Reference

NBS

Publications

nBSIR 82-1667

TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES - V

_i i i TEMPERATURE

To

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

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d2-ioo7

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By

Fracture and Deformation Division

National Bureau of Standards

Boulder, CO 80303

NBSIR 82-1667 UC 20b, c

TECHNICAL REPORTS

MATERIALS STUDIES FOR

MAGNETIC FUSION ENERGY

APPLICATIONS AT LOW TEMPERATURES - V

Edited By

R.P. Reed and N.J. Simon

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

May 1982

Sponsored By

Department of Energy

Office of Fusion Energy

Washington, D.C. 20545

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

SUMMARY v ORGANIZATIONAL CONTACTS vii

PROGRAM DESCRIPTION ix

HIGHLIGHTS OF RESULTS 1 STRUCTURAL ALLOYS

STRUCTURAL ALLOYS PROGRAM 13

DEFORMATION OF METASTABLE AUSTENITIC STEELS AT LOW TEMPERATURES. ... 15

TEMPERATURE DEPENDENCE OF FLOW STRENGTH OF Fe-20Cr-16Ni-6Mn-0. 2N

AND Fe-18Cr-10Ni-1.5Mn-0. IN (304LN) AUSTENITIC STEELS 29

TENSILE AND FRACTURE PROPERTIES OF MANGANESE-MODIFIED AISI

304 TYPE STAINLESS STEEL ; 59

MAGNETIC FIELD EFFECTS ON TENSILE BEHAVIOR OF ALLOYS 304

AND 310 AT 4 K 71

MARTENSITIC TRANSFORMATIONS IN TYPE 304 AUSTENITIC STAINLESS

STEELS 85

FRACTURE TOUGHNESS OF CF8 STAINLESS STEEL CASTINGS IN LIQUID HELIUM. . 107

DUCTILE FRACTURE WITH SERRATIONS IN AISI 310S STAINLESS

STEEL AT LIQUID HELIUM TEMPERATURE 145

MECHANICAL PROPERTY MEASUREMENTS AT LOW TEMPERATURES 171

PREDICTED SINGLE CRYSTAL ELASTIC CONSTANTS OF STAINLESS-STEEL 316 . . 185

MANGANESE CONTRIBUTIONS TO THE ELASTIC CONSTANTS OF FACE-CENTERED

CUBIC Fe-Cr-Ni STAINLESS STEELS 189

ANOMALOUS LOW-TEMPERATURE ELASTIC- CONSTANT BEHAVIOR OF

Fe-20Cr-16Ni-6Mn 213

WELDING AND CASTING

WELDMENTS AND CASTINGS PROGRAM 231

WELDMENTS AND CASTINGS FOR LIQUID HELIUM SERVICE 233

FRACTURE PROPERTIES OF A 25Mn AUSTENITIC STEEL AND ITS WELDS AT 4 K. . 245

DEFORMATION AND FRACTURE BEHAVIOR OF DUPLEX AUSTENITE/DELTAFERRITE MATERIALS AT 4 K 269

THE EFFECT OF DELTA-FERRITE ON THE MECHANICAL PROPERTIES OF

CF8M STAINLESS STEEL CASTINGS AT 4 K 289

ULTRASONIC INSPECTION OF STAINLESS STEEL BUTT WELDS USING

HORIZONTALLY POLARIZED SHEAR WAVES 319
CONTENTS (Cont'd)

Pa<ge

SINGLE-CRYSTAL ELASTIC CONSTANTS IN NONDESTRUCTIVE EVALUATION

OF WELDS 345

SOUND VELOCITY AS A TEXTURE PROBE: APPLICATION TO

STAINLESS-STEEL-316 WELDS 353

NONMETALLICS

NQNMETALLICS PROGRAM 375

CURRENT STATUS OF STANDARDIZED NONMETALLIC CRYOGENIC LAMINATES .... 381

EFFECT OF CRYOGENIC TEMPERATURES ON THE MECHANICAL PERFORMANCE

OF GLASS-FABRIC-REINFORCED LAMINATES 391

MECHANICAL PROPERTIES OF PLASTIC COMPOSITES UNDER LOW

TEMPERATURE CONDITIONS . 407

THERMAL CONDUCTIVITY OF G-10CR AND G-11CR INDUSTRIAL LAMINATES

AND THEIR COMPONENT PARTS AT LOW TEMPERATURES .... . . 411

WAVE PROPAGATION AND ELASTIC CONSTANTS IN PARTICULATE AND

FIBROUS COMPOSITES 429

ELASTIC CONSTANTS AND INTERNAL FRICTION OF FIBER-REINFORCED COMPOSITES 441

ELASTIC CONSTANTS OF FIBER-REINFORCED BORON-ALUMINUM: A CRITICAL

COMPARISON OF OBSERVATION AND THEORY . . . 449

TECHNOLOGY TRANSFER

TECHNOLOGY TRANSFER PROGRAM 479

NBS-DOE WORKSHOP: MATERIALS AT LOW TEMPERATURES 481

ACKNOWLEDGMENT 490

iv
SUMMARY

This report contains results of a research program to produce material

property data that will facilitate design and development of cryogenic

structures for the superconducting magnets of magnetic fusion energy power

plants and prototypes. The program was conceived and 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.

The reports presented here summarize the fifth year of work on the low

temperature materials research program. Highlights of the results are

presented first. Research results are given for the four main program areas:

structural alloys, weldings and castings, nonmetal 1 ics , and technology

transfer. Objectives, approaches, and achievements are summarized in an

introduction to each program area.

The major portion of the program has been the evaluation of the low

temperature mechanical and physical properties of stainless steel base metals,

welds, and castings, with particular emphasis on the nitrogen-strengthened

stainless steels. Stainless steels with manganese additions and other high

manganese steels have also been investigated. Work has been done on the

production and standardization of nonmetal 1 ics , primarily industrial

laminates, for low temperature applications and on the measurement of their

properties at cryogenic temperatures. A brief summary is given of the fifth

NBS/DoE Vail Workshop held in October 1981.

v
Note

:

Certain commercial equipment, instruments, or materials are

identified in this paper to specify the experimental procedure adequately. In no case does such identification imply recommendation or

endorsement by the National Bureau of Standards, nor does it imply that

the material or equipment identified is necessarily the best available

for the purpose. Papers by non-NBS authors have not been reviewed or

edited by NBS . Therefore, the National Bureau of Standards accepts no

responsibility for comments or recommendations contained therein.

vi
ORGANIZATIONAL CONTACTS

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

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

Program Monitor D. Beard

National Bureau of Standards, Boulder, Colorado

Program Manager R. P. Reed

Structural Alloys

Elastic Properties

Welding and Casting

Nonmetal 1 ics

Technology Transfer

University of Wisconsin,

Wisconsin 53706

Program Manager

University of Colorado,

Colorado 80309

R. P. Reed

R. L. Tobler

J. M. Arvidson

H. M. Ledbetter

H. I. McHenry

T. A. Whipple

C. M. Fortunko

M. B. Kasen

H. M. Ledbetter

R. D. Kriz

N. J. Simon

Engineering Research

D. Larbalestier

Mechanical Engineering

S. K. Datta

(301) 353-4958

(FTS) 233-4958

80303

(303) 497-3870

(FTS) 320-3870

(303) 497-3870

(303) 497-3421

(303) 497-3424

(303) 497-3443

(303) 497-3268

(303) 497-5795

(303) 497-3523

(303) 497-3558

(303) 497-3443

(303) 497-3547

(303) 497-3687

Building, Madison,

(608) 263-2194

Department, Boulder,

(303) 492-7750

VI 1

PROGRAM DESCRIPTION

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

Structural Alloys for Superconducting Magnets in Fusion Energy Systems , was

included in volume IV (1981) of this series. Through continuous interactions

with all low temperature design, construction, and measurement programs, such

as the Large Coil Project, 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. 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 each fall in Vail, Colorado. Starting with this annual report,

handbook pages presenting the available data for specific materials will be

distributed with the annual report.
Table 1. Outline of the NBS/DoE Program on Material Studies for

Magnetic Fusion Energy Applications at Low Temperatures.

Program Area Organization Program Description

1. Characterization

and development of

strong, tough alloys

2. Characterization

and development of

strong, fatigueresistant alloys

3. Characterization

4. Characterization

and modeling of martensitic start temperatures

A. Structural Alloys

NBS Assessment of low temperature

properties of selected aus- tenitic alloys containing

varying concentrations of

C, N, and Mn with a Fe-Crbase. Assessment of Japanese

austenitic alloys with Fe-Mn

base.

NBS

NBS

Universi ty

of

Wi scons in

Assessment of fatigue and

fatigue crack growth rates

of candidate structural

alloys, including 300 series

steels, Fe-Mn base alloys,

and age-hardened alloys.

Measurement of elastic,

tensile, fracture toughness,

and fatigue crack growth

rate properties as a function

of temperature for selected

austenitic stainless steels

and aluminum alloys. Study

of effects of grain size,

martensitic transformations,

anc( alloying on low temperature behavior.

Study to assess, empirically,

the relation between alloy

content and the temperature

at which martensite forms

on cooling for commercial

grades of AISI 300 series

stainless steels.

x
Program Area Organization Program Description

B. Welds

1. Stainless steel NBS

welds and castings

2. Stainless steel NBS

welds

3. Testing program NBS

and Castings

Investigation of the metallurgical factors that affect

the mechanical properties of

stainless steel weldments

and castings at cryogenic

temperatures. Involves

metal lographic observations

of duplex austenite/delta

ferrite microstructures,

in deformed and fractured

stainless steels. Effects

of ferrite and nitrogen

content on the strength

and toughness at 4 K are being studied in stainless

steel castings; this work

will be extended to weldments .

Study of effects of oxygen

and delta-ferrite content

on submerged arc weldments

at 4 K. Investigation of

the effects of weld reinforcement and austenite

stability on weld strength.

Improvement of methods of

ultrasonic testing.

Continuation of mechanical

property testing at 4 K of

welds and plate material, in

support of superconducting

magnet design and construction.

C. Nonmetal 1 ics for Magnet Structures

1. Standardization NBS Continuing cooperation with

industry to establish and

refine cryogenic-grade speci

fications for insulating

laminates and coding systems

for laminates.

xi
Program Area Organization Program Description

2. Characterization NBS

3. Property determination NBS

and model ing

D. Technology Transfer

1. NBS/DoE Workshop NBS

2. Handbook NBS

Thermal conductivity measurements of composite components

at cryogenic temperatures to

aid in establishing models

for predicting the thermal

conductivity of a variety of

laminates. Investigation of

failure modes of laminates

under compression at cryogenic temperatures.

Development of dynamic

methods of determining

elastic properties of laminated composites. For a woven glass-fiber/epoxy

composite, experimental determination of the complete

nine-component elasticconstant tensor. Study of

the local-stress distribution in a glass-fiber/

epoxy composite "unit cell"

using finite-element methods.

An annual workshop to present

research results to the fusion

community, to discuss new problems, and to promote

interaction between interested parties.

Handbook data pages on mechanical and physical

properties of AISI 316

stainless steels are published as an addendum to

this report. Data pages

on 21-6-9 stainless steel

and AISI 304 stainless

steels will be prepared

for the next annual report.

XI 1
HIGHLIGHTS OF RESULTS

1

HIGHLIGHTS OF RESULTS

STRUCTURAL ALLOYS:

Tensile and Fracture Properties of Austenitic Stainless Steels

A series of experiments on AISI 310, AISI 304N, manganese-modified AISI

304, and nitrogen-strengthened AISI 304 are reported with emphasis on the

analyses of fracture and stress-strain characteristics. For analysis, stressstrain curves of metastable austenitic steel alloys were divided into three

sections; the stress and strain parameters associated with each section were

related to composition and martensitic transformation effects. The addition

of manganese to Fe-Cr-Ni metastable steels increased the fracture toughness at

4 K, while maintaining or slightly increasing the tensile yield strength.

Measurement methodology continues to be emphasized. A review paper is

included on tensile, fracture toughness, and fatigue low temperature measurements. The AISI 310 J-integral fracture toughness measurements were interpreted; here the alloy exhibited multiple serrations during testing of compacttensile specimens, yet the crack extension was by ductile tearing.

Preliminary data on the effect of magnetic fields on deformation of

austenitic steels at 4 K are reported. In particular, no effect on flow

strength of AISI 304 and 310 alloys was observed for continuously applied 7-T

fields at 4 K. Cycling of the fields on and off during testing at 4 K also

produced no change of flow strength.

WELDING AND CASTING:

Stainless Steel Weldments

Nitrogen-strengthened austenitic Cr-Ni stainless steels are commonly

considered for use as structural alloys in superconducting magnets because

3
they have a good combination of strength, stiffness, and toughness at 4 K.

However, these nitrogen-strengthened stainless steels do not have good welding

properties because of the difficulties in finding a matching strength filler

alloy with sufficient toughness. Consequently, a new high-manganese austenitic steel, 25Mn-5Cr-lNi , was evaluated and found to have a favorable combination of strength, toughness, and fatigue crack growth resistance at 4 K for

both base plate and welds.

A new approach to ultrasonic inspection of welds has been developed using

horizontally polarized shear waves that are transmitted and received by

electromagnetic acoustic transducers (EMATs). Higher sensitivity than

previously available is attained with this system. Ultrasonic techniques were

also used to measure the elastic properties of a series of 316L stainless

steel weldments with varying ferrite content. The results showed strong

elastic anisotropy in the welds and little sensitivity of the elastic constants to ferrite content.

Stainless Steel Castings

CF8M castings are being studied for two reasons: (a) there is interest

in their use as structural elements for superconducting magnets and (b) the

factors affecting fracture and deformation modes are more easily observed

because their duplex austenite/del ta ferrite structure is coarser than that of

weldments. Fracture toughness results show a decrease in toughness with

increasing delta-ferrite content up to about 15 percent, followed by essentially constant fracture toughness at higher ferrite content. Metal lographic

studies have provided an explanation for this behavior: a continuous fracture

path through the ferrite is established at about 15 percent delta-ferrite.

4
NONMETALLICS:

Standardization

Work continued on refining the specification for the G-10CR grade of

cryogenic high-pressure industrial laminate. A revised draft incorporating

input and suggestions from the fabricators has been completed and distributed

to the fabricators for comment. Major additions were specifications for the

cure cycle and minimum specifications for mechanical and physical properties.

Two additional laminators have joined three other manufacturers as

producers of G-10CR.

Characterization

The thermal conductivity at cryogenic temperatures has been determined

for two glass-fabric-reinforced epoxy-matrix laminates having different

reinforcement-to-resin ratios in an attempt to determine the individual

contribution of each to the total conductivity.

A polyimide-matrix variant of G-10CR has been characterized for mechanical properties down to 4 K. The mechanical performance of this variant,

which ORNL found to have good radiation resistance, was found to be substantially inferior to that of conventional G-10CR.

The cryogenic performance of G-10CR produced by two companies that have

recently started production of the material was screened to 76 K.

Property Determination and Modeling

1. At the first Japan-U.S. Conference on Composite Materials (Tokyo,

January 1981), Ledbetter presented a review of NBS studies of

anisotropic elastic constants and internal friction of fiberreinforced composites. Materials that were studied include:

boron-aluminum, boron-epoxy, graphite-epoxy, glass-epoxy, and

aramid-epoxy. In all cases, elastic-constant direction dependence

5
could be described by a relationship developed for single crystals

of homogeneous materials. Elastic stiffness was found to vary

inversely with internal friction.

2. At the same conference, Datta, Ledbetter, and Kinra presented a

theoretical-experimental study of wave propagation and elastic

constants in particulate and fibrous composites. For two types of

composites--particulate and fiber-reinforced--dynamic elastic

properties were studied both theoretically and experimentally. The

two composites contained, respectively, randomly distributed spherical inclusions and aligned continuous fibers, both in a homogeneous

matrix. The theory described aligned, identical ellipsoidal inclusions. The theory applies to both spherical inclusions and short

fibers as special cases. Previously Bose and Mai presented a

similar theory for continuous fibers. The theories estimate the

effective propagation speed of a plane harmonic wave, average the

scattered field by the Waterman-Truell procedure, and use the Lax

quasi-crystalline approximation. Theory and observation agree quite

well. Particulate composites were studied in a through-transmission

water-immersion tank, while the fiber composite was studied by both

pulse-echo-overlap and resonance methods.

3. Datta and Ledbetter completed a critical comparison of observation

and theory. Elastic constants, both the C..'s and the S..'s, were

13 13

measured and calculated for a laminated, uniaxially fiber-reinforced

boron-aluminum composite. Three theoretical models were considered:

square-array, hexagonal -array , and random-distribution. By combining several existing theoretical studies on randomly distributed

fibers, a full set of elastic constants can be predicted for this

6
model. The random-distribution model agrees best with observation,

especially for off-diagonal elastic constants. Considering all nine

elastic constants, observation and theory differ on the average by

six percent.

4. During his NRC-NBS postdoctoral appointment in our laboratory, Kriz

studied ply cracks and fracture strengths of graphite/epoxy laminates

at 76 K. Quasi-isotropic laminates with a ply-stacking sequence of

[0/±45/90]

s and [0/90/±45]

s were fabricated from T300/5208 graphite/

epoxy and quasi-statical ly loaded in tension at 76 K. Fibers in the

0° plies, which are oriented unidirectionally parallel to the load

axis, carry the largest portion of the tensile load; the weaker 90°

and ±45° plies crack at loads much lower than the fracture strength.

From a fractographic viewpoint, at 76 K, laminate ply cracks dominate

the fracture process in adjacent plies. To understand better

how defects affect laminate strength, we examined the effect of ply

cracks on the fracture of the load-bearing 0° plies. An idealized

linear-elastic finite-element model was used to predict the distribution of stress in the 0° ply near the crack tip. Variations in

the residual -stress state caused by large temperature changes and

absorbed moisture were included in the analysis. Experiment indicated that absorbed moisture significantly alters the fracture

strength and fracture surface of a dehydrated [0/90/°45]

s laminate

tested at 76 K. The fracture surfaces of dehydrated laminates

illustrate that the 0° ply fractures along several 90° ply cracks.

When absorbed moisture saturates a [0/90/±45]

s laminate, a single

90° ply crack dominates the fracture of the 0° ply, and the laminate

fracture strength decreases by eight percent. A population of 37

7
samples statistically verified that moisture decreases strength;

furthermore, skewness of the population to low strengths indicated a

weak-link phenomenon that is indicated by a Wei bull distribution.

The Wei bull shape parameter for fracture of the dehydrated laminates

is 17.6, which increases to 19.0 when saturation causes a single

ply crack to dominate the final fracture. A chi-squared confidence

test for both dehydrated and saturated populations yielded confidence limits better than 90 percent. Similar fractographic and

statistical investigations on [0/±45/90]

s and [Og] laminates were

considered.

A manuscript is now in preparation for presentation at the ASTM

Symposium on Effects of Defects in Composite Materials (13 December

1982, San Francisco, California).

5. Dr. Kriz, as part of his NRC-NBS postdoctoral studies, also completed a study to monitor elastic-stiffness degradation. In particular, he studied degradation due to moisture absorption in graphite/

epoxy. However, the method applied, in principle, to any elastically anisotropic material that degrades by any mechanism:

moisture, mechanical fatigue, irradiation, et cetera. The method is

based on the change in direction of the energy-flux vector (Poynting

vector). Two short manuscripts have been submitted for publication

in Composites Technology Reviews and in the proceedings of the ASNT

spring conference (22-25 March 1982, Boston, Massachusetts).

TECHNOLOGY TRANSFER:

The annual NBS/DoE Workshop on Materials at Low Temperatures at Vail,

Colorado in October 1981 was attended by about sixty representatives of the

8
materials and magnet design communities. Again, the meeting was viewed

constructively; it served as a focal point to identify and discuss magnet

construction or design problems related to materials. For a few who have

become recently involved in cryogenic applications, the workshop was educational .

Handbook pages and supporting documentation have been prepared for

AISI 316 stainless steels and are published as an addendum to this report.

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. These pages will also be submitted to the advisory committee of the Materials Handbook for Fusion Energy Systems.

9

STRUCTURAL ALLOYS

11

STRUCTURAL ALLOYS PROGRAM

LEADER: R. P. Reed, NBS

STAFF: R. L. Tobler, J. M. Arvidson, NBS

CONTRACTS: Prof. D. Larbalestier, U. Wisconsin, Madison, WI,

OBJECTIVES:

(1) Development and characterization of strong, tough, structural alloys

for use at 4 K in superconducting magnets.

(2) Development and characterization 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 (1981):

(1) J-integral fracture toughness assessment of AISI 310 (4-300 K).

(2) Review of low temperature mechanical property test procedures.

(3) Assessment of CF8 stainless steel castings.

(4) Characterization of stress-strain behavior of metastable austenitic

steel s. (5) Measurement of tensile and fracture properties of manganese-modified

Fe-Cr-Ni base steels.

(6) Preliminary assessment of influence of magnetic fields on deformation of austenitic steels at 4 K. (7) Study of prediction of martensitic start temperatures in Fe-Cr-Ni

austenitic steels.

RESEARCH THIS YEAR (1982):

(1) Continued research on effects of magnetic-fields on 4-K deformation

of austenitic steels.

(2) Construction of 500,000-N (110,000-lbf) capacity tensile-fatigue

testing facility for the temperature range 4-300 K. (3) Characterization of selected Japanese Fe-Mn base austenitic steels.

(4) Initiation of fatigue testing program in the temperature range

4-300 K. (5) Study of the temperature dependence of the flow strength of austenitic steels.

(6) Continuation of study of martensitic-start temperatures in Fe-Cr-Ni

austenitic steels.

13

DEFORMATION OF METASTABLE AUSTENITIC STEELS AT LOW TEMPERATURES*+

R. P. Reed and R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Commercial grades of Fe-Cr-Ni austenitic stainless steels are metastable

at low temperatures. Most of these steels do not transform on cooling, but do

transform during deformation. Stress-strain curves reflect the transformation

characteristics. There are typically three distinct stages of the stressstrain curve of polycrystalline Fe-Cr-Ni alloys at low temperatures. The

stress-strain characteristics are discussed with respect to martensitic

transformation.

*Work supported by Office of Fusion Energy, Department of Energy.

