Temperatures," in Advances in Cryogenic Engineering,

Vol. 24, K. D. Timmerhaus, R. P. Reed, and A. F. Clark, eds., Plenum

Press, New York (1978), pp. 82-90.

5. E. L. Brown, T. A. Whipple, and G. Krauss, "Metallography of Duplex Steel

Castings," in Materials Studies for Magnetic Fusion Energy Applications

at Low Temperatures - VI , NBSIR 83-1645, R. P. Reed and N. J. Simon,

eds., National Bureau of Standards, Boulder, Colorado (1983), pp. 243-271.

271
6. C. W. Fowlkes and R.L. Tobler, "Fracture Testing and Results for a Ti - 6A1 - 4V Alloy in Liquid Helium Temperature," Eng. Fract. Mech., Vol . 8

(1976), pp. 487-500.

7. Y.-W. Cheng, "A Computer-Interacti ve Fatigue Crack Growth Rate Test

Procedure," in Materials Studies for Magnetic Fusion Energy Applications

at Low Temperatures - VI , NBSIR 81-1645, R. P. Reed and N. J. Simon,

eds., National Bureau of Standards, Boulder, Colorado (1981), pp. 41-51.

8. R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering

Material

s

, John Wiley and Sons, New York (1976), p. 468.

272
Table I. Chemical Composition (wt.%) and Mechanical Properties

at 4 K of CF8M Castings

Heat #47640 Heat # 48988 Heat #49021

1% ferrite 87o ferrite 29% ferri te

Carbon 0.06 0.06 0.05

Manganese 1.10 0.38 0.39

Si 1 icon 0.59 1.16 1.11

Chromi urn 1.80 19.6 22.5

Nickel 13.2 10.6 9.8

Molybdenum 2.12 2.1 2.3

Nitrogen 0.05 0.05 0.05

o (MPa) 581 653 851

o* (MPa) 1215 1221 1164

%

u el ongation 48 21 11

K

]c

(J) (MPa-mi 2

) 352 148 105

Table II. Summary of Stage II Fatigue Crack Growth at 4 K of CF8M

Casting from da/dN = A(aK)

Ferrite Content (%) A (mm/cycle) m ak

1 range (MPa*m 2

)

1 0.272 X 10“ 93.63 23 to 83

8 0.342 X 10" 83.08 23 to 68

29 0.159 X 10" 9

3.99 20 to 60

273
LIST OF FIGURES

Figure 1. Plot of da/dN vs. AK for CF8M casting with 1% delta ferrite.

Figure 2. Plot of da/dN vs. AK for CF8M casting with 8% delta ferrite.

Figure 3. Plot of da/dN vs. AK for CF8M casting with 29% delta ferrite.

Figure 4. Summary of CF8M castings and AISI 316 fatigue data at 4 K.

Figure 5. Fracture surface of CF8M casting with 1% ferrite at low magnifica

tion showing the relative roughness of the surface. The fracture

surfaces of the castings with 8 and 29% ferrite were similar.

Figure 6. SEM photomicrograph of fatigue fracture surface of CF8M casting

with 1% delta ferrite and low AK conditions.

Figure 7. SEM photomicrograph of fatigue fracture surface of CF8M casting

with 1% delta ferrite and high aK conditions.

Figure 8. SEM photomicrograph of fatigue fracture surface of CF8M casting

with 8% delta ferrite and low AK conditions.

Figure 9. SEM photomicrograph of fatigue fracture surface of CF8M casting

with 29% delta ferrite and low AK conditions.

274
da/dN,

mm/cycle

AK, ksi VTrT

Figure 1

10 30 50 70

'“ 10“3

" - 10"4

- 10"6

10"6

10"7

AK, MPa/rn

Plot of da/dN vs. AK for CF8M casting with 1% delta ferrite

275

da/dN,

in/cycle
da/dN,

mm/cycle

AK, ksi VTrT

Figure 2

10 30 50 70

“ - 10"4

- 10“3

- 10“5

10-e

10-7

AK, MPa Vm"

Plot of da/dN vs. AK for CF8M casting with 8% delta ferrite.

276

da/dN,

in/cycle
da/dN,

mm/cycle

AK, ksi VTrT

Figure 3

10 30 50 70

10-3

10“4

10’5

10"e

10’7

AK, MPa VTrT

Plot of da/dN vs. AK for CF8M casting with 29% delta ferrite.

277

da/dN,

in/cycle
da/dN,

mm/cycle

AK, ksiVlrT

Figure 4.

AK, MPaVm"

Summary plot of fatigue data at 4 K of CF8M castings and AISI

316.

278

da/dN,

in/cycle
4 K fatigue fracture surface

L

1 cm

Figure 5 Fracture surface of CF8M casting with 1% ferrite at low

magnification showing the relative roughness of the surface.

The fracture surfaces of the castings with 8 and 29 :

. ferrite

appeared to be similar.

279
« 100 un

5 ym

Figure 6. SEM photomicrograph of fatigue fracture surface of CF8M casting

with 1% delta ferrite, low AK conditions.

280
Figure 7.

100 vm

i i 20 vm

SEM photomicrograph of fatigue fracture surface of CF8M casting

with 1% delta ferrite, high AK conditions.

281
Figure 8.

t j

100 ym

20 ym

SEM photomicrograph of fatigue fracture surface of CF8M casting

with 8% delta ferrite, low AK conditions.

282
Figure 9.

100 ym

1 0 ym

SEM photomicrograph of fatigue fracture surface of CF8M casting

with 29% delta ferrite low AK conditions.

283

NOHME TALUCS

285

NONMETALL ICS PROGRAM

LEADERS: M. B. Kasen, H. M. Ledbetter, NBS

STAFF: M. W. Austin, R. D. Kriz, NBS

CONTRACTS: S. K. Datta, University of Colorado

OBJECTIVES:

(1) To measure, model, and understand the properties of composites

that enter essentially into the conception, design, construction, operation, and performance of magnetic-fusion-energy

equipment.

(2) To cooperate with industry to establish and refine

cryogenic-grade specifications for insulating laminates and

coding systems for laminates.

RESEARCH PAST YEAR (1983):

(1) Kriz. Continuous-damage mechanics model of fracture in

laminated composites.

(2) Kriz. Redistribution of localized stresses near damage in woven composites at low temperatures

(3) Kasen. Continuation of a program on the standardization of

cryogenic grades of insulating and structural laminates in

cooperation with industry.

RESEARCH THIS YEAR (1984):

(1) Kriz. Damage accumulation in woven composites at low

temperatures

(2) Kriz. Development of fiber optics to study damage accumulation

in woven composites at low temperatures

(3) Kasen. Development of improved test methods for determining

the effect of cryogenic temperatures on composite material

performance

287

CONTINUOUS DAMAGE MECHANICS

MODEL OF FRACTURE IN LAMINATED COMPOSITES

M. P. Wnuk* and R. D. Kriz

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A modified version of the Kachanov damage accumulation law is employed to

study the damage kinetics in laminated composite materials, such as epoxy-graphite laminates. The objective is to measure the characteristic

events in the final stages of the failure process in composite materials

following the "characteristic damage state" (CDS).

The process of localization and spread of damage ahead of the dominant

matrix crack is viewed as a sequence of nucleation and propagation phases,

both of which may be described by use of the internal damage parameter. T... scalar quantity reflects the ratio of the current crack (or pore) density to

its saturation, or critical level. It is shown that the "continuous damage

mechanics" (CDM) approach is useful in modeling a damage

mainly of the fiber breaks generated ahead of the matrix

around the plane of a prospective fracture, thus forming

embedded within the stress field of the dominant crack. ^ . w.

type of damage applies to the failure process that follows formation

CDS observed in a number of laminated materials.

Thi s

field consisting

crack and clustered

the "damage band"

Description of

of

thi s the

^On leave from the University of Wi sconsi n-Mi 1 waukee

289
.
1. Introduction

Changes in the inner structure of multiphase materials leading to the

failure of a structural component can be divided into two basic stages: The

first one includes formation and growth of microscopic damages, such as

vacancies, voids, micropores, and the like, randomly distributed throughout

the body. This stage can be called a "latent" phase of the fracture process.

It is terminated at the instant when the microdefects localize in a small

volume of material leading to a formation of a dominant macroscopic crack.

Propagation of this visible crack constitutes the second stage of the fracture

process. When the length of such a crack or its rate reaches the critical

value, the final rupture of a component takes place.

Although the damage occurring during any particular phase of life of a

composite laminate may assume different forms (such as matrix cracking,

interfacial debonding, delamination, formation of transverse cracks or

so-called ply cracks, and fiber breakage), the nature and sequence of

occurrence of these specific events justifies our general description of the

damage accumulation process. One important feature of this process is the

ability to 1 oca! i ze the critical damage to a domain that represents only a

small fraction of the material volume. When stress concentrators are not

present, microdefects generated in the initial stage of fracture are randomly

distributed. Although the initial formation of damage is random, the final

rupture is localized in a well-defined region ( e . g . , a plane in the simple

case of two-dimensional fracture). Furthermore, decohesion does not occur

simultaneously within this region. Rather, it is a result of the coalescence

of microcracks and, ultimately, is realized in the form of crack propagation

initiated at a certain site.

291
Reifsnider et al . [1] have pointed out that those laminates that develop

relatively little visible damage during the latent phase of the fracture

process (and, thus, show almost no loss of strength for the most of their

life), display rapid and severe localized damage towards the end of their life

resulting in "a residual strength curve that becomes almost a step function."

A phenomenon of this type has been called a "sudden death" by Chou and

Croman [2]. Reifsnider [3] suggested that one of the most common scenarios

occurring just prior to the final stage of fracture in composite laminates is

the formation of a regular and highly reproducible system of transverse cracks

(called "ply cracks"). This system is so typical for the composite laminates

that a new name has been coined, "characteristic damage state" (CDS) [3,4] and

used extensively in making predictions regarding residual strength and life of

laminated composites. An interesting proof of the occurrence of the CDS has

been provided by the experimental work of Kriz [5], Figure la shows a

photograph he obtained using an edge replica technique. The photograph

clearly shows that a single transverse crack has penetrated the 90° ply and

then stopped at the interface between 90° and 0° laminae. Ahead of this ply

crack, which includes both matrix and fiber fractures in the 90° ply, one can

see a number of fiber breaks appearing as dark spots in the picture. Before

the dominant crack may penetrate* into the 0° ply, which is the critical

element in sustaining the load prior to final rupture, a sufficient number of

fibers must break, not entirely at random, but in a preferential manner,

clustering around the plane of the prospective final fracture. The aim of

this work is to provide a quantitative description of such damage localization

*We note that the ply crack may or may not cross the interface between the two

adjacent laminae, depending on the ratio of cohesive strength within the

cracked lamina and the bonding strength (adhesion) occurring at the interface

between the two laminae. Some insight into this problem may be gained by a careful study of an early work by Cook and Gordon [6].

292
and the growth process occurring within the stress field generated ahead of

the dominant transverse matrix crack.

2. Mathematical Modeling of Damage Accumulation

Now we focus attention on the failure process, which begins with the

appearance of the CDS and ends with the total loss of structural integrity of

the composite laminate.

Although the primary component of the damage in this stage is fiber

breakage, which is generated ahead of the dominant crack shown in Fig. la,

other forms of damage, such as matrix cracking, void growth and coalescence,

are also present. The theory, which allows one to model the process of damage

accumulation and the associated extension of the dominant crack that interacts

with the damage field, stems from the continuous damage mechanics (CDM). This

model accounts for stress redi stribution due to advancement of the crack and

allows one to describe the effect of such stress redistribution on the rate of

damage growth. The basic assumption underlying this mathematical modeling is

a modified version of Kachanov's law [7,8]. In its original form, the Kachanov

law relates the rate of damage growth, dw/dt, to the net-section stress, s,

that is,

doj/dt = Cs v

(1)

Here C and v are material constants, while the net-section stress, s

( = P/

e ff ) , and the nominal stress, o(=P/A ), are related as follows:

c = P - P — O

( n \ A

eff V1 - 1 - “

The scalar quantity, w, which has been identified as the internal damage

parameter, represents the deterioration of the cross section that transmits

the tensile load due to the formation and accumulation of microdefects. If

293
the area actually transmitting the load is called the "effective area," A

eff 5

then u)A o represents the fraction of the initial area A

q that no longer transmits

any load. A plausible interpretation of the physical meaning of the parameter

oo was given by Rousselier [9] and Mroz [10]. These authors considered oo to be

a ratio of the defect density, say d , to the critical or "saturation" level

of the defect density, say d . Thus, setting oo = d

v /dc

, one would obtain

oo = 0 for an undamaged state and oo = 1 for a fully damaged state. The formula

oo = d

v /d

c suggests that experimental verification of the CDM predictions

concerning composite laminates can be obtained; for example, the crack density

may be estimated either by direct measurements of crack traces (an optical

technique) or by indirect measurements by a wave-scattering method (see Hadley

[11] and Datta et al . [12]). In fact, any experimental procedure that allows

for monitoring stiffness, elastic constants degradation, or both in a composite

laminate subject to sustained or cyclic loading will shed light on the physical

law governing the time dependence of the internal damage parameter. An

example of such a law of damage accumulation is the Kachanov equation, which

in its classic form may be obtained by combining equations (1) and (2) as

fol 1 ows

doo _ r dt

' L (3)

v

1 - 7

This equation defines the time-dependent quantity to as a function of the

uniform stress, o. A modified version of the basic equation (3)* reads:

*Yet a more general form of the modified Kachanov law is

^0

du) O < 0 th

<

C

th

(4a)

l-oo 0 - 0

th

where o., denotes a certain stress threshold below which there is no visible

th

damage generation. For stresses near the crack front, however, >> o^, and

then equation (4a) reduces to equation (4).

294
in which the stress, o , no longer is the uniform tensile stress but equals

the actual stress occurring at the front of an initial stress concentrator

,

such as a sharp crack. Since o changes not only with the distance from the

crack front (when the crack is stationary) but also undergoes a continued

redistribution while the crack propagates, equation (4) may no longer be

reduced to an ordinary differential equation. As we will show, the governing

equation that results from the modified Kachanov's law, even for the simplest

case of a constant external load, becomes a nonlinear integrodifferential

equation. To state the problem somewhat differently, the difficulty of

predicting the damage parameter, oj, at any instant, t, and any location ahead

of the crack front (point P in Fig. 2) now becomes dependent on all the stress

states that existed at this particular location before the crack front had

reached the control point, P. Although equation (4) may be readily integrated

t \) -iU)(r,t) = 1 - [1 - C(\) + 1) q/ [r(x), t] dx]

v

(5)

this form is not of much help unless there are further details concerning the

stress, o^., generated (a) ahead of the stationary crack for the latent phase

of the fracture process, and (b) ahead of a moving crack for the second phase

of the fracture process.

Assuming that the symbol o ( P ,

1 ) = o (a 1 ,r ,) denotes the stress

U Zj P P induced at the point P while the crack tip is located at the point P

1 , we

shall distinguish the following stress fields:

1. o (a ,r ) = o (a, a ), stress field ahead of a stationary crack where

Zj U U Zj U (r

0

= p* + a - a

Q

)

295
2 . o (a,r') = a (a, a'), stress field ahead of a moving crack where

( r ' = P * + a - a'

)

3. o (a ,p*) = o (a ,a ) = o (a ), the stress at the tip of the initial

Li vj Li vj U Li VJ crack ( r = p*) , and

4. o

z (a,p*) = c (a,a) = o (a), the stress at the tip of the "final"

current crack tip (r = p*).

The notation o (a,r) emphasizes that the stress, o , depends on two

variables: current crack length, a, and the distance measured from the crack

front, r. On the other hand, the symbol o (a,a') indicates that after

replacing r by the quantity shown in the parentheses for each of the cases

listed above, the stress, o , becomes dependent on just one variable: crack

length. For the propagation phase (a f 0), we consider a to be a time-like

variable, and in fact, all the integrals with respect to time are replaced by

integrals with respect to the crack length. Note that such a transformation

is possible only when the crack propagates (a f 0), because then da and dt can

be used interchangeably, and therefore, dt = da/a.

If time is eliminated consistently whenever it appears in the problem

(see the Appendix), equation (5) may be expressed in the following form:

da

dt

= -Co^(a)

d

31 0^ (a, a'

)

da

dn

1 (a,aQ

) da

( 6 )

Here the symbol a' denotes the rate of crack growth evaluated at the instant

t ' , or, equivalently, for the crack length a

1 . Note that a' is a shorthand

notation for a = a(a'). Both terms appearing in the denominator of equation (6)

involve not only stress, but also its gradient do^/dr (or do^/da, since a is

used as a yardstick to measure the current distance from the crack tip). The

only quantity yet unexplained is fi^(a,a

Q

). The amount of damage generated at

296
the point P (see Figs, lb and 2) at the end of the latent phase of fracture

(t = tj) is fij. During this phase, the crack remains stationary, and its

length equals a . In general, the damage parameter, ft, is defined by the

following equation:

ft = Al - uj' ) V

doj' = 1 - (1 - u>) V+1

(7)

0 v + 1

The lower limit for ft is zero (correspond!' ng to the undamaged state, u) = 0),

and the upper limit of ft (corresponding to the "saturation" level of damage,

a) = 1 ) is the critical value ft = (1 + v)~ . The damage parameter, ft, is

directly related to stress, o , that is

t v ft(r,t) = C Q

f o

z

[ r( t ) , t] dx (8)

In fact, equation (8) may be used to formulate the fracture criterion

based on the damage accumulation concept. The criterion may be verbalized as

follows: for a collapse of a material element located at the distance r from

a dominant crack tip [which generates the stress field o (r,t)], it is

necessary that the time integral of the vth power of the stress, o , attains

the critical value, ft .

To evaluate the amount of damage generated at any instant during the

latent phase of the fracture process (0 < t < t^), say ft

' ^ , we substitute

o (a, a ) for o in equation (8). If the stress o (a, a ) is represented by the

2j U Z> Zj 0

function Y(r ) with r = p. + a - a . we may write:

0 0 0

Kt / 9 \ o (a, a ) = —LL_°1 Y(r ) (9)

L 0 /o 0

in which Kj(a

Q

) is the stress-intensity factor [as defined in the LEFM (linear

elastic fracture mechanics)] associated with the initial crack length a 0

.

297
This form inserted into equation (8) gives:

n

1 (a,aQ

) = ft Y(r

0

) rTpTT

r

o

= p *+ a - a o

t <_ 1

( 10 )

Interestingly, this expression is valid for an arbitrary loading history,

o = o(t), where o denotes the external load (see the Appendix for algebraic

details). Equation (10) predicts the amount of damage that will be created

ahead of the main crack during a time interval less than the incubation time,

tj, or the so-called first critical time. It is a simple matter to show that

for an arbitrary loading history, o(t), the incubation time is determined by

the relation:

t

Q

f o v (t)dt

^c (2 tt P *) v/2

C k^(a

0 )YS

(ID

Here, Y* = Y(p*), and kj(a

Q

) is the "reduced" stress-intensity factor, which

does not include the loading parameter. Recalling the usual form [13]

Kj(t,a

0

) = o(t) /ira

Q

F(a

0

/b) (12)

in which c(t) is the external load and F(a /b) is the geometry-dependent

factor, we may rewrite equation (12) as follows:

Kj(t,a

o

) = o(t)kj(a

o

), kj = F(a

Q

/b) (13)

Plots of ft^ vs. the reduced distance from the crack tip, r Q /p* = 5 , obtained

at two values of the normalized time, t/t^, are shown in Fig. 3a. These plots

were constructed by assuming input data for Y(r )/Y*, that is, the stress

distribution ahead of the dominant ply-crack shown in Fig. la. An analytical

298
form of the function Y(r ) was obtained by a Hermitian interpolation performed

on the numerical solution by the finite-element method [5].

The distinct differences between the distributions of damage shown in

Fig. 3b suggest that the exponent v has a very strong effect on the nature of

the damage accumulation process. For v > 1 there is only a minimal amount of

damage generated during the latent stage of fracture at a site some distance

from the crack front. However, the opposite is true for v < 1, e.g., v = 0.1.

When v < 1, the damage built up at the control point P during the time

interval (0, t^) reaches nearly the critical level. Upon completion of the

latent phase, relatively little life is left for the material element located

at P. Therefore, the propagation phase rapidly leads to the final rupture or

"sudden death" of the component.

To conclude this section, let us evaluate the "residual damage,"

which is the amount of damage generated at a given point while the crack front

is advancing toward that point. Evaluation of fir, involves numerical

integration of the expression

in which a(a') is found from the equation of a moving crack [equation (6)].

