REFERENCE

NB8IR 85-3025

NAT L INST. OF STAND & TECH R.I.C. NBS»^

cations^ AlllDH SET577 LJ

TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES -VIII

To

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

Prepared by

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

NBSIR 85-3025

TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES -VIII

Edited by

p Rood

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

May 1985

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

SUMMARY V

ORGANIZATIONAL CONTACTS vi

PROGRAM DESCRIPTION vii

HIGHLIGHTS OF RESULTS 1

WELDING

Welding Program 11

Summary of Mechanical Property Measurements of Welds 12

Stainless Steel Welding Program

T. A. Siewert 13

Tensile and Fracture Properties of an Fe-14Mn-8Ni-lMo-0.7C

Fully Austenitic Weld Metal at 4 K

R, L, Tobler, R. E. Trevisan, and R. P. Reed 15

Predicting the Toughness of SMA Austenitic Stainless

Steel Welds at 77 K

T. A, Siewert 29

NONMETALLICS

Nonmetal lies Program 47

Mechanical-Damage Effects in Woven Laminates at Low Temperatures

R. D. Kriz and W, J. Muster 49

Nonmetallic Material Standardization - Materials and Test Methods

M. B. Kasen 87

Elastic Representation Surfaces of Unidirectional Graphite/Epoxy

Composites

R. D, Kriz and H, M. Ledbetter 99

STRUCTURAL ALLOYS

Structural Alloys Program ....... 119

Summary of Mechanical Property Measurements of Structural Alloys . . 120

Strength and Toughness Goals for Cryogenic Steels

H. I. McHenry 121

Nickel and Nitrogen Alloying Effects on the Strength and

Toughness of Austenitic Stainless Steels at 4 K

P. T. Purtscher and R. P. Reed 123

iii
CONTENTS (continued)

STRUCTURAL ALLOYS (continued)

Low-Temperature Sound Velocities in 304-Type Stainless Steels:

Effect of Interstitial C and N

H. M. Ledbetter 145

Linear-Elastic Fracture of High-Nitrogen Austenitic Stainless

Steels at Liquid Helium Temperature

R, L. Tobler, R. P. Reed, and P. T. Purtscher 151

Cleavage-like Fracture in Fe-18Cr-3Ni-13Mn-0. 37N Austenitic

Stainless Steel at Liquid Helium Temperature

R. L. Tobler and D, Meyn 167

Notch Tensile Measurements and Fracture Toughness Correlations

for Austenitic Stainless Steels

R. P. Reed, R. L. Tobler, and D. T. Read 181

Elastic Constants and Instability in Face-Centered-Cubic Metals

H. M. Ledbetter 193

Monocrystal-Polycrystal Elastic Constants of a Stainless Steel

H. M. Ledbetter 207

Elastic-Constant Anomalies at the Neel Transition in

Fe-18Cr-3Ni-13Mn

H. M. Ledbetter and E. W. Collings 219

Automatic Near-Threshold Fatigue-Crack Growth-Rate Measurements

at Liquid Helium Temperature

R. L. Tobler and Y. W. Cheng 229

Fatigue Crack Initiation from Notches in Austenitic Stainless Steels

R. L. Tobler and Q. S, Shu 251

Stacking-Fault Energies in 304-Type Stainless Steels: Effects

of Interstitial Carbon and Nitrogen

H. M. Ledbetter and M. W. Austin 271

TECHNOLOGY TRANSFER

Technology Transfer Program 297

NBS-DOE Workshop: Materials at Low Temperatures 299

Cryogenic Steels for Superconducting Magnets: Developments in

Japan

H. I. McHenry 323
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 1984 are summarized in an initial "Highlights of

Results" section and reported in detail in the technical papers that form the

main body of this report. The technical papers are presented under four

headings reflecting the main program areas: Welding, Nonmetallics , Structural Alloys, and Technology Transfer. Objectives, approaches, and achievements are summarized in an introduction to each program area.

A new welding laboratory has been developed. This facility, equipped

for precise control of gas metal arc, gas tungsten arc, and shielded metal

arc welding processes, is already assisting in the careful, controlled

preparation of weldments for low temperature study. Our finite-element

modeling experience has been used to study damage effects in glass/epoxy

laminates (G-10CR, G-11CR) at low temperatures. The stress-strain characteristics were correlated with the sequence and types of damage accumulation.

This study should contribute to our longer range objective of establishing

mechanical property criteria for safe design of low temperature composite

structures. A new alloy development criterion, the quality index, has been

proposed to take into account both strength and toughness considerations.

This quality index has been applied to consider the amount of nickel and

nitrogen additions necessary to achieve specific low temperature strength and

toughness objectives in austenitic stainless steels. The development of test

equipment has been completed that measures, with computer assistance and

control, the fatigue threshold stress-intensity levels. Measurement data at

4 K are presented for selected austenitic steels. New low temperature

strength and toughness data for nitrogen-strengthened Fe-Cr-Ni-Mn austenitic

stainless steels are given. Correlations of fracture toughness with associated fracture morphology have led to the discovery of faceted areas that have

been associated with {111} face-centered cubic planes in high-nitrogen

alloys. The effect of carbon and nitrogen on stacking fault energies in

austenitic stainless steels has been measured. Previous estimates of the

contribution from interstitial alloying elements to the stacking fault energy

had been widely divergent. New elastic property data on high-manganese

austenitic stainless steels are reported.

Note : Certain commercial equipment, instruments, or materials are identified

in this report to specify the experimental procedure adequately. In a few

instances, company names are used to Identify the source of specific re- search. 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.

V
ORGAH/ZATIOHAL COMTACTS

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 V. K. Der (301 ) 353-5736

(FTS) 233-5736

National Bureau of Standards, Boulder, Coloradc) 80303

Program Manager R. P. Reed (303) 497-3870

(FTS) 320-3870

Welding H. I. McHenry (303) 497-3268

T. A. Siewert (303) 497-3523

D. P. Vigliotti (303) 497-3222

Nonmetallics M. W. Austin (303) 497-3504

M. B. Kasen (303) 497-3558

R. D. Kriz (303) 497-3547

H. M. Ledbetter (303) 497-3443

Structural Alloys J. M. Arvidson ( 303 ) 497-3424

Y. W. Cheng (303) 497-5545

H. M. Ledbetter ( 303 ) 497-3443

H. I. McHenry (303) 497-3268

P. T. Purtscher ( 303 ) 497-5789

D. T. Read ( 303 ) 497-3853

R . P . Reed ( 303 ) 497-3870

R. L. Tobler (303) 497-3421

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

vi
PROGRAM OiSCRIPTlOH

The overall objective of the program is to assist in the design, con- struction, and safe operation of low-temperature magnetic fusion energy (MFE)

systems, especially superconducting 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 Systems," 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

low- temperature design, construction, 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 those members of the magnetic

fusion energy community involved with low- temperature materials.

vli
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. Welding

1 . Austenitic-steel welds NBS Evaluation of the strength and

toughness properties of weldments at 4 K. Continuation of

studies to understand the

mechanisms by which residual

delta ferrite, Mn, and interstitial elements affect the

deformation and fracture of

stainless-steel welds.

B. Nonmetallics for Magnet Structures

Standardization NBS Continued cooperation with

industry to refine cryogenicgrade specification for commercial, nonmetalllc, bulk-insulating laminates.

Controlled test-specimen

development

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 non- metallic composite insulators.

International cooperation NBS,

Rutherford

Laboratory

Osaka

University

Agreement to cooperate in

development of specimens,

material selection, and test

procedures in developing

radiation-resistant insulating

materials

Influence of damage NBS,

Swiss

Federal

Laboratories

Determination of the influence

of microcracks on design

properties, such as stiffness

and strength.

vlii
Table 1 (continued)

Program Area Organization Program Description

C. Structural Alloys

1 . Strong, tough alloys NBS

2. Strong, fatigue-resistant NBS

alloys

3. Low- temperature codes NBS

and standards

4. Physical properties NBS

Assessment of low-temperature

properties of selected

austenitic alloys containing

varying concentrations of C, N,

and Mn with an Fe-Cr-Ni base.

Assessment of Japanese austenitic

alloys with an Fe-Mn base.

Study of fatigue and fatigue

crack-growth rates of candidate

structural alloys, including 300

series stainless steels, Fe-Mn

base austenitic alloys, and

age-hardened alloys.

Research to establish lowtemperature mechanical test

standards, now emphasizing

tensile, fracture toughness,

and fatigue.

Measurement of properties, such

as elastic constants, thermal

expansion, and volume;

especially, alloying effects.

D. Technology Transfer

1 . NBS-DOE Workshop NBS Presentation of research results

to the fusion community,

discussion of new problems, and

interaction between magnet

designers, material specialists,

and other interested people

during a workshop.

2. Handbook NBS Analysis of mechanical properties of AISI 304 high-nitrogen

content stainless steels with

respect to temperature and

interstitial content (1984).

Distribution (1985) of pages of

the data handbook for AISI 304

(N, LN , HN , LHN ) stainless

steels and for AISI 31 6L and 304

weldments. Preliminary work on aluminum alloy 2219 data.

XX

HIGHLIGHTS Of RESULTS

1

HIGHLIGHTS Of RESULTS

WUBIHG

A welding laboratory was established for detailed study of the welding

arc and preparation of highly characterized welds for cryogenic mechanical

property evaluations. The laboratory contains an adaptive control GMA

welding system that controls the weave width and contact-to-tip distance by

sensing the arc voltage. By means of an on-board computer using preprogrammed algorithms, the unit continuously controls heat input and travel

speed. A transistorized current regulator permits interference-free power for

careful study of the welding arc. The laboratory contains power supplies for

GTA , GMA, and SMA weldings, gas mixing systems, and other support equipment.

A fully austenitic weldment produced by a filler metal manufacturer was evaluated at ^ K. The undiluted weld metal had a composition of Fe-15Mn-8Ni1MO-0.7C and was produced by submerged arc welding a 21 -mm plate using a butt

joint conf iguraiton . The yield strength (1115 MPa) and toughness (Kj^ = 19^

MPa/m) combination compares favorably with existing base metal properties for

AISI-304 type alloys.

A linear equation based on previously published data was developed to

predict the 76-K CVN toughness for shielded metal arc deposit compositions.

This study proposed a simpler and more accurate predictive equation to help

select improved compositions for future applications. Analysis of 79 weld

deposits revealed that calculated FN was the most significant term for

predicting the CVN toughness. This term, when allowed to be negative, was also an excellent predictor of toughness for the fully austenitic compositions and the AISI type 316 compositions, although no mechanism was proposed.

HOHMBTALUCS

standardization

We continue to work with representatives of the United States laminating

industry to provide magnet builders with commercial sources of standardized,

reliable, nonmetallic insulating materials. We have ongoing consultation

with users and manufacturers about the adequacy of specifications.

Controlled Test-Specimen Development

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

research, we have developed new methods to produce specimens that combine the

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

flexibility in component selection and treatment. We refined the system for

producing uniaxially reinforced, 3~ to 4-mm-diameter rod specimens and now

can produce specimens of excellent quality from liquid-mix epoxy-resin

systems. We are modifying the technique for hot-melt epoxy and polyimide

3
resin systems. These specimens will be subjected to radiation in the NLTNIF

reactor at ORNL and then evaluated for radiation degradation by means of

short-beam shear and torsional shear tests.

International Cooperation

A cooperative program with laboratories in Japan and England has re- sulted in the production and testing of specimens with identical configuration. All members of the Japanese group (headed by Prof. T. Okada at Osaka

University and including individuals at Kyoto University, the University of

Osaka Prefecture, and the Hoxan Corporation) have successfully produced

specimens containing glass, graphite, and silicon-carbide fibers by using the

NBS method. Performance has been evaluated in three-point flexure. Similar

success was achieved by Dr. D. Evans of the Rutherford Laboratory in England.

An effective exchange of information is continuing. We plan to exchange

specimens and report our results jointly in 1985.

Property Determination and Modeling

1 . Measurements on the influence of damage at 76 K on the mechanical

performance of woven composites at low strains . We predicted and measured

the influence of crack formation on the mechanical performance of standard

glass epoxy laminates (G-10CR, G-11CR) at low strains and low temperatures.

Damage was modeled by finite elements as microcracks confined to fiber

bundles that were oriented transverse to the tensile load direction. From

experiments we studied the formation of damage as a collection of fiber

breaks and transverse fiber bundle cracks. We discovered that the sequence

and types of damage, at strains well below ultimate, control the discontinuities (knees) in the load-deformation (stress-strain) diagrams. However,

between knees, the material remains linear elastic at low temperatures. We

found that G-11CR has two knees and three distinct moduli, whereas G-10CR has

only two moduli and a single knee at a lower strain than G-11CR. A decrease

in moduli measured near the first knee compares well with predictions of

finite-element theory.

2. Elastic representation surfaces of unidirectional graphite/epoxy

composites . From our studies on f iber-reinforced materials, we found several

new properties by examining the elastic representation surfaces. In particular, unidirectional graphite/epoxy exhibits a high elastic anisotropy and

unusual geometrical features in its elastic-property polar diagrams. From a five-point component (hexagonal symmetry) elastic stiffness tensor, we computed and displayed representation surfaces where large variations in

Young's modulus, Poisson's ratio, torsional modulus, and linear compressibility are due to peculiar geometries: large negative Poisson's ratios

result from changes in fiber volume fraction and tilt angles away from

symmetry planes. On the basis of Christoffel equation solutions, we described some unusual elastic-wave-surface topological features. Some new,

unexpected results include: a shear-wave velocity that exceeds a longitudinal-wave velocity in the plane transverse to the fiber and a wave that

changes polarization character from longitudinal to transverse as the propagation direction sweeps from the fiber axis to the transverse plane.

4
STRUCTURAL ALLOYS

Strong, Tough Alloys

Major accomplishments for the year include the following:

The tensile strength and fracture toughness at 4 K were studied as a function of nickel (6 to 15 wt.?) and nitrogen (0.09 to 0.28 wt.?) contents

for eight austenitic stainless steels. Results indicate that nitrogen

increases the tensile yield strength and decreases the fracture toughness,

Kj^(j). Nickel has little significant effect on tensile yield strength but

increases the fracture toughness. A new parameter, called the quality index,

is presented and defined as the product Oy-Kj^CJ). This index relates to the

capacity of the alloy to achieve greater strength or toughness, but not at

the expense of the other parameter. Nickel alloying is shown to increase the

quality index; nitrogen has little effect.

Thirty-two alloys were included in a study of conventional notch tensile

testing as a method of fracture toughness characterization for austenitic

stainless steels at liquid helium temperature, M K. For the same austenitic

stainless steels, tensile and J-integral fracture toughnesses [Kj^(J)] were

also measured. For these materials, the notch tensile strength toj^jg)

generally increases with yield strength (Oy). and the Oj^^g/Oy ratios are typically much greater than 1.0. Correlations among Kj^(J), and Oy were assessed. The best correlation was found between the ratio cffjTS'^^Ic

and the toughness, Kj^(J).

Strong, Fatigue-Resistant Alloys

A new facility is in use that facilitates the difficult and timeconsuming measurement of threshold fatigue. It is capable of measuring

fatigue-crack growth rates as low as one angstrom (less than one lattice

spacing) per load cycle in the temperature range 295 to 4 K. Near- threshold

fatigue-crack growth rates and threshold stress intensity factors are especially important data because they are used to determine the stress

limits below which existing cracks cease to grow.

This new fatigue-testing apparatus is completely and automatically

controlled by a computer. It consists of a servo-hydraulic test machine, a vacuum- insulated cryostat, a minicomputer, and temperature-control system.

The computer systematically decreases the test loads until the threshold for

crack growth is reached. The fatigue-crack growth rate measurements extend

over four orders of magnitude, from 10"^ to 10"^*^ m/cycle. A typical test

cycles 6.4-mm-thick specimens at a frequency of 40 Hz for 4 days, 24 hours a day—a total of 13 million fatigue cycles.

5
Preliminary data have been reported on alloys 304L, 304LN, and 316. The

threshold stress intensity factors vary from 1 to 8.5 MPa/m for these

alloys at M K.

Physical Properties

The physical properties provided at least three types of information:

material characterization, key design parameters, and tests for anomalous

behavior

1 . Anomalous low-temperature elastic-constant behavior was identified

in two austenitic alloys. Near 5^ K, the alloy Fe-20Cr-1 6Ni-6Mn undergoes a magnetic transition. The bulk modulus begins to soften at a higher temperature, near 150 K. Near 191 K, all elastic constants of the alloy Fe-l8Cr3Ni-12Mn exhibit anomalous behavior arising from a paramagnetic-to-antif erromagnetic spin-glass transition.

2. The effect of interstitial carbon and nitrogen on low-temperature

sound velocities in 30^-type stainless steels was studied. Nine alloys

containing between 9.3 and 1.3 atomic percent carbon and nitrogen show

low-temperature physical-property anomalies associated with a magnetic

transition. Contrary to existing reports, the magnetic transition temperature decreases sharply with increasing interstitial content.

3. New measurements were made of the monocrystal Voigt elastic-stiffness constants (C-|-], C-| 2

» and for Fe-1 9Cr-1 ONi . By means of seven

models, these are related to the measured polycrystal elastic constants.

Codes and Standards

Cooperation has been established between NBS, industry, and other

government laboratories within a Metal Properties Council (MPC) Low Temperature Task Group to develop this program. The task group prepared a proposal

to provide the information needed to extend tensile test standards to very

low temperatures. The program considers the effects of strain rate on specimen heating (and, therefore, flow strength) and grain size (to establish

minimum specimen sizes). Potential research contractors have submitted

responses to this proposal. The final contractor will be selected soon, and

MPC is now soliciting organizations to obtain the necessary funds to support

this program.

6
UCHNOLOGY TRAHSHR

An NBS-DOE Workshop on Materials at Low Temperatures was held in Vail,

Colorado on October 1^-17, 198^4. The workshop brought together material

specialists and magnet designers to report recent research and to identify

and discuss structural materials problems in superconducting magnet design

and construction for fusion energy systems. In addition to the formal

presentation sessions, there were discussion meetings to formulate research

objectives in structural alloys, welding, and nonmetallics . The proceedings

of this informal workshop were not published; however, a copy of the program

and an informal summary of the proceedings may be found in the Technology

Transfer section of this report.

Handbook and supporting documentation pages have been prepared for AISI

304 (N, LN, HN, LHN) stainless steels and will be 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, and fatigue crack growth rate. The scope of the handbook has been

expanded to include analysis and correlation of AISI 304 properties with

respect to interstitial carbon and nitrogen content. The AISI 304 pages will

be submitted to the advisory task group of the ’’Materials Handbook for Fusion

Energy Systems” for their review process. Handbook pages on AISI 316 alloys

and Fe-21 Cr-6Mn-9Ni are being reviewed. Preliminary work on handbook pages

covering AISI 304 electromagnetic and thermal properties and AISI 304 and

31 6L welds is in progress

The Japan Atomic Energy Research Institute initiated a program in 1982

to develop cryogenic steels for use in the large superconducting magnets

planned for their Fusion Experimental Reactor. The target properties for the

cryogenic steels are a yield strength of 1200 MPa and a fracture toughness of

200 MPa/m at 4 K. Five Japanese steel companies have developed candidate

alloys that met or nearly met the property goals. Progress on developing

these steels was reviewed at a U.S. /Japan workshop in December 1984 and is

summarized in this report.

7

WELdlUG

•. > t ;

-

',

’ fS

'f.-K.::

y^'i -

9

WELVniG PROGRAM

LEADER: T. A. Siewert, NBS

STAFF: H. I. McHenry, D. P. Vigliotti, NBS

OBJECTIVES:

1. Investigation of the metallurgical factors that affect the mechanical

properties of stainless-steel weldments at cryogenic temperatures.

2. Contributions to the development of improved filler metals for welding

stainless steels for liquid-helium service.

3 . Evaluation of the mechanical properties of weldments at 4 K. 4. Development of methods of detecting defects and evaluation of their

significance in stainless-steel weldments.

RESEARCH PAST YEAR (1984):

1 . A welding laboratory was established for detailed study of the welding

arc and highly characterized weld for mechanical property studies.

2. The tensile properties and fracture behavior of a Fe-1 5Mn-8Ni-1 Mo-O.TC

fully austenitic weldment were evaluated at 4 K.

3 . Improved predictive equations for 76 -K Charpy V-notch tests were developed.

4. Mechanical properties testing at 4 K in support of superconducting

magnet design and construction continued.

RESEARCH THIS YEAR (1985)

1 . The effect of various Interstitial elements will be evaluated in type

31 6L GMA weldments at 76 and 4 K.

2. A series of weldments based on a type 308 composition and with varying

alloy additions will be used to clarify the effects of manganese and

nitrogen in SMA weldments for cryogenic service.

3 . The tensile properties and fracture toughness of an electron beam weld

in 75 -mm-thick 304LN will be measured at 4 K.

4. Mechanical property testing at 4 K in support of superconducting magnet

design and construction will continue.

11
Suinniary

of

Mechanical

Property

Measurements

of

Welds K o o 00 CO

o>

00 oo

=1

KTi >:o o oI I oo CO

00 00 o o LD iT) E3C c <

s: z O 05 £35

VO CO

LD 00

LT) t-H UO LO

12

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.
STAINLESS STEEL WELDING PROGRAM

T. A. Siewert

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 8 O 303

This past year has been one of transition in the NBS welding program as

the Fracture and Deformation Division has developed the capability to prepare

specialized weldments and is planning to take a more active role in welding

research for cryogenic applications.

NBS Welding Laboratory

The capability to prepare specialized weldments was achieved through the

formation of a welding laboratory. This laboratory was designed to be selfsufficient and versatile. It has the necessary equipment to perform all tasks

in the production of weldments from plate preparation to the final inspection.

Three welding processes are being used [gas metal arc (GMA), gas tungsten arc

(GTA), and shielded metal arc (SMA)], and three classes of material are being

welded (stainless steel, aluminum, and low alloy steel). The laboratory is

equipped with an adaptive controlled GMA welding system, a GMA weld weaving

system, various power supplies, a multicomponent shielding gas mixing system, a rotating weld table, an oxyacetylene cutting table, and other support equipment.

This equipment has been installed in a large bay, which contains an overhead

crane (2-t capacity). This bay also contains new wiring to the power supplies

and piping for distributing the shielding gas to the various weld stations.

The welding laboratory serves two major functions: One is to advance

the science of welding through clarifying the interactions of the welding electrode with the arc, the shielding gas or slag system, and the molten weld pool.

The second function is to produce highly characterized test specimens for

evaluation by the NDE and mechanical property groups. Not only can these

specimens be produced much more rapidly than previously, but the unique capabilities of welding might be used to fabricate novel test specimens for better

evaluation of material behavior.

The welding program has received further direction from a discussion

session entitled "Research Objectives in Welding" at the NBS-DOE Workshop on Materials at Low Temperatures held October 14-17, 1984 (see page 299). The 4-K

property goals for welds in cryogenic structures are:

Goals

Interim Yield Strength

Fracture Toughness

1000 MPa

150 MPa/m

Eventual Yield Strength

Fracture Toughness

1000 MPa

200 MPa/m

13
We are encouraging industry participation in the development of consumables and

procedures that will meet these goals by assisting in some of the cryogenic

testing. Since these cryogenic tests are difficult to perform and testing

facilities are not widely available, a screening program has been established

to evaluate the candidate welds. The sequential steps include a 76-K Charpy

V-Notch (CVN) test of the weldment by the producer. Welds with an absorbed

energy above 54 J will be forwarded to the NBS Fracture and Deformation Division for tensile testing at 76 K and comparison with a screening goal of 750

MPa. Further toughness and strength tests at 4 K will be conducted at NBS if

the properties meet the screening goals.

Current Projects

Several electrode manufacturers and fabricators have expressed interest in

the screening program established to meet the goals of the NBS-DOE Workshop.

Several SMA weldments are anticipated during the year, and a fabricator is

intending to furnish an electron beam weld in 50-mm AISI type 304LN plate.

The effect of interstitial elements (in stainless steel welds) on the

cryogenic mechanical properties are being studied. In previous programs,

nitrogen and carbon have been studied in plate materials. However, the

predictive equations for strength and toughness are not valid for welds of

similar compositions. Mechanical properties and microstructures of welds with

various interstitial elements will be evaluated to determine which interstitials

can increase the weld strength with the least degradation of the toughness.

Another program involves the study of the interaction of manganese and

nitrogen in stainless steel weld metal. Previous studies have either varied

the manganese level while holding the nitrogen level virtually constant or kept

their ratio nearly constant. In this program, the two elements will be varied

independently, using test design matrices with both fixed and varying ferrite

number (FN), to assess their individual and combined effects on strength and

toughness. We will also assess the effect of molybdenum and boron addition on

the properties of these stainless steel welds.

Completed Projects

A fully austenitic weldment produced by a filler metal manufacturer was evaluated at 4 K. The undiluted weld metal had a composition of Fe-15Mn-8Ni1MO-0.7C and was produced by submerged arc welding a 21-mm plate using a butt

joint configuration. The yield strength (1115 MPa) and toughness (Kj^^ = 194

MPa/m) combination compares favorably with existing base metal properties for

AISI 304 type alloys.

A linear equation based on previously published data was developed to

predict the 76-K CVN toughness for shielded metal arc deposit compositions.

This study proposed a simpler and more accurate predictive equation to help

select improved compositions for future applications. Analysis of 79 weld

deposits revealed that calculated FN was the most significant term for predicting the CVN toughness. This term, when allowed to be negative, was also an excellent predictor of toughness for the fully austenitic compositions and the

AISI type 316 compositions, although no mechanism was proposed.

14


Tensile and Fracture Properties of

an Fe-14Mn-8Ni-lMo-0.7C Fully

Austenitic Weld Metal at 4

*

R. L. Tobler, R. E. Trevisan and R. P. Reed

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

A fully austenitic steel butt weld 21 mm thick was produced by submerged

arc welding using an experimental filler metal composition: Fe-14Mn-8Ni-lMo0.7C. The tensile and fracture properties of this weld were measured in

liquid helium to evaluate its candidacy for applications at 4 K. The yield MPa* strength (1115 MPa) and toughness (Kj = 192 *m^) combination of this

material compares favorably with existing base metal properties for AISI 304

type alloys. A conventional ductile fracture consisting of void formation and

coalescence was evidenced in both tensile fracture toughness specimens.

Keywords: austenitic steel; cryogenic testing; fracture toughness; low

temperature tests; mechanical properties; microstructure; tensile

properties; weldments.

+ Work supported by the U.S. Department of Energy; not subject to copyrinht.

Submitted to Cryogenics .

* Guest worker, on leave from the Department of Engineering, UNICAMP,

Campinas-Sao Paulo, Brazil.

15
INTRODUCTION

This paper describes the 4 K tensile and fracture toughness properties of

a newly developed, fully austenitic Fe-14Mn-8Ni-lMo-0, 7C weld metal. Austenitic welds usually contain a small amount of second phase 6-ferrite to prevent

hot cracking on cooling to room temperature. The 6-ferrite, however, is

undesirable for extreme cryogenic service since 6-ferrite is embrittled at low

temperatures. A study of the fully austenitic Fe-14Mn-8Ni-lMo-0. 7C composition is therefore of interest for the development of fully austenitic

welds for cryogenic service.

To exclude the formation of 6-ferrite and achieve a fully austenitic weld,

an appropriate chemical composition must be selected according to the Delong

diagram. Elmer, McHenry, and Whipple [1] tested several fully austenitic

stainless steel compositions in the form of as-welded plates. They concluded

that, while additional research is necessary to identify the optimum chemical

composition and weld process variables, it is possible to obtain

microfissure-free austenitic welds that have attractive strength/toughness

properties at 4 K. In this paper we consider an Fe-14Mn-8Ni-lMo-0. 7C filler

metal composition, describe its mechanical behavior at 4 K, and compare its

performance with stainless steel welds and AISI 304 type base metals.

MATERIAL

The material tested was a submerged-arc butt weld produced using two sections of 21-mm-thick mild steel plate and Fe-14Mn-8Ni-lMo-0. 7C electrode. The

steel plates were each coated with 2 layers of weld metal to minimize dilution

in the actual weld. Welding was performed in the flat position using 3.175-mm

tubular wire at 450 A, 30 V, and 5.9 to 6.8 mm/s travel speed with neutral

16
flux and a 38.1 mm electrical stickout. The chemical composition of the weld

is given in Table 1. Radiography indicated that this weldment met the

requirements of AWS A5.23.

Microstructures viewed normal to the longitudinal direction of the weld

are shown in Figs. 1 and 2. Figure lA is representative of the dendritic austenite phase revealed by etching with 1% nital solution. No 6-ferrite is present, as verified by electrolytic etching with KOH. Examination of a total

cross-sectional area of 200 mm^ revealed only one interdendritic microfissure,

which is shown in Fig. IB. Also present was a homogeneous distribution of MnS

and FeS inclusions, which is a common feature in welded steels, as shown in

Fig. 2.

EXPERIMENTAL PROCEDURES

Tests at 4 K were performed in a cryogenic apparatus [2] with material in

the as-welded condition using tensile and compact specimens with the orientations shown in Fig. 3.

The tensile properties in the longitudinal weld direction were determined

-4 -1

by testing two specimens at a strain rate of 4.2 x 10 s . The specimens

were 6.35 mm in diameter and 44.3 mm in gage length. Uncertainties in strength

measurements are less than ±3%. Three compact specimens were also prepared.

These were 20 mm thick (B) and 50.8 mm wide (W), with W/B =2.5 [3]. The

planar dimensions were those of a standard 25.4-mm-thick Kj^ test specimen

with W/B =2.0, but the notch was modified to allow loadline deflection measurements [2,3].

Two compact specimens failed to provide useful results: the first, with

a relatively short crack length (a/W = 0.50), failed by cleavage in the mild

steel at the loading pin holes; the second developed an irregular crack front.

17
A third specimen (a/W = 0.69) was tested successfully and analyzed using linearelastic and elastic-plastic methodologies [3,4]. Uncertainites in Kj^ determinations are estimated at about 10%. Also, the 4 K fracture surface was examined with a magnetic torsion balance device and by scanning electron microscopy.

RESULTS

The 4 K tensile properties of the Fe-14Mn-8Ni-lMo-0. 7C weld metal are

listed in Table 2, and the tensile fracture surface is shown in Fig. 4. A

conventional cup-and-cone fracture is manifested but the final cross-sectional

area is slightly elliptic, owing to the anisotropy of plastic deformation.

Higher magnifications of the flat fracture (center) and shear fracture (circumferential) zones are shown in Figs. 5 and 6. The flat fracture zone shows

circular dimples and pores which evidence a conventional ductile failure

mechanism consisting of void coalescence (Fig. 5). The shear fracture zone

shows elliptic dimples and some porosity (Fig. 6). There is no evidence of

brittle failure mechanisms.

The 4 K fracture test results are summarized in Figs. 7 and 8. The Kq

j, value according to the ASTM E 399-83 procedure is 144 MPa*m^ while the Kj^

estimate according to J-integral calculations is 192 MPa*m^. However, neither

value can be considered a valid measurement of for reasons given below.

The Kq value calculated from the curve of Fig. 7 is invalid because of

failure to satisfy the specimen thickness requirement (section 9.1.3, ASTM E

399-83) and also because the 1.15, exceeds the allowable limit

of 1.10 (section 9.1.2, ASTM E 399-83). The actual specimen thickness is 20.2

mm, whereas 42 mm may be required for valid results, according to the Kj^ test

standard.

18
J- integral calculations were performed using the same test record (Fig.

7) used to obtain Kq. Valid J-resistance curves could not be obtained, however, because load-point instabilities occurred, followed by arrests, giving

the displacement-controlled test record the serrated appearance shown in

Fig. 7. The occurrence of such instabilities represents unloading at the

crack tip which is unacceptable according to the ASTM E 813-81 test procedure.

From the practical side, serrations limit the number of J-Aa data points

that can be obtained in single specimen tests, since unloading compliance

measurements can only be performed at points of crack arrest. As a result, we

obtain the pseudo-resistance curve shown in Fig. 8. Since the Aa increments

associated with serrations are uncontrollable, only two data points fall in

the prescribed Aa interval defined by the 0.15 to 1.5 mm offset limits of E

813-81. Failure to obtain four data points within the specified interval

invalidates the results according to sections 3.1 (note 2) and 9.3.2 of ASTM

E 813-81. Nevertheless, an estimate of

^Ic was calculated from the apparent

from Fig. 8 as follows [4]:

Kjj.(J) = = [207 GPa • 178 kJ/m^]^^ ^ -^^2 MPa-m^

Figure 9 shows the fracture surface at the center of the compact specimen

after testing at 4 K. The fracture surface is 100% dimpled. In addition,

examination of the 4 K tensile and fracture specimen surfaces with a magnetic

torsion balance indicated that no a' (body-centered cubic) martensite had

formed during the loading to fracture at 4 K. The sensitivity of the balance

is 0.2%. Therefore this fully austenitic steel appears ductile and fully

stable against martensitic phase transformation during deformation to fracture

at 4 K.

19
DISCUSSION

Fracture mechanics data for weldments at 4 K are rare because of the

experimental complexities of testing at cryogenic temperatures. However,

fracture toughness data for seven fully austenitic steel weldments are

reported in the work of Elmer, McHenry, and Whipple [1], and their data are

compared with ours in Fig. 10. These data represent similar specimen

orientations and data reduction procedures, although other factors such as

grain size, weld process, and manufacturing variables were uncontrolled.

As seen in Fig. 10, the performance of the Fe-14Mn-8Ni-lMo-0. 7C weld containing no chromium compares well with the data for fully austenitic stainless

steel weld compositions. In general, the weld metal data demonstrate an inverse trend between toughness and strength which is analogous to the trend for

AISI 304 type base metals, although the scatter is larger for welds. It is

also evident that some of the fully austenitic weld metal compositions, including Fe-14Mn-8Ni-lMo-0. 7C, nearly match the properties of the unwelded base

metals.

Note that the above comparison is based on TL orientations [3] for the

base metal and welds. Since welds are highly anisotropic, comparisons based

on other fracture plane orientations could give different results.

Although serrations affect the interpretation and calculation of fracture

test results, the consequences of their occurrence in 4 K test records has

never been properly studied. Previously, several base metals of relatively

high strength displayed similar serrations and invalid curves [5]. Also,

as discussed in a study of AISI 310 steel, serrations at 4 K are common even

in very ductile materials [6]. In the ductile materials, there is probably a

correspondence between the occurrence of serrations in fracture tests and discontinuous yielding in tensile tests owing to adiabatic heating [6]. So far.

20
the approach to characterizing the fracture toughness of these materials has

been to calculate as if the serrations were absent, and on this basis the

comparisons of Fig. 10 were made.

Finally, it must be noted that during specimen fabrication the weld metal

was found to be extremely difficult to machine, and carbide tools were necessary. The Fe-14Mn-8Ni-lMo-0. 7C weld metal is a close relative of the Hadfield

manganese steels which have high work-hardening capacities. Poor

machinabil ity is therefore a significant disadvantage of this weld metal

composition.

ACKNOWLEDGEMENT

The weld was fabricated by Teledyne-McKay and provided to NBS through the

courtesy of Dr. D. J. Kotecki ; we are indebted to him, and also to Mr. R. P.

Walsh of NBS who conducted the tensile tests. Helpful discussions with

Dr. T. A. Siewert of NBS are also gratefully acknowledged.

REFERENCES

1. J. W. Elmer, H. I. McHenry, and T. A. Whipple, Strength and Toughness of

Fully Austenitic Stainless Steel Filler Metals at 4 K, in NBSIR 81-1645,

Materials Studies For Magnetic Fusion Energy Applications At Low

Temperatures - IV (1981) 289-302.

2. 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) 17-28.

3. Standard Test Method for Plane Strain Fracture Toughness of Metallic

Materials, ASTM Designation E 399-83, 1984 Annual Book of ASTM standards,

Amer. Soc. Test. Mater., Philadelphia (1984) 519-554.

4. Standard Test Method for J, , A Measure of Fracture Toughness, ASTM

Designation Soc.

Test. Mater.

E 813-81, 1984 Annual Book of ASTM Standards, Amer.

, Philadelphia (1984) 763-781.

21
5. R. L. Tobler, D. T. Read, and R. P. Reed, Strength/Toughness Relationship

for Interstitial ly Strengthened AISI 304 Stainless Steels at 4 K Temperature, in Fracture Mechanics; Thirteenth Conference, ASTM STP 743, R. Roberts, Ed., Amer. Soc. Test. Mater., Philadelphia (1981) 250-268.

6. R. L. Tobler, Ductile Fracture with Serrations in AISI 310S Stainless

Steel at Liquid Helium Temperature, in: Elastic-Plastic Fracture:

Second Symposium, Volume II-Fracture Resistance Curves and Engineering

Applications, ASTM STP 803, C. F. Shih and J. P. Gudas, Eds., Amer. Soc.

Test. Mater., Philadelphia (1983) 763-776.

Table 1. Chemical composition of the weld deposit (wt. %).

Fe Mn Ni Mo C P S Si

balance 14.41 8.05 1.08 0.704 0.013 0.009 0.41

Table 2. Tensile properties of Fe-14Mn-8Ni-lMo-0. 7C weld metal at 4 K.

Specimen

No.

Yield strength,

a^, MPa

(ksi)

Ultimate strength,

MPa

(ksi)

Elongation in

44 mm gage length,

%

Reduction of

area,

%

1 1180 1390 20.3 23

(171) (202)

2 1050 1140 14.7 15

(152) (165)

Avg 1115 1265 17.5 19

(162) (184)

22
Figure 1. Etched microstructures of the weld fusion zone.

23
Overall weldment dimensions:

22x100x533

All dimensions in mm.

(not to scale)

Figure 3. Orientation of the tensile and compact specimens in the weldment.

24
Figure 4. Cup-and-cone fracture morphology of 4 K tensile specimen

25
Figure 5. Scanning electron microscope view of flat fracture

(center) section of 4 K tensile specimen.

26
LOAD,

50 I

Z

40

Fe-14Mn-8Ni-1Mo-0.7C Weld Metal

B = 20.2 mm W = 50.8 mm

DEFLECTION, S , mm

Figure 7. Load-deflection test record

for a precracked compact

fracture specimen at 4 K.

Figure 8. J-resistance curve at 4 K.

27
Figure 9. Scanning electron microscope view of the 4 K fracture topography of the compact specimen.

YIELD STRENGTH, CTy, MPa

Figure 10. Compilation of strength-versus-toughness data

for fully austenitic welds at 4 K, including

comparison with AISI 304 type base metals at 4 K.

28


Predicting the Toughness of SMA

Austenitic Stainless Steel Welds at 77 K*'*'

Thomas A. Siewert

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

Austenitic stainless steels often provide the best combination of

strength and toughness for cryogenic applications: however, the weld toughness is frequently much lower than that of the base metal. This study

proposes a more accurate and simpler model for developing improved filler

metal compositions.

Several previous studies of the weld toughness were analyzed separately

and in combination using a stepwise regression method and an expanded

variable list. The total data base consisted of chemical composition,

ferrite number (FN), and the Charpy V-notch (CVN) toughness at 77 K of 79

austenitic stainless steel welds deposited by the shielded metal arc process.

Analysis of the complete data base revealed that the FN calculated from the

Schaeffler diagram was the most significant variable for predicting the CVN

toughness. The predictive equation produced a better correlation between the

measured and predicted values of weld toughness than the previously published

predictive equations.

The group of 36 fully austenitic welds and the group of 21 type 316 welds

in the data base were analyzed by the same procedure. In both cases the

ferrite number was found to be the most significant predictor of toughness.

* Publication of the National Bureau of Standards, not subject to copyright.

Supported, in part, by the U.S. Department of Energy.

29
1 .0 Introduction

Austenitic stainless steels are often chosen for support structures in

cryogenic service because of their high toughness. Unfortunately, the weld

toughness can be considerably lower than that of the plate material, especially for shielded metal arc welds. ^ Previous studies have correlated

stainless steel weld composition and toughness at 77 This paper, using

a stepwise regression technique, reexamines these data and develops improved

correlations between the composition and toughness. Four improved predictive

equations are compared to the previously developed equations.

Siewert^ and Szumachowski and Reid^*^ statistically correlated the Charpy

V-Notch (CVN) toughness at 77 K to the composition, for a wide variety of

stainless steel welds produced by the SMA process. These studies developed

equations for quantitative prediction of the weld toughness based on the

weld’s chemical composition. However, these studies used a six- or seven-variable model with the variables chosen from a very limited data set.

Siewert reported the predictive equation

CVN (ft‘lbf) = 62 - 60 C - 7 Mn - 2.5 Cr + 2.9 (Ni-Mo) - 0.75 FN (la)

which, when converted into SI units by multiplying the ft*lbf units by 1.36

to obtain joules, becomes

CVN (J) = 8M - 82 C - 10 Mn - 3-^ Cr + 3-9 (Ni-Mo) - FN (1b)

where the elements are in weight percent and FN (ferrite number) is the

measured value from the weld. The value (a correlation of the measured

value with the predicted value) was 0.61.

Szumachowski and Reid reported the predictive equation

CVN (ft*lbf) = 82.9 - 175.8 C + 0.42 Mn - 0.90 Cr + 2.16 Ni - 0.80 Mo

- ill.

N - 3.45 (coating) (2a)

which, when converted to SI units, becomes

CVN (J) = 113 - 239 C + 0.57 Mn - 1.22 Cr + 2.94 Ni - 1.09 Mo

- 151 N - 4.69 (coating) (2b)

where the elements are in weight percent. The value of either 15 or 16

should be inserted for coating to distinguish between the lime (-15) and

rutile (-16) slag system designations when evaluating their effect on the

toughness. In this case the R^ value was 0.69.

This paper uses a broader data base than the earlier study, ^ analyzes the

effects of additional elements, includes interactive terms such as compounds

and various mathematical representations of delta ferrite, and then selects

30
the variables from the combined data bases by a stepwise regression technique. This process provides a clearer ranking of the factors that control

the 77 -K weld-metal toughness and so provides more detailed guidance for

future improvements in electrodes.

2.0 Procedure

The data bases of Siewert^ and Szumachowski and Reid3>^ were combined

because they had similar ranges of compositions, welding procedures, and CVN

testing procedures. But, because a systematic error due to slight differencs

in the slag system or weld procedure for the two bases could exist, a term

distinguishing the two bases was included in the analysis.

Siewert's data base was expanded by the addition of a number of elements,

which had been measured but not included in the data analysis. Percentages

by weight for these elements —0, Ti , V, Co, and Cu—were added to the base

(Table 1). Szumachowski and Reid's data were used as originally published

and are not listed here.3»^

Additional variables were generated by forming products between various

elements to determine if these interactions might be significant. The

variables FNCD, FNCS, FNCH, and FNCB are mathematical representations of the

various constitution diagrams used to predict the FN (the third letter of

each variable emphasizes that they were calculated, and the last letter of

each term refers to DeLong, Schaeffer, Hall, and Babcock and Wilcox, respectively). ^ These constitution diagrams, developed to predict FN from the

composition, were reduced to equation form and listed in this Welding

Research Council publication. Table 2 defines the variables, both elements

and combinations, that were used in the analysis of Table 1. Table 3 defines

the variables that were common to both data sets and so used for the various

analyses of the combined sets.

A multiple linear regression model was used. A stepwise regression

technique was used to select variables to be included in the model. This

procedure computes the correlations between all the variables and the

dependent variable, CVN. It then selects the variable most highly correlated

with CVN and enters it into the model. Using partial correlation coefficients as before, it next selects the variable whose partial correlation with

CVN is the highest. This process is repeated until none of the variables

selected can meet the selection criterion, based on an F-statistic. In this

study, an F value of 4.0 was chosen as the critical value in the stepwise

regression technique. (F is defined as the square of the quantity-regression

coefficient divided by the standard error. F can also be expressed roughly

as a 95 percent confidence level or a ratio of best parameter estimate to

standard error, of 4.0.)

3.0 Results and Discussion

3.1 Analysis of Table 1 (I 8 welds)

This table (the expanded Siewert data base) contained variables that were

not in the Szumachowski and Reid data base; 0, Ti , V, Co, Cu, and their

interactive terms. The predictive equation computed from these data is

31
CVN (J) = 38 - 0.68 FNCD - 1.67 FN (3)

where FNCD and FN are defined in Table 2. The results are summarized in

Table 4.

The value of 0.94 indicates this model fits the data better than the

previous model did (Equation 1), even though the new model has only two

variables (the measured ferrite number) and FNCD (a representation of the

ferrite number). FNCD is listed in Table 2 as a mathematical equation with

many terms, but its physical significance is that of one variable, the

potential to form ferrite or, when negative, the relative reluctance to form

ferrite. FNCD was the first variable selected by the stepwise technique,

indicating it was the most significant variable in predicting the CVN

toughness. It was slightly more significant (21 percent) than FNCS but

substantially more significant (200 percent) than Ni, the variable of third

highest significance.

The second iteration resulted in the addition of FN to the model. None

of the other variables met the requirements of an F value of 4.0 (corresponding to a 95 percent confidence level). The choice of FN (the measured

ferrite number and so always positive) in this iteration indicates a slight

difference in the effect of ferrite in the positive and negative potential

regions. Changes in FN in the positive (measured) region have a greater

effect on toughness than changes of ferrite potential in the negative region.

The list of variables not in the equation (Table 4) should also be

reviewed because variables with an F value greater than 2.0 came close to

meeting the selection criterion. Both C and Cr had negative coefficients,

which agree with the negative coefficients previously reported (Equations 1 and 2). The negative coefficient for Co is of questionable significance

because of the limited range of values. The negative coefficients for CMn,

CCr, and CN might indicate some interactions are occurring.

Since none of the variables unique to Table 1 were found to be significant, the two data bases were combined to improve the accuracy of the model.

The larger base clarified the slight indication of some correlation of these

other terms.

3.2 Analysis of the Combined Data Base (79 Welds)

The predictive equation computed from the data is

CVN (J) = 19-1.4 FNCS - 890 C^ + 1.4 Ni (4)

where FNCS and C^ are defined in Table 3- The results are presented in

Table 5. The value of 0.73 indicates a poorer fit than that of Table 4.

However, with just three terms, the model has a better fit than that of

reference 2 with 6 terms (Equation 1) or reference 4 with 7 terms (Equation 2).

This time FNCS was the variable first selected by the stepwise technique.

Its F value of 149 indicated substantially greater significance than the F

value of 110 for FNCD, the F value of 108 for FNCH and FNCB, and the F value

32
of 97 for Ni. Clearly, negative ferrite potential, in general, and FNCS,

here in particular, is the most significant variable in predicting the

cryogenic toughness. The variable FNCS differs from FNCD in several characteristics. Two of these are considered to have a significant effect on the

program's choice of the best term.

1 . The term FNCS is based on the Schaeffler constitution diagram that covers a wide range of compositions and many different phase regions (Fig. 1).^

For this reason, it is expected to be accurate for the ranges in compositions included in the data bases. In the Schaeffler diagram, the constant

ferrite lines pivot around an axis with a varying angular orientation. The

negative ferrite isopleths (constant ferrite lines) were also chosen to vary

with a variable spacing, unlike the parallel and equally spaced negative

ferrite lines used by Szumachowski and Reid. 3 The variable FNCD is based on

the DeLong constitution diagram, which covers of a small region of the

Schaeffler diagram that was refined specifically for the ferrite-containing

austenitic stainless steels. The type 330 compositions in the data base

fall far outside the intended bounds of applicability.

2. The variable FNCD includes nitrogen. Nitrogen has the two opposing

effects of reducing the FN (which improves the toughness according to equations 3 and 4 and reference 7) while degrading the toughness, at constant FN.^

Apparently it is hard to resolve these conflicting effects since the program

chose the term without nitrogen (FNCS).

To clarify these two effects, another variable FNCSN was produced, incorporating the nitrogen factor from FNCD into the FNCS equation. Its F value of

134 seems to indicate that both nitrogen and the narrower intended range of

the DeLong diagram reduce the statistical significance of FNCD for the

combined bases, with range of the diagram having the larger effect.

In the second iteration of the stepwise technique, C^ was added to the

model. Its F value was approximately double that of C, the second largest

value. This variable indicates the deleterious effect of carbon, substantially increasing in its effect at higher concentrations. This is quite

surprising, as the type 330 stainless steel compositions had both the best

toughness and the greatest carbon concentrations. This model suggests a type

33 OL might produce substantial improvements in toughness.

In the third and last iteration, Ni was chosen. The addition of this

variable emphasizes the beneficial effect of nickel on the toughness, even beyond its effect in the term FNCS.

The list of the variables not in the equation yields further clues to the

effects of the variables that do not quite meet the significance standards

but could indicate a trend. Those with an F value above 1 are now considered

since this is the largest data base, and possible trends can be investigated

in the following analyses of certain regions of applicability. The variable

C is positively correlated and seems to indicate that C^ slightly overestimates the negative effect of C. The variable S is positively correlated,

because the type 330 compositions tend to have the highest sulfur levels

while producing the best toughness. The variable CMo is negatively correlated, giving an indication of a possible interaction. The term base gives a

33
slight indication of differences between the two data bases. Six nitrogencontaining variables —N, MnN, CrN , FNCD , FNCH and FNCB—have negative

correlations. This is a good indication that nitrogen is having a deleterious effect, but its effect is not significant over the entire range

of compositions. Although Szumachowski and Reid^ indicated a number of

compositions where nitrogen seemed to have a clearly detrimental effect,

there might be other compositions where the effect is less pronounced. These

other compositions would be of interest since nitrogen could be added to

increase the strength without degrading the toughness, similar to what has

been accomplished with the plate material.®

A search was made for other variables (especially higher order effects)

that would improve the model. After the model was fitted, all the observed

values, predicted values, and residuals from the statistical computations

were plotted against all the variables in Table 3. No trends were observed.

Therefore, the model seems to be the best that can be obtained for the entire

data base. For a better understanding of the applicable range of the model,

selected portions of the data base were examined in more detail.

3.3 Analysis of 36 Fully Austenitic Welds

The fully austenitic compositions were selected by choosing FNCS to be

less than or equal to zero. The results are presented in Table 6. The

predictive equation is

CVN (J) = 5 - 2.3 FNCS - 1000 C2 + 82 Si (5)

where FNCS, C^ , and Si are defined in Table 3-

In general, the model is a confirmation of that obtained for the combined

data bases (Table 5). The slightly higher coefficient for FNCS offsets the

effect of Ni in the other model. The choice of Si with a positive coefficient is surprising. Silicon is generally considered to reduce the toughness. Its choice is probably due to the high silicon levels in some of the

high toughness compositions, similar to the choice of C^ in the previous

model

The list of variables not in the equation gives some guidance as to

possible trends that did not meet the significance requirements. Since this

analysis considers only a portion of the entire data base, the value of 2.6

for base indicates a slight difference between the two data bases that had

been combined in this study. This is probably due to slight differences in

the manganese content in the type 330 compositions. The variables Cr, CCr

and FNCD indicate some positive correlation while N, CMn, and MnN indicate

some negative correlation. Less significance is attributed, in general, to the

list of variables not in the equation since the data set is smaller.

34
3.^ Analysis of Type 316 Welds

As indicated, type 316 stainless steel, primarily the low-carbon grade

31 6L, has been used for the majority of recent cryogenic construction. It

has produced good toughness while resisting the microf issuring associated

with the fully austenitic compositions. Results of the 21 type 316 compositions are summarized in Table 7. The predictive equation is

CVN (J) = 49 - 2.7 FNCS - 95 MnN - 2 FN (6)

where FNCS, MnN, and FN are defined in Table 3.

Once again, FNCS was determined to be the most significant predictor of

cryogenic toughness. The previously observed^ detrimental effect of nitrogen

in this grade is indicated best by the variable MnN. The variable FN is

again an indicator that the presence of ferrite is more detrimental than the

increase in ferrite potential in the negative region. None of the variables

that had not been included in the equation had F values greater than 2.

4.0 Conclusions

Based on a statistical correlation between SMA weld compositions and

their Charpy V-Notch toughness, the following conclusions are drawn:

1. Ferrite number, calculated by the Schaeffler diagram and allowed to be

negative, is consistently the most significant predictor of CVN toughness

in welds at 77 K. The importance of this variable was not recognized in

previous studies.

2. Other variables, such as measured FN, Ni , Si, ferrite number calculated by

the DeLong diagram (FNCD) and C^ , can be significant, depending on the

range of compositions considered.

3. Over the entire range of austenitic stainless steel weld compositions

considered, the best predictive equation at 77 K is:

CVN (J) =19-1.4 FNCS - 890 C^ + 1.4 Ni (4)

where the variables are defined in Table 3«

4. Further improvements in the toughness of electrodes for cryogenic service

can best be obtained by decreasing the ferrite potential. Such fully

austenitic compositions will require further study of the microf issuring

tendency.

5.0 Acknowledgment

The author appreciates helpful discussions with D. Vecchia in the

Statistical Engineering Division of the Boulder Laboratories and assistance

in the computer calculation from L. Drake, who spent the summer in the

Statistical Engineering Division of the Boulder Laborator ies.

35
6.0 References

1 . "Low Temperature Materials Workshop for Magnetic Fusion Energy - An Informal Summary," in Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures - VIII, R. P. Reed, ed. , NBSIR 85-3025,

National Bureau of Standards, Boulder, Colorado, p. 305.

2. Siewert, T. A., "How to Predict Impact Energy from Stainless Steel

Composition," Weld. Des. Fabr., June 1978, p. 88.

3. Szumachowski , E. R., and Reid, H. F., "Cryogenic Toughness of SMA

Austenitic Stainless Steel Weld Metals: Part I - Role of Ferrite,"

Weld. J., Nov. 1978, p. 325-S.

4. Szumachowski, E. R., and Reid, H. F. , "Cryogenic Toughness of SMA

Austenitic Stainless Steel Weld Metals: Part II - Role of Nitrogen,"

Weld. J., February 1979, p. 34-S.

5. "H2 Embrittlement of Austenitic Stainless Steel with Special Consideration Given to Sigma Phase," Weld. Res. Bull. 240, Aug. 1978.

6. Schaeffler, A., "Constitution Diagram for Stainless Steel Weld Metal,"

Met. Prog., 56 , 1946, p. 680.

7 . DeLong, W. T. , "Ferrite in Austenitic Stainless Steel Weld Metal,"

Weld. J., July 1974, p. 173"S.

8. Read, D. T., McHenry, H. I., Steinmeyer, P. A., and Thomas, R. D., Jr.,

"Metallurgical Factors Affecting the Toughness of 31 6L SMA Weldments at

Cryogenic Temperatures," in Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures - II, NBSIR-79-1 609 , R. P. Reed, ed.

National Bureau of Standards, Boulder, Colorado, 1979, p. 315.