+To be published in Advances in Cryogenic Engineering--Material s Vol. 28,

R. P. Reed and A, F. Clark, Eds, Plenum Press, New York (1982).

15

INTRODUCTION

The reaction of a solid to continuously increasing applied

tensile load is portrayed using a stress-versus-s train curve. From stress-strain curves the Young’s modulus, yield strength,

ultimate tensile strength, percent elongation and work hardening

characteristics can be obtained. Typically, following the elastic

deformation region, a metal or alloy work hardens at a decreasing

rate until localized specimen necking initiates and the ultimate

strength of the specimen has been reached.

The stress-strain characteristics at low temperatures of

commercial grades of polycrystalline austenitic stainless steels

containing about 18 wt% chromium and 8 wt% nickel are not con- ventional. The anomalous behavior is thought to be caused by the

martensitic transformation of face-centered-cubic austenite to

body-centered-cubic (a') and hexagonal close-packed phases. This

paper suggests that the plastic deformation of metastable austenites is composed of three stages, and uses a series of Fe-18Cr8Ni-l-6Mn, 0.1-0.2N alloys, tested at 4 K, to demonstrate the

usefulness of this characterization.

EXPERIMENTAL PROCEDURES

The tensile tests were conducted in liquid helium using a strain rate of 0.02 min

-

"*'. Strain was recorded using a clamp-on

strain-gage extensometer . Strains larger than about 0.10 were

*Work supported by Office of Fusion Energy, Department of Energy.

17
computed using ioad-time graphs of each test. Other experimental

details, alloy compositions, and alloy hardness and grain size

are discussed by Tobler and Reed [1,2].

TENSILE STRESS-STRAIN CURVES

Typical stress-strain curves of metastable polycrystalline

austenitic stainless steels at temperatures between 4 and 295 K

are illustrated in Fig. 1 for an Fe-l8Cr-8Ni alloy. Compositions

refer to weight percent. Alloys of this type remain ductile at

Strain, e

Figure 1. Typical stress versus strain curves (engineering) for

polycrystalline Fe-18Cr-8Ni austenitic stainless steel.

18

Stress,

cr

(ksi)
low temperatures, exhibit considerable work hardening, have a region of low work hardening at 195, 76 and 4 K, and have discontinuous yielding at 4 K. The stress-strain curves for a series

of Fe-18Cr-8Ni-l-6Mn with 0.1 and 0.2N are presented in Figs. 2 and 3, respectively. For purposes of clarity, the discontinuous

yielding serrations have been deleted; instead only the maximum

flow stress values are plotted and the load drops are omitted.

The presence of an easy glide region is very apparent, followed

by a region of high work hardening.

STOASM, €

Figure 2. Stress-strain curves at 4 K for series of Fe-18Cr-8Ni0.1N alloys with 1-6 wt% Mn.

19
STRAIN

Figure 3. Stress-strain curves at 4 K for series of Fe-18Cr-8Ni0..2N alloys with 1-6 wt% Mn.

DISCUSSION

For characterization and analysis, the stress-strain curves

of such metastable polycrystalline austenitic alloys can be

considered to have three stages of plastic deformation. These

will be referred to as stages I, II and III. The stress-strain

curve in Fig. 4 identifies these stages and (following single

crystal nomenclature) assigns stress and strain symbols for the

onset of the three stages. Stage I represents the first stage of

plastic deformation, beginning at the elastic limit and ending at

the onset of easy glide (usually about e = 0.02). The yield

strength is included in this stage. Stage II is the easy glide

region. Stage III represents the region of high work hardening.

Since stable austenitic steels do not exhibit the stages of

the stress-strain curves discussed above, it is likely that these

stages are associated with martensitic transformation. The

remainder of this paper concerns correlations between the stresses

and strains of the three stages with parameters, such as composition, that affect austenite stability or represent martensite

concentration.

20
Plastic

Elastic Stagas

Figure 4. Identification of three stages of plastic deformation

in austenitic stainless steels at low temperatures.

Stage I: In our study sufficiently accurate measurements

were not obtained of the onset of Stage I, and aj. It is

likely that only very small amounts (< 1%) of martensite form in

this stage. Suzuki, et al [3], from studies on an 18Cr-9Ni

steel, suggest hexagonal close-packed (hep) martensite formation.

Olsen and Azrin [4]

,

using a TRIP steel (Fe-9Cr-8Ni-4Mo-2Si) that

is less stable than a normal austenitic stainless steel suggest

that stress-assisted body-centered-cubic martensite formations

contribute substantially to early austenite deformation. Within

the sensitivity of our x-ray (> 2% hexagonal close-packed, > 2% a')

and magnetometer (> 0.2% a') measurements, no marteniste formation was detected. In any case, the initial martensite formation is

thought to contribute to the observed decrease of flow strength

at decreasing temperatures below about 200 K [3,4,5].

The yield strength (o

y

, flow strength at plastic strain = 0.002) is within stage I. As shown in Fig. 5, ay

is linearly

dependent on Mn content, increasing with increasing Mn. The

linear dependence matches that of a Il5 the stress at which

Stage II begins. The increase of a y

with Mn is considerable,

about 33 MPa/wt% Mn, but not as high as the increase of cr y

from

nitrogen addition. From Fig. 5, it is shown that an addition of

0.1 wt% N increases cr y

about 50%. Note that the dependence of cv on wt% Mn is independent of N content. The strength increases

from N and Mn additions may arise from two sources: (1) Increased

austenite stability [6,7]. This results in less martensitic

21
Weight % Mn

Figure 5. Tensile yield strength and stage II a and at 4 K

as a function of wt% Mn.

transformation, and, consequently, less work hardening and

(2) Solid-solution strengthening. Approximately 0.1 wt% N is

equivalent to 8 wt% Mn in contribution to strengthening.

Stage II: The stress to initiate stage II (ajj) linearly

increases with Mn content (see Fig. 5), but ejj is essentially

independent of Mn until 6% Mn is added (Fig. 5); at this concentration e-Q is larger. Similarly to a y

, N addition has a much

stronger influence on ajj, compared to Mn. The strain, tjx, is

independent of N content. In this stage, there is little work

hardening. Work softening has been reported [8] and this stage

has been termed "easy glide" [9]. Reed and Gunter [9], noting

the easy glide region and measuring (using x-rays) the increase

22
of hep martensite in the region, suggested that Stage II was caused by hep formation in slip bands. Suzuki, et al, observed

bee formation at slip band intersections using transmission

electron microscopy and proposed that these martensite laths act

as "windows," promoting dislocation mobility at slip-band intersections .

Stage III: The transition to the region of high work hardening rates, stage III, is denoted by a strain, £ill> and a stress, ct-j-jj. These are plotted in Fig. 6. The strain, £ill>

Figure 6. Stage III ^ III

and e pxi

at ^ K as a function ot wt Mu

23
has greater scatter and apparently increases with increasing Mn.

The stress, increases mildly and linearly with increasing

Mn content. In contrast to Stage II, the dependence of e-j-jj and

a III on Mn aPPears to be conditioned by the N content. Stage III

begins at lower stresses and lower strains for 0.1 wt% N, compared to 0.2 wt% N. The rate of work hardening, da/de, decreases

with increasing Mn, as shown in Fig. 7. The addition of N also

lowers the rate of work hardening and slightly affects the de-.

pendence of Mn content. N contributes to the reduction of da/de

about ten times more strongly (on the basis of wt% addition) than

Mn.

Figure 7. Rate of work hardening versus wt% Mn for alloy series,

at 4 K.

In Fig. 4 of the Tobler and Reed paper [1] in this volume,

L he normalized percent a* martensite (divided by the percent

uniform elongation within the measurement length) is plotted as a function of composition [Mn + Ni + 10 (C+N) ] . Using these data

and Fig. 7, the dependence of work hardening rate in stage III on percent a martensite per unit elongation is shown in Fig. 8.

Clearly, there is a strong linear correlation, and the rate of

24
% hc.c. Martensite /% Elongation

Figure 8. Rate of work hardening versus "normalized" martensite

function (wt% a’ martensite divided by % elongation)

for alloy series at 4 K.

work hardening can be regarded as a function of austenite stability with respect to a' formation as determined by composition.

This dependence may imply that a* formation in stage III is

distinct from stage II (and possibly stage I) formation at slip

band intersections. A second possibility is that sizable a’

formation produces sufficient accommodation deformation, resulting

from the associated y

-> a ' volume expansion, to increase the

defect concentration (and work hardening) sufficiently more than

the transformation strains serve to produce specimen strain.

The fracture toughness variation with composition is difficult to assess (see Ref. 1). Typically, at 4 K for a series of

stable and metastable austenitic alloys, the toughness (Kj

c (J))

varies as the reciprocal of the ay

(1) . Since the stability of

the alloys has been demonstrated to affect the stress-strain

characteristics, one may expect that the plastic zone at the

crack tip of the specimens may also be affected. The extent of

easy glide in stage II may influence the shape of the zone of

crack-tip plasticity; more easy glide may result in more planar

and local extension of the plastic zone ahead of the crack tip.

25
Such net-section yielding phenomena would be expected to result

in lower effective fracture toughness. Indeed, a linear relationship is obtained if one assumes that KIc (J) ~ a ( e iii-e n) + b(—) where the proportionally constants a and b are related by

a ^

b with the units of K

Ic

(J) in MPa/m and O

y

in MPa.

SUMMARY

We have suggested that stress-strain curves of metastable

austenitic stainless steels have three stages of plastic deformation. Using stress-strain curves for a series of Fe-18Cr-8Ni

alloys with varying Mn (1-6 wt%) and N (0.1, 0.2 wt%) contents

the parameters of stress and strain associated with the onset of

the three stages have been demonstrated to correlate very well

with alloy content. Alloy content affects austenite stability.

Correlations of thermodynamic stability, elastic-plastic fracture

toughness, and solid solution strengthening with the parameters

of the three stages will be explored in future papers.

REFERENCES

1. R. L. Tobler and R. P. Reed, "Tensile and Fracture Properties

of Manganese-Modified AISI 304 Type Stainless Steel," Ad - vances in Cryogenic Engineering (Materials) , Vol. 28, Plenum

Press, New York (1981), pp.

2. R. L. Tobler and R. P. Reed, "Tensile and Fracture Properties

of Manganese-Modified AISI 304 Type Stainless Steel," in:

Materials Studies for Magnetic Fusion Energy Applications at

Low Temperatures IV , NBSIR 81-1645, R. P. Reed and N. J.

Simon, eds., National Bureau of Standards, Boulder, Colorado,

pp. 77-100 (1981).

3. T. Suzuki, H. Kujima, K. Suzuki, T. Hashimoto, S. Koite, and

M. Ichihara, "Plastic Deformation and Martensitic Transformation in an Iron-Base Alloy," Scripta Met . , 10:353-358 (1976).

4. G. B. Olson and M. Azrin, "Transformation Behavior in Trip

Steels," Metall . Trans. A, 9A:713-721 (1978).

5. R. L. Tobler, R. P. Reed, and D. S. Burkhalter, "Temperature

Dependence of Yielding in Austenitic Stainless Steels," in:

Mater ials Studies for Magnetic Fusion Energy Applications at

Low Temperatures III , NBSIR 80-1627, R. P. Reed, ed..

National Bureau of Standards, Boulder, Colorado, pp. 51—78

(1980).

26
6 . G. H. Eichelman and F. C. Hull, "The Effect of Composition

on the Temperature of Sponteneous Transformation of Austenite

to Martensite in 18-8-Type Stainless Steel," Trans. Am. Soc.

Met., 45:77-104 (1953).

7. I. Williams, R. G. Williams, and R. C. Capellero, "Stability

of Austenitic Stainless Steels Between 4 K and 373 K," Proc . Sixth Int * 1 . Cryogenic Eng . Conf . , IPC Science and Technology

Press, Guildford, Surrey, England, pp . 337-341 (1976).

8. R. P. Reed and C. J. Guntner, "Stress-Induced Martensitic

Transformations in 18Cr-8Ni-Steel , " Trans . AIME , 230 : 1713-

1720 (1964).

9. C. J. Guntner and R. P. Reed, "The Effect of Experimental

Variables Including the Martensitic Transformation on the

Low-Temperature Mechanical Properties of Austenitic Stainless

Steels, Trans. ASM , 55:399-419 (1962).

27

TEMPERATURE DEPENDENCE OF FLOW STRENGTH OF Fe-20Cr-16Ni-6Mn-0.2N AND

Fe-18Cr-10Ni-1.5Mn-0.1N (304LN) AUSTENITIC STEELS*

R. P. Reed, R. L. Tobler, and J. W„ Elmer

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Recent studies have suggested the possibility of three anomalies in the

temperature dependence of the flow strength Fe-Cr-Ni and Fe-Cr-Ni-Mn austenitic stainless steels. Reduction of flow strength at decreasing temperature

may be associated with the onset of* martensite transformation, the magnetic

transition at the Neel temperature, and low temperature dislocation dynamics.

The tensile flow strength was investigated in the temperature range 4 to 295 K

for two annealed polycrystall ine alloys: Fe-20Cr-16Ni-6Mn-0.2N steel (produced in the USSR) and Fe-18Cr-10Ni-0. IN steel (AISI 304LN). The former alloy

is stable with repect to strain-induced martensitic transformations, the

latter metastable.

Major conclusions are: (1) The temperature dependence of the flow

strength of the two alloys is best characterized by a linear dependence of

log o versus T. The more stable Fe-20Cr-16Ni-6Mn-0.2N alloy exhibits a linear

slope (log c-T) over the entire temperature test range. The less stable

Fe-18Cr-10Ni-1.5Mn-0.1N alloy exhibits two linear ranges on a log a versus T

plot. (2) Temperature change experiments at constant specimen strain indicate

reversibility of flow strength at temperatures below about 100 K. (3) The

reported anomalous low temperature decreases of the flow strength associated

with the Neel transition temperature and very low temperatures for austenitic

steels were not confirmed by this study.

*Work supported by Department of Energy, Office of Magnetic Fusion Energy, and

the National Science Foundation.

29

INTRODUCTION

Austenitic stainless steels are used extensively as the structural materials in cryogenic systems, and knowledge of the dependence of their strength

on temperature is sometimes essential for proper design. This study addresses

the temperature dependence of the tensile flow strength in the range 4 K to

room temperature.

Recent studies [1-3] of Fe-Cr-Ni and Fe-Cr-Ni-Mn austenitic stainless

steels have reported three anomalies in the temperature dependence of the flow

strength. These anomalies consist of sharp decreases of strength on the order

of 100 MPa occurring over narrow temperature intervals between room temperature and 4 K. One type occurs only in metastable steels and is associated

with the onset of austenite-to-martensite transformation, usually at about

200 K. For both stable and metastable steel compositions, two additional

anomalies are reported at temperatures between 60 and 35 K and between 20 and

4 K. The flow strength decrease in the temperature interval 60 to 35 K has

been attributed to the paramagnetic-to-anti ferromagnetic transition at the

Neel temperature, where the elastic constants are known to decrease 1 to

2 percent. It has been suggested that flow strength reductions below 20 K

result from possible dislocation tunneling mechanisms [2]. Studies in our

laboratory [4-6] have identified the decrease in flow strength associated with

austenite instability with respect to martensitic transformations. However,

we have not been successful in detecting the other two anomalies. The observations of different investigators are discussed in this paper. Data are

presented for an Fe-20Cr-16Ni-6Mn-0.2N steel (produced in the USSR and independently tested by two research laboratories) and for an Fe-18Cr-10Ni-1.5Mn0. IN steel (AISI 304LN). The former alloy was expected to be stable with

respect to martensitic transformations, the latter metastable.

31
MATERIAL

The test material was a 25-mm plate of nitrogen-strengthened austenitic

stainless steel, obtained from the Raton Institute of Electrowelding, Kiev,

USSR. The material was tested in the as-received condition, which is characterized as follows:

Composition (wt.%) : Fe-20. 3Cr-16.4Ni -6. IMn-O. 19N-0.06C-0.21Mo-0.26Si0.025 P-0. 026S-0.09Cu.

Hardness : Rockwell B88, at 295 K after machining tensile specimens.

Microstructure : Equiaxed austenitic grains, free of carbonitride precipitation when viewed at 400X.

Grain size : Average grain diameter of 39 ym (ASTM No. 6.4).

The AISI 304LN material was received from a commercial U.S. supplier. It

was one of nine alloys produced from three 136-kg vacuum-induction-melted

heats, split with respect to carbon level, and teemed into 76 cm x 200 cm x

360-cm hot-topped cast-iron ingot molds. The ingots were then reheated and

soaked at 1561 K, hot-rolled to 25-mm-thick plates and air cooled. The plate

was final annealed at 1332 K for one hour and water quenched.

Composition (wt.%) : Fe-18.0Cr-9.91Ni-l.50Mn-0.016P-0.017S-0.57Si0.205Mo-0. 197Cu-0.037C-0. 12N.

Hardness : Rockwell B79 at 295 K after machining tensile specimens.

Microstructure : Equiaxed austenitic grains.

Grain Size : Average grain diameter of 105 ym.

PROCEDURE

In a previous study, unpolished, longitudinally oriented specimens were

used to measure tensile yield and ultimate strengths, as well as ductility, at

selected temperatures [6]. In this study, transverse-oriented specimens were

32
used for yield strength measurements at variable temperatures. These specimens were 6.25 mm in diameter and 25 mm in gage length. The specimens were

electropol ished in perchloric acid solution (70 percent methanol, 25 percent

glycerol, 5 percent perchloric acid) to remove scratches and cold-worked

material from machining operations. A total of 0.1 mm (4 mils) was removed

from the diameter, which is about four times the scratch depth.

Tensile tests used a screw-driven machine at a crosshead velocity of

_3

8.5 x 10 mm/s, with apparatus previously described [7]. Variable temperatures were achieved using controlled thermal conduction from cryogenic fluid

reservoirs attached to the load train and electric heaters on the specimen

grips. The automatic regulators used in this study are capable of maintaining

specified temperatures to ± 0.2 K, with an estimated absolute uncertainty of

± 1 K [6]. A Chrome! -constantan thermocouple was attached to the center of

the gage length of one calibration specimen to check the temperature control.

A strain-gage extensometer was clipped on to the specimen between two set

screws at a gage length of 25 mm. Calibrations were performed using a vertically mounted micrometer at 295, 76, and 4 K. Sensitivity varied from

'69 mV/cm at 295 K to 72 mV/ cm at 4 K. Indirect calibration was also performed at intermediate temperatures. This was done by elastically loading a

dummy specimen at selected temperatures; the extensometer sensitivity was

inferred from apparent specimen compliance after correction for the temperature dependence of Young's modulus. The ratio of recorder pen travel in mm to

specimen extension in mm was about 300.

Specimen-to-specimen scatter of the temperature dependence of the flow

strength was eliminated by performing temperature change tests on some specimens. To test a single specimen at three to five temperatures, the procedure

in Figure 1 was used. A specimen was loaded to a strain within the range

33
0.0005 to 0.002 at then unloaded, cooled to T

2

, and reloaded until plastic

flow resumed. Cooling to the lower temperature usually took 10 to 20 minutes.

Additional loadings at lower temperatures were also performed, and the flow

strength obtained by extrapolating to the original strain at the first

loading.

RESULTS AND DISCUSSION

Magnetic measurements [6] at 295 K after low temperature (76, 4 K) deformation confirmed that the Fe-20Cr-16Ni-6Mn-0.2N alloy does not exhibit any a'

(body-centered cubic) martensitic transformation and that the Fe-18Cr-10Ni1.5Mn-0.1N alloy is metastable and partially transformed to a' martensite.

This was expected since calculations listed in Table 1 of T^

s [8] (the temperature at which a' martensite is expected to begin to transform on cooling), and

T

md [9] (the highest temperature of deformation-induced a' martensite) are

both quite low for the Fe-20Cr-16Ni-6Mn-0.2N alloy and T

^ for the Fe-18CrlONi -1 . 5Mn-0 . 1 N alloy is sufficiently high. Stacking fault energy (SFE)

calculations listed also in Table 1, indicate that the Fe-20Cr-16Ni-6Mn-0.2N

alloy is relatively more stable with respect to the face-centered cubic to

hexagonal close-packed (e) strain-induced transformation.

Alloy Fe-20Cr-16Ni-6Mn-0.2N :

Tensile test results for unpolished specimens are presented in Figure 2

for the Fe-20Cr-16Ni-6Mn-0.2N alloy. Yield and flow strengths increased

strongly as temperature was lowered, while ductility decreased moderately.

Between 295 and 4 K the yield strength rose from 338 to 1120 MPa, a factor of

3.3. The ultimate strength increased by a factor of 2.3, reaching 1611 MPa at

4 K. Despite one specimen which had an exceptionally low elongation

(14 percent), the average elongation and reduction of area at 4 K remain high

34
(30 and 42 percent, respectively). These trends are typical for nitrogenstrengthened, fully austenitic, stable stainless steels.

The elastic constants for Fe-20Cr-16Ni -6Mn-0.2N steel [12] are shown in

Figure 3. The E (Young's) and G (shear) moduli show a regular, nearly linear

increase as temperature is reduced from 300 K, until a plateau is approached

below about 76 K. In the 60 to 48 K range, the E and G moduli decrease by

about £ percent. This decrease marks the Neel temperature, T^, at which there

is a change in magnetic ordering from paramagnetic to anti ferromagnetic

conditions. The midpoint of the transition is about 54 K. These data were

used to guide the choice of temperatures for the yield strength measurements

near Tr

The yield strength data near T^ are of special interest. Since a decrease of the shear modulus occurs at T^, it has been suggested that the magnetic ordering phenomenon might have a measurable effect on resistance to dislocation movement, and, hence, tensile flow strength. As indicated below, we

were unable to detect any effect, and so our data do not support the conclusions of other investigators testing a similar heat of the same steel [1].

The yield strength results are presented in Figure 4, which compares data

from this study (Table 2) with those of our previous study (Table 3) and with

USSR data (Table 4). Between 300 and 4 K, the results show approximate conformation to an exponential function given as follows:

ay

= 1170exp (4.2 x 10“ 3

T) (1)

Most of the data fit this equation to within about 6 percent, although two

points deviate by larger amounts (-10 percent at 295 K, +8 percent at 60 10

.