Examples of the damage distributions resulting from numerical evaluation of

equation (14) are shown in Fig. 4. Again, to illustrate the distinct differences

in possible scenarios of the damage accumulation process, these two values for

the Kachanov exponent were used: v = 0.1 and v = 2. Since for \> < 1 most of

the mi crostructural damage is generated during the latent stage of fracture,

it becomes obvious why in this case the second phase of failure process, crack

propagation, constitutes only a minor part of the total life of the component.

299
The opposite is true for v > 1. This effect is demonstrated by the three

curves shown in Fig. 5a, which represent the final outcome of the mathematical

model, namely the integral curves resulting from a numerical solution of the

integrodifferential equation (6). Note that both the crack length and time,

as plotted in Fig. 5a, are nondimensional

Fig. 5b shows the three curves representing the three hypothetical

failure processes obtained for v = 2, the characteristic structural length

p*/b = 0.02, and the initial crack length x q

= a

Q /p* = 10 for the three

different states of stress generated ahead of the dominant ply crack. The

trend in the failure development process (shown in Fig. 5b) is the same as

that inferred from the stress analysis of ply cracks in laminates [5] using

the finite-element method (compare with Fig. 5c). Through-thickness variation

of the tensile stress, o , in the 0° ply is shown in Fig. 5c for three cases:

X

1. Mech - mechanical load only with no residual stress,

2. Dry - stresses in No. 1 altered by mismatch in thermal contractions

between bonded layers when cooled from room temperature to 76 K.

3. Wet - absorbed moisture swells individual layers and alters stresses

in the dry case. Stress gradients shown in Fig. 5c are approximated

by derivatives of a fourth-order polynomial:

where coefficients A, B, C, and D are given in Table 1. At 76 K the stress

gradient for the mechanical load is substantially altered by the dry residual

stresses. When moisture is absorbed, swelling in the 90° ply increases the

stress near the crack tip, and consequently, the crack growth rate in Fig. 5b

increases for the wet case.

(15)

300
Table 1. Coefficients for Stress Gradients Shown in Fig. 5c

Case ABC D

Dry 0.724 x 10" 5 0.607 -0.172 x 10" 10 0.12 x 10

Wet 0.115 x 10“ 4

3.045 -0.437 x 10' 10 -0.212 x 10

Mech 0.672 x 10" 5 3.411 -0.299 x 10" 10 -0.124 x 10

3. Discussion of Results and Conclusions

Although the stacking sequence of the laminate used in Kriz's experiment [5]

[0, 90°, + 45°, -45°]<j, differs from the stacking sequence [90°, 0°]<~ for

which our calculations have been performed, the basic conclusions of this work

may be extended to other geometries and in particular, they remain valid for

the laminates with the stacking sequences favoring formation of the transverse

matrix cracks [1,2] during the early stages of damage accumulation process.

Figure 6 shows an edge view of a specimen that corresponds exactly to the

geometrical configuration of a double-edge-notch tensile specimen chosen for

the numerical examples presented in the preceding sections.

As we show in the Appendix, the geometry-dependent function

4> ( a ) = Kj(a)/Kj(a

Q

) ( 16)

that enters into the governing equation (6) controls the damage generation

only during the second stage of failure process. This fact is reflected by

301
the form of equations (10) and (14). The first of these equations contains no

<{> function at all, while the second one relates 4> explicitly to the ^damage,

the damage generated during the propagation phase of the main crack, and to

the geometry of the (cracked) structural component as defined by the ratio of

the stress-intensity factors (see equation (16)). Therefore, for the case of

\> << 1, when the initiation phase plays a dominant role in the nucleation of

damage, the effect of the 4> function on the development of the failure process

becomes negligible. In fact, by performing a series of "numerical

experiments," one may prove that when v << 1, the integral appearing in the

denominator of the governing equation of motion (6) has very little effect on

the final outcome of the integration process. Thus, the equation for the rate

of growth of the matrix crack interacting with a damage field generated in the

adjacent ply assumes the form referred to as the "limit case"

[a] I (1/tp U

(a)/F

2 (a)

V << 1 (17)

Here t^ denotes the first critical time (end of the incubation phase), and the

function can be obtained from the known stress distribution, Y(r), namely

F

2 (x) = YUs ) o v-1 dy(E

0 V

Y73x }

5 = 1 + x - x

(18)

where

Y* Y(l), x - a/ p* , x Q

- a Q

/ p*

, ^

£q r^/p*

When these expressions are substituted into equation (14), the geometry-dependent

function <j> cancels out. Therefore, the damage generated during the second

phase of failure may be represented simply as an integral of known functions,

302
y(x.x') = Y( C)/Y* and y(x,x

Q

) = YUq )/Y*, in which £ = r/p* = 1 + x - x' ,

i = r /p* = 1 + x - x . 0 * 0

In the limit case, the final form for ^

reads

[n9 ] 2 / y (x,x' ) y

2 v « 1 x Q

v-1

(x',x

0

)

dy(x' ,x Q

) dx 1 dx

(19)

Figure 7 shows an example of the ^

evaluated at v = 0.1 from the exact

equation (14) and from the approximate equation (19). The conclusion is that

the approximate form [equation (19)] provides a valuable tool for an evaluation

of the damage generated during the propagation phase whenever the Kachanov

exponent, v, is small relative to one. Moreover, the numerical tests have

shown that when x> « 1, the value of ^obtained for any pair of numbers, x q and x, becomes negligibly small as compared to the value of evaluated from

equation (10) at t = t^, namely

B

1 = B

C

[ Y ( ro )/Y(p* )]V

( 20 )

This equation, along with the expression defining the incubation time, t^,

o v (t)dt

v << (°c (2^P.)

V/2

|

1 C „V/, \ v V (

( 21 )

and with equation (17) provides the basis for quantifying the two phases of

the failure process in laminated composites. The first and the second

critical times can now be estimated using these relationships. When the "time

zero" is identified with the establishment of the CDS, and when it may be

shown that the Kachanov exponent, \), does indeed assume values close to zero,

we obtain the following estimates (0 << o

c

):

303
( 22 )

tj 1 (n

c /o^C)(2p*/ao

) u/2 /Fv

(a o/b)Y^

flj = fi c [Y(r

o )/Y(p*)] v

, r0= p* + a - a Q

(in which o

c denotes the ultimate tensile strength of the reinforcing fiber).

Since ^

<< we also have

tg << ^

and T ~ t, (23)

The- symbol T denotes the life of the composite laminate and is obtained as the

sum of the critical times, T = t^ + t^. For a general loading history and

when the condition o << o is not satisfied, the first critical time, t. , has

c 1 to be evaluated numerically as a root of equation (21). However, when the

applied stress is maintained constant upon creation of the characteri Stic

damage state, say 0 = o

o

= constant, and when the LEFM formulae for a pair of

edge cracks penetrating a tensile specimen (see Fig. 6) are employed, an

estimate for the first critical time results from equation (10). With a

constant stress, 0 , and Y. ~ 1, we have

o —

(24)

The symbol p* denotes the radius of a reinforcing fiber, a is the depth of ply

crack, and 2b denotes the width of a component (see Fig. 6). The material

constants C, fl , and v, which appear in the damage accumulation law (equation

4), must be determined empirically. The function F may be obtained from the

LEFM catalog of the K factors. Assuming occurrence of brittle fracture in an

isotropic medium for the configuration under consideration (double-edge-notch,

DEN), we would have the following closed form solution (see the K factors in

Ref. 13):

304
( 25 )

Again, it is noted that for the case of the exponent v approaching zero, even

large variations in the form of the F-function (and, thus in the $ function)

will have only a minor influence on the predicted life span of a structural

component subjected to tensile load, c .

An alternative way of writing equation (24) is

in which the constant, B, and the reference time, t^, are defined as follows:

Interestingly, equation (26) predicts an experimentally confirmed linear

relationship between the logarithm of the nondimensional applied stress,

o /o , and the logarithm of the nondimensional time, t,/t D (see Fig. 8). The

slope of this line is the negative of the reciprocal of the damage exponent v.

Of course, for arbitrary loading histories, o(t), some deviations from the

straight line shown in Fig. 8 are expected.

Degradation of elastic moduli and fracture toughness may be related to

the "crack density" parameter, which in our model is represented by the

internal damage parameter, oj = d

v /dc

. Watt et al . [14] suggested various

(o

o/oc )V

= B( W (26)

(27)

t R

- l/Co«

305
forms (linear and nonlinear) of the "mixture formulae," which allow for

evaluation of the bulk and shear moduli in a multiphase aggregate, provided

that the initial moduli of each component are known and that the pore density

is given as a function of time [compare equation (5)]. The determination of

the average fracture toughness of a multiphase material is a somewhat more

difficult task. However, under certain simplifying assumptions, the average

toughness of the epoxy-matrix graphite-fiber-reinforced composites may be

predicted as a function of time for a given specimen geometry and loading

history. We intend to address this topic in a subsequent paper, in which we

will discuss an estimation procedure method involving a technique of Morozov

and Fridman [15] (named "section method") and an approximation procedure

suggested for multiphase materials by Rao [16]. The present work provides a

quantitative basis for evaluation of residual strength of laminated

composites. We hope that the model developed here will prove useful in

predicting the deterioration of fracture toughness of composite materials due

to a time-dependent damage accumulation process.

4. Summary

A modified version of the Kachanov damage accumulation law has been

employed to study the damage kinetics in composite materials, such as epoxygraphite laminates embrittled by low temperature. The purpose of this study

was to quantify the two basic phases of failure process in laminated composites

(1) localization of microdefects and (2) spread of a dominant crack after

formation of the so-called characteri stic damage state (CDS).

Considerations of interaction between the dominant crack and the field of

secondary cracks, such as fiber breakage generated ahead of the macroscopic

fracture front, lead to a certain nonlinear integrodifferential equation which

defines the rate of the dominant crack growth. Numerical solution of this

306
equation is possible if the stress and the stress gradient prevailing in the

neighborhood of the macrocrack are known. Since these quantities are difficult

to obtain analytically, the finite element method has been employed. In this

way, stress distributions for an epoxy-graphite laminate, damaged by a dominant

ply crack due to tensile load applied at a temperature of 76 K were obtained.

These numerical results were then approximated by Hermitian polynomials, which

were substituted into the governing equation. Subsequent numerical integration

of this equation provided means for quantitative predictions regarding microand macrodamage accumulation and the fracture process in laminated composites.

Of particular practical importance is the observation that relates

time-to-fai 1 ure to the applied stress level and material properties. For a

constant load condition, a simple relationship has been given that suggests an

inverse power law between the applied load and the time-to-fai 1 ure. When a

log-log scale is used for plotting, the resulting graph is a straight line

(see Fig. 8). Since the slope of this line depends on the Kachanov parameters

C and v, which are inherent in the mathematical model, further research should

focus on experimental determination of the load vs. time-to-fai 1 ure relationship.

Acknowl edgments

This study was sponsored by the Fracture and Deformation Division of the

National Bureau of Standards while Professor Wnuk was on leave from the

University of Wisconsin-Milwaukee. A portion of the study at low temperatures

was sponsored by the Department of Energy, Office of Fusion Energy.

References

1. K. L. Reifsnider, E. G. Henneke, W. W. Stinchcomb, and J. C. Duke, Damage

Mechanics and NDE of Composite Laminates, in Mechanics of Composite

Materials: Recent Advances, eds., Z. Hashin and C. T. Herakovich (1982),

pp. 399-420.

2. P. C. Chou and R. Croman, Residual Strength in Fatigue Based on the

Strength-Life Equal Rank Assumption, J , Compos . Mater . , Vol . 2 (1978),

pp. 75-84.

307
3. K. L. Reifsnider, Introduction, in Damage in Composite Materials , ASTM

STP 775, American Society for Testing and Materials, Philadelphia (1982),

pp. 552-563.

4. J. E. Masters and K. L. Reifsnider, An Investigation of Cumulative Damage

Development in Quasi-Isotropic Graphite/Epoxy Laminates, in Damage in

Composite Materials , ASTM STP 775, American Society for Testing and

Materials, Philadelphia (1982), pp. 40-62.

5. R. D. Kriz, Influence of Ply Cracks on Fracture Strength of

Graphite/Epoxy Laminates at 76 K, in Effects of Defects in Composite

Materials , ASTM STP 836, American Society for Testing and Materials,

Philadelphia, in press.

6. J. Cook and J. E. Gordon, A Mechanism for the Control of Crack

Propagation in a Brittle System, Proc. Roy. Soc. A, Vol . 282 (1964),

p. 508-520.

7. L. M. Kachanov, Theory of Creep (in Russian), Nauka Publishers, Moscow

(1966).

8. L. M. Kachanov, Some Problems of Creep Fracture Theory, in Advances in

Creep Design , Applied Science Publishers, London (1971), pp. 21-29.

9. G. Rousselier, Finite Deformation Constitutive Relations and Ductile

Fracture, in Proceedings of IUTAM Symposium on 3D Constitutive Relations

and Ductile Fracture, ed. S. Nemat Nasser, Elsevier - North Holland, New

York (1981), pp. 331-355.

10. Z. Mroz, Discussion on Session 7, in Proceedings of IUTAM Symposium on 3D

Constitutive Relations and Ductile Fracture , ed. S. Nemat Nasser,

Elsevier - North Holland, New York (1981), pp. 405-409.

11. K. Hadley, Dilatancy: "Further Studies in Crystalline Rock," Ph.D

Thesis, M.I.T., Cambridge, Massachusetts (1975).

12. S. K. Datta, H. M. Ledbetter, and R. D. Kriz, Calculated Elastic

Constants of Composites Containing Anisotropic Fibers, Int, J. Solids

Struct

, in press.

13. H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of Cracks

Handbook , Del Research Corp., Hellertown, Pennsylvania (1973).

14. J. P. Watt, G. F. Davies, and R. J. O'Connell, The Elastic Properties of

Composite Materials, Rev. Geophys. Space Phys., Vol. 14 (1976),

pp. 541-563.

15. E. M. Morozov and Y. B. Fridman, Crack Analysis as a Method to Study

Fracture Character!' sti cs (in Russian), Zavod. Lab. , No. 8 (1966),

pp. 977-984. Reviewed by M. P. Wnuk in "Review of Some Russian Papers

Pertinent to the Fracture of Solids," Technical Report GALCIT SM 67-9,

California Institute of Technology, Pasadena (Sept. 1967). Also in V. Z. Parton and E. M. Morozov, Elastic Plastic Fracture Mechanics (translated

from Russian), Mir Publishers, Moscow (1978), pp. 74-87.

308
APPENDIX

1 . Distribution of damage ahead of the transverse matrix crack during the

two phases of failure process.

During the latent phase of fracture process (a = 0), the nondimensional

damage parameter, i s evaluated as follows:

n [ Q

i

(

t ) Jq < t < t.j

t = C J [a

v

(P, P')] dt 1 0

L a = 0

(Al)

Since the crack length,

a

Q = const, the stress, does not depend on

time and it may be factored out. If we identify in equation (Al) with

°r( a » aj = -wjT= [Y(rJ]

\/2 «P*

r = p* + a - a o o (A 2 )

and when the first critical time is introduced

t, = <a

c /C).-* (a 0

) (A 3 )

then equation (Al) reduces as follows

t n

i (t ”o < t < t n

c UY(r0 )/Y*] v (t/t

1 ))r . p*

^ ++ a - a o o

(A 4 )

i This equation predicts = 0 at time zero, and the maximum value

n.

1 nc

[ Y <r

0

)/Yj;

. . p* + a - a rt o * o

( A5)

at a time equal to the first characteristic time, t^ . Of course, at the

point P' (see Fig. 2), that is when r

Q - p*(or when a = a ), we obtain

309
the critical damage ( P

' ) = «

c

, while at some distance away from the

crack front, say at point P shown in Fig. 2, the amount of damage generated at

the end of the incubation phase is predicted by equation (A5). The resulting

distribution Q-j = Q-j (

Q

) is shown by the top curve in Fig. 3a.

The first critical time t^ is defined as the time at which the material

element adjacent to the tip of an initial crack collapses. This occurs when

the integral

I <a

Q

) df ' (A6)

attains the critical value, . Since the stress a^a^ = Kj(a

Q

)Y*/

v/2ir p* does not depend on time, the integral (A6) equals o^(a

o )t^, and

therefore

t

1 = (Qc /C)

(K

1 (aQ )YJ v

(2ir p*)

v/2 ( A7

)

Applying the fracture criterion (8) to the second phase of the failure

process, we can evaluate the amount of damage generated within the time interval t-j < t' < t. Here, t coincides with the instant at which material

element located at the point P (see Fig. 2b) collapses. Now, the stress

distribution avaries not only with the distance from the current crack

tip but also it is time dependent, since at any fixed point in space, say P,

the stress is elevated when the crack front propagates toward this point. The

integral

ft 2 (t) = C [oJ(P.P')] dt

a ^ o

(A8)

310
may be replaced by an integral with respect to the current crack length

a Q (a) = C J Oy(a.a')

a o

da 1

a (a 1 )

( A9

)

When the nondimensional crack length x = a/p* and the nondimensional time

e = t/t^ are introduced, the expression (A8) assumes the form

a,(x) - a J $

v (x') [Y(x,x' )/Y*] v

, x = dx/de (A10)

i c x 0

X(x')

in which the geometry dependent function $ is defined as the ratio of the

stress intensity factor for a current crack and that for the initial crack,

i .e.

4>(x) = K

i (x)/K

i (xq

) (All)

The function Y(x,x') is the familiar nondimensional stress ahead of a

moving crack, Y(£). in which the distance £ is expressed as r/p* =

1 + x x'. We note that the rate of crack propagation x' appearing in the

expression (A10) has to satisfy the governing equation (6), or (A20).

2 . Derivation of the governing equation (6) .

Two basic premises underlie the derivation process: (a) that the stress

distribution ahead of a propagating crack is of the form

o

E (P,P') o

z (a ,a ’

)

K (a 1 ) V^ttp*

[Y(r)]

r = P* + a a' (A12)

and (b) that a material element at any location along the prospective frac

ture path collapses when the following critical damage criterion is satisfied

311
c (A13)

Decomposing

t

J o' (P,P') dt • =

o

the integral in equation (A13) into two parts

n t

C J [<5y ] . dt' + C J [o*].

o a = o t^ a^o

and identifying the first part with the damage generated during the latent

phase of failure process,^, see equation (A5), we obtain

(A14)

t

C J [Oy]. dt' = Q - fl, (A15)

t

] * a * o

c 1

Next, we eliminate time by the time-like variable a(t). Replacing dt' by

da ' /a(a ' ) , we obtain

a Ha 1 C J o' (a, a') = a - a,(a) (A16)

a 0 a(a')

When this equation is differentiated with respect to time, remembering that

d[ ]/dt = ad [ ]/da, one arrives at

a

a C J (a, a') [da/a(a')] + C c^(a,a) = -adOj/da (A17)

a o

Solving for the rate of crack growth gives

-Cay(a)

a = (A18)

C J f- ay(a,a') + dQ, /da

a„ a(a')

312
which is identical with equation (6). We note that both terms appearing in

the denominator of (A18) involve not only the stresses o^a.a 1 ) and

o

J.(a,a

o

) but also their gradients.

These gradients are always negative, and therefore the entire expression

on the right-hand side of equation (A18) is positive.

Let us introduce the nondimensional variables

x = a/p* , e = t/t-j

x' = a'/p*, x Q = a Q /p* ( A 1 9

)

in which p* denotes the characteristic structural length (such as fiber

radius), while the critical time t-j is defined by equation (A7). Substitution of (A19) into equation (A18) yields the nondimensional version of the

governing equation, useful in further numerical studies, namely

dx

de

-1 V , V V <t> (x)

X o

J 4

> V

(x , )F

1 (x,x*)[dx'/x(x 1 )] + F 2 (x)

(A20)

Here, the function <$>(x) is geometry dependent, as indicated by equation

(All), while the other two auxiliary functions,

F^ and F^are defined as

f ol lows

F ( x x ' ) = - {(^-^) —

}

r * } u Y^ ; Y^d5 1 5 = 1 + x - x

F

2 (x) = F1 (x, x Q

)

( A 2 1

)

These forms were used in generating the curves shown in Figs. 5a and 5b.

313
3. Correction of the critical damage level. ft, due to a non zero initial

damage associated with the existence of the characteristic damage state .

A final comment regarding modification of the expression for the critical

value of the damage parameter (ftc

) is in order. If the "time zero" coincides with creation of the characteristic damage state, then we would expect

the initial value for the Kachanov parameter, to, to be greater than zero.