36
WELD

DEPOSIT

COMPOSITIONS

-

BASIS

FOR

REFERENCE

7,

WITH

ADDED

VARIABLES

(Elements

in

Weight

Percent)

Z

> ri O

C\jONCMLn»—

o

0) L.3

05

(00) s: OCOvO«:3''OvOvDv.D'0 -a'Oir»OOOvO(\J

3O

m^OGOOv^v£)ooco — oooooooooooooooooo

oooooooooooooooooo \o iTNvDvo irNLnmir'Lnmm'X) inir»t^ir>vo

ou

ooco<s3'LO-^ojocococ\jrot^a'»— L^^a^voa^

— — roO»— 0 «- 0*-00 oooooooooooooooooo

cnLnoocvjc\jooo^o«-*-oocM'^c\j oooooooooooooooooo

vDinf^t^-a'vDiriOoood'ja’rnmmt— ro^«— OOCT't^v£>COCOt*“COOOCOr^t-“SOt^O^ OOOOOOOOOOOOOOOOOOmO'

oooooooooooooooooo

00 -^v£> 0 -a''£>.=TO>3‘irvCOOfMOv£>-^vD lti'X>-= OOOOOOOOOOOOOOOOOO 3''0 CNt'-iO'X) int— oo^ LT'co mmoco

oooooooooooooooooo

CMOOO*— ir»»—(\jv£>c\j0sjf-*— oooojmojO (\)OOOOOOOOOOOC\JC\JC\JOOO

^oo^o^^o^CT^o^CT^o^o^oCT^^ommo^o

»-c\j (\j»— »—

<\i^oor\j<=TOCTN\DcrNco^cT'«— ocTN*-a>:3

' c^^oa^a^o^o^o^c>CT'OOL^'L^^coc— L^l 0^o

iTvcocoaNO*vx)t*“cnromir»moomt^.=Tcooo oooooooooooooooooo oooooooooooooooooo

ir'ir\ir^m-=r^v£>ro(\iLn^:3'coir'i/^-=T<3't^ oooooooooooooooooo

c

s:

(\j CO ma^•=T coco CM mcMvo t— romo 0^•— O^OOvO c*-ur» 00^0 LTNinvC CT'O' (M*-*-*-r-^-<\lCM — — O

o

^mc'^sDrot^romOtTNOOOiAOOOOO' O^OOOOOOOOOCM CMLTNmCM^m^-^ LTiCnOOir*cnO'^CM — OOCMOO OOOOOOOOOOOOOOOOOO

u

0- H

iT» vov.DirNirv'^sotr»ir»j>Lnir»ir»*“

J ar J '^OCOcOOOcOCOcCCOcOCOOOvOs£)OCO ^^OOOOOOOOO mmmmmmmmmrommmmmrnm — — mo

37

308L
TABLE 2

VARIABLES USED IN THE ANALYSIS OF TABLE 1

VARIABLE DEFINITION

C

— Mn - Si -

P - S

- Or - Ni - Mo - FN Measured on weld;

Coating 5 is entered for a -15 coating and 6 for

a -16 coating

0

-

Ti - Co - V

- Cu - c2 C • C

Mn^ Mn • Mn

CMn C • Mn

CCr C • Cr

CN C • N MnO Mn • 0

SiO Si • 0

MnN Mn • N

CrN Cr • N

TiN Ti • N

Tie Ti • 0

FNCD -30.65 + 3.^9 (Cr + Mo + 1.5 Si)

- 2.5 [Ni + 30 (C + N) + 0.5 Mn]

FNCS -39.1 + 43.5 (Or + Mo + 1 . 5 Si + 0.5 Cb - - 5.8)/ (Ni + 30 C + 0.5 Mn + 2)

FNCH -13.77 + 2.88 (Cr + 1.21 Mo + 0.48 Si)

- 3.125 (Ni + 0.11 Mn + 0.0086 Mn^

+ 24.5 C + 18.6 N)

FNCB -15.35 + 3(Cr + 1.21 Mo + 0.48 Si)

- 3.18 (Ni + 0.11 Mn + .0.0086 Mn2

+ 24.5 C + 18.6 N)

38
TABLE 3

VARIABLES USED IN THE ANALYSIS OF THE COMBINED DATA BASES

VARIABLE DEFINITION

C

— Mn - Si -

P - S

- Or - Ni - Mo - FN Measured on weld;

Coating 5 is entered for a -15 coating and 6 for

a -1 6 coating

Base Term to distinguish the 2 data bases

C • C

Mn^ Mn • Mn

CMn C • Mn

CCr C • Or

ON C • N

MnN Mn • N

CrN Or • N

CrNi Or • Ni

FNCD -30.65 + 3.49 (Or + Mo + 1.5 Si)

- 2.5 [Ni + 30 (C + N) + 0.5 Mn]

FNCS -39.1 + 43.5 (Or + Mo + 1.5 Si + 0.5 Cb

- 5.8)/ (Ni + 30 C + 0.5 Mn + 2)

FNCH -13.77 + 2.88 (Or + 1.21 Mo + 0.48 Si)

-3.125 (Ni + 0.11 Mn + 0,0086 Mn^

+ 24.5 C + 18.6 N)

FNCB -15.35 + 3 (Or + 1.21 Mo + 0.48 Si)

- 3.18 (Ni + 0.11 Mn + 0.0086 Mn^

+ 24.5 C + 18.6 N)

39
TABLE ^

PREDICTIVE EQUATION BASED ON TABLE 1

Variable

Std. Error

Coefficient of Coefficient F*

(y intercept)

FNCD

38

-0.68 0.07 102

FN -1.67 0.41 •17

r2 = 0.94 Compositions Analyzed = 18

Variables Not in Equation

Var iable Partial Correlation F*

C -0.42 3.0

Mn -0.26 1 .0

Si -0.07 0.06

P 0.32 1.6

S 0.24 0.9

Cr -0.36 2.1

Ni -0.29 1 .3

Mo 0.002 0.0

N 0.07 0.08

Coating -0.21 0.7

0 -0.18 0.5

Ti -0.35 2.0

Co -0.45 3.5

V -0.25 0.9

Cu -0.05 0.04

C2 -0.33 1 .8

Mn^ -0.22 0.7

CMn -0.42 3.0

CCr -0.38 2.4

CN -0.36 2.1

MnO -0.31 1 .5

SiO -0.11 0.2

MnN -0.23 0.8

CrN -0.11 0.2

TiN -0.30 1 .4

TiO -0.30 1 .3

FNCS 0.30 1 .4

FNCH 0.35 1 .9

FNCB 0.35 1 .9

A value of 4 is necessary to enter the equation.

40
TABLE 5

PREDICTIVE EQUATION BASED ON COMBINED DATA BASES

Std. Error

Var iable Coef f ic ient of Coefficient F*

(y intercept) 19

FNCS -1 .4 0.26 26

C2 -890 193 21

Ni 1 .4 0.45 10

r2 = 0.73 Compositions Analyzed =79

Variables Not in Equation

Var iable Partial Correlation F*

C 0.13 1 .3

Mn -0.09 0.6

Si 0.11 0.8

P -0.02 0.02

S 0.18 2 .

Cr -0.12 1 .

Mo -0.04 0.2

N -0.16 2.2

FN 0.02 0.02

Coating -0.07 0.4

Base -0.13 1 .3

Mn2 -0.08 0.5

CMn -0.08 0.5

CN -0.02 0.02

CCr 0.08 0.5

CMo 0 1 2.1

MnN 1 o • 3.4

CrN -0.17 2.2

CrNi -0.05 0.2

FNCD -0.12 1 .0

FNCH -0.14 1 .4

FNCB -0.14 1 .4

*A value of 4 is necessary to enter the equation.

41
TABLE 6

PREDICTIVE EQUATION BASED ON THE FULLY AUSTENITIC COMPOSITIONS

Std. Error

Variable Coefficient of Coefficient F*

(y intercept) 5 FNCS -2.3 0.31 54

C2 -1000 200 24

Si 82 20 16

r2 = 0.76 Compositions Analyzed = 36

Variables ;Not in Equation

Var iable Partial Correlation F*

C 0.16 0.8

Mn -0.19 1 .2

P 0.23 1 .7

S -0.15 0.7

Cr 0.29 2.8

Mo -0.02 0.01

N -0.24 2.0

FN -0.16 0.8

Coating -0.23 1 .8

Base -0.28 2.6

Mn^ 0.20 1.4

CMn -0.29 3.0

CN 0.09 0.2

CCr 0.27 2.5

CMo -0.20 1 .3

MnN -0.29 2.9

CrN -0.09 0.2

FNCD 0.31 3.3

FNCH 0. 1

0.4

FNCB 0.12 0.5

*A value of 4 is necessary to enter the equation.

42
TABLE 7

PREDICTIVE EQUATION BASED ON THE TYPE 316 COMPOSITIONS

Var iable

Std. Error

Coefficient of Coefficient F*

(y intercept) 49

FNCS -2.7 0.49 31

MnN -95 26 1 4 FN -2 0.78 7

r2 = 0.87 Compositions Analyzed = 21

Variables Not in Equation

Var iable Partial Correlation F*

C 0.28 1.4

Mn -0.15 0.4

Si 0.20 0.7

P 0.28 1 .4

S 0.12 0.25

Cr 0.10 0.16

Ni 0.10 0.43

Mo 0.16 0.15

N 0.15 0.39

Coating -0.05 0.04

Base -0.05 0.04

C2 0.25 1 .0

Mn^ -0.16 0.41

CMn 0.25 1 .05

CN 0.24 0.98

CCr 0.28 1 .34

CMo 0.29 1 .42

CrN 0.18 0.52

CrNi 0.09 0. 1 4 FNCD 0.25 1 .0

FNCH 0.25 1 .0

FNCB 0.24 1 .0

*A value of is necessary to enter the equation.

43
Chromium Equivalent = % Cr + % Mo + 1.5 x % SI + 0.5 x % Cb

Figure 1. Schaeffler Diagram, illustrating the distribution of the weld compositions.

44
HOHMETALLICS

45

HOUMETALUCS PROGRAM

LEADERS: M. B. Kasen, H. M. Ledbetter, NBS

STAFF: M. W. Austin, R. D. Kriz, NBS

OBJECTIVES:

1. Measurement, modeling, and understanding of the properties of composites

that enter essentially into the conception, design, construction,

operation, and performance of magnetic-fusion-energy equipment.

2. In cooperation with industry, the establishment and refinement of

cryogenic-grade specifications for insulating laminates and test methods

for materials selection.

RESEARCH PAST YEAR (1984):

1 . Comparison of theory and experiment on the influence of damage in woven

composites at low temperatures on load-deformation behavior at low

strains

2. Study of elastic representation surfaces of unidirectional composites.

3. Development of radiation-resistant insulators for magnetic fusion energy

systems that utilize superconducting magnetic confinement at low temperatures.

RESEARCH THIS YEAR (1985):

1 . Study of the relationship between damage and load-deformation behavior

of woven composites at low temperatures for cyclic mechanical and

thermal loads.

2. Development of improved test methods for new polymer materials subject

to neutron irradiation at low temperatures.

3. Development of a computer program to calculate the load-deformation

behavior of metallic-nonmetallic laminates structures at low temperatures .

47



MECHANICAL-DAMAGE EFFECTS

IN WOVEN LAMINATES AT LOW TEMPERATURES

Ronald D. Kriz

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standard

Boulder, Colorado 80303

Walter J. Muster

Metals Division

Swiss Federal Laboratories for Materials

Testing and Research (EMPA)

Dubendorf, Switzerland

Large quantities of nonmetallic woven composites will be used in

magnetic fusion energy structures at low temperatures. We predicted and

measured the influence of crack formation on the mechanical performance of

standard glass/epoxy laminates (G-10CR, G-11CR) at low temperatures.

Mechanics of the load-deformation response of a unit cell of weave was predicted by a finite element model that assumes generalized plane strain.

Damage was modeled as macrocracks confined to individual fiber bundles that

were oriented transverse to the tensile load direction. FVom experiments

with tension loads, we studied the formation of damage as a collection of

fiber breaks, fiber bundle cracks, and delaminations between adjacent fiber

bundles. Earlier experiments had shown that the strain to failure of the

laminate increased when the components became brittle at low temperatures.

We explain this behavior from results of our studies on the formation of

damage in three-layer laminates of G-10CR and G-11CR at 76 K and 295 K: we

49
measured fiber bundle cracks in the laminate interior and individual fiber

fractures at the laminate edges by a replication technique. We discovered

that the sequence and types of damage, at strains well below ultimate, control the discontinuities (knees) in the load-deformation (stress-strain)

diagrams. However, between the knees, the material remains linear elastic at

lower temperatures. We found that G-11CR has two knees and three distinct

moduli; G-IOCR has only two moduli and a single knee at a lower strain than

G-11CR. Decrease in moduli measured near the knees compared well with predictions from the finite element model.

Introduction

Magnetic-fusion-energy (MFE) power plants may use large quantities of

nonmetallic composites [1]. There are a variety of applications where woven

glass/epoxy laminates can provide thermal insulation, electrical insulation,

and structural support. For instance, in the structural design of superconducting magnets at 4 K, nonmetallics are used primarily as electrical insulation where only small mechanical loads occur. However, when cooled to liquid

helium temperature (4 K), large internal stresses can occur within these

structures because of large differential thermal contractions between metals

and nonmetals. When these thermally induced stresses are combined with

stresses induced by small mechanical loads (magnetic loads), microcracks may

initiate at applied loads well below the yield strength. The formation of

large numbers of microcracks could limit the electrical, thermal, and

mechanical usefulness of these materials for MFE applications. The coalescence of microcracks and voids could also limit their usefulness as barriers

for containment of cryogenic liquids and gas.

50
In anticipation of these MFE applications, standardization of G-10CR and

G-11CR woven glass/epoxy high pressure industrial laminates* was established

for low temperatures in cooperation with the National Bureau of Standards

[2,3]. Standardization of these materials for low temperature applications minimized the variability in electrical, thermal, and mechanical

properties that concern the MFE designer.

In this study, we measured the variability in mechanical performance

caused by the formation of damage in a unit cell of plain weave (see Fig. 1).

The concept of a unit cell was introduced by Ishikawa [4]. Previous studies

by Kriz [5] on the unit cell predicted the influence of damage on Young's

modulus and the redistribution of internal stresses. Variations in moduli

and internal stresses were calculated by a finite-element model (FEM). Some

details of the FEM and the idealized damage are repeated here for comparison

with the formation of actual damage observed from experiment. This FEM provides only a limited explanation of the relationship between damage and the

peculiar nonlinearities (knees), see Ref. 6, in the load-deformation diagrams.

Since theory failed to provide a complete explanation of these nonlinearities, we reported the correlation between nonlinearities and individual damage events at predetermined loads. From these observations we

determined which type of damage had the most influence. To date, only fiber

breaks and transverse cracks in the resin of the fill fiber bundles (fill

resin cracks) were recorded for thin laminates loaded in tension.

The primary difference between G-11CR and G-10CR is that G-11CR contains an

aromatic amine component in the epoxy-resin to improve radiation resistance.

51
Theory

The unit cell of a woven structure was defined by Ishikawa [^4] as the

smallest repeating structural unit. The plain-weave unit cell shown in

Fig. 1 can be further characterized by four identical geometries in planes A,

B, C, and D. In each of these planes we assumed generalized plane strain.

Hence, the FEM [5] allowed out-of-plane nodal displacements. With these

idealizations we approximated the three-dimensional load-deformation behavior

with a two-dimensional grid.

Figure 2 is a schematic representation of the weave geometry of the four

planes in Fig. 1 . For simplicity in calculations, we approximated a constant

fiber curvature, 6, for all elements in the warp region of Fig. 2. The

boundary conditions shown in Fig. 2 simulated the idealized symmetrical

structure of a laminate with two woven layers (see Fig. 3a). The curvature, 0, shown in Fig. 2 is equivalent to the maximum curvature shown in

Fig. 3a. This model is limited to transverse cracks in the resin of the

internal fill fiber bundles (see Fig. 3a). Hence, only 50 percent of all

possible fill resin cracks were modeled. To study the significance of fill

resin cracks with weave geometry, we varied 6 (Fig. 3a) from 0° to 45°. For

a woven laminate, it is physically impossible to require 0 = 0°. Hence, the

condition of 0 = 0° in Fig. 3b represents a special limiting case for the

woven laminate, where the fill resin crack can be compared with the ply crack

in a 0°/90° laminate.

The finite element grid of Fig. 2 contained 1004 elements and 543 nodes.

Each element had three nodes with three degrees of freedom per node. Out-ofplane displacements allowed the calculation of the three-dimensional strain

state. Exact details of this element formulation are given in Refs. 5 and 7.

52
Components of the element stiffness matrix, which has been modified for e are

given in Appendix A.

Because of the many simplifications in this model, we can only approximate the behavior of the unit cell. From these approximate calculations, we

chose not to emphasize absolute values but rather changes in the behavior

that are caused by variations in weave curvature, temperature, and formation

of fill cracks. Another approximation in this model occurs near the crack

tip at point "d” of Fig. 2 where the dimension of the smallest element was

restricted to the size of one glass fiber diameter (100 um). Although

stresses closer to the crack tip can be approximated by smaller elements,

this method assumes material homogeneity, which is violated when the element

size approaches the size of heterogeneity (100 ym). For metals with small

grain size this is not a problem, but for fiber-reinforced materials, predictions of stress singularities should be confined to within one fiber diameter

of the crack tip.

The applied in-plane and out-of-plane strains, and £y, are calculated

from thin-laminate-plate theory [8], which assumes zero stress through the

thickness:

yyNx/ ( Axx^yy A^y) (1)

XyNx/(AxxAyy A^y) (2)

where Ayy, and are laminate midplane stiffness [9] that are calculated from elastic properties listed in Table 1. The fiber and matrix

properties were calculated from experimental results of Dahlerup-Peterson and

Perot [10], and from these results composite properties were calculated using

53
equations of Hashin [11]. From experiment, the laminate load, = 175 N/mm,

near the knee was used to calculate the strains = 0.011 and Cy = 0.0017.

Young's moduli in the damaged and undamaged state were calculated using these

strains, and the resulting stress was obtained by summation of nodal forces

along the surface x = 0 with a unit depth. A worst-case thermal load of

AT = -318 K was chosen for the operating temperature of 76 K, and a strainfree state was assumed at 395 K. Under these load conditions we predicted

the influence of weave curvature and fill-crack damage on the elastic

behavior of a unit cell at 76 K. Results of these calculations are compared

with experiment in the following section.

Experiment

A total of thirteen G-10CR and fourteen G-11CR tensile specimens were

cut by shear from panels of cryogenic grade laminates [2]. For all specimens, the warp fiber bundles were aligned with the load axis. Both panels

were 0.5-mm thick with three layers of a plain weave. All specimens were

5.0-cm long and 1 .77~cm wide. The edges of six specimens of each material

were polished so that edge damage could be recorded by the replication technique described in Ref. 12. There are four test groups shown in Table 2;

specimens of each type were tested at 295 K (room temperature) and 76 K

(liquid nitrogen).

The cryogenic test fixture is shown in Fig. 4. The fixture was designed

to allow free access to the polished edge for replication of damage. The

extensometer , shown in Fig. 5, was mounted from the side opposite the

polished edge. All specimens were quasi-statistically loaded in tension at

20 N/s. The first three specimens from each group listed in Table 2 were

54
loaded in tension to ultimate fracture strength. From these results one

specimen with a polished edge from each group was loaded to 80 percent ultimate and impregnated with an x-ray dye penetrant of zinc iodide solution

while under a static load of 1000 N. A second specimen with a polished edge

was loaded in increments of 200 N. Damage at the edge of these specimens was

recorded by replication at room temperature after each load increment. For

76-K tests, a warm-up period was required before replication of edge damage

at room temperature.

From these preliminary tests, we observed peculiar nonlinear behavior at

76 K that required additional tests. Additional specimens of G-10CR and

G-11CR were loaded in tension at predetermined loads to determine a possible

correlation between these nonlinearities and cracks in the fill fiber bundles. Densities of fill cracks were determined by observation through the

thicknesses of the semitransparent thin laminates. Fill crack densities

observed in the interior of the laminate were compared with fill cracks

observed on replicas that were taken from the same specimen.

Results and Discussion

A summary of present and previous experimental results are given in

Table 3. Our results compare well with the previous studies [2, 13], except

we report two additional Young’s moduli (E 2 , E

3

) and a strain (e-p) that

locates the first knee in the stress-strain diagram. A second knee was

observed for G-11CR, but is only reported here as a change in modulus between

E^^ and E^^ . These new parameters are defined geometrically at 76 K in

Fig. 6 for G-1 OCR and in Fig. 7 for G-11CR. At room temperature (295 K)

bimodulus behavior does not exist (see Fig. 8 ). Other studies [5, 14,]

55
reported similar bimodulus results at low temperatures but no explanations

are given for this behavior. In this study, we examine relationships between

damage accumulation and these nonlinearities.

The stress-strain response of a bisphenol A epoxy resin, representative

of resin used in G-10CR and G-llCR, is included in Figs. 6, 7, and 8 for comparison. The failure strain of the resin at 295 K is larger than those of

G-10CR and G-11CR. At 76 K, the opposite is true: we observed that the

epoxy failure strain, was much lower than laminate fracture strains.

We also observed that is slightly lower than This observation

implies that the first knee at 76 K could be related to a resin failure in

the laminate. Because the resin is constrained in the fiber-reinforced laminate, we predict that the resin will fail at a lower strain (e| <

This prediction requires experimental verification of epoxy failures th..t

correspond with knees in the stress-strain diagrams.

From experimental observations we correlated individual damage events to

nonlinear behavior in the stress-strain diagrams (see Figs. 9-1 6). At 76 K

we observed several epoxy failures in the fill fiber bundles of G-10CR and

G-11CR prior to the knee (see Figs. 12 and 16). In all cases prior to fracture we observed only cracks in the resin of the fill fiber bundles (fill

resin cracks) and individual fiber fractures in the warp fiber bundles.

There was no evidence of large delamination events either prior to or after

laminate fracture. Hence, in Table 4 only the initiation of fill resin cracks

and fractures of warp fibers are correlated with laminate load. For both materials, larger loads were required to initiate damage at lower temperatures.

After the initiation of damage we measured the growth of this damage

with increasing load. To correlate damage events with stress-strain non56
linearities, we inverted the conventional stress-strain format and superposed

the damage growth on the same diagrams with load as the common abscissa (see

Figs. 9, 11, 13 , 15). In all cases damage increased exponentially with

increasing load. The nonlinearities shown in Figs. 9 and 11 correlated well

with the growth of fill resin cracks in G-10CR at 76 K and 295 K, but the

growth of warp fiber fractures at much lower loads had no influence on these

nonlinearities. From these experiments we conclude that fiber fractures do

not contribute to changes in Young’s modulus. For all types of damage we

drew a continuous curve through a limited set of experimental measurements.

Here we assumed that there are no discontinuities in the growth rate of

damage. More accurate measurements would be required to measure the presence

of growth rate discontinuites, which may be partly responsible for the second

knee in Fig. 15.

The bimodulus behavior of G-10CR at 76 K is compared in Fig. 17 with the

change in modulus predicted by FEM where only 50 percent of fill fiber bundles were modeled with resin cracks. From experiment we observed resin

cracks in all fill fiber bundles (100 percent). Hence, the decrease in

modulus for G-10CR in Fig. 17 is larger than that predicted by the FEM. The

thin-slice approximation for FEM appears to be a serious oversimplification,

which models only a portion of the woven structure. A complete threedimensional model would provide a more accurate prediction, but the twodimensional model sufficiently predicts the correct trend, which is a drop in

modulus caused by the accumulation of one resin crack in each fill fiber

bundle

For G11-CR at 76 K we observed several resin cracks in the fill fiber

bundles (see Fig. 16) and consequently measured a much larger drop in modulus

57
at the first knee than that in G-10CR (Table 3). At the same load in Figs.

11 and 15 we observed more than twice the number of fill resin cracks in

G-11CR than in G-10GR, but the moduli of G-11CR and G-10CR are similar at

3000 N because of an increase in modulus for G-11CR from to . This

increase in modulus at the second knee in Fig. 7 could be caused by straightening of warp fiber bundles after multiple resin cracks in the fill fiber

bundles. Unfortunately, there is no evidence of warp bundle straightening at

76 K, because replicas were taken at reduced loads after warm-up to prevent

formation of new damage. For thicker laminates multiple cracking will still

occur, but straightening of warp bundles may be suppressed because of the

constraint through the thickness. Hence, the second knee for G-11CR may be a

result of the thin specimen geometry.

The fill resin cracks observed at the edge with replicas did not match

with interior fill resin cracks. Because of the semitransparent property of

the thin laminate, we observed the formation of all interior fill resin

cracks by light transmission through the thickness. Fill resin cracks originated at the interior and grew towards the edge. Not all interior fill resin

cracks extend to the laminated edge. Hence, for woven laminates edge damage

is not representative of interior damage. The opposite is true for nonwoven

laminates, where transverse ply cracks originate at the edge and extend the

full width of the specimen [11].

Fiber fractures observed at the edge are also not representative of

fiber fractures in the laminate interior. For nonwoven graphite/epoxy

laminates, Schulte et al. [15,16] demonstrated that at the laminate edges,

fibers failed at lower loads because of the reduced cross-sectional area of

sectioned fibers and flaws induced by polishing. Consequently, at the

58
laminate edges there are typically large numbers of fiber fractures that

occur randomly. When the plane of the laminate edge intersected the thickest

portion of a warp fiber bundle, we observed large numbers of random fiber

fractures. For G-11CR we observed large number of random fiber fractures at

295 K and fewer fiber fractures at 76 K (see Figs. 14 and 16). A high density of fiber fractures always occurred near the fill resin crack tip at

76 K. This observation is consistent with stresses predicted by FEM in the

warp region near the fill crack tip (see Fig. 18): when the temperature

decreases we predict an increase in when 6 = 0 and only a small decrease

in 0 ^ for larger angles of 0. For G-10CR we did not observe this trend where

fill cracks did not dominate fractures of warp fibers (see Figs. 10 and 12).

Again, these discrepancies may be caused by edge effects discussed by

Schulte; we recommend a closer examination of warp fiber fractures in the

laminate interior.

Although fiber fractures do not influence the modulus, the accumulation

of fiber fractures in warp bundles influences ultimate strength because the

warp fiber bundles carry the largest portion of the tension load. If more

fiber fractures occur at the laminate edge, then we may be observing the

damage state that initiates ultimate fracture. The edge damage state of

G-10CR at 295 K in Fig. 13 revealed unusually large displacements between

broken fiber ends only within the fractured region. Also, there were

observed fewer fiber fractures on the edge of G-11CR than in G-10CR at 76 K,

which may account for the higher laminate fracture strength of G-11CR.

For both G-1 OCR and G-11CR only small delaminations were observed after

fracture. Prior to fracture no delaminations occurred at either 295 K or

76 K. Previous studies [17] for nonwoven laminates showed that delaminations

59
can originate from the tips of transverse ply cracks at the interlayer interface. For woven laminates with 6 = ^5° we predicted (see Fig. 19) by the FEM

a decrease delamination stresses when the fill resin crack occurs and when

the temperature decreases to 76 K. Hence, in this study we predicted and

experimentally verified that delaminations are prevented for moderate to

large weave curvatures by the formation of fill resin cracks at low temperatures.

Soft x-rays of damaged specimens impregnated with zinc-iodide solution

(see Ref. 16) could not detect the presence of fill resin cracks. The zinciodide dye-penetrant works well with graphite/epoxy materials; but it is

inadequate for detecting damage in glass/epoxy materials. A variety of

voltages, currents, and exposure times revealed only the woven structure of

laminates that were known to have extensive damage. The exact nature of

internal damage remains unknown for these laminates.

Summary

From experiments of 76 K and 295 K we observed that damage in specimens

of G-10CR and G-11CR accumulated as resin cracks in fill-fiber bundles and

individual fiber fractures in warp-fiber bundles. Only small regions of

delamination were observed between warp and fill fiber bundles after laminate

fracture. For both materials, larger loads were required to initiate damage

at 76 K. Except for G-11CR at 76 K, warp fibers always fractured before the

formation of fill resin cracks. In general, fiber fractures were observed as

random events that were not related to fill resin cracks. In G-11CR at 76 K,

fiber fractures always occurred within a region of stress concentration near

the tip of the resin crack.

60
From a finite-element analysis we predicted a decrease in Young’s

modulus, which was modeled by formation of resin cracks in 50 percent of the

fill fiber bundles. In G-10CR and G-11CR at 76 K, a high density of fill

resin cracks was observed at a strain similar to the failure strain of the

neat resin. From theory we predicted that a high density of fill resin

cracks would result in a reduced modulus, or a knee, in the stress-strain

diagram. For both materials at 295 K we observed a nonlinear stress-strain

diagram with no knees. At 76 K we observed two knees and three moduli for

G-11CR where the third modulus increased in value (see Fig. 15). For G-10CR

at 76 K, we observed only one knee at a strain lower than the first knee of

G-11CR. The second knee for G-11CR may represent a rapid growth of fill resin

cracks, < E-|^\ followed by a straightening in warp fibers and an

increase in modulus > E^^ . Fractographic evidence of multiple fill resin

cracks in G-11CR supports this explanation. Before laminate fracture.

Young’s moduli for both materials were approximately equal. Between knees,

the stress-strain response in tension was linear for both materials. Most of

the accumulated damage and nonlinearities in the stress-strain diagrams

occurred at strains well below fracture. This is an important consideration

for design applications where these materials are only loaded to small

strains.

Fiber fractures had no influence on the appearance of the stress-strain

diagrams. For G-10CR at 295 K, large numbers of fiber fractures occurred

randomly and large crack opening displacements (CODs) were observed in the

region of laminate fracture. At a lower temperature we observed fewer fiber

fractures and measured a higher laminate fracture strength. If the temperature is decreased, we predicted by FEM a decrease in stress in the warp

region where fiber fractures occur. This prediction implies a higher

61
strength at lower temperatures. From FEM we also predict a decrease in

delamination stresses with a decrease in temperature when fill cracks are

present. Experiments verified minimal delaminations.

From both theory and experiment, we conclude that the weave geometry is

beneficial at lower temperatures; when fill resin cracks occur delaminations

are prevented at the fill-warp interface.

Acknowledgments

This study was sponsored by the U.S. Department of Energy, Office of

Fusion Energy. Material was supplied by Spaulding Fiber Company Inc.

Cryogenic tension fixture was machined by Mr. Dale Thoel at NBS.

References

1. M. B. Kasen, Composite laminate applications in magnetic fusion energy

superconducting magnet systems. Proceedings of the 1978 International

Conference on Composite Materials , 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-11CR

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. 171-177 (1981).

4. T. Ishikawa, Anti-symmetric elastic properties of composite plates of

satin weave cloth. Fiber Scl . Technol. , Vol. 15, pp. 127-145 (1981).

5. R. D. Kriz, Influence of damage on mechanical properties of woven com- posites at low temperatures. Compos. Technol. Rev. , in press.

6. H. Benz, I. Horvath, K. Kwasnitza, R. K. Maix, and G. Meyer, Worldwide

cryogenics - Switzerland Cryogenics at BBC Brown, Boveri & Co., Ltd.,

Cryogenics , Vol. 19, pp. 3~15 (1979).

7. A. P. Nagarkar and C. T. Herakovich, "Nonlinear temperature dependent

failure analysis of finite width composite laminates," VPI-E-79-36,

Virginia Polytechnic Institute and State University, Blacksburg,

Virginia (1979).

62
8. R. Y. Kim and H. T. Hahn, Effect of curing stresses on first ply fail

in composite laminates, J. Compos. Mater. , Vol. 13» PP» 2-1 6 (1979).

9. R. M. Jones, Mechanics of Composite Materials , McGraw-Hill, New York,

pp. 1^17-173 ( 1975).

10. K. Dahlerup-Peterson and A. Perrot, "Properties of Organic Composite

Materials at Cryogenic Temperatures," CERN; ISR-BOM/79-39 , Geneva,

Switzerland (1979).

11. Z. Hashin, "Theory of Fiber Reinforced Materials," NASA-CR-1 97^, NASA

Langley Res. Cent., Hampton, Virginia (1972).

12. D. 0. Stalnaker and W. W. Stinchcomb, in Composite Materials; Testing

and Design (Fifth Conference) , ASTM STP 67^, American Society for

Testing and Materials, Philadelphia, pp. 620-641 (1979).

13 . H. M. Ledbetter, Dynamic elastic modulus and internal friction in G-10CR

and G-11CR fiberglass-cloth-epoxy composites. Cryogenics , Vol. 20,

pp. 637-640 (1980).

14. M. B. Kasen, Mechanical and thermal properties of f ilamentary-reinfor ced

structural composites at cryogenic temperatures 1: Glass-reinforced

composites. Cryogenics , Vol. 15, pp. 327-349 (1975).

15 . K. Schulte and W. W. Stinchcomb, Damage development near the edge of a composite specimen during quasi-static and fatigue loading. Compos

Techol. Rev. , Vol. 6, pp. 3~9 (1984).

16. R. D. Jamison, K. Schulte, K. L. Reifsnider, and W. W. Stinchcomb,

"Characterization and analysis of damage mechanisms in tension-tension

fatigue of graphite/epoxy laminates," Effects of Defects in Composite

Materials, ASTM STP 836 , American Society for Testing and Materials,

Philadelphia, pp. 21-55 (1984).

17 . A. L. Highsmith, W. W. Stinchcomb, and K. L. Reifsnider, "Effect of

fatigue-induced defects on the residual response of composite

laminates," Effects of Defects in Composite Materials , ASTM STP 836 , American Society for Testing and Materials, Philadelphia, pp. 194-216

(1984).

63
Appendix A

The elemental stiffness matrix that is commonly used for laminated plate

analysis has been changed to include rotations of the fiber orientations within

the x-z plane of Fig. 2 . In Ref. 6 an elemental stiffness matrix was constructed for a three-node generalized plane strain simple element that allowed

for arbitrary rotations in the y-z plane. Here we reconstruct a similar element with the same symbolic notation as in Ref. 6, but only rotations in the

x-z plane are included in the calculations.

For an arbitrary rotation in the x-z plane, we have rewritten the

orthorhombic material stiffness matrix in contracted notation, where the subscripts ( 1 , 2 , 3 ) correspond to the (y,x,z) coordinates in Fig. 2 .

Tensor transformati on; = ai^ajsSktaiuCpstu (A 1 )

Transformation array: ^ij 1 2 3

T 1 0 0

2 0 COS0 sine

3 0 -sinO COS0

(A 2 )

Constitutive relation: {a} = [C] {e} (A 3 )

°1

02

T23

^13

>

=

1

^12

^13

Cl 4

0

0

^12

C22

C23

C24

0

0

^13

C23

C33

C34

0

0

Cl 4

C24

C34

C44

0

0

0

0

0

0

C55

C56

0

0

0

0

C56

C66

ei

^2

^3

T23

Ti3

Ti2

(A 4 )

64
where o and t are normal stresses and shear stresses, e and Y are normal

strains and engineering shear strains, and are imansformed material

stiffnesses written below as functions of the warp angle 6 defined in Fig. 2.

C

C

C

C

C

C

C

C

C

C

C

C

C

1

=

1

22 = m^C22 n^C33 + 2m^n^(C23 + 2Ci(i|)

33

= p ^^^22 m^C^^ 2m^n^(C22 2Ci|i|)

= n^m^(C22' + C33) + (m^ - n^)^C44 - 2n^m^C23

55 = m^C^^ +

66 = n

2 C55 . m^C 55

1 2

= m^C-|2 + n

2

Ci 3

13

= n^C-|2 + ra2Ci3

1 4 = nm (C-|2 - 0^2)

56

= nm (C55 ~ ^66)

23

= n^ra^(C22i + C33) + (m^ + n^)C23 -

24 = -nm^ C22I + mn3c33 + nm(m^ - n^)(C23 + 2C44)

34

= —n^mC22 + m^n C33 + nm(n^ - m^)(C23 + 2C44)

(A 5 )

where n = sine and m = cose.

In Ref. 6 the elemental stiffness matrix [K] is calculated by premultiplying the material stiffness matrix [C] by the transpose of the

connectivity array [B]"^ and postmult iplying the result by the connectivity

array [B]:

[K] = [B]T [c] [B] (A6)

where the connectivity array [B] relates the out-of-plane strain and nodal

65
displacements (u^, v^, ) ; i = 1,2,3 to the strains [e].

[e] = [B] u^, v^, w^}, i = 1,2,3 (A7)

[B] =

A,^ 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 b d g

0 a c e

0 0

a c

0 0

b d

0 0

0 0

0

e

0

g

0

0

0

0

b

a

0

0

0

0

d

c

0

0

0

0

g

e

0

0

(A8)

where A|^ is the element area and a, b, c, d, e, are other geometric

parameters for the element defined in Ref. 6.

When we perform the operations in Eq. A6, we obtain the symmetrical

components K— ^ji element stiffness array [K]. When the out-ofplane strain is a known quantity (applied strain), then the first row of [K]

is irrelevant and the first column of [K] becomes a known quantity, which is

added to the known load vector [F], The components of the remaining [9 x 9]

element stiffness array are:

K

K

K

K

K

K

K

K

1

12

13

22

23

33

^5

[b^C^^ + 2abC^g +

[bd^55 +(cb + ad)C55 + acC55]/A^;

[bgC55 + (be + ag)C55 + aeC55]/A|^

[d^C^^ + 2cdC56 +

[dgC55 + (ed + cg)C55 + ceC55]/A|^

[g2c55 + 2egC55 +

[a2C22 2abC24 b2C44]/A|^

[acC22 (sd + bc)C24 + bdCij^l/Af^

(A9)

66
Kij5 = [aeC22 +(ag be)C24 + bgCui^j/A;^

^i\j ~ [a^2^ ab(C22 b^24 ^^^k

K^ig = [d(aC2g * bCgij) + c(aC 24 + bCi|i|)]/A[^

^49 = [g(aC22 ^ t>Cgi|) + e(aC24 ' bCi^L|)]/Aj^

^55 ” [c^22 ^ 2 cdC24 • d^iji|]/A[^

K56 = [ceC22 + (eg + de)C24 + dgCiii^l/A^,

KgY = [b(cC22 dCgi|) + a(cC24 dCi|i|)]/A[^

Kgg = [cd(C23 + + c ^24 * d^gi|)]/A|^

^59 ” [g(cC23 + dCgij) + e(cC24 + dCi|i|)]/Aj^

^66 = ^^^22 2 egC 24 + g^C4n)]/A,<

= [e(bC23 + aC 24 ) + gCbCgii + aC[|i[)]/A^^

^68 “ [d(eC2g + gCgi|) + c(eC 24 * gCi|i|)]/A|^

= [g^34 + ge(C23 ^ ^ 44 ^

Kyy = [b^33 + 2abcC3i| + a^ijij]/A[^

^78 “ [dbC33 + (da + 08)0311 + caC)|ij]/A|^

= [bgC33 + (ag + 08)0314 + eaOi4i4]/A|^

Kgg = [d^33 + 2 dc03 i4 + c^i4 i4 ]/Aj^

Kgg = [dgCgg + (go + ed)C3n + ceCi4i4]/Ai^

K99 = [g^33 + 2 geC

3

i

4 + e^i4 i|]/A|^

from the first column of the [K] array we add the following terms to the load

vector

F( 4 ) = -(aC 42 + 80414)^4

F(5) = -(CC42 + dC4i4)^4

F(6) = “(®(^12 S^l4^^1

(A 10 ) F(7) = “(8042 + 00414)^4

F(8) = “(d042 + 00414)^4

F(9) = -(gC43 + 0044)^4

67
All remaining and are set equal to zero.

When a thermal load is induced by a temperature change, free thermal

T*

rp rp

T* strains {e|, £ 3

. ^23^ subtracted from the left side of Eq. A7,

and becomes an unknown quantity. Hence, we now have a [10 x 10] element

stiffness array where the arrays are arranged to include these additional

terms in the tenth row and column of [K]:

^ 4,10 - aC-,2 + bCi 4 %,10 = CC12 + dC-| 4

^6.10 = eC^2 + gC^ 4

^7,10 = bC-13 + aCi 4

^8,10 = dC^2 + cCi 4 S,10 = gCi2 + eCi 4

^10,10 ^ll\

Additional terms, , are added to the load vector:

F(1) = F(2) = F(3) = 0

F(4) = aQ + bR

F(5) = cQ + dR

F( 6 ) = eQ + gR

F(7) = bS + aR

F( 8 ) = dS + cR

F(9) = gS + eR

where Q — ^I 2 ^'l' ^ ^ 22^2

8 ~ C-| iiel + C2i|E2

S — Ci^Ei ^ 23^2

*^23^3 ^2M'^23

''^23

*^ 33^3 *^ 3^''^23

(All )

(A12)

68
FdO) '1

r'T ^1 + C

n -T . n

12"-2 + C

.T . o 13^3 + C 1 )i Y U'23

Although the material is linear elastic, superposition of [K] matrices

for known) and (^i

unknown) is not possible because the arrays and

their solutions are unique. Superposition of results is only possible after

the solution of unknown displacement vector for each case.

69
Table 1 . Elastic-thermal properties

ISOTROPIC CONSTITUENTS* TRANSVERSELY ISOTROPIC

COMPOSITE t

PROPERTY BISPHENOL E GLASS

EPOXY FIBER GLASS/ EPOXY (Vf. = 0.50)

Young's modulus, E = 7.16 E = 82.22 = 44.69

GPa Et = 17.88

Shear modulus, G = 2.77 G = 32.55 ^2,t = 6.801

GPa Gtt = 6.888

Poisson’s ratio V = 0.293 V = 0.263 ^2,t = 0.278

= 0.298

Coefficient of

* — — p II 5.963

thermal expansion. p rf

' II 23.39

^Properties from Ref . 9.

tElastic properties from Ref. 10.

= volume fraction of glass fibers.

Subscript £, indicates fiber direction; subscript t indicates transverse plane.

Table 2. Specimens tested

TEMPERATURE G-1 OCR G-11CR

3 for static fracture 3 for static fracture

76 K 1* for x-ray damage 1* for x-ray damage

1* for replica damage 1* for replica damage

3* for fill resin crack count 4* for fill resin crack count

3 for static fracture 3 for static fracture

295 K 1* for x-ray damage 1* for x-ray damage

1* for replica damage 1* for replica damage

^Indicates specimens with polished edges for damage replication.
Table

3*

Summary

and

comparison

of

experimental

results

CCu

CO ic: Ci3 CCo

CO

Ct} cco Cl- 3

m r- rO CO m m CM

^

CM CM CM

0^ LP> lT» CTN 00 o o m

CJ\ CJS ON O

o m o

O CT'

vO 'O m

CO ^

tn o in LTN

r- on m m

o o o on

CO CO vO

m o~- onico

CO — —

CO o^lc^

CM m CM Ion on c>- CO Uo

C7^ ON CT^IcjN

O C^loo CO ^ 00 C^ ^ =r ^ ^

on vo vO CO

IT -3

-

c*- on oni o^

.zr ^ .=r o

t— CO CO |co

00 c— Ion 0- m o

CO CO vo|co

ON vO I f—

-=r CM c- ^

.=r zT onKa*

ON m O 00 ON CM m CM 00 vO C^

CZa 00 vO • CM CM CM CM V—

cc

vT3 03 < ’sA. .c CL a. CL ff) i_> O o o c 00 —

—

H

c

3 CO —

CO 0) •o 3*C * 3»t £. H t- o r— CM on 4-> v-H X Cz: Cz3 Cz3 CO (J W CO

ON CO O' I CM

CM m — o

QuX

CO

f-o

71

Subscripted

values

are

defined

in

Figs.

6,

7,

and

8.

UTS

indicates

ultimate

strength.
Table Comparison of loads for initiating damage

[warp fiber fracture load (N)/fill resin fracture load (N)].

TEMPERATURE G-10CR G-1 ICR

295 K [500/800] [ 500/500]

76 K [600/1800] [1500*/1300]

* Warp fiber fractures coincided with fill resin fractures.

Figure 1 . Unit of cell of woven-fabric composite,

72
Figure 2. Thin slice of unit cell. Theta, 6, denotes angle between warpfiber orientation and the x direction.

NX

a)

N

b)

Fill Resin

Figure 3a.

3b.

Two-layer woven laminate with an interior fill resin crack.

0°/90° laminate with 90° ply crack.

73
74
Figure 6.

Figure 7.

STRAIN, %

Geometric characteristics defined for the stress-strain response

of G-10CR in tension of 76 K with neat resin.

Geometric characteristics defined for the stress-strain response

of G-11CR in tension at 76 K with neat resin.

75
Figure

Figure 9.

0 12 3 4

STRAIN, %

The stress-strain response of G-10CR and G-11CR at 295 K with

neat resin.

STRESS. N/mm2

0 100 200 300 400 500

CO

liJ q:

CO

lU

CD

LLC

E

o

COo

<

cco

-1 800

600

- 400

-200

LOAD, N

CO

CLUJ

CD

CL

cr<

c

E

o

COo

<

cro

Correlation between damage formation and stress-strain response

of G-10CR in tension at 295 K.

76
ID

0>

CsJ

QC0O1 o

toC

<uE

OJo

CO ^ J

Cl

CO

GOcc • QJ 01 Q. 1-1 O D

XJ ^ O O CO <0 1-1 1-1 >X-| o

1—

J

to CO 00 c

Vj -r^

CO O-J

U-i (U o

XJo c z o• fj00 • OJ O'• 0) oO £ o z

to x: o

COO CO o -

xJ CO

oO to C T3C

X) 0) cO !-• CL O

to -O (1) .-J

1-1 O

C

O <J o ot

-1

a ^ E

to c

X3

X o J

of -

x: o

u-i xo

77
Figure

STRESS, N/mm2

0 200 400 600 800

-i800

to

UJ

cr

q: H

UJm

Li. c

E

o

CO

bCo

<

COO

600

400

-200

1 1 . Correlation between damage formation and stress-strain response

of G-10CR in tension at 76 K.

78

CRACK/cm

in

WARP

FIBERS
Top View

G-10 CR 76 K

Side View

2800 N

Figure 12. Top and edge views of damage

Damage in top views are fill

shadows below the surface.

2800 N

corresponding to loads of li?. M.

resin cracks often observed as

79
STRESS, N/mm2

0 200 400 600 800

CO

US

CL

CL

UJ

CD

800

- 600

CO

crLU

CO

LiL

CL

DC<

c

E

u

•*<. COo

<

cro

Figure 13. Correlation between damage formation and stress-strain response

of G-llCR in tension at 295 K.

80
81
Figure

LOAD, N

15. Correlation between damage formation and stress-strain response

of G-11CR in tension at 76 K.

82
83

16a.

Top

and

edge

views

of

damage

corresponding

to

loads

of

Fig.

15.
Top

View G1

CR

76K

3!^^

84

3000 N

3200 N

Figure

L6b.

Top

and

edge

views

of

damage

corresponding

to

loads

of

Fig.

15.
Q

,

degrees

Figure 17. Influence of internal fill cracks on woven unit cell Young's modulus

a comparison between FEM and experiments for G-IOCR.

85
Figure 18. Stress concentrations in warp fiber bundle above fill resin crack

along line a-b in Fig. 2: results from Ref. 5.

Figure 19. Stress concentrations in warp fiber bundle above fill resin crack

along line c-d in Fig. 2: results from Ref. 5.

86
I

r1

):i

NONMETALLIC MATERIAL STANDARDIZATION -

MATERIALS AND TEST METHODS*"^

M. B. Kasen

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

The system for producing uniaxially reinforced, mm diameter rod specimens described in the Sixth Annual Progress Report^

has been refined and validated by production of excellent quality

specimens using liquid-mix epoxy resin systems. The methodology is

undergoing further modification to permit use of hot-melt epoxy and

polyimide resin systems as will be required for the experimental

program to be conducted in the NLTNIF reactor at ORNL. Preliminary

studies indicate that short beam and torsional shear test methods

will be useful in evaluating radiation degradation. Development of

these and other applicable test methods are continuing. A cooperative program established with laboratories in Japan and in England

has resulted in the production and testing of specimens having an identical configuration. An effective interchange of laboratory

data is continuing.

OBJECTIVES

To provide, in cooperation with ORNL and LANL, specimens required for

studies to develop organic insulators having the cryogenic neutron irradiation resistance required for MFE systems utilizing superconducting magnetic

confinement. To develop test methods and analytical procedures for assessing

radiation damage. To stimulate and participate in international cooperation

directed toward accomplishing these objectives.

PROGRESS AND STATUS

We have demonstrated that specimens containing up to 58 volume percent

glass fiber can be produced without macroscopically visible defects using

epoxy resin systems that have a workable viscosity at room temperature. We

* Work supported in part by the Office of Fusion Energy, U.S. Department of

Energy.

To be published in "Seventh Annual Progress Report on Special Purpose

Materials for Magnetically Confined Fusion Reactors," U.S. Department of

Energy (1985).

87
are presently experimenting with a resin system similar to that used in manu- facturing the G-11 type of industrial laminate and with several polyimide

(bismaleimide ) systems. These systems must be worked in the hot condition.

We are therefore investigating various methods of introducing heating into

the production apparatus. Many resins of interest must be blended with a solid cure agent. We have therefore installed a 900 watt ultrasonic system

to facilitate blending without the use of solvents. It has been successfully

used to blend the G-11 resin system.

We have demonstrated that specimens 19 mm long can be successfully

tested in short beam shear. We have also demonstrated that such specimens

can be successfully tested in the torsional shear mode. These test modes are

of importance in evaluating radiation degradation of the fiber-matrix

interface

A Japanese group, headed by Prof. T. Okada, ISIR, Osaka University and

including individuals at Kyoto University, The University of Osaka Prefecture,

and the Hoxan Corporation, has successfully produced specimens containing

glass, graphite, and silicon carbide fibers using the NBS method. Performance

has been evaluated in three-point flexure. A similar effort has been undertaken by Dr. D. Evans of the Rutherford Laboratory in England. An effective

exchange of information is continuing, and plans are being made for exchange

specimens and for joint reporting of results during 1985.

SPECIMEN DEVELOPMENT

Specimen Quality

Our initial objective was to develop techniques for producing specimens

free of macroscopic defects. We initially selected a resin system composed of

a low viscosity bisphenol A epoxy resin cured with a low viscosity liquid

polyamide. This produced an almost transparent specimen, facilitating the

quality evaluation. We later introduced a system based on a standard

undiluted bisphenol A epoxy resin cured with a liquid aromatic amine, modified with polyoxypropylenediamine. This system was suggested by Dr. Evans as

a candidate radiation resistant impregnation or potting resin. These systems

have a workable viscosity at or slightly above room temperature, simplifying

the production process. Figure 1 illustrates that the quality objective was attained

The following procedure was established:

Step 1: Resin Mixing

Gomponents are weighed out in a 100 ml beaker to produce a mix of

about 80 ml. Gomponents are manually stirred.

Step 2: Resin Degassing

As recommended by Dr. Evans, the resin is vacuum degassed while

being stirred to break up the surface tension. This is accomplished by a wire frame connected to a shaft penetrating a rotating vacuum seal. Stirring

88
speed is 60-70 rpm. Vacuum is provided by a mechanical forepump. A bleed

valve controls the pressure level to prevent overflow of the resin during the

initial stages of degassif ication. A typical degassing operation requires

iJO-60 minutes. The vacuum chamber consists of a glass bell jar, permitting

infrared heating of the resin to reduce its viscosity and to increase the

rate of degassing.

Step 3 - Preparing the Fiber Reinforcement

The basic reinforcing element is a glass fiber tow 600 mm long,

folded in the center to provide a doubled tow 300 mm long. The volume fraction of glass obtained from introducing various multiples of the basic

element into the tube mold is calculated from knowledge of the weight of this

element, the density of the glass, and the volume of the tube. For the type

of glass used in these experiments, incorporation of 4, 5, 6, and 7 doubled

tows produces calculated glass volume fractions of 335^, ^1^, ^ 9 % and 58/J,

respectively, in a 3 mm i.d. tube mold. The doubled tows are tied in the

center with a nylon monofilament line to facilitate pulling into the tube

mold.

Step Vacuum Impregnation

Impregnation is performed in the apparatus illustrated in Figure 2.

Degassed resin is allowed to rise to the level of the pinchclamp, which is

then closed to permit evacuation of the air in the glass strands. The

pinchclamp is then opened and the resin is allowed to rise to just above the

level of the glass fibers. With proper degassing, this can be accomplished

without excessive bubble formation. Admitting atmospheric pressure into the

system accomplishes the fiber impregnation.

Step 5: Drawing into the Mold

The drawing procedure is illustrated in Figure 3- The nylon line

is passed up the tube mold bore and the mold end is inserted under the resin

in the impregnation tube. The glass tows are manually started up the tube

mold while maintaining a head of resin, after which the pulling rate is con- trolled at about 2 cm/min by a variable speed motor. When the mold is

filled, the end is capped to prevent loss of resin during the cure cycle.

The NBS process uses commercially available PTFE tubing, 3 nmi i.d., 7 mm

o.d., 300 mm long, as the specimen molds. The tubing is selected to have a smooth interior. Specimens may also be made in glass tube coated with a release agent. However, PTFE is preferred, as it reduces the possibility of

contaminating the resin during the cure cycle.

The vacuum system used in this process contains a cold trap that can be

activated to prevent contamination of the glass fibers by back streaming of

the pump oil.

89
step 6: Specimen Cure

The PTFE tube mold is held in a tight fitting glass tube during

cure to maintain specimen straightness. Curing takes place in a pressure

vessel constructed from copper pipe. A pressure cure has been found neces- sary to prevent formation of surface defects. Approximately 5 kg/cm^ (70

psi) of nitrogen has been found to produce excellent results.

Neat resin specimens are produced by vacuum drawing of the degassed

resin into the tube molds followed by pressure curing.

Step 7: Specimen Removal

Specimens may be either pushed or pulled from the PTFE molds, which

may then be reused.

As shown in Table 1, the coefficients of variability in diameter among

rods produced with a given mold are on the order of 0.15^ to 0 . 3>%

,

indicating

excellent dimensional reproducibility. Dimensional differences between the

molds reflect differing lots of PTFE tubing. A total of 22 rods were dimensioned in this experiment.

Many systems of interest to this program require neating to above room temperature to achieve a workable viscosity. For example, a typical resin of the

type used in the G-11 industrial laminate is quite viscous below about 60-65° C.

The bismaleimide types of polyimide resin, which are of great interest to this

program because of excellent radiation resistance, require processing temperatures on the order of 150° C. Modifications are currently being made to the production apparatus to accommodate these requirements.

Many of these resin systems require blending of a liquid resin with a solid cure agent. In commercial practice, solvents are frequently added to

reduce the melting temperature. However, this cannot be done with the NBS

method, as evolution of such solvents during the cure cycle would cause

porosity. Hodges and St. Clair^ have recently demonstrated that ultrasonic

energy may be used to blend many such systems without the use of solvents.

Figure 4 illustrates results obtained at NBS on the G-11 type of resin using

a 900 W, 20 kHz, self-tuning ultrasonic system.