35
Figure 5 shows only the data at test temperatures between 4 and 100 K.

For these results, combined with our previous data, the data spread for five

tests at 4 K is ± 55 MPa, owing primarily to specimen-to-specimen variability.

The previously tested specimens [6] were longitudinal and unpolished (28

finish), but the results are indistinguishable from the electropol ished transverse specimens. It appears that the scatter at 76 and 4 K is similar.

Therefore, the anomalous 7-percent drop of a at T^, as reported by Yushchenko

et al. [1], falls well within specimen-to-specimen variability determined in

our study. This suggests either that the anomaly reported at T^ is not a real

material effect or that the work of Yushchenko et al . [1] is more precise, reflecting a superior testing technique or less material variability.

To eliminate the obscuring effect of specimen-to-specimen variability,

single-specimen temperature-change tests were performed. The results from

these tests tend to support the conclusion that no anomalous decreases of

strength occurred. In Figure 5, the multiple data points from single specimens are linked with straight lines. These trend lines have nearly equivalent

slopes and do not cross over one another. One specimen was tested first at

60 K, then at 50 K, but the strength did not decrease, as would have been

expected from the trend line drawn by Yushchenko et al . [1] through this

temperature interval.

In the temperature-change tests, it was assumed that strain history effects are negligible, e.g., that the pattern of the dislocation movement is

physically unchanged by the temperatures involved. A flow stress increase on reloading at the second (lower) temperature is then just the measure of stress

needed to continue plastic deformation for the same dislocation mechanism at a lower temperature.

36
The flow strength (a

f

) is proportional to the shear modulus (6) and the

dislocation density (P) through the relationship

= a Gb p

where a usually has a value between 0.2 and 0.5 (e.g., Conrad [13]). The

i percent decrease of G measured at T^ for the Fe-20Cr-16Ni-6Mn-0.2N alloy

would not alone be sufficient to account for the 7-percent decrease of a

y

, as

reported by Yushchenko et al . Indeed, the 1-percent effect is indistinguishable from experimental scatter in a measurements. The single-specimen change

test conducted at 60 and 50 K shows an increase of with a magnitude equivalent to that expected from the exponential function of Eq. (1).

Finally, it should be pointed out that in addition to the Neel temperature anomaly, Soviet authors have also reported a 15-percent decrease of a

for other Fe-Cr-Ni stainless steels at temperatures between 20 and 4 K [2,3].

This has not been explained completely, but dislocation tunnelling process is

a possible explanation [2,3]. However, the present data for Fe-20Cr-16Ni-6Mn0.2N steel indicate no anomaly at this temperature either. Yushchenko

et al . [1] do not present data below 20 K for this particular steel, so

confirmation is lacking.

Alloy Fe-18Cr-10Ni-1.5Mn-0.1N : Tensile flow strength data at strain offsets of 0.0005 and 0.002 (yield strength) are plotted as a function of temperature in Figure 6 and listed in Table 5. Plotted linearly versus temperature, the dependence of flow strength is slightly concave upwards with decreasing temperature. The difference between the 0.002 and 0.0005 strain flow

strengths is also plotted versus temperature in Figure 6. Approximately, the

37
difference doubles at 4 K, compared to room temperature, indicating that at

low strains the rate of work hardening increases at lower temperatures.

The ratio of the flow strength at 0.0005 plastic strain at 76 and 4 K to

295 K is 2.3 and 2.9, respectively. At a strain of 0.002, the ratios of 76

and 4 K flow strengths to room temperature flow strength are 2.2 and 2.8,

respectively. Cottrell and Stokes [14] originally suggested that these ratios

are a constant, independent of strain. But, within the strain range measured,

there is a slight trend for the ratio to decrease at higher strains.

Temperature-change experiments were also performed on the Fe-18Cr-10Ni

alloy. In Figure 7, the measurements from seven specimens are plotted. In

all of these measurements, the temperature was lowered after reaching strains

between 0.0005 and 0.002. The temperature dependence found from singlespecimen tests is plotted as a smooth curve in Figure 7. All specimens exhibited normally rising flow strength with a decrease in temperature, with the

possible exception of the specimen originally strained at 295 K. The change

of strength achieved from the changing of temperature matches that obtained

from individual tests at the two temperatures. Thus, the flow strength

contributions are reversible with temperature (in the range 4 to 190 K) for

these alloys at the low strain levels at which measurements were obtained.

This implies that there was no change in deformation mechanism for this alloy

at temperatures below 190 K.

Our data and data for a similar Fe-18.25Cr-9.7Ni-0.91Mn-0.01S-0.29Si0.01C alloy [3] are presented for comparison in Figure 8. Whereas all three

of the anomalies were reported in the USSR steel, none of them were evident in

our steel, which is similar in base composition and in total interstitial

content.

38
The temperature dependence of the flow strength of the Fe-20Cr-16Ni-6Mn0.2N alloy is included in the linear plot of oy

-T of Figure 6 and that of the

Fe-18Cr-10Ni-1.5Mn-0.1N is included in the log a-T plot of Figure 4. Clearly

the temperature dependences of the flow strength of the two alloys are different and cannot be characterized by the same equation form. From Figure 4

one may suggest that the dependence of the flow strength on temperature of the

Fe-18Cr-10Ni-1.5Mn-0.1N alloy may be characterized by a change of deformation

mechanism below about 200 K, producing two linear regions (4 to 200 K, 200 to

300 K) in the log a-T graph. The temperature change experiments (Figure 7) do

not conflict with this characterization. The austenite of the Fe-20Cr-16Ni6Mn-0.2N alloy is relatively very stable and is expected to have higher

stacking fault energy [10,11] and lower M^ (below 0 K) than the Fe-18Cr-10Ni

1.5Mn-0.1N alloy, owing to the higher concentrations of nickel, nitrogen, and

manganese. Furthermore, a transformation was detected in Fe-18Cr-10Ni1.5Mn-0.1N specimens deformed to 0.002 strains at 76 and 4 K, and the estimated T . for this alloy is calculated to be about 179 K (Table 1).

md

The temperature dependences of the two alloys, normalized with respect to

the shear modulus, are plotted in Figure 9; they are not identical. The

Fe-20Cr-16Ni-6Mn-0.2N alloy, considered to have a higher stacking fault

energy, (Table 1) has a steeper temperature dependence. This corresponds to

the form of the temperature dependence as a function of stacking fault energy

found for several face-centered cubic elements [13].

SUMMARY

Two austenitic stainless steel alloys were measured in tension between 4

and 300 K and compared with other data for identical or similar alloys. One

alloy contains 20Cr, 16Ni , 6Mn, and 0.2N; the other contains 18Cr, lONi

,

1.5Mn, and 0.1N and is an AISI 304LN.

39
1. The reported anomalous low temperature dependences of the flow

strength associated with the Neel transition temperature and very

low temperatures (<20 K) for austenitic steels were not confirmed by

this study.

2. Temperature change experiments indicate reversibility of flow

strength at temperatures below about 100 K. This implies that the

deformation mechanisms do not change at low temperatures for these

alloys

.

3. The temperature dependence of the flow strength of the two alloys is

best characterized by a linear dependence of log a versus T. The

more stable Fe-20Cr-16Ni-6Mn-0.2N alloy exhibits a linear slope of

log o versus T over the entire temperature test range (4 to 295 K).

The less stable Fe-18Cr-10Ni-l .5Mn-0. IN alloy, partially transforming to body-centered cubic martensite at low temperatures,

exhibits two linear ranges on a log a versus T plot, one from 4 to

about 200 K, the other from about 200 to 295 K.

40
REFERENCES

1. Yushchenko, K. A., Verkin, B. I., Ilichev, V. Ya., and Klimenko, I. N.,

"The Influence of Magnetic Structure on Temperature Dependence of the

Yield Strength of 20Cr-16Ni-6Mn Steel at Low Temperatures," in Advances

in Cryogenic Engineering-Materials, Vol . 28, Plenum Press, New York,

67-72 (1982).

2. Ilichev, V. Ya., Medvedev, Ya. M. , Shapovalov, I. A., and Klimenko, I. N.

"Low Temperature Anomaly of the Temperature Dependence of the Flow

Stresses in Iron-Chromium-Nickel Alloys," Fizika Metallov i

Metal 1 ovedenie 44 , No. 2, 173-176 (1980).

3. Verkin, B. I., Ilichev, V. Ya., and Klimenko, I. N., "The Low Temperature

Change of the Magnetic Structure and Plastic Properties of Fe-Cr-Ni

Alloys," in Advances in Cryogenic Engineering-Materials, Vol. 26, Plenum

Press, New York, 120-125 (1980).

4. Reed, R. P. and Simon, N. J., editors, "Material Studies for Magnetic

Fusion Energy Applications at Low Temperatures - IV, National Bureau of

Standards, Boulder, CO, NBSIR 81-1645, (1981).

5. Tobler, R. L., Beekman, D. H., and Reed, R. P. , "Low-Temperature Dependence of Yielding in AISI 316 Stainless Steels," unpublished, National

Bureau of Standards, Boulder, CO (1981).

6. Reed, R. P., Tobler, R. L., Elmer, J. W. , McHenry, H. I., and

Yushchenko, K. A., "Strength and Toughness of USSR Fe-20Cr-16Ni-6Mn-0.2N

Weldments at Cryogenic Temperatures, in Proceedings of the Eighth International Cryogenic Engineering Conference, IPC Science and Technology

Press, Guildford, Surrey, England, 797-801 (1980).

41
7. Read, D. T. and Tobler, R. L., "Mechanical Property Measurements at Low

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

Plenum Press, New York, 17-28, (1982).

8. Ei chelman , G. H. and Hull, F. C., "The Effect of Composition on the

Temperature of Spontaneous Transformation of Austenite to Martensite in

18-8-Type Stainless Steel," Transactions of the American Society for

Metals 45, 77-104 (1953).

9. Williams, I., Williams, R. G., and Capellero, R. C., "Stability of

Austenitic Stainless Steels between 4 K and 373 K," in Proceedings of the

Sixth International Cryogenic Engineering Conference, IPC Science and

Technology Press, Guildford, Surrey, England, 337-341 (1976).

10. Schramm, R. E. and Reed, R. P., "Stacking Fault Energies of Seven Commercial Austenitic Stainless Steels," Metallurgical Transactions 6A 1345-

1351, (1975).

11. Rhodes, C. G. and Thompson, A. W., "The Composition Dependence of Stacking

Fault Energy in Austenitic Stainless Steels," Metallurgical Transactions 8A, 1901-1906 (1977).

12. Ledbetter, H. M. and Austin, M. W., "Low-temperature elastic properties

of an Fe-20-16Ni-6Mn alloy," in Material Studies for Magnetic Fusion

Energy Applications at Low Temperatures - V, R. P. Reed and N. N. Simon,

editors, National Bureau of Standards, Boulder, CO, NBSIR (1982).

13. Conrad, H., "The Cryogenic Properties of Metals," in High-Strength

Materials, V. F. Zackay, Editor, John Wiley & Sons, NY, 436-509 (1965).

14. Cottrell, A. H. and Stokes, R. J., "Effects of Temperature on the Plastic

Properties of Aluminum Crystals," Proceedings of the Royal Society A233,

17-34 (1955).

42
Table 1. Calculations of Stacking Fault Energy and

Austenite Stab i 1 ity.

Alloy

T

[8] ms

(K)

T

^

'md

(K)

SFETM

(10' 5 J/m

2

)

SFE^

11 ^

(10

-5

J/m

2

)

Fe-20Cr-16N-6Mn-0.2N -898 -5 84 36

Fe-18Cr-10Ni-l . 5Mn-0. IN -106 179 28 23

43
Table 2. Yield Strength Measurements for Fe-20Cr-16Ni-6Mn-0.2N

Stainless Steel (Transverse, Electropol ished)

.

Specimen

Temperature

(K)

Yield Strength, a (MPa) y

1 38 1029

2 45 993

3 295 356

4 4 1190

5 76 886

6 20.5 1034

7-1 57 898

7-2 41.5 958

8-1 67 896

8-2 30.5 1040

8-3 4 1151

9-1 59.5 955

9-2 50 1000

9-3 10 1167

44
Table 3. Yield Strength Measurements for Fe-20Cr-16Ni-6Mn-0.2N

Stainless Steel .*

Specimen No. Temperature

(K)

Yield Strength, a (MPa) y

1C B3 - 343

2C B3 - 333

2C B2 - 465

7

- 525

4 153 609

2-1 100 765

1C B1 76 832

2C B2 76 878

1 76 838

8 76 823

6 60 979

2-3 58 951

4 40 1028

3 18 1069

5 15 1082

2 4 1077

B2 4 1096

B4 4 1186

* Longitudinal specimens, as machined, 28 finish.

45
Table 4. Yield Strength Measurements* for Fe-20Cr-16Ni-6Mn-0.2N

Steel

.

Temperature

(K)

Yield Strength, o (MPa) y

20 1122

31 1008

42 946

51 904

57 880

58 923

62 934

68 893

72 863

80 848

102 770

108 769

114 748

123 700

162 595

184 550

300 ~340?

* USSR data [1-3]; taken using ruler and interpolation from published graphs.

46
Table 5. Tensile Results, Fe-18Cr-10Ni-1.5Mn-0.1N Steel.

Flow Strength

Specimen

No.

Temperature

K

c0.0005

MPa

°0 . 0002

MPa

a0.002' a0.0005

MPa

4 295 230 262 32

3 190 350 408 48

17 150 400 458 58

5 145 418 460 42

1 120 448 490 42

2 83 482 569 87

6 72 530 614 84

10 70 536 * --

8 57 553 619 66

11 35 561 * --

7 29 603 670 67

9 4 593 685 92

12 4 657 736 79

16 4 662 750 88

Multiple straining started at 0.0005 strain.

47
LIST OF FIGURES

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

. Temperature change test procedure to obtain reversible change of

flow strength at two temperatures.

. Tensile properties at 295, 195, 76, and 4 K of alloy Fe-20Cr-16Ni6Mn-0.2N.

. Elastic properties of Fe-20Cr-16Ni-6Mn-0.2N steel (G = shear

modulus, E = Young's modulus, v. = Poisson's ratio [12]).

. Yield strength versus temperature for Fe-20Cr-16Ni-6Mn-0.2N steel,

summarizing data from this study and other studies [1-3,6]. Also

included are average data of Fe-18Cr-10Ni-l .5Mn-0. IN alloy.

. Yield strength data at cryogenic temperatures, showing specimen-tospecimen variability and trend, as reported by other studies [1-3].

. Flow strength at strains of 0.0005 and 0.002 as a function of

temperature for Fe-18Cr-10Ni-1.5Mn-0.1N alloy. Also included are

average data of Fe-20Cr-16Ni -6Mn-0.2N alloy.

. Flow strength of Fe-18Cr-10Ni-1.5Mn-0.1N alloy at strain of 0.002

(yield strength) measured from specimens sequentially cooled and

strai ned.

. Comparison of data from Verkin et al . [3] and this study for Fe18Cr-10Ni alloys.

. Normalized temperature dependence of the flow strength at 0.0002

strain for both alloys.

48
o

49

flow

strength

at

two

temperatures.
1800

1600

1400

1200

1000

800

600

400

200

0

90

80

70

*-• w 60

o

S> 50

o. 40

30

20

jre 2. T

T T

Fe-20Cr-16Ni-6Mn-0.2N

annealed

Ultimate, C7U

si le properties at 295, 195, 76, and 4 K of alloy Fe-20Cr-16Ni-

-0.2N.

50
1.10 r

-il.io

51

Figure

3.

Elastic

properties

of

Fe-?0Cr-16Ni

-6Mn-0.

2N

steel

(G=

shear
Yield

Strength,

(7

v

,GPa

Figure 4. Yield strength versus temperature for Fe-20Cr-16Ni-6Mn-0. 2N steel,

summarizing data from this study and other studies [1-3,6]. Also

included are average data of Fe-18Cr-10Ni-l .5Mn-0. IN alloy.

52
oo

in

h9S Q> o 2

in a>aE

a> I10

CM

53

Figure

5.

Yield

strength

data

at

cryogenic

temperatures,

showing

specimen-tospecimen

variability

and

trend,

as

reported

by

other

studies

[1-3].
BdO ‘niBuejis mo|J

54

temperature

for

Fe-18Cr-10Ni-1.5Mn-0.1N

alloy.

Also

included

are
0.75k

Fe18Cr10Ni-1.5Mn-0.1N

55

Figure

7.

Flow

strength

of

Fe18Cr-10Ni

-1

.5Mn-0.

IN

alloy

at

strain

of

0.002

(yield

strength)

measured

from

specimens

sequentially

cooled

and

strained.
8*0

o

BdO ‘LU6uejis «0|d

56

Figure

8.

Comparison

of

data

from

Verkin

et

al

.

[3]

and

this

study

for

Fe-
+o

LU

CO3

CO

UJ

o.s

LU

57

Figure

9.

Normalized

temperature

dependence

of

the

flow

strength

at

0.0002

strain

for

both

alloys.

TENSILE AND FRACTURE PROPERTIES OF MANGANESE-MODIFIED

AISI 304 TYPE STAINLESS STEEL*

R. L. Tobler and R. P. Reed

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A series of ten low-carbon AISI-304-type austenitic stainless steels

having 1 to 6% Mn and 0.1 to 0.2% N were produced and tested to determine the

effect of these elements on properties at 4 K. Tensile tests (at 295, 76, and

4 K) and J-integral fracture toughness tests (at 4 K) were conducted on

developmental steels containing 18.25 to 19.50% Cr, 7.9 to 8.75% Ni , and 0.02

to 0.03% C. All steels were hot-rolled at 1450 K (2150°F) from ingots to

25.4-mm (1-in) plates. The 4-K yield strengths ranged from 620 MPa (90 ksi)

to 1068 MPa (155 ksi), increasing strongly with nitrogen content.

Unacceptably low toughness was observed in the low manganese compositions,

whereas the fracture toughnesses of alloys containing 6% Mn were equivalent to

those of conventional AISI 304 stainless steels.

+To be published in Advances in Cryogenic Engineering-Materials, Vol. 28,

R. P. Reed and A. F. Clark, Eds, Plenum Press, New York (1982).

59

INTRODUCTION

The AISI-300 series stainless steels are austenitic Fe-Cr-Ni

alloys offering relatively low strength but excellent cryogenic

ductility and toughness. Recently, nitrogen-strengthened grades,

such as AISI 304 N or AISI 304 LN, have attracted attention as possible substitutes for applications demanding higher strength.

Nitrogen is a relatively inexpensive strengthener , and it stabilizes the austenitic structure with respect to martensitic phase

transformation. A disadvantage of the nitrogen strengthened

grades is that they are more difficult to fabricate. To overcome

this disadvantage, manganese additions (greater than the normal 1 or 2 wt.%) have been recommended. The potential advantages of

manganese-modified type AISI 304 LN steels are: (1) consistent

fabricability, (2) consistent weldability, and (3) reliable

supply in all product forms 1

. Other studies-- ' have reported

potential advantages with manganese additions. It was the

purpose of this study to investigate the effects of manganese on

the 4 K mechanical properties of nitrogen strengthened AISI 304 L

type alloys. Therefore, a series of steels containing 1-64 Mn

and 0.1-0. 2% N were prepared, tested, and compared with previous

results for Fe-18Cr-10Ni stainless steels 5 ’ 6

.

MATERIALS

Ten stainless steel plates were obtained from a commercial

steel manufacturer. These steels had chemical compositions as listed in Table 1. Heats 69, 70, 73 and 74 have compositions

corresponding to AISI 304 LN; the other heats are modif ications

.

Grain size ranged randomly from 49 to 57 pm diameter and hardness

61
Table 1. Compositions of normal (Mn = 2% or less) and modified

(greater than 2% Mn) type 304 LN stainless steel.

Weight Percent

Heat

No . C Mn P S Si Cr Ni Mo Cu N

69 0 .,025 1 ..02 0 ..022 0 ..013 0..53 18.,19 8.,68 0 .,32 0 .,30 0 .,11

70 0 .,028 2..00 0,.021 0 ..013 0 ..63 18..10 8.,66 0 ..31 0 .,28 0 .,11

71 0 ..025 3..85 0,.023 0,.013 0 ..59 18.,22 8.,70 0 .,31 0 .,29 0 ..11

72 0 .,021 5..81 0 ..023 0..014 0,.64 18..06 8..62 0 .,33 0 .,30 0 ..11

73 0 .,025 1 ,.19 0..023 0 ,.015 0,,60 19.,36 7..81 0 .,32 0 .,28 0 .,19

74 0 ..022 2..01 0 ..023 0 ..013 0 ,.64 19..35 7..89 0 ..32 0 ..30 0 ,.19

75 0 .,024 3..85 0 ..022 0 ,.014 0 ..65 19..25 7..84 0 ..31 0 ..31 0 ..21

76 0 ..033 5..79 0 ,.024 0 ..014 0 ..61 19.,48 7..83 0 ..31 0 ..31 0 ,.21

77 0 ..026 4,.03 0 ..023 0 ..014 0,.62 18.,71 8..22 0 ..31 0 .,30 0 ..15

78 0 ..031 5..80 0 ,.024 0 ,.014 0 ,.62 18..42 8..29 0 ..31 0 .,30 0 ,.15

from Kg 82 to 94. No precipitation at grain boundaries was observed from careful light microscopy examination of the microstructures for all heats.

All steels were produced from ingots (12.7 x 12.7 x 17.8 cm)

which were hot-rolled at 1450 K to plates approximately 25 mm

thick. The plates were annealed at 1340 K for one-half hour,

then water quenched and acid pickled. Grain boundary segregation was suspected in the lower Mn alloys. Solution treatments at

1560 K for one hour with a water quench were made on heats 69 and

78. Following this anneal, compact fracture specimens were

machined

.

EXPERIMENTAL PROCEDURE

Tensile tests were conducted using equipment, procedures,

and specimen geometry previously described 5

. The specimens were

machined in the transverse orientation. The load-vs-def lection

curves were recorded using the outputs from a commercial load

cell and strain-gauge extensometer . The crosshead rate was

8 . 5 yms 1

.