Assuming that such initial damage exists and equals toQ

, we may redefine

the parameter ft (see equation (7)) as follows:

ft = \ (i-<o‘ )d«' =

to

(l-o.

0

) U+1

- (l-a,)^1

v+1

(A22)

At t = 0, to = co 0

, and we again recover ft = 0. However, for the

other limit, when the internal damage parameter, to, attains its critical

value, <o=l, the capital omega assumes the level

ft =

c

(1 -CO ) 2 g_

v+1

v+1

(A23)

Since ftc enters into all pertinent expressions which describe damage accumulation and growth, acceptance of equation (A23) requires that an additional material property, namely the relative void density at the onset of the

characteri stic damage state (<o ) , be introduced into the model. Therefore, the number of independent material constants is increased by one; and,

in order to match the experimental data with the mathematical model, one needs

to determine all three constants, namely <o Q

, v,and C.

314
Figure Captions

1. (a) Characteristic damage state observed shortly prior to the final

failure of an epoxy-graphite [0°, 90°, 45°, -45°]g laminate. The

crack seen in the photograph penetrates the 90° piy while the black

dots ahead of it represent secondary fractures, such as fiber breaks

contained within the adjacent 0° ply. Both primary and secondary

fractures were made visible by an edge replica technique (see

Ref. 5).

(b) Mathematical model of the physical state depicted in Fig. la. The

model stems from the continuous damage mechanics (CMD).

2. State of stress, o ( P ,

1 ) , generated at the point P while the crack tip

is located at the point P' depends on the distance r ,. This distance

is shown for (a) stationary crack, and (b) a propagating crack. Symbol

p* denotes the characteri sti c mi crostructural length.

3. (a) Distribution of internal damage (ft.) constructed from stress

distributions ahead of a dominant ply crack shown in Fig. la.

(b) Distribution of the internal damage (ft.) generated during the latent

phase of fracture process (t <_ t. ) when the dominant crack is

stationary. A pronounced difference in the damage accumulation

pattern is noted between the two situations corresponding to values

for the exponent v of 0.1 and 2.

4. Distributions of the internal damage (ft ?

) generated during the second

phase of fracture process associated with propagation of a dominant crack

(t. < t < t ?

). Two distinctly different situations are obtained from the

exponent v being less than one (\> = 0.1) and greater than one (\) = 2).

5. (a) Second phase of fracture process, that is the dominant crack

propagation as calculated for v = 0.1, v = 2, and v = 4 and a stress

field, o , generated by a ply crack traversing the remaining

1

i gament

L that is 0° ply (the crack is shown in Fig. 1).

Nondimensi onal crack length, x = a/p*, is shown as a function of

nondimensi onal time, <j) = t/t^.

(b) Length of the ply crack vs. time (both nondimensi onal i zed , v = 2)

shown for the three different stress fields generated ahead of the

ply crack contained in a laminated epoxy-graphite composite in the

unrelaxed state (curve labeled "mech") and two relaxed states

corresponding to the "wet" and "dry" condition of the laminate. The

input data used to generate the three curves shown was taken from

the finite-element studies of Kriz [5] (see Fig. 5c).

(c) Through-thickness variation of o in 0° ply shown in Fig. la for

three cases: 1. Mech - mechanical load only with no residual

stresses at room temperature, 2. Dry - superposition of residual

thermal stresses at 76 K in a dehydrated condition, 3. Wet - superposition of residual stresses caused by swelling when laminate

is saturated with abosrbed moisture.

315
6 . Simplified version of a stacking sequence [90°, 0°]<. for which the

double-edge-notch configuration would apply. This configuration was assumed for the purpose of numerical integration of the governing

equation 6 (see the curves shown in Figs. 5a and 5b).

7. Comparison between the damage distributions, ftp , pertaining to the second

phase of fracture, as evaluated from the exact (curve 1) and approximate

(curve 2) equations. When the exponent v is much less than one (v = 0.1), both curves are almost identical.

8. Straight line shown represents the relation between the constant applied

stress, 0 , and the first critical time, t. [see equation 26]. Cohesive

strength 8f the reinforcing fiber, o , is ased to normalize stress, while

the reference time, t D (=l/Co v

), is employed to normalize time.

K C

316
-Xo

*o

rO

QJ QJ

rO x: S_ r— S_ rO QJ

rO CD "O ~3- C

•r- OJ

cn qj

-t-J c D1 0- XI O *r— QJ 1— -O ro S_ QJ -l-J 3

xi DX 3 -l-J 4-> • CD O CD

QJ ro CD ro

O +j r— 3

-t-J ro X3 C/1 4- C

S_ -r- XZ

CD ro >1 . o E XI QJ 3 -—

ro -l-J S- ro 1X1 S_ r— XQ .-o CL QJ C • C/3— S- o 4-

l-r- QJ CJ QJ i— O XI -O QJ CsL +J 1X1 *5 -r- </) s- <3- 4- QJ O 1 >1 -O QJ XI i— C/1 c C/1

t/) * CL ro fT3 v-—

-o o1X1 0 XI CD o/SHrf Q) «o- O CD S_ 3 > cn 3 rO CT

CQ Sn cn E •i— k. QJ O Q) r— 3 o c/1 O XI «N s_ XI

XU CTi 4-J cn CL CD >* O „ C/1 QJ

S_ XI

QJ 4-J

A QJ 0 QJ 3 4-J LL 4-1 O 4-J 4-J O ro

rO i—

ro CD CQ CD 4-J S_ ro • t— C/1 QJ 4-J S_ i

4-J QJ <4- • CL I e*o

lO

O) •«- cnxi

to Q- E (T3 ro -o

S_cni >1xo

QO)c

ro 4->

i/i

•i

s_

QJ 4-J o

ro 4-

SO

to XI O) o S_3

to •«—

CD >, CL S_ro -C -O

CLC

roO

S- CD cn <u o cn O +-> JC c

Q- CD

l/l CD CD XC s4-> CL

QJ c S-

<D

S_ CL

CD o cn O -o

CD

-t-> c c

CD ro U

tO nXJ

"O

ro CD

CD -O

XI •<-

-l-J to C > c xi cd

CD 4-> "O

CD 4— t- ro c/1 O S E

cn

317
Fig. 1(b) Mathematical model of the physical state depicted in Fig. la. The

model stems from the continuous damage mechanics (CMD).

318
Fig- 2b

time = t

1

Blunt Crack

a o

Sharp Crack

'ppFig. 2. State of stress,

tip is located at the

distance is shown for

Symbol p* denotes the

o (P,P')> generated at the point P while the crack

point P' depends on the distance r ,. This

(a) stationary crack, and (b) a prBpagating crack,

characteristic mi crostructural length.

319
DAMAGE

PARAMETER

ft'.

DISTANCE FROM CRACK TIP

Fig. 3(a) Distribution of internal damage (ft..) constructed from stress

distributions ahead of a dominant ply crack shown in Fig. la.

320
DAMAGE

PARAMETER,

DISTANCE FROM CRACK TIP

Fig. 3(b) Distribution of the internal damage (ft,) generated during the latent

phase of fracture process (t <_ t,) when the

i dominant crack is stationary.

A pronounced difference in the damage accumulation pattern is noted

between the two situations corresponding to values for the exponent v of

0.1 and 2.

321
0.04

Q_

h-

*

O

<

CO

o

o

CO

LU

o

z

<

I-coQ

u ‘d313WVdVd 39VWVCI

a; ss^. cu

03 4-> aj 1X3 _c m aj -M 03 C s- O cn

cr>4- •<- c: o +-> "o

•I- (D C

1- C 3 ID

=3 O +-> -T3 -r- -r- ^ -M 00 i—

"O ID

aj cn+j o p « c

id a <u ii L- O ^

ai s- aj ?

c cm

O) M— cr>-c: cu

+-> TD C

*r- O

CXI3 >> —

CS i— C

"O P D

CL) C_> _C= a; +-> C +J cn ro •<- 03 •r P U) E U 1/) 1/> 03 O T- CU TD </) TD ,

(/)

i— 1X3 O CD

03 3 c

C tO | •!— to CL) CD cu _o

+-> o • c O «*—- P

£- c\j CL -M -M

CD C

_c a) v 1 aj

-4-> i- sc P -M o

M— +-> CL O u v|x

Its O) CO r~H c P P QJ • o — _sz -—

•r— 4- P-> CM

-M O -iLa E ii _Q CL) fX3 o

•i— to c s- p

S- <X3 C_> 4 -M .SC CO CL+J TD CU

•r— c (U c Q TD ro c: o C Cr

O •!- «X3 C

l) E P IB

• (D O D C WD OP

322
50

O

z

LU 40

1/ = 0.1 2.0 4.0

NONDIMENS 10 NAL TIME

Fig. 5(a) Second phase of fracture process, that is the dominant crack

propagation as calculated for v = 0.1, v = 2, and v = 4 and a stress field, o , generated by a ply crack traversing the remaining

ligament that is 0° ply (the crack is shown in Fig. 1). Nondimensional crack length, x = a/p*, is shown as a function of

nondimensional time, <j> = t/t^.

323
Fig. 5(b) Length of the ply crack vs. time (both nondimensional ized, v = 2)

shown for the three different stress fields generated ahead of the ply

crack contained in a laminated epoxy-graphite composite in the unrelaxed

state (curve labeled "mech") and two relaxed states corresponding to the

"wet" and "dry" condition of the laminate. The input data used to

generate the three curves shown was taken from the finite-element studies

of Kriz [5] (see Fig. 5c).

324
100

w

>< b oo

oooo

N.O

CDO

inoo O ''t

co 0.

in

co CU

cu CO

i- CO in i

O CO a> as -a

4- CL) i- 3 cu

S- -t-> "O -Q

ro +-> in -r— s_ i—i in in CO i— <u o • i

rO S- X2

O') ro E ra

•<- 3 S- 4- U_ -O O) o x: • f— x: C CO +J c i—

•I- d) o 2

S- 1— *1

c ro 4-> TO 2 O 3 •!- CU o c "O co 4-> -C •r- O ro

CO xi CO CL S-

-t-> O) S- 3

>>•<- S- CU 4-> •— 2 CL ro Q_ 4- 3 in O co O l CO o c SC 1 i

o o

c. •r- -t-J CU

•1- TO 4-> CU +J

rO •r- rs rO XD CO c o <— o • • f

CL CO E

4— r— s_ ro O to QJ •> r— u CL C c -r- 3 O O o sc co •<— CU

•i— tO 4-> XI

-M xi 1 -i— 2

ro

O "O

•r- CU >> sc cn

s- E s- o c

CO

O (J • p— > 1 1 • "O l

CO _c C\J cu CU

CO c_> -t-> 2

cu a) «« ra CO C z CU S_

S- -TO >3 o 3 >>X3 • 1— • +j XI x: rO CU “O

4-> S- -O CD 1 cu C/1 xi • • CL ro 13 o> co E (V o aj cu c U o in

S- ra

-t-> *1—

l/> x: o E ix CD f

o cn

a>O CO cn ^ cu s- r-. CD o s_ • — x: 4-> +-> 4~> IX) +-> to ra cn

N

325
t t t t t I

90° 0° 90°

90° Ply

Ply Crack

90° Ply

Ply Crack

Damage Zone

(= localized fiber

fracture zone)

Fig. 6. Simplified version of a stacking sequence [90°, 0°]^ for which the

double-edge-notch configuration would apply. This configuration was assumed for the purpose of numerical integration of the governing

equation 6 (see the curves shown in Figs. 5a and 5b).

326
NONDIMENSIONAL TIME

Fig. 7. Comparison between the damage distributions,

second phase of fracture, as evaluated from the exact

approximate (curve 2) equations. When the exponent v one (v = 0.1), both curves are almost identical.

pertaining to the

(curve 1) and

is much less than

327
>-

Fig. 8. Straight line shown represents the relation between the constant

applied stress, o , and the first critical time, t, [see equation 26].

Cohesive strength°of the reinforcing fiber, o , isused to normalize

stress, while the reference time, t

D (=l/Co^)

,

c

i s employed to normalize

time. K c

328
INFLUENCE OF DAMAGE ON MECHANICAL PROPERTIES

OF WOVEN COMPOSITES AT LOW TEMPERATURES

Ronald D. Kriz

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Large quantities of nonmetallic woven composites will be used in magnetic

fusion energy (MFE) structures at low temperatures . We studied the influence

of crack formation, residual thermal stresses, and weave curvature on the

mechanical performance of G10-CR glass/epoxy laminates. Improved material

performance was suggested by the load-deformation response of a unit cell of

plain weave. A generalized plane-strain finite-element model was used to

predict crack-tip singularities and redistribution of stresses within a thin

slice of warp-fill fiber bundles. The model predicts that warp curvature and

thermal stresses at low temperatures are beneficial in reducing crack-tip

singularities of fill cracks. The opposite is true for stiffness, which is

decreased both by curvature and fill cracks. Results of this model provide

the MFE designer a tradeoff between stiffness and strength.

329

INTRODUCTION

Large quantities of nonmetallic composites are forecast for use in future

designs of magnetic-fusion-energy (MFE) power plants. ^ In many applications,

nonmetallic composites are used both as structural support and as thermal

insulation. In superconducting magnets, nonmetallics are used primarily as

electrical insulation. However, when cooled down to liquid-helium

temperatures, large internal stresses can occur within MFE structures because

of large differential thermal contractions between metals and nonmetals. When

internal stresses are combined with mechanical loads, microcracks may initiate

well below the ultimate strength of the composite. Large numbers of voids and

microcracks could limit the mechanical usefulness of these materials.

In anticipation of MFE applications, standardization of G10-CR and Gll-CR

National Electrical Manufacturers' Association (NEMA) grade woven-fabric

2 3

glass/epoxy laminates was established at the National Bureau of Standards. *

Variability in mechanical, electrical, and thermal properties was minimized to

provide the MFE designer with improved mechanical properties. Here we

demonstrate the variability in mechanical performance caused by crack

initiation in a unit cell of plain weave (Fig. 1). The thermal -mechani cal

response of the unit cell was studied in a damaged state to predict changes in

the mechanical properties. Improvement in material performance was suggested

by modeling redistribution of loads within a damaged unit cell. Changes in

stiffnesses and load stresses were calculated by a finite-element model.

ANALYSIS

4

The unit cell of a woven structure is defined by Ishikawa as the smallest

repeating structural unit. The plain-weave unit cell shown in Fig. 1 can be

further characterized by four identical patterns in planes A, B, C, and D.

The finite-element model assumes generalized plane strain exists in all four

331
planes. Hence, the elastic response of the unit cell can be predicted by

studying the three-dimensional load deformation response within a single plane

parallel to the load direction, as shown in Fig. 2. Several load conditions

of tension, shear, and compression are possible. Preliminary results given

here focused on tensile loads, N , shown in Figs. 3a and 3b. The displacements within the x-z plane of Fig. 2 are linear functions of x, y, and z

coordinates and out-of-plane strain,

u = ai + a

2 x + a^z ( 1 )

v = a* + a.x + a.z + ye,

w = ay + agX + agZ

where the a. terms are evaluated in terms of nodal displacements. The ini K

plane and out-of-plane strains, e x and e^, are calculated from thin-1 aminate5 plate theory, assuming zero stresses through the thickness:

e = A N /(A A -A ) x yy x M xx yy xy'(2a)

e = -A N /(A A -f\c

) y xy x xx yy xy'

(2b)

where A , A , and A are laminate midplane stiffnesses calculated from

xx’ yy’ xy K

elastic properties listed in Table 1. A laminate load of N = 175 N/mm

A yielded J strains e = 0.01095 and e = 0.001741. A worst-case thermal load of

x y

AT = -318 K was chosen at 77 K, assuming a strain-free state exists at 395 K

(cure temperature). With these load conditions, we studied the influence of

internal fil 1 -fiber-bundle fracture (Fig. 3b) on the elastic-mechanical

response and internal stresses of the unit cell.

DISCUSSION

Stiffness

For nonwoven laminated plates, stiffness can be predicted by thin332
laminate-plate theory.

6

For woven laminated plates, Ishikawa and

Choi/ predicted stiffnesses for several different weaves by modifying existing

thin-laminate-pl ate theory. Here we predicted the woven laminate stiffness by

measuring the load-deformation response of a finite-element model of the unit

cell. The finite-element model used the elastic properties listed in Table 1,

where epoxy and fiber elastic properties were calculated from experimental

results^ and composite elastic properties were calculated using equations of

Hashin/

Figure 4 shows the influence of warp-fiber orientation, e, on the elastic

response of the unit cell with and without a fill-fiber-bundle crack. As

expected, the elastic modulus increased with increasing alignment of warpfiber bundle along the load axis. Most interesting was the pronounced

influence of fill-fiber-bundle cracks on modulus for large warp angles, e.

Internal Stresses

Before mechanical loading, large internal stresses are caused by

differential thermal contractions between warp and fill-fiber bundles at 77 K.

For nonwoven laminates, these internal stresses can influence the sequence of

damage formation and reduce fracture strength/ 6

In this study, the internal

stresses were predicted for the unit cell with and without a fill-fiber-bundle

crack. The stress-free condition was assumed at a cure temperature of 395 K.

Cooling to 77 K caused large changes in internal stresses.

Regions of expected large internal stresses are shown in Fig. 2 along

lines a-b, c-d, and e-d. Variations in stress distributions along these lines

are compared in Figs. 5, 6, and 7. For all these figures, solid lines

indicate stress caused by a moderate mechanical load of 175 N/mm with different

warp curvatures, ranging from 0° to 45° (see Figs. 3a and 3b). The superposition of residual thermal stresses at 77 K is shown by dashed lines for

333
minimum and maximum warp orientations of 0° and 45° respectively.

In Fig. 5, stresses normal to the warp-fill interface are compressive at

6 = 45°, far from the crack tip. Prior to crack formation these stresses were

tensile. Hence, subsequent crack formation in this region was eliminated by

the presence of a fill-fiber-bundle crack. In both the fill region and matrix

region, stresses decreased with increasing warp orientation. The opposite was

true prior to crack formation. If fill-warp interface debonding is a problem,

fil 1 -fiber-bundle cracks are beneficial when warp orientations are large at

low temperatures.

Figure 6 illustrates that the largest stress existed near the crack tip

in the warp-fiber bundle. Stresses far from the crack tip in the warp-fiber

bundle were most affected by warp orientation, 0, shown in Fig. 3b. Larger

loads were carried by smaller warp angles. The addition of thermal residual

stress decreased the far-field stresses. The same pattern was observed for

stresses near the crack tip. Again, we observed beneficial effects from the

interaction of thermal stresses and warp curvature.

Figure 7 shows that the debonding stresses in warp-fiber bundle above the

f i 1

1 -f i ber-bundl e crack were increased by curvature and thermal stresses.

This pattern was not understood because large compressive stresses should

exist in this region.

We have not established a failure criterion for woven laminated structures.

Instead, we have focused on stress distributions near and far from the crack

tip. In metals studies on stress, distributions near crack tips of dominant

11 12 cracks provided the fundamental basis for a fracture criterion. ’

Unfortunately, cracks in composite laminates with or without curvature may not

be dominant. Hence, a failure criterion based on a single dominant crack in

composites is an idealization that is often forced into practice without

334
experimental verification. Before a failure criterion is developed, experimental

verification of a dominant crack is necessary. Until a failure criterion is

established, we assume a decrease in stress near a crack tip corresponds to

increased strength.

CONCLUSIONS

In general, warp-fiber curvature and thermal stresses at low temperatures

are beneficial in reducing crack stresses near the tip of a fill-fiber-bundle

crack. Formation of fill cracks decreases the stiffness more for large

warp-fiber curvatures than for small curvatures. Hence, a tradeoff between

stiffness and strength is evident when choosing warp-fiber curvature. The

designer interested in woven structural laminate performance at low temperatures can improve performance by proper selection of materials and by choosing

curvature for improved stiffness or strength.

ACKNOWLEDGMENT

This study was sponsored by the U.S. Department of Energy, Office of

Fusion Energy.

335
REFERENCES

1. M. B. Kasen, Composite laminate applications in magnetic fusion energy

superconducting magnet systems, Proceedings of the 1978 International

Conference on Composite Materials , AIME, Toronto, Canada (1978).

2. M. B. Kasen, G. R. MacDonald, D. H. Beekman, Jr., and R. E. Schramm,

Mechanical, electrical, and thermal characterization of G-10CR and G- 1 ICR

glass/epoxy laminates between room temperature and 4 K, Advances in

Cryogenic Engineering, Vol . 26, Plenum Press, New York, pp. 235-244

(1980).