Fiscal Year 1985 Plans

Our current objective is to produce fiber-reinforced and neat-resin

specimens of the following types for use in initial radiation studies in the

NLTNIF reactor:

1) G-llCR system approximation

2) Polyimides

a) PG-llCR approximation

b) Developmental bismaleimide

90
3) Rutherford epoxy potting resin

The G-llCR specimens are intended to provide a baseline of performance

reflecting current material usage. The PG-llCR specimens are intended to

simulate the current polyimide variant of the CR laminate grades. The developmental bismaleimide system is representative of the latest polyimide resin

development technology. The potting resin is included in response to a rec- ommendation made by participants at the 1984 NBS/DOE Vail Workshop (see the

workshop summary on page 299). Additional resin systems may be included upon

recommendation of the program participants.

Additionally, procedures will be developed for producing specimens

having silane glass finishes containing systematically increasing hydrogen

contents. These will be useful in evaluating the influence of finish

chemistry on interfacial degradation. Consideration will also be given to

producing specimens reinforced with boron-free E glass and with glass of

higher intrinsic strength.

TEST METHOD DEVELOPMENT

Mechanical Tests

Since the fiber-matrix interface is expected to be a prime location for

damage accumulation during irradiation, shear, properties are expected to be

an important test parameter. We have therefore investigated the feasibility

of performing flexural shear tests on the rod specimens. The fixture illustrated in Figure 5 is similar to a conventional 3~point fixture for conducting apparent interlaminar shear strength tests, differing primarily in

contouring of the supports and of the loading nose to accommodate round

specimens. Required specimen length is only 15 mm for a 3 mm diameter speci- men tested at a span/depth ratio of 3.0. This makes it very economical of

material and minimizes the volume required during irradiation.

An initial series of tests was conducted with this fixture at 295 K and

76 K. Five specimens each from two rods manufactured with the bisphenol

A/polyamide resin system and containing either 50 or 60 v/o type E glass

reinforcement were tested at each temperature. As illustrated on Figure 6, a series of distinct load drops appeared on the load-time curves of specimens

tested at 76 K, indicating onset of consecutive shear failures with increasing stress. Continuous bending over of the 295 K curve is attributed to the

exceptional room temperature ductility of the selected resin system. This

precludes failure by the shear mode.

A typical 76 K shear failure is illustrated in Figure 7. Narrow shear

bands initially progressed into the specimen in an inverted V configuration from

the point of contact with the loading nose. These bands subsequently acted as nuclei for massive shear failures that propagated along the specimen length,

giving rise to the observed load drops.

The 76 K test data, summarized in Table 2, reflect the stress required to

initiate the first massive longitudinal shear failure (first load drop). The low

coefficients of variability suggest that this may be a viable test mode at

91
cryogenic temperatures. The small influence of fiber volume fraction on shear

strength was not unexpected because shear strength is known to pass through a maximum in the vicinity of 50-60 v/o fiber content.

While the flexural shear test method appears potentially useful, the

complexity introduced by the continuously changing stress state makes it

difficult to quantify the results. An alternative would be to conduct shear

tests in torsion. Exploratory tests conducted at 76 K showed that it was possible to induce longitudinal shear in this manner. It was further found

that the required torsional stress could be introduced by means of copper

tube end caps frozen onto the specimen ends. The ability to grip specimens

in this manner might prove useful in evaluating damage accumulation as a function of applied stress using the dynamic resonance technique. The

presence of bulky end caps could interfere with the sensitivity of such measurements.

Fiscal Year 1985 Plans

The following test methodology objectives must be met to prepare for the

initial irradiation series to be conducted at the NTLNIF facility:

1) Development of apparatus and techniques for comparing mechanical

performance of specimens before irradiation and after warming to room temperature following irradiation.

2) Development of procedures for relating changes in failure mode to

changes in mechanical performance and to the molecular level damage introduced by the irradiation.

Additionally, consideration will be given to the following objectives

which must be met in preparation for future test programs:

1) Development of approaches to assessing mechanical performance of

specimens after irradiation without warmup.

2) Development of methodology for assessing damage accumulation during

warmup after irradiation.

3) Development of methods for mechanical testing while under irradiation.

INTERNATIONAL COOPERATION

Rutherford Appleton Laboratories (England)

Dr. David Evans has communicated his initial experience in preparing

specimens using the NBS technique and has described the initial test results

obtained during room temperature testing in three-point flexure. While

promising, excessive variability indicated a need to improve both the quality

92
of the specimen and to refine the testing technique. Dr. Evans is presently

investigating a process for direct vacuum impregnation of the specimens at

final size.

Dr. Evans has developed a prototype fixture permitting sequential

flexural testing of a series of specimens at 4 K without requiring intermediate warmup. He has also been very helpful in suggesting candidate resin

systems for inclusion in the initial test series.

ISIR, Osaka University (Japan)

Professor Toichi Okada has organized a cooperative effort between ISIR,

KURRI (Kyoto University), The University of Osaka Prefecture, and the

Cryogenic Technology and Development Center, Hoxan Corporation, to investigate the feasibility of standardizing the fabrication and testing of

composite specimens using the NBS technique. Specimens fabricated with two

types of epoxy matrix and reinforced with glass, graphite, silicon carbide,

and alumina were fabricated by Hoxan and tested in three-point flexure at

295 K and at 76 K by the other three participants. Results of this study

were reported at the 1984 ICMC Conference on Nonmetallic Materials and

Composites at Low Temperatures in Heidelberg, West Germany.^ They concluded

that the production method was simple and effective. However, they also

experienced excessive variability in flexural test data. They are presently

investigating a four-point testing procedure that they hope will produce more

consistent results.

Fiscal Year 1985 Plans

We have tentatively agreed that each laboratory should attempt to produce identical specimens to validate the concept of standardization. A com- monly agreed upon type of resin and type and quantity of glass reinforcement

would be used. The specimens would be exchanged between laboratories for

comparative evaluation. An assessment of specimen uniformity will also be

made by an independent laboratory.

We have also tentatively agreed to a joint reporting of results at the

1985 ICMC Conference or at the NBS/DOE Vail Workshop.

REFERENCES

1. M. B. Kasen, "Materials and Test Methods," pp. 48-52 in Special

Purpose Materials Annual Progress Report for Period Ending October 1, 1983 , DOE/ER-01 1 3/3 , U.S. Department of Energy, May 1984.

2. W. T. Hodges and T. L. St. Clair, "Ultrasonic Mixing of Epoxy

Curing Agents," NASA Technical Memorandum 85643 , National Aeronautics and

Space Administration, Langley Research Center, Hampton, Virginia, 1983.

93
3. T. Okada, S. Nishijima, H. Yamaoka, K. Miyata, Y. Tsuchida,

K. Mizobuchi, Y. Kuraoka, and S. Naraba, "Mechanical Properties of Unidirectionally Reinforced Materials," presented at ICMC Conference on Materials and

Composites at Low Temperatures, Heidelberg, West Germany (1984). To be

published in Nonmetallic Materials and Composites at Low Temperatures 3 , Plenum Press, New York.

Table 1 . Variability in diameter (mm) among rods produced by

PTFE tube molds.

Tube No. Avg. St. Dev. CV

1 3.0793 0.00732 0.0024

2 2.9727 0.00881 0.0030

3 2.9580 0.00316 0.001 1

Table 2. Flexural shear data at 76 K.

Volume Fraction Rod No. Strength (MPa) Std. Dev. CV

50 1 23.6 1 .0 0.042

2 23.0 2.0 0.087

23.3 1 .5 0.064

60 1 23.3 1 .

0.047

2 23.6 0.3 0.013

23.5 0.8 0.034

94
Figure 1 . Transparency of a 3 mm diameter specimen containing 58 v/o

glass indicates excellent fiber wetting and absence of porosity.

A

Figure 2. Impregnation is performed by evacuating the

a 12.7 mm (0.5 in) diameter inner tube (A). The resin

into the tube, and atmospheric pressure is admitted to

impregnation (B).

glass tows in

is transferred

complete the

95
Figure 3- The impregnated glass tows are pulled into

the 3 mm diameter PTFE tube mold while maintaining a head of resin to prevent entrainment of air. The

unused resin may be recovered.

Figure M. G-11 resin system as hand mixed (A)

and after three minutes of ultrasonic blending (B).

96
Figure 5. Sketch of fixture for

testing 3 nim diameter specimens

in flexural shear. Specimen is

15 mm long. Figure 6. Typical load-time curves obtained

during flexural shear tests. Serrations at

76 K indicate onset of longitudinal shear.

Figure 7. Typical longitudinal shear failure at 76 K. Arrow

indicates the point of contact of the loading nose. Shear bands

have propagated into the specimen, forming an inverted V and acting

as the nucleating point for massive longitudinal shear failure.

97
'V!

. <'

'i

i f

''

. I

I M


Elastic Representation Surfaces of Unidi rectional

Graphite/Epoxy Composites''

R. D. Kriz and H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303 USA

Unidirectional graphite/epoxy composites exhibit high elastic anisotropy

and unusual geometrical features in their el astic-property polar diagrams.

From the five-component transverse-isotropic elastic-stiffness tensor we

compute and display representation surfaces for Young's modulus, torsional

modulus, linear compressibility, and Poisson's ratios. Based on Christoffelequation solutions, we describe some unusual elastic-wave-surface topological

features. Musgrave considered in detail the differences between phase-velocity

and group-velocity surfaces arising from high elasti-c anisotropy. For these

composites, we find effects similar to, but more dramatic than, Musgrave' s.

Some new, unexpected results for graphite/epoxy include: a shear-wave

velocity that exceeds a longitudinal velocity in the plane transverse to the

fiber; a wave that changes polarization character from longitudinal to

transverse as the propagation direction sweeps from the fiber axis to the

perpendicular axis.

Key Words: graphite/epoxy; acoustic properties; elastic properties; energy

flux deviation; group velocity; mode conversion

''Published in Recent Advances in Composites in the United States and Jap an. ASTM SIR 864, 1985.

99
INTRODUCTION

Graphite/epoxy composites with unidirectional fiber reinforcement exhibit

transverse-isotropic elastic symmetry; thus, five independent elastic

constants. In matrix form, one can represent the elastic-stiffness tensor as

[C,j] =

C C C 0 ^11 ^12 ^13

f f 0 Oil u

^33 ^

'44

'44

(Cii-Ci2)/2

( 1 )

which is symmetrical, that is = C^. The elastic compliances, ^

, relate

inversely to the C^.^:

[S,j] = [C.j]

-1

( 2 )

In form, the S.. matrix looks identical to the C.. matrix except that Src = 13 ij ^ bb

2(S^^-S^2^.

While Eq. 1 displays all the elastic-constant information as an "irreducible

set," it displays directly very little of the wealth of practical information

and interesting geometrical properties contained in C...

* sJ For uniaxial graphite/epoxy, the present study considers many geometrical

features of the elastic-constant tensor. For example: representation surfaces

of Young's modulus, torsional modulus, linear compressibility, and Poisson's

ratio. Following Musgrave [1], who studied materials such as zinc, we

consider the velocity and slowness surfaces and find some remarkable features

100
concerning the acoustic-energy flux. Following Ledbetter and Kriz [ 2 ], who

focused on orthotropic materials, we find some peculiarities also in graphite/

epoxy. First, a shear velocity exceeds the longitudinal velocity in the plane

perpendicular to the fibers. Second, a wave changes polarization character

from longitudinal to transverse as the wave direction sweeps from the fiber

axis to the perpendicular axis.

CALCULATIONS

Elastic representation surfaces

Representation of elastic properties by geometrical surfaces has obvious

utility, as described by Nye [ 3 ]. Following a procedure outlined by

Lekhnitskii [ 4 ], representation surfaces can be derived via the general

elastic-compliance fourth-rank-tensor transformation:

^ijkl ®im ^jn ^kr ^Is ^mnrs ( 3 )

Here we choose the x^ axis parallel to the fibers of a unidirectional

fiber-reinforced composite. We assume isotropy in the x^-X2 plane, transverse

to the fibers. For hexagonal (transverse-isotropic) symmetry, transformations

for all elastic constants are axially symmetric about x^. Thus, elastic

constants depend only on rotations, +0, away from x^ toward the x^-X2 plane.

Transformation equations for Young's modulus, E^le), torsional modulus, T^Ig),

shear modulus, 622(0)5 linear compressibility, K2 (g), and Poisson's ratio,

\)32 (g), are in Voigt notation;

-1

E3 (0) = 5^3(0) = + x(2S^3 ^ ^44

" 'll

+ X (S-,1 + S33 2 S ^3 - S^^) ( 4 )

101
( 5 )

T-^0) E [s;,(e) + S^5(6)]/2 = S„ + (1 - X)(S,, - Sj2 - S^^/Z)

+ 2x(l - x)(S^2 ^33

“ ^^13 ~ ^44^

^23(0) = + 4x(l - x)(S^^ + $22 " ^^13 ~ ^44/^) (^)

K3(e) = $22 + S^2 ^13 ^ ^^11“ ^ 33

’^ ^12" ^13^

V (0) E -S' (0)/S' (0) = E (0)[S + x(l - x)(S + S - 2S - S )1 (8)

32 23 33 3 13 H 33 13 44

2 where x = cos 0. We also consider the transformation of v^2 shown in Fig.

1 where there are two rotations: a around x^ followed by 3 around x'^. Given

the tilt angle a, we calculated v^2 ^2”^3 doubl^^

rotation we find:

= -Sj2(a,3)/S’^(a) = -{ (S^

^ + $22

- S44)cos^a sin^a cos^3

+ 5^2^°^^^^ sin^3 + S^2tc0S^3(cos'^a + sin^a) + sin^a sin^3]}/sj^(a) (9)

where

SJi(a) = S^2(^0 -

When the tilt angle is zero 3 equals 0 and Eq. 9 reduces to

2 2 I ^13(0) = -[5^2^'"^ ® 3^2^05 0]/S-j

1 (a) (11)

Based on Eqs. 4-11, we give polar diagrams, Figs. 2-8, that represent the

unusual anisotropy of various elastic constants of unidirectional graphite/

epoxy.

102
Acoustic representation surfaces

The influence of elastic constants, calculated from Eqs. 4-11, on stresswave propagation is represented by polar diagrams of the eigenvalue solutions

to Christoffel's equations [1];

cosines of the wave vector measured from the principal material axes x^j, p is

the mass density, is the Kronecker delta, v is the phase velocity that

propagates along n^ , and

p^ are the particle-displacement direction cosines.

eigenvector, p^ , for each phase velocity. The orientation of the particle

displacement with respect to the wave vector is denoted by subscripts (t, qt,

qJl) on the phase velocities: t means that

p^

is transverse to n^

qt (quasi-transverse) means that the largest component of

p^ is transverse to

n^ (0 < n^p^ < 1/2); and qJl (quasi-longitudinal) means that the largest

component of

p^ is parallel to n^ (1//2 < n^p^ < 1). Along principal material

axes, pure transverse waves and pure longitudinal waves must exist for all

2 wave phase velocities. The eigenvalue solutions, pv , are the roots of the

characteristic equation, written as the determinant of Eq. 12:

( 12 )

where C

i jkl

is the fourth-rank elastic-stiffness tensor, n. are the direction

Solution of Eq. 12 yields three eigenvalues, pv , and the corresponding

(13)

0

103
Velocity surfaces are calculated from Eq. 13 by considering all possible wave

vector orientations. Because of hexagonal elastic symmetry, the velocity

surfaces are also axially symmetrical around x^. Thus, solutions to Eq. 13

are calculated as functions of +0 from x^:

v^(e) = [(C^^cos^ 0 + sin^ 0 )/p]^^^ (14)

Vqf(0) = [(C44 + C^^sin ^0 + C 33cos ^0 - /C)/2p]^^^ (15)

Vq^( 0 ) = [(C^4 + C^^sin ^0 + C 33 cos ^0 + /C)/ 2 p]^^^ (16)

where

C = [(C^^-C44)sin^0 + (C44-C33)cos^0]^ + (6^3 + C44)^sin^20

One should note that subscripts t, qt, and qJl represent only labels. In

special cases, displacements t, qt, qJl, and i may coexist on the same

phase-velocity surface [2]. Thus, rarely, Eqs. 15 and 16 yield polarizations

different from the designated qt and qJL subscripts. Equation 14 represents an

exception where v^ is always a pure-transverse wave for all orientations.

Intersections of these velocity surfaces with the isotropic x^-X

2 plane

yield three concentric circles with pure-longitudinal or pure-transverse

modes. Unlike isotropic materials, the two pure-transverse velocities

calculated from Eqs. 14 and 15 do not coincide in the isotropic x^-X

2 plane

where:

Vt(90) = ; Vq^(90) = (C„/p)^''^ (17)

104
The eigenvector solutions to Eq. 12 are the particle displacements.

1

’• P

2

• P

3

^

"•

Pi = [n^ (Cii + Ci2)/2]^''^/[pv^-{Cii-Ci2)/2-C,4ri3] (18)

2

P

2

“ ^ ^12)/2f^ /[pv +(n2"Pi)Cii/2+Ci2/2-n3C^^] (19)

Pj= [203(0^ 3+C44)^/(C^^+Cj2)]^^^/(pv^+(n2-n^)C^4+n3[2(C23+C^4)^/(Cjj+Cj2)+C33]}

( 20 )

The acoustic energy may propagate in a direction different from the wave

vector. This direction of propagation is the energy-flux vector and the

corresponding velocity of propagation is the group velocity, v^. For

homogeneous plane waves, the energy-flux vector and v coincide [5]. For

y isotropic materials, energy-flux vector and group velocity coincide with the

wave vector and with phase velocity. For anisotropic materials the

energy-flux vector deviates from the wave vector by an angle, A. For plane

homogeneous waves, the same deviation angle exists between phase and group

velocities:

Vg(0,A) = v(e)/cos A (21)

Polar diagrams of group velocities can be calculated from Eq. 21. We follow

Musgrave [6] and plot v^ as a function of 0' = 0 + A. Due to the deviation of

energy-flux, group-vel oci ty surfaces appear distorted when compared with

phase-velocity surfaces. Hence, polar diagrams of v^ are also called energy

surfaces

One calculates the deviation angle. A, from the direction cosines (n^

,

L^) of the wave vector and energy-flux vector, respectively:

105
A ( 22 ) = -1 , cos

For orthorhombic symmetry, Kriz [7] gave the direction cosines, L^, of

the energy-flux vector. For hexagonal symmetry, with transformations in the

x^-x^ plane (n^ = 0), these become;

'"1 ^66^1^Z"Z ‘'44PlP3"3 (23)

Lj *'22P2^2 *'23P2P3’'3 * ''44^P2'’3'^3 *

P3'’2^ (24)

4 “ 42P?3 + 43P2P3"2 44<P^3 ^ P2P3"2> (25)

Effects of fiber volume fraction on the effective C^. were calculated

using relationships derived by Datta, Ledbetter, and Kriz [8].

RESULTS AND DISCUSSION

Polar diagrams shown in Figs. 2-8 were calculated using the elastic

constants in Table 1. Matrix and graphite-fiber elastic constants were

obtained from Ref. 9. For comparison. Table 1 includes elastic constants

for other polyacrylonitrile (PAN) graphite fibers.

The peculiar elastic behavior caused by the elastic anisotropy of the

graphite fibers is shown in Figs. 2-8 at various fiber volume fractions. At

zero volume fraction (V^ = 0.0) the matrix is isotropic and spherical

representation surfaces (circular cross sections) are observed for all elastic

constants. The largest orientational variations in elastic constants occur at

= 1.0. At intermediate V^, we see that Poisson's ratios, linear

compressibility, and Young's modulus are more affected by small changes in V^.

106
Torsional and shear modulus are affected less. Both Poisson's ratios and

exhibit large negative values. For this is caused by variations in

and for this is caused by variations in tilt angle, a. In all cases,

the Poisson's ratios satisfy the bounds derived by Christensen [12]:

-1 < ^^2 5 3

^ 1/2

(26)

Elastic anisotropy exerts similar influences on the acoustic

representation surfaces. Figures 9 and 10 demonstrate the influence of fiber

volume fraction on phase-velocity and group-velocity surfaces. Large changes

in flux-deviation angles, shown in Fig. 11, occur at low V^. Hence, the cusps

observed on the group-velocity curves in Fig. 10 result from changes in flux

deviations

Figure 12 shows surprising behavior of the particle displacement orientations at = 1.0. For the v^j^ surface the displacements in the x^-x^ plane

undergo a transition from pure longitudinal along x^ to pure shear along

Consequently, in the x^-X

2 plane one observes a shear wave moving faster than

a longitudinal wave. While peculiar, similar properties were reported by

Ledbetter and Kriz [2] for orthorhombic crystals. In orthorhombic crystals,

this rare occurrence of v,>v„ leads to the interconnection of v^„ and v . t l qg. qt

surfaces into a single surface (also see Musgrave [13]). For hexagonal

symmetry we observe C^^ = C

22

when = 0.96 and consequently v^ = v^ in the

X-J-X 2 plane. At volume fractions higher than 0.96 one observes a mode transition without the v „ and v , surfaces interconnecting into a single surface.

q£ qt 3

This mode transition can be observed in Fig. 13. There the displacement

deviations, 6 = cos”^n^p^, from the wave vector are shown versus G. In Fig.

107
13 one observes that fiber volume fraction effects a smooth mode transition.

The mode transition starts at Vj. = 0.3 where v „ transitions into v . at

f ql qt

0 = 56°. This transition does not continue into v^; v^^ transitions back to

Vqj^. From G = 56° to 0 = 62° one observes a partial mode transition

> Vqj^). As increases, this mode transition continues predictably, for

> 0.96, Vq^ transitions into v^. Thus, 1, qJl, qt, and t particle

displacements are observed along a single surface.

While Hashin's composite-cylinder-assemblage model [l4j can predict

elastic constants for systems approaching = 1.0, the geometric limit for

hexagonal -packed circular fibers is = it/(2/3) or 0.907, which is less than

the volume fraction required for mode transition.

Such mode transitions can occur in composites at < 0.907 when fiber

constant >> 022* Such a change in fiber elastic anisotropy could result

from changing the fiber texture; but for fibers studied to date exceeds

C

22 by only 5 to 20 percent.

The peculiar elastic anisotropy discussed above depends strongly on the

fiber-elastic-constant values. The elastic constants for PAN graphite fibers

shown in Figs. 2-8 at = 1.0 were extrapolated by Kriz and Stinchcomb [9]

using Hashin's composite-cylinder-assemblage model [14]. The correction ~

KpTT/(KpTT + 2 ), noted by Hashin [15], changes the elastic constants

predicted in Ref. 9 less than one percent over the full range of fiber

volume fractions. Thus, the fiber clastic constants in Table 1 are accurate

and compare well with constants evaluated independently by Dean and Turner

[10] and by Smith [11]. The wel 1 -devel oped radial structure of PAN graphite

fibers observed by Diefendorf et al . [16] is consistent with the transverseisotropic symmetry reported by Kriz and Stinchcomb [9]. Fiber constants

108
listed in Table 1 satisfy mechanical-stability conditions, that is Eq. 1 must

be positive-definite. The fiber Poisson's ratios also satisfy the bounds of

Eq. 26.

CONCLUSIONS

At low fiber volume fractions, Young's modulus E3, linear compressibility

K3, and Poisson's ratios \)3o and ^^^3 are influenced most by the graphite-fiber

anisotropy. Shear modulus 0^3 and torsional modulus T3 are less affected by

fiber anisotropy. Large negative values were observed for Poisson's ratios

x)^3 and V32, which were also influenced by fiber anisotropy. Poisson's ratio

V32 is sensitive to small variations in fiber volume fraction. Poisson s

ratio v^3 is sensitive to rotations around the X2 axis. Graphi te-f iber

anisotropy also affects both phase and group velocities, particularly the

latter. In the x^-X2 plane the fiber constants C^^ > C22 cause a shear-wave

speed to exceed a 1 ongi tudinal -wave speed-, consequently the longitudinal wave

along X3 transitions into a pure shear wave in the x^-X2 plane. This mode

transition depends on fiber volume fraction.

ACKNOWLEDGMENT

This work was supported partly by the Department of Energy, Office of

Fusion Energy. During 1980-1982 Dr. Kriz was a National Research Council/National

Bureau of Standards Postdoctoral Research Associate.

109
REFERENCES

1. Musgrave, Crystal Acoustics , Holden-Day, San Francisco, 1970, p. 83.

2. Ledbetter, H. M. and Kriz, R. D., "Elastic-Wave Surfaces in Solids," Physica

Status Solidi (b), Vol . 11, 1982, pp. 475-480.

3. Nye, J. F., Physical Properties of Crystals , Oxford U. P., London, 1957,

pp. 143-148.

4. Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body , Holden-Day,

San Francisco, 1963, p. 51.

5. Hayes, M. and Musgrave, M.J.P., "On Energy Flux and Group Velocity," Wave

Motion, Vol. 1, 1979, pp. 75-82.

6. Musgrave, M. J. P., "On the Propagation of Elastic Waves in Aeolotropic

Media II. Media of Hexagonal Symmetry." Proceedings of the Royal Society

of London, Vol. 226, 1954, pp. 356-366.

7. Kriz, R. D., "Mechanical Properties for Thick Fiber Reinforced Composite

Materials Having Transversely Isotropic Fibers," Masters Thesis, College of

Engineering, Virginia Polytechnic Institute and State University, Blacksburg,

Virginia, 1976.

8. Datta, S. K. , Ledbetter, H. M. , and Kriz, R. D., "Calculated Elastic Constants

of Composites Containing Anisotropic Fibers," International Journal of Solids

and Structures, Vol. 20, 1984, pp. 429-438.

9. Kriz, R. D. and Stinchcomb, W. W., "Elastic Moduli of Transversely Isotropic

Fibers and Their Composites," Experimental Mechanics, Vol. 19, 1979, pp. 41-49.

10. Dean, G. D. and Turner, P., "The Elastic Properties of Carbon Fibers and

Their Composites," Compoistes, Vol. 4, 1973, pp. 174-180.

11. Smith, R. E., "Ultrasonic Elastic Constants of Carbon Fibers and Their Composites," Journal of Applied Physics, Vol. 43, 1972, pp. 2555-2561.

12. Christensen, R. M. , Mechanics of Composite Materials, John Wiley and Sons,

1979, p. 79.

13. Musgrave, J. J. P., "On an Elastodynamic Classification of Orthorhombic Media,"

Proceedings of the Royal Society of London (A), Vol. 374, 1981, pp. 401-429.

14. Hashin, Z., "On Elastic Behavior of Fiber Reinforced Materials of Arbitrary

Transverse Phase Geometry," Journal of Mechanics and Physics of Solids,

Vol. 13, 1965, pp. 119-134.

15. Hashin, Z. , "Analysis of Properties of Fiber Composites with Anisotropic

Constituents," Journal of Applied Mechanics, Vol. 46, 1979, pp. 543-550.

16. Diefendorf, R. J., Riggs, D. M. , and Sorensen, I. W. , "The Relationships of

Structure to Properties in Graphite Fibers," Technical Report No. AFML-TR-72-

133, p. 65, Air Force Materials Laboratory, Wright-Patterson Air Force Base,

Ohio.

110
Table 1. Matrix and graphite fiber elastic properties in units

of GPa, except \) which is dimensionless

^33

rCii Ci2 f^13 C44 ^32 V12

Matrix^ Ref. 9 8.63 8.63 4.73 4.73 1.95 0.354 0.354

Fiber^ Ref. 9 235 20.0 9.98 6.45 24.0 0.279 0.490

Ref. 10 240 20.4 9.40. 10.5 24.0 0 . 35 0.497

Ref. 11 221 19.4 6.60-^ 5.8 20.3 0.23 0.32

Composite^ (V^=0.6) 144 13.6 7.0 5.47 6.01 0.284 0.497

1. Epoxy matrix composition is tetraglycidyl 4,4' diaminodiphenyl methane

cured with diaminodiphenyl sulphone (TGDDM-DDS).

2. Graphite fibers are pyrolized from polyacrylonitrile fibers.

3. calculated from

4. Composite properties are calculated from equations derived in Ref. 8.

Ill
Fig. 1 Coordinate transform.ations for v ^3 (a, g).

Uniaxial load along Xi " = Xt '

X3

Fig. 2 Polar diagram of Young's

modulus E 3 for various fiber

volume fractions, in GPa.

X3

Fig. 3 Polar diagram of torsional

modulus T 3 for various fiber

volume fractions in GPa.

112
023

, in GPa.

X3

113
X3

Fig. 7 Polar diagram of Poisson's

ratio vi3 for various tilt

angl es , a (see Fig . 1 ) , at

a fiber volume fraction of

0 . 6 .

Fig. 6 Polar diagram of Poisson's ratio V32

for various fiber volume fractions.

X'3

V, =1.0

114
’I''qtVqtFig. 9 Phase-velocity polar diagram

for four volume fractions.

Fig. 10 Group-velocity polar diagram

corresponding to Fig. 9.

WAVE-VECTOR ORIENTATION, ©(degrees)

Fig. 11 Flux-deviation directions for various fiber volume

fractions. For clarity, v^ curves are omitted.

115
X3

Fig. 12 Polar diagram of displacement directions superimposed on the phase-velocity

surfaces at = 1.0. For clarity, only one quadrant is shown.

WAVE-VECTOR ORIENTATION. B (degrees)

Fig. 13 Displacement-direction deviations for v For higher

fiber volume fractions, a mode transition occurs.

116
STRUCTURAL ALLOYS

117

STRUCTURAL ALLOYS PROGRAM

LEADER: R. P. Reed, MBS

STAFF: J. M. Arvidson, Y. W. Cheng, H. M. Ledbetter, H. I. McHenry,

P. T. Purtscher, D. T. Read, R. L. Tobler, 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 low-temperature

property measurements and structural design.

RESEARCH PAST 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 304LN, 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. Studies on low-temperature elastic properties of austenitic steels.

7. Initiation of a program to measure the stacking-fault energy of highmanganese austenitic steels.

8. Continuation of efforts to establish a program to develop low-temperature mechanical-property test standards.

RESEARCH THIS YEAR (1985)

1. Characterization of 316 LN alloys obtained from Japan and Germany.

2. Study of thermally activated deformation processes in austenitic steels.

3. Low-temperature creep measurements on 304, 316, and 310 alloys.

4. Threshold fatigue measurements to study effects of R ratio and frequency

on 4-K measurements.

5. Measurement of stacking-fault energy of Fe-l8Cr-8Ni base alloys with

varying nitrogen and manganese concentrations.

6. Measurement of low-temperature elastic properties of selected austenitic

steels.

7. Continuation of interaction with Metal Properties council to develop

low- temperature mechanical-property test standards.

8. Cooperative studies with industry to study 316-type alloys and replacement of nitrogen with manganese.

119
SUMMARY OF MECHANICAL PROPERTY MEASUREMENTS OF STRUCTURAL ALLOYS

Alloy

(Designation)

Country

of Supplier

Tensile

295,4 K

Elastic

295-4 K

Fracture Toughness

295,76,4 K

Fatigue Crack

Growth Rate 295,76,4 K

Fatigue

S-N

4 K

* Report Volume

(page)

AUSTENITIC STEELS Fe-19Cr-9Ni

(304) U.S. I. II, III

IV, VI, VII

I, II, III

IV, VI, VII

I, II, III, IVII, III, IV I 1(15, 71, 213), 11(79, 149,

175) ,111(15,91,105,

117) ,IV(37, 101,203,215,

227) ,V(71) ,VI(73) ,VII (13),VII(47),VII(75),

VIK157)

Fe-19Cr-9Ni

(304L) U.S. II, III, IV

I, II, IV III, IV III, IV 1(213), 11(79, 123, 175),

111(15), IV(37, 101, 131,

302,215)

Fe-19Cr-9Ni-N

(304N) U.S. I, III, IV

IV I, III, IV I, III, IV 1(93) ,111(15) ,IV(37,

101,203,215)

Fe-19Cr-9Ni-N

(304LN) U.S. II, III, IV,V,VI

IV II, III, IV II, III, IV II 11(35,79) ,111(15) , IV (37,101,203),V(29),VI

(113)

Fe-19Cr-9Ni1 to 8Mn

(304LN)

U.S. IV,V IV,IV(77),V(15,59,189)

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

Fe-17Cr-13Ni-2Mo

(316) U.S. I, II, III,

IV, VI

VI I, II II I 1(15,71) ,11(79) ,111(49,

105,117),IV(147),V(185)

VI(87) ,VI(157)

Fe-17Cr-13Ni-2Mo

(316LN) U.S. II II II 11(79)

Fe-25Cr-21Ni

(310) U.S. V, VI, VII III, VI V 111(105,117) ,V(71,145)

,

VK73) ,VII(65)

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

,

VIK85)

Fe-21Cr-6Ni-9Mn

(21/6/9) U.S. I III, VI I I 1(15, 71), 111(91),VK157)

Fe-21Cr-12Nl-5Mn U.S. I, II III I, II I, II 1(93), 11(79), 111(91)

Fe-17Cr-18Mn-0.5N U.S. VII VIK65)

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

Fe-13Cr-22Mn-0.2N Japan VII VIK65)

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

Fe-19Nl-9Co

(200-300 grades)

U.S. IV IV(237)

Fe-5Cr-25Mn-0.2C Japan VII VIK65)

Fe-5Cr-26Mn Japan VI VK181)

Many alloys Review

IV,V,VI

Review

IV,V,VI

Review

IV,V,VI

Review

IV,V,VI

,

VII

Review

IV, VI IV(17,257) ,V(171)

,

VI(11),VI(127),VI(157),

VIK103)

ALUMINUM ALLOYS Al-4Mg

(5083-0)

U.S. IV II 11(35) ,IV(185)

Al-6Cu-0.2Mn-0. IFe (2219-T87)

U.S. II II II II 11(19)

SUPERCONDUCTORS

Nb-45Ti U.S. III 111(133)

Materials Studies for Magnetic Fusion Energy Applications at Low Temperatures: NBSIR 78-884 (I); NBSIR 79-1609 (II); NBSIR 80-1627 (III); NBSIR 81-1645 (IV); NBSIR 82-1667 (V); NBSIR 83-1690(VI); NBSIR 84-3000 (VII). 120


STRENGTH AND TOUGHNESS GOALS FOR CRYOGENIC STEELS

Harry I . McHenry

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

Superconducting magnets for future fusion devices will require cryogenic

steels with improved combinations of strength, toughness, and weldability.

To guide the development of these steels, possible research goals were discussed at the 1984 NBS-DOE Workshop (see page 299), and subsequently,

goals for the strength and toughness of cryogenic steels were set as follows:

Yield Strength,

MPa at 4 K

Fracture Toughness,

MPa/m at 4 K

Base Metal 1000 200

Weld

One process 1000 200

Two processes 1000 150

The base metal properties are intended for plates and other product forms up

to 1 00-mm thick. For alloys that meet these property goals, other factors

will be evaluated, such as fatigue strength, physical properties, relative

cost, and suitability for thickness greater than 100 mm.

There are two sets of property goals for welding. One process, presumably gas tungsten arc (GTA) welding, will be qualified to meet the same property goals as the base metal in all welding positions. This process

could be used at any location in the magnet structure. A minimum of two

other processes will be qualified for use in locations where the maximum

stress is less than 75/S of the maximum design stress. For these locations,

the weld will match the base metal in yield strength and flaw tolerance. The

latter will be achieved by requiring a weld metal toughness of 150 MPa/m,

that is, 75)S of the base metal toughness. The relaxed tolerance on weld

toughness is intended to permit more efficient welding practices when the

welds are located in low stress areas.

The base metal strength and toughness goals are based on two requirements: (1) the strength and toughness values must exceed the NBS strengthtoughness trend line for austenitic stainless steels at 4 K and (2) the yield

strength goal is the highest value on the trend line that has adequate

toughness in 100-mm-thick plate. Adequate toughness is regarded as any

toughness value that exceeds the ASTM validity requirement for plane strain

fracture in 100-mm-thick plate with the specified yield strength.

121
The requirements are shown graphically in Figure 1 . The NBS trend line

shows that as yield strength increases there is a linear drop in fracture

toughness. The ASTM validity requirement for 100-mm-thick plate shows that as yield strength increases, the fracture toughness measurement capability

increases linearly. The two lines cross at a yield strength of 1000 MPa,

where the level of toughness required to avoid plane strain fracture is

200 MPa/m. Thus, the requirements are yield strength greater than 1000 MPa

and fracture toughness greater than 200 MPa/m.

These levels of strength and toughness are considered to be achievable

using state-of-the-art manufacturing technology. However, to consistently

meet these property requirements in heavy sections and in weld metals,

improvements are required in stainless steel processing technology and in

welding materials and procedures.

Fig. 1. Materials research goals for cryogenic steels at 4 K.

122


NICKEL AND NITROGEN ALLOYING EFFECTS ON THE STRENGTH AND TOUGHNESS OF

AUSTENITIC STAINLESS STEELS AT 4

P. T. Purtscher and R. P. Reed

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

The tensile strength and fracture toughness at 4 K were studied as a function of Mi (6 to 15 wt.5?) and N (0.09 to 0.28 wt.^) contents for eight

austenitic stainless steels. Results indicate that N increases the tensile

yield strength and decreases the fracture toughness, Kj^(J). Nickel has

little significant effect on tensile yield strength but increases the fracture toughness. The temperature dependence of the yield strength, Oy,

follows the relationship Oy = where is the yield strength at 0 K

and A is the slope of In Oy vs. T. The parameter A is proportional to the

stacking fault energy. Nickel increases stacking fault energy and austenite

stability. Lower Ni alloys exhibited brittle facets on fracture surfaces

examined using scanning electron microscopy. The brittle facets are {111}

austenite planes and are related to slip-band faulting. A new parameter

called the quality index is presented and defined as the product Oy*Kj^(J).

This factor relates to the capacity of the alloy to achieve greater strength

or toughness, but not at the expense of the other parameter. Nickel alloying

is shown to increase the quality factor; N has little effect.

INTRODUCTION

To constrain magnetic forces developed in high-field superconducting

magnets, structural alloys that are strong and tough at 4 K are required. It

has been demonstrated that N is a potent solid-solution strengthening agent

in austenitic stainless steels at 4 K.^ However, the toughness of the high-N

alloys decreases as the strength increases.^ It is desirable to study the

roles of Ni and Mn on toughness of high-N austenitic stainless steels.

Perhaps by modest alloying changes, their low temperature toughness can be

improved while maintaining high strength.

In this study Ni content was varied from 6 to 15 wt.5S in austenitic

stainless steel base alloys containing 19/J Cr, 6% Mn, low C, and 0.09 to

0.28^ N. Tensile strength and fracture toughness of the alloy series were measured in liquid helium and correlated with Ni and N contents.

^Research sponsored by the Office of Fusion Energy, U.S. Department of

Energy.

Intended for publication in Advances in Cryogenic Engineering--Materlal3 , volume 32.

123
EXPERIMENTAL PROCEDURE

The eight laboratory heats of steel included in this study (see Table 1

)

were supplied by E. 0. Paton Institute of Electrowelding, Kiev, USSR. The

chemical analyses were performed at the Colorado School of Mines, Golden,

Colorado. All alloys were completely austenitic and in the form of

25 -mm-thick plates. They were tested after solution treatment at 1060°C for

1 h and subsequent water quenching. The procedures and accuracies for tensile

testing of round specimens and fracture toughness tests (J-integral) using

compact-tension specimens have been discussed elsewhere . All tests were conducted in liquid helium. Martensitic (body-centered cubic) transformation

was monitored at room temperature, after testing at low temperature, using

magnetic torsion balance equipment, which was previously calibrated to

estimate volume percent. Scanning electron microscopy (SEM) and transmission

electron microscopy (TEM) were used to study the associated fracture mor- phology and dislocation structures.

The average results of the tensile and fracture toughness tests at A K are listed in Table 2.

Typical engineering stress versus engineering strain curves at A K are shown in Fig. 1 . The high-N alloys are characterized by high yield strengths

and a lack of work hardening at large deformations. The lower N, less-stable

alloys exhibit the characteristic three stages of stress-strain behavior

identified earlier by Reed and Tobler;^ note particularly alloy 739

(Fig. If). It is apparent that N increases Oj (the elastic limit); N and Ni

reduce and finally eliminate stage II [associated with hexagonal close-packed

(e) martensite and body-centered cubic (a') martensite at slip-band intersections] and stage III (associated with a*-induced work hardening). Discontinuous yielding occurred in all measurements, and the load drops near fracture

ranged from about 25/^ for the stronger alloys to about for the more ductile alloys.

The temperature dependence of the tensii<= vipiri .<=ii-.rpno-i-.h . a . was

Fig. 2. There is a linear relationship between J,n Oy and temperature,

similar to that of other austenitic steels.^ The least stable alloy, 739,

containing only about 8.7 wt.5K Ni, exhibits little change of yield strength

in the region between about 100 to 200 K. This region has been identified

previously for metastable alloys® and is associated with the a' and e martensitic transformations

The tensile yield strength is a strong function of the C and N content,

as shown in Fig. 3- Here the function C + 2N is used. Reed and Simon^ found

this to be a representative function when they used regression analysis to

describe all Oy data on AISI 304 type alloys at 4 K. The data of this paper

closely correspond to those from earlier research on Fe-19Cr-10Ni base

alloys.® The 0 at 4 K is strongly dependent on interstitial content.

Strengthening from solid solution additions' of Ni is small and insignificant.

RESULTS

measured for three alloys from 4 to 295 K.

124
The fracture toughness, Kj^(j), was estimated from J-integral measurements at 4 K and is plotted against Oy in Fig. 4. Some data points fall

within a band containing most of our earlier results° that primarily portray

the effects of C and N alloying. But, there is not good conformance: alloy

has considerably better properties; alloys 413, 414, 520, and 739 have

lower corresponding Kj^(J) to Oy ratios.

The effect of Ni content on fracture toughness is shown in Fig. 5.

Notice the clear trend of increasing toughness with increasing Ni in the

19Cr-4Mn-0.02C-(0.26-0.28)N alloys (413-416). From Table 2 it is clear that

the alloys with lower N contents form no systematic series with respect to

dependence of toughness on Ni content; presumably the N varies too much to

permit comparison solely on the basis of Ni. Analyses of the data (Table 1)

reveal that, at constant Ni content, toughness tends to be less at higher N

content. This is also apparent from Fig. 1, considering that N content

accounts for o variation. Therefore, the values of Kj^(J) reported for the

lower N content alloys (739, 740, 741) were adjusted to include consideration

of N variability. From Fig. 4 a clear trend of decreasing K^^(J) with increasing Oy at 4 K has been found when C and N are systematically varied® and

Kj^(J) = 500 - O.30y (in MPa) (1 )

The average tensile yield strength at 4 K for the high-N content alloys

(413-416, 520) is 1030 MPa. The corresponding Kj^(J), from Eq. 1, is

191 MPa/m. The fracture toughness of each low-N alloy was calculated, using

Eq. 1, from their yield strength values. To normalize, these calculated

values were subtracted from the measured Kj^(J).

The initial dislocation structures of alloys 413 and 4l6 were observed

with TEM thin foils. Alloy 413 (low toughness, low Ni, high N) exhibited

stacking faults in the annealed condition (Fig. 6); in alloy 4l6 (high toughness, high Ni , high N) no stacking faults were observed in the annealed dislocation structure.

The fracture appearances in the surface area associated with the critical J-integral measurements were characterized by SEM. The fracture surfaces

of the high-N alloys (413-416) are shown in Fig. 7. As Kj^(J) increases, the

fracture morphology becomes more dimpled (microvoid coalescence). Nonmetallic inclusions are associated with most dimples, as shown in Fig. 8. These

large (3~4 pm) inclusions are Mn silicates, according to energy-dispersive

x-ray analysis.

At low-Ni content [low Kj^(J)], the fracture surfaces are faceted. There

are small, step-like facets and large (size of grain) flat facets. The

large facets, shown in Fig. 9, are apparently {111} planes of austenite.

Linear traces on the faceted surfaces, such as those shown in Fig. 9b,

correspond to other {111} traces, if we assume the surface is {111}. Their

appearance is very similar to those recently identified as {111} by Tobler,^

who used back-scattered Laue x-ray analysis and described them as regions of

"slip-band decohesion."

*The highest temperature at which a* martensite forms at constant plastic

deformation.

125
DISCUSSION

Strength

All alloys, except ill 6, partially transformed to body-centered cubic

(a') martensite during plastic deformation. The average volume percent of a' that formed throughout the gage length, normalized by dividing by the percent

elongation, correlates well with of Williams et al.^^ This is

summarized in Table 3 and illustrated in Fig. 10. Williams et al. conducted

regression analyses of various Or, Ni , Mn, Si, C, N, and Mo chemistries after

compressive deformation and used 45^ elongation and 2 to 5^ a' as a basis for

T^^. Alloy 520 is outside the trend of the other alloys (see Fig. 10).

From earlier work,^ the temperature dependence of the tensile yield

stress is best portrayed as

(Oy/G) = ia^/G^)e (2)

where is the yield strength at 0 K, G is the shear modulus, and G^ is the

shear modulus at 0 K. Because we have not measured the shear modulus of most

of the alloys in this series, the shear moduli are omitted in Fig. 2 and

a y

-AT

was used.

(3)

Since G changes only about 6% from 4 to 295 K, there is little difference between Eqs. 2 and 3-

Reed and Arvidson^ pointed out that there may be a correlation between

the temperature dependence of the tensile yield strength (constant A of Eq.

3) and the stacking fault energy; it is evident in Fig. 11.

The stacking fault energies (Y) of Fe-Cr-Ni austenitic stainless steels

have been estimated. ^ ^On the basis of weak-beam electron microscopy

data, Rhodes and Thompson^ ^ argue realistically that the regression analysis

of other electron microscopy and x-ray data by Schramm and Reed”' ^ produced Y values that were too large. However, the Mn contribution suggested by Rhodes

and Thompson is probably too large and results in very large values of Y in

Fe-Gr-Ni-Mn austenitic steels. Brofman and Ansell”'^ examined the contribution that C makes to the stacking fault energy of austenitic stainless steels

and concluded that C additions raise Y, in a proportion similar to the con- tribution of C to T^g [the martensite (a') start temperature]."^

Currently in our laboratories the effects of both C and N are being

studied and have been tentatively reported to increase Y.^ For Fig. 11 we have chosen to use the Schramm-Reed analysis, compiled in Table 3. which

produces admittedly high Y, but we think accurate relative values of Y in

view of the major alloying elements Cr, Ni, and Mn.

126
The primary deformation mechanism in stage I (see Ref. 5) of polycrystalline austenitic steels at low temperatures may be associated with crossslip. Schoeck and Seeger^^ predict a linear dependence of the 5,n o vs. T for

stage III single-crystal cross-slip as the rate-controlling deformation

mechanism. More recently, Escaig^° has developed a cross-slip model that

predicts a linear dependence of flow strength on temperature. Clearly, we must continue studies to identify and characterize the rate controlling

deformation mechanism in austenitic steels.

Toughness

There is strong dependence of fracture toughness on Ni content (Fig. 5)

when the N content is held constant. SEM photomicrographs of the fracture

surfaces at the initial fatigue-sharpened crack tip are shown in Fig. 7. It

is apparent that as Ni content decreased, the corresponding fracture surfaces

exhibit a transition from dimpled to faceted surfaces. These faceted surfaces, shown at higher magnification in Fig. 8, are cleavage-like in appearance but do not show the characteristic river patterns found on the cleavage

facets of body-centered cubic alloys. The surface is probably a {111}

austenite plane, considering the orientations of {111} slip-band traces (see

Fig. 8) and the similarity to regions in another high-N austenitic stainless

steel, which were identified as {111} austenite by Tobler.^ Similar fracture

features have been observed in austenitic stainless steels charged with H and

fractured at room temperatures.^'^’''® The study of Hannula et al.”''^ shows a similar trend, in that brittleness increased with decreasing austenite

stability

Further study of the possible origin of apparently brittle {111} austenite was pursued with optical microscopy. The microstructure of the tougher

alloy, 740, after several percent elongation is shown in Fig. 12, and that of

the more brittle alloy 413 after similar elongation is shown in Fig. 13. The

microstructure of alloy 740, containing 11.5^ Ni,is characterized by lathlike a' martensite formation, contained within {111} austenite sheets and by

lath-like a' martensite that formed at {111} slip-band intersections. The

microstructure of alloy 413, containing only 5.6^ Ni, is composed of many

{111} slip-band traces. These slip-band traces are broader than those

observed in alloy 740 and more distinctly etched. Less a’ formation was noticed at slip-band intersections. Therefore, one may conclude that there

is more extensive faulting in the lower Ni alloy. Other possible conclusions

are: more extensive stacking-fault clusters exist, more hexagonal closepacked martensite is formed, or deformation twins are produced within the

{111} slip-band packets. Obviously, very careful transmission electron

microscopy must be performed to sort out distinctions among these three possible fault structures. In any case, the fault product or products within

the slip-bands become more brittle at very low temperatures in higher N

content austenitic stainless alloys, affecting the measured fracture toughness deleteriously and exhibiting regions of slip-band decohesion on the

fracture surface.

127
THE QUALITY INDEX

Nickel and nitrogen contribute quite differently to the low temperature

mechanical behavior of austenitic stainless steels. Nickel improves toughness

and does not affect strength; nitrogen improves strength and reduces toughness. For most structural applications, both strength and toughness are required. It is useful, we believe, to consider both of these parameters

tog-ether, as the product ay-K]-Q(J), and to examine the effects of alloying on this product, called the quality index. In Fig. 14, Ni content is plotted

versus the quality index. Increasing Ni content increases this index.

Stated another way, increasing Ni content leads to improved low temperature

mechanical behavior, either increased toughness or increased strength or a combination of both.

The effect of C and N on the quality index is plotted in Fig. 15. Additions of C and N have little effect on the quality of mechanical behavior.

Figure 3 shows that increased N content increases strength, and toughness is

sacrificed.

SUMMARY

A series of eight austenitic stainless steels with varying Ni and N

contents were measured at 4 K to determine tensile strength and fracture

toughness. The results of the study are:

1 . Nitrogen addition raises the tensile yield strength and reduces

fracture toughness.

2. Nickel addition raises the fracture toughness and has little effect

on strength.

-AT

3. The temperature dependence follows the relation ffy = °o ®

parameter A is directly proportional to the stacking fault energy.

4. Factors that contribute to the cleavage-like facets on fracture

facets (associated with low toughness) are high interstitial content, low stacking fault energy, and stress concentration. These

surfaces have been associated with slip-band decohesion on {111}

austenitic planes.

5. A quality index, defined as the product ay»Kj^(J), has been proposed

to suggest the quality of mechanical behavior. Nickel is shown to

increase the quality index nitrogen has little effect.

ACKNOWLEDGMENTS

The Office of Fusion Energy, Dr. Victor Der, Project Monitor, sponsored

this research. We owe special thanks to Robert Walsh for performing careful

tensile measurements at low temperatures and to Lonnie Scull for conducting

all of the chemical analyses used in this report. We thank the Department of

Metallurgy, Colorado School of Mines, for providing the facilities for

accurate chemical analyses.

128
REFERENCES

1. R. P. Reed and N. J. Simon, in: "Advances in Cryogenic Engineering

Materials," vol . 30, Plenum Press, New York(1984), pp. 127-136.

2. R. L. Tobler, D. T. Read, and R. P. Reed, in: "Fracture Mechanics:

Thirteenth Conference," ASTM STP 743, American Society for Testing and

Materials, Philadelphia (1981), pp. 250-268.

3. R. P. Reed and J. M. Arvidson, in: "Advances in Cryogenic Engineering--

Materials," vol. 30, Plenum Press, New York (1984), pp. 263-270.

4. D. T. Read and R. L. Tobler, in: "Advances in Cryogenic Engineer ing--

Materials," vol. 28, Plenum Press, New York (1984), pp. 17-28.

5. R. P. Reed and R. L. Tobler, in: "Advances in Cryogenic Engineering

Materials," vol. 28, Plenum Press, New York (1982), pp. 49-56.

6. R. L. Tobler, R. P. Reed, and D. S. Burkholter, in: "Advances in

Cryogenic Engineering —Materials," vol. 26, Plenum Press, New York

(1980), pp. 107-119.

7. R. P. Reed, in: "Materials at Low Temperatures," American Society for

Metals, Metals Park, Ohio (1983), pp. 295-341.

8. R. L. Tobler and R. P. Reed, in: "Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures —III," NBSIR 80-1627, R. P.

Reed, ed.. National Bureau of Standards, Boulder, Colorado (1980), pp.

1 7-48.

9. R. L. Tobler and D. Meyn in: "Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures —VIII," NBSIR 85-3025, R. P. Reed, ed.. National Bureau of Standards, Boulder, Colorado (1985), pp.

167-179.

10. I. Williams, R. G. Williams, R. C. Capellaro, in: "Proceedings of Sixth

International Cryogenic Engineering Conference," IPC Science and

Technology Press, Guildford, Surrey, England (1976), pp. 337-341.

11. R. E. Schramm and R. P. Reed, Metall. Trans . 6A:1345-1351 (1975).

12. C. G. Rhodes and A. W. Thompson, Metall. Trans . 8A: 1901-1906 (1977).

13 . P. J. Brofman and G. S. Ansell , Metall. Trans. 9A:879-880 (1978).

14. H. M. Ledbetter and M. W. Austin, in: "Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures —VIII," NBSIR 85 -X, R. P. Reed, ed.. National Bureau of Standards, Boulder, Colorado (1985).

15 . G. Schoeck and A. Seeger, in: "Defects in Crystalline Solids," The

Physical Society, London (1955), pp. 340-346.

16. B. Escaig, J. Phys . 29:225-234 (1968).

17 . S.-P. Hannula, H. Hanninen, and S. Tahtinen, Metall. Trans. 15A:2205-

2211 (1984).

18 . G. R. Caskey, in: "Fractography and Materials Science," ASTM STP 733.

American Society for Testing and Materials, Philadelphia (1981), pp.

86-97.

129
Table 1 . Chemical Composition and Metallurgical Characterization

Alloy Composition (wt.?) Grain Size

(pm)

Hardness

Cr Ni Mn C N S P Si (Rg)

i(13 18.8 5.6 4.1 0.020 0.256 0.005 0.014 0.25 175 84

1)14 18.4 8.9 4.2 0.018 0.281 0.005 0.014 0.28 200 82

415 20.5 12.8 5.5 0.024 0.265 0.004 0.015 0.34 385 81 416 20.8 14.9 5.2 0.028 0.277 0.004 0.015 0.41 225 82 520 19.8 5.8 3.2 0.014 0.260 0.004 0.012 0.41 340 85 739 18.7 8.7 3.7 0.01 4 0.093 0.005 0.013 0.23 325 72 740 19.7 11.5 3.9 0.012 0.141 0.005 0.013 0.27 340 72

741 20.8 14.7 4.4 0.016 0.197 0.004 0.014 0.33 320 76

Table 2. Mechanical Property Results* at 4 K

Tensile Strength Fracture Toughness Alloying Variables

Alloy °y °u Elongation Kic(J) Ni N (MPa) (MPa) (%) (MPa/m) (wt.$) (wt.?)