Single-specimen J-integral tests were used to measure

fracture toughness. The technique incorporates a computer to

enable digital data acquisition and J-resistance curve plotting

during the tests, as described previously 5 ’ 6

. The compact

fracture toughness specimen was 24.6 mm thick and 50.8 mm wide.

The notch was machined in the TL orientation, as defined in

ASTM E-399-78a 7

.

62
The fracture specimens were fatigue cracked at 76 K to a crack length, a, between 27.25 and 31.44 mm (a/W - 0.535 to

0.620). The maximum load used in fatigue precracking was 22 kN

.

The specimens were then loaded in displacement control. As the

load increased, partial unloadings (10%) were performed periodically. Using a crack-length-vs-compliance correlation, the crack

length at each unloading was inferred and used to obtain the

crack extension increment (Aa) from the difference of the initial

precrack length. The J value at each unloading point was calculated using the expression: J = AA/Bb, where A is the MerkleCorten factor, A is the area under the load-vs-def lection curve

at the unloading point, and b is the specimen ligament (b = W - a).

Scatter in the J-resistance curves led to uncertainties of

± 15% in the values of JT . Ic

The J values were converted to K estimates, denoted

Kj (J), using a Young’s modulus value of TUB. 8 GPa, a Poisson's

ra£io of 0.30, and the standard formula relating the elastic J to

Tc

5

-

Magnetic measurements, using a bar magnet, torsion balance

were used to estimate the percent bcc (ferromagnetic) martensite

that formed during deformation. A calibration had previously

been made relating data obtained from the torsion balance device

to volume percent bcc martensite 8. The measurements were all

made within the gage length, in the uniform elongation section.

X-ray techniques previously described 8

, (measurement and

computation of integrated peak intensities of fee, bcc, and hep

structures) were used to estimate the amount of bcc martensite on

the fracture surface of compact tension specimens. The area of

the specimens examined was restricted to near the pre-crack tip

to ensure some relationship to the plastic-zone at initiation of

crack growth. In all x-ray measurements no hep phase was ever detected on the crack surface.

Hardness measurements were made using a diamond pyramid

indentor and a 10 g load. Hardness traverses on annealed

specimens with polished surfaces were conducted to attempt to

detect segregation effects at grain boundaries.

RESULTS AND DISCUSSION

Tensile Properties

The tensile properties of the steels tested in this study

are plotted in Figs. 1 through 3 and tabulated in Ref. 5. In

these figures comparison is made with trend lines from a previous

study 8

. As shown in Fig. 1, the yield strength (o ) data for the

63
Fig. 1 Effect of carbon plus nitrogen content on yield

strength of stainless steels, at various temperatures.

present Fe-T8 . 25-19 . 5Cr-7 . 90-8 . 75Ni steels (open symbols) agree

well with previous data trends for Fe-18Cr-10Ni steels (solid

lines). The 295 K data confirm a previous conclusion: the yield

strength is a linear function of C+N content 6

, for the composition

range studied. The 4 K data also confirm the existence of a kink

in the a -vs-C+N plot at C+N contents between 0.127 and 0.157

wt . % . iX our previous study 6

, this kink was attributed to the

structural instability of the austenitic phase at lower interstitial contents. In the present study at 4 K there is a clear

trend of increasing a values with higher Mn contents at C+N

contents from 0.131 t$ 0.138 wt.%. Apparently, the kink at 4 K

is removed by the stabilizing effect of Mn additions at this

critical interstitial content with respect to the martensitic

transformation.

The ultimate tensile strength results of the present study,

shown in Fig. 2, are also in general agreement with expected

trends. The data at room temperature fall on the same trend line

that was previously reported for the Fe-18Cr-10Ni stainless

steels. The 4 K data show a minor variation, probably owing to

the austenite stabilizing effect of Mn modifications. As more manganese is added at a given interstitial concentration level,

64
2,000

Fe- 18 Cr- 8tolO Ni Steels

Fig. 2 Effect of carbon plus nitrogen interstitials on

ultimate strength at two test temperatures.

the austentite is progressively more stable during tests at 4 K; as a result, less martensite is formed during testing and

ultimate tensile strength is reduced as Mn concentration is

increased to 6%.

Figure 3 shows the spread of the elongation and reduction of area measurements for the ten steels. Not all of the ductility

values are typical of commercial stainless steels. In particular, the reduction of area values for the developmental steels

containing 1-4% Mn are lower compared with values previously

reported for Fe-18Cr-10Ni steels 6 or other commercially available

AISI 304 LN steels. Only the 6% Mn-modified steels possess

ductility values at the expected levels.

Magnetic measurements made on the fractured tensile specimens

were converted to percent martensite, and "normalized" by dividing

by the strain corresponding to the uniform elongation where the

measurements were made. This procedure assumes a linear dependence

of martensite formation with strain. The data are plotted versus Mn + Ni + 10(C+N) concentration in weight percent in Fig. 4. At

higher solute concentrations the amount of martensite per unit

strain is reduced. A ratio of the relative alloying contributions was chosen to provide a good fit to the data, and the result

65
Fig. 3 Ductility of

stainless steels.

Fig. 4 The effect of

alloy content on martensite formation at

4 K at the crack tip

in compact tensile

specimens and within

uniform elongation

section of tensile

specimens

.

Mn+Ni+10(C+N), wt.%

66

%

bcc

Martensite
follows approximately the prediction of the dependence of M

temperature found by Williams 5 for compression of Fe-Cr-Ni alloys

at low temperatures. However, from Fig. 4, it appears that the

dependence on N content is not linear with Mn + Ni content. Also,

the dependence of bcc martensite at compact specimen fracture

surfaces is not linear with solute alloying concentration.

Fracture Toughness

The J^. results obtained for one specimen of each of the ten

different sEeel compositions tested are tabulated 5 and the 1C (J)

values are plotted in Fig. 5. The K^(J) data follow regular

trends depending on Mn and N content. Solid lines have been

drawn to connect data representing constant Mn contents; for each

Mn content the 0.1 N composition is represented by the symbol

at the lowest yield strength, whereas the 0.2 N composition is

represented by the higher yield strength, and 0.15 N is intermediate. From Fig. 5 it is clear that higher N at a given Mn content

lowers the K-^CJ) value. It is also clear that Mn has a favorable

effect, raising both the strength and the toughness of these

developmental alloys.

Fig. 5 Fracture toughness-vs-yield strength results for Mn-K

modified steels of the present study, as compared with

previous results for AISI 304 type stainless steels.

67
The major observation is that the 6%-Mn-modif ied steels have

acceptable fracture toughness, whereas the modifications containing 1-4% Mn display inferior properties. The 1 and 2% Mn steels

are particularly poor, having estimated values as low as 117 MPa-m1 ’ 2

. Their load-deflection fracture toughness test

records showed a nearly linear-elastic behavior, with regions of

instability (serrations) . This evaluation is based on comparison

with the previous results for a series of nine Fe-18Cr-10Ni

stainless steels containing variable C+N contents. As shown in

Fig. 5, the 6% Mn-modified steels exhibit an inverse K (J) vs.

a relationship at 4 K and, within the measurement error indicated

b^ the error bars shown in the figure, the inverse-linear trend

falls along the lower bound of the scatter band of data for the

Fe-18Cr-10Ni steels.

The cause of the unexpected low K (J) values of the 1-4% Mn

grades is not clear and we have examined several possibilities.

The nominal compositional variations between the 1-2% Mn steels

of this study and the Fe-18Cr-10Ni-l . 5Mn steels of the previous

study include a 1.25-2.5% difference in nickel content which may

be significant. Metallurgical factors, such as interstitial segregation, may also contribute to the low fracture toughness of the

1-4% Mn steels of the present study. However, light microscopy

revealed no evidence of sensitization or other obvious microstructural differences. Microhardness traverses across grain boundaries and centers failed to detect any hardness variations.

Evidence of an abnormal condition in the 1, 2, and 4% Mn

steels was obtained by scanning electron microscopy performed on

the fracture surfaces of the compact specimens subsequent to J

testing at 4 K. Figure 6 presents typical results. Specimens

containing 4% Mn or less exhibited unusual features consisting of

isolated facets (probably intercrystalline fracture) surrounded

by a matrix of numerous very fine dimples. In contrast, the

three heats containing 6% Mn (heats 72, 76, and 78) all showed a more completely dimpled fracture mode, with relatively large dimples; this type of fracture was also observed in the Fe-18Cr-10Ni

steels of our previous study, which had good fracture toughness.

The only apparent distinction between thermal-mechanical treatments of the two alloy series was the temperature of hot-working

of the billet. The hot-rolling temperature of the initial 304 LN

alloy series was 1560 K (2350°F) and the rolling temperature of

the 1-6 wt.% Mn alloy series was 1450 K (2150°F). In addition,

plates from heats 69 and 78 were re-solution annealed at a higher

temperature, machined into compact- tensile specimens, and tested

at 4 K. The values of K (J) (heat 69-133 MPa*m^’ 2

; heat 78-172

MPa^m 1

’ ) were about 15%"

C lower than those reported in Fig. 5.

This decrease was presumably caused by the increased grain size.

In any case, the re-solution treatment failed to eliminate the

problem of low toughness.

68
40 ym 100 ym

Fig. 6 Micrographs of fracture surfaces of low- (heat 69, left)

and high toughness (heat 72, right) austenitic stainless steels.

X-ray diffractometer measurement data of the amount of

martensitic transformation phases on the fracture surface near

the crack tip of compact tensile specimens, tested at 4 K, are also shown in Fig. 4. As the alloy stability increases the

amount of transformation during early crack formation is reduced.

However, in all heats and tests the amount of transformation was extensive (> 64%), indicating large amounts of local plastic

deformation in the region of the crack tip. We have also detected

large amounts of transformation in the tough Fe-18Cr-10Ni austenitic steels 0

. In Fig. 4 notice that a tough alloy (heat 72) exhibited

more crack tip martensite (81%) than two of the alloys (heats 74,

75) that exhibited marginal toughness. Therefore, it is difficult

to argue that martensitic transformation, per se, results in re- duced toughness. The rate of transformation per unit strain and

the mechanisms of transformation must be considered. A possibility

remains that the martensitic transformation which influences the

stress-strain characteristics, produces a modified plastic zone. This modified zone in turn may influence J- integral measurements.

CONCLUSION

The data of this study show that 6% Mn-modified AISI 304 LN

stainless steel can be produced, having conventional tensile and

fracture toughness properties equivalent to standard AISI 304 LN

stainless steel when tested at 4 K. However, the 1-4% Mn heats

tested in this study displayed some unusual apparently brittle

fracture features in association with relatively low fracture

toughness. The cause of this behavior has not yet been established, but the problem deserves a full investigation.

69
ACKNOWLEDGMENTS

The stainless steel plates were produced by Armco, under the

direction of R. H. Espy of Armco ' s Research and Technology Division. E. L. Brown, now at the Colorado School of Mines, contributed metallographic assistance, and D. Baxter of NBS conducted

many of the tensile and fracture toughness tests. The work was

sponsored by the Department of Energy, Office of Fusion Energy.

REFERENCES

1. R. H. Espy, "Stainless Steel Alloy Development," presented

at NBS/DoE Workshop on Materials at Low Temperatures, Vail,

Colorado, October 16-18, 1979.

2. T. Kato, M. Fujikura, T. Soh, and K. Ishida, "Effects of

Alloying Elements on the Austenite Stability and Mechanical

Properties of Austenitic Stainless Cast Steels at Cryogenic

Temperatures," Denki Seiko , 48 (3) :179-190 (1977).

3. J. Hochmann, "Le role des additions demanganese dans les

aciers inoxydables austenitiques, " Materiaux et Techniques , Spec. Issue 6_5:69-87 (1977).

4. A. B. Meade and R. Oppenheim, "Tief temperatureigen schaftor

stickstof flegierter aus tenitische chrom-nickel-(Molybdan)

sonie Chrom-Mangan-Nickel-Stakle und deren Eignung als

Kaltzahe Stahle," DEW-Technische Berichte , 1_2:13-19 (1972).

5. R. L. Tobler and R. P. Reed, "Tensile and Fracture Properties

of Manganese-Modified Fe-18Cr-8Ni Type Austenitic Stainless

Steels," in: Materials Studies for Magnetic Fusion Energy

Applications at Low Temperatures - IV , NBSIR 81-1645, R. P.

Reed and N. J. Simon, eds., National Bureau of Standards,

Boulder, Colorado, pp. 77-100 (1980).

6. R. L. Tobler, D. T. Read, and R. P. Reed, "Strength and

Toughness Relationship for Interstitially Strengthened

AISI 304 Stainless Steels at 4 K," in: Materials Studies

for Magnetic Fusion Energy Applications at Low Temperatures - IV , NBSIR 81-1645, R. P. Reed and N. J. Simon, eds.. National

Bureau of Standards, Boulder, Colorado, pp. 37-76 (1981).

7. Standard Method of Test for Plane Strain Frac.ture Toughness

of Metallic Materials (Designation E399-74) , in: 1974

Annual Book of AS TM Standards , Part 10, American Society for

Testing and Materials, Philadelphia, Pennsylvania pp . 432-451

(1974)

.

8. R. P. Reed and C. J. Guntner, "Stress-Induced Martensitic

Transformations in 18Cr-8Ni Steel," Trans. AIME , 230:1713-

1720 (1964).

9. I. Williams, R. G. Williams, and R. C. Capellero, "Stability

of Austenitic Stainless Steels Between 4 K and 373 K," Proc

.

Sixth Int'l. Cryogenic Eng. Conf . , IPC Science and Technology

Press, Guildford, Surrey, England pp. 337-341 (1976).

70
MAGNETIC FIELD EFFECTS ON TENSILE BEHAVIOR OF

ALLOYS 304 AND 310 AT 4 K*

R. P. Reed and J. M. Arvidson

Fracture and Deformation Division

J. W. Ekin and R. H. Schoon

Electromagnetic Technology Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Our experiments were conducted to assess the effects of a steady magnetic

field on the austenite stress-strain characteristics at 4 K. Wire specimens

(0.64 mm dia.) of both a stable Fe-26Cr-20Ni (AISI 310) and metastable

Fe-18Cr-9Ni (AISI 304) were measured. A 7-T magnetic field was produced by a

split-pair NbTi superconducting magnet with radial access ports and the field

was applied perpendicular to the tensile specimen axis. Tests were conducted

at 4 K with the field off, with the field on, and with the field switched on

and off after prescribed amounts of plastic deformation. The Young's modulus,

tensile yield strength and tensile stress-strain curves were measured. The

results are summarized here: (1) During magnetic field on/off experiments, no

change in austenite flow strength of either alloy was observed from the

application or absence of a 7-T field and (2) There was no detectable affect

of a constant 7-T magnetic field on the yield strength and Young's modulus of

either alloy. However, the specimen-to-specimen yield strength data scatter

was large and the application of magnetic field would not necessarily produce

changes of flow strength in excess of the data scatter. Discussion is also

presented on magnetic field effects on discontinuous yielding and cold worked

alloys.

*Work supported by Department of Energy, Office of Magnetic Fusion Energy.

71

INTRODUCTION

The application of magnetic fields has been demonstrated to enhance

body-centered cubic (bcc) martensitic transformations in ferrous alloys.

Korenko and Cohen^ have recently reported research on an Fe-22.5Ni-4Mn alloy

at 6-T fields demonstrating that the magnitude of the applied field significantly influences transformation kinetics; higher fields raise the temperature

of possible transformation and increase the amount of transformation. There

has been an abundance of USSR papers discussing the use of strong (up to 35 T)

pulsed fields to enhance transformation in Fe-Ni , Fe-Ni-Cr and Fe-Mn steels

( 2 ) (e.g., Voronchikin, Romashev, Fakidov). '

(3) Bolshutkin, Desnenko, and Ilichev' ' have studied the plastic deformation

of a series of Fe-18Cr, 8-25Ni alloys at 4 K exposed to steady-state and

transient magnetic fields and found small changes of flow strength that have

been attributed to magnetostriction and Joule heating effects. They found

that the flow strength of Fe, 18Cr, 8 - 1 5 N i alloys decreased on application of

a 3.4 T magnetic field. The amount of strength decrease was between 1.0 and

5.0 MPa, reaching about 0.6% of the flow strength. The flow strength decrease only became detectable after plastic strains of about 0.05 and increased rapidly with increasing strain to a limiting strain of about. 0.10.

However, Bolshutkin, et al.^^ found that in more stable alloys (Fe, 18Cr,

20-25Ni ) the flow strength increased (instead of decreased) with application

of 3.4-T field. In these steels, the increase of flow strength varied from

2.0 to 3.0 MPa, beginning at strains near 0.01 and saturating at strains near

0 . 02 .

These experiments were conducted to begin assessment of the effects ot

magnetic fields on austenite flow characteristics at 4 K. Many experiments

73
have shown that strain-induced martensitic transformations in Fe-Cr-Ni stainless steels affect the low temperature flow strength. At low strains, transformation apparently enhances strain and/or reduces the rate of work hardening. However, at larger strains, b.c.c. martensitic transformation corre-

( 4 ) lates excellently with increased work hardening. Therefore, two questions

need to be answered: (1) Do applied fields up to 7 T enhance strain-induced

martensite transformation in Fe-18Cr-8Ni steels? and (2) Does an enhanced

martensite transformation result in higher or lower flow strengths under an

applied magnetic field?

MATERIALS

Two stainless steels, AISI 304 and AISI 310, were selected for this test

series. One steel (AISI 304) is metastable with respect to austenite-tomartensite transformation and transforms during plastic deformation at temperatures below about 200 K; the other steel (AISI 310) is completely stable

with respect to martensitic transformation. Both were purchased as 0.64-mmdiameter wire in cold-drawn condition. Annealing times of 7.5, 15, and 30 min

at 1340 K (1950 °F) produced yield strength reductions from 400 to 305, 285,

and 290 MPa, respectively, at room temperature for the AISI 310 alloy.

Annealing of AISI 304 at 1340 K (1950 °F) for 30 min resulted in a yield

strength reduction from 321 to 233 MPa at room temperature. Thereafter, all

annealed wire specimens were produced by vacuum annealing at 1340 K (1950 °F)

for 30 min.

EXPERIMENTAL PROCEDURE

The apparatus has been described previously by Ekin. v Tensile load and

a perpendicular magnetic field were simultaneously applied to wire specimens

at 4 K. The magnetic field was produced by a 7-T split-pair NbTi magnet with

radial access ports, allowing perpendicular application of the field to

74
the specimen. A schematic of the apparatus is shown in Fig. 1. These specimens were tested in straight sections, each with a 27.5-cm-long gage length.

The magnet produces a 7-T field perpendicular to a 6.3-cm length of the specimen at its center. On each side of this central section, the field strength

decreased linearly over an 8 cm length to 0 T. Therefore, while only about i

of the specimen is exposed to 7 T, the entire specimen is exposed to some magnetic field. Magnetic field accuracy was ± 1.0%, and homogeneity over the

sample central section was of the order of ± 1.0%.

The specimens were gripped at either end by soft silver soldering into

copper channels, one fixed and one attached to the load train through a selfaligning universal joint. Strain was measured by taking the vertical displacement of the pull rod, as indicated by an LVDT electronic displacement

sensor, and dividing by the gage length. The stiffness of the load train,

relative to the sample, yields an accuracy in these measurements of ± 0.04%.

Load was applied by a 2-kN servohydraul ic testing system and measured by a

compatible load cell in series with the pull rod. Load was measured to within

± 0 . 2 %.

The specimens were strained at a constant rate of 0.002 cm/cm/min using

the testing system's interval function generator and a linear ramp wave form.

All of the specimens were strained between 0.025 and 0.040 at 4 K. Some experiments were conducted by sequentially turning the magnetic field on and o

+jr

during the test. In such tests, the specimen was unloaded, but kept at 4 K,

prior to field change. A schematic of the stress-strain curve during these

tests is shown in Fig. 2.

EXPERIMENTAL RESULTS

All experimental data for AISI 310 are tabulated in Table I, and the experimental data for AISI 304 are summarized in Table II. In these tables, ANN

75
refers to annealed, and CD refers to cold drawn fas received). To determine

the percent (bcc, a') martensite in the specimens at room temperature following deformation, a bar-magnet with a torsion spring was used. This appaf 6

1

ratus has been previously described and calibrated/ ' Martensite was detected in all AISI 304 specimens strained at 76 and 4 K, but not in the

AISI 304 specimens strained at room temperature. No martensite was detected

in AISI 310 specimens.

DISCUSSION

Magnetic-field on/off measurements

Experiments in switching the magnetic field while the 304 or 310 specimens were held at 4 K did not reveal any change of flow strength. That is,

after application of field, there was no accompanying increase or decrease of

flow strength at 4 K. This implies, of course, that any attendant increase of

martensitic transformation in alloy 304 (not definitively detected) did not

measurably affect flow strength.

Constant-field measurements

There was no detectable effect of a 7-T magnetic field on the yield

strength at 4 K of either the 304 or 310 alloys. However, the data scatter is

large and the application of the magnetic field would not necessarily produce

changes of flow strength in excess of the scatter of yield strength values.

The magnetic field did not affect the initiation of discontinuous yielding

in the cold-drawn 310 alloy. No discontinuous yielding was observed in the

annealed 310 alloy to strains of 0.04. In contrast to the 310 alloy behavior,

serrated yielding was observed at lower strains for annealed alloy 304,

compared with a cold-drawn condition. Data from Table II on the influence of

magnetic field on strain to initiate discontinuous yielding in alloy 304 are

not definitive. In the cold-drawn condition, the application of field may

76
slightly reduce the strain necessary for discontinuous yielding to begin; in

the annealed condition the trend is apparently reversed.

CONCLUSIONS

The experiments reported here have produced no evidence that the application of a transverse magnetic field of 7 T at 4 K affects the tensile stressstrain characteristics of AISI 310 and 304 alloy wire.

Other variables that need to be considered include the effects of

(1) pulsing fields, (2) longitudinal fields, (3) higher fields, and (4) larger

specimen strain.

77
REFERENCES

1. Korenko, M. K. and Cohen, M., "Martensitic Transformation in High Magnetic Fields," Proc. Conf. on Martensitic Transformations, ICOMAT 1979,

24-29 June 1979, Massachusetts Institute of Technology, Cambridge,

Massachusetts, 388-393 (1981).