3. M. B. Kasen and R. E. Schramm, Current status of standardized nonmetallic

cryogenic laminates, Advances in Cryogenic Engineering, Vol. 28, Plenum

Press, New York, pp. 271-177 (1981).

4. T. Ishikawa, Anti -symmetric elastic>properties of composite plates of

satin weave cloth, Fiber Sci . Techno! . 15: 127-145 (1981).

5. R. Y. Kim and H. T. Hahn, Effect of curing stresses on first ply failure

in composite laminates, J. Compos. Mater . 13: 2-16 (1979).

6. R. M. Jones, Mechanics of Composite Materials, McGraw-Hill, New York,

pp. 147-173 (1975).

7. K. Dahl erup-Petersen and A. Perrot, "Properties of Organic Composite

Materials at Cryogenic Temperatures," CERN ISR-BOM/79-39, Geneva,

Switzerland (1979).

8. Z. Hashin, "Theory of Fiber Reinforced Materials," NASA-CR-1974, NASA

Langley Research Center, Hampton, Virginia (1972).

9. T. Ishikawa and T. W. Chou, Stiffness and strength behavior of woven fabric composites, J. Mater. Sci . 17: 3211-3220 (1982).

10. R. D. Kriz, Influence of ply cracks on fracture strength of

graphite/epoxy laminates at 76 K, "Effects of Defects in Composite

Materials," American Society for Testing and Materials, Philadelphia,

Pennsylvania (1982), in press.

11. C. E. Inglis, Stresses in a plate due to the presence of cracks and sharp

corners, Trans. Inst. Nav. Architects , 55: 219-241 (1913).

12. A. A. Griffith, The phenomena of rupture and flow in solids, Philos.

Trans. R. Soc. Lond. A221: 163-197 (1921).

336
Table

1.

Elastic

properties * CO » 0) o

S" CM

ffl co co o w 0) co

CO CM CM "c o b o co

CO rx

CO * CM o o a

CO *“x a CO G a co G co G

co

00

CO • CO3 CO CO G

N. lO 3

“Oo

CM CM

CO

co a - E G o

CO

CO

ffl cd

JC

G (/)

ffl a ffl G a CO G 00 LU ix m »

CO3 CO CM LU 3

r- CM o K CM o 00 ffl 09 E

CO

aGx—

CO* “o =** c LU 3 *x o * ffl m > >*X #

4- *35 oii CO O w a a) >•! >" o c ffl £) a ® o =

*» *. O CO CO c — 0u f » o CO C ffl ® B a uj £ o ® o

SS .2 § § >Xoa®

"X

co

CO

CO

O ffl

m CO

G

®c

ffl CL®

CO

w.®>

toc

co *«o

a»oo

oo

CM

VCb6"co

'35c

coax®

COc

ffl 3£ « ® E O w O ®

oo

COa>

ui

uo6m>"w

>»Xoa®

•x.«aG

CO®

ffl u

:=

n

/»x

©

r oc 1 .E

co CO3

CO®

t.Eo co

CO

y

II

|l*

01 « ® O ffl ^ o 3 ^ "O “ C « c — o

.2 3 » 0^0 ffl CO ** w t_ •* a ® ® w a coo § CO k- — a a O 3 - > CO *

337

-JComposite

properties

calculated

from

equations

in

Ref. 8
LIST OF FIGURES

Figure 1. Unit cell of woven-fabric composite.

Figure 2. Thin slice of unit cell. Theta denotes angle between warp-fiber

orientation and the x direction.

Figure 3a. [0/90 ] s laminate with 90° ply crack.

3b. Two-layer woven laminate with fill crack.

Figure 4. Influence of fill crack on woven unit cell Young's modulus.

Figure 5. Stress concentrations in warp fiber bundle above fill crack along

line a-b in Fig. 2.

Figure 6. Stress concentrations in warp fiber bundle above fill crack along

1 ine c-d in Fig. 2.

Figure 7. Debond stresses in warp-fiber bundle above fill crack along line e-f

in Fig. 2

338
N

*t

339

Figure

1.

Unit

cell

of

woven-fabric

composite.
MATRIX

Q_

*

340

Figure

2.

Thin

slice

of

unit

cell.

Theta

denotes

angle

between

warp-fiber

orientation

and

the

x

direction.
* A

\

<TJ

341

Figure

3a.

[0/90]s

laminate

with

90°

ply

crack.

3b.

Two-layer

woven

laminate

with

fill

crack.
Figure 4. Influence of fill crack on woven unit cell Young's modulus.

342
BdW'-S

343

Figure

5.

Stress

concentrations

in

warp

fiber

bundle

above

fill

crack

along
140m

I

h

20

psl

Xio

<0

lO

m

O)

6

oo6

N

6

op

6

m

6

Bdfll ‘xp

344

Figure

6.

Stress

concentrations

in

warp

fiber

bundle

above

fill

crack

along

line

c-d

in

Fig.

2.
150

psi

xIO 3

I <D

345

Figure

7.

Debond

stresses

in

warp-fiber

bundle

above

fill

crack

along

line

NONMETALLIC MATERIAL STANDARDIZATION -

MATERIALS AND TEST METHODS*"

1"

M. B. Kasen

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

SUMMARY

The industrial specification for production of the G-10CR grade of

cryogenic hi gh-pressure laminate has been revised and accepted by U.S.

manufacturers . The objective was to make the specification as generic,

as possible without adversely affecting performance and to add a material

performance criteria to the specification. G-10CR and G- 1 ICR products have

been produced by five U.S. industrial laminating firms. No significant

differences in cryogenic mechanical properties were found among G-10CR

material produced by these manufacturers. This indicates that the

specifications are fulfilling their intended purpose. An efficient system for

producing research materials for systematic screening of the parameters

influencing cryogenic radiation resistance was devised. Laboratories in Japan

and England have agreed to actively cooperate with NBS in further development

of this system.

*Work supported in part by the Office of Fusion Energy, U.S. Department of

Energy.

+To be published in "Sixth Annual Progress Report on Special Pupropose Materials

for Magnetically Confined Fusion Reactors," U.S. Department of Energy (1984).

347

OBJECTIVE

To provide, in cooperation with industry, controlled grades of stateof-the-art insulating laminates for superconducting magnet construction. To

provide highly characterized test materials for studies to develop insulators

of improved cryogenic radiation resistance. To stimulate international

cooperation in nonmetallic insulator cryogenic radiation studies.

PROGRESS AND STATUS

Development of the CR grades of high-pressure industrial laminate reflected

the need for commercial sources of controlled grades of laminates to be used

in construction of developmental superconducting magnets. This was accomplished

by NBS-industry development of component and processing specifications for

NEMA G-10 and G-ll type materials having minimal performance variability at 4

K. This minimal variability was confirmed by laboratory testing. Radiation

resistance was not optimized for these materials.

The requirements for test specimens to be used in screening of parameters

affecting radiation resistance at 4 K were defined and consideration was given

to the most efficient method of their production. A common approach has been

agreed upon by NBS, the Rutherford Laboratory (UK) and Osaka University

(Japan). Each laboratory will construct a similar apparatus and will compare

resul ts .

DEVELOPMENT OF CR-GRADE INSULATING LAMINATES

Specification revision . The CR-grade insulating laminates are high-quality,

glass-fabric reinforced epoxy products representative of the best high-pressure

industrial laminates currently produced in the United States. They are distinguished from conventional NEMA G-10 and G-ll products by being produced

to component and manufacturing process specifications commonly agreed upon by

the industry. This approach was required because the conventional NEMA grades

are generic products providing specified electrical performance at room temperature. These criteria can be met by a variety of laminate components

and production methods that introduce significant performance variability at

cryogenic temperature.

The original specifications as established in 1978 required use of a specific manufacturer's epoxy resin and permitted only one type of finish to

be used on the glass fabric. The laminating industry found this to be

unnecessarily restrictive, as chemically and functionally equivalent epoxy

resins and finishes were available from other manufacturers. The G-10CR

specification was therefore modified at industry request to permit use of the

functionally equivalent products.

The original specifications did not contain minimum performance criteria

because such data were not available and manuf acturers did not have the

capability of testing at cryogenic temperatures . However, several users of

the CR materials expressed a desire to have a performance criteria. This has

been done by adding minimum requirements for mechanical, physical, and electrical

properties at room temperature. All specification modifications have been

reviewed and accepted by the manufacturers.

349
Variability analysis . G-10CR laminates produced by five United States laminating

firms were tested in tension, compression, and interlaminar shear at 295 K and

76 K to assess variability among manufacturers. Only the warp direction in the

plane of the laminate was considered.

The results, obtained by procedures described elsewhere, 1 are summarized

in Table 1. This Table reports averages, standard deviations, and coefficients

of variation for the nine to eleven specimens tested in assessing each parameter.

Lower tolerance limits on the properties are also reported, based on confidence

limits of 99% and a confidence coefficient of 0.95. Assuming that the distribution of test results is normal, and that the materials evaluated are representative of commercial products produced by each company, there is a 95% probability

that 95% of the production will produce values higher than the lower tolerance

limits. The assumption of a normal distribution of strength properties may be

questioned--in particular, at cryogenic temperatures where the matrix becomes

embrittled. However, there were insufficient data to justify assuming a different distribution, and the error introduced by the assumption is believed

to be very smal 1

Table 1 Performance of G-10CR Cryogenic Grade Insulating Laminates

Lower

Standard Coefficient tol erance Property Average deviation of variation limit 1

295 K

°T

°c

431 MPa 27.0 MPa 6.26% 306 MPa

390 MPa 30.8 MPa 7.89% 254 MPa

4

V

27.8 GPa 1.29 GPa 4.64% 22.0 GPa

0.159 0.014 8.67% 0.098

e T

°ILS

1.97% 0.35% -- -- 48.1 MPa 2.48 MPa 5.17% 33.7 MPa

76 K

°T

o

r

817 MPa 71.4 MPa 8.74% 500 MPa

703 MPa 52.1 MPa 7.41% 472 MPa

Ex 32.1 GPa 2.72 GPa 8.47% 20.1 GPa

1 V 0.208 0.023 11.2% 0.106

e T °ILS

3.05% 0.395% -- -- 68.7 MPa 5.99 MPa 8.72% 43.0 MPa

1 Confidence limits 99%, confidence coefficient 0.95

Data on the coefficient of variation and on lower tolerance limits for

tensile strain at failure are not reported because failure of the strain

gauges at stresses below maximum required that this parameter be estimated

from a strip recording. This significantly reduced the accuracy of the

measurements, and precluded a determination of a meaningful variability.

350
When applied to a single production lot of G-10CR, our test procedures

produced coefficients of variation of about 4% for tensile strength, Young's

modulus, and shear strength, and about 9 % for compressive strength, Poisson's

ratio, and failure strain. This suggests that the coefficients of variation

in the present study primarily reflect uncertainties in the test procedure and

intrinsic material variability. It is therefore concluded that differences in room or cryogenic mechanical performance of products produced to the G-10CR

specification by different companies are probably not statistically significant.

The specification therefore appears adequate to ensure the desired product

uniformi ty.

The coefficient of variation is higher at 76 K than at 295 K for most

properties. This is an expected consequence of matrix embrittlement, which

severely limits the operative relaxation processes, making the strength

properties more sensitive to the presence of small flaws. Residual stresses

combined with the possibility of microcracking also increase the variability

in the elastic properties at cryogenic temperatures as compared to room

temperature. Although not determined, it is probable that the coefficient of

variation would be somewhat higher at 4 K than at 76 K.

Recent data have suggested that the compression specimen used in this

study may be sensitive to edge effects, and that the average and lower tolerance

limits for this parameter may be lower than those of bulk material. It is

probable that the interlaminar shear values are also conservative because

available methods for testing this parameter can only approximate a pure shear

Research Materials . The objective is to produce an efficient specimen for

screening the parameters influencing performance of organic insulators under

neutron and gamma irradiation at 4 K. These data will then be used to design

functional insulating laminates to meet the requirements of specific magnet

designs.

The desired specimen characteri sties are as follows:

These requirements reflect the space limitations in the test reactor and

the large number of variables that must be investigated. Examples are type, cure state, and purity of the resin and type, density and finish of the fiber.

The effect of residual stress must also be investigated.

Samples machined from fabric-reinforced laminates are deficient in almdTt

all of the desired specimen characteri sties . Furthermore, it is not possible

to make a meaningful comparison of data among laboratories testing laminates

of different construction. It is therefore concluded that the desired characteristics can only be met by the specimens containing uniaxial fiber reinforcement.

condition.

-small size

-minimal edge effects

-neat or reinforced resin

-easily varied components

-highly characterizabl

e

-simple and inexpensive

-adaptable to a variety of tests

-simple stress analysis

-compatible with test facilities

at different laboratories

351
Such specimens could be machined from uniaxial panels produced from

preimpregnated tape. This approach would be adaptable to all resins and

fibers of interest. However, the cost would be very high if a large number of

variables are to be evaluated. Also, additional variability would be introduced

from machined surfaces, imprecise fiber alignment and from residual molding

stresses

A more efficient approach appears to be offered by the production method

illustrated in Fig. 1. A system based on this principle is presently under

construction at NBS-Boulder. Here, resin-wetted fiber strand bundles are pulled into a tube mold by a drawing wire and are in-situ cured. After

removal from the mold, the rods may be cut to the desired length and tested

without further machining. Neat resin specimens may be produced by drawing

resin up the tube and curing. A typical as produced rod would be 3.2 mm in

diameter and 500 mm long. Several rods can be produced simultaneously. This

technique is routinely used by industry to produce experimental glass-reinforced

polyester specimens. Production of epoxy matrix specimens is not straightforward

due to the lower shrinkage of epoxies on curing which increases problems in

specimen removal from the mold. Nevertheless, as illustrated in Fig. 2, use

of a proper mold release agent can overcome this problem. The method is most

easily used with resin systems that are liquid at room temperature. Hot melt

resin systems present more difficulties; however, it is believed that most of

the problems can be overcome by proper technique. Should this not be

possible, the required specimens could always be produced by the more expensive

flat plate laminating process.

The suggested specimen configuration is well adapted for testing in

flexure and compression, and it can be directly used in dynamic resonance experiments to assess the state of internal damage. It is also very adaptable

to use in test apparatus permitting the sequential cryogenic testing of a number of specimens without warmup of the test fixture. Its simplicity

facilitates a quantitative correlation between internal stress state and

damage, and the economy of production permits a large number of variables to

be studied at a very low cost.

International Cooperation . Cooperative efforts to develop and refine a specimen production method based on the principle illustrated on Fig. 1 are underway between NBS, the Rutherford Appleton Laboratory, UK, (Dr. David

Evans) and the Institute of Science and Industrial Research, Osaka University,

Japan (Dr. Shigehiro Nishijima). Each facility will build its version of the

proposed method. The first task will be to determine if the systems developed

in each laboratory are capable of producing functionally the same test material.

This will be done by each producing specimens using a commonly agreed upon

resin system, fiber type, fiber content, and cure cycle. Resin and processing

conditions will be provided by the Rutherford Laboratory. Fiber will be

provided by the Owens-Corning Research Laboratory. Owens-Corning will also

provide the analysis of each laboratory's production.

If this effort is successful, the next step will be to address commonality

in test methodology and in approaches to analyzing test data. It is anticipated

that this will eventually lead to more detailed cooperative programs involving

materials selection and radiation conditions.

352
REFERENCES

1. M. B. Kasen, G. R. MacDonald, D. H. Beekman, and R. E. Schramm, "Mechanical,

Electrical, and Thermal Characterization of G-10CR and G- 1 ICR Glass

Cloth/Epoxy Laminates Between Room Temperature and 4 K, Adv. Cryo. Enqr.

26:235 (1980).

353
o

<-> SC oo

•i— -i— ro 03 "O

cr><C _q O —

>> -a

s- s- <d a r— o

s- > o

o s_ s_ 4- a) +-> oo c: oo (D O

sc s- u

O)E fD oo u E

a> o oo CL i. c

00 M— *r—

i

O) "O i—

+-> aj o *1

t— CL

CO i

o =3 M—

CL. CL O

E

O cu cu a s_ +J

03 03 03 s_ C 00

*1

i- cu

<_) CL) JC

Z3 -O I—

TJ •I

O 4-

s_ . C--U

GJ <_3 S-o +-> 4- aj <

u

2: s- -o 1 *r— o c 2

-o *i

+-> oo cu ai aj c - E ClZ *p— M- • T3

QJ • 03

00 OO O SC >•, n. •1- _o o c

s- a» —

a. cu ca

•

(_>

i

00 T3

r—

• c o

oo O E *i— *

1— r Ll_ +-> cu . 03 JO

~a +-> 03

S- 03

354

variaD

i

e-speea

motor

(Uj

and

gearbox

(E)

through

a

cable

(F)

passing

over

support

structure

(j),

permitting

multiple

rod

production.

The

filled

mo

are

removed

from

the

structure

and

oven

cured.

Lining

of

the

molds

with

,

release

agent

facilitates

removal

of

the

cured

specimens.
355

Fig.

2

Typical

3.2

min

diameter

glass-fiber

reinforced

epoxy

rods

produced

by

the

method

illustrated

in

Fig.

1.

Resin

formulation

was

Epon

328/Versamid

140.

Fiber

volume

fraction

was

70%.

MECHANICAL PROPERTIES OF CONCRETE MORTAR AT LOW TEMPERATURES

*

+

J. M. Arvidson

Fracture and Deformation Division

National Measurement Laboratory

L. L. Sparks

Thermophysical Properties Division

National Engineering Laboratory

E. Steketee

Fracture and Deformation Division

National Measurement Laboratory

National Bureau of Standards

Boulder, Colorado

ABSTRACT

This report includes test results conducted at ambient (295 K) , dry-ice

and alcohol (195 K) , liquid nitrogen (76 K) , and liquid helium (4 K) temperatures. The compressive properties reported are Young's modulus, yield (at

0.2% offset) and maximum strengths, and elongation (elastic and plastic).

Test specimens (5.1 cm diameter x 10.2 cm) were instrumented with a specially

designed, diametrically opposed, cryogenic strain-gaged extensometer that

minimizes possible errors due to specimen bending during the test.

Key Words: Compressive strength; concrete mortar; elongation; low temperature; maximum strength; mechanical properties; yield strength; Young's modulus.

Supported by the Maritime Administration, U. S. Department of Commerce and

Office of Fusion Energy, U. S. Department of Energy.

•j* Published as report number NBSIR 82-1658, National Bureau of Standards,

Boulder, Colorado (1982).

357
\
1. Introduction

Concretes are attractive materials for construction of large low-temperature installations because of lower material cost and economies of fabrication compared to alternative construction methods. Furthermore, they exhibit favorable mechanical and thermal

properties for use in low- temperature applications. Although these materials are presently used to some extent in LNG and LPG construction, lack of confidence in their

crvogenic behavior has restricted their use or has resulted in overly conservative and

expensive designs. This reflects the lack of dependable cryogenic thermal and mechanical

properties data and a poor understanding of the effect of field-fabrication variables on cryogenic performance.

Potential LNG- or LPG-oriented applications of concretes are diverse. Concrete is

currently used for barge hulls and for ground-based storage facilities [1,2]. Proposals

and designs for construction of large seagoing tankers and floating terminals, in which

both the hull and the primary LNG containment systems are made of concrete, are also being

considered. Possible applications of special concretes such as lightweight, cellular,

fiber reinforced, and polymer will depend on their cryogenic properties which are not

known at this time.

The research described below is part of a broader program to determine the thermal

and mechanical properties of aggregate composites. The mechanical properties of two

concrete mortars were determined at ambient (295 K) , dry-ice and alcohol (195 K) , liquid

nitrogen (76 K) , and liquid helium (4 K) temperatures. The properties reported here are compressive Young's modulus, yield strength (at 0.2% offset), maximum, ultimate, flexural,

and splitting strengths, Kj

c

, and elastic and plastic elongations.

2. Materials Characterization

The physical properties of two concrete mortars (designated mix 1 and mix 2) were studied in this program. Mix 1 was made by a commercial-cement company and mix 2 was made

at the National Bureau of Standards. Both mixes utilized Portland type I cement and a resin air-entraining agent. The aggregate used in mix 1 is commonly known as Elgin sand and

that used in mix 2 is commonly referred to as Clear Creek sand. The chemical makeup and

sieve analysis of each type of aggregate are shown in tables 1 and 2. Both mortars were

mixed using the following ratios (by weight): water/cement = 0.5, aggregate/cement = 3.4.

The air content of the hardened mortars was 11.0 and 17.7 vol.%, respectively, and the

evaporable moisture contents were 8.1 and 10.8 wt.% relative to the oven-dry weight. I he

mixing procedure described in ASTM C192 was utilized for both mixes.