413 1075 1418 11 75 5.6 0.26

414 950 1650 42 143 8.9 0.28

415 1000 1580 32 204 12.8 0.27

416 1160 1630 22 239 14.9 0.28

520 960 1216 7 87 5.8 0.26

739 460 720 40 273 8.7 0.09

740 720 1370 42 244 1 1 .5 0.14

741 870 1425 29 254 14.7 0.20

*Averages of 2 or 3 measurements.

Table 3. Tensile Characteristics

Alloy Estimated

Stacking Fault Energy

(mJ/m^)

Estimated

Is

Slope of J,n Oy vs. T,

A (10'3 MPa/K)

Average % Martensite

Tensile Elongation

i)13 8 309 1.73

414 28 224 0.67

415 58 97 0.16

416 71 47 4.60 0 520 7 316 0.97

739 26 275 2.50 1 .72 740 45 186 3.95 0.74

741 67 80 0.07

AISI 304 24 3.38 —

AISI 316 55 4.54 —

AISI 310 98 6.13

130
Stress,

MPa

Stress,

MPa

1800

1600

1400 -

Alloy 413

(a)

Strain

Fig. la and b. Stress versus strain (engineering values) at 4 K for alloys (a) 413 and (b) 4l4.

(b)

131
Stress,

MPa

Stress,

MPa

Strain

Fig. 1c and d. Stress versus strain (engineering values) at 4 K

for alloys (c) 415 and (d) 4l6.

132
Fig. 1e and f. Stress versus strain (engineering values) at 4 K for alloys (e) 520 and (f) 739.

133
Stress,

MPa

Stress,

MPa

Strain

(g)

Fig. Ig and h. Stress versus strain (engineering values) at 4 K

for alloys (g) 7^0, and (h) 7^1-

134
Fig. 2. Temperature dependence of the yield strength for Ml 6, 739. and ?M0 alloys

Fig. 3. Tensile yield strength at M K as a function of C and N content < + • Line indicates trend of a series of nine 19Cr-10Ni steels with vary ng

and N contents.^

135
Tensile Yield Strength, o-y, (MPa)

Fig. 5 . Fracture toughness at 4 K,

estimated from J-integral

measurements, versus Ni

content

Fig. 4. Tensile yield strength versus fracture toughness at 4 K. Band represents previous data.®

O' ^ ^ ' 0 5 10 15 20

Nickel Content, wt. %

136
» 1 0.2 y m

Fig. 6. Transmission electron microscopy photographs of initial

structure of alloy M13« Arrows point out stacking faults.

137
138

200

fjLm

Fig.

7.

Fracture

surfaces

at

crack

tip

of

alloys

(a)

413,

(b)

4l4,

(c)

415,

and

4l6

(SEM

photomicrograph).
20 ym

Fig. 8. Higher magnification SEM photograph of alloy 41

Notice inclusions within most dimples.

139
5 ym

I

(b)

Fig. 9. Cleavage-like areas that become apparent in the more brittle

alloys: (a) alloy ^13, low magnification SEM photomicrograph

(b) alloy ^^ 3 , high magnification SEM photomicrograph

140
Fig. 10. Th© normalized average amount of ot' martensite within the gage length

of tensile specimens (after deforming at M K) plotted against the

calculated md temperatures (based on chemical composition).

Fig. 11. Temperature dependence of yield strength (A of Eq. 2) versus estimated

stacking fault energy, based on chemical composition. Three circled data

points represent AISI 304, 316, and 310 alloys from a previous study .

141
10

/im

(b)

10

142

Fig.

12.

Microstructure

of

alloy

740

after

several

percent

elongation

at

Parts

a,

b,

and c

are

at

1000X;

part d

is

at

2000X.
143

Fig.

13

.

Microstructure

of

alloy

413

after

several

percent

elongation

at

Parts

a,

b,

and

c

are

at

2000X;

part

d

is

at

1000X.
X

CD O

c

ro O

o

iC

>> b

30

28

26

24

22

20

1816

14

1210

8

6

4

20 56 7 8 9 10 11 12 13 14 15 16

Nickel Content, wt.7o

Fig. 14. The quality index a^-Kj^CJ) at 4 K plotted against

Ni content. Band of data includes a series of nine

19Cr-10Ni steels with varying C and N contents.®

Fig. 15. The quality index o^-Kj^CJ) at 4 K plotted against C and

N content. Solid line represents data of a series of

nine 19Cr-10Ni steels with varying C and N contents.

144


LOW-TEMPERATURE SOUND VELOCITIES IN 304-TYPE

STAINLESS STEELS: EFFECT OF INTERSTITIAL C AND N

H. M. LEDBETTER

Fracture and Deformation Division, Center for Materials Science

National Bureau of Standards, Boulder, Colorado 80303, USA

Between T = 293 and 4 K, we measured the longitudinal ultrasonic velocity of

nine 304-type stainless steels with various C+N contents: 0.3 to 1.3

atomic percent. All alloys showed similar behavior: a regular increase in

velocity down to approximately 100 K; below this, an anomalous decrease caused

by a magnetic transition. The alloys varied in two ways: (1) contrary to

some reports, increasing C+N decreases the Ndel temperature strongly,

approximately 13 K per atomic percent; (2) the magnitude of the

1 ow- temperature elastic softening associated with the Ndel transition

decreases slightly with increasing C+N content.

Key words: alloying; austenite; carbon; elastic constants;

face-centered-cubic alloy; interstitial; iron alloy; nitrogen;

sound velocity; stainless steel

Intended for Res Mechanica Letters

145
INTRODUCTION

Recently, Ledbetter and Austin^ reported the effects of interstitial carbon

and nitrogen on the ambient-temperature elastic constants of 304-type stainlesssteel alloys. They found that all the elastic stif fnesses--Young modulus,

shear modulus, bulk modul us--decrease 0.5 to 0.9 percent per atomic percent

solute. The Poison ratio remains unchanged. Using Eshelby's model, they

related the elastic-stiffness decrease to volume increase. In another study

2

Ledbetter and Austin used x-ray diffraction and Archimedes-method mass

density to determine the volume change due to interstitial C+N in an fee

crystal structure. Both C and N increase volume. Despite its smaller size, N

is more effective. We attribute this to stronger interatomic bonding for C

atoms. For N, volume increases approximately 0.7 percent per atomic percent

interstitial

The 1 ow-temperature properties of these alloys are of interest for two reasons.

First, because of their ductility and toughness, they see many 1 ow-temperature

applications where the elastic constants are key design parameters. Second,

at low temperatures these alloys undergo a magnetic transition that affects

the elastic constants. Conversely, elastic constants (or their companion

sound velocities) can be used to study the phase transition, which remains

only partially understood.

146
Reported here is a preliminary study of the low-temperature elastic properties

of 304-type stainless steel with varying C+N content. Longitudinal velocity,

v^, was measured nearly continuously between 293 and 4 K. This velocity gives

the longitudinal modulus

where p denotes mass density. This modulus contains both dilatational and

shear modes, because

= B+(4/3)G (2)

where B denotes bulk modulus and G shear modulus. Thus, changes in either

dilatation resistance or in shear resistance appear in C^.

EXPERIMENT

Materials were described in detail previously^ For nine alloys the average

weight-percentage chemical composition was 18.9Cr, lO.ONi, 1.5Mn, balance Fe

and trace elements. Table 1 gives the C+N contents. Rockwell B hardness

increased continuously with C+N, from 73.4 to 88.5. Grain size ranged from 78

to 105 ym, averaging 88 ym.

Sound velocities were determined by a pulse-echo-overlap method at frequencies

3 near 10 MHz by methods described previously .

147
RESULTS

Figure 1 shows the principal results: the variation of between 293 and 4 K

for three alloys with different N contents. For clarity, results for the

other six alloys, which vary C content, are omitted. They cluster around each

of the three N-content curves. Table 1 also contains estimated T^^ temperatures

based on the midpoint temperature between C^(max) and C^(min). Figure 2

graphs these magnetic transition temperatures.

DISCUSSION

Qualitatively, all nine alloys behave similarly during cooling from 293 to 4

K. On average, increases 4.3 percent. This compares with 4.0 and 3.7 for

copper and nickel, respectively. Higher C+N reduces Tj^, that is stabilizes

the fee crystal structure against magnetic ordering. A simple interpretation

here is that C+N dilates the fee crystal structure, thus requiring lower

temperatures to achieve the lower interatomic spacing required for direct

4 magnetic-exchange interactions . This finding contradicts that of Warnes and

5 King who, with respect to Tj^, cite the "negligible influence of the

interstitial solutes C and N". Figure 1 shows a nonnegl igible effect:

approximately 13 K per atomic percent interstitial. The measurement scatter

precludes deciding whether C or N is more effective in lowering Tj^. To settle

this, we plan to measure magnetic susceptibility versus temperature.

The C^ softening upon cooling through the magnetic transition is approximately

the same for all nine alloys, -1.5 to -2.0%. This effect is quite large.

148
c Using relationships developed by Eshelby for point centers of dilatation,

this softening implies a volume change at the magnetic transition of about

+1.0%. No accurate dilatometric measurements exist to confirm this. But

recently, Ehrhart et al.^ studied y-iron precipitates = 70 K) by x-ray

diffraction and found a volume increase of 0.3% at the magnetic transition.

The decreased elastic softening with Increased C+N relates also to the

dilation. Increased interatomic spacing causes a weaker magnetic interaction,

a smaller volume change, and a smaller elastic-constant anomaly.

ACKNOWLEDGMENT

This study was supported by the U. S. DoE Office of Fusion Energy. J. T. Ward

and M. W. Austin assisted with measurements.

REFERENCES

1. Ledbetter, H. M. and Austin, M. W., to be published, available in report

NBSIR 84-3000 (1984).

2. Ledbetter, H. M. and Austin, M. W., to be published, available in report

NBSIR 84-3000 (1984).

3. Ledbetter, H. M., Frederick, N. V., and Austin, M. W., J. Appl . Phys. 51

(1980) 305.

“

4. Ledbetter, H. M., to be published, available in report NBSIR 84-3000

(1984).

5. Warnes, L. A. A. and King, H. W., Cryogenics _I^ (1976) 659.

6. Eshelby, J. D., 0. Appl. Phys. ^ (1954) 255.

7. Ehrhart, P. Schonfeld, B., Ettwig, H. H., and Pepperhoff, W., J. Mag.

Mag. Mater. ^

(1983) 79.

149
RELATIVE

LONGITUDINAL

MODULUS

C^(T)/C/

(293)

Table 1

c

(at. pet.)

N

(at. pet.)

C+N

(at. pet.) (K)

0.13 0.15 0.28 52

0.27 0.15 0.42 52

0.41 0.15 0.56 52

0.17 0.47 0.64 50

0.31 0.47 0.78 50

0.43 0.47 0.91 46

0.14 0.95 1.09 39

0.26 0.95 1.21 44

0.39 0.95 1.34 41

Fig. 1 Longitudinal modulus from

T = 293 K to 4 K for three

304-type stainless steels

with varying C+N content.

Near 50 K, elastic softening

occurs owing to a Neel transition (paramagnetic-antiferromagnetic)

C+N CONTENT, at.%

Fig. 2 Effect of interstitial

C+N on the magnetic

transition temperature.

150


LINEAR-ELASTIC FRACTURE OF HIGH-NITROGEN

AUSTENITIC STAINLESS STEELS AT LIQUID HELIUM TEMPERATURE*

R. L. Tobler , R. P. Reed, and P. T. Purtscher

Fracture and Deformation Division

National Bureau of Standards

Boulder , Colorado

Four Fe-Cr-Ni-Mn austenitic stainless steels containing 0.14, 0.26,

0.28, and 0.37 .% N were fractured in a liquid helium environment at 4 K,

and valid measurements of the linear-elastic plane-strain stress-intensity

factor, Kjq, were obtained in most cases. Interstitial nitrogen significantly strengthens these steels at low temperatures so that relatively

brittle fractures occur under plane-strain conditions at 4 K, despite the

fact that these alloys are moderately ductile in uniaxial tension. The

brittle failure mechanism at 4 K involves a form of cleavage or slip-band

decohesion, as evidenced by the formation of transgranular facets on {111}

crystallographic planes.

Key words: austenitic stainless steels; cryogenic properties of materials;

fracture mechanisms; fracture toughness; mechanical properties;

tensile properties; stainless steel alloys.

*Work supported by the U.S. Department of Energy; not subject to copyright.

151
INTRODUCTION

The AISI 300 series austenitic stainless steels are traditional candidates for structural applications at cryogenic temperatures. With specified

allowable nitrogen contents up to 0.16 vit.%, the yield strengths of these

steels may reach 800 MPa at liquid helium temperature, 4 K. A practical

means of achieving still higher strengths is to increase the manganese

content so as to accommodate more nitrogen. To this end the Fe-Cr-Ni-Mn-N

austenitic stainless steels were developed.

The Fe-Cr-Ni-Mn-N steels are stronger at 4 K than AISI 300 series

steels, but less readily available and less well characterized with respect

to mechanical properties, physical properties, and service experience. This

paper presents fracture toughness data for four such steels containing 0*14,

0.26, 0.28, and 0.37? N. Owing to the relatively high strengths achieved at

4 K, linear-elastic plane strain fracture toughness (Kj^) tests were possible

with 25 . 4-mm-thick compact specimens following the ASTM E 399-83 method.

Toughness measurements and fractographic observations are reported here, and

comparisons are made with other nitrogen-strengthened Fe-Cr-Ni-Mn-N steels

[1-5] and AISI 304 type steels [6] that are candidates for structural applications in fusion energy magnets operating under high stress fields in liquid

helium.

MATERIALS

A description of the test materials, including composition, form, heat

treatment, mechanical properties, and grain size, is given in Tables 1, 2,

and 3- In Table 3> the properties at 295 K are quoted from the mill sheets,

whereas the properties at 4 K were measured in the laboratory using 6.4-mmdiameter tensile specimens with 25 . 4-mm gage lengths (two tests per material). The materials are referred to by their nominal compositions and

commerical designations as follows:

1) Fe-l6Cr-8Ni-8Mn-0. 14n

2) Fe-19Cr-7Ni-9Mn-0.26N

3) Fe-20Cr-8Ni-2Mn-0.28N

4) Fe-20Cr-7Ni-8Mn-0.37N

(Nitronic 60*)

(Nitronic 40*)

(AISI 304 HN)

(AISI 216)

The Fe-20Cr-7Ni-8Mn-0. 37N steel was received in a hot and cold forged

condition and was annealed in the laboratory prior to testing. The other

three steels were received and tested in their annealed conditions. Also,

the Fe-1 6Cr-8Ni-8Mn-0 . 1 4N steel contained one-half percent of a magnetic

second phase at 295 K prior to testing, whereas the others were fully

austenitic, as verified by examination with a magnetometer.

Because rectangular bars or plates of suitable thickness (25.4 mm) were

not commercially available, cylindrical bars of Fe-1 6Cr-8Ni-8Mn-0 . 1 4N

,

Fe-20Cr-8Ni-2Mn-0. 28N , and Fe-20Cr-7Ni-8Mn-0 . 37N steels were obtained. These

* Trade names are used here to describe the steels tested, and their use for

this purpose in no way implies endorsement or recommendation by NBS.

152
bars were 76, 159, and 92 nun in diameter, respectively. Compact specimens

were machined in RL orientations [7], and tensile specimens were extracted with

the principal axes transverse to the longitudinal bar directions so that the

fracture plane orientations in both specimens would be similar.

In the case of Fe-1 9Cr-7Ni~9Mn-0. 26N steel, a rectangular bar was obtained and compact specimens of the TL orientation [7] were tested according

to the usual practice.

PROCEDURES

Two tests per steel were performed using 25 . 4-mm-thick (B) compact

specimens. These specimens had a width (W) of 50.8 mm, a W/B ratio of 2, and

standard planar proportions as per ASTM E 399~83 [7]. The notch was modified

as shown in Figure 1 , and a calibrated clip gage was positioned at the loadline in anticipation that J-integral measurements might be performed in some

cases. (This modification proved unnecessary.)

Using the cryogenic apparatus described elsewhere [8,9], fatigue cracks

of length a were introduced by computer-controlled sinusoidal loading at a stress ratio (R) of 0 . 1 and at a frequency of 14 Hz. The cracks were initiated at liquid nitrogen temperature (76 K) , but the final 5 mm or more of

crack growth was at liquid helium temperature (4 K) . The AK value during

fatigue was maintained constant at 30 MPa^m^^^^ by computer-controlled load

reductions performed every 0.13“tnni increment of crack growth. After fatigue

cracking at 4 K, the fracture toughness tests were performed at a stroke rate

of about 0.05 mm/s.

RESULTS AND DISCUSSION

Representative 4-K fracture test records for the steels of this study

are shown in Figure 2. Type I load-displacement curves [7] were observed

in each test. There was always a slight degree of nonlinearity during the

terminal stages of loading, and sometimes a few small increments of unstable

crack extension were observed prior to final fracture.

The calculated Kq and Kjq parameters are listed in Table 4, with

pertinent specimen dimensions and validity criteria. As defined in

ASTM E 399- 83 , Kq is a conditional toughness measurement. To qualify as a valid Kj^ measurement, the relative crack length must be in the range:

0.45 S a/W S 0.55 (1

)

The following additional requirements must also be met:

^^max^^Q = "I •

"1 0 ( 2

)

2.5(KQ/ay)2 ^ B, a ( 3 )

For most tests these criteria are satisfied, and valid data are tabulated. But in the case of Fe-1 9Cr-7Ni-9Mn-0.26N steel, valid data

153
were not obtained, owing to violations of Eqs. 2 and 3* J-integral tests of

this steel were likewise invalid since fast-fracture prevented the development of a complete four-point resistance curve, as required according to the

elastic-plastic test procedure, ASTM E 8l3~8l [10].

As a guide to rank the toughness of Fe-1 9Cr-7Ni-9Mn-0. 26N relative to

the other steels, the specimen strength ratios, R 3 Q, were calculated according to ASTM E 399-83 [ 7 ]. RgQ is the ratio of the maximum nominal net

section stress to the material's yield strength. This parameter is a function of the maximum load the compact specimen can sustain; it is especially

useful here because all specimens are the same size and shape. As shown in

Figure 2 and Table respectively, and are highest for the Fe-19Cr7Ni-9Mn-0.26N steel, a strong indication that its fracture toughness exceeds

the values for the other steels in this study.

The fracture toughness results are plotted versus yield strength in

Figure 3. In general, the Fe-20Cr-8Ni-2Mn-0 . 28N (AISI 30^1 HN) result of this

study fits the trend for AISI 30^1 type steels [6], while the Fe-1 9Cr-7Ni-9Mn0.26N and Fe-20Cr-7Ni-8Mn-0. 37N steel results fit the trend for other previously tested Fe-Cr-Ni-Mn-N steels [3“5]. However, the Fe-1 6Cr-8Ni-8Mn-0 . 1 4N

steel is highly deviant and demonstrates an exceptionally poor fracture

toughness for its given value of yield strength.

Fractographic features of these steels are illustrated by scanning

electron microscopy in Figures 4 through 6. All the 4-K fracture surfaces

display areas of cleavage-like transgranular facets. On the macroscopic

scale, the facets are smooth, flat, and highly refective. On the microscopic

scale, there are obvious steps and visible slip line markings. Judging from

the near 60° angles between the slip-line markings, the facets evidently form

on { 111 } crystal planes. The {111} crystal plane indices were confirmed by

x-ray diffraction in a study of a related steel, Fe-1 8Cr-3Ni-1 3Mn-0.37N [11].

Since the {111} planes are the active slip planes of the austenite phase, the

failure process may be slip-plane decohesion.

In an on-going study of nitrogen-strengthened austenitic steels [12],

the occurrence of facets on the fracture surface, concomitant with a degradation of toughness at 4 K, has been correlated with decreasing nickel

content. Unpublished data indicate that manganese content is also an important variable [13]* Apparently chemical composition plays a significant

role in the fracture process of these austenitic stainless steels at 4 K, but

the mechanism by which chemical composition affects the fracture mode has not

yet been identified.

With the unaided eye, a "woody" type of texture covers the surface of

the Fe-1 6Cr-8Ni-8Mn-0. 1

n steel (Fig. 4), significantly different from the

macroscopic appearance of the other three alloys (Figs. 5 and 6). The alloy

with the woody-textured fracture surface has a lower toughness than expected

for its respective yield strength. The same alloy contained one-half of one percent of a nonaustenitic phase (probably delta ferrite) prior to testing.

The woody texture of the fracture surface and the presence of a second phase

indicate that the material may not have been processed properly, which

resulted in the relatively poor fracture toughness.

154
SUMMARY AND CONCLUSIONS

Austenitic stainless steels containing a high level of nitrogen are prone to brittle fracture at low temperatures despite their face-centered

cubic crystal structures. In this study, 4-K fracture toughness tests were performed on 25. 4-mm-thick compact specimens of Fe-Cr-Ni-Mn steels containing

O.lM, 0.26, 0.28, and 0.37 wt.5^ N. Type I linear-elastic fracture test

records were observed, and and Kq data ranging from 90 to 166 MPa*m”'^^ are reported. Brittle fracture under plane-strain conditions is associated

with a cleavage-like failure mode consisting of transgranular facets that

form along the {111} family of slip planes in the austenite lattice. Thus,

the failure mechanism at 4 K may involve slip-plane decohesion, as documented

for tests of a related Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel [11].

REFERENCES

1. A. Nyilas and L. Yan , Fracture Toughness Determination of 21Cr-6Ni-9Mn

Stainless Steel at 4 K. Report 03“03-02P1 2C , Institut fur Technische

Physik, Kernforschungzentrum Karslruhe, Federal Republic of Germany

(July 1984) 16.

2. J. M. Wells, R. Kossowsky, W. A. Logsdon, and M. R. Daniel, Structural

Materials for Cryogenic Applications, Research Report 76-9D9-CRYMT-R1

Westinghouse Electric Corporation Research and Development Center,

Pittsburgh, Pennsylvania, Final Technical Report (October 9, 1976) 181.

3- R. L. Tobler and R. P. Reed, Tensile and Fracture Behavior of a Nitrogen

Strengthened Chronium-Nickel-Manganese Stainless Steel at Cryogenic

Temperatures, in: Elastic-Plastic Fracture, ASTM STP 668, J. D. Landes,

J. A. Begley, and G. A. Clark, Eds., American Society for Testing and

Materials, Philadelphia, Pennsylvania (1979) 537“552.

4. D. T. Read and R. P. Reed, Toughness, Fatigue Crack Growth, and Tensile

Properties of Three Nitrogen-Strengthened Stainless Steels at Cryogenic

Temperatures, The Metal Science of Stainless Steels, Metallurgical

Society of the AIME, New York (1979) 92-121.

5. D. T. Read and R. P. Reed, Fracture and Strength Properties of Selected

Austenitic Stainless Steels at Cryogenic Temperatures, in: Materials

Studies for Magnetic Fusion Energy Applications at Low Temperatures-II

,

NBSIR 79- 1609 , National Bureau of Standards, Boulder, Colorado (1979)

81 - 122 .

6. R. L. Tobler, D. T. Read, and R. P. Reed, Strength/Toughness Relationship for Interstitially Strengthened AISI 304 Stainless Steels at 4 K

Temperature, in: Fracture Mechanics: Thirteenth Conference, ASTM STP

743 , Richard Roberts, Ed., American Society for Testing and Materials,

Philadelphia, Pennsylvania (1981) 250-268.

155
7. Standard Test Method for Plane-Strain Fracture Toughness of Metallic

Materials, ASTM Designation: E 399-83, 1984 Annual Book of ASTM Standards, Section 3, Metals Test Methods and Analytical Procedures, American Society Testing and Materials, Philadelphia, Pennsylvania (1984)

519-554.

8. D. T. Read and R. L. Tobler, Mechanical Property Measurements at Low

Temperatures, in: Advances in Cryogenic Engineering, Vol. 28, R. P. Reed and A. F. Clark, Eds., Plenum Press, New York (1982) 17-28.

9. C. W. Fowlkes and R. L. Tobler, Fracture Testing and Results for a T1-6A1-4V Alloy at Liquid Helium Temperature, Eng. Fract. Mech.

8:487-500 (1976).

10. Standard Test Method for djp, A Measure of Fracture Toughness, ASTM

Designation: E 8l3“8l, 1984 Annual Book of ASTM Standards, Section 3,

Metals Test Methods and Analytical Procedures, American Society Testing

and Materials, Philadelphia, Pennsylvania (1984) 763-781.

11. R. L. Tobler and D. A. Meyn, Cleavage-like Fracture in Fe-1 8Cr-3Ni-1 3Mn0.37N Austenitic Stainless Steel at Liquid Helium Temperature, in:

Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures —VIII, NBSIR 85-3025, R. P. Reed, Ed., National Bureau

of Standards, Boulder, Colorado (1985) 167-179.

12. P. T. Purtscher and R. P. Reed, Nickel and Nitrogen Alloying Effects on

the Strength and Toughness of Austenitic Stainless Steels at 4 K,

in: Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures —VIII, NBSIR 85-3025, R. P. Reed, Ed. National Bureau of

Standards, Boulder, Colorado (1985) 123-144.

13 . P. T. Purtscher and R. P. Reed, National Bureau of Standards, Boulder,

Colorado, unpublished results.

156
Table

1.

Mill

chemical

analyses

(wt.^S)

v£5 o ] I 1 L> ) I • 1 O

o>

O CM ] m LO r • ] • O o CM o 3 ? v£) 1 O • 1 • 1 o o

c^ ro ur»

O

CM CM

m o. o O o o o o o o m <7^ o o CM o

co o o o o o o o o

zr o C-- m in

CO • • o o o

GO o o

LT» vX> o O o o o O o o o O c>^ o o

v£5 CO t-- z CM CM o O o o

=Tm

m c o m CO

s: • • • CX) a^ CO

c^

m CM m:) C7N z • • CO vO CO vO

c^ CM

L. .=r CM CO a • • • \X> o^ o CT\ CM * z z z z

CO c^

CM CMm o O o o c c c c 2 s: s: s:

CO CO CM GO I 1 L. •iH -•H ••H 0 z z Z z 4.5 CO c^ CO c^

CO 1 1 :e c. t. £. t- o o O o o o Y Y

CM CM 0 0 0 0

Uw Cau Cau Cxw co

•rH

‘rH •ocoo

X3Cs

J-o

I-

(D

n3

CM

CD

ct3 H

*0

0)

CO

0) Hco

J-)

“DcooEuo

Cim

x:oc

0)3

Q*

XIo

c.<u3

cr

t.

(D

4-> fO5

x:

f\j

L.0

4->

(TJ 3mI oo Oo

'sD O

T30

»—

O

Q.

•oc

fc

*o0

r-H fU0CC

CC o00

s.1 4-5 OX o

4-5 mo>o

*o0oaoc

CO

•o0

CO0cc

CO

•o00

L-1 4-5 OX

X0c03

cr

L-0

4-5 (03

Czj o

C\J o

•o0

CO0cc

COco

4-5 3

i-H o

CO

S-CO XS

*o§o

L.EEI vO

L.CO X5

L.

CO3c

CO

4J> 00

t-EE1

LT» CMXI

IT» (M

L.CO J3

*oC3O

L.

<0 oIEEI ON

IT*

OIc

s:

00IL. O

t*-IL. CJONI0

Lu

O0CM10

Cju

157

Fe-20Cr-7Nl-8Mn-0.

37N

92-mtn-cJia.

round

bar

Hot

and

cold

forged,

and

annealed:

1093°C, 3

h,

water

quench
a>

4-> ocm • CO CO M -tJ

CCJ Q,

CDo

0)

X

Jj) CD COs - c

Jj o

CO

CD 4-5

4-5 -r-4 •o

Ct-I

C o oo

CDN "O

•t—I CD

CO >

CD

C

—

•H

O

CC3 CD

a. bO 1CO *0 03 c

(03 0> x:

CO 4-> (p ^ o

X. Cm

0)Q, 0) O t.

03 Ou

CO rH CP

03O -*-> •-H C (P

ct3 Q.

x: o o t.

(p Om

cn

0)

t-H x^

03 H

05

CO

COcM

03 r—

J- E o 50 50 50 O 3. zr CO

rHM CO

05 CO 3 05c /—X CO -=r CM O •o CD CO 05 CJ5 05 O 3 QC

cc 03 •—

PC co

•M 03

4-> 05 o tm C75 CM 50 3 < o CM CM LO 50 on CM 1/5 CM

05 Ci_ C-- CM Cr- CM LO

cc

O co

•H

4-> 03 CM CO LTS bO • C vX5 m CM «- t- oo =T o '—' m IT» >- =r on

iH

Ci]

05 x:

4-5 03

05 bO CL E C S LO ^ O C-- LO 0- C75 CM

•r-« 05 -=T -=r o in 50 CM 50 50

4-5 3 c— oo c— 50 C-- C^ 05 OO

f—i 4-5 3 «

T— 1

*— 35 00 D

JC

4-5 03 bO CL o C S ^ O CM «- .1- in 1/5 CO

<—

05 t- a> o ^ 50 o 05

05 5- ^ 05 on CM ^ CM oo on

•iH 4H >) >H CO O

05

L.3

4-5 05

t.

0)Q. Ln -=r LO ^ m LT5 E .r—

o^ 05 05 C75

05 CM CM CM 05J H

fO z z z z 50 CO C-- *— CM CM on o O o o c c c c

s: s: s: s: CO C75 CM CO

•H .i, .i, z z z z

CO 0- 00 0- 1 1 I 1 05 t- t. t. •H CJ o o o

t. 50 05 o

05 CM CM

4-5 I 1 1 1 03 05 0 0 0

2: Cjl Cxri Cxrf Cb coocoo

•O

0) M

05

0)cc

05>.

t,O

05

L.O

r)

05

0) JZ

4->

t,o

<u

05

t,

05

05

CO

05 M

4^

0)Q.O

CL

05

158
Table

4.

Fracture

toughness

test

results

at

CM

CO e

o; 03 1 «— 1 1 — o ON in c o a- I On 1 t CTn Os o o ^ S r— p— x: w 3OH CM

<V 'V. r— 3 €• JD

n

O cy 03 03 CO MD

cO x; CL C^ «—

n MD

O ON in

L,

X CO o> ^ »— OS OS o o

Cju

szc o

0> 00 CM CO -=r CO -=T ^ CO

t. *-> o OS OS CM

m sO tr^ t- vO

4-> 03 CO

00 o: cc CD

OO

O o o

jjU) r-s o c 03

1) >» QO in CO

<D

O S Os o vO a^

4-> OS CM CM on

C/}

CM c >» o o\ LTs ro CM

m CT\ t— on CM

5_

O

<D Os •— on to- CM CM in ^

a> 4-> /—

r- CM -=r t— •— .— ,

•rH LO S

s. • s

CO C_> CM o

•rH

4-> 03 cn a.

T3X «- oo

n on ^ CO in

03 03

O

O f— r— o o o o O e

Uu

s:

4-> c

0) CIJ on > 00 3 • \ vO 0- CM •=r in on vo on os

03 o 03 CM

O ^ OS «- o CM on CO os

rH 03 vo un

n

m inm in in 00 on

0) c. I ON

a: o o o o o o o o o a^ o^ CJ os on on 2 u H

CD CO c 2 <«

<i> 2 H E •• o o o o o o m o H CO Cm

£: r-s. LO tn

mn o o os in CO <t 0 o J.) s ir» vO ^ c— c— os kO <

0) *o 3 S Cm on

a. •pH o o o o o o o o Cm 0 • CO 3 u*3 in n n in in in in 0

CM • • os

•> CM • c

CO • Os 0 c CO on

03 0)

C S c r-v O [T> o o in o o o 0- 0 0

•rH s m CM o o CM in in in CD o o CD B m in n n in *=r in in c CO —.• 0 0 '—

a c ITl LTl in m in in in in Cl) CO H CM CM CM CM CM CM CM CM 4-> CO CD 0

0) /\

CO 1

>—

p • CM oo m >*

cx 0 in 0

CO z r- CM »- CM r- CM p- CM • \ 0 or or

a. x:

/\ 'v >—• X Z z z z 3 03 in vO CO c— \ B

CM CM

m 03 Q- CM

dO o o 0} 0) 0) 1 1 1 1 CO ff) CO c c c c 3 3 3 2 2 2 2 03 CX3 03

(X) c^ CM 00 0 0 0 1 1 1 1 o; 0) <U

•<^ •pH mH •pH £3 £3 z z Z z CO t- 00 t*- 0 0 •0

rH 1 1 1 1 >"H hH c

03 s. s. L. x: 03

*<H o o o u M3 Os o o «

<D «— r— CM CM U 1 \ \ 1 a or

03 0) 0) 0) o S Czr CL4 Cx4 U4 03

n

159
63.5

.Width,W=50.8

. 28.58 ; 12.70

Dimensions

in mm

Figure 1 . Compact specimen used in this study.

160
LOAD,

P

LOAD.

DEFLECTION. 8 DEFLECTION. 8

DEFLECTION, 8 DEFLECTION, 8

Figure 2. Representative 4-K fracture toughness test records for steels of

this study.

161
YIELD STRENGTH, <Ty, MPa

Figure 3- Fracture-toughness-versus-yield-strength trend at 4 K for steels

of this study compared with previously tested austenitic stainless

steels: (1) Fe-1 6Cr-8Ni-8Mn-0. 1 4, (2) Fe-1 9Cr-7Ni-9Mn-0. 26N

,

(3) Fe-20Cr-8Ni-2Mn-0.28N, (4) Fe-20Cr-7Ni-8Mn-0 . 37N

162
Figure 4. Fractographic appearance of Fe-1 6Cr-8Ni-8Mn-0. 1

n steel fractured

at 4 K.

163
Figure 5. Fractographic appearance of Fe-1 9Cr-7Ni-9Mn-0 . 26N steel fractured

at K.

164
Figure 6. Fractographic appearance of (A) Fe-20Cr-8Ni-2Mn-0. 28N and

(B) Fe-20Cr-7Ni-8Mn-0 . 37N steels fractured at 4 K.

165
J


CLEAVAGE-LIKE FRACTURE IN

Fe-l8Cr-3Ni-l 3Mn-0.37N AUSTENITIC STAINLESS

STEEL AT LIQUID HELIUM TEMPERATURE^

R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

and

D . Me yn

Materials Science and Technology Division

Naval Research Laboratory

Washington, DC 20375

Contrary to usual expectations for the face-centered cubic crystal

structure, some nitrogen-alloyed austenitic stainless steels exhibit brittle

fracture at temperatures approaching absolute zero. In this paper, plane

strain fracture toughness and fractographic data are presented for an

Fe-1 8Cr-3Ni-1 3Mn-0. 37N steel tested at liquid helium temperature (4 K). Low

toughness (Kj^^ = 71 MPa-m^"^^) and linear-elastic loading behavior was observed in 25-mm-thick compact specimens at this temperature, in association

with a high tensile yield strength and a brittle failure mode consisting of

transgranular facets. The transgranular facets produced in a coarse-grained

sample of this steel at 4 K were identified by Laue x-ray diffraction and

slip-line trace analysis as having formed on {111} austenite planes, which

implies that slip-plane decohesion may be the brittle failure micromechanism.

Key words: austenitic steel; cleavage; cryogenic properties; face-centered

cubic crystal structure; fractography ; stainless steel alloy.

"^Work supported by the U.S. Department of Energy; not subject to copyright.

167
INTRODUCTION

According to traditional views, face-centered cubic (fee) metals do not

fracture by cleavage [1,2]. However, several exceptions have been cited

recently in the literature [3“9]. For example, rhodium and iridium cleave in

inert environments at room temperature [3,^]; nickel and Al-6Zn-3Mg cleave in

liquid metals at various temperatures [5]; and high-strength nitrogen-alloyed

austenitic (fee) stainless steels cleave at liquid nitrogen temperature [6].

This note discusses brittle fracture in an austenitic stainless steel,

Fe-1 8Cr-3Ni-1 3Mn-0 . 37N , tested in liquid helium at 4 K. Valid plane strain

fracture toughness (Kj^) data for this steel at 4 K are reported, a cleavagelike failure mechanism is described, and the crystal plane indices of the

transgranular facets produced during fatigue and fracture are identified by

x-ray diffraction and slip-line traces.

MATERIAL

The test material was a 25 . 4-mm- thick plate of Fe-1 8Cr-3Ni-1 3Mn-0 . 37N

austenitic stainless steel in the commercially annealed condition: 1080°C for

1 h and water quenched. The mill chemical analysis in weight percent is:

Fe-1 8.09Cr-3.26Ni-1 3 • 22Mn-0 . 37N-0 . 038C-0 . 1 2Mo-0 . 52Si-0 . 005S-0. 028P . The

material in the as-received condition has an average austenite grain diameter

of 48 ym and a microstructure free of carbide precipitation. The mechanical

properties are listed in Table 1

PROCEDURE

Fracture toughness tests according to ASTM E 399-83 [11] were performed

using compact specimens 25. 4-mm thick (B) and 50.8-mm wide (W). Two specimens

were machined from the as-received material, and one from laboratory annealed

material. The laboratory anneal (1093° C, 37 h, water quenched) was applied to

a sample of the Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel to enlarge its grains. Each

specimen was fatigue cracked at stress-intensity factor ranges from 20 to 50

MPa*m^^^ and then fractured at 4 K. The average grain diameter of the laboratory-annealed specimen was large enough (about 1 mm) to permit Laue x-ray

microbeam analysis of individual crystal facets situated on the fracture surface of the polycrystalline aggregate.

RESULTS

A representative 4-K, load-versus-deflection curve for the Fe-l8Cr-3Ni13Mn-0.37N steel in the as-received condition is shown in Figure 1. A type I [11] linear-elastic behavior is observed, with only slight nonlinearity prior

to fast fracture.

The compact specimen fracture surface, shown in Figure 2, displays no shear lips. The fatigue and overload failure zones are both covered by smooth,

highly reflective facets resembling the cleavage facets commonly seen in bodycentered cubic (bcc) metals fractured at low temperatures . There is a relatively large degree of fatigue crack curvature, the edge crack lengths being

168
about 1^4 percent shorter than the three-point average crack lengths calculated according to ASTM E 399-83* Thus, the crack front curvature is sizable

but does not exceed the 15 percent limitation set by section 8.2.2 of ASTM E 399-83 [11]. Magnetometer and x-ray examination of the ^ K fracture surface

revealed no detectable bcc martensitic phase; the sensitivities were 0.2 and

3 percent, respectively.

The Kj^ measurements for the as-received material are listed in Table 2.

Also listed are specimen dimensions and test validity criteria as defined in

the ASTM E 399-83 standard. The results for a chevron-notched and a straightthrough notched specimen proved indistinguishable: The values are nearly

equal, and crack front curvature is identical, which indicates that the type

of crack-starter notch has no influence at all on the final crack front

shape.

Figures 3 and 4 show facets produced in the coarse-grained specimen of

Fe-l8Cr-3Ni-1 3Mn-0.37N steel during fatigue and fracture at 4 K. The facet

planes in both zones are oriented at angles from 90'’ to 53"^ with respect to

the loading axis, or 0° to 37 from the macroscopic plane of fracture. As

shown at higher magnification in Figs. 5 and 6, the facets display steps and

slip-line markings, but no river patterns such as observed on classical

cleavage facets for ferritic steels.

Three facets in the fatigue failure zone of this specimen were examined

by Laue x-ray diffraction. All three facets were identified as {111} planes

in an fee structure, and the crystallographic directions in these {111}

planes were apparently randomly oriented with respect to the crack propagation direction.

The overload zone facets for the coarse-grained specimen were also identified as {111} planes, on the basis of the 60° angle between the slip-line

markings and between facet edges. Again, three facets in this zone were

x-rayed. The planar indices could not be confirmed by x-ray diffraction

because the diffraction technique produced no spot pattern, only general

blackening due to the level of microplastic deformation induced at fracture.

(The crystallographic directions for overload facets could not be determined,

either). However, the fact that the overload zone facets are oriented like

those in the fatigue zone indicates that they are also {111} planes.

DISCUSSION

According to a simple classical model, the occurrence of ductile or brittle fracture at a given test temperature depends on whether the yield

strength (a^) or .cleavage strength (a^) is reached first [1,2]. For metals,

Oq is relatively high and temperature insensitive. A critical factor, then,

is the magnitude of and its rate of increase at low temperatures

In most bcc metals and alloys, including ferritic steels, Oy is strongly

temperature dependent. As temperature is lowered, the lattice resistance to

slip progressively increases until at some point 0 ^ is exceeded before slip

can occur. As a result, cleavage is common in bcc materials at low temperatures [1]. For fee metals and alloys, including austenitic stainless steels.

169
Oy is typically low and not strongly temperature dependent. For many years,

exceptions were unknown and there was a strong tendency to generalize that

"slip occurs readily in fee metals at all temperatures, their shear strengths

are always lower than their cleavage strength, and they always fail in a ductile manner" [2].

Now, exceptional behavior has been discovered. Tensile loading of

iridium in inert environments at room temperature, or of aluminum in liquid

mercury, produces cleavage on {001} planes [3.5]. Corrosion fatigue cracking

in aluminum alloys also produces cleavage on {001} planes [8]. Cleavage on

{111} planes has also been observed in fee metals under conditions of fatigue

in alloys with coarse-grained structures and limited cross-slip [9].

For austenitic steels, cleavage was reported by Caskey [6] for an

Fe-1 7 . 4MCr-l 5 . 31 Mn-0 . 4/0. 6N alloy in tensile tests at 78 K. The fracture

surface displayed cleavage facets lying along coherent twin boundaries,

transverse to the tensile axis. The fracture progressed by brittle microcracking across individual grains, followed by ductile fracture of the

intervening material. The faceted failure mechanism was attributed to

deformation faulting and to e-phase formation. Similarly, a series of

Fe-Cr-Mn-Ni steels was brittle at low temperatures [12-15]; this was attributed to several possible mechanisms, including the formation of brittle

martensites and the high localization of strain arising from deformation

fault ing.

The Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel of this study is related to the

Fe-Cr-Mn-Ni steels discussed above, all having been developed for the eco- nomical replacement of nickel by manganese and nitrogen. Manganese increases

the solubility for nitrogen, which is the most potent austenite strengthening element at low temperatures. Thus, the steel of this study contains

0.37^ nitrogen and Oy more than triples between 295 and 4 K. Presumably,

this strength increase promotes brittle fracture at 4 K, according to the

classical model discussed above.

Various definitions of cleavage have been offered, leading to a problem

of terminology. According to ASTM E 616-81 [16] standard terminology,

cleavage is simply defined as "separation of a crystal along a plane of fixed

orientation relative to the three-dimensional crystal structure within which

the separation process occurs, with the separation process causing the newly

formed surfaces to move away from one another in directions containing major

components of motion perpendicular to the fixed plane." The facets on the

Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel surfaces satisfy this definition of cleavage.

Because the facets form along {111} planes (i.e, the active slip planes of

the austenite), the failure mechanism might be defined as slip-plane decohesion or shear band cracking. However, all of the facets form at angles

nearly parallel to the macroscopic fracture plane (i.e., high angles to the

load axis), whereas shear band cracking is normally associated with 30 to

60° angles. The distinction between cleavage and slip-band decohesion in

this steel is being investigated further.

170
The measurements (70.2 and 71.0 MPa*m’’'^^) agree well with the

average Kq value (71 MPa*m^^^) reported by Read and Reed [10] for tests of

the same heat of steel. Their Kq values are reported as invalid because they

failed to satisfy the crack front curvature requirements of ASTM E 399-74,

the current standard at the time. Similar curvature occurred in the present

study, but our measurements are valid because the curvature tolerances were relaxed in the updated ASTM E 399-83 standard. Although the fracture toughness of the Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel seems low for an austenitic alloy,

in fact it meets expectations for steels of its strength level, on the basis

of the known inverse trend of Kj^ versus Oy [10].

SUMMARY AND CONCLUSIONS

The strength of Fe-1 8Cr-3Ni-1 3Mn-0 . 37N austenitic stainless steel

increases dramatically at low temperatures, owing to high nitrogen content.

At 4 K, where Oy reaches 1540 MPa, linear-elastic fracture occurs in 25-mmthick fatigue-cracked specimens subject to plane strain conditions. In this

paper, valid data (70.2 and 71.0 MPa*m^^^) are reported at 4 K for the

as-received steel of 48-)jm grain size, and the brittle fracture mechanism

involving cleavage-like transgranular facets was examined, using a coarse- grained specimen of the steel prepared for x-ray diffraction. After fracture

in liquid helium, the transgranular facets were identified as {111} planes,

and on this basis it is suggested that the microfailure mechanism of this

steel at 4 K may involve slip-plane decohesion.

REFERENCES

1. A. S. Tetelman and A. J. McEvily, Jr., Fracture of Structural Materials,

John Wiley and Sons, New York (1967) 212.

2. D. A. Wigley, Mechanical Properties of Materials at Low Temperatures,

Plenum Press, New York (1971) 1~325.

3. S. S. Hecker, D. L. Rohr, and D. F. Stein, Brittle fracture in iridium,

Metall. Trans. _9A (1978) 481-487.

4. C. Gandhi and M. F. Ashby, On fracture mechanisms of iridium and criteria for cleavage, Scr. Metall. j_3 ( 1979) 371-379.

5. C. F. Old, Micromechanisms of crack growth in liquid metal environments,

Met. Sci. Aug. -Sept . (1980) 433-440.

6. G. R. Caskey, Jr., Fracture of Fe-Cr-Mn austenitic steel, Report

DP-MS- 78 - 68 , E.I. du Pont de Nemours and Co., Aiken, South Carolina

(1978) 21

7. S. P. Lynch, Cleavage in face-centered cubic metals. Met. Sci. 15 (1981)

463-467.

8. G. G. Garrett and J. F. Knott, Crystallographic fatigue crack growth in

aluminum alloys, Acta Metall. 23 (1975) 841-848.

171
9.

K. R. L. Thompson and J. V. Craig, Fatigue crack growth along cleavage

planes in an aluminum alloy, Metall. Trans. (1970) 1047-1049.

10. 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 Steels, E. W. Collings

and H. W. King, Eds., Metallurgical Society of the AIME , New York (1979)

92-121 .

11. Standard Test Method for Plane-Strain Fracture Toughness of Metallic

Materials, ASTM Designation E 399-83, 1984 Annual Book of ASTM Standards, Section 3, Vol. 03-01, American Society Testing and Materials,

Philadelphia (1984) 519-554.

12. F. W. Schaller and V. F. Zackay, Low temperature embrittlement of

austenitic Fe-Cr-Mn-Ni alloys, Trans. ASM, ( 1959 ) 609.

13- C. M. Hsiao and E. J. Dulis, Effect of interstitial carbon plus nitrogen

and precipitation reactions on the properties of austenitic Cr-Mn-C-N

steels, Trans. ASM, ^ (I960) 855.

14. J. C. Shyne , F. W. Schaller, and V. F. Zackay, The tensile and yield

strength of Cr-Mn-N steels at low temperatures, Trans. ASM, ^ (I960)

848.

15. J. D. Defilippi, K. G. Brickner, and E. M. Gilbert, Ductile to brittle

transition in austenitic chromium-manganese-nitrogen stainless steel,

Trans. Metall. Soc. AIME, 245 (1969) 2141.

16.

Standard Terminology Relating to Fracture Testing, ASTM Designation

E 616-82, 1984 Annual Book of ASTM Standards, Section 3, Vol. 03-01

American Society for Testing and Materials, Philadelphia (1984)

671-684.

172
0)

(U

4-> COo

J-) c(1) 4-J CO3

cc3

>-

c>~i OI C

roI

roIt- 0

OD1 (U

[ij

•a

CD>

•iH 0

CJ0

t-I m0o00

•i-H 4-3 L0

Cio

t-cxc0

x:o0 ^ (Ti ^ (0

<y 0) ^ 3 c oa on 1 -o OC <T* o t, O <TJ a: X cO 03

<D

4-) t, ^ m mo O < ^ m c\j 3 ' O <i-. <D O

CCco

4J

03 ^ MO ^

to ^ LTi C ^O

rHuX

toc

<D

t. 4J ' 0) 03 mO t—

CL CT^ T~

0) S GO

4J

w

03£

4-> X

COCO

03 4J ^ O

O

CO 03

O

CL ^ LTV •o s:

/—

03

>-t

0)3

4^

03

t. ^

o> i*:

m ^

a>-' <a^ E C\J 03 0

r—

0H

xc;

4-3 000

4-3 0O

•iH

4-3 C0

4-3 03

03

oooIcS

no1 •rH 2

CO1i- O

COI0

Cij

"O0>000

t-1 00

i.o

Ci-4

03

4-3 0

T3000C

x:bO3o

4-3 0

t-3

4-3 O0

tCxj

CM0I—

X30

Ef\j

'~E

03 CM o O CL • • M S O

bC tC\J • >>

CO

O

•o CO \

0) 03O

t,

C

•-I ^ 3 O ^

O’m E CM

0)

X • E • • cc 4J CM ' iT\ in o

Jj

03 <y

cc a.

•o

Xm

CO 03 o o O E • • J OuX4-> bOC

03 0) > rH

CM

03

O CM

f-H 03 3 m

m

0) £_ >v X O CC o o X

-U

tcc

03 0^ >-H bO LTl o

03 bm

L.

O mO

03 03 E • > L. E m mO < O 03 ^ CM CM C

03E * ir> o X CM o O 4-> ^ v£> <D -O E • Q. S o O

CO 3 3 —

m LO

CO

C CO

03 03 E C o ir» o CM O O ^

03 -H E • o. s: E m

m

CO ^ CD CM CM c

x:to30a

x:4^1 4-> x: o bO

x: L. fH O 03 > 03 4J ca 0) L. o >. X 4-> 2 ^ o (0

Specimen

number

CM

173
DEFLECTION. S

Figure 1 . Load-versus-def lection test record at 4 K for chevron-notched

specimen of Fe-1 8Cr-3Ni-1 3Mn-0 . 37N steel in the as-received

condition

174
Figure 2. Macroscopic fracture surface

appearance of chevron-notched

Fe- 18Cr- 3Ni- L3Mn-0 . 37N steel

after testing at 4 K:

a) fatigue zone, T = 76 K,

b) fatigue zone, T = 4 K,

c) overload failure zone,

T = 4 K, and

d) final fracture after re- moval from the cryostat,

T > 4 K.

175
Figure 3. Crystallographic facets on the fatigue failure zone of coarse- grained Fe- 18Cr- 3Ni- 13Mn-0 . 37N steel fractured at 4 K.

176
Figure 4. Crystallographic facets on the overload fracture zone of coarsegrained Fe-18Cr-3Ni-13Mn-0. 37N steel fractured at 4 K.

177
178
Figure 6. Slip-Line traces on an overload zone facet ( facet a of Fig. 4)

179

. • >

NOTCH TENSILE MEASUREMENTS AND FRACTURE TOUGHNESS

CORRELATIONS FOR AUSTENITIC STAINLESS STEELS*

R. P. Reed, R. L. Tobler, and D. T. Read

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

Thirty-two alloys were included in a study of conventional

notch tensile testing as a method of fracture toughness characterization for austenitic stainless steels at liquid helium

temperature, 4 K. For the same austenitic stainless steels,

tensile and J-integral fracture toughness [Kj^(j)] measurements

have also been conducted. For these materials the notch tensile

strength generally increases with yield strength (Oy), and

the 01^73/Oy ratios are typically much greater than 1 . 0 . Correlations between Oj^^S’ ^Ic^*^^’ °y assessed. The best data

fit was found between the ratio, Ofjxs^^Ic ^ toughness.

Unfortunately, from this relation there is not uniqueness

of from Oj^-ps* Therefore at this time it is not considered

practical to obtain estimates of from notch tensile tests for

austenitic steels at 4 K. However, one may compare the J-integral

fracture toughness and cylindrical bar notch tensile measurements. There are three regions: ( 1 ) linear elastic Coj>j'p5

increases as Kj^(J) increases]; (2) elastic-plastic

[0fj'p5

is

essentially independent of Kp^(J)]; ( 3 ) plastic *^screases as Kp^(J) increases]. The elastic-plastic (transition) region is

associated with a plastic zone that extends completely through

the notched cross-sectional area.

Key words: austenitic stainless steels; cryogenic properties of

materials; fracture toughness; mechanical’ testing of materials;

notch tensile tests.

INTRODUCTION

For austenitic stainless steels used in structural components of superconducting magnets, elastic-plastic fracture toughness evaluations at K are usually required for qualification of base metals and welds. Two acceptable

methods of quantitative fracture toughness measurement under elastic-plastic

conditions are the J-integral and the crack-tip-opening displacement (CTOD)

tests; both require large specimens with fatigue precracking to provide a sharp crack front. The complexity of measurement methodologies and difficulties in interpretation of test data prevent many laboratories from adopting

these tests.

^Contribution of NBS, not subject to copyright. Intended for publication

in Advances in Cryogenic Engineering--Materials , volume 32 .

181
Impact tests are less expensive. Unfortunately, they provide only a qualitative measure of toughness and are unsuitable at 4 K because adiabatic

heating occurs during straining prior to fracture. Adiabatic temperature

rises of up to 150 K have occurred^ and are possible because of the very low

specific heat of metals at 4 K and the high strain rate from impact loading.

This paper assesses the use of the notch tensile test to estimate the

elastic-plastic fracture toughness of austenitic stainless steels. Notch

tensile tests were performed on austenitic steels at low temperatures^”^ long

before quantitative elastic-plastic fracture toughness methods became

available. Subsequently, they have been used for direct measurement of the

plane-strain fracture toughness of aluminum and steel alloys. Specimen

machining costs less than compact tensile specimens and the test methodology

is simple, requiring no strain gages or displacement measurements.

The ratio of notch tensile strength unnotched tensile yield

strength (a ) is accepted as a qualitative indicator of fracture toughness:

ratios greater than 1.0 indicate tough behavior (ability to deform plastically in the presence of stress concentration). A simplified stress concen- tration factor, , is given by

= ( d / 2 r )^^2 (1 )

where d is the width between the notches and r is the notch radius. Typical

values used with cylindrical or flat specimens range from 4 to 7 for

steels^ and from 16 to 23 for aluminum alloys.

Kaufman et al.'^ summarized an extensive room temperature notch tensile

measurement program on aluminum cylindrical specimens. The alloys (agehardened 2024, 2124, 7075, 7475) generally exhibited linear-elastic fracture

behavior. The plane-strain fracture toughness (Kj^) initially increased with

increasing However, at higher toughness levels, tended to be less

dependent on They found that the ratio ^ss approximately

linearly dependent on Kj^ at low ratios (-0.85 to 1.25). At higher values

(-1.25 to 1.45), the ratio tends toward less dependency on Kj^.

All previous notch tensile tests of alloys exhibiting elastic-plastic

fracture behavior, such as austenitic steels at 4 K, have been used for

qualitative toughness evaluation, and until now there appears to have been no attempt to correlate notch tensile measurements with measurements. In

this study, thirty-two austenitic stainless steels were tested at 4 K, and

the relationships between 0j^-p 3

. Oy, and were determined from the previously published 4-K tensile and J-integral fracture toughness data for these

alloys.