2. Voronchikin, L. D., Romashev, L. N., and Fakidov, I. G., "Influence of

the Initial State of Austenitic Steel on the Martensitic Transformation

in a Strong Magnetic Field." Fizika Metallov i Metal lovedenie, Z6_,

No. 5, 948-951 (1968).

3. Bolshutkin, D. N., Desnenko, V. A., and Ilichev, V. Ya., "Low Temperature

Plastic Deformation of Fe-Cr-Ni Steels in Magnetic Fields to 2.71 x

10

6

Am

-1

," Cryogenics, 19, 231-234 (1979).

4. Reed, R. P. and Tobler, R. L., "Deformation of Metastable Austenitic

Steels at Low Temperatures," in Advances in Cryogenic EngineeringMaterials, Vol . 28, Plenum Press, New York (1982).

5. Ekin, J. W., "Fatigue and Stress Effects in NbTi and Nb^Sn Multifilamentary Superconductors," in Advances in Cryogenic Engineering-Materials,

Vol. 24, Plenum Press, New York, 306-316 (1978).

6. Reed, R. P. and Guntner, C. J., "Stress-Induced Martensitic Transformations in 18Cr-8Ni Steel," Trans. AIME, 230, 1713-1720 (1964).

78
AISI

310

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Steel

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LIST OF FIGURES

Figure 1

Figure 2

Table I.

Table II

. Schematic of apparatus to apply tensile force and magnetic field to

wire specimens.

. Schematic of applied tensile load versus specimen strain with

magnetic field applied "on", then "off".

LIST OF TABLES

Experimental conditions and data for AISI 310 alloy.

. Experimental conditions and data for AISI 304 alloy.

81
82

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83

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MARTENSITIC TRANSFORMATIONS IN TYPE 304

AUSTENITIC STAINLESS STEELS

F.J. Lamelas, 0. C. Larbalestier and H. W. King*

Materials Science Center

University of Wi sconsi n-Madi son (*Department of Engineering Physics, Dalhousie University)

The following is a progress report for the period June 1980 to December

1981 on contract #NB80RAC0031. Further characterisation of these alloys is in

progress and some of the conclusions presented here are to be regarded as tentative.

85

Introduction

The problem of martensitic transformations in the common austenitic

stainless steels is well-known and frequently met^ 1 ®^. Surpri si ngly , many

features of the transformation remain unclear. Some of these features are the

question of the mode of transformation: a) whether austenite ( y ) breaks

down directly to a' martensite or through the intermediate martensite ( e ),

b) whether e is a true phase with the hep structure or whether it is

faulted y , and c) whether and how the morphology of the martensites varies

when produced spontaneously on exposure to low temperatures or under the

simultaneous action of plastic flow and low temperatures.

The significance of these structural questions has acquired a more

practical aspect with recent investigations of the low temperature mechanical

properties of the austenitic steels such as 304 and 304N. Dalder^) for

example, finds that the 4K yield strengths of the 304N steels are about

2 0 k s i less than expected. Reed^) has noted that there is an anomalous

decrease in yield strength with decreasing temperature in some unstable

steels. This behavior appears to result from slip induced transformations to

martensite (both e and a'.) The reductions in yield strength are practically significant in that current designs of fusion reactor systems

could usefully use extra yield strength without running into fracture

toughness limitations.

The principal scope of the present work was to develop an equation for

the temperature M at which martensite first forms on cooling in the absence

s of externally applied stress. An equation, due originally to Eichelman and

Hul 1 , does already exist. Rearranged into degree Kelvin and weight percent

form with an added Mo factor, it i s( 2 )

M (K) = 1578 - 61.1 [Ni] - 41.7 [Cr] - 33.3[Mn]

s

- 27 . 8 [Si ] - 1667 [C+N] - 36.1[Mo]

This equation was originally developed for lower alloy steels than the A IS I

300 steels and extensive studies by two of the present authors have shown that

87
the equation is only an approximate guide to the behavior of the 300 steels at

cryogenic temperatures

.

The present report is an interim progress report on the characterisation

of some thirty specially melted steels in and around the 304 stainless steel

specification.

Experimental Procedures

1) Alloy Preparation

Alloys were prepared by the addition of pure chromium, iron, and nickel

to a base alloy of type 304 stainless steel. A base alloy was used in order

to provide the special steels with a typical range of tramp elements in

addition to the basic Fe-Cr-Ni elements, e.g. Mn, Si, Mo, Cu, C, N. (See

ternary diagram. Fig. 1) The alloys were arc -melted in an argon atmosphere,

homogenized for 24 hours at 1050 C, rolled and/or swaged to approximately 80%

area reduction, and then annealed for 1/2 hour at 1050 C. All heat treatments

were done in quartz tubes with sufficient argon to balance atmospheric

pressure at 1050 C. Samples were protected with a wrapping of Nb foil to

prevent interactions between the quartz and the samples during the heat

treatment. Multiple samples were cut from each heat for further

exami nation.

The stated chemical compositions in this report are those calculated from

a special analysis of the base alloy (see Table 1) and a knowledge of the

added weights of pure Fe, Cr or Ni . In no case was the weight change on melting >1%. Sample chemical analyses will be performed at the conclusion of

the programme. It is interesting to note that the C content of our alloys

makes them barely out of the low C grade but that the N content is about twice

as large.

88
in

sr

ro

CM

O

cr>

co

FIGURE 1. Alloys under investigation.

89

WEIGHT

PERCENT

NICKEL
Table 1

ements Wt.%

N 0.079

C 0.034

S 0.006

P 0.031

Ni 9.78

Cr 18.76

Mn 1.71

Si 0.52

Mo 0.47

Cu 0.29

Sn 0.017

Co 0.21

Composition of stainless steel base alloy as analysed

by National Spectrograph! c Laboratories

2. Resistivity Measurements

a) Continuous Measurements

Continuous measurements of resistance vs. temperature were made by means of a 4 terminal resistance rig mounted on the base of an Oxford Instrument Company

continuous flow cryostat. (See Fig. 2 and 3). Resistance was measured with a Keithley Model 503 mi 1 1 iohmmeter with the analog voltage output fed into the

Y-axis input of an XY recorder. Temperature measurement was obtained with a CLTS (cryogenic linear temperature sensor) mounted next to the sample. A

90
CON T/NUOUS FLOW CRYOSTAT

FIGURE 2

91
SAMPLE

MYLAR

TAPE

II

l

IL

l—OFHC CU BLOCK

CL TS

- BE-CU CURRENT

AND VOLTAGE CLIPS

FIGURE 3. Four terminal resistance rig mounted

on OFHC block for thermal stability.

92
constant current of 10 pA was passed through the CLTS, and 'the voltage across

it (linearly proportional to temperature) was measured with a DVM whose analog

output was fed into the X axis of the XY recorder. The samples were cooled at

about 5K per minute to less than 10K. Faster rates tended to produce a temperature differential between sample and thermometer. The permissible

cooling and heating rates were established by experiments with a fully stable

steel for which the cooling and heating curves coincided. Transformati on to

martensite produced an irreversible increase in resistivity (see figures 8, 9

and 10.) Below about 40K all samples show a reversible increase in

resistivity and this is believed to be due to the anti-ferromagnetic ordering

occuring at these temperatures.

b ) Fixed Temperature Measurements

Samples were also quenched to various temperatures between 273K and 4K

using a variety of fixed temperature baths (Table 2).

TABLE 2

T(Kel vi n) BATH

273 H 0 at ice point

2

227 Chlorobenzene m.p.

196 Dry ice & methanol

156 Ethanol m.p.

113 Isopentane m.p.

77 Liquid N

4 Liquid He

Resistivity measurements were made with a standard 4 terminal apparatus.

93
3. Magnetisation Measurements

M vs. H curves were obtained with a DC integration magnetometer. The

magnetisation rig consists of two sensing coils, each of approximately 20,000

turns, connected in a series opposed configuration. One coil is intentionally

wound with more turns than the other so that its output can be potted down to

balance the coil set when the empty coil pair output is integrated during a field sweep. Most measurements were performed in a liquid nitrogen cooled 0.5

Tesla copper solenoid fitted with a R.T. bore. Measurements were also made at

4K in fields up to 19 Tesla in order to assess the stability of some of the

less stable steels in high magnetic fields.

The potenti ©metric balancing technique described above produces a baseline which is essentially zero in comparison to a sizeable magnetisation,

e.g. that produced by a sample that has undergone substantial martensitic

transformation. However this baseline is not negligible in comparison to the

magnetisation of the paramagnetic y phase or in fact samples consisting of

y and a very small (< # 1%) amount of a' martensite. In order to measure

paramagnetic susceptibilities of the order of 1Q“ 4 we used a ballistic

measurement technique: the sample was repeatedly withdrawn and inserted into

the sensing coil as the field was ramped. The difference in integrator output

voltage with the sample in and out of the coil is proportional to the sample

magnetisation (Fig. 6).

The volume % of transformation to a* martensite was calculated by

measuring the saturation magnetisation of the sample and expressing this

magnetisation as a percentage of the calculated saturation magnetisation of a totally transformed alloy of the same composition. The saturation

magnetisation of the fully transformed alloy was calculated using a common

band model (

.

94
c. . c2 _ SENSING COILS

VBALANCING POT

*

2-

.5 mfl SHUNT

C-3—

CU SOLENOID

MAGNETOMETER CIRCUIT

FIGURE 4

SENSING COIL

DC MAGNETOMETER

WITH ONE COIL REMOVED

TO SHOW SAMPLE HOLDER

FIGURE 5

95
FIGURE 6. Typical M vs. H curve with non-zero baseline

indicated by ballistic technique.

96

FIELD
4. Metallography and Light Microscopy

Samples were prepared for observation using standard metal 1 ographic

techniques: grinding with successive grades of silicon carbide, polishing with

diamond paste, and finally electropolishing with an acetic acid-chromium

trioxide solution. Grain boundary etching was performed by electroetching in

oxalic acid solution and a glycerol /HCl/HNO^ solution was used to reveal the

a' martensite.

Results

The raw data available for the interpretation of the low temperature

behaviour of these steels generally consists of:

1. A resistance-temperature trace from RT to about 10K

2. The magnetisation of the sample used in 1. both before and after

cool i ng

3. The resistivity, magnetisation and light metal lographic

observation of one face of the sample used in

quenching experiments.

An overview of the data is shown in Table 3 and examples of the 3 types

of R/T curve observed are shown in figures 8, 9 and 10. Stable steels of high

alloy content showed no transition to e or a ' , having an R/T curve with

no hysteresis, as shown in figure 8. The low temperature cusp seen in this

and all traces is believed to be due to antiferromagnetic ordering. This type

of behaviour has been designated type 1 or stable behavior.

97
Figure 9 portrays a gradual transition, the increase in resistance being

rather progressive and occurring over a range of temperature, sometimes 20 to

50 K. This is named a type 2 or weak transition and is obtained for many

steels of intermediate alloy content.

Figure 10 shows a sharp form of transition in which there is a marked

irreversible increase in resistance which occurs over a rather narrow

temperature range (< 5K). This is called a type 3 or strong transition. This

is found for low alloy steels.

The behaviour of the steels is further summarised in figure 7. Although

not all steels have yet been examined it appears that there is a gradual

change in behaviour from the higher alloy steels which are quite stable,

through those exhibiting a weak transition, to those having a strong

instability. The dividing line between the stable and unstable steels appears

to be drawn from about 2QCr/8Ni to 18Cr/llNi, while only the leanest

18Cr/8Ni steel shows a strong transition.

An examination of Table 3 reveals a number of interesting features:

(i) The calculated M (M *) is always lower than the experimental

s s M . Four of the seven unstable steels have values of M -M * between

s s s 110 and 135K, the three other values falling significantly outside this

range. Additional samples remain to be tested, and individual sample

analyses must be performed before this observation should be regarded as confi rmed.

(g)

(ii ) Fiedler, Averbach and Cohen

1 reported that 1% of a' martensite

produced a resistivity increase of about 0.5%. Our measurements indicate some variation about this figure and clearly show the magnetic measurements as more

sensitive. The quenching experiments (in which resistance and magnetisation

were measured and one end face of the sample observed) are in all cases in

accord with the continuous cooling R/T traces, although in the case of the

19.1 Cr/8Ni alloy no transition was observable in the R/T trace while a transformation to 1-2% a

' could be detected magnetically.

98
(iii) The morphology of the martensite was always that of a' laths

within sheets of stacking faults or e . Since X-ray measurements have so far

been inconclusive it is not certain whether the sheets are truly e or faulted

y. In at least 3 alloys (15.6 Cr/8.1Ni, 17. lCr/8. 9Ni and 18.5Cr/8Ni) the

sheets were visible before the a' could be detected, while for other alloys

(18.1Cr/8Ni, 18.5Cr/9Ni) both sheets and a' appeared between the same pair

of quench temperatures and it could not be determined whether M (e) was indeed greater than M (a')

s

(iv) A suprising result is the highly non-linear response of alloys to

cooling. All the steels which transformed had M values which were determined

s to be > 1 70K . Marginally higher alloy steels with M * values of 25 to 50K

s lower in fact showed no transformation to a' , even though experimental

values in the 100 to 170K range would have been expected. This behaviour is

consistent, however, with the result that martensite is formed less easily in

steels plastically deformed at 4K than 77K

1 .

Summary

A series of some 30 steels in the 304 range have been made and

characteri sation of their spontaneous martensite breakdown on cooling is in

progress. The most important interim results appear to be

(i) Experimental M values in unstable steels are consistently higher, by

about 120K, than the values predicted from the Eichelman and Hull equation.

(ii) The behaviour of the 304 steels is highly non-linear, there being a marked change in the extent of the transformation as the alloy content

increases. M values of <170K have not been found, although they are

s predicted by the Eichelman and Hull equation.

99
(fii) The mode of transformation in these steels is always consistent with

previous workers who observed a

1

as laths occurring in sheets of e or faulted y .

Acknowl edgements

We are grateful to undergraduate senior project students Sarah Helfrich

and John Krebsbach for help and Dr. R. P. Reed for helpful discussions on a number of points.

References

1. R. P. Reed, Martensitic Phase Transformations, National Bureau of

Standards, to be published.

2. 0. C. Larbalestier and H. W. King, Cryogenics, 13, 160, (1973).

3* E.N.C. Dalder, Lawrence Livermore Laboratory, Paper at 1981 Vail

Meeting on Low Temperature Constructional Materials.

4. G. H. Eichelman and F. C. Hull, TASM, 45, 77-104, (1953).

5. 0. C. Larbalestier and H. W. King, Proc Int Cryogenic Eng Conf

ICEC-4, IPC Science and Technology Press (1975) 338.

6. H. W. King and D. C. Larbalestier, Cryogenics 21, 521, (1981).

7. C. J. Curtis and F.C. Sherwin, Brit. J.A.P., 12, 344, (1961).

8. H. C. Fiedler, B.L. Averbach, and M. Cohen, TASM, 47, 267 (1955).

100
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101
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102

as-annealed

condition.
FIGURE 7. Alloy classification based on resistive

and magnetic measurements.

WEIGHT

PERCENT

NICKEL
RESISTANCE

RESISTANCE

FIGURE 8

NO TRANSITION

( TYPE /

J

-NO HYSTERESIS

ON WA RMUP

JL ~/0 K TEMPERA TURE ~ 300 K

104
RESISTANCE

105

FRACTURE TOUGHNESS OF CF8 STAINLESS STEEL CASTINGS

IN LIQUID HELIUM*

E. L. Brown, T. A. Whipple, and R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

Fracture toughness measurements for CF8 stainless steel

castings in liquid helium at 4 K are reported. Single-phase (austenite)

and duplex (austenite + 6-ferrite) castings were tested. On the basis

of estimates from J-integral data, the plane-strain fracture toughness

(Kj

c

) of castings containing 3.2 to 14.5% 6-ferrite ranged from 84 to

1 /2 179 MPa*m at 4 K. In contrast, a fully austenitic casting (0% 6-

1/2 ferrite) exhibited a Kj value of 331 MPa*m , which is nearly equivalent

to the toughness of a wrought AISI 304 stainless steel of a similar

strength. Optical and scanning electron microscopy studies indicate

that the inferior toughness of castings containing 6-ferrite may be

chiefly attributed to the brittleness of this body-centered-cubic phase

at cryogenic temperatures and its distribution in the microstructure.

Key Words: Cast stainless steel; cryogenic properties of materials;

fracture toughness; J-integral tests; low-temperature

properties; stainless steels

Work supported by Brookhaven National Laboratory and the Department of

Energy, Office of Magnetic Fusion Energy.

107

INTRODUCTION

Cast stainless steels are being considered for structural applications in high-energy superconducting devices operating at 4 K [1].

Castings offer economic advantages over wrought products where large,

complex shapes are required. Owing to microstructure, however, the

mechanical properties of castings are often inferior compared with those

of wrought products. There are few published studies of the mechanical

properties of cast stainless steels at cryogenic temperatures . In

particular, there are no fracture toughness data for stainless steel

castings at 4 K. Since fracture toughness is a critical design parameter for any large cryogenic structure, a brief study was conducted

to provide such data for CF8 castings.

CF8 stainless steel is the cast counterpart of wrought AISI 304.

The base composition for both AISI 304 and CF8 is: Fe, 18 to 20% Cr,

and 8 to 12% Ni . But AISI 304 is virtually 100% austenite (y) at room

temperature, whereas CF8 typically contains a body-centered-cubic second

phase, delta (6 ) -ferrite, within an austenitic matrix. The amount of 6

-

ferrite is controlled by manufacturing variables; from zero to 40%

6 -ferrite may be present in CF8, although typically there is not more

than 20% [1]. Delta-ferrite in the austenite matrix generally increases

the strength and lowers the fracture toughness of welds and castings [2],

especially at cryogenic temperatures [3]. At room temperature the 6

-

ferrite is considered advantageous, serving as a strengthener and grain

refiner while improving weldability. At cryogenic temperatures the

6 -ferrite is relatively hard and brittle, and, as demonstrated quantitatively

109
in this paper, even small amounts of 6-ferrite (3.2 to 14.5%) can have

a detrimental effect on fracture toughness. The present work is a

continuation of mechanical property sutdies initiated at Brookhaven

National Laboratory, and Brookhaven provided the fracture specimens from

the steels previously tested [1].

MATERIALS

Samples from six CF8 stainless steel tubes, centri fugal ly cast by

three separate manufacturers, were tested. One casting had a single-phase,

ful ly-austenitic structure (0% 6-ferrite), whereas all others had a

duplex (austenite plus 6-ferrite) structure. The tubes had a 0.495-m

outside diameter and a 19-mm wall thickness. After casting, five of the

tubes were solution-treated at 1040°C for 2 h. However, one heat containing

12% 6-ferrite was not solution treated, but was tested in the as-cast

condition. The heat designations, chemical compositions, and volume

percentage 6-ferrite of the castings are listed in Table 1.

PROCEDURES

Specimens and Apparatus : Tensile tests at 4 K were performed using

smooth bar tensile specimens [1]. Fracture toughness tests were conducted

at NBS using compact specimens. The compact specimens were 12.7-mm

thick (B) and 50.8-mm wide (W), having planar dimensions that were

previously diagrammed [4]. For all tests in this study, the notches

were machined parallel to the tube axes in a CL orientation [5], which

is shown in Figure 1. The notch was modified to enable clip-gage placement

at the loadline, and the starting notch-to-width ratio was 0.3. Tests

at 4 K were achieved by immersion in liquid helium, using the cryogenic

test facility previously described [6].

110
Precracking : Using a sinusoidal load cycle, a frequency of 25 Hz,

a maximum load of 12 kN, and a minimum-to-maximum load ratio of 0.1, the

compact specimens were precracked at 76 K to a crack-length-to-width

ratio (a/W) of 0.5. Final precracking was then performed at 4 K, extending the a/W ratio to 0.57. The final maximum fatigue stress in1/2 tensity factor was 51 MPa*m , and the maximum fatigue load was between

40 and 55% of the observed maximum loads in subsequent J tests.

J-integral testing : Although 5 -ferrite undergoes a ductile-tobrittle transition as temperature is lowered to 4 K, the 1 2 . 7-mm-thick

CF8 castings at 4 K retain sufficient levels of plasticity to invalidate

direct measurements of Kj

c (the plane-strain fracture toughness) via the

linear-elastic ANSI/ASTM Method E-399-78a [5]. Therefore, singlespecimen J-integral tests were used to measure Jj

c

, which is a material

parameter for nonlinear elastic fracture conditions enabling quantitative

toughness comparisons of ductile materials to be made [7].

The computer-aided unloading-compliance technique [4] was used.

The precracked specimens were incrementally loaded in displacement

control, and periodic unloadings were performed during the course of the

test. The load reduction during unloading was typically ten percent of

the maximum load. Using a crack-length-vs. -compl iance correlation, the

crack extension increment (Aa) at each unloading was inferred. The J

value at each unloading point was calculated from the expression:

J = where x is the Merkle-Corten factor, A is the area under the

load-vs. -deflection curve at the unloading point, and specimen dimensions B and b are defined in Figure 1 [7].

Ill
J-resistance curves consisting of many sets of J and Aa data points

were generated, and Jj was taken as the point of intersection of the

resistance curve and the nearly vertical blunting line. The blunting

line is given by J = 2 Aa where is the average of the yield and

ultimate strengths. The Jj data were used to obtain estimates of Kj ,

denoted Kj

c (J):

(J) ( 1 )

Young's modulus E, was taken to be 206.8 GPa at 4 K and Poisson's ratio,

v, was taken as 0.3.

In these tests, the Aa values inferred from compliance measurements

and the actual Aa values measured on heat-tinted fracture specimen

surfaces were not in exact agreement. The inferred values were less

than the actual values, by up to 50%. One reason for the disagreement

is that the crack extension in specimens containing 5 -ferrite was nonuniform, as noted by example in the text (see section entitled Fracture

surface topography under RESULTS). This phenomenon causes a sizable

error in the slope of the J-Aa curve, but has less effect on the measured

Jj

c values. The estimated uncertainty of the experimental Jj values

is ±30%, which translates to an uncertainty in the calculated Kj (J) of

± 15 %.