Mix 1 was designed to produce a mortar with a compressive strength of approximate]'.

17.2 MPa (2500 psi). To maintain this strength until testing, the 10-day-old specimens

were placed in a freezer held at 0°C. The hydration process, which causes concretes to increase in strength as they age, is slowed considerably at this temperature. Prior i. the 0°C aging, the specimens were aged in covered glass molds for 24 h at 23°C and then

removed from the molds and placed in saturated-lime water at 23°C for 7 days. Upon r> :

-

. from the lime-water bath, they were wrapped in plastic and aluminum foil for shipment.

359
Table 1. Primary components of aggregates by percentage of

particle count remaining on standard sieves.

Mix Component

No. 8 (2.36 mm)

Standard Sieves

No . 16

(1.19 mm)

No. 30

(0.60 mm)

1 Carbonate 80.3 79.8 64.3

Chert 8.9 11.0 — Granite 3.6 2.4 — Basalts 3.4 2.0 1.2

Quartzite 3.0 4.3 — Quartz-Chalcedony — — 26.5

Feldspar — — 7.6

2 Granite 67.4 66.4 33.2

Metamorphics 7.2 3.7 1.5

Basalts 6.8 2.7 1.8

Quartz 12.4 17.2 44.9

Feldspar 5.7 7.2 15.9

Table 2. Sieve analysis of the aggregates used in mix 1 and mix 2.

Standard Sieve Percent Passing

Number Size (mm) Mix 1 Mix 2 (Elgin) (Clear Creek)

4 4.75 100 99

8 2.36 78 80

16 1.18 63 59

30 0.60 46 29

50 0.30 10 7 100 0.15 0 0

Mix 2 was made in two batches separated by 8 months. Mix design and conditioning for

both batches were identical. The mortar was formed in airtight plastic molds and aged in

the mold for 2 days at 23°C. After removal from the molds, the specimens were immersed in

a saturated lime-water bath at 23°C. They remained in the bath until tested. The age of

the specimens at the time of testing was from 79 to 215 days.

3. Specimens

The solid core specimen geometry was chosen for the compression and splitting

strength tests; specimens measured 5.1 cm in diameter and 9.9 cm long, as recommended by

ASTM C469-65, C496-71, and C873-77T. The flexural strength test specimens were 10.1cm x 1.8 cm x 4.6 cm per ASTM C78-75.

The ends of all specimens to be tested in compression were ground parallel and

perpendicular to the longitudinal axis to within ±6.3 x 10 4 cm. All mix 1 samples were completely saturated with lime-water solution and then kept at 0°C until the time for

testing. All mix 2 specimens were stored in a lime-water solution and were removed just

prior to testing.

4. Test Procedure

Tests were performed using a commercial 1.0 MN (2.2 x 10 5 lbf) servohydraul ic

static/fatigue test machine. The manufacturer's specifications indicate that the load

360
ing .stem .accuracy is ±0.5% of indicated load or ±0.25% of the load range in use,

. . • v« r is greater, on all load ranges. The crosshead speed used for all tests was

. i cm min and is accurate to ±0.1% of set speed at all loads and speeds. Compression

. i mens were instrumented with specially designed, diametrically opposed cryogenic

tr. nn-gage extensometers . This method for sensing strain worked at all temperatures,

. i lading total immersion in liquid nitrogen and liquid helium. Prior to each test,

irticular care was taken to insure coaxial alignment of all test components (e.g.,

c tauter ram, specimen, dewar) to insure uniaxial loading.

Specimen failure modes indicated a well-aligned system with a minimum of bending,

uniform, conically shaped fractures emanating from the specimen ends to the center.

Some testing was carried out to determine plane strain fracture toughness of mix 2. Short-rod specimens with a single chevron in the configuration proposed by Barker and

Buratta [3] were prepared. The diameter was 5.1 cm and the length was 10.2 cm. Testing

at all temperatures was carried out in a newly designed fixture that operates like a pinch-type clothespin to load the chevron-notched specimen in tension.

l'his fixture has a lever-arm ratio of 2:1 and can be fitted into most universaltesting machines. The plane strain fracture toughness, K SR, was calculated using the

following equation proposed by Baker and Baratta [3] and modified by Beech and Ingraffea

[4]:

K t SR

Ic

AP

,3/2

where A is a dimensionless calibration constant

geometry), P is the load at crack instability,

kith one exception the specimens fractured

in the body of the specimen.

^22.5 ± 15% (dependent on specimen

and B is the specimen diameter.

across the chevron; one specimen fractured

5. Results

The compressive Young's modulus for mix 1 increased in value from room temperature to 195 K, and then at 76 and 4 K it decreased by approximately 30 percent (table 3). The

compressive strength, however, increased as the test temperature decreased. Also, only at

195 K did mix 1 show a maximum compressive strength before reaching its ultimate.

The compressive modulus, proportional limit, and ultimate compressive strength for

mix 2 all increased in value as the test temperature decreased (table 4) . As shown in

table 5, the splitting tensile strength increased from 295 to 195 K and then remained the same down to 76 K. The modulus of rupture (flexural strength), however, shows a peak

value at 195 K.

The plane strain fracture toughness, K^SR, for short-rod specimens of mix 2 are tabulated vs. temperature in table 6. The room temperature results on moist mix 2 mortar

are comparable to the fracture toughness reported for two kinds of rock [5]:

TYPE OF

ROCK

MPa* m

1/2

Kt SR

Ic

. . 1/2 psi 1 m

Limestone 0.99 900

Granite 2.48 2250

The results in table 6 show that there was a substantial increase in SR as temper ituri was lowered initially, but no additional increases as temperature was 'lowered further.

Splitting strength showed the same trend with decreasing temperature. It is like

1

. th.it the pronounced increase in toughness with decreasing temperature is related to chan.' in the internal structure of the moist specimens as the water entrained in the pore fr« > .•

361
and expands and then contracts with further cooling. Monfore and Lentz [6] discuss

possible effects of freezing on concrete.

The plane strain fracture toughness of mix 2 mortar y( table 6) is low compared to the

fracture toughness of structured steels i.e., 54.9 MPa'm1 - (50 ksi’in 1 2 ). This comparison suggests that concrete is not a suitable structural material under tensile loading.

Nevertheless, the low cost and widespread availability of concrete may favor its

application in compressive-loading situations.

Table 3. Effect of temperature on compressive Young's modulus and compressive

strength for moist concrete mortar (mix 1).

Test Compressive Compressive Strength

Temperature Young's Modulus o Maximum+ a Ultimate!

K GPa ksi MPa ksi MPa ksi

295 15.9 2300 — — 23.0 3.34

8.6 1250 — — 21.8 3.16

22.4 3250 — — 23.4 3.40

x = 15.6 2270 22.7 3.30

195 27.2 3950 — — — 56.5 8.20 53.8 7.81 —38.1 —5530 49.1 7.12 47.6 6.90

57.4 8. 32 56.9 8.25

x = 32.7 4740 54.3 7.88 52.8 7.65

76 14.3 2070 — — 71.1 10.31

31.0 4490 — — 107.8 15.64

17.7 2570 — — 90.9 13.18

22.8 3300 — — 87.9 12.75

x = 21.5 3110 89.4 12.97

4 23.0 3340 — — — —

+a Maximum: maximum stress the specimen reached durin g the test.

to Ultimate: stress at failure.

Table 4.. Effect of temperature on compressive properties

for moist concrete mortar (mix 2) .

Test Compressive Proportional Ultimate Compressive

Temperature Young '

s

Modulus Limit Strength

K GPa ksi MPa ksi MPa ksi

295 15.25 2210 14.45 2.10 31.23 4.53

19.80 2800 15. 65 2. 27 28.40 4.12

X = 17.26 2510 15.05 2. 19 29.82 4.32

195 30.65 4450 33.04 4. 79 89.19 12.94

33.78 4900 28.87 4.19 93.22 13.52

X = 32.22 4680 30.96 4.49 91.21 13.23

76 38.59 5600 120.9 17.53

44.71 6480 — 102.5 14.87

X = 41.65 6040 111.7 16.20

362
['able 5. Effect of temperature on splitting and flexural

strength of moist concrete mortar (mix 2).

Test Splitting Tensile

Temperature Strength* Modulus of Rupturet

K MPa ksi MPa ksi

295 2.32 0.34 5.25 0.76

2.64 0.38 5.25 0.76

x = 2.48 0.36 5.72 0.83

x = 5.41 0.78

195 6.62 0.96 13.44 1.95

9.69 1.41 13.88 2.01

x = 8.15 1.19 x = 13.66 1.98

76 5.96 0.86 9.26 1.34

8.54 1.24 11.91 1.73

x = 7.25 1.05 x = 10.59 1.54

*ASTM C496-71 splitting tensile strength = T = 2P/fT£d

where: T = splitting tensile strength, MPa (or psi)

P = maximum applied load, N (or lbf)

1 = length, mm (or in)

d = diameter, mm (or in)

+ASTM C78-75

where: R =

P =

1 =

b =

d =

2 modulus of rupture = R = 3P£/2bd

modulus of rupture, MPa (or psi)

maximum applied load, N (or lbf)

span length, mm (or in)

average width of specimen, mm (or in)

average depth of specimen, mm (or in)

Table 6. Fracture toughness of short rod moist concrete mortar specimens (mix 2)*

Temperature, K Kt SR

Ic 1/2 ,

. . 1 / 2 . MPa*m (psi* m )

P

c kg (lb)

295 0.88 (800) 41.0 (90.28)

0.95 (860) 41.8 (92.16)

0.88 (800) 39.3 (86.54)

195 2.26 (2060) 101.0 (222.56)

2.24 (2040) 99.9 (220.30)

2.04 (1860) 91.8 (202.32)

2.20 (2000)

t

97.9 (215.80)

76 1.91 (1740) 85.1 (187.70)

*A11 test specimens were 5.08 cm in diameter.

tSpecimen fractured in body away from chevron.

363
6. References

[1] B. C. Gerwick, "Design and Construction of Prestressed Concrete Vessels," Paper

Number OTC 1886, presented at the Fifth Annual Offshore Technology Conference,

Houston, Texas, (1973).

[2] B. C. Gerwick, "State of the Art Report - Durability of concrete Structures Under

Water," presented at the International Association Colloquium-Liege, Belgium (June 5,

1975).

[3] L. Barker and Barrata: Comparison of fracture toughness measurements by the short

rod and ASTM standard method of test for plane strain fracture toughness of metallic

materials (E 399-78), J Test. Eval

8(3) :97 (1980).

[4] J. F. Beech and A. R. Ingraffea, Three dimensional finite element calibration of the

short-rod specimen, accepted for publication in the Int'l. J. Fract. , in press.

[5] A. R. Ingraffea and H. Y. Ko, Determination of the fracture parameters for rock,

paper to appear i_n: "Proceedings of the International Symposium on Absorbed Specific

Energy," Budapest, Hungary (Sept. 1980), in press.

[6] G. E. Monfore and A. E. Lentz, Physical properties of concrete at very low temperatures , PCA Res . Dev . Lab

4(2) : 33 (1962).

[7] Mindess, Sidney, "Application of Fracture Mechanics to Cement and Concrete," presented at the 81st Annual Meeting of the American Ceramic Society, Cincinnati, Ohio,

Paper 1-S II - 79 (1979)

364
TENSILE, COMPRESSIVE, AND SHEAR PROPERTIES OF A 64-kg/m 3

POLYURETHANE FOAM AT LOW TEMPERATURES*1

'

J. M. Arvidson

Fracture and Deformation Division

National Measurement Laboratory

L. L. Sparks and C. Guobang^

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Polyurethane foam, having a density of 64 kg/m 3

, was tested at 295, 111,

76 and 4 K. The material properties reported are Young's modulus, prcfportional limit, yield strength (at 0.2% offset), tensile, shear, and compressive

strengths, and elongation (elastic and plastic). To perform these tests, a unique apparatus was developed. This apparatus permits tension, compression,

and shear testing of materials at any temperature ranging from 295 to 1.8 K. Strain is measured with a concentric, overlapping-cylinder capacitance extensometer that is highly sensitive and linear in output.

Key Words: Compressive strength; elongation; foam; insulation; low temperatures; mechanical properties, proportional limit; shear strength; tensile

strength; yield strength; Young's modulus.

Supported by the Gas Research Institute, Chicago and the Office of Fusion

Energy, U. S. Department of Energy.

^Published as report number NBSIR 83-1684, National Bureau of Standards,

Boulder, Colorado (1983). Also published in Advances in Cryogenic

Engineering- Materials , vol . 30, Plenum Press, New York (1984), pp. 97-104.

^Guest worker at NBS. Department of Thermal Science, Zhejiang University,

Hangzhon, Zhejiang Province, People's Republic of China.

365

1. INTRODUCTION

Polyurethane foams are used in many structural as well as insulating

applications in which knowledge of material performance in extreme

environments (e.g., at liquefied natural gas, liquid nitrogen, and liquid

helium temperatures) is essential. Accurate data, predictive capability, and

standardized methods and materials improve the selection and development of

materials for these applications. The mechanical properties reported here are

part of a broader effort to understand and predict the thermal and mechanical

behavior of expanded plastics (foams) in cryogenic environments.

The tensile, compressive, and shear properties of polyurethane foam,

having a density of 64 kg/m 3

, were determined using a test fixture developed

specifically for this program [1]. This fixture provides the capability of

determining the above material properties at any temperature from ambient

(295 K) to 1.8 K. Tests can be done in a cold gaseous atmosphere or in

liquids, such as helium (4 K), nitrogen (76 K) , and dry ice and alcohol

(195 K). The fixture has also been designed to test materials at the above

temperatures while under static pressures ranging from subatmospheric to

approximately 0.3 MPa (43.7 psia).

A strain extensometer that was developed for use with soft viscoelastic

materials utilizes concentric overlapping cylinders and the change in electrical

capacitance to detect specimen strain [2]. This type of extensometer does not

attach directly to the specimen, so the effect of instrumentation on the

experimental results is negligible (verified to contribute <2.5 x 10" m for

our specimen geometry). The extensometer works well in cryogenic environments,

is accurate, and is linear for large strains [3,4]. The capacitance extensometer

system designed for this work had a linearity range in excess of 2.5 cm when

used with the current foam specimen geometry (2.9-cm diameter by 9.9-cm length).

367
Similar extensometers can be designed for specific sensitivities and extents

of linearity [5]. As long as the capacitance extensometer is situated in a

stable fluid (i.e., single phase and nonboiling) the resultant is a very high

signal-to-noise ratio. These sensors function in gases as well as in liquids

and the device is only sensitive to the dielectric constant of the test

medium. The original calibration of the system, for example, can be performed

at room temperature in air. To conduct a test in any other medium (e.g.,

liquid nitrogen) the original calibration need only be corrected for the

change in dielectric constant [6].

2. MATERIAL CHARACTERIZATION

The material tested in this study is a nominal 64-kg/m 3 polyurethane foam

designated as GM35. This amorphous organic polymer is a thermosetting foam.

Our supply of this material was obtained from the NBS Office of Standard

Reference Materials (OSRM) in Gaithersburg, Maryland. The OSRM distributed

this and other expanded plastics for the Products Research Committee [7,8].

These materials were commercially produced and designated as General

Materials.

The bulk supply of GM35 was a 0.1-m x 0.6-m x 0.6-m slab (figure la).

The orientation of the elongated cell axis for the material used in the

physical properties tests was determined optically from statistical evaluation

of photomicrographs. The ratios of cell height to cell width for the

principal orthogonal planes of the physical test specimens were: x/y = 0.94 ±

0.34, z/x = 1.60 ± 0.65, z/y = 1.51 ± 0.58. The uncertainties given represent

estimates of one standard deviation. The cell orientations relative to the

orthogonal axes of the bulk slab are shown in figure lb.

368
The density of this resin-gas composite was found to be 62.22 ± 0.28

kg/m 3

, 62.52 ± 0.11 kg/m 3

, and 62.56 ± 0.13 kg/m 3 after conditioning at 23°C

and 24, 50, and 92 percent relative humidity respectively. The uncertainties

given are estimates of one standard deviation.

3. SPECIMENS

Test specimens taken from the x/y or z/x plane in the bulk supply (see

figure 1) are designated "longitudinal" when loaded parallel to the z direction

Conversely, specimens taken from the x/y plane and loaded parallel to either

the x or y direction are designated "transverse".

The tensile specimens were rods 9.9-cm long and 2.9-cm in diameter. This

specimen was used to determine Young's modulus, proportional limit, yield

strength (at 0.2% offset) , and elongation (extrapolated using ultimate

tensile strength). For the determination of ultimate tensile strength, a

reduced section specimen was used. Its gage length was 5.1 cm and its

diameter was 1.9 cm. All tensile specimens were epoxied to polycarbonate

grips, which were threaded to accomodate the tensile pull-rod system. The

reduced-section geometry forced fracture to occur within the gage length,

thereby eliminating the effect of biaxial stresses at the grip ends.

The compression specimens were 2.54-cm long and 2.9-cm in diameter.

These specimens did not require grips.

Shear specimens were 1.9 cm x 2.54 cm x 0.4 cm. The specimens were

epoxied to two flat plates and each plate was attached to the upper and lower

tensile pull-rod system, respectively. An aluminum cylinder was slipped over

the specimen and plates to help maintain alignment and minimize induced torque

during testing. In addition, the cylinder has a built-in resistive heater

that is controlled by a thermocouple to produce and maintain the desired test

temperature.

369
4. TEST PROCEDURES

Most tests were conducted at 295 K(air), 111 K(gaseous helium), 76 Illiquid

nitrogen), and 4 K (liquid helium). To minimize thermal shock to the specimen,

the liquid helium or nitrogen was transferred at a very slow rate. The tensile

and compressive properties included: Young's modulus, proportional limit,

yield strength (at 0.2 percent offset), tensile and compressive strengths, and

elongation (elastic and plastic).

Since an ASTM shear strength test method is not available for soft

cellular materials such as these foams, several methods were carefully considered, and a version of the guillotine- type shear test was selected. Many

specimen geometries (thicknesses and widths) were tested to find the best

combination that most consistently failed in shear. At least three tests were

conducted at each temperature; in some cases, more tests were run to determine

material variability. Prior to testing, all specimens were "conditioned" in

an environmental chamber for not less than four days at 23°C and 50 percent

relative humidity. Each specimen was tested shortly after removal from the

environmental chamber. All tests were conducted in a conventional compression/

tension test machine at a strain rate of 5 x 10 min . (Varying the rate

-4 - 2 -

from 5 x 10 to 5 x 10 min had no measurable effect on results.)

5. RESULTS

Results are presented in figures 2 through 15 and tables 1 through 6.

The bars on the figures indicate the data spread from replicate tests.

Scatter is typically higher for compression and shear than for tensile tests;

this is because the compressive and shear tests are more sensitive to problems

such as misalignment (tensile specimens self-align during the test). Unlike

the 32-kg/m 3 foam that was tested previously [1], the cell orientation of the

64-kg/m 3 material agreed very well with the bun-line orientation

370
(i.e., the vertical or "rise" direction is denoted as longitudinal). Tensile

results shown in figures 2 through 6 are Young's modulus, ultimate strength,

and strain- versus- temperature, as well as stress- versus-strain curves for all

temperatures. In addition to the above properties, compressive results

include yield strength (at 0.2% offset), proportional limit versus temperature,

and a typical load-versus-displacement curve, as shown in figures 7 through

14. The shear results are given in figure 15.

Tensile, Young's modulus, proportional limit, yield strength, ultimate

strength, and shear strength values all increase as temperature decreases from

295 K to 4 K. The longitudinal orientation results have the highest values.

As shown in figure 4, tensile strain decreases with temperature, and the

material becomes brittle at temperatures below 111 K. The compressive Young's

modulus versus temperature, as shown in figure 7, indicates a decrease in mean

values from 111 K to 76 K, for both longitudinal and transverse specimens.

The same behavior was also noted for a 32-kg/m 3 polyurethane foam material

that was previously tested [1]. Using the Student's "t" test for small sample

size, the longitudinal and transverse compressive data were calculated for 76

and 111 K. The results indicate a level of confidence of >99.95% for the

transverse and 88% for longitudinal tests that the mean compressive modulus at

76 K is lower than the mean compressive modulus at 111 K [9], Figure 11

indicates a deformation capability during compression at low temperatures.