EXPERIMENTAL PROCEDURES

The compositions and metallurgical variables for the alloys tested are given in other papers (see Table 1). These alloys include laboratory heats

as well as mill heats. All alloys were completely austenitic (prior to

182
testing) and were tested in the annealed condition. The materials were supplied in the form of 25-mm-thick plates, except for the N-60 and AISI 216

steels, which were in the form of 76- and 92-mm-diameter bars, respectively.

The tensile, notch tensile, and compact-tension (fracture-toughness)

specimen geometries are shown in Fig. 1. The tensile and notch tensile

specimen axes were oriented transverse to the longitudinal bar or plate

directions. The compact specimens were oriented with the notch plane normal

to the transverse (plate) or radial (bar) directions, and crack propagation

was along the longitudinal plate or bar directions. Thus, for each specimen

type the fracture plane was similarly oriented with respect to microstructure .

Notch tensile tests were conducted at ^ K using a crosshead rate of 8.3 x

10"'^ mm/s on two specimens per alloy. A 0.127-mm notch-tip radius was specified for each specimen. Notch radii, measured after grinding were

varied from 0.125 to 0.135 mm. The stress concentration factor, , from

Eq. 1 is M. 3 to 4.5. During testing, plots of load versus time were re- corded, and 0 |^j'p 3 was calculated from the maximum load divided by the original

notched cross-sectional area.

The tensile properties used in this paper for analysis were previously

measured at a plastic strain rate of approximately 1.5 x 10"^. At 4 K the

yield and ultimate strength inaccuracies are about ± 2 %, strain measurement

inaccuracies are about ± and estimates of material variability for yield

and ultimate strengths are about ± 5^. Notch tensile strength measurements

reflect inaccuracies and material variabilities similar to those for the

tensile strength measurements.

In most cases, the 4-K fracture-toughness data referred to in this paper

represent estimates based on J-integral tests. For several high-strength

steels (N-50, 18/18, N-40, N-60, and AISI 216), the data represent direct

measurements of Kj^. The fracture test procedures are discussed extensively

in references 18 and 20.

Specimen strain was initially monitored by using load-time chart traces

and converting to crosshead travel, remembering to correct for load-train

deflection. This procedure is thought to be sufficiently accurate except

when load drops occur during plastic deformation at the notch tip prior to

fracture. Most of the austenitic steels were tough enough for load drops to occur. Estimation of notch strain during such load drops was not possible.

Therefore, a strain-gage extensometer was recently adapted to fit the notch

tensile specimen and used to measure notch strain to fracture for alloys

N-40, N-60, and 210.

RESULTS

The notch-tensile data for each austenitic stainless steel are listed in

Table 1. Also given are tensile yield strength (Oy), ultimate tensile

strength (a^), fracture toughness, and the notched-to-unnotched tensile

strength ratio. In most cases the data represent averages of at least two

measurements taken at 4 K.

183
All th© st6©ls t©st©d in this study hav© a opjTs/ ratio ranging from

1.07 to 4.15, with most valu©s w©ll abov© 1.0. Th©r©ror©, all th© ann©al©d

aust©nitic stainl©ss st©©ls ar© r©lativ©ly tough by th© conv©ntional notch

tonsil© tost critorion.

Usually as th© tonsil© yiold strongth of austonitic stainloss stools

incroasos, thoir notch tonsil© strongth also incroasos, as shown in

Fig. 2. This contrasts with th© accoptod invors© rotation botwoon Kj^(J) and

Oy, shown in Fig. 3 for th© austonitic stools includod in this study. In

Fig. 2 thor© ar© som© glaring ©xcoptions to th© dopondonco: In

particular, th© strong 18/18 alloy has a yiold strongth of 1780 MPa, and th©

vory tough 413 alloy has a notch tonsil© strongth of 2920 MPa.

Th© corrolation botwoon th© notch tonsil© strongth and th© J-intogral

fractur© toughnoss at 4 K is not obvious (so© Fig. 4). Th© 413 and 4l6

alloys, both of which hav© vory high valuos of Oj^j-pg, fall outsid© any tronds,

howovor

W© found ©xcollont corrolation botwoon th© log of th© ratio dj^j-pg /Kp^(J)

and Kj^(J) (so© Fig. 5). Hor© again, th© alloys 413 and 4l6 doviat© from th©

othor alloys, but thoir doviation is much mor© modost than that shown in

Fig. 4. Th© host fit ©quation of data in Fig. 5 is

Oj^TS = 44Kp^(J) ©xp -6.54 x lO'^Kp^CJ) (2)

whor© Oj^Yg has units of MPa and Kjq(J) has units of MPa/m. Equation 2, also

plotted in Fig. 4, adequately depicts most of th© data. Unfortunately,

Kic(J) is not unique for given d|^'p 3 valuos.

Th© ratio dj^-ps^'^y directly proportional to Kj^^CJ), as shown in Fig. 6.

Hor© Eq. 2 is also includod and adequately represents th© data. Sine© all

those steels. Including th© high-strength alloys, hav© dj^^^g/Oy ratios greater

than 1.0, they ar© all classified as ductile and tough in th© macroscopic

sense. On th© microscopic scale, howovor, som© of th© alloys showed significant portions of brittleness. Th© brittle micromochanisms include slip-band

docohosion, twin boundary parting, and intergranular failure, all of which

produce smooth reflective facets on th© fractur© surfaces of th© tensile,

notch tensile, and fractur© toughness test specimens at 4 K. Th© proportion

of ductile and brittle mechanisms varies with metallurgical factors, such as composition and strength.

DISCUSSION

Because multiple values of fracture toughness correspond to single notch

tensile strength values (Fig. 4) and because the ratio of notch tensile

strength to tensile yield strength is rather insensitive to the value of

fracture toughness (Fig. 6), measurement of the notch tensile strength does

not provide quantitative fracture toughness information.

184
The results plotted in Figs. 2-6 are interpreted further: From Fig. 4 it

is evident that, under linear elastic fracture mechanics conditions, there is an approximate correlation between and Kj^(J) following Eq. 2, when

Kj^(j) < 100 MPa/m. This same trend of direct proportionality between Kj^

and was demonstrated by linear elastic notch tensile measurements of

aluminum alloys by Kaufman et al . ^ At high toughness levels [Kj^(j) > 200

MPa/m, corresponding to lower yield-strength steels], decreases with

increasing Kj^(J). The lower yield strength alloys are ductile, and under

the notch tensile loading conditions of our specimens, they experienced

significant plastic deformation prior to fracture. In the intermediate

toughness range of austenitic stainless steels at 4 K [100 MPa/m ^ Kj^(j)

^ 200 MPa/m], Oj^^c is approximately independent of Kj^CJ), and there is

transition from linear elastic to fully plastic fracture behavior. The

tendency toward transition and independence of Oj^j’p 3 on was also demonstrated by Kaufman et al . ^ ^ for aluminum alloys at room temperature. Ductile

alloys were not included in their study; therefore, they did not detect the

entire transition range.

One can approximate the transition by considering the plastic zone size

? 1 (rp) under plane strain conditions:

Tp = (1/3tt) (K/Oy)2 (3)

where K is the stress intensity factor and r is the distance ahead of the

crack tip to the edge of the plastic zone. To achieve a plastic zone throughout the cross section, 2rp must be at least equivalent to the diameter

of the notched specimen (5.1 mm). Then

K/Oy = [(5.1 mm/2)(3TT)]''/2 (4)

Assuming that such conditions are reached when the stress intensity

factor reaches Kj^(J), then from Eq. 4:

Oy s 7Kjj^(J) (metric units) (5)

These assumptions may be checked by referral to Figs. 2 through 4. When

Kj^(J) is 150 MPa/m, is 2430 MPa at the approximate midpoint of the

transition from linear elastic to fully plastic behavior (Fig. 4). A yield

strength of about 1150 MPa corresponds to these associated Kj^(J) and

values (Figs. 2 and 3)- Or, o = 7.7 Kj^^(J), close to the prediction of

Eq. 5. The modest disparity of the ratios implies that plane strain conditions do not quite exist with this specimen configuration: use of plane

stress conditions [r = 1 /tt(K/o„)^] would considerably underestimate the

ratio Oy/KjQ.

In cylindrical notch tensile specimens with K^. = 4.5, the transition from

linear elastic to fully plastic behavior seems to occur when the plastic zone extends throughout the specimen cross section under the notch. Under fully

plastic conditions, the notch tensile strength is associated exclusively with

material strength, and hence, there is strong correlation with yield strength

To extend the range of one-to-one correlation of Oj^,pg with Kj^ or Kj^(J), the

185
stress concentration factor at the notch tip must be increased, but decreasing the notch radius requires costly machining or grinding. Increasing

specimen diameter precludes the use of the test for plate thicknesses of

12 mm or less and also increases the required cryostat load capacity above

that which is normally available.

A possible improvement over the conventional notch tensile test is

another technique, which uses an instrumented notch tensile specimen to

obtain crack opening displacement (COD) data. COD measurements for notched

specimens might be converted to J-integral data for correlation with conventional J-integral fracture toughness measurements. Accordingly, we analyzed

the chart recordings of load versus time to estimate the displacement of each

notch tensile test. Unfortunately, the correlation between estimated and

measured extension was poor, primarily because of the numerous load drops

that occur during the tests at M K. We are now measuring the notch opening

displacement directly with clamp-on strain-gage extensometers, and further

analysis of notch tensile COD measurements awaits new data from this approach.

CONCLUSIONS

At present there is no advantage in using notch tensile measurements of

austenitic stainless steels to obtain quantitative fracture toughness

information.

J-lntegral fracture toughness, compact-tension specimens, and cylindrical-bar notch tensile measurements have been compared. The notch-tensileversus-fracture toughness correlation shows three regions:

1. Linear elastic, where increases as Kj^(J) increases

2. Elastic-plastic, where is essentially independent of Kj^CJ)

3. Plastic, where is directly related to Oy and inversely related

to Kj^(J) [since Kj^(J) is inversely related to Oy]

The transition region (elastic-plastic) is associated with a plastic zone

that extends completely through the notched cross-sectional area.

ACKNOWLEDGMENTS

This research was sponsored by the Department of Energy, Office of Fusion

Energy, Dr. V. Der, Project Monitor. The test materials include developmental heats prepared by the research laboratories of U.S. Steel (alloys 2-9),

Armco Steel (alloys 70-78), and E. 0. Paton Institute of Electrowelding

(alloys 739-'416). The careful work of J. Gerlitz and R. Walsh of NBS in

performing the notch tensile tests is very much appreciated.

186
REFERENCES

1. W. G. Dobson and D. L. Johnson, in: "Advances in Cryogenic Engineering

Materials," vol. 30, A. F. Clark and R. P. Reed, eds. Plenum Press,

New York (198^), pp. 185-192.

2. D. T. Read and R. P. Reed, in: "Advances in Cryogenic Engineering

Materials," vol. 26, Plenum Press, New York (1980), pp. 91-101.

3. K. Ishikawa, K. Hiraga, T. Ogata, and K. Nagai , Cryog. Eng . (Tokyo)

18(1 ):2-9(1983).

U. C. J. Guntner and R. P. Reed, Trans. Am. Soc. Met . 55: 399-^41

( 1962 ).

5. A. Randak , W. Wessling, H. E. Bock, H. Steinmaurer, and L. Faust,

Stahl Eisen , 91:1255-1269 (1971).

6. A. Hurlich and W. G. Scheck, in: "Advances in the Technology of

Stainless Steels and Related Alloys," ASTM STP No. 369, American

Society for Testing and Materials, Philadelphia (1963)f PP. 127-143.

7. G. R. Irwin, Report 4763, Naval Research Laboratories, Washington,

D. C. (1956).

8. J. G. Kaufman and E. W. Johnson, in: "Advances in Cryogenic Engineering,"

vol. 6, Plenum Press, New York (i960), pp. 637-649.

9. C. M. Carmen, D. F. Armiento, and H. Markus, J. Basic Eng. 87:904-916

(1965).

10. R. P. Wei and F. J. Lauta, Mater. Res. Stand. 5:305-310 (1965).

11. W. F. Brown, Jr. and J. E. Srawley, "Plane Strain Crack Toughness

Testing of High Strength Metallic Materials," ASTM STP 410,

American Society for Testing and Materials, Philadelphia (1966).

12. J. G. Kaufman, G.-T. Sha, R. F. Kohm, and R. J. Bucci, in: "Cracks and

Fatigue," ASTM STP 601, American Society for Testing and Materials, Philadelphia (1976), pp. 169-190.

13. P. T. Purtscher and R. P. Reed, in: "Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures - VIII," R. P. Reed,

ed., NBSIR 85-3025, National Bureau of Standards, Boulder, Colorado

(1985), pp. 123-144.

14. R. L. Tobler, D. T. Read, and R. P. Reed, "Fracture Mechanics:

Thirteenth Conference," ASTM STP 743, R. Roberts, ed., American

Society for Testing and Materials, Philadelphia (1981), pp.

250- 268 . 15. R. L. Tobler and R. P. Reed, in: "Advances in Cryogenic Engineering--

Materials," vol. 28, R. P. Reed and A. F. Clark, eds; Plenum

Press, New York (1982), pp. 83-92.

16. D. T. Read and R. P. Reed, Cryogenics 21:415-417 (1981).

17. D. T. Read and R. P. Reed, in: "The Metal Science of Stainless Steels,"

E. W. Collings and H. W. King, eds.; Metallurgical Society of the

AIME, New York (1979), pp. 92-121.

18. R. L. Tobler, "Elastic-Plastic Fracture, Second Symposium; Fracture

Resistance Curves and Engineering Applications," vol. II, ASTM STP

803, C. F. Shih and J. P. Gudas, eds., American Society for

Testing and Materials, Philadelphia (1983), pp. 11-763-11-776.

187
19. R. L. Tobler, R. P. Reed, and P. T. Purtscher, in: "Materials Studies for

Magnetic Fusion Energy Applications at Low Temperatures —VIII,"

R. P. Reed, ed., NBSIR 85-3025 National Bureau of Standards,

Boulder, Colorado (1985), pp. 151-165.

20. D. T. Read and R. L. Tobler, in: "Advances in Cryogenic Engineering

Materials," vol. 28, R. P. Reed and A. F. Clark, eds.; Plenum

Press, New York (1982), pp. 17-28.

21. J. W. Hutchinson, Trans. ASME 50:1042-1051 (1983).

Table 1. Mechanical Properties of Austenitic Stainless Steels at 4 K.

Specimen

Number

°NTS

(MPa)

°u (MPa)

739 1910 1480 740 2190 1370

741 2340 1420

414 2538 1652 520 1377 1220 413 2920 1580

415 2040 1390

416 2690 1630

2 1700 1550

3 1870 1530

4 2030 1570

5 2120 1700

6 2230 1630

7 2460 1640

8 2480 1740

9 2390 1700

70 2060 1620

71 2030 1580

72 2180 1510

73 2170 1810

74 2300 1520

75 2340 1670

76 2340 1580

77 2250 1650

78 2400 1570

304L 1880 1680 304LN 2080 1 660

316 1880 1300 N-50 2330 1890

310 1880 1260 18/18 1910 2050 N-40 2520 1660 N-60 1540 1350 216 2280 1820

Oy

(MPa)

°NTS^°y Kic(J)

(MPa/m)

460 4.2 273 720 3.0 244 870 2.7 254 950 2.7 143 960 1 .4 87 1020 2.9 204 1040 2.0 75 1160 2.3 238

440 3.9 —

530 3.5 337 740 2.7 266 880 2.4 230

900 2.5 235 1190 2.1 124 1180 2.1 137 1290 1.9 124

660 3.1 192 720 2.8 215 760 2.9 243 880 2.5 117 960 2.4 121 990 2.4 149 1050 2.2 162 860 2.6 206 900 2.7 205

610 3.1 310 790 2.6 214 710 2.6 268

1450 1 .6 106^

640 2.9 285 1780 1 . 1 75a

1200 2.

136® 990 1.6 91®

1400 1.6 107®

Reference for Material

Characterization

13

13

1313

1313

1313

11) 11) 11) 11) 11) 11) 11) 11)

15

1515

1515

1515

1515

1616

1617

18

19

19

19

19

^Data for these steels represent direct measurements; all other data

represent estimates of from J-integral tests.

188
12.7 mm

(O.SOin)

Tensile

Notch Tensile

Fig. 1. Tensile, notch tensile, and compact-tension specimens

used in mechanical property measurements.

189
Fig. 2. Notch tensile strength versus tensile yield strength

of annealed austenitic stainless steels at ^ K.

Fig* 3* Tensile yield strength versus fracture toughness of austenitic

stainless steels at ^ K. Solid line is the trend line reported

earlier for austenitic stainless steels at 4

190
Fig. Notch tensile strength versus fracture toughness of austenitic

stainless steels at 4 K. Solid line is Eq. 2.

Fracture Toughness, Kic(J), MPa >/nT

Fig. 5. Ratio of notch tensile strength to fracture

toughness plotted against fracture toughness

of austenitic stainless steels at 4 K.

191
Fracture Toughness , Kic(J), MPa v/ttF

Fig. 6. Ratio of notch tensile strength to tensile

yield strength versus fracture toughness of

austenitic stainless steels at 4 K.

192


Elastic constants and instability in f ace-centered-cubic metals

H. M. Ledbetter

Fracture and Deformation Division, National Bureau of Standards,

Boulder, Colorado 80303, USA

For face-centered-cubic crystals, the single-crystal elastic constants, the

C..*s, reveal not only the well-known tendencies toward mechanical

instability, but also another instability, which we call "chemical". Besides

considering the fee elements, we consider also Fe-Ni alloys and Fe-Cr-Ni

stainless steels. We suggest an interatomic-force-constant explanation of

this instability.

Key words: chemical instability; elastic constants; face-centered-cubic

metals; interatomic force constants; iron-nickel alloys; mechanical

instability; mechanical properties; phase transition; stainless steels.

Submitted to Phase Transitions

193
Crystal-structure instability interests both theorists concerned with

solid-state cohesion and materials engineers concerned with practical applications of materials. On one hand, we seek to avoid instability. For example,

the well-known low-temperature structural transformation in austenitic stainless steels produces a second phase that deteriorates the matrix properties.

On another hand, the martensitic transformation in ferritic steels produces

desirable high-strength properties. Also, a leading superconductivity

specialist remarked recently that to produce higher-T^ materials he would

"look for systems that should exist, but won't - unless one can persuade

them." In other words, make unstable materials metastable. The better we

understand relationships between physical properties and instabilities, the

higher our proficiency to control their occurrence, harmful or helpful.

For f ace-centered-cubic (fee) metals this note describes a correlation

between single-crystal elastic constants and lattice instability, the tendency

to transform to either another crystal structure or to another state of order.

This is not the well-known mechanical instability discussed by Born and

Huang [1], but a "chemical" instability that manifests itself in the elastic

constants. By chemical, we mean related to basic interatomic forces. Recently,

Nakanishi [2] reviewed thoroughly the elastic-constant/lattice-instability

relationships, especially for martensitic phase transformations.

In 1976, Ledbetter and Moment [3] published Fig. 1, a diagram used to

describe the unusual elastic behavior of fee Pu. This figure contains

considerable information. For the usual three Independent cubic-symmetry

Voigt elastic stiffnesses— plots two dimensionless ratios:

y

= ^ 12^^11 ^~ ^44^^11' Cauchy relationship, ^^2~^44’ ^ straight

line from (0,0) to (1,1). The point (0.5, 0.5) identifies the prediction of

an fee nearest-neighbor-only central-force model. Most fee elements occur in

194
the upper half of the diagram and mostly in the left half. The boundaries x=0

and y=l correspond to mechanical-stability conditions: ^ 44

^^ (C^

The third mechanical-stability condition, (C^ ^^+2C

^^ 2

) y>-0.5, does not

appear in the diagram; but this is of no consequence because no fee elements

exhibit negative values. Straight negative-slope lines emanating from

(0,1) correspond to various values of Zener’s anisotropy ratio

A =

All points in the diagram’s field correspond to mechanically stable crystal

structures

That Th and Pu occur to the right of x=0.5 provides a crucial basis for

this note. All elements to the left of x=0.5 are stable; they exhibit a

single crystal structure between T=0 and the melting point. Both Th and Pu

are unstable. At high temperatures, Th transforms to a body-centered-cubic

crystal structure. Plutonium is notoriously unstable. Between ambient and

melting temperatures it exhibits six allotropes: a (monoclinic), B

(monoclinic), y (orthorhombic), 6 (fee), 6 ’ (tetragonal), e (bcc) . (One can

conjecture that lower temperatures may reveal further allotropes, perhaps

triclinic.) Thus, despite high values of x, representing high elastic

rigidity with respect to ( 100) [ 001 ]-type deformation, both Th and, especially,

Pu are unstable. It may be significant that elements on the diagram’s left

tend to be dominated by s-p electrons in their cohesive properties. In Th and

Pu the d and f electrons enter strongly into cohesion.

The tendency of Th and Pu toward chem.ical instability, despite their

mechanical stability, encourages one to examine other systems with high x,

especially alloys.

Figure 2 shows the variation of x with Ni content for Fe-Ni alloys.

195
Points for pure fee iron were determined either by extrapolations or by

theory. We see that x is maximum near 30 pereent Ni and reaehes a relatively

high value, 0.8. Of eourse, this eomposition region is well known for its

instability and the ineipient fee-bee transformation [4]. That x deereases

before the struetural transformation oeeurs suggests a possible magnetie

transition that stabilizes the fee strueture for a while. Magnetie-property

measurements between 25 and 35 pereent Ni would be very useful in

understanding this unusual pretransformation behavior.

Figure 3 shows a y-x diagram for austenitie (fee) stainless steels, whieh

eonsist mainly of Fe, Cr, Ni, and Mn. These alloys are well known for their

instability. At low temperatures they undergo magnetie [5] and/or struetural

(to bee) [6] transformations. Plastle deformation of these alloys induees

transformations to either bee or eph (elose-paeked-hexagonal) struetures [7].

This diagram Ineludes points for fee Fe, Co, and Ni. Iron’s allotropy is well

known: bee at low and high temperatures, fee between [8]. Cobalt, fee at

high temperatures transforms to eph at 603 K. Elastie eonstants of

hypothetieal fee Mn and hypothetieal fee Cr remain, apparently, unestimated.

(Reeently, Moruzzi et al. [9] estimated the bulk modulus of fee Mn to be

2.91 GPa, 95 pereent of that for bee Fe. The bulk modulus equals

(Cj^j^ + Thus, unless the C^^ of fee Mn behaves abnormally, its

elastie eonstants may resemble Fe’s.)

A possible explanation of these instabilities lies in the foree eonstants,

whieh relate more direetly to forees between pairs of atoms in solids. Many

f oree-eonstant models exist [10]. For fee lattiees, Leibfried and Breuer [11]

eonsider a three-foree-eonstant model summarized in Fig. 4. The three parameters

eonsist of a longitudinal spring, fj^, and two different transverse springs,

and f^» eorresponding to bending along [001] and [110], respeetively . The

196
coupling matrix for this model is

-<j) ij

a 3 0

3 a 0

0 0 Y

( 2 )

Physically, negative denotes the force in the i direction on the atom at

the origin when the atom at d is displaced a unit length in direction j . If

liii the displacement vector corresponds to an eigenvector, then corresponds

X Xr to 3 Spring constHnt* ny syuuuG try ^ ~ t 22

snd ^ “

y 2]^ ~

~ Components such as vanish because force and

displacement are perpendicular, thus no coupling. Diagonalization of (f)

gives three eigenvalues:

ij

f^ = a + 3 (3)

f2 = Y (4)

f

3 a - 3 (5)

Leibfried and Breuer relate the f’s to the six eigenvalues of the 6x6 Voigt

C, . matrix:

ij 12 4 ff = (4C + 2C + 3C) 12 4 ^2 " l2

- 2C + 30

*3' t

where a denotes cubic unit-cell size.

From the cubic-symmetry invariants.

( 6 )

(7)

( 8 )

2C

4C

1c

3C

5C

Cii + 2C^2

^ U"^12

C = 2C

44

(9)

( 10 )

( 11 )

197
the f’s relate to the Voigt C^^’s:

h ' f

^ ‘^12'" '^ 44 ’ (12)

£2 =f (-C

11 * 20

^4

) (13)

*3 ' 4

^*^11 ®12 *^44^ (14)

and vice versa:

=11 = i

" ^£

3

) (15)

'=12 = i

- 2^2 - (16)

'=44 ' i

^ . £

3

) (17)

More-interesting physical combinations are:

<Sl-S2

) - I

" ^£3 * 5£3) (17)

3B = (Cjj£2C^3> =1 (4£3 - 4£j -4£3) (18)

<S2-=44) = i

<-«2 - «3> (19)

A=2C^^/(C^^-C^

2

> = (2f^+4f2+2f3)/(f^+2f2+5f3) ( 20)

( 21 )

is resistance to shear on a [ 110 ]-type plane in a [ 110 ]-type

direction. Since this deformation involves both bond stretching (and shortening) and bond bending, not surprisingly it includes f

2

> and f^.

is three times the bulk modulus (reciprocal compressibility). Since uniform

dilatation changes bond lengths but not bond angles, it may seem surprising

that the bulk modulus B depends on f

2 and f^ in addition to f^. This occurs

because the spring constants f

2 and f^ relate also to many-body forces.

(Recall that the third-order perturbation-theory calculation of Axilrod and

Teller [12] for Interactions between triplets of atoms contained three interatomic distances

^ 23 ’ ^13— three included angles— Y

2 —with

being the angle between r

^^2 ^13’^ ^12~^44 Cauchy (noncentral198
force) discrepancy for cubic crystals. Thus, if accidently f^^f^j then the

material will appear to have central forces by the familiar Cauchy criterion

C,^ = C,,. Thus, this criterion is necessary but not sufficient. The Zener

12 44

anisotropy ratio. A, depends on all three force constants. For vanishing

many-body forces = f^ = 0), A = 2. Thus, departures of A from this value

also indicate the contribution of many-body forces. In summary, vanishing

many-body forces imply that =

20^^^ ” ^^44 “ > where C* = ’

Finally, elastic isotropy demands that C’ = or that - ^^2

~ ^^44 ~

In terms of force constants, isotropy demands that f^^ = Sf^ “ ^^

2

’ ^ condition

that arises only accidently.

Table 1 contains single-crystal elastic constants and force constants for

fee elements and selected alloys. Except for Th and Pu, all fee elements

exhibit a negative f- 2' Both Fe-Ni and Fe-Cr-Ni stainless steels also exhibit

a negative

Consider now a typical metal—copper, where C^^=1.696, and

C, =0.754*10^^N/m^. Thus, f./a=0.9185, f „/a=-0. 0470, and f„/a=-0.0705 in the

44 i 2 J same units. Table 2 shows how the three force constants contribute to various

elastic constants and to the elastic anisotropy, A. For both A and

we made the very rough approximation that both ^3 small compared

with fj^. Except for the Cauchy discrepancy, *^^ 2~^

44 ’ every

elastic constant. As expected, many-body effects show most strongly in

also strongly in C', A, and ^

12 ^^

W

bulk modulus is least

sensitive to many-body terms. In all cases except the force constant

contributes less than the f^ force constant; bending out of the ( 100 ) plane

contributes less than bending in the plane. Negative and f^ values

apparently imply instabilities with respect to bending. But one must remember

199
that the bending springs represent many-body, not two-body, interactions.

Thus, they do not represent simple local effects but, rather, complicated

"environmental", long-range effects. Even if all springs are longitudinal and

positive, a negative transverse spring can arise quite naturally. Table 2

contains results also for stainless steel. We call this instability "chemical"

for two reasons. First, we want to distinguish it from the usual Born-Huang

mechanical instability. This does not preclude an eventual mechanical

explanation: volume effects, phonon instabilities, higher-order elastic

constants, et cetera. Second, we feel the eventual explanation must relate

closely to the molecular orbitals, an approach used mainly by chemists [13]

but adopted recently by some physicists [14]. Examination of existing singlecrystal elastic constants reveals that no other types of materials—ionic,

covalent, intermetallic compounds (Nb^Sn, CuZn) —occur in this region of the

y-x elastic-constant diagram. Interestingly, three fee van der Waals solids

Ar, Kr, Xe—occur near Th. The instability of these solids is also well

known [15]. Another class of materials, the alkali metals (Li, Na, K, Rb, Cs)

would also be expected to occur in this Instability region [16]. Their fee

elastic constants remain unmeasured, but they were calculated recently by a

pseudopotential method [17]. From these results, all five alkali metals

cluster in a relatively small region of the y-x diagram. For fee Na, for

example, C. , = 0.0818, = 0.0651, C, , = 0. 0613* 10^ ^N/m^. Thus, x = 0.941,

11 12 44

y

= 0.796, well into the instability region, with an x value exceeding even

that of Pu. This instability of the fee alkali metals suggests that d-type

wave functions may not be necessary for instability; there is general acceptance that the cohesive properties of alkali metals are determined completely

by s-type (spherical symmetry) wave functions.

200
We now summarize. Many previous studies recognize that mechanical

lattice stability requires the nonvanishing of three elastic constants:

(Cii

- evidence for incipient lattice instability.

For fee metals, the present study suggests a new incipient-instability

criterion: x = ^ testable cases, where we know the C _

,

the criterion holds. All stable fee metals—Al, Au, Pb et cetera— exhibit

C

12

/C

11

ratios between 0.2 and 0.4. By invoking an interatomic-force-constant

model, we see that corresponds to f = 0, where f

2 denotes a

transverse spring constant corresponding to a force and a displacement along a

[001]-type direction.

Acknowledgment

This study arose from research sponsored by the U.S. Department of

Energy, Office of Fusion Energy.

References

1. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford,

London, 1954), pp. 140-154.

2. N. Nakanishi, Elastic constants as they relate to lattice properties and

martensite formation, in Progress in Materials Science, Volume 24

(Pergamon, London, 1980), pp. 143-265.

3. H. M. Ledbetter and R. L. Moment, Elastic properties of f ace-centeredcubic plutonium, Acta Metall. 891-899 (1976).

4. L. Kaufman and M. Cohen, Thermodynamics and kinetics of martensitic

transformations, in Progress in Metal Physics, Volume 7 (Pergamon,

London, 1958), pp. 165-246.

5. E. W. Collings and S. C. Hart, Low-temperature magnetic susceptibility

and magnetization studies of some commercial austenitic stainless steels,

Cryogenics 521-530 (1979).

6. C. M. Wayman, The crystallography of martensitic transformations in

alloys of iron, in Advances in Materials Research (Interscience, New

York, 1968), pp. 147-304, especially pp. 280-292.

201
7. R. P. Reed, Martensitic phase transformations, in Materials at Low

Temperatures (Amer. Soc. Met., Metals Park, 1983), p. 295.

8. F. Seitz, The Modern Theory of Solids (McGraw-Hill, New York, 1940),

pp. 487-488.

9. V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated Electronic

Properties of Metals (Pergamon, New York, 1978), p. 80.

10. R. A. Moore and J. C. Upadhyaya, Comparison of the major force-constant

models for cubic systems using a self-consistency condition. Can. J.

Phys. 2053-2065 (1979).

11. G. Leibfried and N. Breuer, Point Defects in Metals I (Springer-Verlag,

Berlin, 1978), p. 42.

12. B. M. Axilrod and E. Teller, J. Chem. Phys. JJ_, 299-300 (1943).

13. C. A. Coulson, Valence (Oxford, London, 1963).

14. W. A. Harrison, Electronic Structure and the Properties of Solids

(Freeman, San Francisco, 1980).

15. M. L. Klein and J. A. Venables (eds.). Rare Gas Solids (Academic, New

York, 1977).

16. G. Grimvall and I. Ebbsjo, Polymorphism in metals, Phys. Scripts 12 , 168-172 (1975).

17. H. M. Ledbetter and T. Suzuki, "Binding energies, elastic constants,

and phase transitions in sodium: a pseudopotential study," to be

published

202
Table

11 2 Monocrystal elastic constants for fee elements. Units are 10 N/m , except X, y, A are dimensionless.

Element Si S2 "44 B C A y X

A1 1.0675 0.6041 0.2834 0.7586 0.2317 1.2231 0.5659 0.2655

Cu 1.6839 1.2142 0.7539 1.3708 0.2349 3.2101 0.7211 0.4477

Au 1.9234 1.6314 0.4195 1.7287 0.1460 2.8733 0.8482 0.2181

Ir 5.800 2.4200 2.5600 3.5467 1.6900 1.5148 0.4172 0.4414

Pb 0.4953 0.4229 0.1490 0.4470 0.0362 4.1160 0.8538 0.3008

Ni 2.5080 1.5000 1.2350 1.8360 0.5040 2.4504 0.5981 0.4924

Pd 2.2710 1.7604 0.7173 1.9306 0.2553 2.8096 0.7752 0.3159

Pt 3.4670 2.5070 0.7650 2.8270 0.4800 1.5938 0.7231 0.2207

Pu 0.3628 0.2673 0.3359 0.2991 0.0478 7.0346 0.7368 0.9259

Rh 4.126 1.935 1.841 2.6653 1.0955 1.6805 0.4690 0.4462

Ag 1.2400 0.9400 0.4650 1.0400 0.1500 3.1000 0.7581 0.3750

Th 0.7530 0.4890 0.4780 0.5770 0. 1320 3.6212 0.6494 0.6348

Table 2. For a typical metal, copper, and for stainless steel,

relative contributions of three force constants to

various elastic constants.

Copper Stainless Steel

s s ^3 s s

Si 1.00 0.00 -0.08 0.00 -0.12

"l2 1.00 0.10 0.23 -0.17 0.36

"44 1.00 -0.10 -0.08 0.17 -0.12

C 1.00 -0.10 -0.38 0.17 -0.59

B 1.00 0.05 0.08 -0.09 0.12

"l2 "44 0.00 -1.00 -1.00 -1.00 -1.00

"11 "12 2"44 -1.00 -0.10 0.23 0.17 0.36 A 1.00 (0.0)® (0.31) (0.00) (0.47)

"l2^"ll 1.00 (0.10) (0.31) (-0.17) (0.47)

^Parentheses

relative to indicate

unity.

the approximation that both and are small

203
A = 00

Fig, L. Reduced elastic stiffnesses for fee elements. Zener's anisotropy

ratio is denoted by A. The Cauchy relationship central

forces appears as a line. The center point corresponds to a firstneighbor (1 nn) only central- force model.

1.0 1 r 1 r0.8 -

0.6

K

\ \ \ ^ A ^

A

J H “G

0.4

• ANS60

A A

^ STM069

i

EC64 O D71

0.2 L ^ J66 o HW73 -

D BCT68 LR73

n 1 SA68 , V KQ81, , 20 40 60

NICKEL, wt.%

80 100

Fig. 2. For fee Fe-Ni alloys, the variation of x=C^^/Cj^^ with composition.

Maximum near 30 Ni corresponds to an instability.

204
C44/C11

Fig. 3. Reduced elastic stiffnesses for fee Fe-Cr-Ni stainless steels.

Compare with Fig. 1. Face-centered-cubic Fe and Co points were

obtained either from theory or from extrapolation.

Fig. 4. Face-centered-cubic unit cell showing eigenvectors and eigenvalues

of the coupling matrices to the nearest-neighbor atoms at

h. 0]-type positions.

205
» ,

'

, (

I .-*

'tsOTfay

#^; 4l' i. «-,l|<

V tk>

} '',^^y

’v'l*’''

:>

«ii

'..''I,*

3

* '•-R

!w-\' ^ ’ X> ,nlir:T'"TM ,

^ ,if- W-.;;';:t> _J

••'

. . ..

’

. AL . >1 -» - — JU ilvAi. '

,'.j'W,'»'*W^4

i tifi |^‘. i,

!' i;<} v< r.)

. -•’;,??' .' '

'

' '/ ---•-‘—

*. yf)t A ‘ .i";,' iV'v ,

'

^

f.'!

U BT: 'i- :i:'.Mltl


Monocrystal-Polycrystal Elastic Constants of a Stainless Steel

H. M. Ledbetter

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

Boulder, Colorado 80303, USA

For a f ace-centered-cubic steel, we report new measurements of the monocrystal

Voigt elastic-stiffness constants: ^12’ ^44‘ monocrystal steel,

Fe-19Cr-10Ni , corresponds closely to the well-known AISI-304 austenitic

stainless steel. Considering seven theories for the monocrystal-polycrystal

elastic constants, we find the Hershey-Kroner-Eshelby theory agrees best with

measurements. It predicts the shear modulus within two percent of observation, where the Voigt-Reuss first-order bounds differ by forty-nine percent.

We review ten sets of Fe-Cr-Ni C.. results and find that both Zener’s elastic

anisotropy and the ^-^ 2^ ^11 constant within five percent.

Key words: alloy; austenite; crystal physics; elastic constants;

f ace-centered-cubic alloy; iron alloy; monocrystal; polycrystal; stainless steel

Published in Physica Status Solidi , volume (a)85 (1984), pp. 89-96.

207
1 . Introduction

The relationship between monocrystal physical properties (represented by

tensors) and polycrystal physical properties (scalars) remains one of the most

intriguing unsolved problems in crystal physics. Tensor ’averages' have been

proposed for many physical properties, including dielectric constant, diffusivity, elastic constants, electrical conductivity, magnetic permeability,

magnetostriction, piezoelectric constants, and thermal conductivity.

In terms of averaging, elastic constants have received more attention

than most other physical properties. Voigt [1] was first to suggest how the

fourth-rank elastic-stiffness tensor, C...,, could be averaged to obtain the

ijkl

two independent quasi-isotropic elastic constants: the bulk modulus, B, and

the shear modulus, G. Forty years later, Reuss [2] showed that Voigt's

solution is not unique. Landau and Lifshitz [3] point out that "there is

therefore no general relation between the moduli of elasticity of a polycrystal and those of a single crystal of the same substance." Many ingenious

approximate averaging methods have been developed, too many to enumerate here.

Most of these are either described or referenced in reviews by Hearmon [4]

,

Reran [5], Ledbetter [6], Kroner and Koch [7], and Watt et al. [8]

Until a generally accepted averaging method arises, interest remains high

in testing various models against ’careful measurements. For both ambient and

low temperatures, Ledbetter [9,10] recently did this for copper. He considered eight models: Voigt, Hashin-Shtrikman , Hershey-Krbner-Eshelby , Hill

(arithmetic). Hill (geometric), Aleksandrov, Ledbetter-Naimon, and Reuss.

Among these, the Hershey-Krbner-Eshelby model worked best, predicting the

quasi-isotropic polycrystal shear modulus within 1%.

208
The study reported here tests the various monocrystal-polycrystal models

for the elastic constants of an fee Fe-Cr-Ni alloy. This alloy possesses

technological interest because it approximates the chemical composition of

AlSI-304 stainless steel, probably the best known and most widely used stainless-steel alloy. This study represents the first test of elastic-constant

averaging models for a nondilute ternary alloy. While the alloy exhibits

macroscopic paramagnetism at ambient temperature, all constituents — Fe, Cr,

Ni — exhibit ferromagnetism, antiferromagnetism, or both. Thus, local interatomic interactions may be nonparamagnetic . Because the alloy is concentrated, contains magnetic species, and possesses considerable technological

interest, we undertook the present study.

2 . Experiment

a. Monocrystal

An alloy of nominal weight-percent composition Fe-19Cr-10Ni was vacuum

melted and vacuum cast from high-purity metals. Monocrystals 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. (In subsequent measurement and analysis, we ignored this small

departure from a [110] axis.) Specimen dimensions were 1.5 x 1.5 x 0.7 cm.

3 Mass density measured by Archimedes’s method was 7.937 g/cm .

b. Polycrystal

For these, we used the twenty AISI-304-type stainless-steel alloys

studied previously by Ledbetter et al. [11] in their as-received wrought-andannealed conditions. Their average weight-percent chemical composition was

18.6 Cr, 9.3 Ni, 1.3 Mn, with other trace elements. Their average Archimedes209
3

method mass density was 7.880 g/cm . Their average grain size measured 88 ym.

ranging from 68 to 105. Figure 1 shows a typical microstructure.

c. Measurements

We measured sound velocities, longitudinal and transverse, by a pulseecho-overlap method described previously [11]. For the polycrystals, the

percent standard error was 0.3% for v^ and 0.6% for v^. This includes all

possible error sources: chemical composition, thermal-mechanical treatment.

measurement method, and so forth. For the monocrystals, the percent standard

error was approximately

3. Results

0.1%.

Table 1 gives, for both monocrystal and polycrystal, the measured sound

velocities together with the derived elastic-stiffness constants calculated

from

C = pv^ (1)

where C denotes elastic

the polycrystal.

stiffness; p, mass density; and v, sound velocity. For

and

= Cj = pv/ (2)

= G = pv^^ (3)

where denotes longitudinal modulus and G shear modulus. For a monocrystal,

along a [110] direction.

o

II= = <Si"S2"2C44)/2 (4)

=ti

and

-

«t2

= pvj.2^ = (Cjj-Cjj)/2 (6)

210
From Eqs. (4) - (6) one obtains the usual three independent Voigt elastic

stiffnesses: C, , , and C,,. For the monocrystal, the bulk modulus is

11 12 44

B =

while for the polycrystal it is

B = - (4/3)G (8)

Based on seven averaging methods, Table 2 gives predicted quasi-isotropic

elastic constants. For this table, E denotes Young modulus, G shear modulus,

and V Poisson ratio. All averaging methods predict the same bulk modulus, B =

11 2 1.60010 N/m , following Eq. (7). For details of the mathematical relationships associated with the various methods, see Ledbetter [6] or references to

the original studies given in [9].

4

Discussion

Results in Table 2 show clearly that, among the seven averaging methods

considered, one method agrees best with observation: the Hershey-KrbnerEshelby method. It predicts the shear modulus within 2%, the Young modulus

within 2%, the bulk modulus within 1%, and the Poisson ratio within 2%. Part

of the discrepancy may arise from the slightly different chemical compositions

of the monocrystal (19Cr - lONi) and the average polycrystal (18.6Cr - 9.3Ni -

1.3Mn, plus trace elements). Note also that observation lies much closer to

the Hashin-Shtrikman upper bound than to the lower. Especially, this occurs

for Poisson's ratio. If real, this suggests that the polycrystal is not

perfectly disordered, that it contains texture, characteristic grain shape, or

characteristic grain-boundary geometry. But, present results permit no

conclusions concerning these matters.

For cubic-symmetry monocrystals where Eq. (7) gives the bulk modulus, the

211
averaging problem amounts to predicting another elastic constant. Most models

predict the shear modulus. The Hershey-Krbner-Eshelby method does this by

considering an anisotropic nonhomogeneity embedded in an isotropic matrix.

Eshelby [12] gave a relatively simple discussion of this inclusion problem,

which leads to a cubic equation for the shear modulus G:

G^+aG^+3G+Y=0 (9)

where

a=(5C^^+4C^2)/^ (10)

6=-C^^(7C^^-4C^2)/S (11)

and

'‘-'=44<SrS2>('=ll"2Ci2)/8 ( 12 )

An interesting feature of Eq. (9) is that it contains the bulk modulus.

In the H-K-E model, the cubic-symmetry shear moduli are not sufficient for

predicting G. Other models — Voigt, Reuss, Hill, Aleksandrov, for example —

do not require B to predict G. The question arises: why does the resistance

to shear deformation depend on the resistance to dilation? In isotropic

media, we know since Stokes [13] that G and B are the two independent elastic

constants representing extreme types of deformation: shape change without

volume change and volume change without shape change, respectively. We can

factor any general deformation into dilation and shear components. Thus, is

this G(B) dependence real or an artifact of the model? Will the final model

be of the form G(C^^, C’, B) or simply G(C^^, C’)?

Recently, Gairola and Kr'dner [14] derived a simple formula for calculating all the bounds for and the self-consistent (infinite bound) value of

the shear modulus of a macroscopically isotropic cubic-symmetry polycrystalline aggregate. The numerical results agree exactly with the Hersey-Krbner212
Eshelby method. The approach differs from the spherical-inclusion problem

described above, but it leads to the same results. Using a unified method

[15, 16], they derive the result (in their notation):

where

G = a„G + 6-G + Y

2 o 2 o G + a ^ G B 1 o 1 o 1

(13)

aj^=(45K+24y+36v)/40

a2=(2v+3y)/5

6^=3K(2y+3v)/20

6^=3 (6<v+9<y+20yv) / 40

Y=3<yv/4

k=(C^^+2C^^)/3

v=(Cii-Ci2)/2

y=c

44

(14)

(15)

(16)

(17)

(18)

(19)

( 20 )

( 21 )

One can easily verify that putting G^=°° and G^=0 leads to the Voigt and

Reuss bounds, G and G , the so-called first-order upper and lower bounds,

V K

G^^^ and G,,.. If instead one puts G =y=G,, and G =v-(C. ,-C, „) /2 (y and v are

(1) o44 o 1112

the zeroeth-order bounds G^°^ and G, , then one obtains the Hashin-Shtrikman

(o)

( 2 ) bounds, G and G^

2

)

• This self-consistent renormalization scheme yields

either the odd-order or the even-order bounds. Either set leads to G

(oo)

G^^^= G(self-consistent) in exact agreement with Eq. (9). Some authors call

(3) the third-order bounds, G and G^^) » Kroner bounds.

Finally, we collect and discuss briefly all previously reported monocrystal stainless-steel elastic constants. Table 3 contains ten sets of

reported elastic constants, converted where necessary to the G^^ : Gj^^, C^

2

»

and Table 3 contains also B and C’ together with the Zener anisotropy:

A = ( 22 )

213
The table shows also results for fee Fe, Co, and Ni. The Ni results were

measured. The Co results were obtained by extrapolation from measurements on

Ni-Co alloys. Diesburg's [23] result for Fe was also obtained by extrapolation, using Fe-Ni alloys. Johnson's [22] result for Fe eame from theory based

on fitting a two-body eentral-foree interatomie potential to Fe’s seeond-order

bee elastie eonstants. For the ten Fe-Cr-Ni alloys in Table 3, the Zener

anisotropy shows remarkable near-eonstaney : A = 3.53 - 0.17, a standard error

of 5%. Also nearly eonstant, we find the ratio ~ 0.652 - 0.025, a

standard error of 4%. These empirieal ratios provide an opportunity for

ealeulating the three monoerystal elastie eonstants from the two quasiisotropie polyerystal elastie eonstants. Ledbetter [26] used this approaeh to

estimate the monoerystal elastie eonstants of 316-type stainless steel. In

that study, based on only four Fe-Cr-Ni alloys, he used A = 3.51 and ^j^2^^11

~

0.635.

5 . Conelusions

For an austenitie stainless-steel alloy, we eonsidered the monoerystalpolyerystal elastie-eonstant relationship. Among seven models, the HersheyKrbner-Eshelby model works best.

Aeknowledgment

This study was supported by the U.S. DoE Offiee of Fusion Energy.

Mr. J. T. Ward assisted with measurements. Mr. M. W. Austin contributed in

many miscellaneous ways. Dr. N. F. Fiori of Cabot Corporation loaned the

monocrystals. Dr. D. T. Read contributed the photomicrograph.

214
References

[1] W. Voigt, Ann. Phys . 38 , 573 (1889).

[2] A. Reuss, Z. Angew. Math. Mech. 9^, 49 (1929).

[3] L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon,

London 1959 (p. 40).

[4] R. F. S. Hearmon, in Physics of the Solid State, Academic, New York

1969 (p. 401).

[5] M. J. Reran, Phys. Stat. Solidi (a) 365 (1971).

[6] H. M. Ledbetter, J. Appl. Phys. 1451 (1973).

[7] E. Kroner and H. Koch, SM Archives _1, 183 (1976).

[8] J. P. Watt, G. F. Davies, and R. J. O’Connell, Rev. Geophys. Space

Phys. U. 541 (1976).

[9] H. M. Ledbetter, J. Phys. D: Appl. Phys. L3, 1879 (1980).

[10] H. M. Ledbetter, Phys. Stat. Solidi (a) 477 (1981).

[11] H. M. Ledbetter, N. F. Frederick, and M. W. Austin, J. Appl. Phys.

M, 305 (1980).

[12] J. D. Eshelby, in Progress in Solid Mechanics, Volume II, NorthHolland, New York 1961 (p. 130).

[13] G. G. Stokes, described in I. Todhunter and K. Pearson, A History of

the Theory of Elasticity and of the Strength of Materials, Cambridge

U.P., Cambridge 1886.

[14] B. K. D. Gairola and E. Kroner, Int. J. Eng. Sci. j_9, 865 (1981).

[15] E. Kroner, J. Phys. F: Met. Phys. 8, 2261 (1978).

[16] B. K. D. Gairola, in Proceedings Continuum Models of Discrete

Systems, U. Waterloo P., Waterloo Canada 1980.

[17] G. Bradfield, J. Iron Steel Inst. 2^, 616 (1964).

[18] K. Salmutter and F. Stangler, Z. Metallkd. 1 (1960).

[19] M. Kikuchi, Trans. Jap. Inst. Met. j_2, 417 (1971).

[20] M. C. Mangalick and N. F. Fiore, Trans. Metall. Soc . AIME 242, 363

(1968).

215
[21] D. S. Kupperman, personal communication (1982). See also D. S.

Kupperman and K. J. Reimann, IEEE Trans. Sonics Ultrasonics SU-27, 7 (1980).

[22] R. A. Johnson, Phys. Rev. 145 , 423 (1966).

[23] D. Diesburg, Ph.D. Thesis, Iowa State University (1971).

[24] H. J. Leamy and H. Warlimont, Phys. Status Solid! 523 (1970).

[25] G. A. Alers, J. R. Neighbours, and H. Sato, J. Phys. Chem. Solids

j[3, 40 (1960).

[26] H. M. Ledbetter, Brit. J. NDT 34, 286 (1981).

Fig. 1. Microstructure of a typical polycrystalline 304-type stainless-steel

alloy in its wrought and annealed condition. LN denotes low carbon

content and high nitrogen content. The specimen came from a commercial plate; L denotes rolling direction; T, transverse in-plate

direction; and S, through-plate-thickness direction.

216
Table 1

Sound-velocity and elastic-constant results

Monocrystal Polycrystal

p(g/cm^) 7.937 7.880

v^(cm/ys) 0.6121 0.5759

''tl 0.3988 0.3134

'^t2 0.2052 -

2.974 2.614

(Cn-Cjj)/2 0.334 0.774

^44 1.262 -

^11 2.046 2.614

^12 1.377 1.066

B 1.600 1.582

E - 1.996

V

- 0.290

Table 2

Polycrystalline elastic constants predicted by averaging monocrystal

elastic constants

11^ 2 (10 N/m ) 1? 2 (10 N/m )

V Method

2.255 0.891 0.265 Voigt

2.025 0.785 0.289 Hashln-Shtrikman, upper

1.850 0.708 0.307 Hashin-Shtrikman , lower

1.938 0.746 0.298 Hashin-Shtrikman , average

1.960 0.756 0.296 Hershey-Kr'dner-Eshelby

1.934 0.745 0.299 Hill, arithmetic

1.928 0.742 0.299 Aleksandrov

1.901 0.730 0.302 Hill, geometric

1.596 0.598 0.334 Reuss

217
Table 3

Monocrystal elastic constants of f ace-centered-cubic Fe-Cr-Ni alloys;

11 2 units on elastic constants are 10 N/m , except A, which is dimensionless

Alloy

(Cr-Ni)

Si ^12 S4 B C A Source

12-12 2.109 1.403 1.225 1.638 0.353 3.47 Bradfleld [17]

12-18 2.332 1.627 1.226 1.862 0.353 3.48 Salmutter, Stangler [18]

18-12 1.912 1.179 1.386 1.423 0.367 3.78 Kikuchi [19]

18-12 2.159 1.446 1.289 1.684 0.357 3.62 Bradfleld [17]

18-lA 1.98 1.25 1.22 1.49 0.365 3.34 Mangalick, Fiore [20]

18-19 1.91 1.19 1.24 1.43 0.360 3.44 Mangalick, Fiore [20]

19-10 2.05 1.38 1.26 1.60 0.334 3.78 Present

19-10 2.07 1.32 1.23 1.57 0.375 3.28 Kuppennan [21]

19-14 2.05 1.33 1.27 1.57 0.360 3.58 Kupperman [21]

19-19 2.04 1.33 1.26 1.57 0.355 3.55 Kupperman [21]

Fe 2.51 1.57 1.12 1.89 0.470 2.38 Johnson [22]

Fe 2.760 1.735 1.363 2.08 0.513 2.66 Diesburg [23]

Co 2.398 1.634 1.334 1.89 0.382 3.49 Leamy, Warlimont [24]

Ni 2.516 1.544 1.220 1.87 0.486 2.51 Alers, Neighbours, Sato [25]

218


ELASTIC-CONSTANT ANOMALIES AT THE NEEL TRANSITION IN Fe-1 8Cr-3Ni-1 3Mn*

H. M. Ledbetter

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

Boulder, Colorado 80303

E. W. Collings

Battelle Columbus Laboratories

Columbus, Ohio 43201

Elastic constants of an 1 8Cr-3Ni-1 3Mn austenitic stainless steel were measured ultrasonically between room temperature and liquid-helium

temperature. All the elastic constants change anomalously and reversibly

near 191 K, which magnetic susceptibility measurements show to be the Neel

(paramagnetic-to-antiferromagnetic) transition temperature.

Key words: austenite; elastic constants; iron alloy; low temperatures

magnetic susceptibility; Neel transition; stainless steel; ultrasonic waves

INTRODUCTION

A recent study [1] showed that an Fe-21 Cr-6Ni-9Mn stainless steel is

elastically anomalous near 1 30 K. All the elastic stiffnesses — Young's

modulus, shear modulus, and bulk modulus — decrease anomalously during

cooling, and Poisson's ratio increases. It was speculated that these changes

reflect a Neel (paramagnetic-to-antif erromagnetic ) transition.

A study is reported here for a similar alloy, Fe-1 8Cr-3Ni-1 3Mn . Its

higher manganese content suggested a possibly higher Neel transition and

perhaps a larger elastic anomaly. The previous study [1], which covered the

temperature range 76-295 K, left unresolved the question of the very low

temperature behavior of the elastic constants. The present study covers the

4-295 K temperature range. More importantly, it includes magnetic-susceptibility measurements to detect and characterize any magnetic transitions.

EXPERIMENT

Material

Two 2 . 5 -cm plates from different heats were obtained from a commercial

source. The vendor's chemical analysis in weight percent is: 18.09 Cr, 3-26

Ni, 13.22 Mn, 0.37 N, 0.52 Si, 0.12 Mo, 0.038 C, 0.028 P, 0.005 S. In its

as-received annealed condition, the Rockwell B hardness is 92 and the grain

size is ASTM size 6.

^Contribution of NBS, not subject to copyright.

To be published in Materials Science and Engineering.

219
Specimens

For elastic-constant measurements, a rectangular prism 1.4 cm x 1.6 cm x 1.7 cm was prepared with opposite faces flat and parallel within 3 ym.

Absolute Ultrasonic-Velocity Measurements

Room- temperature ultrasonic velocities were measured using a pulse-echo

method for both longitudinal and shear waves near 7 and 6 MHz, respectively.