Microscopy : Specimens of the centrifugally cast CF8 stainless

steel were subjected to scanning electron microscopy after fracture

testing, as well as optical microscopy before and after testing.

112
Specimens from heat numbers 429517 (0% 6 -ferrite) , 82118 (8% 6 -ferrite)

and 526631 (14.5% 6 -ferrite) were prepared for optical examination by

standard metallograhpic polishing procedures. The 0% 6 -ferrite microstructure

was revealed by electroetching with aqueous oxalic acid solution

(10 g/100 ml H^O; 2 V, 295 K) . The 8 and 14.5% 6 -ferrite microstructures

were revealed by electroetching in a ION KOH solution (^2 V, 295K). The

latter procedure tinted the 6 -ferrite light brown to light blue in

color.

Observations were made on specimens obtained by sectioning the

tested compact specimens. Specimens for general assessment of the

microstructure in an untested state were obtained from regions remote

from the crack front. The compact specimens were also sectioned perpendicular to the crack front and macroscopic crack plane in order to

make observations of the crack profile in the region of plane-strain

loading. Specimens for general microstructure assessment were viewed on

two surfaces: perpendicular to the casting radius, R, and perpendicular

to the casting axis, L. This was done to determine anisotropy in the

microstructure introduced during solidification and cooling of the

casting.

RESULTS

General microstructural assessment: The microstructures of untested material are depicted in Figures 2 and 3. The single-phase

austenitic casting structure is characterized by a coarse grain structure

and a uniformly distributed porosity. Note the surface "rumpling"

produced by electroetching. This is due to local variations in chemical

113
composition produced by solidification. Although the general distribution

of the porosity is uniform, on a finer scale the porosity is mainly

confined to "troughs" in the surface relief, which correspond to interdentri tic

regions in the as-solidified microstructure. Figures 3(a) and (b)

depict two other interesting aspects of cast grain structure associated

with the grain boundaries:

(1) There is an obvious traversing of dendrite arms (delineated by

surface rumpling) by grain boundaries. This indicates the

occurrence of grain growth in the solid state after solidification

is complete. A good example of this is located at A in Figure 2(b).

(2) There is a marked difference in grain morphology between

grains viewed in the two sections. The grains in Figure 2(a)

are elongated whereas the grains in Figure 2(b) are equiaxed.

Similar anisotropies are to be expected for the other ferrite

contents.

The as-cast 8 and 14.5% 6-ferrite microstructures are characterized

by filamentary particles of 6-ferrite that sometimes appear to form

diffuse cel 1-1 ike networks [Figure 3(a) and (b)]. An interesting feature of the 6-ferrite that is especially obvious in the 14.5% microstructure is the faceting of many 6/y interfaces.

Mechanical properties : The yield strength, ultimate strength, and

elongation measurements for the materials of this study (as measured by

Lee[l]) are listed in Table 2. At 4 K, the fully-austenitic, (zeroferrite) casting exhibited a 413 MPa yield strength and a 46% elongation.

These tensile properties are comparable to handbook values for AISI 304

stainless steel. Castings containing 6-ferrite show higher strength and

114
lower elongation compared with the fully austenitic casting. The yield

strengths range from 413 to 689 MPa, and elongations range from 47 to

10.7% for 6-ferrite contents from 0 to 14.5%. But there is not a perfect

correlation between the tensile properties at 4 K and the 6-ferrite

content, because the lowest elongation at 4 K (10.7%) is reported for

the 12% 6-ferrite casting that was not solution-treated.

Figures 4 and 5 show selected load-versus-deflection records and Jresistance curves obtained during fracture tests of compact specimens.

The single-phase (y) and duplex (y+ 6) castings differ markedly in their

fracture behavior. The presence of 6-ferrite lowers the critical J

value as well as the deflection at maximum load. In every case, fracture

progresses by a series of instabilities that give the load-versusdeflection curves a serrated appearance. The load drops corresponding

to the serrations are relatively small in magnitude, especially for the

zero-ferrite casting. It is possible that these serrations represent

unstable plastic deformation, unstable crack extension, or both.

The critical J values and Kj

c estimates for each CF8 specimen are

listed in Table 2, and the yield strength-versus-fracture toughness data

are plotted in Figure 6. Also shown in Figure 6 is a band of data for

wrought plates obtained from tests on a series of AISI 304 type stainless

steels in which property variations were achieved by altering the interstitial

carbon and nitrogen contents [4]. The fracture toughness data for the

wrought plates were derived from 24. 5-mm-thick compact specimens of the

TL orientation [5], tested with the same Jj technique used in testing

115
CF8. This provides a good comparison of the 4-K properties of Fe18/20Cr-8/12Ni stainless steels in both the wrought and cast forms.

The data for AISI 304 wrought plate clearly show an inverse linear

relationship, the toughness decreasing with increasing strength. Similarly,

for CF8 castings, higher strength is generally associated with lower

toughness. But the detrimental effect of the 6 -ferrite on the fracture

toughness of castings at 4 K is quite severe and clearly outweighs any

strengthening benefits. As shown in Figure 6, the single-phase austenitic

casting is nearly equivalent in toughness to wrought plate having a

similar yield strength, whereas duplex castings containing 3.2 to 14.5%

6 -ferrite exhibit toughness values well below half the values for wrought

steels at similar yield strengths.

Crack profiles : Microstructural observations of the crack profile

in J-tested specimens demonstrated that the fracture of the 0% 6 -

ferrite specimen was accompanied by extensive plastic deformation and

martensitic transformation. Figure 7 depicts the nature of martensitic

transformation within slip bands of the plastic deformation. It is

evident that the pre-existing voids in the microstructure influence the

fracture behavior, as discussed below.

Figure 8 depicts the crack profile for the 14.5% 6 -ferrite material. Fracture of this casting is associated with less extensive

plastic deformation and martensitic transformation than in the 0% 5 -

ferrite casting. The fracture path in the 14.5% 5 -ferrite specimen is

tortuous and the failure mechanism differs markedly from that of the 0%

6 -ferrite specimen. The 14.5% 6 specimen shows numerous regions of

apparent void formation at 6 /y interfaces, as well as the presence of

116
cracked 5 particles in advance of the crack tip. There is also ample

evidence of crack branching.

Fracture surface topography : At low magnifications the casting

fracture surfaces appear rough, and this roughness appears to increase

with the 5 -ferrite content (Figure 9). The 0 % ferrite casting fracture

surface is relatively smooth, regular, and close to the nominal plane of

the machined notch. In contrast, the 12% 6 -ferrite casting fracture

surface is particularly rough, and deviates at an angle of 15° to the

notch plane. The 12% 6 -ferrite specimen is also unique in that the main

crack front was irregular, running ahead of numerous small ligaments

that remained behind the main crack front. After J-testing, heattinting, and final fracture, the 12% 6 -ferrite fracture surface exhibited a unique speckled appearance caused by unoxidized areas at sites

where ligaments of the ductile y phase had remained intact.

Fracture in the 0% 6 -ferrite casting at 4 K occurred exclusively by

a ductile, dimpled failure mechanism involving void coalescence, despite

the fact that body-centered-cubic martensitic phase transformations

occurred in the plastic zone prior to crack extension. As shown by

scanning electron microscopy in Figure 10, the dimple pattern is actually duplex: large isolated dimples, representing preexisting porosity

or inclusion sites, are surrounded by a network of smaller dimples

arising from nucleation and growth owing to slip. Figure 10(a) shows a

strip-like zone transverse to the direction of crack extension, wherein

the average dimple size is smaller than in areas outside this zone; this

variation probably reflects the influence of cast macrostructure and

117
perhaps represents fracture along intercol umnar, as opposed to transcolumnar, grain paths.

As shown in Figures 11 through 13, the scanning electron micrographs of the castings containing 8, 12, or 14.5% 6-ferrite reveal a

mixed failure mode at 4 K. This mixed mode consists of cleavage in the

6 phase and dimpled failure in the partially transformed y phase. For

the 8% 6-ferrite casting, Figure 11(b) shows a 6-ferrite particle that

has cleaved on three orthogonal planes, the fracture apparently originating at a large pore near the 6/y interface. Higher magnifications of

the 14.5%- and 12% 6-ferrite specimens are shown in Figures 12(b), and

13.

DISCUSSION

Microstructural observations : Considerable research has been

conducted into the evolution of microstructure in austenitic stainless

steel welds and castings [8-16]. These studies have centered about

factors affecting the volume fraction, scale, and morphology of 6-

ferrite. The present investigation illustrates the potency of relatively

minor variations in steel chemistry in producing a significant variation

of the volume-percent 6-ferrite (0 to 14.5%). With the exception of the

0% 6-ferrite casting, the castings employed in this work solidified with

ferrite as the primary phase (first solid phase to form) so that the

microstructure can contain an appreciable amount of ferrite upon completion

of solidification. The greatly reduced volume fraction of 6-ferrite

actually observed in the microstructure upon coding to room temperature

(Figures 2 and 3) is then due to a solid-state 6->y transformation subsequent

to solidification.

118
Extensive solute-redistribution as well as microstructural change

takes place during the 6->-y transformation. Controversy exists as to

whether the 6+y transformation occurs via a massive or diffusion-controlled

nucleation and growth mechanism. Whatever the actual mechanism, the

faceting and characteristic angles frequently observed between facet

variants indicate the presence of low-energy interfaces with a high

degree of lattice matching. Other studies at the authors 1 laboratory

have indicated the facet morphology to be consistent with a KurdjunovSachs type of orientation relationship between 6 and y, this orientation

relationship has been observed previously [12].

A note of caution should be introduced with regard to general

microstructural assessment of 6-ferrite in an austenitic stainless

steel. On any given plane of polish, the 6-ferrite appears dispersed in

the austenite matrix with only occasional indications of continuity.

Investigations involving dissolution of the matrix have indicated the 6-

ferrite is partly to completely continuous above approximately 10% [17].

This could have significant implications with respect to deformation and

fracture behavior by limiting the mean free path through a region of the

austenite matrix. Thus, the network distribution of 6-ferrite and its

brittleness at 4 K may have contributed to the relative coarseness of

the 12% 6-ferrite specimen fracture surface.

The difference in grain morphology observed on different specimen

sections [Figures 2(a) and (b)] is consistent with the heat flow during

119
casting and the manner in which the compact specimens were cut from the

centrifugal casting. Figure 1 is a schematic diagram of the centrifugal

casting and the specimen position. Heat flow, as indicated on the

diagram, is in a radial direction. Investigation of the microstructure

produced by the 6 transformation in primary-6 -sol idifying steels

has indicated that the resulting austenite grains are columnar and

follow heat flow regardless of the prior solidification structure [18].

Thus, the longitudinal axes of the elongated austenite grains are parallel

to the crack front in our CL-oriented specimens. One might not expect

to find a significant difference in mechanical properties if compact

specimens of the LC orientation (Figure 1) had been tested. However, if

specimens of a third orthogonal orientation were available (cracks

propagating radially, through the tube thickness), a property dependence

on orientation might be expected since the longitudinal axes of the

grains would then be perpendicular to the crack front. Limited testing

on austenitic stainless steel welds [19] suggests that the grain size in

the plane of the crack profile controls fracture behavior. The rationale

tendered for this behavior is that in a plane-strain, ductile fracture

mode the strain is confined to the above-mentioned plane, and the plastic

zone size at the crack tip is then affected by the grain size in that

plane. Even though the austenitic grain size in the 6 -ferrite containing

specimens is expected to behave in a similar manner, the 6 -ferrite in

these steels becomes the overiding factor in deformation and fracture

behavior. This is especially so since the 6 -ferrite structure is generally

not strongly associated with the final austenite grain structure in

castings.

120
Fracture toughness comparisons : The J-integral data of this study

must be interpreted cautiously. The degree of specimen-to-specimen

variability in Jj

c values is not known since there was no replicate

testing. Of the six different specimens tested, three did not satisfy

criteria for valid J^

c data as formulated in the recommended method of

testing (see notes to Table 2). Nevertheless, the J-integral technique

used in this study appears to have yielded the first practical estimates

of Kj

c for these materials at liquid helium temperature.

Although the present results are discussed primarily as a function

of the 5 -ferrite, the 6 -ferrite content was not the only variable in

these tests. The castings were produced by different suppliers using

variable composition and cooling rates. In particular, the 1 2%-6 -

ferrite casting was not solution heat-treated. Solution heat treatment

offers benefits such as slightly reducing the 6 -ferrite content, modifying the 5 -ferrite morphology by rounding off angular corners of the

as-cast 5 phase, and dissolving carbides [1]. Therefore, lack of solution heat treatment may account for the lower tensile ductility and

lower fracture toughness of the 1 2%-6 casting compared with the 14.5T5 casting [1].

Fracture mechanisms : The fracture mode of the fully austenitic

casting with its higher volume fraction of interdendritic voids differs

significantly from that of the 6 -ferrite containing castings. The

pre-existing void distribution appears to play a major role in the

fracture process of the 0%^ -ferrite steel. The crack in Figure 7

appears to be extending and branching by the growth and subsequent

linking of voids. The mechanism of void growth is presumably via their

121
intersection with slip bands and might be enhanced by the internal

stresses and strain associated with the martensitic transformation. The

ligaments between the preexisting voids eventually rupture in a ductile

manner to complete the crack extension. Consequently, the fracture

surface consists of a duplex size distribution of dimples, as observed

in Figure 10. The striations visible on the inside of the large dimples

are then slip lines owing to the intersection of slip bands, surface

rumpling owing to martensitic transformation, or both. We noted earlier

that the amount of strain and martensitic transformation product in the

0%-6 -ferrite specimen is relatively large, owing to the larger plastic

zone developed during J-testing of this high toughness material. But

the role of the martensitic transformation on fracture behavior is

unknown at this time.

Based on the observations recorded in this study, the following

picture of the fracture process for duplex CF8 castings containing up to

14.5% 6 -ferrite has been formulated: the 5 -ferrite phase or 6 /y interfaces

fracture first, at localized areas within the plastic zone ahead of the

crack front (Fig. 8). The austenite then fails by ductile void coalescence

in those ligaments necessary to bridge gaps between the fractured 6

phase (Fig. 11). The crack front advances by linking many fractured 6

particles that are not necessarily coplanar. Consequently, the fracture

surfaces of 5 -ferrite containing specimens are more tortuous than those

of the fully austenitic specimens (Figs. 8,9), and the fracture surfaces

apparently display a higher percentage of cleavage than would be expected

based on the proportion of 5 phase encountered on a perfectly planar

122
section through the microstructure. That the 6 -ferrite is brittle at

4 K is demonstrated by the cleavage fractures in SEM micrographs. But

the specific roles played by void formation at 6 /y interfaces, martensitic

transformation, and possible constraints imposed by the relatively hard

5 phase on the softer y phase are uncertain at this time.

Finally, it is interesting that in concurrent studies, CF8M (316)

castings with simi 1 ar 6 -ferri te content possessed higher fracture toughness,

less evidence of martensitic transformation, and practically no evidence

of ferrite cracking in areas ahead of the main crack front. This

suggests a variation in behavior due to alloying. The highly-alloyed

CF8M matrix is more stable compared with CF8, and it is possible that

the composition of the 5 -ferrite is also different from that of the CF8

casting. Data for ferritic steels at 4 K show a strong beneficial

effect of Ni on toughness [20]. If the Ni contents of the two 6 ferrites

(CF8 vs. CF8M) were significantly different, this might explain the

observed differences in fracture behavior and also indicate an important

variation in ductility of the ferrite at low temperature.

SUMMARY

The fracture behaviors of six CF8 stainless steel castings in

liquid helium at 4K were studied and compared. On the basis of microstructure,

there are two categories of materials. The results are summarized as

follows

:

1) Single-phase austenitic CF8 castings are capable of exhibiting

cryogenic tensile and fracture properties nearly equivalent

123
to the properties of wrought steels having a similar composition.

The Fe-1 8Cr-l 1 Ni casting tested in this study at 4K exhibited

a Kj estimate of 331MPa*m^ 2 and a yield strength of 413 MPa.

Slight differences in properties between cast and wrought

steels may be attributed to the presence of solidification

shrinkage porosity and the greater chemical inhomogeniety

associated with castings, as well as grain size effects. Interdendritic porosity in CF8 evidently combines with smaller

voids formed during straining to produce a duplex dimpled

failure mode.

2) In duplex CF8 castings, the presence of body-centered cubic

6 -ferrite severely reduces tensile ductility and toughness.

For CF8 specimens containing 3.2 to 14.5% 6 -ferrite, the

1 /2 estimated Kj

c values at 4K ranged from 84 to 179 MPa*m , or

about half the fracture toughness expected for wrought steels

of similar compositions. Failure in the duplex castings

occurs by cleavage of the 6 -ferrite, followed by ductile void

coalescence of the surrounding austenite at load levels

significantly higher than required to fracture the 6 -phase.

The adverse effects of 6 -ferrite are reflected in all aspects

of fracture behavior.

ACKNOWLEDGMENT

The authors gratefully acknowledge the assistance of Drs. D. Dew-Flughes,

J. Chow, and K. S. Lee of Brookhaven National Laboratory, in providing

the test materials, tensile property data, and manuscript review.

124
REFERENCES

1. Dew-Hughes, D. and Lee, K. S., The Choice of Steel for the Isabelle

Magnet Tubes, Adv. Cryo. Engr. , Vol . 26, 1981, pp. 151-157.

2. Zemzin, V. N. and Petrov, G. L., Influence of Ferrite Content on

the Properties of Austenitic Weld Metal, Svarka. Proizvod. , No. 5,

1967, pp. 5-8.

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

Metallurgical Factors Affecting the Toughness of 31 6L Weldments at

Cryogenic Temperatures , Weld. J. Res. Suppl . , Vol. 59, 1980, p. 104-s

4. Tobler, R. L., Read, D. T. , and Reed, R. P., Strength/Toughness

Relationship For Interstitial ly Strengthened AISI 304 Stainless

Steels At Four Kelvin, presented at the Thirteenth National Symposium on Fracture Mechanics, Philadelphia, PA, June 1980.

5. Standard Method of Test for Plane Strain Fracture Toughness of

Metallic Materials (Designation E 399-74), 1974 Annual Book of ASTM

Standards, Part 10, American Society for Testing and Materials,

Philadelphia, PA, 1974, pp. 432-451.

6. Fowlkes, C. W. and Tobler, R. L., Fracture Testing and Results for

a Ti-6A1-4V Alloy at Liquid Helium Temperature, Engr. Fract. Mechs.,

Vol. 8, 1976, pp. 487-503.

7. Clarke, G. A., Andrews, W. R. , Begley, J. A., Donald, J. K.

,

Embley, G. T., Landes, J. D. , McCabe, D. E., and Underwood, J. H.,

A Procedure for the Determination of Ductile Fracture Toughness

Values Using J Integral Techniques, J. Test. Eval . , Vol. 7, No. 1,

1979, pp. 49-56.

125
8 . Lippold, J. C. and Savage, W. F. , Solidification of Austenitic

Stainless Steel Weldments: Part 1-A Proposed Mechanism, Weld. J.

Res. Suppl

.

, Vol . 58, No. 11 , 1979, p. 330-s.

9. David, S. A., Goodwin, G. M., and Braski, D. N., Solidification

Behavior of Austenitic Stainless Steel Filler Metals, Weld. J.

Res. Suppl. , Vol. 58, No. 11, 1979, p. 330.

10. Suutala, N., Takalo, T., and Moisio, T., The Relationship Between

Solidification and Microstructure in Austenitic and AusteniticFerritic Stainless Steel Welds, Met. Trans. A , Vol. 10A, No. 4,

1979, p. 512.

11. Suutala, N., Takalo, T„, and Moisio, T., Single-Phase Ferritic

Solidification Mode in Austenitic Stainless Steel Welds, Met.

Trans. A , Vol. 10A, No. 8, 1979, p. 1173.

12. Suutala, N., Takalo, T., and Moisio, T., Ferritic - Austenitic

Solidification Mode in Austenitic Stainless Steel Welds, Met.

Trans. A , Vol. 1 1 A , No. 5, 1980, p. 717.

13. Lippold, J. C. and Savage, W. F., Solidification of Austenitic

Stainless Steel Weldments: Part 2 - The Effect of Alloy Composition on Ferrite Morphology, Weld. J. Res. Suppl. , Vol. 59, No. 2,

1980, p. 48-s.

14. McTighe, J. M. and Beech, J., The Structure of As-Cast Austenitic

Stainless Steels, J. Res. , SCRATA, No. 37, 1977, p. 43.

15. Raghunathan, V. S., Seetharaman, S., Venkadesan, S., and Rodriguez, P.,

The Influence of Post Weld Heat Treatments on the Structure, Composition and the Amount of Ferrite in Type 316 Stainless Steel Welds,

Met. Trans. A , Vol. 10A, No. 11, 1979, p. 1683.

126
16. Hammar, 0. and Svensson, U., Influence of Steel Composition on

Segregation and Microstructure During Solidification of Austenitic

Stainless Steels, in Solidification and Casting of Metals , Pro -

ceedings of an International Conference on Solidification , University of Sheffield, England, 1977, p. 401.

17. Gill, T . P . S . , Dayal, R. K. , and Gmadamoorthy , J. B., Estimation

of Delta Ferrite in Austenitic Stainless Steel Weldments by an

Electrochemical Technique, Weld. J. Res. Suppl

.

, Vol . 58, No. 12,

1979, p, 375- s

.

18. Fredriksson, H., The Solidification Sequence in an 18-8 Stainless

Steel, Investigated by Directional Solidification, Met. Trans. ,

Vol. 3, No. 11, 1972, p. 2989.

19. Whipple, T. A., McHenry, H. I., and Read, D. T., Fracture Behavior

of Ferrite-Free Stainless Steel Welds in Liquid Helium, Weld. J.

Res. Suppl. vol. 60, No. 4, 1981, p. 725.

20. Tobler, R. L., Mikesell, R. P., and Reed, R. P. 5 Cryogenic Effects

on the Fracture Mechanics Parameters of Ferritic Nickel Alloy

Steels, in: Fracture Mechanics , ASTM STP 677, C. W. Smith, Ed.,

American Society for Testing and Materials, Philadelphia, PA, 19 9,

pp. 85-105.

127
Table

1.