However, since the polyurethane material is incapable of true plastic

deformation at cryogenic temperatures , this apparent plastic strain is caused

by individual cells that collapse during testing. Figures 12 and 13 show the

stress-versus-strain behavior of longitudinal and transverse specimens at 295,

111, 76, and 4 K. Figure 14 is an actual record of load-versus-displacement

Tor a typical specimen. The load drops illustrate points

371
at which individual or multiple cells fail under stress. Owing to material

variability, the stress-strain graphs were plotted as smooth curves, which do

not show the cell failure phenomena. Each stress-strain curve, at a given

temperature and orientation, is the average of three or more specimens tested.

6. DISCUSSION

Polyurethane foam behavior is typical of polymers in general, with large

mechanical property changes such as a complete loss of ductility and a doubling

of Ej (Young's modul us- tens ion ) following a temperature reduction from 295 K

to 4 K. Certain longitudinal properties, like shear strength and E^ (Young's

modulus-compression), exhibit maximum values between the two extreme

temperature limits; however this is probably not a true material behavior but

an effect influenced by material variability and orientation irregularities.

The anomalous behavior of compressive Young's modulus as shown in figure 7

appears to be a real effect. As stated previously, the 32-kg/m 3 polyurethane

foam tested exhibited the same drop in modulus from 111 to 76 K. In addition,

a third density of polyurethane foam (96-kg/m 3

) has recently been tested and

it shows the same trend.

Sectioning after testing revealed that cell orientation varied slightly

from the orientation of the mold axes (see figure 1). It is generally thought

that foam specimens from the center of a large billet have uniform cells

oriented with respect to the vertical, but this is not true of foams formed on

a continuous or bun-line production facility. The cell orientation reflects

the movement of the foaming resin. However, as shown in this higher density

foam, the problem of cell orientation with respect to vertical is not as

severe as with less dense materials. Cells in the x-z plane of the material

reported here have only a 86 to 87° inclination to the x-axis (figure 1).

372
Specimens tested previously in liquid nitrogen [1] appeared to have

slightly lower shear strength values than those tested at the same temperature

in cold helium gas. This may be an indication of environmental sensitivity.

Nitrogen at low temperatures is deleterious to a number of other polymeric

materials. Thermoplastics have exhibited crazing or reduced fracture strengths,

or both when tensile tested in cold liquid or gaseous nitrogen, but not in

vacuum or helium environments [10]. Environmental effects must ultimately be

taken into account in design applications.

The authors are indebted to Robert S. Bell and Ronald D. Kriz for their

assistance in the preparation of this manuscript for publication.

References

[1] J. M. Arvidson and L. L. Sparks, "Low Temperature Mechanical Properties

of a Polyurethane Foam", NBSIR 81-1654, National Bureau of Standards,

Boulder, Colorado (November, 1981).

[2] R. P. Reed, J. M. Arvidson, and R. L. Durcholz, Tensile properties of

polyurethane and polystyrene foams from 76 to 300 K, in: "Advances in

Cryogenic Engineering," Vol . 18, K. D. Timmerhaus, ed.j'Flenum Press, New

York (1973), pp. 184-193.

[3] J. M. Roberts, R. B. Herring, and D. E. Hartman, The use of capacitance

gauge sensors to make precision mechanical property measurements, j_n:

"Materials Technology," American Society for Mechanical Engineers, New

York (1968), pp. 87-96.

[4] "High-Temperature Capacitive Strain Measurement System," NASA Tech. Brief

B75-10069, NASA (1975).

[5] P. C. F. Woldendale, Capacitive displacement transducers with high

accuracy and resolution, J. Sci. Instrum. ( J. Phys. E) 1:817 (1968).

[6] G. R. White, Measurement of thermal expansion at low temperatures

,

Cryogenics , 2:151 (1961).

[7] "Materials Bank Compendium of Fire Property Data," Products Research

Committee, J. W. Lyons, chairman. National Bureau of Standards,

Washington, D.C. (1980).

[8] W. G. Jurevic, "Structural Plastics Applications Handbook Supplement 1 Test Methods," Technical Report AFML-TR-67-332 (1969).

373
[9] J. W. Dally, Statistical treatment of experimental data, Experimental

Mechanics 19(11) :421 (1979).

[10] A. Hiltner and E. Baer, Mechanical properties of polymers at cryogenic

temperatures. Polymer 15:805 (1974).

374
List of Figures

Figure 1(a)

(b)

Figure 2.

Figure 3.

Fi gure 4.

Figure 5.

Fi gure 6.

Figure 7.

Fi gure 8.

Figure 9.

Fi gure 10.

Figure 11.

Figure 12.

Figure 13.

Fi gure 14.

Figure 15.

bulk supply.

Tensile Young's modulus versus temperature.

Ultimate tensile strength versus temperature.

Tensile strain versus temperature.

Tensile stress versus strain (longitudinal orientation).

Tensile stress versus strain (transverse orientation).

Compressive Young's modulus versus temperature.

Compressive strength versus temperature.

Compressive proportional limit versus temperature.

Compressive yield strength versus temperature.

Compressive strain versus temperature.

Compressive stress versus strain (longitudinal orientation).

Compressive stress versus strain (transverse orientation).

Compressive load versus displacement (transverse orientation).

Shear strength versus temperature (longitudinal and transverse).

List of Tables

Table 1. Tensile test results for a 64-kg/m 3 polyurethane foam.

Table 2. Compressive test results for a 64-kg/m 3 polyurethane foam.

Table 3. Shear strength test results for a 64-kg/m 3 polyurethane foam.

Table 4. Summary of tensile test results for a 64-kg/m 3 polyurethane foam

(average values).

Table 5. Summary of compressive test results for a 64-kg/m 3 polyurethane- foam

(average values).

Table 6. Summary of shear strength test results for a 64-kg/m 3 polyurethane

foam (average values).

375
Figure 1(a). Bulk supply of bun-line-produced, 64-kg/m3 polyurethane foam.

(b). Cell orientation relative to the major coordinate axes of the

bulk supply.

376
YOUNG'S

MODULUS,

MPR

100.0 I 1 i

0. 0

-0.0 50.0 100.0 150.0 200.0

TEMPERATURE,

250.0 —f 0.0300.0

Figure 2. Tensile Young's modulus versus temperature.

377

YOUNG'S

MODULUS,

KS
TENSILE

STRENGTH,

MPfl

Figure 3. Ultimate tensile strength versus temperature.

378

TENSILE

STRENGTH,

PS
TENSILE

STRAIN,

%

379
STRESS,

MPfl

380

STRESS,

PS
1 1 1 1

STRAIN

Figure 6. Tensile stress versus strain (transverse orientation).

381

STRESS,

PS
YOUNG'S

MODULUS,

MPfl

382

YOUNG'S

MODULUS,

KSI
COMPRESSIVE

STRENGTH,

MPR

383

CONPRESS

I

VE

STRENGTH,

PS
PROPORTIONAL

LIMIT,

MPA

TEMPERATURE,

Figure 9. Compressive proportional limit versus temperature.

384

PROPORTIONAL

LIMIT,

PSI
YIELD

STRENGTH

(FIT

0.27.

OFFSET

),MPR

TEMPERATURE,

Figure 10. Compressive yield strength versus temperature.

385

YIELD

STRENGTH

(AT

0.2%

OFFSET),

PSI
COMPRESSIVE

STRRIN,%

386
STRESS,

MPR

STRAIN

Figure 12. Compressive stress versus strain (longitudinal orientation).

387

STRESS,

PS
STRESS,

MPA

STRAIN

Figure 13. Compressive stress versus strain (transverse orientation).

388

STRESS,

PS
LORD,KN

Figure 14. Compressive load versus displacement (transverse orientation).

389

LORD,

LB
SHEAR

STRENGTH,

MPA

TEMPERATURE,

Figure 15. Shear strength versus temperature (longitudinal and transverse).

390

SHEAR

STRENGTH,

PS
Table 1. Tensile test results for a 64-kg/m 3 polyurethane foam

Specimen

number

Test

temp.

,

K

Specimen Young's

orientation3 MPa

modul us

,

psi

Proportional limit,

MPa psi

Yield strength

(at 0.2% offset)

MPa psi

Ultimate tensile strength

MPa psi

Tensile strain, %

Elastic Plastic Total

2LT.1LRT 295 L 31 .63 4587 0.304 44.09 0.572 82.96 1 .027 148.95 3.1 2.8 5.9 4LT.3LRT 295 L 32.13 4660 0.315 45.68 0.602 87.31 0.957 138.79 3.1 2.8 5.9 6LT.5LRT 295 L 29.51 4280 0.338 49.02 0.636 92.24 1 .000 145.03 3.1 3.9 7.0

x = 31.09 4509 0.319 46.26 0.603 87.50 0.995 144.26 3.1 3.2 6.3 2TT.1TRT 295 T 14.59 2116 0.156 22.63 0.262 38.00 0.639 92.67 4.5 5.8 10.3 4TT.3TRT 295 T 14.00 2030 0.145 21 .03 0.252 36.55 0.662 96.01 4.6 6.7 11.3 10TT.9TRT 295 T 14.08 2042 0.171 24.80 0.262 38.43 0.638 92.53 4.6 5.5 10.1

x = 7432 2063 0.157 22.82 0.260 37.66 0.646 93.74 4.6 6.0 10.6 22LT.15LRT 111 L 58.80 8528 - - - - 1.204 174.61 1 .9 0 1.9

24LT.1 7LRT 111 L 58.75 8521 - - - - 1 .041 150.98 1 .9 0 1.9 34LT.21LRT 111 L 60.20 8730 - - - - 1.101 159.68 1.7 0 1.7

x = 59.25 8593 - - - - T3T5 161.76 175 O 175

24TT.19TRT 111 T 25.58 3710 - _ - _ 0.637 92.38 2.4 0 2.4 26TT.23TRT 111 T 25.84 3748 - - - - 0.611 88.61 2.3 0 2.3 42TT.25TRT 111 T 26.63 3862 - - - - 0.573 83.10 2.3 0 2.3

x = 20? 3774” - - - - 0.607 88.03 23 O 23

8LT.9LRT 76 L 64.97 9423 - - - - 1.136 164.75 1.9 0 1 .9 12LT.11LRT 76 L 60.80 8818 - - - - 1.286 186.51 1 .8 0 1.8 14LT.13LRT 76 L 63.91 9269 - - - - 1.247 180.85 1.9 0 1.9

x = 6337 9175 - - - - 1 .223 177.37 1.9 0 1 .9 12TT.11TRT 76 T 27.82 4035 - - - . 0.750 108.77 2.6 0 2.6 14TT.13TRT 76 T 28.31 4106 - - - - 0.723 104.86 2.6 0 2.6 16TT.17TRT 76 T 27.68 4014 - - - - 0.721 104.57 2.6 0 2.6

x = 27.94 3557 - - - - 0.73) 106.07 73 0 73

16LT.19LRT 4 L 78.14 11333 . - - _ 1.172 169.97 1.5 0 1.5 18LT.23LRT 4 L 75.78 10990 - - - - 1.242 180.13 1.5 0 1.5 32LT.25LRT 4 L 74.26 10770 - . - - 1.149 166.64 1 .6 0 1.6

x = 76.06 TT03T - - - - 1.188 172.25 1.5 0 1 .5 18TT.15TRT 4 T 33.19 4814 - - - _ 0.702 101.81 2.0 0 2.0 20TT.27TRT 4 T 32.99 4785 - - - - 0.641 92.96 2.0 0 2.0 30TT.31TRT 4 T 31 .54 4574 - - - - 0.662 96.01 2.1 0 2.1

x = 32757 4724 - - - - 0.668 96.93 2.0 0 23

a L: longitudinal; T: transverse

391
Table 2. Compressive test results for a 64-kg/m 3 polyurethane foam

Specimen Test Specimen Young's modul us

,

Proportional limit, Yield strength Maximum compressive Compressive

number temp.

,

orienta- (at 0.2% offset)

,

strength. strain, %

K tion a MPa psi MPa psi MPa psi MPa psi Elastic Plastic Total

26LC (A) 295 L 23.08 3347 0.355 51.49 0.498 72.22 0.668 96.88 2.8 2.8 5.6 26LC (B) 295 L 20.37 2954 0.405 58.74 0.482 69.90 0.668 96.88 3.2 3.4 6.6 28LC (B) 295 L 21 .63 3137 0.382 55.40 0.504 73.10 0.680 98.62 3.0 4.4 7.4

x = 21.69 3146 0.381 5572T 095 7T77? 0.672 97.46 05 375 53

32TC (A) 295 T 7.86 1140 0.121 17.55 0.222 32.20 0.360 52.21 4.4 3.1 7.5 32TC (B) 295 T 8.30 1204 0.136 19.72 0.219 31.76 - a

- - - - 38TC (A) 295 T 7.95 1153 0.174 25.24 0.270 39.16 0.378 54.82 4.5 2.6 7.1

x = 8.04 1166 (043 20? 037 3T737 055 53752 ?75 273 773

28LC (A) 111 L 105.81 15346 0.715 103.70 0.817 118.49 1 .078 156.34 1 .0 8.4 9.4

28LC (B) 111 L 87.19 12645 0.664 96.30 0.823 119.36 1 .063 154.17 1 .2 10.5 11.7

30LC (A) 111 L 88.72 12867 0.657 95.28 0.792 114.86 1 .121 162.58 1.3 8.3 9.6

x = 93.91 T35T5 075 M IS. 811 117.57 1.087 157.70 T7? O TO

40TC (B) 111 T 30.07 4361 0.389 56.42 0.482 69.90 0.734 106.45 2.4 9.9 12.3 40TC (C) 111 T 30.07 4361 0.362 52.50 0.409 59.32 0.722 104.71 2.3 10.7 13.0

47TC (A) 111 T 33.46 4853 0.334 48.44 0.378 54.82 0.730 105.87 2.1 8.0 10.1

x = 31.20 4525 0.362 52.45 0.423 5T735 029 105.68 273 575 1T.8

31 LC (A) 76 L 85.13 12346 0.846 122.70 0.970 140.68 1.179 170.99 1.4 7.7 9.1 31LC (B) 76 L 87.77 12729 0.873 126.61 0.962 139.52 1.160 168.23 1.3 8.2 ' 9.5

31 LC (C) 76 L 82.03 11897 0.753 109.21 0.897 130.09 1.131 164.03 1.4 7.2 8.6

x = 84.98 1232? 02? 119.51 0.943 136.76 1.157 1 "67“ 7 5 T7? 777 O

38TC (A) 76 T 16.80 2436 0.376 54.53 0.552 80.06 0.792 114.86 4.6 5.9 10.5

38TC (B) 76 T 17.72 2570 0.341 49.46 0.537 77.88 0.792 114.86 4.4 7.6 12.0 49TC (A) 76 T 16.85 2444 0.349 50.62 0.539 78.17 0.781 113.27 4.5 7.3 11.8

x = 17.12 1483 0.355 51.54 0?3 705 088 ll?.33 ?75 573 TIT?

33LC (A) 4 L 79.55 11537 0.765 110.95 0.897 130.09 1.156 167.65 1.5 5.9 7.4 33LC (B) 4 L 53.17 7711 0.850 123.28 0.955 138.50 1.183 171 .57 2.2 7.4 9.6

33LC (C) 4 L 99.43 14420 0.846 122.70 0.947 137.34 1.210 175.49 1.2 8.7 9.9 35LC (A) 4 L 137.69 19969 - 0.765 110.95 1.206 174.91 0.9 8.5 9.4

x = 92.46 T3?55 020 118.98 031 129.22 T7T55 172.41 1 .5 7.6 57T

35TC (B) 4 T 43.48 6306 0.294 42.64 0.387 56.13 0.807 117.04 2.1 8.4 10.5 48TC (A) 4 T 46.29 6713 0.475 68.89 0.579 83.97 0.850 123.28 2.0 14.3 16.3

49TC (B) 4 T 45.17 6551 - - - - 0.838 121.53 - - - x = 44.98 6523 0.384 55.77 0.483 70.05 0.832 120.62 o TIT? 13.4

a Stress continued to increase as strain increased - no maximum reached.

392
Table 3. Shear strength test results for a 64-kg/m 3 polyurethane foam

Specimen

number

Test

temperature

,

K

Specimen

orientatioi

Shear strength,

MPa psi

SL4 295 L 0.428 61.99

SL6 295 L 0.581 84.19

SL7 295 L 0.514 74.53

x = 0.508 73.57

ST6 295 T 0.681 98.68

ST7 295 T 0.661 95.90

ST8 295 T 0.663 96.19

x = 0.668 96.92

SL11 111 L 0.697 101 .01

SL12 111 L 0.728 105.54

SL1 3 111 L 0.694 100.67

x = 0.706 102.41

ST1

111 T 0.704 102.09

ST1111 T 0.729 105.65

ST13 111 T 0.791 114.67

x = 0.741 107.47

SL1 76 L 0.727 105.38

SL2 76 L 0.739 107.13

SL3 76 L 0.705 102.23

x = 0.724 104.91

ST4 76 T 0.821 119.07

ST9 76 T 0.546 79.19

ST1

0

76 T 0.759 110.00

x = 0.709 102.75

SL8 4 L 0.612 88.70

SL9 4 L 0.691 100.18

SL1

0

4 L 0.712 103.20

x = 0.672 97.36

ST1 4 T 0.909 131.78

ST3 4 T 0.739 107.08

ST5 4 T 0.975 141 .37

x = 0.874 126.74

393
Table 4. Summary of tensile test results for a 64-kg/m 3 polyurethane foam (average values)

Material

property

Specimen

orientation 295 K Temperature

111 K 76 K 4 K

Young 1 s L 31.09 (4,510) 59.25 (8,590) 63.23 (9,170) 76.06 (11,030) modulus

,

MPa (psi)

T 14.22 (2,060) 26.02 (3,770) 27.94 (4,050) 32.57 ( 4,720)

Proportional L 0.319 (46.26) - - - limit,

MPa (psi)

T 0.157 (22.82)

Yield strength L 0.603 (87.50) - - - (0.2% Offset),

MPa (psi)

T 0.260 (37.66)

Ultimate ten- L 0.995 (144.26) 1.115 (161.76) 1.223 (177.37) 1.188 (172.25)

sile strength,

MPa (psi)

Tensile strain, %

T 0.646 ( 93.74) 0.607 ( 88.03) 0.731 (106.07) 0.668 ( 96.93)

Elastic L 3.1 1.8 1 .9 1.5 Plastic 3.2 0 0 0 Total 6.3 1 .8 1 .9 1.5

Elastic T 4.6 2.3 2.6 2.0

PI astic 6.0 0 0 0 Total 10.6 2.3 2.6 2.0

Table 5. Summary of compressive test results for a 64-kg/m3 polyurethane foam (average values)

Material Specimen Temperature

property orientation 295 K 111 K 76 K 4 K

Young ' s L 21.69 (3,150) 93.91 (13,620) 84.98 (12,320) 92.46 (13,410)

modul us

,

MPa (psi)

T 8.04 (1,170) 31.20 ( 4,530) 17.12 ( 2,480) 44.98 ( 6,520)

Proportional L 0.381 (55.21) 0.679 ( 98.43) 0.824 (119.51) 0.820 (118.98)

1 imi t

,

MPa (psi)

T 0.143 (20.84) 0.362 ( 52.45) 0.355 ( 51.54) 0.384 ( 55.77)

Yield strength L 0.495 (71.74) 0.811 (117.57) 0.943 (136.76) 0.891 (129.22)

(0.2% Offset),

MPa (psi)

T 0.237 (34.37) 0.423 ( 61.35) 0.543 ( 78.70) 0.483 ( 70.05)

Maximum compres- L 0.672 (97.46) 1.087 (157.70) 1.157 (167.75) 1.189 (172.41)

sive strength,

MPa (psi)

T 0.369 (53.52) 0.729 (105.68) 0.788 (114.33) 0.832 (120.62)

Compressive strain. % Elastic L 3.0 1.2 1.4 1.5 Plastic 3.5 9.0 7.7 7.6

Total 6.5 10.2 9.1 9.1

Elastic T 4.5 2.3 4.5 2.0 Plastic 2.8 9.5 6.9 11.4

Total 7.3 11.8 11.4 13.4

394
Table 6- Summary of shear strength test results for a 64-kg/m 3 polyurethane foam (average values)

Test

temperature, K Specimen orientation Shear

MPa

strength,

psi

295 L 0.508 73.57

T 0.668 96.92

111 L 0.706 102.41

T 0.741 107.47

76 L 0.724 104.91

T 0.709 102.75

4 L 0.672 97.36

T 0.874 126.74

395

TENSILE, COMPRESSIVE, AND SHEAR PROPERTIES OF A 96-kg/m3

POLYURETHANE FOAM AT LOW TEMPERATURES*"

1

"

J. M. Arvidson and R. S. Bell

Fracture and Deformation Division

National Measurement Laboratory

L. L. Sparks and C. Guobang 1 Chemical Engineering Science Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Polyurethane foam, having a density of 96 kg/m3

, was tested at 295, 111,

76 and 4 K. The material properties reported are Young's modulus, proportional limit, yield strength (at 0.2% offset), tensile, shear, and compressive

strengths, and elongation (elastic and plastic). The test apparatus permits

tension, compression, and shear testing of materials at any temperature

ranging from 295 to 1.8 K. Strain is measured with a concentric, overlappingcylinder, capacitance extensometer that is highly sensitive and linear in

output. The extent of linearity was in excess of 2.5 cm for the cylinder

_ 6 geometry chosen, and the signal noise level was only 10 cm/ cm.