Procedures and equipment were described previously [2]. Briefly, a voltage

is applied sinusoidally to a quartz piezoelectric transducer bonded to a specimen with phenyl salicylate. The electrical pulse is converted to a mechanical pulse, is transmitted through the specimen, is reflected from the

flat specimen surface, and is transmitted back to the transducer that acts as

a receiver, partially converting the pulse to an electrical signal that is

displayed on a calibrated oscilloscope. From the pulse’s transition (roundtrip) time, t, the sound velocity is computed from v = 2H/t, where 2, is the

specimen length. The elastic constants are computed by C = pv^, where p is

the mass density. Different elastic constants are obtained for different

types of waves: shear, longitudinal, etc. When the systematic error is

neglected, the uncertainty in the reported elastic constants is about 0.1

percent

Relative Velocity Measurements

The changes in the velocity of sound with temperature were determined by

a pulse-superposition method [3]. Briefly, the pulse repetition rate is

adjusted so that the time between pulses equals two transit times. This is

done by dividing the carrier frequency, f, by a fixed integer, N. Thus, f/N

= 1/2t = v/4£. The oscilloscope display between applied pulses consists of

the sum of all odd-numbered echoes, and the carrier frequency is adjusted (as

temperature is changed) to maximize the amplitude of the summed-odd-echo

envelope. When the dimensional change is neglected, the change in elastic

constant is dC/C = 2dv/v = -2dt/t = 2df/f, where a typical sensitivity in

df/f is 10”^ or better.

Magnetic-Susceptibility Measurements

Magnetic susceptibilities were measured at room temperature by the Curie

technique using an electronic microbalance and an electromagnet fitted with

"constant-force" pole caps 18 cm in diameter. The vertical magnetic force

field (if X 9}T/3 z) at the sample reference position was calibrated using a 486.77 mg piece of high-purity platinum, whose susceptibility (0.977 yemu/g

at 293 K) and susceptibility temperature dependence (6.3 x 10 emu/g*deg

from 260 to 300 K) were measured by Budworth, Hoare, and Preston [4]. Further details concerning these measurements are given elsewhere [5].

220
RESULTS

Table 1 shows the variation with direction of both longitudinal and

shear elastic velocities. Since elastic anisotropy is clearly negligible,

velocities reported below represent arithmetic averages over three directions. Table 2 shows variations of elastic constants between heats and between heat treatments. Clearly, these variables effect only small changes.

Table 3 shows the variations in elastic constants with temperature; Fig. 1 also displays these. Figure 2 shows perhaps the most important result: the

correlation between elastic-constant behavior (represented by = pv|) and

magnetic susceptibility.

DISCUSSION

Magnetic-susceptibility, x» results shown in Fig. 2 demonstrate

conclusively that a Neel ( paramagnetic-to-antiferromagnetic ) transition

occurs at 191 K. A sharp, field-independent maximum in the x“T curve provides simple, unambiguous evidence for a Neel transition [6].

All the elastic constants behave anomalously around the Neel

temperature, Tj^j, as shown in Fig. 1, that is, both dilatation-type (B) and

shear-type (G) elastic constants behave anomalously. Regular (paramagnetic)

materials show smoothly increasing E, G, and B and decreasing v with

decreasing temperature. Poisson’s ratio, which is usually affected only

slightly by most metallurgical variables [7], changes particularly abruptly

for the present alloy and provides a good indicator of the magnetic

transition. Except for Poisson's ratio, all the elastic constants exhibit

regular behavior at temperatures sufficiently separated from Tpj. The

bulk-modulus softening well above Tj^ indicates either that compressibility

increases premonitor ily to the Neel transition or that a second transition

(of unknown character) precedes the Neel transition during cooling.

Elastic constants, change at any phase transition because they

relate intimately to the interatomic potential, 0(r). Thus, the elastic

constants are [8]:

P ^ ijkl 3n..8n, , ij kl

where U is the thermodynamic internal energy

U = 1/(2V°) I $(r)

which is summed over all ion pairs; denotes the Brugger strain and V°

denotes atomic volume. Clearly, any strain-dependent contribution to the

energy contributes also to the elastic constants. Thus, either changes in

$(r) or changes in ionic arrangement affect the C —

221
In the present case $(r) is affected by antiferromagnetic ordering, the

energetics of which parallels ferromagnetic ordering in many ways. In

several studies [9,10] relationships between ferromagnetic ordering and

changes in elastic constants have been discussed and in a few studies the

antiferromagnetic case has been considered [ll-l^l]. The authors discuss this

topic in detail elsewhere [15].

Other thermodynamic properties related to $(r), e.g., thermal expansivity and specific heat, should also behave anomalously near Tj^. Existing

thermal expansivity data on these alloys are insufficiently precise {hl/l

about 10"^) to detect the transition. Specific-heat measurements on this

alloy were made at low temperatures, but not near [16]. If no specific-heat

anomaly occurs near Tj^, then sound velocities or elastic constants may provide the most sensitive indicator of the transition.

In summary, all elastic constants of Fe-1 8Cr-3Ni-1 3Mn behave anomalously

near 191 K, which magnetic-susceptibility measurements show to be the

temperature of a Neel (paramagnetic-to-antiferromagnetic) transition. Such

anomalies in the physical properties are expected at a magnetic transition,

consistent with their dependence on the interatomic potential. These

findings agree with those reported previously for Fe-21 Cr-6Ni-9Mn , whose

lower Neel temperature reflects its lower manganese content.

ACKNOWLEDGMENTS

This study was supported by the U.S. Department of Energy. Most of the

ultrasonic measurements were made by M. Austin.

REFERENCES

1. H. M. Ledbetter, Mater. Sci. Eng. 29, 255-260 (1977).

2. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics jj4, 246-249

(1974).

3. H. J. McSkimin, J. Acoust. Soc. Amer. 12-16 (1961).

4. D. W. Budworth, F. E. Hoare, and J. Preston, Proc. R. Soc. Lond. A 257 , 250 (1960).

5. E. W. Ceilings and R. D. Smith, J. Less Common Met. £8, 187-198 (1976).

6. A. H. Morrish, Physical Principles of Magnetism (Wiley, New York, 1965),

p. 452.

7. W. Keter and H. Franz, Metall. Rev. 6, 1-55 (1961).

8. D. C. Wallace, Thermodynamics of Crystals (Wiley, New York, 1972),

p. 19.

222
9. G. A. Alers, J. R. Neighbours, and H. Sato, J. Phys. Chem. Solids 1

. i<0-55 (1960).

10. G. Hausch, Phys. Stat. Solidi (A) J_5, 501-510 (1973).

11. W. P. Mason, Phys. Rev. 715-723 (1951 ).

12. D. E. Eastman, J. Appl. Phys. 3]_, 996-997 (1966).

13. P. Makhurane and P. Gaunt, J. Phys. C 2, 959-965 (1969).

111. K. Kawasaki and A. Ikushima, Phys. Rev. B j_, 31^3~3151 (1970).

15. H. M. Ledbetter and E. W. Collings, in Metal Physics of Stainless Steels

(TMS-AIME, New York, 1979, 22-40).

16. E. W. Collings and R. D. Smith, Advances in Cryogenic Engineering , vol.

24 (Plenum, New York, 1978, 214-223).

Table 1. Elastic wave velocities in Fe-1 8Cr-3Ni-1 3Mn at T = 295 K.

Propagation

Direction

Longitudinal

Velocity

(cm/ps)

Shear

Velocity

(cm/ps)

X = through thickness 0.5701 0.31 61

y

= transverse direction 0.5698 0.3153

z = rolling direction 0.5697 0.3161

Mean value 0.5699 0.3158

Std. deviation 0.0002 0.0005

223
Table 2. Room- temperature (T = 293 K) sound velocities and elastic constants

for Fe-1 8Cr-3Ni-1 3Mn.

Heat 1 Solution Treated,

Furnace Cooled

Heat 1 Solution Treated,

Water Quenched

Heat 2

Hot Rolled,

Annealed

Mass density (g/cm^) 7.830 7.817 7.835

Long, velocity (cm/ps) 0.5699 0.5633 0.5697

Shear velocity (cm/ps) 0.3163 0.3104 0.31 43

Long, modulus (10^^ N/m^) 2.543 2.481 2.543

Shear modulus (10^^ N/m^) 0.783 0.753 0.774

Bulk modulus (10^^ N/m^) 1.499 1.477 1.511

Young’s modulus (10^^ N/m^) 2.001 1.931 1 .983

Poisson’s ratio 0.277 0.282 0.281

Std. deviation of v^ 0.0003 0.0003 0.0009

Std. deviation of v^ 0.0002 0.0005 0.0013

224
Table 3- Elastic constants of Fe-1 8Cr-3Ni-1 3Mn at selected temperatures.

Temp.

Longitudinal

Modulus

Young '

Modulus

Shear

Modulus

Bulk

Modulus

Poisson '

Ratio

(K) (10^^ N/m^) (10^’’ N/m^) (10^’’ N/m2) do’’^ N/m^)

300 2.493 1 .949 0.761 1 .478 0.280

280 2.502 1 .962 0.767 1 .479 0.279

260 2.510 1 .975 0.773 1 .479 0.278

240 2.517 1.986 0.778 1 .480 0.276

220 2.522 1 .995 0.782 1 .479 0.275

200 2.524 2.002 0.786 1 .476 0.274

180 2.484 1 .953 0.764 1 .465 0.278

160 2.467 1 .941 0.760 1 .454 0.277

1 40 2.470 1 .944 0.761 1 .456 0.278

120 2.477 1 .949 0.763 1 .460 0.278

100 2.487 1 .957 0.766 1 .466 0.278

80 2.492 1.961 0.768 1.468 0.277

60 0.768

40 0.771

20 0.773

4 0.773

Estimated 0.025

Uncertainty

0.022 0.005 0.010 0.004

225
POISSON'S

RATIO

YOUNG'S

MODULUS

(10llN/m2)

TEMPERATURE (K)

Fig. 1. Temperature dependence of four elastic constants: E Young’s modulus; G, shear modulus; B, bulk modulus

(reciprocal compressibility); and v, Poisson’s ratio

226

BULK

MODULUS

(lOllN/m^)

MODULUS

(lOl^N/m^)
MAGNETIC

SUSCEPTIBILITY

(10

®emu/g)

LONGITUDINAL

MODULUS

(IQllN/m^

2.54

2.52

2.50

2.48

2.46

20

19

18

17

16 0 100 200 300

TEMPERATURE (K)

Fig. 2. Temperature dependence of longitudinal modulus = pv| and

magnetic susceptibility. As discussed in the text, these

results evidence a Neel transition at 191 K.

227



AUTOMATIC NEAR-THRESHOLD FATIGUE-CRACK

GROWTH-RATE MEASUREMENTS AT LIQUID HELIUM TEMPERATURE"^

R.L. Tobler and Y.W. Cheng

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

The development of a fully automated test apparatus for near-threshold

fatigue crack growth rate measurements in a liquid helium environment is described, and some initial results for AISI 300 series stainless steels are

presented. The experimental apparatus consists of a servohydraul ic test

machine and a cryostat, complete with minicomputer, programmable arbitrary

waveform generator, programmable digital oscilloscope, and fully automatic

liquid helium refill system. The technique uses 6.4-mm-thick compact specimens subjected to systematically decreasing loads, with 24-h operation at

40 Hz, the crack growth being continuously monitored by specimen compliance

measurements. The results presented in this study include da/dN-versus-AK

curves and threshold fatigue stress intensity factors, AK^^, at 4 K for AISI

304L, 304LN, and 316 stainless steels. The near-threshol d fatigue behaviors

of these materials are similar, and the fatigue crack growth rate trends at

intermediate AK levels nearly agree with published results.

Key words: austenitic stainless steels; computer-automated test systems;

cryogenic properties of materials; fatigue of materials; fatigue crack growth

rates; threshold stress intensity factors.

^Contribution of NBS; not subject to copyright.

229
INTRODUCTION

Recent workshop presentations [1,2] indicated that fatigue properties are

essentia! to the design of some magnetic fusion energy structures. Of special

interest are the near-threshold fatigue crack growth rates (da/dN) and threshold stress intensity factors of austenitic stainless steels. These

parameters relate to alloy development and structural design analyses since

they lead to the identification of conditions below which existing cracks can

not grow in fatigue. Experimental determinations of these parameters are

needed because few cryogenic measurements exist, and there are no reliable

prediction schemes.

Hooper [1] showed that near-threshold fatigue crack growth data at rates

as low as 10 m/cycle would permit more accurate life predictions in the

toroidal field coil cases of tokamak-type superconducting magnets. Tokamak

machines operate in pulsed mode and could accumulate hundreds of thousands of

cycles (N) during a lifetime at 4 K. The potential savings from efficient

alloy selection and design would more than compensate for the expense of

threshold fatigue measurements at 4 K.

Previous threshold fatigue studies [3-5] dealt primarily with ferritic

steel behavior at ambient temperature. For these materials it is known that

the da/dN-versus-AK curves on log-log coordinates typically have a sigmoidal

shape, and that metallurgical effects are relatively strong in the nearthreshold region. The applicability of fatigue crack growth thresholds to

very high-cycle rotating machinery such as steam turbine rotors has become

well established; load ratio, environment, and alloy microstructure have been

identified as major factors affecting material performance.

At cryogenic temperatures, the available threshold fatigue data for

austenitic stainless steels suitable for engineering applications are limited

to AISI-304 type (i.e., Fe-18Cr-10Ni ) steels and JBK-75 (i.e., Fe-14Cr-29Ni

)

230
base metal and welds. The data for JBK-75 [6,7] were obtained at 295, 77, and

4 K at stress ratios of 0.1 and 0.8. The data for AISI 304 [8,9] do not extend below 77 K and were obtained for R ratios of 0.05 and -1. Our purpose is

to expand this data base to include other materials and test variables. In

this paper we describe a fully automatic threshold fatigue test apparatus and

present our first measurements for AISI 300 series austenitic stainless steels

tested in liquid helium at a stress ratio (R) = 0.1.

TEST METHODOLOGIES

Threshold fatigue testing is notoriously difficult and time-consuming,

and the additional requirement of maintaining a liquid helium environment

significantly increases the cost of testing. Therefore, the choice of test

methodology is important. At least two approaches are possible for cryogenic

studies: the ultrasonic technique and the automated closed-loop servohydraulic technique.

The ultrasonic technique was successfully used by Stanzl and coworkers

[9-11] at test temperatures down to 77 K. This method offers the advantage of

high frequencies (e.g. , 20 kHz), which greatly reduces the test duration (the

frequency is typically 100 Hz or less for closed-loop servohydraul ic apparatus). We rejected this method for liquid helium testing, however, reasoning

that adiabatic heating is bound to occur in the crack tip plastic zones

causing problems of temperature control.

The alternative pursued here is an automated test system that allows

continuous testing, data collection, and load adjustments to be performed by

computer in the absence of an operator. Automation minimizes testing time and

operator attention while reducing data scatter, owing to higher precision in

crack length measurement and better control of data point spacing. The automatic procedure is also relatively easy to implement with minimal operator

231
training, and it eliminates subjective interpretation and operator bias. In

designing a cryogenic system we referred to the work of Li aw et al . [7],

Williams et al . [12], and Cheng and Read [13] and incorporated additional

modifications, consistent whenever possible with proposed and existing

standards [14-16].

EXPERIMENTAL APPARATUS

The experimental apparatus consists of a 100-kN servohydraul ic test machine and cryostat, a programmable digital oscilloscope, a programmable arbitrary waveform generator, a minicomputer, and an automatic liquid helium

refill system. The complete apparatus is shown in figure 1.

The servohydraul ic machine has an inverted stage with its actuator above

a cantilevered cryostat load frame. The specimen is pinned at the bottom of

the load frame and enclosed during cryogenic tests in a vacuum- i nsul ated

stainless steel Dewar. The frame columns are fiberglass-reinforced plastic

tubes and the loading rod is plastic-impregnated wood. Nonmetallic materials

of low thermal conductivity were employed to reduce the steady-state heat leak

into the Dewar. The cryostat design and associated instrumentation are

described in detail elsewhere [17-19].

The servohydraul ic machine includes a servo control system with two dc

conditioners, a valve drive, a signal amplifier, and a load cell. A conventional function generator and electrical cycle counter are also provided in

the machine console but these are not used in automatic threshold fatigue

testing. Instead, the fatigue cycle counts are calculated by computer from

the test frequency and elapsed time, and a programmable arbitrary waveform

generator is used since the applied load levels vary with time.

The programmable digital oscilloscope contains two 15-bit 100 kHz digitizers and serves as an analog-to-digital (A/D) converter. The problems en232
countered with slower A/D converters (interruptions during the testing and low

test frequencies) are eliminated because of the high-speed A/D conversion rate

and the f reeze-and-hol d memory capability of this oscilloscope. This unit

also provides a continuous display of the 1 oad-versus-di spl acement

relationship from which crack closure effects can be monitored.

The minicomputer includes a cathode ray tube (CRT) terminal, a line

printer, a dual floppy disc storage unit, and a digital plotter. The minicomputer uses 16-bit words and has 128-K words of memory. The minicomputer

also contains an internal clock that reads to 1/60 s. The IEEE-488/GPIB instrument interconnection bus is used for the interface between the computer

and the programmable digital oscilloscope, and between the computer and the

programmable arbitrary waveform generator. The sequence of operation and

interactions between the various components is represented by a flow diagram

in figure 2.

To keep the specimen fully submerged in liquid helium for continuous

24-h operation at 4 K, an automatic refill system was incorporated (figure 3).

The system consists of a 30.5-cm superconducting liquid-level detector, a

level controller, a conventional three-way solenoid valve, a pressurized helium gas cylinder, and a 500-J2. liquid helium supply Dewar. A vacuum- jacketed

flexible copper transfer line connects the supply Dewar to the cryostat.

Except for this custom-built transfer line, all components of the liquid

helium refill system were obtained commercially.

The liquid helium in the cryostat is monitored by the level detector,

which is attached to one of the load frame columns. The desired minimum and

maximum level limits are set on the controller, and these limits trigger the

solenoid valve that regulates liquid helium transfer.

Operation is as follows: First, the supply Dewar is pressurized and

liquid helium transfers into the cryostat. When the liquid reaches the

233
maximum limit, the solenoid switch vents the pressure in the supply Dewar to

the atmosphere and the liquid helium transfer stops. As the fatigue test

proceeds, the steady state boil -off gradually causes the liquid in the

cryostat to fall to the minimum level. At this point the vent closes, the

supply Dewar is repressurized, and liquid helium again transfers into the

cryostat. When the maximum level is reached, the process repeats.

Tests at 4 K consume one standard K-cylinder of helium gas per day and

4.5 of helium per hour. The evaporated helium is released to the atmosphere

and not recovered because the installation of a gaseous helium recovery and

liquefaction system is too expensive at this time. Tests at other temperatures are also possible. For example, tests in liquid nitrogen at 76 K use a

system similar to that shown in figure 3, but nitrogen is substituted for helium and a nitrogen level detector and controller are used.

SPECIMEN GEOMETRY AND CLIP GAGE

The compact specimen geometry chosen for this study is shown in figure 4.

The specimen width (W) is 76.2 mm and the thickness (B) is 6.4 mm. The relatively large W/B ratio of 12 provides a sizable ligament for crack growth

while minimizing the fatigue load requirements. The initial machined notch is

22.7-mm long (a/W = 0.3) and the notch tip radius is 0.127 ± 0.05 mm.

Specifications for grips, fixtures, and specimen preparation are detailed in

ASTM E 647-83 and other relevant documents [14-16].

The clip gage used in threshold fatigue tests is a variant of the ring

gage previously described [19]. We modified it to use very short beams which

enable the gage to be tightly mounted close to the specimen. This stabilizes

the gage against vibration and reduces the signal noise. Calibrations at 295,

76, and 4 K indicated that the gage calibration factors are independent of

temperature to within 2 percent.

234
TEST PROCEDURE

Crack length (a) is measured by the compliance technique with a clip gage

mounted at the specimen edge. Compliance is defined as the specimen deflection per unit load, which depends on crack length for a given material and

specimen geometry. The load cell and clip gage signals were interfaced to the

computer, enabling the crack length to be inferred once per minute and displayed on the CRT terminal.

A flow chart for the automated near-threshol d fatigue crack growth test

is shown in figure 5. At the beginning of a test, the input parameters are

typed into the computer through the CRT terminal. These parameters include

specimen identification, specimen dimensions. Young's modulus, selected time

interval for measuring crack length, intermediate load level for compliance

measurement, initial AK , stress ratio, C (defined below) and test frequency. The time interval for measuring crack length is short enough that the

crack growth increments will not exceed the recommended values in ASTM E

647-83. The intermediate load level for compliance measurement is used to

avoid errors due to crack closure effects [7,12].

As the specimen is fatigued under the prescribed loading conditions and

cyclic frequency, a crack initiates and begins to grow. When the preselected

time interval (1 min) for crack length measurement is reached, the computer

requests the compliance data from the oscilloscope, which instantaneously

freezes the 1 oad-versus-di spl acement signals in memory and transmits them to

the computer. It correlates the data to a straight line using a linear leastsquares fit. A linear correlation coefficient of 0.995 or better is usually

obtained. From the resulting compliance, the instantaneous crack length is

computed using Saxena and Hudak's [20] calibration function. The precision of

the computed crack length is typically within 0.04 mm.

235
Only a portion of the load-versus-displacement curve is used for the

compliance calculation (i.e., the part from a specified intermediate load

level to a value corresponding to 95 percent of the maximum fatigue load).

The specified intermediate load is typically the mean load, because this is

usually larger than the crack closure loads. The upper 5 percent of the load

is excluded to eliminate any noise in the signals at maximum load during highfrequency tests.

As the crack grows, the difference between the current-measured crack

length and the last recorded crack length is checked against a specified value

(0.5 mm), which is within the recommended values of ASTM E 647-83. If the

increment of crack growth is equal to or greater than the specified value, the

computer calculates N, AK, and da/dN. The line printer also prints the calculated compliance, the linear least-squares correlation coefficient, and the

values a, N, da/dN, and AK. All these data are stored on floppy disks for use

in post-test analyses.

In near-threshold fatigue tests, the loads are progress! vely decreased in

the decreasing-AK technique. The load levels are calculated from the following equations [15]:

AK == AK^ exp[C'(a - a^)]

AP = BW^ AK/f(a/W) for the compact specimen

( 1 )

( 2 )

Pmax

- AP/(1 - R); P . = P mm max

(3)

where

P = maximum load max

P . = minimum load

mi n

R P . /P mm max

B = specimen thickness

W = specimen width

236
a = the current crack length

a^ = the crack length at the beginning of the test

f(a/W) = [2 + (a/W)][0.886 + 4.64(a/W) -13.32(a/W)2 + 14.72(a/W)3

- 5.6(a/W)4]/[l - (a/W)]3/2

AK = current crack-tip stress-intensity range

AK^ = crack-tip stress-intensity range at the beginning of the test

C = a constant

For a typical decreasi ng-AK technique, C (Eq. 1) is assigned a small,

negative number such as -0.08. Other types of tests can also be performed,

depending on the choice of the value of C. For example: C is set at a small

positive value for an i ncreasi ng-AK technique, or C is set equal to zero for

a constant-AK technique.

The sequence of operations is as follows (see figure 5): after each

crack length measurement, the crack length is compared with the last stored

crack length to ensure that a specified measurable amount 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 grows a certain amount (e.g., 0.13 mm), the new AK is calculated from

equation (1) and the new crack length is stored. The load levels are then

adjusted using equations (2) and (3).

At the relatively high frequencies desired in near-threshol d fatigue

testing, hydraulic lag can occur. Then, the specimen is not actually

subjected to the load range commanded by the computer (or waveform generator).

Overprogramming is sometimes necessary to overcome the problem. Automatic

overprogramming is a trial -and-error process whereby the computer monitors the

values of and

^ through the programmable digital oscilloscope and

makes necessary changes to achieve the commanded values of P and P . . ^ max mm

237
During the test, point-to-point data reduction is used to calculate AK

and da/dN from a and N. If the results of AK versus da/dN scatter excessively,

the seven-point incremental polynomial method can be used to smooth the results

after the test is completed.

The computer programs for post- test analyses include the following capabi 1 i ti es:

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 for several different specimens on one graph (for

compari son)

6. Calculating the material constants C and n in the Paris equation

da/dN = C(AK)*^ [15] and drawing the regression line through the

data.

It was observed in preliminary tests that crack closure, a common cause

of nonlinear compliance behavior, became more pronounced at lower loads as the

crack grew longer and the threshold region was approached. To minimize the

influence of crack closure, determinations at relatively short a/W values

were desired. For this reason the da/dN-versus-AK curves in this study were

_ 8 - 2Q obtained in two steps. The rates from about 10 to 10 m/cycle were first

is measured by the decreasi ng-AK technique starting at AK = 15 MPa*m with C =

-0.08 and f = 40 Hz. After reaching AK^^ at 10 m/cycle, the test was

stopped. The second data set was then measured by the i ncreasi ng-AK technique, starting again at about AK = 15 MPa*m^ but with C = 0.10 and f = 10 or

_8

20 Hz. This second data set provided the rates above 10 m/cycle and ap-

" 6 preaching 10 m/cycle.

238
For simplicity in this study, the da/dN-versus-AK curves and results

are presented on the basis of the applied AK values with no corrections for

crack closure. Since there are no accepted "standard" values for da/dN-versusAK or for these materials, no meaningful statements can be made about the

accuracy of results. The measurement precision is commensurate with current

practice as discussed in the appropriate standards [14-16].

MATERIALS

The tested materials were plates of AISI 304L, 304LN, and 316 stainless

steels in the as-received annealed condition. The AISI 304L and 304LN plates

were 25-mm thick, whereas the AISI 316 plate was 50.8-mm thick. Tables 1 and

2 list the alloy compositions and 4-K mechanical properties. The

near-threshol d fatigue test specimens were machined in the TL orientation.

RESULTS AND DISCUSSION

The da/dN-versus-AK curves at R = 0.1 for the AISI 300 series austenitic

stainless steels tested in this study are shown in figures 6 through 8. The

fatigue crack growth rates extend four orders of magnitude, from 10 ^ to

10 m/cycle, and are two orders of magnitude lower than any rates previously

published for this alloy at cryogenic temperatures. At their lowest values

(10 m/cycle) the rates correspond to 1 Angstrom per load cycle, or less

than one lattice spacing per load cycle. The AK^j^ values (operationally defined at 10 m/cycle) for AISI 304L, 304LN, and 316 are 7.4, 8.3, and 8.5

}<

MPa*m , respectively, at 4 K.

The data trend for AISI 304L (figure 6) is sigmoidal, as expected, but

the rates for this heat at intermediate AK values are higher than rates reported for other AISI 304L heats. The alloy tested in this study has significantly higher nitrogen and lower nickel content than previous heats [21], and

these compositional variations likely contribute to the 4-K rate differences.

239
The data for AISI 304LN are compared with a trend for previous measurements [21] on the same plate of steel at higher AK levels in figure 7. The

previous data represent tests of 25. 4-mm-thick compact specimens (W/B = 2) of

similar orientation and at frequencies from 20 to 25 Hz; the present data

represent 6. 4-mm-thick specimens (W/B = 12) at 20 Hz. The two independently

determined trends are in reasonable agreement, although the previous measurements are slightly higher for unknown reasons. A similar observation is made

for the AISI 316 stainless steel in figure 8, where comparison is again made

with previous data [22] from 25. 4-mm-thick specimens (W/B = 2) of the same

plate of steel.

When the three steels are compared (figure 9) we see that the AISI 304L

steel exhibits the lowest AK., value while the values for AISI 304LN and 316

th are nearly identical. A correction for crack closure might affect this comparison. Nevertheless, it appears that the differences in the near-threshold

fatigue behaviors of these AISI 300 series steels at 4 K are not very great.

SUMMARY

A fully automatic computer-controlled apparatus was designed and assembled to conduct near-threshol d fatigue crack growth rate tests at liquid

helium temperature, 4 K. In response to crack growth as monitored by compliance measurements in 6. 4-mm-thick compact specimens, the fatigue loads are

systematically decreased until the operationally defined threshold for fatigue

crack growth is reached at 10 m/cycle.

At present, a near-threshold test lasts 4 days with 24-h operation and is

performed at a frequency of 40 Hz. Typically, thirteen million fatigue cycles

are applied to a given specimen. The liquid helium consumption rate is

240
4.6 £/h, and the total liquid helium cost is about $1500 per threshold measurement. Modifications continue to be made to improve the accuracy of the measurements and to reduce costs.

The present test system was used in a preliminary study of AISI 300 series

stainless steels at 4 K and at a stress ratio of 0.1. The results consist of

da/dN-versus-AK curves and threshold stress intensity factors, AK.. . The AK..

th th

values for AISI 304L, 304LN, and 316 stainless steels are 7.4, 8.3, and 8.5,

respectively. The scope of future testing will be expanded to include

temperature, stress ratio, and frequency effects for these steels.

ACKNOWLEDGMENT

This research was sponsored by the Office of Fusion Energy, Dr. V. Der

project monitor. The authors are grateful to Dr. P. K. Liaw, Westinghouse

Research and Development Center, and to Dr. D. T. Read, National Bureau of

Standards, for helpful discussions and for reviewing the manuscript.

241
REFERENCES

1. R.J. Hooper, Use of crack propagation rate test data in establishing

design allowable stresses, presented at the NBS/DOE Workshop on Materials

at Low Temperatures, October 17-19, 1983, Vail, Colorado.

2. P. Komarek, Structural material investigation in conjunction with

superconducting magnet projects, presented at the NBS/DOE Workshop on Materials at Low Temperatures, October 14-17, 1984, Vail, Colorado.

3. "Fatigue Crack Growth Threshold Concepts," D. L. Davidson and S. Suresh,

Eds., Metallurgical Society of the AIME, Warrendale, Pennsylvania (1984),

p. 565.

4. "Fatigue Thresholds - Fundamentals and Engineering Applications," Vols. I and II, J. BScklund, A.F. Blom, and C.J. Beevers, Eds., Engineering Materials Advisory Services, Ltd., Chameleon Press, London (1982), p. 1174.

5. R.O. Ritchie, Near-threshold fatigue-crack propagation in steels, Int.

Met. Rev. , Rev. 245, Nos. 5 and 6: 205-230 (1979).

6. P.K. Liaw, W.A. Logsdon, and M.H. Attaar, Computerized near-threshold

fatigue crack growth rate testing at cryogenic temperatures: technique

and results, in: "Fatigue at Low Temperatures," ASTM STP 859, R.I.

Stephens, Ed., American Society for Testing and Materials, Philadelphia,

Pennsylvania (1985).

7. P.K. Liaw, W.A. Logsdon, and M.H. Attaar, Automated near-threshold

fatigue crack growth rate testing of JBK-75 stainless steel at cryogenic

temperatures, in: "Austenitic Steels at Low Temperatures," R.P. Reed and

T. Horiuchi, Eds., Plenum Press, New York (1983), pp. 171-185.

8. Y. Katz, A. Bussiba, and H. Matthias, Transitions in fatigue processes at

low temperatures, in: "Advances in Cryogenic Engineering -- Materials,"

Vol. 30, A.F. Clark and R.P. Reed, Eds., Plenum Press, New York (1984),

pp. 339-347.

9. E.K. Tschegg and S.E. Stanzl , Fatigue crack propagation and threshold in

bcc and fee metals at 77 and 293 K, Acta Metal 1

29:33-40 (1981).

10. S. Stanzl and R. Mitsche, High frequency fatigue of metals, crack

initiation and propagation, in: "Fracture 1977," Vol. 2, D.M.R. Taplin,

Ed., University of Waterloo Press, Waterloo, Ontario, Canada (1977),

pp. 749-753.

11. E.K. Tschegg, R.O. Ritchie, and S.E. Stanzl, Ultrasonic methods for

determination of near-threshol d fatigue crack growth rates in "Fatigue

Thresholds - Fundamentals and Engineering Applications," Vol. I,.

J. Backlund, A.F. Blom, and C.J. Beevers, Eds., Engineering Materials

Advisory Services, Ltd., Chameleon Press, London (1982), pp. 99-112.

12. R.S. Williams, P.K. Liaw, M.G. Peck, and T.R. Leax, Computer-controlled

decreasing AK fatigue threshold test, Eng. Fract. Mech. 18:953-964

(1983).

242
13. Y.W. Cheng and D.T. Read, An automated fatigue crack growth rate test

system, in: "Automated Test Methods for Fracture and Fatigue Crack

Growth," ASTM STP 877, American Society for Testing and Materials,

Philadelphia, Pennsylvania, to be published.

14. Standard_test method for constant amplitude fatigue crack growth rates

above 10 m/cycle, ASTM Designation E 647-83, in: "1984 Annual Book of

ASTM Standards, Metals - Mechanical Testing; Elevated and Low-Temperature

Tests," Section 3, Vol . 03.02, American Society for Testing and Materials,

Philadelphia, Pennsylvania (1984), pp. 711-731.

15. Proposed ASTM test method for measurement of fatigue crack growth rates.

Appendix II in: "Fatigue Crack Growth Measurement and Data Analysis,"

ASTM STP 738, S.J. Fludak, Jr. and R.J. Bucci , Eds., American Society for

Testing and Materials, Philadelphia, Pennsylvania (1981), pp. 340-356.

16. 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.

17. C.W. Fowlkes and R. L. Tobler, Fracture testing and results for a Ti-6A1-4V alloy at liquid helium temperature, Eng. Fract. Mech. 8:487-500

(1976).

18. D.T. Read and R. L. Tobler, Mechanical property measurements at low

temperatures, in: "Advances in Cryogenic Engi neeri ng--Material s

, " Vol.

28, R.P. Reed and A.F. Clark, Eds., Plenum Press, New York (1982), pp.

17-28.

19. R.L. Tobler and J.A. Shepic, Design and performance of a ring-shaped clip

gage for fracture mechanics testing, submitted to J. Test. Eval

20. A. Saxena and S.J. Hudak, Jr., Review and extension of compliance

information for common crack growth specimens, Int. J. Fract. 14:453-468

(1978).

21. R.L. Tobler and R.P. Reed, Interstitial carbon and nitrogen effects on the cryogenic fatigue crack growth of AISI 304 type stainless steels, J

Test. Eval. 12:364-370 (1984).

22. D.T. Read and R.P. Reed, Fracture and strength properties of selected

austenitic stainless steels at cryogenic temperatures , " in: "Materials

Studies for Magnetic Fusion Energy Applications at Low Temperatures -- II," NBSIR 79-1609, National Bureau of Standards, Boulder, Colorado

(1979), pp. 81-122.

243
Table 1. Composition of test materials (wt. %).

Material Fe C Mn P S Si Cr Ni Cu Mo Co N

AISI 304L bal. 0.020 1.73 0.024 0.005 0.62 18.20 8.56 0.24 0.40 0.16 0.082

AISI 304LN bal

0.037 1.50 0.022 0.017 0.57 18.0 9.91 0.197 0.205 0.120

AISI 316 bal

0.057 1.86 0.024 0.019 0.58 17.25 13.48 2.34 0.030

Table 2. Measured mechani cal properties of test materials.

Materia! Test

Temp.

(K)

Yield

Strength

(MPa)

Ultimate

Strength

(MPa)

El ongati on

(%)

Reduction

of Area

(%)

Rockwel

Hardness

(Rb)

AISI 304L 295 245 642 66 77 82

4 610 1678 35 48 --

AISI 304LN 295 279 612 68 62 79

4 745 1570 34 42 --

AISI 316 295 228 576 56 73 79

4 711 1301 48 57 --

244
245

igure

1

Fully

automatic

cryogenic

near-threshol

d

fatigue

crack

growth

rate

test

apparatus

used

in

this

study.
Figure 2 A flow chart of the automatic fatigue crack growth rate test system.

246
Figure 3 A schematic of the automatic liquid helium refill system.

Finish except boles, as noted. (Dimensions in millimeters)

Figure 4 The compact- type test specimen used in this study.

247
Figure 5 A summary flow chart of the automated near-threshol

fatigue crack growth rate test.

248
Fatigue

crack

growth

rate,

da/dN,

m/cycle

10

10

10

10

10

Figure

Figure 6 Fatigue crack growth rate data

and threshold stress intensity

factor for AISI 304L stainless

steel at 4 K.

Stress intensity factor range, AK, MPa m‘'/2

Fatigue crack growth rate data

and threshold stress intensity

factor for AISI 304LN stainless

steel at 4 K.

249
Fatigue

crack

growth

rate,

da/dN,

m/cycle

Figure 8 Fatigue crack growth rate data

and threshold stress intensity

factor for ATSI 316 stainless

steel at 4 K.

Figure 9 Comparison of fatigue crack

growth rate curves for AISI

304L, 304LN, and 316 stainless steels at 4 K.

250


FATIGUE CRACK INITIATION FROM NOTCHES

IN AUSTENITIC STAINLESS STEELSt

R. L. Tobler and Q. S. Shu*

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

Fatigue crack initiation from notches in austenitic stainless steels was

studied for the first time using compact specimens of two common cryogenic

alloys: AISI 316 and AISI 304L. The procedure is based on a fracture

- 1/2 mechanics technique whereby AK-p , a parameter proportional to the change

in maximum elastic stress at the notch root, is correlated with the cycles to

initiate a 0.254-mm crack. The effects of some experimental variables

including notch radius, stress level, specimen size, and test temperature

(295, 76, and 4 K) are presented, and the fatigue crack initiation resistances

of the AISI 316 and 304L austenitic steels are compared with martensitic and

ferri tic/pearl

tic steel data at room temperature.

Key words: austenitic stainless steels; cryogenic properties; fatigue; fatigue crack initiation; fracture mechanics; notch tip radius effect.

^Visiting scholar on leave from Zheijang University, Hangzhou, People's

Republic of China.

tContribution of NBS, not subject to copyright.

251
INTRODUCTION

Fatigue crack initiation, long neglected in fatigue studies of structural

alloys at cryogenic temperatures, is explored in this paper using the fracture

mechanics approach promoted by Jack and Price [1]. This approach assumes that

the crack initiation life of a notched specimen correlates with the maximum

elastic stress, S , in the material ahead of the notch, and that S is

’ max ’ ’ max

- 1/2 proportional to the parameter K*p , where K is the applied nominal stress

intensity factor range and p is the notch tip radius. Thus:

2K-(np)-l/2 = = k^S (1)

where k^ is an elastic stress concentration factor and S is the nominal stress.

In Eg. 1, the nominal K is obtained from standard stress intensity expressions where the notch length, £, is used as if it were equivalent to a

sharp crack of length a. Justification for this derives from analysis showing

that the elastic stress field distribution ahead of a blunt crack is similar

in many respects to that ahead of a sharp crack [2]. If the notch length is

much larger than p. Eg. 1 is accurate to within 10% [3,4]; if not, another

method must be used because the notch is no longer crack-like in form.

- 1/2 Further rationale for the use of K-p or S for the characterization

of fatigue crack initiation at notches is set forth by Rolfe and Barsom [5]

and also by Dowling [6]. Previous studies have considered only martensitic

and ferritic/pearl itic steels at room temperature [7-16]. This paper represents the first application to austenitic stainless steels at 295, 76, and

4 K. Several variables influencing the results for austenitic stainless

steels are examined; notch radius, stress level, test temperature, and

specimen size. Fatigue crack initiation threshold behavior is also

considered, and it is concluded that the performance of austenitic stainless

steels can not be predicted from the established trends for nonaustenitic

steels at room temperature.

252
MATERIALS

Commercial grade AISI 316 and AISI 304L austenitic stainless steel plates

were tested in their as-received (annealed) conditions. These steels are

microstructural ly stable at 295 K, but they exhibit partial martensitic phase

transformations during tests at 76 and 4 K. The mill chemical compositions of

these steels in weight percent are listed in Table 1. The conventional

mechanical properties are listed in Table 2.

SPECIMENS

The majority of tests used 6.4-mm-thick compact specimens, as shown in

Fig. 1. These specimens were 76-mm wide and had notch radii of 0.127 ±

0.051 mm. A series of 25. 4-mm-thick, 50.8-mm-wide specimens was also prepared

to demonstrate the specimen size effect. The notches were machined such that

the normal to the notch plane was in the transverse direction of the plate,

and the direction of crack propagation was in the longitudinal direction of

the plate (TL orientation [17]). To study the notch radius effect, variations

of p ranging from 0.076 to 1.27 mm were created by grinding (p < 0.9 mm) or

drilling (p > 0.9 mm). The notch radii were measured from profile photographs

on both faces of the specimen and the minimum p was used. There were no

subsequent notch tip preparations, such as annealing or polishing.

TEST PROCEDURE

Crack initiation was detected by compliance measurements (deflection per

unit load) using a clip gage mounted at the specimen edge. The specimens were

cycled at a stress ratio of 0.1 and at frequencies up to 20 Hz, with periodic

interruptions for single-cycle loadings at 0.02 Hz. During single-cycle

loadings, the load cell and clip gage signals were fed into a minicomputer for

253
real-time data reduction, and a standard compliance function was used to infer

crack lengths. The computer-assisted technique was developed by Cheng and

Read [18].

Plots of crack length versus cycles (a versus N) were recorded and analyzed for the crack initiation data. Crack initiation was defined at N^. as

the number of cycles to achieve a 0.254-mm increment of growth, Aa^. . The

- 1/2 - 1/2 values of N. were then plotted versus AK*p or AK*p , where p is a

critical radius defined below, and AK = K - K . for the fatigue load max mm ^

cycle. Finally, a threshold for fatigue crack initiation was defined as the

_ 2/2 6 value of AK*p^ at N^. = 10 cycles. The threshold corresponds to a level of

0

stress for which fatigue cracks do not initiate below 10 cycles, and its

significance for nonaustenitic steels is discussed by Rolfe and Barsom [5].

During each test the fatigue loads were constant, and AK increased with

Aa. However, the AK increase for Aa^. = 0.254 mm at constant load was negligible, less than 5%. Progressively deeper notches were machined after each

crack initiation measurement so that each specimen could be used three times.

COMPLIANCE ANOMALY AND DEFINITION OF CRACK INITIATION

A typical a-versus-N curve is shown in Fig. 2. Shortly after the test

began there was an apparent decrease of crack length owing to an anomalous

compliance decrease. With continued cycling the compliance gradually increased as a consequence of true crack initiation and growth, the net result

being a shallow minimum in the a-versus-N curves at each temperature.

Possible explanations for this anomaly are offered later in discussion.

Various definitions of crack initiation have been used since the choice

is arbitrary and dependent on test procedure. In previous studies at 295 K,

N^. was most often defined as the number of cycles needed to initiate a

254
0.254-mm crack, as determined by visual observation of the notch tip with a

traveling microscope. In this study using the compliance technique, N^. was

taken a full 0.254-mm increment beyond the true starting notch length.

Increasing Aa^. would shift N^. to higher cycles (see Fig. 3), but this would

only slightly increase the measured threshold for crack initiation as

indicated in Fig. 4.

RESULTS

Notch Radius Dependence

The effect of notch radius on fatigue crack initiation was studied at

76 K for three material/AK combinations. In each case, p was varied while AK

was held constant. The resulting plots of p-versus-N^. , shown in Figs. 3 and

5, have two regions. In the first region, N^. apparently is independent of p,

and in the second region N^. increases with p, according to a nonlinear

function. The critical radius, p^, is found at the intersection of the two

trends, and it represents a radius below which further increases in notch

acuity have no effect on crack initiation life.

To determine p^, several polynomial expressions were fit to the

p-versus-N curves, but the results were strongly biased by the number of terms

- 1/2

in the polynomial. Instead, Fig. 6 presents plots of AK-p versus N^. on

natural logarithmic coordinates. Such plots facilitate the determination of

p^ since the data are then subject to linear least squares fits. The values

of p^ deduced from the intersection points of Fig. 6 are;

AISI 316

—I

II cn K, AK = 46 p = 0.255 mm

AISI 316 (T = 76 K, AK = 23 MPa*m^'^^): p = 0.175 mm

AISI 304L >

V —1 II K, AK = 46 MPa-m^^^): p = 0.290 ^0 mm

1 /? The p^ values for AISI 316 and AISI 304L at 76 K and AK = 46 MPa-m"^' are

nearly equivalent. These results are also equivalent to the result for mild

255
steel where = 0.25 mm at 295 K [1]. The AISI 316 results suggest a possible

dependence on AK, but this point is uncertain owing to sizable data scatter.

Material Dependence

The fatigue crack initiation resistances of the two austenitic stainless

steels at 76 K are compared in Fig. 7. These data were obtained using specimens of constant radius, p = 0.127 ± 0.050 mm. Since this radius is lower

- 1/2 than p^, the data are plotted in terms of AK*p^ . This provides a more

meaningful correlation since any radius lower than p^ would not affect the

crack initiation life.

As shown in Fig. 7, the data for the two steels at 76 K appear to be

grouped relatively close together over most of the range of N, but the

threshold is 25% higher for AISI 304L than for AISI 316. The ultimate t'^nsile

strength, a^, for AISI 304L is also about 22% higher than that of AISI S16 at

76 K (see Table 2). The threshold, therefore, appears to be material

dependent and correlates to a^, as brought out further in discussion.

Temperature Dependence

Figures 8 and 9 show the effects of test temperature on crack initiation

resistance. The curves at all three temperatures (295, 76, and 4 K) were

constructed using the p^ values measured at 76 K (0.255 for AISI 316 and 0.290

for AISI 304L). This approximation introduces uncertainty in the 295- and 4-K

results but was tolerated because the precise temperature dependence of p^ is

unknown and would be costly to determine. For AISI 316, Fig. 8 indicates that

the crack initiation resistance increases monotoni cal ly with temperature

reductions from 295 to 76 to 4 K. The 76 and 4 K data converge at high N, so

that the thresholds at 76 and 4 K are nearly equivalent and higher than at

295 K.

256
For AISI 304L, Fig. 9 indicates somewhat different behavior; Again, the

crack initiation resistance is higher at 76 and 4 K than at 295 K. However,

the 76- and 4-K curves crossover at N^. = 2 x 10^ cycles. Consequently, for N^.

less than 2 x 10^, the fatigue crack initiation resistance is lower at 4 K

than at 76 K, whereas for N^. greater than 2 x 10^, the 4-K resistance is

equivalent or slightly higher than that at 76 K.

Specimen Size

Figure 10 compares 76-K crack-initiation data of 6.4- and 25. 4-mm-thick

specimens taken from the same heat of AISI 316 steel. The width-to-thickness

ratios for these specimens are 12 and 2, respectively. A specimen size effect

is demonstrated, in that crack initiation occurs sooner in the 25. 4-mm-thick

- 1/2 specimens for all values of . The threshold is also 20% lower for

the thicker specimens.

There are two possible explanations for the size effect. First, a

plastic constraint effect may be operative such that the crack initiation

resistance is actually lower for the 25. 4-mm-thick x 50.8-mm-wide specimens

than for the 6.4-mm x 76-mm specimens. Otherwise the size effect may reflect

a limitation owing to the use of a nominal AK, as mentioned in the discussion

below.

DISCUSSION

The use of a nominal AK value to describe notch conditions has been

criticized, since early crack growth is controlled by the notch tip plastic

strain, and since linear elastic fracture mechanics loses significance for

small cracks [19,20]. However, the notch tip strains responsible for fatigue

- 1/2 should correlate with AK*p if the notch tip stresses are relatively small

- 1/2 [6,13], and the AK*p -versus-N^. correlations should still be tenable,

257
assuming that the notch tip plasticity is similar for specimens having similar

- 1/2 values of AK-p [6]. Recently, several models were derived in support of

- 1/2

the AK-p -versus-N^. correlations [21,22]. Therefore, additional experimental work is required to verify the useful limits of these correlations.

Several practical problems of this method became evident in this study.

First, the definition of fatigue crack initiation at Aa^. = 0.254 mm is arbitrary, and its measurement is affected by the compliance anomaly (Fig. 2). An

apparent decrease of crack length with fatigue cycling was also observed in

the work of Fleubaum and Fine [23]. They attribute the anomaly to the influence

of residual compressive stresses induced during the development of the notch

tip plastic zone, or else to an increase in the amount of out-of-plane displacement. Another possible explanation from Nicholas et al . [24] involves a

change in the three-dimensional stress state with cycling such that there is a

stiffening of the effective modulus of the material in the direction normal to

the notch plane.

Another problem arose in connection with the critical radius, p^. Our

findings suggest that may be mildly dependent on the AK level. Also,

might be temperature dependent, because these austenitic steels are microstructurally stable at 295 K but unstable (i.e., transforming to martensite) at 76

and 4 K. To determine precisely for each set of experimental conditions

would require considerable effort and expense. On the other hand, assuming

that is constant at 295, 76, and 4 K increased the uncertainty of results

in Figs. 8 and 9. Future tests should use notches with p greater than p^ to

avoid this problem.

Despite these problems, the fracture mechanics method of this study provided useful information on fatigue crack initiation resistance. Qualitative

agreement is evident between present results and expectations from conventional

S-N fatigue tests. Conventional S-N tests involve both crack initiation and

258
crack propagation, but crack initiation strongly predominates in the high-cycle

range. For N = 10®, the crack initiation stage may account for up to 90% of

the total fatigue life. Therefore, some correlation is expected between

fatigue crack initiation test results and S-N test data in the high-cycle

range.

In general, conventional S-N data for metals at constant temperature show

a trend of increasing fatigue life with increasing g^. Also, a metal's fatigue

resistance typically increases at low temperatures owing to an increase of g^.

Thus, the thresholds for crack initiation for both alloys in this study increased at cryogenic temperatures (Figs. 8 and 9). Also, in Fig. 7, the -25%

higher threshold for AISI 304L relative to that of AISI 316 at 76 K ranks in

proportion to the 22% difference in g^ for these alloys.

As noted earlier, fatigue crack initiation from notches in nonausteni ti

steels has been extensively studied at 295 K, and excellent correlations have

been established between the threshold and tensile properties (g^ or g^).

Generally, the threshold increases with increasing strength, until at sufficiently high strengths (g = 965 MPa or g = 1035 MPa) there is no longer any

y u effect [5]. In Fig. 11, the data trends for martensitic and ferri tic/pearl i tic

steels at 295 K are represented and compared with the austenitic stainless

steel data from this paper at 295, 76, and 4 K.

The thresholds for the two austenitic steels increase with g or g at

y u low temperatures owing to higher strengths, but otherwise there appears to be

no similarity between the austenitic and nonaustenitic steel behaviors. The

correlation of thresholds with g^ (Fig. 11) for austenitic steels is especially

poor. Several plausible reasons for this difference in material dependence

can be given. Under stable conditions (295 K) the austenitic steels workharden according to significantly different stress-strain laws, whereas under

metastable conditions (76 or 4 K) the austenitic steels transform partially to

259
martensitic phases with very high work-hardeni ng capacities. Moreover,

conventional S-N fatigue data for ferritic steels show a true fatigue limit

near 10^ cycles, whereas austenitic steels do not. Instead, austenitic steels

are characterized by an endurance limit that continues to decrease in the

high-cycle range between 10^ and 10^ cycles. In this study, a fatigue crack

0 initiation threshold was arbitrarily defined at N^. = 10 cycles. Tests

9 continuing to 10 cycles may have given different results, but such tests are

time consuming and costly at 4 K, and are therefore beyond the scope of

present study.

SUMMARY AND CONCLUSIONS

A fracture mechanics approach to the characterization of fatigue crack

initiation at notches was applied for the first time to AISI 316 and 304L

austenitic stainless steels at 295, 76, and 4 K. The data presented here are

potentially useful for estimating the crack initiation life of components and

for correlating with other mechanical properties, including conventional

tensile or S-N fatigue data. The following conclusions emerged:

1) The a-versus-N curves inferred by specimen compliance measurements

reveal an anomalous effect whereby the system stiffens and the crack

length apparently decreases by several percent. This anomaly occurs

just after fatigue cycling begins and, apparently, prior to crack

i nitiation.

2) The fatigue crack initiation resistance of austenitic stainless

steels tends to decrease with decreasing notch tip radius until a

critical radius is reached, below which there is no further effect.

3) The fatigue crack initiation resistance of AISI 316 and AISI 304L

austenitic stainless steels increases at cryogenic temperatures, and

the increase at N^. = 10® cycles approximately correlates with the

increase in ultimate tensile strength.

260
4) The fatigue crack initiation resistance of AISI 316 and AISI 304L

austenitic stainless steels is subject to a specimen size effect at

76 K.

5) The fatigue crack initiation threshold behavior of austenitic

stainless steels is dissimilar to and can not be predicted from the

established correlations for martensitic and ferritic/pearl itic

steels at 295 K.

ACKNOWLEDGMENT

This research was sponsored by the Department of Energy, Office of Fusion

Energy, Dr. V. Der, Project Monitor.

REFERENCES

1. A.R. Jack and A.T. Price, The initiation of fatigue cracks from notches

in mild steel plates, Int. J. Fract. Mech. 6, 401-409 (1970).

2. M. Creager and P.C. Paris, Elastic field equations for blunt cracks with

reference to stress corrosion crackina, Int. J. Fract. Mech. 3, 247-252

(1968).

3. T.D. Dudderar and E.M. Doerries, A study of effective crack length using

holographic i nterferometry , Exp. Mech. ]^, 300-304 (1976).

4. K. Heckel and R. Wagner, The tensile fatigue behavior of CT specimens

with small notch root radius, Int. J. Fract. IJ, 135-140 (1975).

5. S.R. Rolfe and J.M. Barsom, Fracture and Fatigue Control in Structures,

Applications of Fracture Mechanics , Prentice Hall, Englewood Cliffs, New

Jersey, 208-231 (1977).

6. N.E. Dowling, Fatigue at notches and the local strain and fracture me- chanics approaches, Fracture Mechanics , ASTM STP 677, American Society

for Testing and Materials, Philadelphia, 247-273 (1979).

7. R.G. Forman, Study of fatigue crack initiation from flaws using fracture

mechanics theory, Eng. Fract. Mech. 4, 333-345 (1972).

8. M.B.P. Allery and G. Birbeck, Effect of notch root radius of the initiation and propagation of fatigue cracks, Eng. Fract. Mech. 4, 325-331

(1972).

261
9 . J.M. Barsom and R.C. McNicol, Effect of stress concentration on fatigue

crack initiation in HY-130 steel, Fracture Toughness and Slow Stable

Cracki ng , ASTM STP 559, American Society for Testing and Materials,

Philadelphia, 183-204 (1974).

10. W.G. Clark, Jr., Evaluation of the fatigue crack initiation properties of

type 403 stainless steel in air and steam environments. Fracture Toughness and Slow Stable Cracking , ASTM STP 559, American Society for Testing

and Materials, Philadelphia, 205-224 (1974).

11. J.T. Barnby and R. Holder, Fatigue properties of a cast steel, Int. J. Fract. 12, 631-637 (1976).

12. A. Baus, H.P. Lieurade, G. Sanz, and M. Truchon, Correlation between the

fatigue crack initiation at the root of a notch and low-cycle fatigue

data. Flaw Growth and Fracture , ASTM STP 631, American Society for

Testing and Materials, Philadelphia, 96-111 (1977).