Chemical

compositions

of

CF8

castings

tested

[11].

CO CTl LO

co 1— CTi 00

O 0 0 O

O 0 • • • • • • O 0 0 O O 0

LO

O lo ^J~ 1 CO

O

r— 0 0 j O o O 0 0 1 O

O

CM C\J l\ CM

•I1— LO CM LO CTl

C/O • • • • • • 0 1 1 ' O

CTl

^J~ CM OvJ

O CM 1— 0 0 0 O O O

C/O • • • • • • 0 0 0 O O O

CTl co cm r— OJ 1 0 0 0 0 O O Cl. 0 0 0 0 O O 0 'vf r^. CTl CTl sz 0 co 0 | LO • • • • • • l 0 0 r_ O O

CO "O

CM un LO LO LO 0 0 0 0 O O O .£: o • • • • • • +-> 0 0 0 O O O cuE

s_cu -M 0 LO CM O •=3“ LO CU • 1“ E l O') CO O 00 00 O l ( -i-> CUc

CT

03E 0 LO 1 ^3- LO CTi S- • • • • • • -a 0 00 00 0 01 CTl O CZ >— CM 1— 1— CM 03a•1—

-£Z <D Q- O <d

a) £Z sLi_ 03 Z Z z Z z CT) O

03 zz 1 -O 1 CM 03 e +> 0 cu

cu e\ E

+-> 0 • 1

O cn

s_ 0 cz

S- ^5 C\J LO • 1—

a> • • • 0 CO

Ll_ 0 co 00 CM 1 3 | I >1 “O JZI CU

+-> _l

03 zz

cu CQ

s_ +J +-> c= 03 r— O £Z

03 *r—

O

a •r— -M S- •| +-> cu

s- fd a) 03 <C <c 03 03 _Q +-> CO S- CU SZ -Cl I CO 1

CM Z3 03 Z3 4-> CD E r— LO ^3" CM CO CM 1

0 CO n3 -r- Z3 LO CTl LO | LO CTl 0 1 03 Z V) z cn VO | LO r\ CO CO cu

cu C\J co CM C\J CM 03 E Q CO CO 00 LO 03 -Q 0

128
Table

2.

Tensile

properties

and

fracture

toughness

results

for

CF8

castings

at4

K. * C\J

<T3'— \ 

i

LO

vu E a —" • i

cn <vj- cn LO o co co r-- cn CM CO »—i

Q_ co i 1 , f 21

r\ 4—

s- o

CD o LO cn CM M 4-> c_> _Q • • • •f- CD E CO co LO 1 , C/1 CD o E i

Ll_ LOCM

r\

r CO

S-cn CM

CDu E a

-4-> >—• — i

1

CM LO cn

p

C '"D

r

D CO CO co CO

1—»

*vt- f—

——

r

DCo • •r— 1 1 +-> 1

CM CO CO CM *=3" 03 1 1 cn CO CO o O o • c ^3- co CO CM i—-

-a CD o CD c 1

s_ 03 LU •r—=3 CL CT

CD jz: S- o

+-> 00 o •1

sc CD JC

+-> 4-> E CD as cn E _C E c 03 +-> •r- CD ID Q_ f— CM CO CM O CO

+-> Sb sr LO o | CM LO 1 o

i— 4-> CM LO CM LO cn +J ZD C/1 r— j P— f " 00

03 CD

CD 1 C_ cn

CD c

_c: 03 3 0

r\ • LO

** £ <* r—

-C £ CD T3 +-> S- »*0 r— cn 13

CD c >> fO CO LO co o cn CO • r— +-> •r- CD b D_ p— LO cn co CM •p- •T3 >- s_ 2:

*=3* co LO 1 H3

+-> 4- LO oo 00 .•O •r— CDcn

LO •T3 c «v 00 cn CD

CD CD E

4-> CM r^. LO £= Ql •r* • 0 • •a -M •r— C_) S- o co co CM r— CD

S- ^ i 1 • *r- o CL

CD

U -£Z "—

00

<4- »—i

4-> o a> oo

sc Z5 •r— E CD i

-C o E «TJ +J

S_ *r— >

4-

a c d CD ~a *p* o TD CL c

CD 00 13 CD n- 4-> <C <c

4-> S_ r— o

JO 3

CO *rC r-- 1— co 1 CM CD .-a S- 4—5 Ll_ S- CD LO CM CO CM > =3 CD u

(J O) -r LO cn LO r— co cn C= 4-5 o_ •T3 4-5 CO cn CO i co o o

(TJ CL) CM CO CM CM CM CD CO 3 4-

s:

q CO CO 00 LO '

co -Q o T3

129
LIST OF FIGURES

1. Compact specimen orientations with respect to tubular casting

stock.

2. As-received microstructure of single-phase CF8 casting: (a) perpendicular to the tube circumference, (b) perpendicular to the tube

radius

.

3. As-received microstructure of duplex CF8 castings containing

(a) 8% 5 -ferrite, (b) 14. 5% 6 -ferri te (sections perpendicular to

the tube radius.

4. Fracture test records for selected CF8 compact specimens at 4K.

5. J-resistance curves for CF8 compact specimens at 4K.

6. Toughness-versus-strength comparison for Fe-Cr-Ni stainless steels

in wrought and cast forms at 4K.

7. Fracture profile in 0% 6 -ferrite CF8 compact specimen.

8. Fracture profile in 14.5% 6 -ferrite CF8 compact specimen.

9. Macroscopic view of the 4K fracture surfaces of CF8 castings:

(a) 0% 6 -ferrite specimen, (b) 12% 6 -ferrite specimen.

10. 4K fracture surface of a 0% 5 -ferrite casting, showing dimpled

failure.

11. 4K fracture surface of an 8% 6 -ferrite casting, showing both

cleavage and dimpled failure modes.

12. The 4K fracture surface of a 14.5% 5 -ferrite casting, showing:

(a) duplex failure mode, (b) cleaved 6phase.

13. The 4K fracture surface of a 12% 6 -ferrite casting, showing

cleavage of a 6 at high magnification.

130
t

Casting

Axis

Perpendicular Specimen (LC)

Figure 1. Compact specimen orientations with respect to tubular casting

stock.

131
(b)

Figure 2. As-received microstructure of single-phase CF8 casting: (a) perpendicular to the tube circumference, (b) perpendicular to the tube

radius

.

132
Figure 3.

(b)

As-received microstructure of duplex CF8 castings containing

(a) 8% 6 -ferrite, (b) 14.5% 6 -ferrite (sections perpendicular to

the tube radius.

133
DEFLECTION,

8,

mils

50

100

150

qi ‘d ‘avoi

E

E

CO

o

LU

Li.

LU

Q

N>l ‘d ‘avoi

134

Figure

4.

Fracture

test

records

for

selected

CF8

compact

specimens

at

4K.
-INTEGRAL,

J,

kJ/m

CRACK EXTENSION, Aa, mils

0 50 100 150 1 1 1 r~

CRACK EXTENSION, Aa, mm

Figure 5. J-resistance curves for CF8 compact specimens at 4K.

135

-INTEGRAL,

J,

lbin/in
YIELD STRENGTH, <r

y , MPa

Figure 6. Toughness-versus-strength comparison for Fe-Cr-Ni stainless steels

in wrought and cast forms at 4K.

136
Figure 7. Fracture profile in 0%

6

-ferrite CF8 compact specimen.

1 37
' T* %

*r/ij

"

-

' Hi ,

' «*.

138

Figure

8.

Fracture

profile

in

14.5%

6

-ferrite

CF8

compact

specimen.
1mm

Figure 9. Macroscopic view of the 4K fracture surfaces

of CF8 castings: (a) 0 % 6-ferrite specimen,

(b) 12% 6-ferrite specimen.

139
Figure 10. 4K fracture surface of a 0% 6-ferrite

casting, showing dimpled failure.

140
(a) 100 ym

(b) 20ym

Figure 11. 4K fracture surface of an 8% 6-ferrite

casting, showing both cleavage and

dimpled failure modes.

141
lOum

Figure 12. The 4K fracture surface of a 14 . 5%6

ferrite casting, showing: (a) duplex

failure mode,(b) cleaved <5 phase.

142
40ym

Figure 13. The 4K fracture surface of a 12% 6-ferrite

casting, showinn cleavage of a 6 at high

magnification.

143

DUCTILE FRACTURE WITH SERRATIONS IN AISI 310S

STAINLESS STEEL AT LIQUID HELIUM TEMPERATURE *

R. L. Tobler and R. P. Reed

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

Fracture toughness tests were performed on annealed austenitic

stainless steel AISI 310S, immersed in liquid helium at 4 K, using

25-mm-thick compact specimens. The Jj results (360 to 380 kJ/m ) from

single- and multiple-specimen test techniques are compared and shown to

be in close agreement. Attention is called to the remarkable failure

process of this steel at 4 K: crack extension occurs by ductile tearing,

while the test records exhibit serrations due to repeated bursts of

unstable plastic flow and arrests. The nature of this behavior is

discussed, and the performance of stable austenitic AISI 310S is compared with that of related steels, including those that transform from

austenite to martensite during testing at 4 K.

Key Words: Austenitic stainless steel; cryogenic properties of

materials; fracture of materials; J-integral tests; lowtemperature properties; stainless steels.

*Work supported by the Department of Energy, Office of Magnetic Fusion

Energy.

145

INTRODUCTION

AISI 310S is a low-carbon (C < 0.08 wt.%) modification of Fe-25Cr20N i stainless steel. This steel has an austenitic (face-centered

cubic) structure, and so remains highly ductile at extreme cryogenic

temperatures. Owing to its high alloy content, the austenitic structure

is completely stable and does not undergo martensitic phase transformations during deformation at low temperatures . Fracture toughness data

for this material at 4 K were desired to serve three purposes:

1) to evaluate the NBS single-specimen Jj measurement procedure,

2) to illustrate the unique serrated plastic flow behavior that

accompanies fracture of such materials at extreme cryogenic

temperatures, and

3) to compare the toughness of a stable austenitic stainless

steel with previously tested metastable stainless steels.

MATERIAL AND SPECIMENS

The tested material was a 25.4-mm-thick plate of AISI 310S in the

as-received condition: annealed at 1950°F (1339 K) , water quenched, and

descaled. In weight percent, the chemistry is: Fe-24.6Cr-20.4Ni1 .65Mn-0.07C-0.70Si-0.18Mo-0.041P-0.027S. The hardness and tensile

properties were measured by conventional methods [1,2] and are presented

in Table 1

.

Six compact fracture specimens of the TL orientation were machined

from the as-received stock. These were not side grooved. The specimen

thicknesses (B) and widths (W) were 25 and 50.8 mm, respectively. A

diagram is given elsewhere [3].

In addition, one side-grooved specimen was prepared from a special

portion of stock that had been reannealed in the laboratory: 1950 vC

(1339 K), 1 h, water quench. Symmetrical side grooves were machined on

147
both faces, reducing the section thickness by 10% (B

net = 22.8 mm). The

notch root radii were 0.100 mm.

PROCEDURES

Precracking was accomplished in liquid nitrogen (76 K) or liquid

helium (4 K) , but the temperature of precracking had no apparent affect

on results. The maximum and minimum fatigue loads were 22 and 2.2 kN,

well below 40% of the maximum load reached in J tests. The final a/W

ratio was nominally 0.62.

Both the single-specimen and multiple-specimen test techniques were

applied. In the absence of accepted standards, the measurement techniques followed those reported elsewhere [3-5]. In the single-specimen

technique, crack extension (Aa) was inferred periodically by unloading

compliance measurements made with computer-aided data analysis. One

specimen was loaded extensively to obtain a well-defined J-resistance

curve. Five similar specimens were also tested with periodic 10% unloadings, but these tests were terminated at successively lower Aa

values according to the multiple-specimen technique [5]. Displacement

control was used. Each specimen was completely unloaded at the end of J

testing and heat- tinted or refatigued to mark the final Aa, which was

measured with a microscope at nine loctions, and averaged.

RESULTS

Loading Behavior

Figure 1 shows a typical load-versus-deflection curve for AISI 31 OS

steel at 4 K. The behavior is fully plastic in that a limit load is

reached. However, the curves are marked by serrations, which become

more pronounced as the test proceeds. Superimposing test records for

148
similarly sized specimens showed that the behavior was reproduci bl e

,

with major serrations occurring at nearly equivalent loads and deflections. Test records for this type of steel at 295 and 76 K (not reported here) do not show these serrations.

Fracture Mode

In appearance, the serrations of Fig. 1 resemble a type of "pop-in"

phenomenon, which is frequently observed in other materials at room

temperature. Such behavior is usually caused by spurts of brittle

cracking and arrest. However, annealed AISI 310S steel is not at all

brittle. A fractured specimen is shown in Fig. 2, and a scanning

electron micrograph of the 4-K fracture surface is shown in Fig. 3. The

microscopy reveals a heavily dimpled fracture surface evidently produced

by void formation, growth, and coalescence. There is no visual evidence

of a change in fracture mechanism or surface markings that might be

associated with the serrations of Fig. 1. Apparently, then, we have

here an example of a material in which a single mechanism of crack

extension (ductile tearing) is associated with first stable, then unstable loading conditions in the same test specimen. Rarely has this

been observed.

J-Resistance Curves and Jj

c

A J-versus-Aa curve for the AISI 31 OS steel from the single specimen

technique is shown in Fig. 4. The curves follow a linear regression

line, as assumed in the recommended procedure [5]. The recommended

procedure also assumes that crack-tip-blunting behavior will conform to

the equation:

Aa = 2Ja

.p

( 1

)

149
where is the average of the yield and ultimate strengths. Although

the data for one specimen did follow this equation, the data for all

other specimens deviated, owing to a slight zero shift during the early

stage of blunting line development just after the first unloading (see

Fig. 4). For the single-specimen technique used in this study at 4 K,

the initial crack length, a^, inferred from compliance was 3 °l lower than

the value measured from broken specimens. This could be attributed to

errors in the compliance function used and in the assumed value of

Young's modulus (206.4 GPa) at 4 K.

Table 2 and Fig. 5 present the relevant J-integral data from the

multiple-specimen technique for AISI 310S at 4 K. These data for

specimens with no side grooves show little scatter, except for one

relatively low toughness specimen, which was excluded from the analysis.

In comparison, the result from extrapolation for the multiple-specimen

2 technique gives Jj

c

= 360 kJ/m , whereas the single-specimen technique

indicates 380 kJ/m

2

.

The Jj

c measurement point was traced to its location on the loadversus-defl ection curve; it does not coincide with the first sizable

load drop or with the attainment of maximum load, but falls intermediate

between these points, as shown in Fig. 1. Since the J value at the

o first significant load drop (^327 kJ/m ) is lower than Jj

c

, the first

load drop must be due only to unstable plastic flow, not true crack

extension. This was confirmed by compliance measurements made before

and after the first load drop: only a small increase of Aa was indicated, not greater than the amount predicted from Eq. (1) for crack tip

blunting.

150
Comparisons of the measured and inferred crack extensions for the

five specimens without side grooves reveal an error that increases

significantly as the J test proceeds, with disagreements as high as 55%.

Since this error is less at low Aa values, the Jj

c measurement from the

single-specimen technique is reasonably accurate (within 5%) of the

value given by the multiple-specimen technique. However, the slope of

the J-Aa curve for the single-specimen technique is inaccurate, being

65% greater than the slope given by the multiple-specimen technique.

Therefore, our unloading compliance technique could not be used to

determine the tearing modulus of the material at 4 K which, based on the

multiple-specimen technique, is 60.

K t Estimates

Ic

The Jj data are often used to estimate the linear-elastic plane

strain fracture toughness, Kj

c

. From the single- and multiple-specimen

techniques, the Kj

c estimates for AISI 310S steel at 4 K are 290 and

285 MPa*m^ 2

, respectively. The uncertainty in Jj

c is ±15%, which

translates to an uncertainty in Kj

c of ±8% [1]. We note, however, that

the existence of K T for annealed austenitic stainless steels has never

been proved, since linear-elastic fracture behavior for these materials

has never been observed. To determine experimentally whether linearelastic fracture behavior could be achieved in AISI 310S at 4 K, it

would be necessary to test a specimen of impractical size, having a

thickness of about 0.5 m:

K

Tr 7

B > 2.5 (^-r = 2.5 ( ay

285 MPa-ni 1/2

645 MPa ) 2 = 0.49 m (2)

151
Fracture Toughness Comparisons

Although it would be interesting to compare the Jj values for

AISI 310S at 4 K and at room temperature, this is impossible because Jj

data for 25-mm-thick specimens are invalid at 295 K. Comparisons are,

therefore, limited to results for other heats and stainless steels that

have also been tested at 4 K.

Logsdon, Wells, and Kossowsky [6] also tested a heat of AISI 310S

steel at 4 K, reporting a Kj

c estimate of 262 MPa*m^ and an 819-MPa

yield strength. The Kj result is quite consistent with ours, because

Kj

c scales as an inverse function of the yield strength, as shown in

Fig. 6. The somewhat higher strength and lower fracture toughness of

the heat tested by Logsdon et al . is easily explained by compositional

differences, notably higher carbon content.

Considerable low temperature fracture toughness data are now available for the two categories of austenitic stainless steels: 1) stable

with respect to phase transformation at 4 K (e.g., AISI 31 OS and Fe20Cr-16Ni-6Mn-0. 2N steels [7]) and 2) metastable with respect to phase

transformation at 4 K (e.g., AISI 304 type steels [3,4]). Figure 6

summarizes data pertaining to the effect of structural stability on

fracture toughness in the Fe-Cr-Ni-Mn system. The results shown in this

figure are for equivalent specimen orientation, specimen size, and test

technique; all of the steels represented in this figure exhibited the

dimpled fracture mode, as verified by scanning electron microscopy. We

see that the data for three stable steels fall within the scatterband

for unstable steels, so that a single inverse-linear dependence on yield

strength appears to govern fracture toughness, regardless of whether

152
martensitic phase transformation takes place or not. Additional data

will be needed to support this conclusion.

Side Grooves

One specimen having side grooves was J-tested, and the inferred Aa

was 24% lower than the measured value. From Fig. 5, the error for an

ungrooved specimen at the same value of measured crack extension would

be 33%. This indicates that side grooves may improve the final Aa

prediction for ductile austenitic stainless steels tested by the unloading compliance technique. Confirmation is needed using deeply sidegrooved specimens.

DISCUSSION

AISI 31 OS at 4 K furnishes a remarkable example of a material that

fails by repeated bursts of instability and arrests, the same mechanism

of failure (ductile tearing) associated with alternating stable and

unstable conditions in a single test specimen. The first few serrations

in the load displacement record result from unstable plastic deformation

that causes crack-tip blunting, but no true crack extension.

Subsequent serrations at J values exceeding Jj are presumed to be

associated with both plastic flow and crack extension by ductile tearing.

As discussed later, this type of ductile fracture with serrations can be

expected in many ductile alloys, but only at temperatures near absolute

zero.

Mechanism of Serrated Flow

The serrations observed in tests of compact specimens at 4 K are

analogous to the serrations observed in stress-strain curves during

conventional unnotched tensile tests. The phenomenon as it occurs in

153
tensile tests is documented in studies of a wide variety of materials at

temperatures below 20 K, including stable and transforming stainless

steels, aluminum, and copper alloys [8-12]. In tensile tests of austenitic stainless steels at 4 K, the serrations begin after small

initial plastic strains of about 2%, and the deformation propagates as a

Luders band [8].

Observations from our tests of AISI 31 OS show that the serrations

at 4 K cannot be attributed to brittle cracking or to phase transformation. The most widely accepted explanation is based on adiabatic

heating, as described by Basinski [9,10] and later confirmed [11],

although not everyone is in agreement [12].

The adiabatic heating model is plausible at 4 K because of the very

strong changes of specific heat (large decrease) and flow strength

(large increase) as temperature is lowered from room temperature to 4 K.

Many materials exhibit these trends, and serrated flow behavior is also

widespread [13]. For AISI 310S, the specific heat shows a 200-fold

reduction between 295 and 4 K [14]. Thus, the amount of thermal energy

necessary to produce an appreciable temperature rise is relatively low

at 4 K.

The adiabatic heating mechanism might be pictured as follows:

Heating during dislocation movement causes appreciable softening, and

deformation becomes unstable. Low thermal conductivity at 4 K (compared

with that at 295 K) contributes to a localization of the heat to produce

load instability. During instability the load drops suddenly and the

plastic flow becomes localized when thermal softening due to heat generated by plastic straining is greater than the strain-rate hardening.

154
The instability is eventually arrested at some strain and temperature

where the flow process becomes stable, owing to local specimen strain

hardening that distributes the load over an ever-increasing area at a

time when the rise of specific heat precludes continued temperature

increases. Once the flow has become stable again, the specimen cools to

4 K, and with further deformation, the process repeats.

As noted in the text, the tensile and fracture test records at 295

and 76 K (not shown) do not exhibit serrations. In fact, serrations of

the type occurring at 4 K are seldom observed at temperatures above

40 K. The instability criterion is satisfied only at the lowest temperatures because 1) the volume specific heat is reduced so that relatively large temperature increases are possible in straining and 2) the

flow stress is more strongly temperature dependent.

Test Methodology

According to the proposed convention [5], two offset lines for data

qualification are drawn parallel to the blunting line at Aa = 0.15 and

1.5 mm, and data falling outside the specified interval are discounted.

Although two data points in Fig. 5 do fall outside the specified interval, both lie on the linear regression line and so were used in the

analysis of results. The near agreement of our single- and multiplespecimen results is taken as evidence that the deviations from the

recommended guidelines are not sufficient to invalidate the conclusions

of this study.

The experimental evidence for AISI 31 OS shows that the initiation

of crack extension at 4 K occurs at a point after the first serration

and before the maximum load. Therefore, taking the first load drop or

155
the maximum load point as the Jj measurement point is an inaccurate

procedure for austenitic stainless steels at 4 K. The unloading compliance technique used here enables Jj to be measured at 4 K with good

accuracy (uncertainty = ±15%), but gives an inaccurate resistance curve

slope (dJ/da). The multiple-specimen technique gives both parameters

accurately, but is more costly in materials and time. Normally, as many

points as desired can be obtained in the single-specimen technique. But

owing to the serrated loading behavior at 4 K, fewer data points are

obtained than usual, since unloadings cannot be performed at points of

instability on the load-versus-deflection curve.