Key Words: Compressive strength; elongation; foam; insulation; low temperatures; mechanical properties; proportional limit; shear strength; tensile

strength; yield strength; Young's modulus.

Supported by the Gas Research Institute, Chicago and the Office of Fusion

Energy, U. S. Department of Energy.

'Published as report number NBSIR 83-1696, National Bureau of Standards,

Boulder, Colorado (1983).

'Guest worker at NBS. Department of Thermal Science, Zhejiang University,

Hangzhon, Zhejiang Province, People's Republic of China.

397

1 INTRODUCTION

In a continuing effort to increase the available knowledge of the mechanical

properties of polyurethane foam (PU) , a foam of density 96 kg/m3 was subjected

to the same test program as was previously conducted on less dense

materials [1,2]. The data presented will complete a three year effort to

characterize the mechanical properties of three densities of PU foam at low

temperatures. Previous reports on the mechanical properties of 32 and 64

kg/m3 density foams may be obtained from the National Technical Information

Service (NTIS) , Springfield, VA 22161 (request NBSIR 81-1654 and NBSIR

83-1684 respectively).

The apparatus used [1,2] has the capability of operating at various

temperatures (295 K to 4 K) , in gas or liquid environments and at pressures

from subatmospheric to 0.3 MPa absolute. Strain is measured by utilizing

concentric overlapping-cylinders and the change in electrical capacitance [3].

This method for strain extensometrv is accurate to better than 0.1 percent,

linear in excess of 2.5 cm elongation, functions well in low temperature

environments, and provides a low-noise output signal (<_ 10 ^ cm/cm) as long as

the device is situated in a stable single-phase fluid [4,5]. The calibration

can be accomplished at room temperature, in air, and to conduct a test in any

other medium (e.g., liquid nitrogen) the original calibration need only be

corrected for the change in dielectric constant [6].

2. MATERIAL CHARACTERIZATION

The material tested in this study is a nominal 96 kg/m3 PU foam. This

amorphous, organic polymer is a thermosetting foam. Our supply of this

material was obtained from a commercial producer.

399
The bulk supply was in the form of a 0.13 X 1.22 X 2.44 m slab; the

coordinate axes relative to these dimensions are z, y, and x respectively.

The orientation of the cell axes was determined optically from statistical

evaluation of microphotographs . The ratios of all height to cell width for

the principal orthogonal planes of the physical test specimens were:

x/y = 1.02 ± 0.50, z/x = 1.14 ± 0.59, z/y = 1.14 ± 0.59. The uncertainties

given represent estimates of one standard deviation. The ratios indicate that

the direction of foam rise is parallel to the z axis, is essentially

perpendicular to the xy plane, and the cellular cross-section in the xy plane

is nearly circular.

The density of the resin-gas composite was found to be 99 ± 3.4 kg/m3

after conditioning at 23°C and 50 percent relative humidity. The

uncertainty given is an estimate of one standard deviation.

3. SPECIMENS

Two tensile specimen geometries were used to determine all mechanical

properties. A rod (epoxied to polycarbonate grip ends) of 9.9 cm in length

and 2.9 cm in diameter was used to determine Young's modulus, proportional

limit, yield strength, and elongation. A reduced-section specimen with a gage

length of approximately 5.1 cm, and 1.9 cm in diameter, was used to determine

the ultimate tensile strength. Using this geometry forced a failure within

the gage length, thus avoiding a premature failure elsewhere due to biaxial

stresses at the epoxied polycarbonate grips.

The compression specimens were rods 2.54 cm long and 2.54 cm in diameter.

No grips were required for these specimens and therefore all compressive

material properties were determined using this geometry.

400
The shear specimens, 1.9 X 2.54 X 0.4 cm, were epoxied to flat plates and

each plate was attached to the tensile pull-rod system. An aluminum cylinder

slipped over the specimen plates with a resistive heater and thermocouple,

built into the cylinder, was used for temperature control during a test.

4. TEST PROCEDURE

Tests were conducted at 295 K (air). 111 K (GN 9

) , 76 K (LN^) , and 4

K (LH ). A minimum of three samples were tested at each temperature, ar.d in

e some cases several more were tested to determine material variability.

Minimization of thermal shock to the sample was accomplished by using very

slow transfer rates of liquid helium or nitrogen; on the order of 0.21 min

A given temperature was held for a minimum of 15 minutes prior to testing, in

order to ensure that the specimen was isothermal.

Each specimen was "conditioned" in an environmental chamber for at least

four days at 23°C and 50 percent relative humidity. Tension, compression, and

shear tests were conducted using a conventional tension/compression test

-3 -1

machine at a strain rate of 5 X 10 min . Preliminary tests were conducted,

-2 -4 -1

varying the strain rate from 5 X 1C to 5 X 10 min . The test results

indicated there was no measurable effect on the mechanical property values.

Tensile and compressive properties reported include: Young's modulus,

proportional limit, yield strength (at 0.2% offset), ultimate strength, and

elongation (elastic and plastic)

5. RESULTS

Results are presented in figures 1 through 12 and tables 1 through 6.

The bars on these figures indicate the data spread from replicate tests. The

scatter is typically higher for compression and shear than for tensile tests

401
because the compressive and shear tests are more sensitive to misalignment

during testing (tensile specimens tend to self-align)

All properties were determined in both the longitudinal and transverse

orientations. The temperature dependent tensile results for Young's modulus,

strength, and strain are shown in figures 1 through 3. Tensile stress versus

strain at all test temperatures is shown in figure A. Temperature dependent

compressive results for Young's modulus, strength, proportional limit, yield

strength, and strain are shown in figures 5 through 9. Compressive stress

versus strain at all test temperatures is shown in figure 10. Figure 11 shows

a typical load versus displacement plot that was taken during an actual test.

The shear strength versus temperature is plotted in figure 12.

Tables 1 through 3 give the tensile, compressive, and shear results for

individual specimens and tables 4 through 6 give the average values for all

tests

Owing to material variability, the stress versus strain graphs were

plotted as smooth curves, which do not illustrate the individual cell failure

phenomena. Each stress versus strain curve at a given temperature and orientation is the average of three or more specimens tested.

6. DISCUSSION OF RESULTS

Compressive and tensile strength, proportional limit, yield strength, and

Young's modulus increase with decreasing temperature. The longitudinally

oriented specimens are always higher in strength than those obtained from the

transverse orientation.

402
As shown in figure 3, tensile strain decreases with temperature as the

material becomes brittle at temperatures below 111 K. Both tensile and

compressive stress versus strain plots (see figures 4 and 10) illustrate the

behavior of longitudinal and transverse specimens tested at 295, 111, 76, and

4 K.

Figure 11 is an actual record of load versus displacement for a typical

specimen. The load drops that occur at low temperature may be associated with

individual or multiple cells collapsing [7,8]. Because the material is less

brittle at room temperature this phenomena is not seen.

The shear strength, as shown in figure 12, increases from room

temperature to 111 K and then levels off as the test temperature decreases to

4 K. The large range of values of shear strength at a given temperature, as

shown in figure 12, could result from misalignment during a test; and except

for tests at 76 K the longitudinal and transverse curves are similar.

It is believed that thermal cycling produces cell degradation [9].

Variables such as thermal cycling, moisture content, aging, and others could

be studied in the near future.

ACKNOWLEDGMENT

The authors are indebted to Edward A. Pierson for his assistance in the

preparation of this manuscript for publication.

403
REFERENCES

[1] J. M. Arvidson and L. L. Sparks, Low Temperature Mechanical Properties of

a Polyurethane Foam, NBSIR 81-1654, National Bureau of Standards,

Boulder, Colorado 80303 (November, 1981).

[2] J. M. Arvidson, L. L. Sparks, and Chen Guobang, Tensile, Compressive, and

Shear Properties of a 64 kg/m3 Polyurethane Foam at Low Temperatures,

NBSIR 83-1684, National Bureau of Standards, Boulder, Colorado 80303

(February, 1983).

[3] R. P. Reed, J. M. Arvidson, and R. L. Durcholz, Tensile Properties of

Polyurethane and Polystyrene Foams From 76 K to 300 K, in : "Advances in

Cryogenic Engineering", Vol. 18, K.D. Timmerhaus, ed . , Plenum Press, New

York (1973), pp. 184-193.

[4] J. M. Roberts, R. E. Herring, and D. E. Hartman, The Use of Capacitance

Gauge Sensors to Make Precision Mechanical Property Measurements, in : "Materials Technology", American Society for Mechanical Engineers, New

York (1968) , pp. 87-96.

[51 "High-Temperature Capacitive Strain Measurement System," NASA Tech. Brief

B75-10069, NASA (1975)

[6] G. K. White, Measurement of Thermal Expansion at Low Temperatures,

Cryogenics , 2 (1961), pp. 151-158.

[7] L. J. Gibson, M. F. Ashby, G. S. Schajer, and C. J. Robertson, The

Mechanics of Two-Dimensional Cellular Materials, Proc. R. Soc. Lond.

A382 (1982), pp. 25-42.

[8] I . J. Gibson and M. F. Ashby, The Mechanics of Three-Dimensional Cellular

Materials, Proc. R. Soc. Lond. A382, pp . 43-59 (1982).

[9] F.. L. Sharpe and R. G. Helenbrook, Durability of Foam Insulation for LH^

Fuel Tanks of Future Subsonic Transports, in Nonmetallic Materials and

Composites at Low Temperatures, (Eds. A. F. Clark, R. P. Reed and

G. Hartwig) , Plenum Press, New York, 1979, pp. 207-230.

404
LIST OF FIGURES PAGE

Figure 1. Tensile Young’s modulus versus temperature

Figure 2. Ultimate tensile strength versus temperature

Figure 3. Tensile strain versus temperature

Figure 4. Tensile stress versus strain (longitudinal and transverse)

Figure 5. Compressive Young's modulus versus temperature

Figure 6. Compressive strength versus temperature

Figure 7. Compressive proportional limit versus temperature

Figure 8. Compressive yield strength versus temperature

Figure 9. Compressive strain versus temperature

Figure 10. Compressive stress versus strain (longitudinal and

transverse)

Figure 11. Typical load versus displacement (arbitrary units)

Figure 12. Shear strength versus temperature (longitudinal and

transverse)

LIST OF TABLES

Table 1. Tensile test results for a 96-kg/m3 polyurethane foam

Table 2. Compressive test results for a 96-kg/m3 polyurethane foam

Table 3. Shear strength test results for a 96-kg/m3 polyurethane

foam

Table 4. Summary of tensile test results for a 96-kg/m3 polyurethane

foam (average values)

Table 5. Summary of compressive test results for a 96-kg/m3 polyurethane foam (average values)

Table 6. Summary of shear strength test results for a 96-kg/m3 polyurethane foam (average values)

405
YOUNG'S

MODULUS,

MPR

Figure 1. Tensile Young's modulus versus temperature.

406
TENSILE

STRENGTH,

MPR

407
TENSILE

STRRIN//

408
STRESS,

MPR

Figure 4. Tensile stress versus strain (longitudinal and transverse).

409
YOUNG’S

MODULUS,

MPfl

410
COMPRESSIVE

STRENGTH,

MPR

4.0

3.5

3.0 -S

i T

4

i'

2.5

ft-

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2 . 0

-

1.5-

1.0-

T ransverse

Longi tudi nal

\

100.0 150.0

TEMPERRTURE,K—i

200.0 250.0

-

l

n

-

300.0

Figure 6. Compressive strength versus temperature.

411
PROPORTIONAL

LIMIT,

MPA

412
YIELD

STRENGTH,

MPR

413
COMPRESSIVE

STRAINS

14.0

2 . 0

-

0 . 0

-

414
STRESS,

MPF1

415
LORD

Figure 11. Typical load versus displacement (arbitrary units).

416
SHEAR

STRENGTH,

MPA

1.4 l 1 1 i

0 . 6

-

0.4 -f

0.0 50.0 100.0 150.0 200.0

TEMPERATURE,

250.0 300.0

Figure 12. Shear strength versus temperature (longitudinal and transverse)

417
Table

1.

Tensile

test

results

fora

96-kg/m 3

polyurethane

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419
Table 3. Shear strength test results for a 96-kg/m3 polyurethane foam

Specimen

number

Test

temperature ,K

Specimen

orientation

Shear strength,

MPa psi

SL1 295 L 0.902 130.76

SL5 295 L 0.812 117.80

SL10 295 L 0.824 119.53

x = 0.846 122.70

ST2 295 T 0.955 138.52

ST9 295 T 0.864 125.33

ST 1 4 295 T 0.860 124.78

x = 0.893 129.54

SL2 111 L 1.218 176.70

SL6 111 L 1.051 152.38

SL1

111 L 1.073 155.67

X = 1.114 161.58

ST4 111 T 1 . 102 159.83

ST6 111 T 1.063 154.18

STIC 111 T 1.162 168.55

X = 1.109 160.85

SL3 76 L 0.938 136.10

SL7 76 L 1.073 155.62

SL 1

76 L 1.062 154.06

X = 1.025 148.59

ST3 76 T 1.150 166.73

ST176 T 1.114 161.59

ST 16 76 T 1.090 158.13

X = 1.118 162.15

SL4 4 L 1.069 155.03

SL9 4 L 1 .152 167.05

SL15 4 L 0.973 141.05

X = 1.064 154.38

ST 1 4 T 0.975 141.48

ST7 4 T 1.014 147.05

ST 13 4 T 1.071 155.32

X = 1.020 147.95

420
Table

4.

Summary

of

tensile

test

results

fora

96-kg/m 3

polyuretane

foam

(average

values)

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Plastic

Total
Table

5.

Summary

of

compressive

test

results

fora

96-kg/m 3

polyurethane

foam

(average

values)

X

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422
Table 6. Summary of shear strength test results for a 96-kg/m 3 polyurethane foam (average values)

Test

temperature, K

Specimen orientation Shear

MPa

strength

,

psi

295 L 0.846 122.70

T 0.893 129.54

111 L 1.114 161.58

T 1.109 160.85

76 L 1.025 148.59

T 1.118 162.15

4 L 1.064 154.38

T 1.020 147.99

423

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF

MECHANICAL PROPERTY DATA FOR TENSILE

TESTING OF COMPOSITE MATERIALS TO

LIQUID HELIUM TEMPERATURE (4 K)*

Metals Properties Council

Low TemperatOre Task Group

Proposal

11 / 25/83

*This proposal was written and approved by the Low Temperature Task Group of

the Metal Properties Council. NBS guidelines for the use of SI units were

not followed.

425

EXPERIMENTAL DATA TO SUPPORT EXTENSION OF

MECHANICAL PROPERTY DATA FOR TENSILE

TESTING OF COMPOSITE MATERIALS TO

LIQUID HELIUM TEMPERATURE (4 K)

Introduction

Organic-matrix, nonmetallic, filament-reinforced composite materials are critical components in many cryogenic structures. They serve as electrical

and thermal insulators and for structural supports in superconducting magnets

required for magnetic fusion energy (MFE) and magnetohydrodynamic (MHD) power

generating systems. The high magnetic fields required for plasma confinement

create large forces that are transmitted through the nonmetal lie components to

the primary metallic structure. In MFE applications, structural integrity

must be maintained after exposure to large fluences of neutron and gamma

irradiation at 4 K. Nonmetallic composites also play a critical role as thermal standoff members supporting helium dewars in cryogenic spacecraft such

as the IRAS satellite. In each of these technologies there is an imperative

to improve performance by pushing the performance of composite materials to

their practical operating limits consistent with structural integrity.

There are currently no standardized mechanical property test procedures

for composite materials at liquid nitrogen (77 K, -320°F) temperatures or below or at liquid helium temperatures (4 K, -452°F). Mechanical testing

under these conditions involve unique considerations as compared to room temperature. Thermal conductivity is considerably reduced and the specific

heat tends toward zero. Consequently, when work is done on a specimen during

testing, the resultant internal heating is not easily removed, leading to

localized adiabatic heating. Special attention must therefore be paid to

control over strain rates if the correct test temperature is to be maintained.

Upon cooling, the organic matrix contracts more than does the reinforcing

fiber and becomes embrittled. This reduces the failure strain of the matrix

and can introduce significant damage in the early stages of tensile or compressive testing. This is observed as a "knee" in the stress strain curve. Embrittlement also increases the probability of premature failure from defects

on the specimen edges. This alters the specimen "size effect" and requires a different specimen configuration if bulk properties are to be accurately

predicted from cryogenic test data.

Testing at liquid helium temperatures is very expensive, both in cryogen

cost and in the time required. Additionally, the increase in strength

associated with low temperatures requires the use of larger test equipment, if room temperature specimen sizes are retained. Developing pull rods, grips,

and cryostats for equipment applying loads in excess of 100,000 pounds is very

costly and ineff icient—to date, none exist in the world. Maximum capacity of

existing cryogenic test systems are typically 20,000 to 50,000 pounds,

dictating the use of smaller specimens than those which have been standardized

for room temperature testing.

The proposed research is designed to produce the information required to

extend existing room temperature composite tensile testing standards to

cryogenic temperatures.

427
I. Internal Specimen Heating

A. Experimental: Strain Rate Effects in Various Media

Specimen heating effects during straining at room temperature are relatively small, usually on the order of a few degrees at strain rates normally

used. But as the test temperature decreases, the specific heat decreases,

causing a greater temperature rise for the same amount of work. This is

exacerbated by the intrinsically low thermal conductivity of nonmetal lie

composites and the further decrease of conductivity with cooling. The heating

effect therefore becomes increasingly pronounced as temperature is lowered,

reaching a maximum at 4 K. The magnitude of this effect will vary for

composites of differing types and orientations of layup. It may also vary

with the media in which the tests are conducted. It is anticipated that

increasing temperature will change the failure mode and reduce the rate and

severity of damage accumulation, thus affecting the mechanical performance.

The objectives of this program are therefore as follows:

1. To determine the maximum strain rate at which cryogenic tensile tests

can be performed on organic matrix composites without functionally

altering the measured parameters.

2. To assure that data generated in different laboratories are of

comparable validity.

It is proposed that this study be conducted with E-glass-fiber reinforced

epoxy matrix laminates of uniaxial construction. This provides the highest

elongation to failure and represents a worst case. It is also reflective of

the most commonly used cryogenic laminates. Testing should be performed at

4.2 K (-452° F), 77 K (-320°F) and at 295°K (68°F). Test environments are liquid helium, liquid nitrogen, and air, respectively.

The experiments should be conducted at strain rates not exceeding those

given in appropriate ASTM documents. Each specimen is to be instrumented to

continuously record internal temperature during testing. Stress-strain curves should be recorded as a function of strain rate so as to relate changes in

mechanical performance to heating. The limiting strain rate criteria should

be a temperature rise not greater than that experienced during room temperature tests conducted in accordance with ASTM procedures.

B. Model Development: Effects of strain rate and test media

Cryogenic tests carried out in liquid media provide relatively good heat

transfer characteristics between the test specimen and coolant. However,

cryogenic tests conducted at temperatures other that of the boiling point of a cryogen require heat transfer through a cold gas. The relatively poor heat

transfer of gasses will magnify the internal heating effects for a given test

procedure. Furthermore, the heat transfer characteristics of gasses and the

thermal conductivity and heat capacity of the specimens will change with

temperature.

428
An experimental program to assess the influence of all these variables

would be prohibitively expensive. A more practical approach is to investigate

development of analytic models that could predict the magnitude of internal

heating in terms of the operative parameters. This task is made easier by the

relatively simple specimen geometry and by relatively good knowledge of the

significant physical properties of the relevant solids, liquids, and gasses.

Work on such models should be correlated with the experimental work of

Test Program 1A, the results of which could serve as a criteria for model

validity. However, additional valaidation tests must be conducted in gaseous

helium and nitrogen. When verified, the appropriate model should then be used

to establish a standard tensile testing procedure.