13. W.G. Clark, Jr., Stress-corrosion crack initiation in high strength type

4340 steel. Flaw Growth and Fracture , ASTM STP 631, American Society for

Testing and Materials, Philadelphia, 121-138 (1977).

14. Y.H. Kim, T. Mura, and M.E. Fine, Fatigue crack initiation and microcrack

growth in 4140 steel. Metal 1. Trans. 1679-1683 (1978).

15. B.L. Braglia, R.W. Hertzberg, and R. Roberts, Crack-initiation in a highstrength low alloy steel. Fracture Mechanics , ASTM STP 677, American

Society for Testing and Materials, Philadelphia, 290-302 (1979).

16. R. Brook, A. Cadman, and C.E. Nicholson, Initiation of short cracks at

notches by fatigue. Proceedings of ICF International Symposium on Fracture Mechanics , Science Press, Beijing, China, 624-628 (1983).

17. Standard terminology relating to fracture testing, ASTM designation:

E 616-82, 1984 Annual Book of ASTM Standards , American Society for

Testing and Materials, Philadelphia, 671-684 (1984).

18. Y.W. Cheng, and D.T. Read, An automated fatigue crack growth rate test

system. Automated Test Methods for Fracture and Fatigue Crack Growth , ASTM STP 877, American Society for Testing and Materials, Philadelphia,

to be published.

19. R.A. Smith, A simplified method of predicting the rates of growth of

cracks initiated at notches. Fracture Mechanics in Engineering Practice , Applied Science Publications, London, 173-182 (1977).

20. R.A. Smith and K.J. Miller, Prediction of fatigue regimes in notched

components, Int. J. Mech. Sci. 201-206 (1978).

21. K. Tanaka, Y. Nakai , and R. Kawashima, Fracture mechanics approach to

fatigue crack initiation from deep notches, Eng. Fract. Mech. 2^,

1011-1023 (1983).

22. K. Tanaka and T. Mura, A micromechanical theory of crack initiation from

notches, Mech. Mater. 1, 63-73 (1981).

262
23. F. Heubaum and M.E. Fine, Short fatigue crack growth behavior in a high

strength low alloy steel, Scripta Metal 1. IB, 1235-1240 (1984).

24. T. Nicholas, N.E. Ashbaugh, and T. Weerasooriya, On the Use of Compliance

for Determining Crack Length in the Inelastic Range, Fracture Mechanics , ASTM STP 833, R.J. Sanford, Ed., American Society for Testing and

Materials, Philadelphia, 682-698 (1984).

Table 1. Composition of test materials (wt.%).

Material Fe C Mn P S Si Cr Ni Cu Mo Co N

AISI 304L bal

0.020 1.73 0.024 0.005 0.62 18.20 8.56 0.24 0.40 0.16 0.082

AISI 316 bal

0.057 1.86 0.024 0.019 0.58 17.25 13.48 -- 2.34 0.030

Table 2. Mechanical properti es of test materials.

Material Test Temperature

(K)

Yield

Strength

(MPa)

Ultimate

Strength

(MPa)

Elongation

(%)

Reduction

of Area

(%)

Rockwell

Hardness

(Rr)

AISI 304L 295 245 642 66 76 82

76 441 1516 44 61 -- 4 610 1678 34 48 --

AISI 316 295 228 576 56 73 79

76 608 1243 62 70 -- 4 711 1301 48 57 --

263
41.900

±

0.250

Finish except holes, as noted.

(Dimensions in millimeters)

gure 1. Compact fatigue crack initiation specimen.

264
Figure 2. Typical a-versus-N curve, where a is inferred by the compliance

method.

FATIGUE CRACK INITIATION

LOAD CYCLES, Nj kilocycles

Figure 3. Effect of notch tip radius on crack initiation life for several Aa.

increments: AISI 304L at 76 K and AK = 46 MPa-m^'^^

265
NOTCH

TIP

RADIUS,

p,

mm

FATIGUE CRACK INITIATION CYCLES, Nj

- 1/2 Figure 4. The -versus-N^. correlations for alternative definitions of

crack initiation.

FATIGUE CRACK INITIATION

LOAD CYCLES, Nj kilocycles

Figure 5. Effect of notch tip radius

on crack initiation life:

AISI 316 at 76 K and at

two AK levels.

266
tiKpy^

,

MPa

10

Figure 6. Plots of fi,n (AK*p"^^^^-versus-

£n (N^. ) for tests where AK is

held constant, p is varied,

and p„ is determined from the

AK*p"^'^ value at the intersection of two straight lines.

FATIGUE CRACK INITIATION CYCLES, Nj

- 1/2 Figure 7. The AK*p -versus-N. curves for AISI 316 and AISI 304L at 76 K. ^0 1 (Arrow indicates runout.)

267
AK-yO

,

MPa

AKp;;i^2_

10 "1 I I I I I

I I "I I I r I' I I1 1

1

1—r r -\I

10'=’ -

10' J I II I 1 1 J I L I I I I I I I I J L 10' 10' 10'

Figure 8.

11. 10 ' FATIGUE CRACK INITIATION CYCLES. Nj

- 1/2 Effect of temperature on the AK*p^ -versus-N^ correlation for

AISI 316 stainless steel. (Arrow indicates runout.)

- 1/2 Figure 9. Effect of temperature on the AK*p^ -versus-N^. correlation for

AISI 304L stainless steel. (Arrow indicates runout.)

268
FATIGUE CRACK INITIATION CYCLES. Nj

Figure 10. Effect of compact specimen size on the fatigue crack initiation

resistance of AISI 316 stainless steel at 76 K. (Arrow indicates

runout.

)

Figure 11. Correlation of fatiguecrack initiation threshold

with tensile properties,

showing differences betweer

austenitic steels and

martensitic or ferritic/

pearl i tic steels.

200 500 1000 2000

Yield strength, Oy, MPa

269

I.

STACKING-FAULT ENERGIES IN 304-TYPE STAINLESS STEELS:

EFFECTS OF INTERSTITIAL CARBON AND NITROGEN*

H. M. Ledbetter and M. W. Austint

By measurement, we studied the problem of stacking-fault probability and

stacking-fault energy in nine 304-type stainless-steel alloys where C-plus-N

content varied from 0.3 to 1.3 atomic percent. In one formulation of the

problem, stacking-fault energy depends on four variables: stacking-fault

probability, unit-cell size, <1 1 1 >-direction Young's modulus, and dislocation

density (or root-mean-square distortion strain). From powders, we determined

stacking-fault probability by x-ray diffraction; we measured shifts of ( 111 ) and ( 200 ) diffraction peaks in both annealed-recrystall ized and heavily

deformed specimens. This analysis also yielded the unit-cell size.

Obtaining the <11 1> Young modulus requires knowing the monocrystalline

elastic constants, j , which we estimated from the polycrystalline elastic

constants with a reverse Kroner method and an assumption about the C 12 /C -11 ratio. We determined the distortion strain from the relative deformationinduced broadening of the (111) and (222) diffraction peaks. With C-plus-N

alloying, unit-cell size increases approximately 0.3 percent, the <11 1> Young

modulus decreases approximately 0.5 percent, stacking-fault probability

decreases approximately 6 percent, and distortion strain increases approximately 2 percent. The combined effects of these variable changes predict

that stacking-fault energy increases approximately 10 percent per percent

interstitial C-plus-N content. Of the four variables, stacking-fault probability contributes most to the increase; for the zero-interstitial-content

intercept, we found 0.016. For stacking-fault energy, we found a zero-solute

intercept of 18 mj/m^. No difference appeared between effects of interstitial C and N. Peak-broadening showed that the effective size of the

coherently diffracting domain decreased approximately 30 percent per percent

solute; the zero-solute intercept was 450 A.

Key words: alloying effect; austenitic steel; face-centered-cubic alloy;

interstitial; iron-base alloy; stacking-fault energy; stainless

steel; x-ray diffraction.

* Intended for Metallurgical Transactions; not subject to copyright.

+ H. M. Ledbetter and M. W. Austin are research metallurgist and materials

research engineer, respectively, at the Fracture and Deformation Division,

Center for Materials Science, National Bureau of Standards, Boulder,

Colorado 80303 .

271
INTRODUCTION

Close-packed crystal structures often contain defects in the stacking

sequence of close-packed (octahedral) planes. We call this defect a stacking

fault . In a face-centered-cubic (fee) crystal structure, a stacking fault

converts the perfect abcabc stacking to either abcbca (intrinsic fault) or to

abebabe (extrinsic fault). Clearly, deformation faults must be intrinsic.

Stacking-fault geometry has received considerable attention. For example,

Hirth and Lothe [1] devoted M8 pages of their dislocation-theory textbook to a description of fee stacking faults, which relate intimately to partial dislocations. Several authors reviewed the subject of stacking faults: Seeger

[2,3], Christian and Swann [^4], and Christian and Vitek [5].

Stacking-fault energy (sfe), T, is what we call the extra energy associated with the stacking defect. Apparently, Heidenreich and Shockley [6]

first estimated this energy; for cobalt they obtained 20 mJ/m^. Hirth and

Lothe [1] gave a table of sfe for thirteen close-packed metals; values range

from 16 mJ/m^ for Ag to 750 mJ/m^ for Rh. For common metals, they reported

166 for A1 , A5 for Cu, 125 for Ni, 125 for Mg, and 140 for Zn. Because we can represent a stacking fault as two coherent-twin boundaries, we expect the

stacking fault energy to be approximately twice the energy of a coherent-twin

boundary

Stacking-fault energy interests both theorists and experimentalists

because it relates closely to various solid-state phenomena. These phenomena

include relative phase stability [7]; cross-slip [3]; and dislocation jogs,

which influence plastic deformation [8]. Rhodes and Thompson [9] mentioned

that sfe affects such metallurgical phenomena as work hardening, stresscorrosion cracking, and hydrogen embrittlement. Adler and Wagner [10] added

to this list several other phenomena: recrystallization, texture, microstructure, and low-temperature creep.

EXPERIMENTAL APPROACHES

Many methods exist for determining sfe experimentally. A review by

Gallagher in 1970 [11] gave twelve methods:

• creep measurements ( microstrain

)

• coherent-twin energy

• deformation twinning

• extended dislocation nodes

• faulted dipoles

• grain-boundary energy

• fault probability, x-ray, normalized

• loop annealing

• rolling texture

• tau-three

• tetrahedra

Although incomplete, this list suggests many approaches to measuring sfe

and shows that sfe relates to many solid-state phenomena.

272
Reported experimental values vary considerably. For Cu, for example,

Gallagher [11] gave twenty-four values with a range of 24 to 165 mj/m^ and a recommended value of 55 mJ/m^.

THEORETICAL APPROACHES

With a few caveats, we can equate the stacking-fault energy to the

energy difference between cph (close-packed-hexagonal) and fee phases. Then

sfe connects closely with the panoply of relative-lattice-stability theory.

For nontransition metals, theory gives reasonable agreement with observation.

Theory gives the correct sign, correct magnitude, and correct structural

trends. For transition metals, the theory of sfe requires further improvement.

To date, no one has calculated the sfe of an Fe-Cr-Ni alloy or of fee Fe

,

where an accepted interatomic potential exists [12]. However, existing calculations for other systems give some insights for Fe. Especially, calculations for Cu assume special importance. Despite Cu possessing a filled

3d shell, its cohesive properties reflect a strong d-electron contribution.

Thus Cu differs from Fe principally in the number of d electrons.

Blandin, Friedel, and Saada [13,14] considered, in the approximation of

pair interactions, the stability of fee crystal structures against twinning

and faulting. Because faults do not affect the number and spacing of

nearest-neighbor atoms, Blandin et al. represented the interatomic potential

by its large-r asymptotic form involving Friedel oscillations. These authors

concluded that the electron-to-atom ratio controls the eph-fee relative

stability.

Using a pairwise central-force approximation and a Morse interatomicpotential function, Cotterill and Doyama [15] calculated for Cu a sfe of

30 mJ/m^. Using a Harrison pseudopotential for Al , they calculated 250 mj/m^.

By considering a series of interatomic potentials, they concluded that the

sfe depends strongly on the chosen potential.

In his book on pseudopotentials in metals, Harrison [16] gave a secondorder-perturbation pseudopotential model for sfe. Although, they did not

calculate sfe, Suzuki and Ledbetter [17] showed that the usual pseudopotential

calculation for sfe includes four terms: Born-Mayer energy (or some equivalent energy to allow for the d-electron interaction); the Madelung-Fuchs

(electron-ion electrostatic) energy; and the first-order and second-order

perturbation-theory band-structure terms.

Hodges [18,19] reported two sfe studies. The first follows the

approach of Blandin et al. [13]. In the second, for four non-3d-band metals

with sp-electron bonding, Hodges used a Heine-Abarenkov pseudopotential to

estimate the sfe. Also, Hodges established a relationship between sfe and

the difference between cph and fee crystal-structure energies.

273
For Pb, Hodges obtained a negative sfe. Bonsignori et al. [20]

attributed this failure to Hodges's local approximation. Using a nonlocal

model, approximated by a phenomenological energy-wavenumber characteristic,

Bonsignori et al. predicted a positive, low sfe.

By a pseudopotential method that one would expect to yield a negative

sfe, Krasko et al. [21] predicted a remarkably accurate value for Cu:

40 mJ/m^.

Using a two-resonance-parameter one-electron band-structure approach,

Pettifor [22] considered the equilibrium crystal structures of the 3d-transition metals and found that the energy difference, AE = E(cph) - E(fcc), varies

cyclically with N, the number of d-plus-outer-s electrons per atom. Pettifor

found fee stable in the ranges 11 > N > 8.6 and 6.7 > N > 4.5. This model

predicts that fee Fe possesses a negative sfe. Pettifor gave possible

reasons why the model gives the wrong sign for AE.

In studying Al, Wilkes and Sargent [23] used a pair potential, calculated 142 mJ/m^, and verified that the energy of an intrinsic stacking fault

equals twice the energy of a twin. These authors pointed out that calculating the sfe provides a good test of a proposed interatomic potential because

the fault does not change the near-neighbor distance. If this distance

changed, it might invalidate the perturbation-theory basis of the interatomic

potential.

Using the Blandin et al. [13] method, Beissner [24] calculated the sfe

of six metals, including Cu, for which he obtained 45 mJ/m^. Beissner con- cluded that a first-order perturbation method succeeds, that exchange and

correlation effects do not contribute, and that one can treat the important

and difficult nonlocal effects approximately by an empirical energywavenumber character istic . For noble metals, this characteristic strongly

affects the calculation. Thus, for 3d-electron metals, Beissner finds little

hope for a successful simple model. Beissner used an up-to-date pseudopotential to construct a real-space potential that was summed over atomic

planes.

To calculate sfe, Vitek [25] used three types of interatomic potentials:

Johnson, Morse, and an oscillation, such as the Harr ison-Pick pseudopotential. For central-force interactions, he found the predictions agreed

with a hard-sphere model.

Using a wavenumber-space calculation, Devlin [26] sought to improve

Beissner *s results. For six metals, including Cu, he found good agreement

between calculation and observation. For Cu, for which he obtained 71 mj/m^,

Devlin found that the band-structure term accounted for 95 percent of the

sfe. Thus, electrostatic and d-electron-o verlap terms are small.

Focusing on transition metals, Beissner [27] improved the previous calculations of Beissner and of Devlin. In his second study, Beissner introduced the third-order term in the perturbation expansion of the total energy.

This term sums the three-ion interaction energies. Beissner went beyond

Pettifor 's model [22] by considering nonresonant scattering. His results

274
depend strongly on valence, especially for valences lower than that of Fe. In

transition metals, Beissner found that sfe depends mainly on two effects:

resonant scattering and three-ion interactions.

A recent study by Esterling et al. [28] considered Cu and obtained 73 mj/m^

for the sfe. These authors considered many different interatomic potentials

and concluded that sfe does not provide a good fitting parameter for empirical potentials.

DEFORMATION FAULTS AND X-RAY DIFFRACTION

Proof that metals contain stacking faults originated with Edwards and

Lipson [29], who studied Co. Their x-ray diffraction patterns showed a remarkable systematic mixture of sharp and diffuse lines. These authors

reasoned that some lines remain unaffected by faults, whereas others change

both position and intensity. In a companion paper, using reciprocal-lattice

concepts, Wilson [30] modeled the Co case. His model predicts the linewidths, that 2,-even lines broaden more than 2,-odd lines, and that total line

intensity changes only slightly.

Cobalt's faults probably originate in a martensitic transformation,

which contains a shear deformation in its mechanism.

Barrett [31] suggested that mechanical stress should cause stacking

faults. He reasoned that such deformation-induced faults must arise

frequently because gliding atomic planes do not know where to stop. For

atoms gliding over an "a" plane, both "b" and "c" sites offer the same number

of near neighbors and the same interatomic forces. Each wrong stop produces

a fault. Barrett [32] pointed out that deformation faults could account for

many observations: strain markings, increased x-ray reflection near slip

bands, deformation-induced disappearance of Kikuchi lines, and hardening of

latent slip planes. Barrett also emphasized that faulting involves low

interfacial energy and small volume-free-energy increase. Later, Barrett

[ 33 ] produced the first direct proof of mechanically induced faults in

metals. He detected stacking disorders in deformed Cu-Si alloys by analyzing

x-ray diffraction patterns from oscillating polycrystals. For non-Laue diffraction streaks, he noted direction, length, and intensity. Barrett relied

on the predictions by Wilson [ 3 ^] and Zachariasen [35,36] that faults do not

widen (11*0) rhombohedral-hexagonal spots because they belong to the class

h-k = 3n, where n denotes any integer, including zero. Barrett also invoked

Zachariasen 's derivation of the intensity distribution along a diffraction

streak. In another study, Barrett [37] measured the (200) line widths in

several plastically deformed fee metals. He concluded that faults contribute

significantly to line broadening.

The subject advanced markedly when Paterson [ 38 ] derived explicit

expressions for fault density, which is given either by the breadth or displacement of the reciprocal-lattice streak. In the x-ray diffraction

pattern, faults cause line broadenings and line shifts. For {111} planes,

for example, two lines remain sharp and unshifted, whereas six become diffuse

and shift to a higher Bragg diffraction angle, theta, the usual diffraction

angle in Bragg’s law. For {200} planes, all six become diffuse and move to

275
lower theta. Paterson says "the intensity distribution, the displacements of

peaks, and the integral breadths ... are determined completely in terms of

a." (Alpha denotes stacking-fault probability, the probability that a given

plane is faulted.) To obtain quantitative details of the x-ray diffraction

pattern, one must convert from the reciprocal lattice to real space and sum

the various contributions using Warren and Averbach [39] multiplying factors.

Paterson's model contains several assumptions that deserve mention:

faults are distributed randomly, exist solely in one set of planes within a monocrystal, and occur in small numbers (small alpha). Also, application

of Paterson's broadening relationship assumes no broadening from sources

other than faults. But we know that lines broaden from other factors: small

coherently diffracting domains and distortions within these domains.

In a remarkable review on the Fourier analysis of line profiles, Warren

[40] effected the above-mentioned rec iprocal-space-to-real-space transformation and gave an expression for alpha based on line shifts:

I

2

- (')

(u + b)h

o -I

A(20°) = 90/3

a tan 9

where the reader should see Warren's Eq. (48) for definitions of terms.

For various hkS!, , Warren tabulated the term within brackets which arises

because the basic equations hold only for one point in reciprocal space.

X-ray diffraction lines represent superpositions (sums) from many reciprocal

points. This summation involves averaging. For the first two fee diffraction lines, Eq. (1) gives

and

A(26^^^)

^(202oo)

Thus

,

A(20 200

45/3

= p ottan0 111

2tt

= 45/3 ^ , -

2 atan02oo

TT

Q 45v^3ct 26ii-|) = -

2 1^^^*^®200 ( 1 /2 ) tan0 -] 1

]

IT

( 2 )

(3)

(4)

Warren gave four advantages for using a measurement suggested by this relationship: (1) the two A20° displacements add because they differ in sign;

(2) sample-position error is compensated partially; (3) error arising from

deformation-induced lattice-constant change is compensated partially; (4) no need arises to measure accurately a single reflection. This relationship

provides a direct determination of alpha, independent of line broadening

caused by particle size and lattice distortion.

For a typical metal (unit-cell size = a = 3*60 A) examined with Cu

radiation (wavelength = A = 1.54 A), Eq. (4) becomes

276
A(202oo -

26i°i 1 ) = -5.31a (5)

Thus, to measure an alpha of 0.001, one needs a peak-position inaccuracy in

26 of approximately 0.005 degrees, perhaps the practical limit of existing

commercial diffractometers.

When stress occurs in the diffracting particles, one must correct Eq. (4)

to allow for the elastic strain. Wagner et al. [41] give this correction in

a relationship written in terms of the lattice constant, a:

^^111 ^^200

= - Ka + Za

where o denotes stress and

Z = (Si 1

- (Si )2oo

( 6 )

(7)

where, for an elastically isotropic material,

Si = -v/E (8)

where v denotes Poisson ratio and E, Young modulus. For anisotropic

mater ials

^1 = ~^hk2,/^hkS, ^9)

Determining and Ej^j^j^ from the monocrystal elastic constants remains an unsolved problem. Many studies used the average of the Voigt (constant

strain) and Reuss (constant stress) models. More recently, some studies used

a Kroner average.

Several notable reviews exist on the relationship between plastic deformation and x-ray diffraction. Greenough [42] reviewed the early studies and

gave 114 references. Warren’s [40] review, emphasizing Fourier analysis of

line profiles, lists 43 references. Welch and Otte’s [43] brief, insightful

literature evaluation contains 60 references. Vasilev and Smirnov [44]

covered a broad field, emphasized Soviet studies, and gave 335 references.

Wagner [45] published an excellent mathematical overview, invaluable to the

practitioner, that includes 91 references.

Relationship between stacking-fault probability and stacking-fault energy

Consider stacking faults to arise from the separation of an fee slip

dislocation into two partial, or so-called half, dislocations of the

Heidenreich-Shockley type:

Y~ [ 101 ] = [ 211 ] + [ 112 ] ( 10 )

277
Then one can derive the following relationship

Y = (1/2V37T )a3Q( 1 1 1 )p/a (11 )

where Y denotes stacking-fault energy; a, unit-cell size; p, dislocation density (cm/cm3); a, stacking-fault probability, and

G(1 1 1 ) = (C^

^ 2

+ 044)73 (12)

is the elastic shear modulus for any direction on a (111) plane, where

denote the three independent cubic (Voigt) elastic stiffnesses.

Many studies get information about sfe by measuring its probability and

making some assumption about density. G(111) tends to vary slowly with com- position, is known for common alloys, and can often be estimated for others.

As described below, this approach to sfe sometimes fails, as for the present

alloys.

One often writes Eq. (11) with mean-square strain substituted for dislocation density. Whether dissociated or not, dislocations distort the lattice

and cause a strain /(<^2). Williamson and Smallman [46] showed that dislocation density and dislocation-induced strain relate according to

p = 2ke2/a2 (13)

where the constant k depends on the model and ranges between 2 and 28. For a screw dislocation, Wilson [4?] gave an exact peak-broadening calculation; for

a face-centered-cubic lattice with Burgers vector = [110], Wilson's model

predicts k = I 6 .I. Rounding this to I 6 , Eq. (13) becomes

p = (32/a2)e2 (14)

and Eq. (11) becomes

Y = ( 4 / 3/ 3tt )aG( 1 1 1 )e2/a (15)

Some risk exists in applying the above relationships to highly mechanically deformed materials. These relationships apply to the equilibrium case where the partial dislocations separate by an equilibrium spacing, the equilibrium stacking-fault width, established by a balance between dislocation

elastic repulsive force and the fault's surface tension. Highly deformed

materials do not represent equilibrium. Stacking faults, which contribute to

the mechanical deformation by relieving the applied stress, may grow wider

than the equilibrium size. Perhaps they extend across the entire crystal.

Taking Y = 20 mj/m^, the equilibrium size for stainless steel is [48]

n = G(111)(bi • b2)/2TTY = (1/24tt) G(111)a2/Y = 57 A (16)

By considering elastic stored energy, Adler et al. [49] rewrote Eq. (15):

Y = (2/5/3)aE(hkiOp2/a (17)

278
where E(hk!l) becomes E(111) for (lll)-type diffraction peaks, where E denotes

the Young modulus perpendicular to the diffracting crystallographic plane.

The factor of 5 in the denominator arises from a study by Adler and Otte [50].

The present study adopts Eq. (17) as the basic relationship among stackingfault energy (T), unit-cell size (a), <1 1 1 >-direction Young modulus [E(111)],

microstrain (e), and stacking-fault probability (a).

STUDIES ON Fe-Cr-Ni ALLOYS

Otte [51] reported perhaps the first x-ray diffraction, although qualitative, study of stacking-fault formation in Fe-Cr-Ni-type alloys. He con- cluded that both Or and Mn lower the stacking-fault energy, Ni lowers it

less, and 0 produces a small effect, probably raising the stacking-fault

energy. Quantitatively studying three alloys —Fe-1 6Cr-1 5Ni , Fe-1 6Cr-l 2Ni

,

and Fe-30Ni —Goldman and Wagner [52] concluded that Ni increases the

austenite stacking-fault energy, and Or decreases it.

The present study used x-ray diffraction methods to study the effect of

interstitial C plus N on the stacking-fault energy of 30^-type austenitic

steel. On this subject, from analysis of published results, Schramm and Reed

[53] reported the surprising chemical-composition dependence:

Y = k + W(Ni) - 0.2 W(Cr) + Ml 0 W(C) (18)

and

Y = 3^ + 1.^ W(Ni) - 1.1 W(Cr) - 77 W(N) (19)

where Y has units of mj/m^ and W denotes weight percent. By surprising we mean that the C coefficient is so large and opposite in sign to the N coefficient. Re-examination of the C effect by Brofman and Ansell [54], using

transmission electron microscopy, led to the conclusion

Y = 16.7 + 2.1 W(Ni) - 0.9 W(Cr) + 26 W(C) (20)

with the C coefficient lower by a factor of 16 than the Schramm-Reed

result. Brofman and Ansell found that their result "concurs with the literature in finding that Y is relatively insensitive to small changes in carbon

content for this ... alloy ...."

EXPERIMENT

Materials

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 AISI-304

stainless steel, nominally Fe-1 8Cr-10Ni-1 . 5Mn-0.01P-0.02S-0.55Si-0.2Mo-0.2Cu

weight percent. The C-and-N contents varied, as shown in the mill chemical

analyses in Table I. The nine plates were produced from three 1 36-kg vacuum- induction-melted heats, split with respect to C level, and teemed into

279
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.

Specimens

We obtained powders by filing bulk material at ambient temperature. We

sieved these powders through a No. 100 screen with a 150-ym opening size. On

the basis of a grain size of 78 to 105 um, deformed powder particles con- tained one to seven crystals. Annealing consisted of heating powders in

evacuated capsules for 30 min at 1000°C. We obtained x-ray diffraction

specimens by sprinkling powders into a viscous grease in a recess in a flat

plate and pressing them lightly to achieve flatness.

In the alloys containing lower C plus N, high mechanical deformation

caused by filing induced fcc-to-bcc ( gamma-to-alpha) phase transition. This

martensitic phase evidenced itself principally as a (llO)-bcc diffraction

peak at a slightly higher 20 than the (lll)-fcc diffraction peak. Annealing

the powders reduced, but did not eliminate, this peak. Because the two peaks

show a 20 separation of approximately one degree, the (llO)-bcc peak was removed readily using a deconvolution procedure. For the cph (epsilon)

phase, we found no evidence. If this phase occurred, one would expect a (0002)-cph diffraction peak at exactly the (lll)-fcc 20 value and a (1011)-

cph diffraction peak at 20 near A6.7 degree.

Equl pment

The measuring apparatus consisted of a commercial horizontal BraggBrentano-focusing, computer-automated diffractometer with a 22-cm diffractometer radius. The diffractometer contained a scintillation counter and a monochromator, a curved-graphite (Johann) type, located between the specimen

and the counter.

Measurements

Using dif fracted-beam monochromatic Cu-K^ radiation at an exciting

potential of 45 kV , we step-scanned at 0.02-degree increments in 20 for

either 90 s or 1500 counts, whichever occurred first. The wider deformed

(111) peak corresponded to approximately 100 measurements. We stored the

measurements in a computer for later processing. We removed K^2 radiation by

Rachinger's method and obtained peak positions by fitting to a Pearson type-7

function

y max

(0 - 0max

2W

-2

(21 )

where denotes maximum intensity; 0, diffraction angle; and W, full peak

width at half-maximum intensity.

280
In both the incident beam and the diffracted beam, we used 1 -mm horizontal

Sollei—slit packs with 4.0-degree vertical divergence slits and 0.05-degree

receiving slits.

The uncontrolled temperature in the diffractometer chamber varied from

26 to 29°C. Typically, all three (111), (200), and (222) peaks were scanned

in 12 h.

We corrected the peaks for both Lorentz scattering factor and for

polarization.

Storing deformed powders at ambient temperatures showed some small so- called self-annealing after approximately 20 days. Both peak breadth and

peak position relaxed measurably toward the annealed values.

Peak Broadening

Aqua [55] established that one can determine x-ray diffraction peakbroadening by three methods: Fourier analysis, integral breadth, and

variance. For the present study, we took the line breadth, B, as the width at

half-maximum intensity fitted to the Pearson function, Eq. (21).

Several methods exist to correct for instrumental peak broadening. For

a Cauchy peak shape, a linear relationship applies:

where subscript d denotes deformed; obs, observed; and a, annealed. For a Gaussian peak shape, the correction is quadratic:

Wagner and Aqua [56] showed that a better relationship lies between these two

limits and is parabolic:

For the present study, we adopted Eq. (24) to correct for instrumental peak

broadening and obtain the widths of diffraction peaks for the deformed case. Wagner and Aqua cite several other studies that support Eq. (24).

Apparently, Dehlinger and Kochendorfer [57] were first to suggest (in

1939) that diffraction-peak breadth arises from two principal sources: particle size, where

Bp = A/D cose (25a)

and strain, where

Bg = k tane (25b)

®d " ^obs ^a ( 22 )

(23)

®d ®obs ®a^^obs (24)

281
In these relationships, D denotes particle size; 0, diffraction angle; A, x-ray

wavelength; and k, a constant. Note that only Bp depends on A. This permits

separating the two terms. Thus,

B = Bp + Bg (26)

or

B COS0 1

I 4e sin0

A D A

Here, we use the result that k = 4e [56], where e denotes the microstrain in

Eq. (17). Thus, a graph of (B cos0)/A versus (sin0)/A gives D as the inverse

intercept and 4e as the slope. To obtain D and <=

, we did this analysis for

the (111) and (222) diffraction peaks. As discussed by Wagner and Aqua [56],

using another set, such as (200) and (400), leads usually to different results

for D and e, especially e, because Young modulus, E(hk2,), depends strongly

on direction.

Estimation of G(111) and E(111)

Because the appropriate-composition monocrystals do not exist, one can

not determine G(111) or E(111) directly. But, the polycrystal elastic con- stants were reported [58]. From these, one can estimate the by the

following method.

Especially for cubic crystal symmetry, the problem of relating the monocrystal elastic constants (C-|-|, C^2> B 44 ) to the quasi-isotropic polycrystalline elastic constants (B, G) has been studied extensively, both theoretically

[ 59 ] and experimentally [60]. The bulk modulus, B, because it is a rotational invariant of the elastic-stiffness tensor, is always given by

B = (C^

^ + 2C-, 2)/3 (28)

even for a highly textured material. The expression for the shear modulus,

G, depends on the assumptions of the model. Considering the self-consistent

problem of an anisotropic monocrystal inclusion embedded in a corresponding

isotropic matrix and assuming stress equilibrium at the interface, Krbner

[61] showed that

g3 + aC2 + BG + Y = 0

where

ct - (5C-|i + 4C-]2)/8

6 = -Ci^ij(7C^i - 4 Ct2)/8

and

^ - Bi|i|(Ci 1 - Ci2)(Ci-| + 2C-|2)/8

(29)

(30)

(31 )

(32)

282
In the forward case, these relationships permit the calculation of B and G

from the

j

, the isotropic from the anisotropic, two elastic constants from

three.

With one additional piece of information, from either theory or observation, from some single relationship among the Cj_j , one can compute the reverse case also. The can be computed from B and G. This additional

piece of information comes from the existing values for fee Fe-Cr-Ni

alloys. Recently, Ledbetter [62] reviewed these. Among these alloys, he

found a surprising near constancy of both

Ci2/Ci 1 = 0.652 ± 0.025 (33)

and Zener's anisotropy index

A = - Ct2) = 3.53 ± 0.17 (34)

Using the first relationship and Kroner's method, one obtains the elastic

constants shown in Table II. We see that within a standard deviation of

one-half percent G(111) does not vary from the value 66.8 ±0.3 GPa.

Similarly, E(111) does not vary from the value 304 ± 2 GPa. Thus, neither

elastic constant accounts for any measurable variation of sfe with composition. One obtains the shear modulus on the (111) plane from Eq. (12) and the

<1 1 1 >-direction Young modulus from

E(lll)"1 = S^^(2Si-i - 28^2 - Si,j4)/3 (35)

where the elastic compliances relate inversely to the elastic stiffness :

CCij] [Sij] . (36)

where I denotes the 6x6 identity matrix. We estimate the uncertainty in both

G( 1 1 1 ) and E(lll) as 2 percent.

Unit-Cell Size

We obtained the unit-cell size, a, from annealed powders. Figure 1 shows a typical case. This figure shows a for various hkH diffraction peaks

plotted versus cos6*cot0, which equals zero when 20 = l80°. Thus, the intei

cept gives the best unit-cell size. The line represents a linear leastsquares fit. The double points represent the and K^2 ^’ef lections. For

the present study, we estimate the uncertainty in a as ±0.0002 A.

RESULTS

Table III contains the study's principal results for the nine alloys:

unit-cell size, stacking-fault probability, root-mean-square distortion

strain, size of the coherent-diffracting domain, and finally, the stackingfault energy. Measured polycrystal and calculated monocrystal elastic

constants occur in Table II. Figure 2 shows these results together with

linear-least-squares trend lines.

283
or

For the stacking-fault energy the best-fit line is

Y(mJ/m2) = 18.3 + 1 .9 A(C + N)

Y(mJ/m2) = 18.3 + 8.2 W(C + N)

( 37 )

(38)

where A and W denote atomic and weight percentages of C plus N. Attempts

failed to separate the C and N effects.

Concerning imprecision and uncertainty, Fig. 2 reflects the first.

Above, we give uncertainties for E(111) and for a. Often, authors estimate

uncertainty in sfe as plus-or-minus 50 percent. Our experience suggests no stronger statement for the present study.

Can we understand the study’s most important result: interstitial C and

N atoms increase the stacking-fault energy of an fee Fe-l8Cr-10Ni alloy? For

this discussion, we sometimes ignore the alloy and focus on unalloyed Fe.

Also, we assume that stacking-fault energy varies as AE = E(cph) - E(fcc),

where E denotes energy.

The energy difference between Fe’s eph and fee forms provides a focus of

several studies: Kaufman et al. [631, Andersen et al. [6^,65], Grimvall

[66], Pettifor [22], and Hasegawa and Pettifor [67]. Among these studies,

both different approaches and sometimes contradictory conclusions arise.

For Fe's three crystalline structures—bcc, fee, eph, Andersen et al.

[64,65] calculated the dependence of magnetic properties on crystal structure

and on atomic volume. Their model involves self-consistent, spin-polarized

band calculations. For transition metals, their results contain many implications: (1) The 3d-band structure determines crystal structure and magnetic

moments. (2) Under compression, "kinetic" energy overcomes "exchange" energy

with a resulting reduction of magnetic moment. (3) The sp-d hybridization is

significant, but less so than s-p hybridization. (4) The number of d electrons and the Stoner parameters are constant, independent of crystal

structure and independent of atomic volume. (5) For a given atomic volume,

paramagnetic potential parameters are independent of crystal structure.

(6) For the bcc crystal structure, paramagnetic fermi level, E^ , occurs at a peak in the density-of-states curve, and not at a peak for the eph crystal

structures. (7) The sp electron energy should not affect crystal structure

because the sp band is nearly isotropic. (8) A ferromagnet ic-bcc to paramagnetic-eph phase transition occurs when the bcc atomic radius is reduced

4 percent. (9) The Fe is ferromagnetic at all volumes exceeding 0.92 of the

bcc equilibrium volume.

Using an itinerant-electron-model spin-fluctuation theory, Hasegawa and

Pettifor [ 67 ] calculated the free energy of the bcc (a, 6), fee (Y), and eph

(a) phases of Fe. They considered effects of both temperature and pressure.

They focused on magnetic band-structure contributions and ignored both

lattice vibrations and short-range magnetic order. They found the following

DISCUSSION

284
results: (1) At zero temperature, the nonmagnetic energy favors r. This

agrees with the observation that the isovalent 4d and 5d nonmagnetic elements

Ru and Os show a cph crystal structure. (2) At zero temperature, the

magnetic energy stabilizes the a phase. (3) The bcc density-of-states curve

shows a strong peak near the fermi level, , where the cph and fee phases

show no peak. Thus, only bcc Fe satisfies the Stoner criterion for ferromagnetism. (4) Pressure (lower volume) decreases the magnetic energy and

favors the cph phase. (5) A eph-fee phase transition occurs at T = 3^0 K

because the eph-phase entropy decreases less rapidly because of a lower

density-of-states near the fermi level. (6) Magnetic interactions dominate

the a-Y-6 phase interrelationships. No need exists to invoke phonon

contributions.

The above studies show that increasing volume favors the fee phase over

the cph phase. Thus, higher atomic volume increases stacking-fault energy in

fee Fe. By x-ray diffraction Ledbetter and Austin [68] showed that alloying

interstitial C plus N into Fe-l8Cr-10Ni increases volume by 0.7V(Fe) per

interstitial atom, where V(Fe) denotes the atomic volume of Fe.

If effective atomic volume determines the C-plus-N effects on stackingfault energy, it may contribute also to effects of substitutional elements:

Cr , Ni , and Mn. For the alloys, the effective atomic volumes equal 11.53 a3.

For the principal elements, the atomic volumes equal 11.71 for Fe, 11. 9A for

Cr , 10.87 for Ni , and 12.21 for a-Mn and I4.4l for T-Mn. Thus, atomic-volume

considerations suggest that Cr and Mn increase sfe and Ni decreases sfe.

Except for Ni , no experimental consensus exists concerning alloying effects

on sfe in Fe-Cr-Ni alloys. Almost everyone agrees that Ni produces a small

increase; if included in Eq. 38, the coefficient for Ni would take a value

of approximately two.

The failure of atomic volume to explain Ni’s effect on sfe suggests

other factors: the electronic density of states —N(E) versus E—and the

electron-to-atom ratio (e/a). Considering only Fe , Cr , and Ni , these alloys

possess an e/a ratio of 6.8 (Fe =7, Cr = 5 , Ni =9, Mn = 6 ) . Using a twoparameter d-resonance model, Pettifor [22] calculated the N(E) curves for

bcc, fee, and cph phases by a hybridized near-free-electron scheme. Pettifor

found that the N(E) curves for fee and cph are practically identical for

e/a i 4, except that cph does not possess a peak near e/a = 7.5, which favors

fee at higher e/a. This extra fee N(E) peak assumes importance for sfe con- siderations. Nickel added to Fe-Cr-Ni would raise the fermi energy more for

the cph case than for the fee case, thus increasing AE(cph-fcc), and thus

increasing the sfe. Conversely, added to Fe-Cr-Ni, both Cr and Mn would

lower e/a, decrease AE(cph-fcc), and lower the sfe. Therefore, considering

both atomic volume and e/a, both factors suggest that Mn decreases sfe. For

Cr and Ni , the two factors suggest opposing effects. From observation for

Ni, the e/a effect dominates the volume effect.

Not considered by Pettifor [22], another factor enters: magnetic

interactions. Much more difficult to consider theoretically, these electron

spin-spin interactions received attention by Andersen et al. [63.64] and by

Hasegawa and Pettifor [67]. As described above, contrary to previous studies, the latter concluded that "phase transitions in iron are driven by the

285
magnetic contributions to the free energy." Although fee Fe-Cr-Ni-Mn alloys

exhibit no macroscopic magnetism, effective local magnetic moments must occur because all four atomic species exhibit either ferromagnetism or antiferromagnetism.

All three of these factors—atomic volume, density of states, and

magnetic interactions —interrelate. Strictly, one can not consider them

separately. Calculations by Andersen et al. [63, 6M] show that local magnetic

moment increases with increasing atomic volume. And we know that increased

volume decreases bandwidth and increases N(E). The study by Madsen et al.

[64] shows relationships among volume, d-state density, and local magnetic

moment.

Although we see how interstitial C and N increase volume, their effect

on electron-to-atomic and on magnetic interactions remains unclear. Using

sound velocity, Ledbetter [69] showed for Fe-Cr-Ni alloys that C and N

increase volume, reduce the magnetic interaction, and suppress the

paramagnetic-antiferromagnetic phase transition that occurs in these alloys

at low temperatures. Magnetic-susceptibility-versus-temperature measurements

confirm the sound-velocity results [70]. We do not know whether C and N

contribute electrons to the free-electron band structure or whether C and N

form local, covalent bonds and local intermetallic compounds such as Fei^C and

Fee.*

CONCLUSIONS

From this study, six conclusions emerge:

1. Interstitial C plus N increase the stacking-fault energy (sfe) of

304- type stainless steel. The increase amounts to approximately 10

percent per atomic percent solute. The intercept ( zero-C-plus-N ) value

of sfe equals 18 mj/m^.

2. Behaviors C and N do not differ significantly.

3. Among four variables, stacking-fault probability (sfp) produces the

largest change in sfe. The sfp decreases approximately 6 percent per

atomic percent solute. The intercept sfp equals 0.016.

4. Considering the other three variables, distortion strain increases approximately 2 percent, unit-cell size approximately 0.3 percent and

both G(111) and E(111) decrease approximately 0.5 percent. Thus, the

unit-cell size and elastic-constant variables nearly offset.

* Before finally publishing this manuscript, the authors intend to add

several topics to the discussion section. These include: the low sfe of

Fe-Cr-Ni alloys compared with fee Ni , the element adjacent to Fe in the

periodic table; the relationship between microstrain and plastic deformation, especially the yield strength; the decrease in coherently diffracting

domain size; and, perhaps, dislocation density.

286
5. The coherent-dif fracting-domain size decreases approximately 30 percent.

The intercept value equals 450 A.

6. Not yet do we understand why C and N increase sfe. Possible factors in

the final understanding include atomic volume, electron-to-atom ratio,

and magnetic interactions.

ACKNOWLEDGMENTS

This study received

Energy.

sponsorship from the U.S.

REFERENCES

DoE , Office of Fusion

1.

J. P. Hirth and J. Lothe: Theory of Dislocations, pp. 306~353» WileyIn terse ience. New York, 1982.

2. A. Seeger: in Defects in Crystalline Solids (Bristol Conference),

pp. 328- 339 , The Physical Society, London, 1954.

3 . A. Seeger: in Dislocations and Mechanical Properties of Crystals,

pp. 243- 329 , General Electric Co., 1957.

4. J. S. Christian and P. R. Swann, in Alloying Behavior and Effects in

Concentrated Solid Solutions, pp. 105-269, Gordon and Breach, 1965.

5 . J. W. Christian and V. Vitek: Rep. Prog. Phys. , 1970, vol. 33,

pp. 307-41 1

6. R. D. Heidenreich and W. Shockley: Strength of Solids, pp. 57-75,

Physical Society, London, 1947.

7. V. Heine and D. Weaire: Solid State Phys., 1970, vol. 24,

pp. 249-463.

8. A. Seeger: in Defects in Crystalline Solids (Bristol Conference),

pp. 391-401, The Physical Society, London, 1954.

9. C. G. Rhodes and A. W. Thompson: Metall. Trans. A, 1977, vol. 8A

pp. 1901-1906.

10. R. P. 1. Adler and C. N. J. Wagner: J. Appl. Phys., 1962, vol. 33,

pp. 3451 - 3458 .

11. P. C. J. Gallagher: Metall. Trans., 1970, vol. 1, pp. 2429-2461.

12. R. A. Johnson: Phys. Rev., 1966, vol. 145, pp. 423-433.

13 . A. Blandin, J. Friedel, and G. Saada: J. Phys. (Paris), 1966, vol. 27,

pp. C3-128-C3-136.

287
14* A. P. Blandin: Phase Stability in Metals and Alloys, pp. 115-12A,

McGraw-Hill, New York, 1967.

15. R. M. J. Cotterill and M. Doyama: Phys. Rev., 1966, vol. 145,

pp. 465-478.

16. W. A. Harrison, Pseudopotentials in the Theory of Metals, pp. 207-209.

Benjamin, New York, 1966.

17. T. Suzuki and H. M. Ledbetter: Philos. Mag., 1983, vol. 48, pp. 83-94.

18. C. H. Hodges: Acta Metall. , 1967, vol. 15, pp. 1 787-1 784.

19. C. H. Hodges: Philos. Mag., 1967, vol. 15, pp. 371-392.

20. F. Bonsignori, V. Bortolani, and G. Velo: Nuovo Ciraento, 1968, vol. 57,

pp. 194-207.

21. G. L. Krasko, V. N. Teiiyants, R. T. Pozvonkova, and Y. 1. Zaslavskii:

Sov. Phys. - Solid State, 1968, vol. 9, pp. 2414-2416.

22. D. G. Pettifor: J. Phys. C, 1970, vol. 3, PP. 367-377.

23. P. Wilkes and C. M. Sargent: Met. Sci. J. , 1972, vol. 6, pp. 216-219.

24. R. E. Beissner: Phys. Rev. B, 1973, vol. 8, pp. 5432-5442.

25. V. Vitek: Philos. Mag., 1973, vol. 18, pp. 773-786.

26. J. F. Devlin: J. Phys. F, 1974, vol. 4, pp. 1865-1882.

21. R. E. Beissner: Phys. Rev. B, 1976, vol. 13, PP. 5131-5135.

28. D. M. Esterling, A. R. McGurn, I. M. Boswarva, and R. J. Arsenault:

Mater. Sci. Eng., 1984, vol. 68, pp. 97-106.

29. 0. S. Edwards and H. Lipson: Proc. Roy. Soc. bond., 1942, vol. I80,

pp 268-277.

30. A. J. C. Wilson: Proc. Roy. Soc. bond., 1942, vol. I8O, pp. 277-285.

31. C. S. Barrett: in Cold Working of Metals, pp. 65-112, American Society

for Metals, Metals Park, Ohio, 1948.

32. C. S. Barrett: in Imperfections in Nearly Perfect Crystals, pp. 97-128,

Wiley, New York, 1952.

33. 0 GO Barrett: Trans. AIME, 1950, vol. 188, pp. 123-135.

34. A. J. C. Wilson: Acta Crystall. , 1952

,

vol. 5, pp. 318-322.

288
35 . W. H. Zachariasen: Phys. Rev., 19^7, vol. 71, pp. 715-717.

36. W. H. Zachariasen: Acta Crystall. , I9I18, vol. 1, pp. 277-281.

37. C. S. Barrett and M. A. Barrett: Phys. Rev., 1951, vol. 81, p. 311.

38. M. S. Paterson: J. Appl. Phys., 1952, vol. 23, pp. 805-811.

39. B. E. Warren and B. L. Averbach: J. Appl. Phys., 1950, vol. 21,

pp. 595-599; J. Appl. Phys., 1952, vol. 23, pp. ^97-500.

40 . B. E. Warren: Prog. Metal Phys., 1959 vol. 8, pp. 147-202.

41. C. N. J. Wagner, J. P. Boisseau, and E. N. Aqua: Trans. Metall. Soc.

AIME, 1965, vol. 233, PP. 1280-1 286.

42. G. B. Greenough: Prog. Metal Phys., 1952, vol. 3, PP. 176-219.

43. D. 0. Welch and H. M. Otte: Adv. X-Ray Analy. , 1963, vol. 6,

pp. 96-120.

44. D. M. Vasilev and B. J. Smirnov: Sov. Phys. Usp. , 1961, vol. 4,

pp. 226-259.

45. C. N. J. Wagner: in Local Atomic Arrangements Studied by X-Ray Diffraction, pp. 219-269, Gordon and Breach, New York, 1965.

46. G. K. Williamson and R. E. Smallman: Proc. Phys. Soc., 1955, vol. B68,

pp. 577-585.

47. A. J. C. Wilson: Research, 1949, vol. 2, pp. 541-542.

48. L. F. Vassamillet: J. Appl. Phys., 1961, vol. 32, pp. 778-782.

49. R. P. I. Adler, H. M. Otte, and C. N. J. Wagner: Metall. Trans., 1970,

vol. 1 , pp. 2375-2382.

50. R. P. I. Adler and H. M. Otte: Mater. Sci. Eng., 1966, vol. 1,

pp. 222-238.

51. H. M. Otte: Acta Metall., 1957, vol. 5, pp. 614-627.

52. A. J. Goldman and C. N. J. Wagner: Acta Metall., 1963, vol. 11,

pp. 405-413.

53. R. E. Schramm and R. P. Reed: Metall. Trans. A, 1 975, vol. 6A , pp. 1345-1351.

54. P. J. Brofman and G. S. Ansell: Metall. Trans. A, 1 978, vol. 9A , pp. 879-880.

55. E. N. Aqua: Acta Crystall., 1966, vol. 20, pp. 560-563.

289
56. C. N. J. Wagner and E. N. Aqua: Adv. X-ray Anal., 1964, vol. 7,

pp. 46-65.

57. U. Dehlinger and A. Kochenddrfer : Z. Krist. Miner. Petrol., 1939, vol.

101 , p. 134.

58. H. M. Ledbetter and M. W. Austin: Mater. Sci. Eng., in press.

59. H. M. Ledbetter: J. Appl. Phys. , 1973» vol. 44, pp. 1451-1454.

60. H. M. Ledbetter: J. Phys. D., 1980, vol. 13, PP. 1879-1884.

61. E. Kroner: Z. Phys., 1958, vol. 151, pp. 504-518.

62. H. M. Ledbetter: Phys. Stat. Solid! (a), 1984, vol. 85, pp. 89-96.

63. L. Kaufman, E. V. Clougherty, and R. J. Weiss: Acta Metall. , 1963,

vol. 11 , pp. 323-335.

64. J. Madsen, 0. K. Andersen, U. K. Poulsen, and 0. Jepsen: in Magnetism

and Magnetic Materials, AIP Conference Proceedings 29, pp. 327-328,

American Institute of Physics, New York, 1976.

65. 0. K. Andersen, J. Madsen, U. K, Poulsen, 0. Jepsen, and J. Kollar:

Physica, 1977, vol. 86-88B, pp. 249-256.

66. G. Grimvall: Phys. Scr. , 1 976, vol. 13, PP. 59-64.

67. H. Hasegawa and D. G. Pettifor: Phys. Rev. Lett., 1983, vol. 50,

pp. 130-133.

68. H. M. Ledbetter and M. W. Austin; National Bureau of Standards, Boulder,

Colorado, unpublished research, 1984.

69. H. M. Ledbetter, Res Mech. , forthcoming.

70. T. Datta, U. South Carolina, Columbia, unpublished research, 1985.

290
(U

IS) 00c

nJ

t. OC

03

CO

CO

CDc

•o

J-05 X

4-> C

CDO

0,CDQ.

4-> x:bO

•<—

(D3Co

•rH

4-)

COo

Cisoo

05O

•»H E

CD

i:: o

CD rHX3

05 H

0)N

CO /—

E c 3. GO

Om in CO CO CM o

GO <y\ o GO 0- 0> CO On

L. o m

05

05

05 05 iS\ in CM

m o in

C • • • • • *D m GO m CO CO

C. C5 CO GO CO GO CO CO

fO 0 X z z CO 0-

O in

v£5 o^ C\J in CO r— (M O o •— »— T— CM CM CM m • o o o o d o O O O o

c^ O' o\ o o O

O

O o m m on CM CM CM a* o O o T— r— CM CM CM z o o o o o O O O O

CO GO On 0-

O 0- in

CMm CO

m n£) a^

m

m CO o o o o o o o o o o o o o o o o o o d o O »— o^ o D <M CM

CJ • • o o o

in in o o c?^ o cu CM

z: • • • o o o o 0- in

inm

m CO • • o o o

ON \D o o o

CO • o o o

C\J CM CM CM

a.

O

O

O

OO

O c C— O CM

z: LTim

•“ z • On o^ O • • o^ On

L.

m

O

m

u • • • GO CO o

CM - (M m in vo 00 o^

291
Table II. Measured Polycrystal and Estimated Monocrystal Elastic Constants.

(Except for dimensionless A, all units are GPa.

)

Alloy B G Cl1 Cl 2 C44 G(1 1 1 ) E(1 1 1 ) A

1 158.8 78.5 206.8 13^.8 128.4 66.8 303.4 3.567

2 159.7 78.8 207.9 135.6 128.9 67.1 304.8 3.567

3 158.5 78.6 206.4 13^.6 128.9 66.9 304 .2 3.591

4 160.0 78.4 208.3 135.8 127.6 66.7 302.4 3.520

5 157.4 78.9 204.9 133.6 130.2 67.2 306.16 3.652

6 157.8 78.5 205.5 13^.0 128.9 66.8 304.0 3.606

7 158.7 78.2 206.6 13^.7 127.7 66.5 302.1 3.552

8 156.2 78.9 203.4 1 32.6 130.8 67.2 306.8 3.695

9 159.2 77.8 207.3 135.2 126.4 66.2 299.9 3.506

Table III. Principal Results

C + N a a e D Y

(at. pet.) (A) (io“3) (A) (mJ/m^

)

0.28 3.5914 0.013 3.05 447 18.8

0.42 3.5915 0.017 3.13 364 14.8

0.56 3.5918 0.017 4.01 450 24.4

0.64 3.5939 0.017 3.61 342 19.5

0.78 3.5951 0.013 3.28 295 21 .6

0.91 3.5945 0.017 3.32 295 16.7

1 .09 3.5988 0.014 3.67 323 23.7

1 .21 3.5996 0.017 3.64 376 20.3

1.34 3.5990 0.012 3.00 260 19.2

292
cos 6 cot B

Fig. 1. For alloy 6, unit-cell size versus cos0 cote, where 0 denotes Bragg

angle. Intercept gives unit-cell size, 3.5945 A, based on a linear-least-squares fit. Double points represent K . and K

p diffraction peaks.

^ ^

293
C+N, at%

o<

LiJ N

CO

Z

<

o

o

Fig. 2. Versus atomic percent carbon plus nitrogen, the variation of six

quantities: stacking-fault energy, stacking-fault probability,

unit-cell size. Young modulus in <11 1> direction, root-mean-square

strain, and size of coherently diffracting domain.

294
TECHNOLOey TRANSFER

295

TECHNOLOey TR/iNSFER PROGRAM

LEADER: N. J. Simon, NBS

OBJECTIVES:

1 . Organization of workshops to promote interaction between designers and

material specialists. Major topics include issues related to low-temperature material needs of the fusion energy program and reviews and new low-temperature data on structural alloys, composites, and weldments.