II. The Stress-Strain "Knee": Effects of strain rate and fiber orientation

A. Experimental: strain rate and temperature effects

Development of a "knee" in the stress-strain curve indicates the onset of

internal damage. It is believed to reflect massive fracture of the matrix

phase, and a shift of the load carrying capacity entirely to the fiber phase.

It usually occurs at a stress significantly below the ultimate tensile

strength of the laminate, and is associated with a decrease in modulus, an increase in damping capacity, and loss of dimensional stability. Its onset

therefore establishes a maximum operating stress in many engineering

applications. The "knee" is prominently observed when crossplied or woven-fabric glass-reinforced laminates are tested in a direction other than

that of principle reinforcement. Figure 1 illustrates the phenomenon as observed in a G-11CR laminate tested in the ±45° direction to the warp and

fill at room temperature. Here, the "knee" reflects debonding at the

fiber-matrix interface. At this temperature, the effect is not often observed

when testing in the fiber reinforcement direction because the strain

capability of most epoxy resins is a reasonably close match to that of the

fiber. But at cryogenic temperatures the strain capability of the matrix

substantially decreases, while that of the glass increases. This causes early

onset of damage whenever glass-reinforced laminates are stressed at cryogenic

temperatures , regardless of the fiber orientation. However, because the

stress-strain curve is steeper at the lower temperatures , the "knee" may not

be as prominent as on Fig. 1.

The objectives of this program are therefore as follows:

1. To develop cryogenic tensile test procedures that accurately document

the onset of the stress-strain "knee", and therefore the onset of

major internal material damage.

2. To determine the effect of strain rate and temperature on the

position of the "knee".

3. To establish standard procedures for establishing the position of the

"knee" in laminates of commercial cryogenic interest.

429
It is proposed that this study be conducted on commercial, glass fabricreinforced, high-pressure epoxy laminates produced to the G-l OCR and G-11CR

specification. Testing should be performed at 4.2 K (-452°F) and at 77 K

(-320°F). Test environments are liquid helium and liquid nitrogen, respectively. Test orientations should be warp, fill, and ±45°.

Experiments should be conducted at strain rates both above and below

those specified in ASTM documents for room temperature tensile testing of

composites. This is required to quantitatively establish the relationship

between strain rate and the point of massive damage introduction. Instrumentation techniques must be developed to provide a high degree of accuracy in

determining the "knee" position on recorded stress-strain curves produced at

different strain rates.

B. Model Development: Effects of strain rate and test media

Position of the stress-strain "knee" will vary with parameters such as fiber orientation, fiber density, fiber type, and resin strength and toughness

in addition to strain rate and temperature. It is impractical to experimentally assess the interaction of all these variables. Consequently, efforts

must be made to devise analytical models that predict their synergistic

effect.

The experimental studies of Test Program 2A will provide useful information on model validity. However, additional validation tests must be conducted

on uniaxial laminates and laminates of crossply construction. When verified,

the appropriate model should be used to establish a standard method of predicting the onset of significant internal damage in engineering structures.

III. Intrinsic Specimen Size Effect

A. Experimental: Configurational dependency with temperature

At any temperature there is a minimum number of replicated basic units of

composite reinforcement that are required in a test specimen if the mechanical

test results are to reflect bulk material properties. These may be a minimum

number of uniaxial fibers or a minimum number of replications of the basic weave unit in a f abric-reinf orced material in the cross section of the specimen.

If fewer than required of such units are present, the determined mechanical

property will usually be lower than that for the bulk material. This leads to

excessive conservatism in design and prevents meaningful comparison of data

between test laboratories. On the other hand, if many more than the required

number of such units are present, the larger than required specimen size

increases the cost of testing. At cryogenic temperatures the problems are magnified by an increase in internal stress, embrittling of the matrix, and by

the increased cost of testing.

The objectives of this program are therefore as follows:

1. To determine the effect of cryogenic temperatures on the test specimen

cross sectional dimensions required to produce consistent tensile strength

data

430
2. To use these data to establish minimum specimen dimensions for such

testing.

3. To establish standard criteria for specimen dimensions so as to ensure reproducibi 1 ity among laboratories and to provide industry with the

most meaningful design data.

It is proposed that this study be conducted with commercial, high-pressure,

industrial laminates produced to the G-10CR or G-11CR specifications. Such

materials are widely used in cryogenic construction, and present a worst case

in size effect considerations. Tests should be performed at 4.2 K (-452°F),

77 K (-320°F) and 295 K (68°F). Evaluation should be made in the warp, fill,

and ±45° direction of the laminate.

B. Model Development

The complexities cited as justification for undertaking modelling programs under under the work proposed in I and II may be repeated here to

justify a similar program on size effect. Again, it is impractical to

experimentally determine the minimum functional size for all of the possible

composite types and orientations of technical interest. At room temperature

the problem is more tractable, as large specimen can be used without substantial penalty. But the imperative to use of as small specimens as is practical

for cryogenic testing justifies a finer tuning of the specifications. This is

of particular importance where it is desired to test a number of specimens

sequentially during one cool down of a cryostat.

The work proposed in Test Program 1 1 IB will be of value in this modelling

study. However, the scope should be increased to include discontinuous glassreinforced specimens as well as fabric-reinforced material.

431
Elongation ( mm

Fig. 1 Load-elongation curve for G-11CR tested in the

-45° direction to warp and fill at room temperature. (K. Fujioka, et al , "Construction of FRP

Dewar by Adhesive Bondinq Method for Large Pulsed

Superconducting Magnet", presented at ICMC/CEC

Conference, Colorado Springs, CO, August 1983.

432
TECHNOLOGY TRAHSEER

433

TECHNOLOGY TRANSFER PROGRAM

LEADER: N. J. Simon, NBS

OBJECTIVES:

(1) To hold workshops to promote interaction between designers and

material specialists. Major topics include design overviews of

fusion energy projects with respect to low-temperature material

needs and reviews and data on structural alloys, composites, and

wel dments

(2) To produce and distribute an annual report as well as monthly highlight reports to OFE/DoE.

(3) To prepare handbook pages and supporting documentation on lowtemperature mechanical and physical properties of structural

materials for superconducting magnets. The pages are to be distributed to workshop attendees and others in the 1 ow-temperature

materials applications community. The pages will also be presented

for inclusion in the "Materials Handbook for Fusion Energy Systems."

RESEARCH PAST YEAR (1983):

(1) "Materials Studies for Magnetic Fusion Energy Appl ications-VI ,"

NBSIR 83-1690, 464 pages (May 1983), editors R. P. Reed and N. J.

Simon, has been sent to the Technology Information Center, ORNL,

and a number of copies have been requested by other interested

persons

(2) Handbook pages and supporting documentation covering mechanical and

physical properties of Fe-21Cr-6Ni -9Mn have been distributed in

preliminary draft form to interested persons. These pages have

also been submitted to the "Materials Handbook for Fusion Energy

Systems." Preliminary work on correlation of AISI 304N and 304LN

tensile properties with nitrogen and carbon concentration has been

completed in preparation for development of handbook pages on these

304 alloys.

(3) Efforts were undertaken to encourage international cooperation in

research to develop radi ation-resi stant laminates to meet requirements for the Engineering Test Reactor.

RESEARCH THIS YEAR (1984):

(1) Tentative plans are to hold the 1 ow-temperature materials workshop

again in October 1984.

(2) "Materials Studies for Magnetic Fusion Energy Appl ications-VI I NBSIR 84-3000, 447 pages (1984), editors R. P. Reed and N. J. Simon,

is the current edition of the annual report.

(3) The AISI 316 handbook pages and the Fe-21Cr-6Ni-9Mn handbook pages

are currently in the review process for "Materials Handbook for

Fusion Energy Systems," and the AISI 304N and 304LN handbook pages

will enter the review process later this year.

(4) Preparation of AISI 304N and 304LN handbook pages will be completed

this year. Preparation of handbook pages on AISI 316L, 304N, and

304LN weldments will be started.

435
(5) Efforts promoting international cooperation in research to develop

radiation-resistant laminates will continue. Interaction between

the U.S. and Japan on structural materials research will be

expl ored

436
NBS-DoE WORKSHOP: MATERIALS AT LOW TEMPERATURES

October 17-19, 1983, Vail, Colorado

N. J. Simon

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A brief summary of the highlights and issues raised at this annual

workshop is presented. The program and the list of registered participants

fol 1 ow thi s summary.

437

A major purpose of the workshop is to bring together representati ves from

the community of users and suppliers of materials for low temperature magnet

applications with those engaged in development and characterization of these

materials. Participants this year came from industry, the national

1 aboratories , the magnetic fusion energy programs, NBS, DoE, and universities.

The proceedings of the workshop are not published, but extended abstracts of

the presentations were provided to those who attended.

The structural and insulating materials used in the superconducting

magnets of fusion energy systems were the subject of this workshop. Current

methods of plasma confinement for tokamak and mirror fusion reactors

necessitate the use of high-field superconducting magnets that operate at

temperatures near 4 K. The technical presentations stimulated much animated

discussion. Some highlights and issues raised are:

1. Some concerns about the overall reliability of superconducting magnet

systems (such as refrigeration, vacuum, leaks, etc.) are not being

addressed in the Large Coil Project testing owing partly to the

complexities of the additional instrumentation that would be required.

It appears that this will remain an open issue for some time (but see

Item 3 bel ow)

2. The U.S. does not have mechanical property requirements for materials as

JAERI does; however, such criteria may be an illusion at this stage when

many important features of the design of fusion reactors have not been

resolved. The Japanese are emphasizing high strength and toughness in

their material requirements, much more than material cost and

weldability. Discussion should be pursued between the U.S. and Japan to

promote more uniform material research objectives.

439
3 . Although the constraints are different from those of fusion systems,

Fermilab has been successful in constructing and operating a complex

cryogenic system consisting of a large number of superconducting magnets

installed in an accelerator 7 km in ci rcumference.

4. Some high field magnet coils in currently planned prototype fusion

systems will not be superconducting. Inserts of copper coils may be used

in tandem mirror configurations. The tokamak prototype using D-T burn to

reach ignition may or may not have superconducting toroidal field (TF)

coils, although the poloidal coils are to be superconducting.

5. A sector module type of tokamak construction that is being considered

would allow interior machine modules shaped somewhat like the segments of

an orange to be inserted between the TF coils.

6. The present designs for tokamaks require fatigue crack growth rate data.

These data may be more important to the designers than fracture toughness

in setting stress levels. However, future fusion reactors might have

steady-state operation. The importance of determining the R-ratio

dependence of the Paris law crack-growth parameters was discussed: so

far, low temperature data on this have been made available to designers

only for Fe-21CR-6Ni -9Mn alloy in the handbook pages (see Item 12).

7. Procurement problems for MFTF-B were caused by the nonuniformity of 304LN

yield strengths, especially for thick ('vlO-cm) plates in the ST

orientation. The nonuniform yield strengths result from excessive grain

sizes. A solution seems to be better understanding and control of

processing with regard to temperatures for hot rolling so that defects

are removed but grain size does not become excessive. Some

characterization of this type of processing has been done in Japan.

440
8. A discussion of future materials needs for mirror fusion reactors brought

up the lack of property data on the thin reinforcing strips to be

co-wound with the superconductor in high-field solenoids. There may be

problems in matching thermal expansion coefficients. Inconel -group

alloys are being considered for this purpose, but these alloys may have a

low thermal expansion only over the narrow temperature range near

ambient.

9. Tests on reinforcement of metastable stainless steel weldments have not

shown notch brittle behavior at 4 K, although martensite is formed with

the test system of 304L base metal with AWS E316L electrodes.

10. Substantial temperature rises invalidate the 1 ow-temperature Charpy tests

carried out in accord with ASTM E-23. Yield strengths are not sensitive

to the strain rate used in testing, but the ultimate tensile strength and

elongation are.

11. A 4 K, gamma and neutron irradiation facility is needed to develop

organic insulators that can withstand the radiation environment of

superconducting magnets in fusion reactors. In late 1985, the National

Low Temperature Neutron Irradiation Facility (NLTNIF) will provide the

high radiation intensities needed as well as capabilities for subsequent

4-K testing without warmup. The Fusion Materials Irradiation Test

facility to be built by Hanford Engineering Development Laboratory in

Washington could have cryogenic capabilities also if suitable cryogenic

equipment were installed, but the facility might not achieve a higher

flux than NLTNIF. A problem with experimental design for NLTNIF is the

internal heat generated in specimens, leading to an undesirable

temperature rise. The international agreement on standardizing

nonmetal lie test methods reported at the workshop fortunately provides

for uniaxial specimens that are of small diameter, so the problem will be

minimized.

441
12. Discussion on progress in codifying data on structural alloys for the

Materials Handbook on Fusion Energy Systems brought out the importance of

including weld data on 316L, since the base material has already been

covered. The desirability of furnishing the supporting documentation

pages to handbook users along with the handbook pages was discussed.

Current policy is that the supporting documentation is on file at HEDL,

available on request. Members of the DoE Analysis and Evaluating Task

Group that were present will try to implement this. Workshop

participants were satisfied with the format of and progress on the NBS

contributions to the Materials Handbook.

442
PROGRAM

NBS/DoE Workshop on Materials at Low Temperatures

October 17-19, 1983

Vail , Col orado

Monday, October 17

Preconference Session (1:00-6:00 p.m.) Metal Properties Council

A. 0. Schaefer, Chairman

Low Temperature Codes and Standards Subcommittee Meeting

Tuesday, October 18

Session 1 (8:30-12:00 a.m.) Magnet Systems

R. P. Reed, Chairman

Introduction R. P. Reed, NBS

Overview - Magnet Development D. S. Beard, DoE

Westinghouse Electric Large Coil Project Materials

Construction of Superconducting Magnets for

A. Jarabak, Westinghouse

Fermilab Accelerator R. Lundy, FNAL

Overview of Recent Activities of FEDC

Future Cryogenic Structural Materials Needs for

F. W. Wiffen, ORNL

Mirror Fusion Reactors R. Scanlan, LLL

Failure of a Large Cryogenic MHD Magnet H. Becker, MIT

Session 2 (2:00-5:00 p.m.) Austenitic Steels

E. N. C. Dalder, Chairman

Problems in the Use of Low-Temperature Materials

Strength of Structural Alloys

Use of Crack Propagation Rate Test Data in

Establishing Design Allowable Stresses

Thermal Activated Glide through Distributions

of Point Obstacles

Progress in Fatigue Testing of Austenitic

Stainless Steels

Research on Iron-Manganese Cryogenic Steels

E. N. C. Dalder, LLL

R. P. Reed, NBS

R. J. Hooper, ORNL

J . W. Morri s , Jr.

,

University of California

R. L. Tobler, NBS

M. J. Strum, University of California

443
Program, continued

Wednesday, October 19

Session 3 (8:30-11:30 a.m.) Properties and Welding for Low-Temperature Service

J. W. Morris, Jr., Chairman

Deformation and Fracture of Duplex Austenitic

Stainless Steel Castings at 4 K: Microstructural Analysis and Mechanical Behavior

Stress-Concentration Effect on Integrity of

Stainless Steel Weldments

New Expressions for Prediction of Microstructures

in High Alloy Austenitic Steels

Effect of Strain Rate on Measured Mechanical

Properties of Stainless Steel at 4 K The Effects of Martensitic Transformations on Low Temperature Mechanical Properties

Materials Handbook for Fusion Energy Systems

T. A. Whipple, Rockwell International

E. L. Brown, Colo. School of Mines

Y.-W. Cheng, NBS

D. Olson, Colorado School of Mines

W. G. Dobson, Teledyne

B. Fultz, University of California

N. J. Simon, NBS

Session 4 (1:30-4:30 p.m.) Radiation-Resistant Organic Insulator Development

M. B. Kasen, Chairman

Elastic Stiffnesses and Local Stresses in WovenFabric Composites at 77 K R. Current and Future Possibilities for Cryogenic

Nonmetal lie Radiation Research R. MIT Development Program for Fusion Reactor

Magnet Insulators H.

Neutron Irradiation Studies of Polymers at LANL D.

Cooperative Programs in Nonmetal lie Radiation M.

Panel Discussion: Nonmetal lie Research for MFE Magnets

Kriz, NBS

Coltman, ORNL

Becker, MIT

Fowler, Jr. , LANL

B. Kasen, NBS

444
NBS DoE WORKSHOP

ATTENDEES

October 17-19, 1983

John Arvidson, MBS

Don Beard, U. S. Department of Energy

Herb Becker, MIT

James Benzinger, Spaulding Fibre

Elliot Brown, Colorado School of Mines

Bernie Carpenter, Colorado School of Mines

Yi-Wen Cheng, NBS

Ralph Coltman, ORNL

Ed Dalder, LLL

Bill Dobson, Teledyne

John Fowler, Jr., LANL

Brent Fultz, University of California

Carl Goodzeit, Brookhaven

Richard Hooper, ORNL

Andrew Jarabak, Westinghouse

Maurice B. Kasen, NBS

Damian Kotecki , Teledyne McKay

Ronald D. Kriz, NBS

R. A. Lundy, FNAL

J. W. Morris, Jr., University of California

Lewis Myers, Carpenter Technology

Carl Osgood, Princeton University

Pat Purtscher, NBS

Richard Reed, NBS

Ron Scanlan, LLL

Joel Self, Colorado School of Mines

John Shepic, Martin Marietta

Nancy Simon, NBS

Mike Strum, University of California

Ralph Tobler, NBS

Robert Walsh, NBS

F. W. Wiffen, ORNL/FEDC

Jerry Wille, McDonnell Douglas

John Wollan, LANL

Tom Whipple, Rockwell International

445
446

Group

photograph

of

1983

NBS/DOE

Vail

Workshop

attendees.
ACKNOWLEDGMENT

The editors wish to express their appreciation to JoAnne Wilken for her

work in preparing the manuscript. She was assisted by Becky Stevenson and

Dianna Wooton.

Marilyn Stieg removed many of the inconsistencies, grammatical errors,

and awkward usages of language. The editors are responsible for those that

remain.

447
NBS-1 14A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 84-3000

2. Performing Organ. Report No. 3. Publication Date MAY 1984

4. TITLE AND SUBTITLE

Materials Studies for Magnetic Fusion Energy Applications at Low Temperatures - VII

5. AUTHOR(S)

R. P. Reed and N. J. Simon, Editors

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

10. SUPPLEMENTARY NOTES

Related Orevious Reports: NBSIR 83-1690, NBSIR 82-1667

NBSIR 81-1645, NBSIR 80-1627, NBSIR 79-1609

NBSIR 78-884

] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

This report contains results of a research program to produce material property data that will facilitate

design and development of cryogenic structures for the superconducting magnets of magnetic fusion energy power

plants and prototypes. The program was developed jointly by the staffs of the National Bureau of Standards

and the Office of Fusion Energy of the Department of Energy; it is managed by NBS and sponsored by DoE. Research

is conducted at NBS and at various other laboratories through subcontracts with NBS. Research results for

1983 are summarized in an initial "Highlights of Results" section and reported in detail in the 22 technical papers that form the main body of this report. The technical papers are presented under four headings reflecting

the main program areas: structural alloys, weldments and castings, nonmetallics, and technology transfer.

Objectives, approaches, and achievements are summarized in an introduction to each program area. Work leading

toward development of strong, tough structural alloys for use in superconducting magnets continued this year, with low temperature studies assessing the quantitative dependence of the yield strength, density, and elastic constants of A I S I 304 stainless steels upon carbon and nitrogen concentration. Tensile property measurements

of developmental austenitic steels from the U.S., Japan, and the U.S.S.R. confirmed a logarithmic dependence

of yield strength upon temperature between 4 K and room temperature. Evidence is presented to show that the flow strength and austenite stability of stainless steels are not significantly affected by 8-T fields at 4 K. New instrumentation developed for low-temperature testing included a computer-assisted apparatus that was used

to measure threshold fatigue. Low-temperature welding research involved an investigation of the weld reinforcement effect on the weld joint strength and measurements of the 4-K fracture toughness of 25MN - 5Cr steel weldments and 320LR electrodes. In the area of nonmetallics, a standardized test specimen was devised for a screening program to develop radiation-resistant composites for magnet insulation, and models to predict damage

in woven glass/ epoxy laminates were tested experimentally at low temperatures. Mechanical properties of concrete mortar and polyurethane foam at 4 K are reported.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper . ... _ Austenitic steels; castings; composites; cryogenic properties; elastic properties;

low temperatures; mechanical properties; nonmetallics; stainless steels; structural

alloys, welds.

13. AVAILABILITY

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