2. Production and distribution of an annual report as well as monthly highlight reports to OFE/DOE.

3. Preparation of handbook pages and supporting documentation on low-temperature mechanical and physical properties of structural materials for

superconducting magnets. The pages are to be distributed to workshop

attendees and others in the low- temperature materials applications community. The pages will also be presented for inclusion in the "Materials

Handbook for Fusion Energy Systems."

RESEARCH PAST YEAR (1984):

1. "Materials Studies for Magnetic fusion Energy Applications —VII," (NBSIR

84-

3000, 448 pages. May 1984, editors R. P. Reed and N. J. Simon) has been

sent to the Technology Information Center, ORNL , and to a number of

interested persons who have requested copies.

2. Handbook pages and supporting documentation covering mechanical properties

of AISI 304 (N, LN, HN, LHN) have been prepared. These pages will be

submitted to the "Materials Handbook for Fusion Energy Systems." Analysis

of the correlation of AISI 304 (N, LN, HN, LHN) mechanical properties with

interstitial nitrogen and carbon content is included. Preliminary work was completed in preparation for development of handbook pages on AISI 316 and

AISI 304 weldments.

3. International cooperation was established in research to develop radiation-resistant laminates to meet requirements for the fusion energy

program.

RESEARCH THIS YEAR (1985)

1. Tentative plans are to hold the low-temperature materials workshop again,

in October 1985.

2. "Materials Studies for Magnetic fusion Energy Applications —VIII," (NBSIR

85-

3025, 341 pages, 1985, editor R. P. Reed) is the current edition of the

annual report.

3. The AISI 316 handbook pages and the Fe-21 Cr-6Ni -9Mn handbook pages are currently in the review process for "Materials Handbook for Fusion Energy

Systems," and the AISI 304 (N, LN, HN , LHN) handbook pages will enter the

review process later this year.

4. Preparation of AISI 304 (N, LN , HN , LHN) handbook pages will be completed

this year. Preparation of handbook pages on AISI 304 weldments will be

completed.

5. Efforts promoting international cooperation in research to develop radiation-resistant laminates will continue. Interaction between the United

States and Japan on structural materials research will be explored.

297



NBS-DOE WORKSHOP: MATERIALS AT LOW TEMPERATURES

October 14-17, 1984; Vail, Colorado

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

The annual NBS-DOE workshop provided the opportunity for discussion of problems, advances, and goals in the development of materials for low temperature superconducting magnet systems for magnetic

fusion energy. Formal and informal discussions centered on welding,

magnet systems, radiation-resistant organic insulators, and structural

alloys

?99
f. 7 , ,1,

t&'S.

K'f

' ;

, - V \ kfiMi; f'fliu, wM

i'

:v./ v m/-

'" * If TV ' ^; 7— ;:#

^

^ . ^••;^r;: 5^1

-1 *

-

I' i;;

.,jr^

ifi . ®

7

Ji l( V B. . 'ff ',,

. '. -^

' 7

'''’

', 1 ' •Y'V'V

’ ’" ’ i» . ,, > /

' . . ..: ,r/ ‘^'-"'*( ".ji:

'" ".

'iffl

;• •^-''^.'r^..,-. vT ; i'r Cv»7,

.' ^,’ycV^=: 5 ‘v7:.: 7,#

•l^l' ' '" ' ;• -,^ I' ' 7 '

: 7

'’ -^"^•.".7

'

i '#7 ^.7- - „i ‘*7^..j

i\ [ i’,''‘\. '';ij( '|’'tf*' ' 'y • >

,’ hr'- 'ii-n

,1 ^'

/“S:

'

, '*' i(;.i

' y*:'

»A

4 'S''Vy® 7y 7 >^: H^Mfci*

V"it‘

•'.;>

;7--'

yy''f¥^

•

I I ij

^7

•V77»

"' 7 :' V. R7

</^

-.,
PROGRAM

NBS-DOE Workshop; Materials at Low Temperatures

October 14-17, 1984

Vail, Colorado

Sunday, October 14

Registration (5:00-8:00 p.m.)

Monday, October 15

Registration (7:30-9:00 a.m.)

SESSION 1 (8:30 a.m. -12:00 m.)

Complimentary cocktails

and hors d' oeuvres

MAGNET SYSTEMS

V. K. Der, Chairman

Introduction

Need for Establishing Design Allowables and

Guidelines for Magnet Systems

Materials Aspects of the Large Coil Program

Status of Fabrication of Superconducting

Magnets for MFTF-B

Structural Materials Research in Japan

Quantitative Materials Research

Objectives: The JAERI Box

R. P. Reed, NBS

V. K. Der, OFE

M. Lubell, ORNL

J. Zbasnik, LLNL

H. I. McHenry, NBS

R. P. Reed, NBS

SESSION 2 (1:30-5:00 p.m.) WELDING FOR LOW TEMPERATURE SERVICE

T, A. Siewert, Chairman

Welding Structures for Liquid Helium Service:

Past, Present, Future

The Effect of Weld Microstructures on the

Fracture Behavior of 316L Weldments at 4 K

Fracture Toughness of Austenitic Stainless

Steel Weld Metal at 4 K

Stainless Steel Heavy Vessel Fabrication

Fully Austenitic - Fissure Resistant Filler

Material

Stainless Steel Welding Research

E. N. C. Dalder, LLNL

J, C. Lippold, Sandia

G. M. Goodwin, ORNL

H. Helmbrecht, B & W

R. A. Bushey, Alloy Rods

T. A. Siewert, NBS

DISCUSSION SESSION 1 (7:30-9:00 p.m.) RESEARCH OBJECTIVES IN WELDING

E. N. C, Dalder, Leader

Tuesday, October 16

Registration (8:00-9:00 a.m.)

301
Tuesday, October 16 (continued)

SESSION 3 (8:30-11:00 a.m.) RADIATION RESISTANT ORGANIC INSULATOR

DEVELOPMENT, M. B. Kasen, Chairman

The ORNL Cryogenic Neutron Irradiation Facility

Nonmetallic Materials Radiation Studies at NBS

Neutron Irradiation Studies of Polymers at LANL

Nonmetallic Materials Radiation Research at MIT

Damage Types in Woven Composites at Low Temperatures

R. Coltman, ORNL

M. B. Kasen, NBS

D, Tucker, LANL

H. Becker, MIT

R. D. Kriz, NBS

DISCUSSION SESSION 2 (11:00 a.m.-

12:30 p.m.)

SESSION 4 (1:30-5:00 p.m.)

RESEARCH OBJECTIVES IN NONMETALLICS

R. R. Coltman, Leader

STRUCTURAL ALLOYS

J. W. Morris, Chairman

Structural Material Investigation in Conjunction

with S.C. Magnet Projects at KFK

Low Temperature Mechanical Properties

Phase Transformations in Fe-Mn Alloys

Effect of Molybdenum on Metallurgical Characteristics of Austenitic Stainless Steels

Near Threshold Fatigue Crack Growth in

Austenitic Stainless Steels

Summary of Strain Rate Effects in Austenitic Steels

Magneto-Mechanical Effects in 304 Stainless Steels

Materials Handbook for Fusion Energy Systems - 304N, LN, HN Cryogenic Properties

Martensitic Transformation Temperatures in

Austenitic Steels

P. Komarek, KFK

R. P. Reed, NBS

J. W. Morris , Jr .

,

Univ. of California

P. J. Grobner,

Climax Molybdenum

R. L. Tobler, NBS

W. Dobson, Binary Assoc.

B. Fultz, Univ. of Calif.

N. J. Simon, NBS

J. Self, CSM

DISCUSSION SESSION 3 (7:30-9:00 p.m.) "JAERI BOX,” STRUCTURAL ALLOY RESEARCH

OBJECTIVES, H. I. McHenry, Leader

Wednesday, October 17

SESSION 5 (8:30-9:30 a.m.) REPORTS FROM DISCUSSION SESSIONS

R. P. Reed, Chairman

SESSION 6 (9:30 a.m. -12:00 m.)

(1:30-5:00 p.m.)

CODES AND STANDARDS --TASK GROUP ON

CRYOGENIC MATERIALS (Metal Properties

Council), H. C. Rogers, Chairman

DISCUSSION SESSION 4 (1:30-5:30 p.m.) TASK GROUP ON CONDUCTOR SHEATH ALLOYS

E. N. C. Dalder, Leader

302
FOREWORD

The annual 198^4 workshop promoted interaction between those involved in

development of low temperature superconducting magnet systems for magnetic

fusion energy and the structural materials research community serving this

effort. There were four formal sessions on Monday, October 15 and

Tuesday, October 16:

• Magnet Systems: Design Concepts, Materials Requirements, Progress

Reports

• Welding for Low Temperature Service

• Radiation Resistant Organic Insulator Development

• Austenitic Steels: Properties and Low Temperature Behavior

Each session included a number of short technical presentations by

representati ves of NBS , universities, national laboratories, fabricators,

and other organizations involved in the fusion program. In addition,

informal sessions were held to review FY85 research objectives; in

particular, to discuss the advisability of setting national quantitative

materials research objectives, similar to those set by the Japan Atomic

Energy Research Institute with respect to strength and toughness for

austenitic steels at 4 K. Objectives for structural alloys, welding, and

nonmetallics were discussed in three separate sessions. Other issues that were discussed included magnet design philosophy with respect to allowable

stress levels, the establishment of material and property priorities for

data compilation and review, and techniques of assessment of the available

low temperature data base for design use. A special task group discussed

issues related to the use of conductor sheath alloys.

Reports from the informal discussion sessions were presented Wednesday

morning, October 17. Those assisting in the preparation of this report

included Victor Der (Office of Fusion Energy), Ed Dalder (Lawrence

Livermore National Laboratory), Harry McHenry (NBS), Nancy Simon (NBS),

Ralph Tobler (NBS), and Ron Kriz (NBS).

Workshop participants representing many companies and laboratories discussed

their research. Therefore, the summary contains company names and trade

names that were integral to the discussions. Such identification does not

imply recommendation or endorsement by the National Bureau of Standards, nor

does it imply that the materials, equipment, or source identified are necessarily the best available for the purpose.

Richard P. Reed

National Bureau of Standards

303

LOW TEMPERATURE MATERIALS WORKSHOP

FOR MAGNETIC FUSION ENERGY - AN INFOR.MAL SUMMARY

Magnet Systems

The theme of this session was materials research objectives to support

design of magnet systems. A permeating issue throughout the workshop was whether or not the U.S. structural materials research program should focus

on quantitative objectives, e.g., target values for strength fracture

toughness and for magnet structures. In this session five presentations

were given on design and materials aspects of magnet systems.

Victor Der (OFE DOE) proposed a need for establishing design allowables

and criteria/guidelines for magnet systems. The need for design allowables was identified for structural alloys and weldments, insulators,

conductors, and cryogenic coolants. An example of allowables and criteria

needs for structural design was used as an illustration. The objective of

this proposal was to begin a program over the next two years to address

the need for allowables and criter ia/guidelines by establishing working

groups to produce an updatable magnet design handbook. Interfaces and

details of the types of working groups were presented. Feedback from the

session audience on this idea was generally positive, i.e., there appeared

to be a consensus that such an activity was needed. However, there were suggestions that the schedule may be rather ambitious in light of a general lack of data to support the determination of design allowables.

Another suggestion was that inspection guidelines should also be included.

There was a concern that it may be difficult to convince scientists to

abide by these guidelines because of a desire to push experiments to their

limits. At the very least, however, this approach should be pursued to

drive the design process for magnet systems.

Martin Lubell (ORNL) reported on the materials aspects of the Large Coil

Program (LCP) at ORNL. An overview of the Large. Coil Test Facility (LCTF)

included a description of the fabrication and installation of the vacuum

tank, the stainless steel bucking post, and the spider-frame base. The

LCP involves international collaborative testing of an array of six 8-

tesla coils, three from the U.S. and one each from Japan, Euratom, and

Switzerland. A detailed discussion was given on the variety of approaches

to the design, fabrication, and assembly of all six coils of a D-shape

profile. These coils are heavily instrumented and therefore their costs

are not representative of that for production coils. Acoustic emission

(AE) monitoring during an intermediate three-coil test indicated that

noises from the winding and from the coil structure were distinguishable.

However, because the signals are still not fully understood, additional

work in this area will be required before AE monitoring could be used as a means of coil protection. It was also suggested that perhaps oval-shaped

coils may better withstand bending moments in magnet structures than

D-shaped coils. Also, oval-shaped coils are likely to be easier and

cheaper to construct. Finally, it was pointed out that structural

analyses of the LCTF is continuing, and that structural analyses of the

coils will be compared with data to be obtained from the six-coil test.

305
Jon Zbasnik (LLNL) reported on the status of fabrication of superconducting magnets for MFTF-B. A strong point was made that each piece of

material used in the magnets and welds was tested at 4 K, and that

considerable time was devoted to X-ray inspections of welds for defects.

The magnet system is comprised of solenoids, Nb-Ti axicells, Nb^Sn axicell

inserts, transition coils, trim coils, and Yin-Yang coils. The solenoids,

12 of about 12,000 kg (27,000 lb) each, are encased in 304LN. The casing,

acting as a structural containment, must also be leak tight for liquid

helium. The solenoids were shipped to LLNL in August 1983. The Nb-Ti

axicells, of about 24,000 kg (54,000 lb) each, are "layer cake" wound.

The first axicells are expected to be delivered in November 1984 and

installed in April-May 1985. The Nb^Sn axicell inserts see the most severe radiation environment in the RFTF-B. The conductor was manufactured by Furukawa who was the only supplier to meet the delivery schedule.

Completion of the first coil is scheduled for November 1984 and the second,

for February 1985. The transition coils, "baseball" in shape, are of two

different sizes, one weighing 41,000 kg (45 tons) and the other 23,000 kg

(25 tons). The coil casing is fabricated from 10-cm (4-in)-thick 304LNSS. All four coils are scheduled for delivery between January and April

1985. The trim coils, 16 in all, are used as correction coils to fine

tune alignments with the transition coils. Trim coil casing is 1.9-cm

(0.75-in) thick 304LN. Winding is complete, close out welding is about

40/S complete, and assembly and installation are targeted for December 1984

through April 1985. The Yin-Yang coils weigh about 330,000 kg (360 tons).

Both Yin-Yang coils are complete and LLNL is now attaching the LN 2 panels

which require a total of 10,000 joints. Installation of the Yin-Yang

coils is scheduled for December 1984. The MFTF-B project attempted to

qualify all the magnet materials used in the magnet system. Although

there will be no opportunity to test the Nb^Sn axicell insert coils before

operation in MFTF-B, a substantial design margin has been built into these

coils

Harry McHenry (NBS), who just completed a year's assignment for the Office

of Naval Research in Tokyo, reviewed current low temperature structural

materials research in Japan. The Japan Atomic Energy Research Institute

(JAERI) initiated a program in 1982 to develop a structural steel alloy

for the large superconducting magnets planned for the Fusion Experimental

Reactor (FER). A set of target properties was established for the new

alloy on the basis of the design requirements for the FER coil system. The

responsibility for developing an alloy with these properties was assumed

by three Japanese steel companies working in conjunction with JAERI:

Japan Steel Works, Ltd.; Kobe Steel, Ltd.; and Nippon Steel Corp. At

first, tensile and Charpy impact tests were conducted at 4 K on 68

candidate alloys.

306
Five alloys were selected from this group for additional research:

Content (wt.?)

Alloy Developer C Cr Ni Mn N Other

1 Nippon 0.02 25 13 -- 0.35

2 Nippon 0.02 27 18 — 0.35

3 Japan Steel 0.02 12 12 10 0.2 5 Mo

H Kobe 0.05 13 5 22 0.2

5 Nippon 0.05 15 1 25 0.2 1 Cu, N

Development activities since mid-1983 included further characterization

using fracture toughness and fatigue crack growth rate tests, primary

processing studies for scaling up to commercial practice, and the development of welding materials and procedures for use with these new alloys.

It is expected that final determination on these five alloys will be made

in late 198^.

The research objectives of the JAERI structural alloy program, described

by McHenry, were formulated from design considerations of the toroidal

field (TF) coils for their proposed Fusion Experimental Reactor. Dick

Reed (NBS) reviewed these. From assessment of the finite element stress

analysis of the proposed coil case and windings, it was concluded that the

maximum design stress would be 500 MPa. Analyses of Nb^Sn superconductor

critical current as a function of strain found that a maximum strain of

0.005 was permissible. Design conditions for both the conductor sheath

and coil case were:

design stress, S 1/3 o^j, tensile ultimate

0 ^S 2/3 Ojj, tensile yield stress

0 ^

S 1/2 0 |j, stress at 0.005 strain

A yield strength at 4 K of 1200 MPa was formulated. This was based on maximum allowable strain for the sheath material of TF coils using Nb^Sn

superconductor . The conductor sheath strain limitation of 0.005 corresponded to an elastic limit of 1000 MPa, which corresponds to a yield

strength of 1200 MPa.

A fracture toughness of 200 MPa/m was proposed based on the minimum stress

to grow a 1-mm surface crack through the 100-mm-thick TF coil-case under

500 MPa stress in fatigue loading.

307
Reed pointed out concern for the lack of ultimate tensile strength (o^)

research objectives if one design criterion is that the design stress must

be less than 1/3 Ojj. Typical ultimate strengths of high-strength austenitic steels (o =1200 MPa) are about 1.6 o . Thus, considering that 1/3

equals about 6^0 MPa and that 2/3 Oy equals about 800 MPa, it is obvious

that rather than Oy would be restrictive on the maximum allowed design

stress

Welding for Low Temperature Service

This session consisted of six presentations on the welding of austenitic

stainless steels and the properties of stainless steel welds at 4 K. The

first presentation was an overview by Ed Dalder (LLNL) that traced

the development of stainless steel welding practices from the mid-70’s to

the present and outlined research and development needed for the next

five years. He emphasized the importance of 31 6L as the principal weld

metal for magnet construction. Early studies provided basic data on strength, toughness, fatigue crack growth and the influence of metallurgical variables on these properties. Presently procedures are developed

for SMA and FCA welding, and a suitable data base exists for using these

processes for magnet construction. Further work is needed to understand

the importance of nitrogen, ferrite, and microfissures on mechanical

properties; to develop a larger data base for design; and to develop more efficient and reliable welding practices, particularly for out-of- position

welding

John Lippold (Sandia National Labs) addressed the dichotomy of the weld

ferrite effect on the properties of 31 6L weld deposits, i.e., ferrite

reduces the incidence of microfissures, but also reduces fracture toughness. Two approaches to future metal formulation that minimize microfissures in low ferrite welds were discussed: a Mn-modified 31 6L and a controlled ferrite number (CFN) 3 i6l. Tests on weld deposits of these

filler metals indicated that at similar strength levels and ferrite

contents (<2?), the toughness of the CFN welds was substantially better

than the Mn-modified welds. A model was proposed to account for these

differences in terms of microstructural inhomogeneity resulting from

elemental partitioning during solidification.

Gene Goodwin (Oak Ridge National Labs) described the selection of welding

processes and weld filler metals for the fabricating of a large toroidal

superconducting magnet. Published toughness values were collected and

compared with SMA, GTA , and FCAW values generated in this study. All three

processes were found to be suitable for the intended service, with the GTA

welds having the highest toughness. The fabrication, including special

fixturing, was also reviewed.

Methods for fabricating heavy section austenitic stainless steel structures were reviewed by Herb Helmbrecht (Babcock-Wilcox) . Emphasis was placed on the strict controls necessary to insure satisfactory properties

in stainless steel welds intended for low temperature service. Using

conventional welding practices, property variability may result because of

308
variations in the welding conditions introduced by changes in the welding

environment, differences in base metal dilution and prcrcedural differences

associated with manual and semiautomatic welding.

The use of fully automatic GMA welding procedures with adaptive controls

was advocated to provide the consistency needed to meet weld metal

property requirements.

Roger Bushey (Alloy Rods) reviewed the substantial reduction in fissuring

tendency possible through trace element control. A standard 320-type

stainless steel was compared with a similar composition with strict controls

on the trace element (particularly phosphorus and sulfur). Fissure bend

test photographs illustrated the lack of fissures in the controlled

composition. The slag system was also shown to affect the fissure

tendency. Further work was recommended to control the merits of low

residual contents on the fissure tendencies of other filler metals for

cryogenic service.

Tom Siewert (NBS) reviewed four projects performed in the preceding year

at the Boulder Laboratory in support of the DOE program. These projects

included three evaluations of weld properties and a fatigue crack growth

study of CF8M castings. The tensile properties and fracture behavior of a Fe-1 5Mn-8Ni-1 Mo-0. 7C fully austenitic weld metal at M K were presented.

The ^ K properties of a Fe-25Mn-5Cr-l Ni composition were compared for three

different welding processes: GTA , SA , and SMAW. Improvements in predictive equations for 76 K Charpy V-Notch tests were explained. The

fatigue crack growths of CF8M castings were compared for various ferrite

levels. These reports are published in more detail in the 198^ and 1985

NBSIR publications.

Nonmetallics

Ralph Coltman (ORNL) reported that work continues on constructing the

National Low Temperature Neutron Irradiation Facility (NLTNIF). This

facility, which is designed to approximate the fluence seen by an MFE

superconducting magnet, will be available to all U.S. researchers interested in studying material behavior in an irradiated environment at

temperatures from 3.5 K to 300 K. It is a moveable open core reactor

operating at 2 MW with a Zircalloy gamma-ray shield. Radiation

characteristics are:

The fixed sample chamber is 4 cm in diameter and 25 cm long. Gradients in

neutron flux vary no more than 10? along the length of the chamber.

Specimens may be removed from the chamber and transferred to a storage

cryostat without warmup. On-line data acquisition will be available to

Fast Neutron Flux:

Thermal Neutron Flux:

Routine Fluence:

Energy Deposition (in A1 ) : :3 X I u r-aus

309
monitor property changes in situ. Other spectra of radiation can be

implemented by changing the shielding. In situ testing while under

irradiation can be performed with appropriate fixtures. The facility is

expected to become operational in late 1985.

Bud Kasen (NBS) described a new simplified specimen configuration and test

procedure that is being investigated to optimize data obtained when

testing nonmetallic organic insulators in a cryogenic irradiation environment. This work is being done cooperatively with laboratories in Japan

(Osaka University) and in England (Rutherford Laboratory). A major objective is to reduce the cost vs. rads of allowable radiation for insulation

materials in MFE superconducting magnets.

Some goals for the proposed test specimens are: small size, no edge

effects, inexpensive, characterizable, defect free, easily produced,

adaptable to a variety of test methods.

The test technique involves pulling a fiber bundle from a resin bath into a tubular teflon tube of about 3 mm i.d. followed by in situ curing. Much

effort was given to developing methods required for producing high quality

specimens. Several new techniques are required: vacuum degassing of

resins while mixing, vacuum preimpregnation of fibers, and curing under

nitrogen gas pressure.

A new technique using ultrasonic energy for resin mixing is under study.

This techique, developed by William (Todd) Hodges (NASA Langley

Research Center), eliminates the use of solvents and extends the range of

polymer systems that can be used with the specimen production system.

Tests have shown that the basic production techniques can produce speci- mens 3 mm in diameter with less than 0.3? variation in diameter.

Initial mechanical tests were conducted by subjecting 15-mm-long specimens

to longitudinal shear a modified short beam shear test. Sequential load

drops in the stress-strain curve were found to correspond to sequential

formation of interlaminar shear failure. With the first load drop taken

as the shear strength criterion, experiments demonstrated an increase in

interlaminar strength from 9.4 MPa at 295 K to 23-3 MPa at 76 K. Development of this and other test methods are continuing.

Dennis Tucker (LANL) reported on cryogenic irradiation studies of G-10CR,

G-11CR Kapton, Bisphenol A epoxy, NP-530* (polyimide), and Spaulrad

1.5 X 10^^ n/m^ E>0.

Mev

2,6 X 10^^ n/m^ E>0.Mev

4.1 X 10^^ n/m^ E>0.1 Mev

Electrical tests:

dielectric constants and loss tangents

dc resistivity

dielectric breakdown strength

310
Mechanical tests at 75 K:

flexural strength (three point bend)

compressive strength

flexural modulus

Experimental results showed some decrease in mechanical strength with

increasing neutron fluence for all test materials; however, only G-10CR

exhibited serious degradation. G-11CR had the highest retained strength

values. G-10CR degradation was the highest of all materials tested. A

comparison of these results with ORNL results on the same materials under

gamma irradiation indicated that the boron content in type E glass

reinforcement may accelerate degradation in a neutron environment.

Future work includes:

irradiation at higher doses

comparison of neutron vs. gamma for polyimide

synthesis, irradiation, and testing of model resin systems

Herb Becker (MIT) presented a short progress report of ongoing efforts at

MIT in which thin sheets of S2-glass/polyimide laminates are being tested

in cyclic compression. Both irradiation and testing were performed at

295 K. Mechanical failure was defined as total breakdown of material into

a powder. Results showed significant losses in resistivity; however, the

lowest obtained resistivity was judged satisfactory for fusion magnets.

Ronald Kriz (NBS) and Walter Muster (EMPA, Switzerland) explained by

analysis and experiment how fiber breaks and fiber bundle cracks can influence the mechanical response of G-10CR and G-11CR thin laminates at

low loads. Analysis also showed a trade-off between stiffness and fill

crack arrest at low temperatures. Experiment showed a strong correlation

between fill cracks and "knees” in the stress-strain curves. Except for

G-IOCR at 77 K, fill cracks and fiber cracks in the warp bundles occur at

the same mechanical load. Except for G-11CR and 77 K, fiber breaks and fill

cracks are not related. Future studies will measure influence of damage

at low loads on thermal physical properties.

Structural Alloys

Peter Komarek's (KFZ, Karlsruhe) talk on structural material investigations in conjunction with superconducting magnet projects in Germany

covered three areas: selection of coil case materials, design approaches

to failure prevention, and methods of NDT inspection of thick austenitic

steel welds.

Candidate materials were characterized by fracture toughness and fatigue

crack growth rate tests including threshold measurements at 300, 77 and

^ K. Electroslag remelted stainless steel demonstrated enhanced toughness,

and an alloy equivalent to AISI 316LN was selected, having Kj^ values of

200 MPa/m for the weldment at K. Based on the improved properties,

critical flaw size calculations showed that a flaw size of ^3.5 mm (as

311
compared with a previous ^ 2mm) was acceptable, and this reduced the

stringency of previous inspection requirements. Methods of NDT inspection

were then considered and it was shown that ultrasonics was applicable to

thick section welds, assuming use of longitudinal waves, angular transmitters, and reduced sensitivity volumes.

In summary, this work shows that structural materials investigations

properly carried out with the establishment of a specific data base can significantly reduce the conservative requirements which otherwise limit

materials use.

Dick Reed followed with an overview of progress in several areas of NBS

research on austenitic stainless steels, OFHC copper, and 1100 aluminum.

Fundamental research is ongoing in areas of tensile, notch tensile, creep,

fatigue, fractography , and physical property investigation. Efforts in

tensile testing have been directed at strain rate effects and temperature

dependence of flow strength. It was noted that the strain rate effects were

found to be proportionately less at ^ K than at higher temperatures. Notch

tensile data failed to provide useful correlations with quantitative fracture

toughness measurement and so are falling from serious consideration as a possible substitute for J-integral test characterization. For the J-integral

results, fractographic investigations suggest that a very fine precipitate or inclusion of a so-far undefined composition nature may account for scatter in

low toughness alloys.

Primary creep at M K occurs in AISI 310 stainless steel at the yield

point, and additional testing is being pursued to define the relevance of

creep to design at ^ K. Collaborative efforts with Colorado School of

Mines, Climax Molybdenum, Carpenter Technology, and welding consumable

suppliers are also being pursued to develop less expensive and stronger

austenitic stainless steels.

Bill Morris’s (U. of California) talk provided an intense description of

three types of Fe-Mn alloys, their characteristic phase transformation

tendencies, and the effects of these transformations on mechanical

property behavior. Three representative types were considered: Fe-16 or -17Mn (a^£->a’), Fe-20 or -25Mn (a-*-e) and Fe~31 or -36Mn (relatively

stable). Changes in work-hardening rates with strain and anomalies in

yield strength ordering owing to phase transf ormations were described and

the relationships between strength, test temperature, and volume fraction

of phases after deformation and fracture were given with consideration of

the relevant mechanisms of alloy softening and hardening.

The fundamental understanding of these binary alloys is important

because it can lead to suggestions for the improvement of high-Mn alloy

steels, and because analogies to the mechanical behaviors of AISI 30^

alloys exist.

312
Paul Grobner (Climax Molybdenum) reviewed the effects of Mo on the (1

)

microstructure, (2) mechanical properties and (3) corrosion resistance of

austenitic stainless steels. Molybdenum encourages the formation of ferrite

and sigma phases and stabilizes carbides and austenite. Molybdenum is also

an effective solid solution strengthener and (compared in terms of weight

percent) only the interstitial elements have a stronger effect on strength.

Molybdenum improves pitting and crevice corrosion resistances and also

improves intergranular corrosion resistance in nonoxidizing environments.

This information is relevant to the consideration of possible austenitic

stainless steel alloy development or modification.

Ralph Tobler (NBS) presented new data describing the near-threshold

fatigue crack growth rates and threshold stress intensity factor parameters of AISI 316, 30ML, and 3Q11LN stainless steels at 4 K. Experimental

data of this kind are needed because few data are available and there are

no reliable data prediction schemes. To obtain these data, a fully

automated computer-controlled test apparatus was designed and assembled.

This apparatus reduces testing time and cryogen costs and will be used to

establish a sizable 4 K data base to meet the emerging needs of designers.

Brent Fultz (U. of California) described the results of a study that

confirms that magnetic fields influence the mechanical properties of

metastable austenitic steels. In fact, the imposition of a magnetic field

on these alloys affects the amount of phase transformation independent of

other variables so that the effects of phase transformation and alloy

stability can be separated and studied for the first time.

Changes in o-e behavior were noted for AISI 304L and 304LN steels as a function of increasing field strengths of 8, 12, and 18 tesla. The

magneto-mechanical effects were more pronounced at higher fields and more

pronounced for AISI 304L than for AISI 304LN. It was confirmed that softening in the early part of the o-e curve was due to the window mechanism,

and that later hardening was due to martensitic phase transformation.

Nancy Simon (NBS) reviewed the results of efforts to correlate mechanical

property data for AISI 304 type stainless steels. These studies were

based on data compiled from a wide variety of sources in support of

handbook publications. Correlations were sought for conventional tensile

properties, fracture toughness, Charpy impact energies, fatigue crack

growth rates, and Young’s modulus, with respect to interstitial content

or temperature. Despite the relatively high variability attending these

interlaboratory results, significant correlations were discovered for o„ vs [C+N] at 300, 77, and 4 K; for ultimate strength vs [C+N] at 300 K, and

for Kj^(J) vs [N] at 4 K. All other correlations were completely

obscured by scatter from uncontrolled variables in the data spliced from

different sources. In these latter cases, weak property dependences on interstitial contents or temperature were often revealed by data taken

from individual laboratories representing a controlled alloy series.

313
Joel Self (Colorado School of Mines) developed a new constitution

diagram and equation for the martensitic transformations of high-alloy

steel welds. The previous equations of Schaeffler and Andrews applied to narrow compositional limits and consisted entirely of linear terms. The new equation is far more general and is based on consideration of data

available for iron binaries and ternaries, low-alloy steels, manganese

steels, austenitic, ferritic, and martensitic stainless steels, and tool

steels. Interactive terms were incorporated in the consti tuitive equation, and the importance of such terms in allowing a more general correla

tion of composition and microstructure in a wide variety of alloys was demonstrated.

Research Objectives in Nonmetallic Materials

(1) The presently available commercial insulating laminates (G-10CR,

G-11CR, and the polyimide variants) should be further evaluated for

cryogenic radiation degradation at high neutron fluence in the ORNL

reactor when it becomes operational in 1985.

(2) Organic insulator materials presently available and their character!

zation state appear to meet the requirements of the designers for con- struction of magnets that will not be subjected to radiation. However,

materials having substantially improved radiation resistance will be

required when designs incorporate magnets subjected to radiation. It was commented that, in the short run, the radiation tolerance requirements

will be higher than in the future, since the initial designs may not have

the extensive blanketing that would be used in a commercial reactor.

Requirements may be for a tolerance equivalent to 10 rads during this

developmental period. This consideration should be factored into the

materials research program.

(3) Meaningful criteria for laminate failure are required. The present

criteria of a 50$ decrease in strength accompanied by visible material

damage were considered questionable.

(M) Improved dissemination of insulator radiation effects data is needed

(5) Research on degradation of potting resins is required.

(6) Carbon insulators should be investigated because they are presently

used on some magnet systems and should be very radiation resistant. An

example is colloidal carbon carried in a volatile solvent. The influence

of residual solvent on radiation resistance should be examined.

(7) Research on developing improved insulators at lower cost should be

continued. Although insulator cost is a small fraction of the total cost

of an MFE reactor, the potential for cost savings on the order of many

millions of dollars exists for a relatively small research funding cost.

Development of insulators less costly to fabricate is a desirable objective.

314
(8) There was a consensus that establishcent of specific nonnetallic

material performance objectives (the JAEHI 5ox principle) cici net have

ready application at the present stage of insulator development.

(9) The use of glass-filled phenolics has good advantages for fabrication, but radiation tolerance is uncertain and should be determined.

(10) From a list of property change information needed as a function of

irradiation dose, mechanical properties have first priority. Dimensional

stability and creep were given high priority wh.ile gas evolution and

electrical properties were felt to be less important.

Research Objectives in Welding

From intense discussions, several research objectives evolved:

(1) Develop a welding consumable, capable of being deposited by at least

two fusion-welding processes, with following ^-K properties:

1.0 GPa (150 ksi) c : 160 M?a/m (150 ksi/in) K-^(J)

1.2 GPa (180 ksi) a^: 200 M?a/m (150 ksi/in) K^^CO)

(2) Using type 31 6L welding consumable as a MODEL, determine effects of

residual elements (P ,Si ,C ,0 ,Nb , etc.) and the purity of the weld deposit on ^-K Kt^(J). Currently, a very large scatter exists in the ^-X data on

0 ferrite number welds.

(3) Starting with GTA or/and C3iA processes, develop appropriate artificial intelligence for a fully automated welding process. Because of

the extreme sensitivity of the weld deposit to minor variations in deposit

conditions, industry representatives recommended automation as the only

way to insure uniformity and reliable fracture toughness.

(4) Use available technology to develop fully automated ultrascnic

niques of nondestructive evaluation of thick stainless steel welds,

of inspection techniques in nonfusion projects using thick sections

facilitate this effort.

(5) Review current weld-metal data bases to develop interim design

allowables and other recommendations for additional work. A data

base has been accumulated on and similar filler materials using

several weld processes, but the information has not yet been collected and

critically evaluated.

techA review

W 1 ^ ^

315
Research Objectives for Structural Alloys

(1) Fe-Cr-Ni austenitic stainless steels should be improved through the

following studies:

Grain size control

Inclusion control/melting practices

Control of residual elements

Thermomechanical processing

Weldability/HAZ studies

Because of the wide range of experience with the Cr-Ni austenitic stainless steels at 4 K and the many advantages of these steels such as commercial availability, weldability and acceptable 4-K properties, the consensus was that these stainless steels would continue to be used in

fusion magnet projects. However, significant problems encountered the

low-temperature use of these stainless steels need to be addressed.

Rejection rates of up to 50? have been reported for thick 30^LN plates

(8-15 cm; 3“6 in) that failed to meet specifications due to very large

grain sizes, ASTM 00 (- 2.5 cm; ~ 1 in). At present, the technology to

produce these plates consistently is not available; therefore, the areas listed above were proposed for investigation.

(2) Alloy Development

Research areas to focus for development of new alloys include:

High-manganese austenitic steels

Reduced- cost/high-strength stainless steels

High-nickel ferritic alloys

New alloy development was seen as important in reaching the long-range

goals of the fusion energy program, but this effort should be subordinate

to improvement of the present Cr-Ni austenitic stainless steels. There

appear to be advantages to high-manganese alloys in regard to thermomechanical processing and decreased sensitivity to impurities and grain

size variation, but there are also aspects of processing that are relatively expensive. A high level of concern was expressed regarding the

weldability of these alloys. No published information on welding has come from the Japanese developers of these alloys, and it was felt that the

Japanese research program had not given sufficient emphasis to the

weldability problems expected for alloys of these compositions.

(3)

Quantitative Goals

In contrast to the Japanese situation, where properties recommendations

were developed as a response to a specific tokamak design, the Fusion Experimental Reactor, the United States does not currently have budgetary

approval for a specific machine. Japanese magnet designers are all

members in one institute, JAERI , whereas United States designers are associated with a variety of institutions and often propose competitive

approaches to fusion design problems. Thus, a uniform viewpoint is

lacking in the United States. However, it was recognized that quantitative goals could serve as a yardstick for progress of materials research

316
programs in developing new alloys. Also, the JAERI effort represented far

greater allocation of resources than is appropriate now in the United

States toward this goal.

(i4) Corrosion Resistance

This was not considered a prime requirement because stainless steel

magnet cases also have to undergo a cleaning cycle.

(5) Ferromagnetic Alloys

It was felt that ferritic alloys should not be eliminated from

consideration, but that better calculation of the expected increases in

applied stress should be made.

Executive Summary of Sessions on Research Objectives

It was realized that the "JAERI box" formulation followed from design

considerations for the proposed Fusion Experimental Reactor and from the

concern of JAERI designers. On the other hand, there are no planned large

projects in the United States at present, and the session discussion did

not produce strong support from designers for quantitative research objectives. However, it was apparent that quantitative research objectives

would be of assistance in guiding fundamental research programs and in

providing a yardstick for the assessment of these programs. In the future

it is quite possible that quantitative research objectives will be derived

from fracture-mechanics ( f itness-f or-service ) assessment, since it will be

necessary to establish maximum allowable weldment flaw sizes and minimum

structural alloy and weldment toughness levels based on maximum service

stress or strain.

The research from the three discussion sessions can be represented in

three principal categories:

(1) For current structural materials, such as 304LN with 31 6L weldments and G-10 and G-11 insulators, there was strong support for data

collection and evaluation, property measurements, assessment of

variables such as creep and fatigue, and improvement through better

processing

(2) Support to begin establishment of design properties was recognized. Effort to begin assignment of design allowables was advocated.

Unfortunately, in most cases this must be initiated with a relatively

sparse data base.

(3) It was realized that for the future a new generation of structural materials must be developed. For these new materials, radiation

must be considered. This includes consideration of lower-cost

higher-strength austenitic stainless steels, high-manganese steels,

ferritic steels, and movement toward more radiation-resistent insulators, such as polyimides. It is in this category that quantitative

research objectives may be set to guide materials research and alloy

producers.

317
Possible quantitative research objectives are:

Structural

Material

Research Objectives

Yield Strength Toughness Others

(MPa) (MPa/m)

Alloy Steel 1100 200 Equivalent to 30 MLN

in fatigue, creep, physical

properties, cost

Conductor Sheath 700 100 Thermal expansion, a

= 10*10"^ K-1 at 293 K,

equivalent to Nb^Sn/Cubronze

Welding Consumable 1000 200 1 welding process

1000 150 2 welding processes

Conductor Sheath Alloy Development Task Group

The problem addressed by this task group is the following: The superconductor of a forced-flow superconducting magnet is subject to large strain

due to the difference in thermal expansion between the conductor and

conductor sheath alloy. The Nb^Sn conductor used in these applications is

particularly sensitive to strain, with strains of the amount expected from

differential thermal contraction causing sizeable degradation of the

critical current. Because the extensive heat treatment required for

reaction of the superconductor/stabilizer complex caused deterioriation in

the mechanical properties of some conductor sheath alloy welds, JBK-75 was selected for this application due to better ductility retention after heat

treatment. However, the large mismatch in thermal expansion between

JBK -75 and the NboSn/Cu conductor has led to suggestions that Incoloy

alloys such as 903 and 905 be used as the sheath material since their

thermal contraction coefficients more closely match that of Nb^Sn.

Discussion by members of the task group confirmed that critical current

density of Nb-oSn could be enhanced by minimizing the thermal contraction

difference between conductor and sheath during cooling from the Nb^Sn

reaction temperature to 4 K (Martin Lubell, MIT; Peter Komarek,

Karlsruhe )

318
Considerations raised with regard to the use of an Incoloy alloy included

the following:

(1) Heat treatment of the Incoloy series alloys is similar to that done

to react the superconductor/stabilizer complex, but the time period would

be of the order of 100 hours as compared to the 1 or 2 hour reanneal at

950°C followed by a water quench used after rolling Incoloy plate. There

is a need to make tests to determine whether ductility is retained after

such heat treatment. Not much work has been done in this area, and a complicated behavior involving both softening and embrittlement has been

reported

(2) Work in progress at LLNL to evaluate the responses of JBK-75 and

Incoloy 9XX (903, 905, 909) iron-based superalloys to possible Nb^Sn

reaction heat treatments shows that: a. JBK-75 - autogeneous (.made without

filler-addition) GTA welds show formation of cellular n phase at weldmetal grain boundaries. No n was seen in unwelded material, b. Incoloy

9XX (903, 905, 909) autogeneous GTA welds, weld HAZs (heat-affected

zones), and unwelded materials show continuous grain-boundary phases after

2H hour exposure at 700-800°C. Identification of phases is under way.

(3) The void fraction has been found to have a substantial effect upon

the magnitude of the compressive forces transmitted to the superconductor

Whether or not a connected path exists for a void fra'ction greater than

about 17% was considered controversial. Considered as a percolation

problem, such a path should not exist, but M. Hoenig (MIT) has evidently

found or calculated effects for a void fraction of around 30-40?. It was recommended that a finite-element analysis of the strain transmitted to

the conductor be done, as this would show how (strained)ZJ(^(unstrained)

varies as a function of void fraction. Herb Becker (MIT) will make

available to LLNL results of finite-element stress-analysis of an I.C.C.S.

conduction-sheath, operating under ALCATOR DCT conditions, so the effects

of 4 K mechanical properties on integrity of sheath alloys may be evaluated.

(4) A suggestion was made that if no suitable sheath alloy could be found

considering both thermal and mechanical properties, the possibility of

reinforcing a sheath with a U-section for sufficient mechanical strength

be considered. However, it was pointed out that this solution would have

the effect of decreasing the gross current density in the magnet because

so much space would be o.ccupied by non-current-carrying material or empty

space.

(5) Crack initiation and growth is an important factor in the selection

of a conductor sheath alloy. Sufficient helium to degrade the 4-K vacuum

insulation can leak through a very small crack. Data on da/dN are evidently available for JBK-75 in a recent article in Cryogenics, but da/dN

data need to be acquired on Incoloy alloys.

319
(6) L. Summers (LLNL) will do mechanical testing of the new alloys under

consideration. His preliminary metallographic studies indicate that a complicated metallurgical structure is present after thermal treatment,

implying that toughness and strength at 4 K may be degraded. Since this

testing should take place before the next meeting and will require at

least three months, the next meeting of the task force was set for

March 8, 1985 at LLNL following the Topical Meeting on Controlled Nuclear

Fusion in San Francisco. The schedule for work at LLNL before this meeting

includes: (a) completion of heat-treatment studies by January 31, 1985

and (b) determination of 4-K tensile and fracture toughness response of

unwelded and autogeneous GTA welds in all four alloys by February 28, 1985.

(7) Possible alternatives to Incoloy alloys include the high manganese

alloys developed in Japan. These alloys also have lower thermal contraction, about 1/2 that of 304. It was suggested that conductor sheath alloy

development be included in the items that the United States wishes to

include in the proposed joint United States/Japan structural alloys

exchange program.

320
NBS-DOE WORKSHOP

Ken Agarwal

General Dynamics

San Diego, California

John Arvidson

NBS

Boulder, Colorado

Frank Babish

Sandvik Steel Co.

Scranton, Pennsylvania

Ken Banks

Teledyne McKay

York, Pennsylvania

Herb Becker

MIT

Cambridge, Massachusetts

Jim Bialek

Princeton Plasma Physics

Princeton, New Jersey

Roger Bushey

Alloy Rods

Hanover, Pennsylvania

Bernie Carpenter

Colorado School of Mines

Golden, Colorado

Ralph Coltman

ORNL

Oak Ridge, Tennessee

Edward Dalder

LLNL

Livermore, California

Victor Der

Office of Fusion Energy

Washington, D.C.

Jack Ekin

NBS

Boulder, Colorado

Brent Fultz

LBL

Berkeley, California

Gene Goodwin

ORNL

Oak Ridge, Tennessee

PARTICIPANTS

Paul Grobner

AMAX Materials Res. Center

Ann Arbor, Michigan

Drew Hazelton

Intermagnetics General Corp.

Guilderland, New York

Philip Heitzenroeder

Princeton Plasma Physics

Princeton, New Jersey

Herb Helmbrecht

Babcock-Wilcox

Barberton, Ohio

Thomas Hordubay

Westinghouse Electric Corp.

Pittsburgh, Pennsylvania

M. B. Kasen

NBS

Boulder, Colorado

Peter Komarek

Nuclear Research Center

Karlsruhe, F. R, Germany

Ronald Kriz

NBS

Boulder, Colorado

John Lippold

SNLL

Livermore, California

Martin Lube 11

ORNL

Oak Ridge, Tennessee

Harry McHenry

NBS

Boulder, Colorado

J. W. Morris, Jr.

University of California

Berkeley, California

Walter Muster

Federal Labs for Materials

Testing

Dubendorf, Switzerland

Lew Myers

Carpenter Tech.

Reading, Pennsylvania

Carl Osgood

Cranbury, New Jersey

Craig Peters

LBL

Berkeley, California

Pat Purtscher

NBS

Boulder, Colorado

Richard Reed

NBS

Boulder, Colorado

Harry Rogers

Drexel University

Philadelphia, Pennsylvania

Joel Self

Colorado School of Mines

Golden, Colorado

Oscar Seth

CBI

Houston, Texas

Tom Siewert

NBS

Boulder, Colorado

Nancy Simon

NBS

Boulder, Colorado

Leonard Summers

LLNL

Livermore, California

Ralph Tobler

NBS

Boulder, Colorado

Dennis Tucker

LANL

Los Alamos, New Mexico

Robert Walsh

NBS

Boulder, Colorado

Jon Zbasnik

LLNL

Livermore, California

321


.i
CRYOGENIC STEELS FOR SUPERCONDUCTING MAGNETS:

DEVELOPMENTS IN JAPAN

Harry I. McHenry

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

The Japan Atomic Energy Research Institute initiated a program in 1982

to develop cryogenic steels for use in the large superconducting magnets

planned for the Fusion Experimental Reactor. The target properties for the

cryogenic steels are a yield strength of 1200 MPa at 4 K and a fracture

toughness of 200 MPa/m at 4 K. Progress on developing these steels was reviewed at a U.S. /Japan workshop in December 1984. Five Japanese steel

companies have developed candidate alloys that met or nearly met the property

goals. The new steels include 25Cr-1 4Ni-4Mn ,1 2Ni-1 2Cr-1 0Mn-5Mo , 1 3Cr-5Ni22Mn and 1 5Cr-l Ni-25Mn . All of the alloys are nonmagnetic, stainless steels

that are alloyed with nitrogen (0.2 to 0.355^). Following the workshop, the

participating steel companies were visited. This report summarizes the

information about these new steels obtained at the workshop and during the

visits

Key words: alloy steel, cryogenic materials, fusion energy, Japan, stainless

steel, steel industry, superconducting magnets.

323
INTRODUCTION

Superconductivity is one of the high technologies that Japan has

targeted for concerted development. There are national programs to use superconductivity to enhance the efficiency of generating, storing, and

transmitting electrical power. Superconducting magnets are being developed

for fusion power devices, magneto-hydrodynamic (MHD) power generators and

high energy physics experiments. Numerous research and development programs

are being conducted to develop these applications and to develop improved

superconducting materials.

The scope of this report is limited to recent developments in cryogenic

steels for structural applications in superconducting magnets. The main source of information was the United States/Japan Joint Planning Workshop on Low Temperature Structural Materials and Standards (Tokyo; December 17 to 21 , 1984), which was held to initiate a program of cooperative research in the area of materials and structures technology for superconducting magnets for

fusion energy systems. The workshop was cosponsored by the U.S. Department

of Energy (DOE) and the Japan Atomic Energy Research Institute (JAERI) and

organized by Dr. Susumu Shimamoto of JAERI and Dr. Victor Der of DO^l, Office

of Fusion Energy. A summary of the workshop topics outside the scope of this

report is given in Appendix A. The thirty Japanese participants represented

the various organizations involved in Japan's effort to develop superconducting magnets for fusion energy: JAERI, National Research Institute for

Metals, universities (Tohoku, Osaka, Tokyo), steel companies (Nippon Steel,

Kawasaki Steel, Japan Steel Works, Kobe Steel, and Nippon Kokan), and electrical manufacturers (Hitachi, Toshiba, and Mitsubishi Electric). The six

U.S. participants represented organizations in the DOE fusion energy program:

Lawrence Berkeley Laboratory, Lawrence Livermore National Laboratory,

Massachusetts Institute of Technology, National Bureau of Standards, and

Princeton Plasma Physics Laboratory. A list of attendees is given in

Appendix B.

REQUIREMENTS ON THE CRYOGENIC STEELS

Cryogenic steels will be used for the main structural members of the

superconducting magnets of the Fusion Engineering Reactor (FER), a tokamak

device being designed by JAERI to demonstrate the technical feasibility of

electrical power generation by fusion energy. Currently in the design stage,

the FER will take ten years to build and is not expected to go into operation until about the year 2000. Even then, it will only be an experimental

reactor, to be followed in the development plan by a prototype reactor and a demonstration reaction. Thus, the market for the steels discussed in this

report will not develop fully until well into the twenty-first century, a good example of the long-term outlook of Japanese industry. In the meantime,

these steels may be useful for other superconductivity projects.

The superconducting magnets being designed for FER are truly enormous

structures. Current designs call for 1 0-m diameter coils in 1 2 T field at

currents of 20 kA. The stored energy is 30 GJ. A dozen or so of these

magnets will be used to confine the hot plasma within a donut-shaped vacuum

324
vessel. A schematic of the conceptual design is shown in Figure 1 . The

principal design features governing alloy selection are the enormous size and

stored energy of the magnets, the extremely high forces exerted by the

magnets, and the limited space available for the structure. These features

result in the need for steels with sufficient strength to perform the required structural functions within the space available, sufficient fatigue

and fracture resistance to operate safely, and sufficient fabricability to be

practical. The choice of materials is further restricted by the adverse

operating environment of the magnet system: a design temperature of 4 K,

magnetic fields up to 12 T, and moderate levels of neutron irradiation.

The Superconducting Magnet Laboratory at JAERI’s new Fusion R & D Center

in Nakamachi, Ibaraki-ken, is responsible for the FER magnet design. In

1981 , a program was initiated to develop a steel that meets the FER design

requirements prior to the start of construction, about 1988. The approach

was to establish a set of target properties and then work together with the

Japanese steel industry to develop a suitable steel. The target properties,

first announced in 1982, are:

For initial screening, Charpy V-notch impact tests at 4 K are used in

lieu of the fracture toughness tests; the property target is 100 J.

The task of developing an alloy with these properties has been undertaken by three steel companies working in conjunction with JAERI: Japan

Steel Works, Kobe Steel, and Nippon Steel. In addition, Nippon Kokan is

working independently to develop an alloy with the same property goals.

Kawasaki Steel is working with JAERI to develop a sheet material with the same property goals after exposure to the thermal cycle required for the

superconductor sheath material. The contracts between JAERI and the participating companies were vaguely described to me as simply the responsibilities of each party in the mutual development program; apparently JAERI

doesn't pay the companies for their developmental efforts.

The yield strength and toughness targets have served as go-no go screening requirements. The magnetic permeability requirement has limited the

consideration of steels to those that are fully austenitic and nonmagnetic.

The corrosion resistance target has led to use of a minimum of \ 2 % Cr . The

remaining targets have not yet had an apparent influence on the alloy development efforts.

• yield strength

• fracture toughness

• fatigue strength

• permeability

• corrosion resistance

• fabricability

• plate thickness

1200 MPa at 4 K

200 MPa/m at 4 K

-316 stainless steel

U ^ 1.02

rust resistance

weldability and machinability

up to 200 mm

THE JAERI/INDUSTRY DEVELOPMENT PROGRAM

325
The development schedule is shown in Figure 2. For initial screening,

tensile and Charpy impact tests were conducted at 4 K on 89 candidate alloys

in four general alloy classes:

• stainless steel (SS) 31 steels

• high-Mn stainless steel (HMSS) 40 steels

• high-Mn steel (HMS) 111 steels

• ferritic steel (FS) 4 steels

A total of 18 stainless steels (9 SS and 9 HMSS) met the yield strength

(> 1200 MPa) and Charpy impact (> 100 J) screening goals. Two high-Mn steels

met the goals but were dropped from further consideration because of insufficient Cr to be stainless steels. One ferritic steel met the goals, but was dropped because of the preference for nonmagnetic steels. Of these, some were of similar chemistry, thereby reducing the number of alloys included in

the second stage of screening (fracture toughness tests at 4 K) to 11 (4 SS

and 7 HMSS); the candidate alloys are shown in Table 1. As shown in

Figure 3, the two high-Mn stainless steels did not meet the strength and

toughness goals; however, the results were judged to be close enough to keep

the steels in the program.

The five alloys developed in the JAERI industry program have excellent

combinations of strength and toughness at 4 K. Thus, the alloy development

phase of the JAERI program has been completed. These alloys also have

satisfactory corrosion resistance and the physical properties are assumed to

be suitable, i.e., low magnetic permeability and acceptable electrical

resistance and thermal expansivity. The remaining tasks for the steel

industry participants are (1) to conduct primary processing studies for

scaling up to commercial practice, (2) to verify that the properties can be

met in the large plates required for the FER , and (3) to develop the welding

materials and procedures for use with these new alloys. The latter task is,

perhaps, the most challenging. It has been undertaken primarily by Nippon

Steel and Kobe Steel, the two major suppliers of welding consummables in

Japan. In addition, JAERI will be conducting fatigue crack growth studies

during 1985 to verify that the new steels have fatigue properties at 4 K that are comparable to those of 316 stainless steel.

VISITS TO PARTICIPATING STEEL COMPANIES

Following the workshop, the U.S. delegates had the opportunity to visit

the Tokyo-area facilities of the four participating steel companies, and in

my case, Nippon Kokan. The facilities visited were as follows:

Japan Steel Works

Kawaski Steel Company

Kobe Steel

Nippon Steel Corporation

Nippon Kokan K.K.

Head Office

Research Laboratories

Chiba Works

Welding Division

Research Laboratories II

Technical Research Center

Tokyo

Chiba

Fuj isawa

Sagamihara

Kawasaki

These visits plus additional details regarding each company's research on cryogenic steels are summarized below.

326