Martensitic Phase Transformations

The role of martensitic phase transformations on fracture toughness

is a subject of fundamental interest, with potential practical applications in the development of austenitic stainless steels. Apparently,

the effects are different for different steel families. Two opposite

trends have been observed:

1) Since martensitic phases forming in metastable austenitic

steels have hep or bcc structures which are typically brittle at 4 K,

it might be expected that transformations at cryogenic temperatures

could reduce the fracture toughness, as in AISI 200 series stainless

steels [15].

2) Since the martensitic phases forming in metastable steels can

absorb energy that otherwise might be converted to crack extension, it

might be expected that these transformations could improve fracture

toughness, as in TRIP steels at 295 K [16].

156
Neither of these trends was observable in our study. From a

simple comparison of stable and transforming steels having similar yield

strengths (as in Fig. 5), we observed that the effects of phase transformation on toughness were negligible for the compositions studied.

Unfortunately, it is not possible to vary the alloy stability while

holding the composition constant. The relative stability of the Fe-CrNi-Mn steels in Fig. 5 is a function of composition and is strongly

dependent on nickel content. The unstable Fe-18Cr-8 to 1 ONi steels

featured in this comparison transformed locally to as much as 90% bcc

martensite, as measured from x-ray examination of the 4 K fracture

surfaces. Such large amounts of martensite were formed gradually with

increasing plastic strain. The initial transformation began locally at

slip plane intersections, and high percentages of bcc phase were detectable only after extensive plastic deformation. Significantly,

fracture surface appearance remained dimpled,. as is the case for stable

steels. The martensite phase transformation did affect the strainhardening behavior of tensile specimens, but how this relates to the Jj

results is not clear.

CONCLUSIONS

J-integral tests were performed on 25-mm-thick compact specimens of

AISI 31 OS stainless steel immersed in liquid helium at 4 K. The major

conclusions are:

1) The unloading compliance technique used here at 4 K gave a

reasonably accurate Jj

c value but an inaccurate J-Aa slope. Improvements to reduce the error in inferred Aa values and blunting line deviations are needed. Side gooves may help.

157
2) Serrations resembling "pop-ins" occurred in the 4 K test

records of compact fracture specimens, analogous to the serrations

observed in conventional tensile tests of unnotched specimens. These

serrations are thought to be caused by plastic flow instability and are

not necessarily associated with true crack extension. Therefore, Jj

should not be measured at the first "pop-in," unless it is demonstrated

that crack extension is the true cause of the instability.

3) The failure mode for this AISI 310S steel at 4 K was ductile

tearing. This same tearing mechanism was associated with both stable

and unstable regions of the load-deflection fracture test record.

4) Comparison of existing data for steels in the Fe-Cr-Ni-Mn

family shows a universal rate of decrease of fracture toughness with

increasing yield strength at 4 K, regardless of whether martensitic

phase transformations occur, suggesting that structural stability does

not necessarily influence toughness.

158
REFERENCES

1. Reed, R. P. and Tobler, R. L., in Advances in Cryogenic Engineering -

Materials , Vol. 28, Plenum Press, New York, 1982, to be published.

2. Ledbetter, H. M. , Weston, W. F., and Naimon, E. R., Journal of

Applied Physics , Vol. 46, 1975, pp. 185-194.

3. Tobler, R. L., Read, D. T. , and Reed, R. P., in Proceedings of the

Thirteenth National Symposium on Fracture Mechanics , American

Society for Testing and Materials, Philadelphia, to be published.

4. Tobler, R. L. and Reed, R. P., in Advances in Cryogenic EngineeringMaterial s , Vol. 28, Plenum Press, New York, 1982, to be published.

5. Clarke, G. A., Andrews, W. R. , Begley, J. A., Donald, J. K.,

Embley, G. T., Landes, J. D. , McCabe, D. E., and Underwood, J. H.,

Journal of Testing and Evaluation , Vol. 7, No. 1, 1979, pp. 49-56.

6. Logsdon, W. A., Wells, J. M. , and Kossowsky, R., in Proceedings

of the Second International Conference on Mechanical Behavior

of Materials , American Society for Metals, Metals Park, Ohio, 1976,

pp. 1283-1289.

7. Reed, R. P., Tobler, R. L., Elmer, J. W., McHenry, H. I., and

Yushchenko, K. A., in: Proceedings of the International Cryogenic

Engineering Conference , ICEC 8, Rizzuto, C., Ed., IPC Science and

Technology Press, Guildford, Surrey, England, 1980.

8. Powell, G. W., Marshall, E. R. , and Backofen, W. A., Transactions

of the ASM, Vol . 50, 1958, pp. 478-497.

9. Basinski, Z. S., Proceedings of the Royal Society , Vol. A240, 1957,

pp. 229-242.

159
10 . Basinski, Z. S., Australian Journal of Physics , Vol . 13, 1960,

pp. 354-358.

11. Read, D. T., in Advances in Cryogenic Engineering-Materials ,

Vol. 28, Plenum Press, New York, 1982, pp. 91-101.

12. Obst, B. and Pattanayak, D. in Advances in Cryogenic EngineeringMaterials , Vol. 28, Plenum Press, New York, 1982, to be published.

13. Wessel, E. T., Transactions of the ASM , Vol. 49, 1957, pp. 149-172.

14. Corsan, J. M. and Mitchem, N. I., in Proceedings of the Sixth

International Cryogenic Engineering Conference , IPC Science and

Technology Press, Guildford, Surrey, England, 1976, pp. 342-344.

15. Brickner, K. G. and Defill ippi, J. D., in Handbook of Stainless

Steels , D. Peckner and I. M. Bernstein, Eds., McGraw-Hill, New York,

1977, Chapter 20.

16. Gerberich, W. W., Henings, P. L., Zackay, V. F., and Parker, E. R.,

in Fracture 1969 , P. L. Pratt, Ed., Chapman and Hall, London, 1969,

pp. 288-296.

160
Table

1.

Mechanical

Properties

of

AISI

310S

Stainless

Steel

cO

to

to

a)E

-aE

fO

O

m co =3: CD ^ i

DC

r

a2uo

O'

rt CO

a>E

<CE

r—

O140 OO EO• r—

+-> o

23 "O

CD DCEO

•r—

CO

O OO CD

05*3- =3- OO EO E

r— 1—

LU

-E

+-> 05E

05E

4-5 00

(O

O 05

a; a. UD

4-> s; CD CM

cO i

E

•f—

4-5 r—

ZD

r\ -E

4-> 05E

0)E

4-> OO CO D_ r— LCD -o S LD *3" r— CM CD

a>

•i

>-

05E

=3

4-> cO CD E CZ 05 *3" 05 CM ClE

05 1—

CM I I OO

05

CMO

C/5 4-> COEEO

to

too

Q-oE

(O

CO Q_

CD

CDOCM

to

23

-ao

toCDE

=5O

>-

+-> cO 4-> cO

"O

OJe

=5to

to

<o 4-> t—I

cO 161
Table 2. J-Integral Fracture Results* for AISI 310S at 4 K

Specimen

No.

a , o’ mmB,mmw,mmJ,

kJ/m

2 Aa

,

mm

1 31.267 25.489 50.8 475 0.673

4 31 .953 25.400 50.8 900 2.304

6

a 31.318 25.456 50.8 413 1.019

7 30.328 25.400 50.8 654 1.290

8 30.378 25.400 50.8 387 0.313

10 30.683 25.476 50.8 621 1.173

x

b 29.718 25.253 50.8 482 0.432

J = 360 kJ/m2

; Ki c

(J) - 285 MPa»m^ 2

where Kj

c (J) is estimated us

i

—

i

o

c_. IIc_, 1

—

1

o

• m 1/2

) ‘ where E = E/(l-v 2

)

== 226 GPa

abnormally low toughness (excluded from analysis).

b reannealed and side grooved 22.860 mm)

.

162
List of Figures

1. Typical load-versus-diffraction curve for AISI 310S steel at 4 K.

2. Fractural compact speciman of AISI 310S steel, tested at 4 K.

3. Scanning electron Microscope picture of AISI 310S compact tensile

specimen fracture surface.

4. J-versus-Aa curve for AISI 31 OS using single-specimen technique.

5. Computed directly measured J-versus-Aa curves for AISI 31 OS using

multiple-specimen technique.

6. Fracture toughness versus tensile yield strength for many austenitic

stainless steels, all measured at 4 K.

163
Load,

AISI 310 S

Figure 1. Typical load-versus-diffraction curve for AISI 310S steel at 4 K.

164
Figure 2. Fractural compact speciman of AISI 31 OS steel, tested at 4 K.

165

1

inch
166

Figure

3.

Scanning

electron

microscope

picture

of

AISI

31OS

compact

tensile

specimen

fracture

surface.
Figure 4. J-versus-Aa curve for AISI 310S using single-specimen technique.

167
-

Integra

I

, J

(k

J-m

2)

Crack Extension, Aa(mm)

Figure 5. Computed directly measured J-versus-Aa curves for AISI 31 OS using

multiple-specimen technique.

168
stainless steels, all measured at 4 K.

169

MECHANICAL PROPERTY MEASUREMENTS AT LOW TEMPERATURES*

D. T. Read and R. L. Tobler

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

The status of mechanical test methods for the liquid-helium temperature

range is reviewed. Fracture toughness testing and the use of toughness data

are emphasized. Facilities and test methods for fracture toughness, fatigue

crack growth rate, tensile, and elastic properties at NBS in Boulder are

described. Apparatus and techniques for temperature measurement and control

during mechanical tests are briefly discussed.

*To be published in Advances in Cryogenic Engineering-Materials, Yol . 28,

A . F. Clark and R. P. Reed, Eds., Plenum Press, New York (1982).

171

INTRODUCTION

Accurate material mechanical properties data at low temperatures are essential for design of economical, efficient, and safe

structures for low temperature operation. Fracture toughness,

tensile properties, and fatigue crack growth resistance characterize the mechanical performance of structural materials. Because

construction of a sizeable welded structure free from geometrical

defects is a practical impossibility, adequate material toughness

is needed to prevent crack growth and eventual fracture at such

defects. Strength and stiffness enable a material to support its

applied loads without stretching or buckling. Adequate fatigue

crack growth resistance allows a part to continue to perform its

function for a lifetime of load cycles. Compromises among

toughness, strength, and fatigue resistance are required because

no one material is best in all properties and because economy in

material costs is necessary.

Previous papers 1-1 have described our earlier apparatus and

techniques for obtaining mechanical property data at low temperatures. In this paper improved measurement techniques for toughness, strength, and fatigue resistance are described. Some brief

remarks on the use of the data are also included.

MEASUREMENT TECHNIQUES

Fracture Toughness

Fracture toughness is the measure of a cracked material's

resistance to tearing and fracture. The most direct measurements

173
of this property are considered to be the fracture mechanics

toughness tests in which K , the critical stress intensity

factor for mode I fracture, or J , the critical J-contour

1 c integral for mode I fracture, are measured. The stress intensity

factor is better-established theoretically and in practice, but

it is only applicable to very large specimens or low-toughness

material. The J-integral is additionally applicable to relatively

small specimens of high-toughness material. The J-R (resistance)

curve concept allows characterization of a material by its crack

propagation resistance over a range of crack extensions instead

of only at the initiation of tearing.

All of these techniques employ a specimen with a fatiguesharpened crack; the specimen is extended to failure in the

low-temperature environment of interest while load and displacement values are continuously measured. Quasistatic loading is

used routinely. The loading may be mono tonic and continuous or

it may be interrupted by periodic partial unloadings. The load

and displacement values are analyzed according to various standard

procedures to obtain L , J T , or a J-R curve.

Ic Ic To date, compact specimens 25 x 61 x 64 mm have been routinely

used, primarily because they offer a high toughness measurement

capability for their size. But 3-pt bend specimens (25 x 25 x 114 mm) are now being developed for J-integral tests at 4 K. The

bend specimen is less expensive to machine.

Apparatus to cool the fracture toughness specimen to 4 K,

extend it to failure in a controlled fashion, and sense and

record load and displacement throughout the test are required.

The apparatus at NBS/Boulder is based on a commercially-supplied

servohydraulic testing device capable of extending a specimen

under load or displacement control with loads up to 100 kN and

displacements of up to 10 cm. The hydraulic actuator which

supplies the load is mounted vertically at the top of the device.

Tensile loads are transmitted through a load cell at room temperature, along a pull rod to the upper clevis grip (Fig. 1). The

specimen is pinned to the upper and lower clevis grips (Fig. 2)

.

The lower clevis grip is attached to a compressive load frame

which transmits the reactive load back up to the actuator mount.

This re-entrant scheme allows the use of conventional dewars

without low temperature force feedthroughs.

Load is sensed by a conventional commercially-supplied load

cell in the room- temperature environment. Displacement is sensed

by a clip gage which is mounted on knife-edges spot-welded onto

the specimen at the load line and retained by the spring action

of the gage beams. These gages are either fabricated in-house or custom-built by a local supplier. The electrical signals from

174
Fig. 1 Low temperature fracture

toughness testing apparatus in use at NBS/Boulder.

the load and displacement gages are conditioned using the conven- tional circuitry built into the commercially supplied mechanical

testing system.

An earlier paper 1 described an elaborate 2 h cool down

procedure, involving installation of copper baffles around the

load frame members, sealing the cryostat lid, and vacuum pumping

of the liquid nitrogen precoolant to reduce its temperature below

76 K. However we usually prefer the following alternative

procedure, which eliminates the baffles and the time consuming

steps involving mechanical pumping. After precooling the cryostat

to 76 K, the dewar of liquid nitrogen is removed, emptied, and

replaced in 30 s . Helium transfer then begins. The use of an outer dewar of liquid nitrogen (double-dewar arrangement) is also

dispensable, especially when the test will be of short duration.

This procedure reduces the time to accomplish cool-down to about

40 minutes, at the cost of several additional liters of liquid

helium.

Several improvements have been made to the instrumentation.

Instead of the carbon resistor liquid level indicator previously

used 1

, we now have a 30 cm continuous liquid level monitor which

attaches to one of the cryostat load frame columns. This meter

175
Fig. 2 Fracture toughness test specimen,

clevis grip, and clip gage.

gives a continuous read out of the helium level in the cryostat

and its relation to the specimen, rather than a simple on/off

indication. Flexible transfer lines with vacuum jackets have

replaced the former rigid transfer lines.

We have also replaced the previous fiberglass-reinforced

plastic dewars with stainless steel dewars. The fiberglass

dewars are more thermally efficient 1

, but leaks that were very

difficult to repair developed after 1 or 2 years of service. The

stainless steel dewars offer fewer maintenance problems. Glass

dewars were used briefly, but these are fragile and eventually

get broken.

We have found that most of our apparatus problems in toughness testing occur because of a malfunctioning clip gage. The

gage must be able to survive many thermal cycles between room and

liquid helium temperature, with attendant moisture and freeze-up

problems, while maintaining its linearity and accuracy. The ring

design clip gage (Fig. 2) is a departure from the double-cantilever beam style displacement gages recommended in the ASTM E 399-

74 Method. The new design consists of an aluminum alloy ( 7075—

T651) ring which is slotted to accept short beams fabricated from

17-7 PH stainless steel. The rear of the ring is reduced in

thickness and provides the bending member onto which four electrical resistance strain gages chosen for good low temperature

performance are mounted. The linear operating range is from 2.5

to 7 mm of opening displacement (higher operating ranges are possible) . Sensitivity is greater and linearity is improved, as

176
compared to double-cantilever designs of the ASTM E 399-74 type.

Conventional laboratory-quality signal conditioning circuitry is

adequate to read out the displacement signal if it contains no excessive electrical noise. Noise can come from inadequate

solder joints, a conductive film of debris on the gage surface, or other sources. Well constructed gages can survive millions of

fatigue cycles and tens of tests at 4 K. The mechanical apparatus

shown in Figs. 1 and 2 has endured hundreds of fracture toughness

tests

.

A recent addition to the NBS/Boulder test apparatus is a minicomputer system for data acquisition, storage, and real-time

analysis. The details of this system are described elsewhere-

.

The signals are applied to the input of a high-resolution analogto-digital converter, from which their values are transmitted to a minicomputer. In the computer, load-displacement data are stored on floppy disk. To conduct a single-specimen J-integral

test, periodic unloadings are performed under manual control to

obtain the instantaneous crack length by the compliance technique.

This involves execution of a sub-program for extracting the

specimen compliance from load and displacement data. The Jintegral is also calculated from load and displacement data. The

computer plots each crack length J-integral data point as soon as

it is acquired. This provides the operator with guidance for

taking the next data point. The loading is under control of the

operator through the machine console; only the data acquisition

is done by computer. This apparatus and cooldown procedure allow

up to four low-temperature toughness tests to be conducted in an

8 h day by the undergraduate and graduate students who conduct our tests.

The single-specimen unloading compliance technique enables

Jj. to be measured with good accuracy, but gives an erroneous measurement of tearing modulus, that is, dJ/da, because of errors

in the crack extension, Aa. The discrepancy between actual and

compliance-measured Aa increases progressively with Aa. Since

this error is less at low Aa values, the J measurement from the

single— specimen technique is reasonably accurate (within 5c of

the value measured when the multiple specimen method) but the

slope of the resistance curve is inaccurate. Comparison of

results from both methods for AISI 310S at 4 K are shown in

Fig. 3.

Measurement uncertainties in individual J values are con sidered to be 5% or less, while the bias due to systematic error

xn the inferred Aa values contributes an uncertainty ot 10.- oi

less to the J

T measurement. The cumulative uncertainty in J

values is estimated to be ±15% or less, so the measurement

uncertainty in K^. values inferred is 8% or less, since is

177
proportional to /j . If errors in fracture toughness associated

with material variability are large, the accuracy of J results

will be further limited.

Strength

In this era of computerized fracture toughness testing the

most familiar mechanical property, strength, must not be neglected.

Tensile testing provides the material yield strength, ultimate

strength, elongation to failure, and reduction of area. Elastic

constants are measured to within ±2% at NBS/Boulder by soundpropagation techniques using separate specimens and apparatus’4

.

Again, apparatus to cool tensile specimens to 4 K, extend

the specimen to failure in a controlled fashion, and sense and

record load and displacement is used. Screw-driven, mechanically

controlled devices are in use at NBS/Boulder for tensile testing

(Fig. 4) . These machines are more economical in initial cost and

laboratory space than the hydraulic testing machines, and tensile

testing does not require rapid testing machine response. Load is

CRACK EXTENSION, Aa (mm)

Fig. 3 Graph of J-integral versus crack extension for AISI 310S

at 4 K. Crack extension values obtained from the compliance

technique using one specimen (open circles) are compared with

optically measured values from five specimens.

178
Fig. 4 Low temperature tensile

testing apparatus in use at

NBS/Boulder

.

transmitted from the fixed upper crosshead with built-in load

cell down a pull rod to the upper specimen grip. The reactive

load is transmitted from the lower grip through a compression

tube to the moving crosshead of the machine. Conventional glass

or stainless steel dewars without force feed-throughs are used

for immersion of the specimen in cryogen during the test. The

extension of the specimen within its gage length is sensed by a cantilever beam gage whose two arms are attached to the specimen

at the ends of the gage section (Fig. 5) . The gage is clipped in

between retaining pins which are fixed to the specimen. When the

specimen has been extended to about 10% strain, the gage simply

falls away. The gages are fabricated in-house or custom made by

a local supplier. Calibrations are conducted at each test

temperature using a vertically mounted dial micrometer.

The yield and ultimate strengths are calculated in the usual

way from the measured load and strains. Uncertainties in tensile

flow strength measurements are estimated at ±2% or less, owing to

uncertainties in specimen dimensions, load values as read from

recorder traces, and (for yield strength) specimen strains from

the extensometer . The elongation and reduction of area are obtained conventionally from specimen dimensional differences

before and after testing.

Flow stress data at temperatures intermediate between the

boiling points of the common cryogens are obtained by controlled

179
Fig. 5 Cantilever beam extension gage

attached to tensile specimen.

thermal conduction using liquid helium or nitrogen reservoirs and

heaters. The experimental arrangement shown in Fig. 6 has been

used in several studies. The specimen is cooled by two cryogen

reservoirs, one at the bottom of the push tube and the other

mounted on the pull rod. The specimen is heated by electrical

resistance heaters wound on each grip. The specimen temperature

is sensed by two diode thermometers, one mounted at each end of

the gage section. The current to the heaters is controlled so that the thermometers, and so the specimen, remain at the desired

temperature (±1 K) . With this apparatus temperatures from 4 to

300 K can be obtained in metal specimens. Nonmetal specimens

must be surrounded by a thermal shield controlled at the desired

test temperature.

In a recent series of experiments, capacitive sensing of

specimen extension was used. Concentric aluminum cylinders, one mounted to each grip, form the two capacitor elements (Fig. 7)

.

A capacitance bridge and a lock-in amplifier were used to detect

specimen extension. This apparatus was needed because attachment

of conventional extensometers to soft viscoelastic foams could

have influenced the measured material properties. The noise

level of the displacement signal was about 0.3 microns. This

could be reduced by at least one order of magnitude for

measurement on metals by reducing the separation between the

capacitance cylinders. In this apparatus the inner capacitor

180
Fig. 6 Experimental arrangement for tensile testing

at temperatures above cryogen boiling points.

tube also served as a thermal shield, allowing the temperature of

the thermally non-conductive foam to be accurately controlled 5

.

Fatigue

The fatigue lifetime of a structural component is characterized by its fatigue crack growth rate (FCGR) . In our laboratory

the servohydraulic apparatus described earlier is also used for

fatigue tests. The specimens used are the same for or J __ testing, but shorter initial crack sizes are specified.

The compliance method of FCGR measurement is the most

suitable method for cryogenic testing. The technique is applicable at all temperatures, even if the specimen is enclosed in a cryostat and inaccessible. It is based on the correlation

between compliance (specimen deflection per unit load) and crack

length: compliance increases as crack length increases. This

method offers advantages for testing thick specimens, because

crack-front curvature is accounted for in the average crack

length derived from the compliance value.

The procedure previously described is illustrated in Fig. S. The specimen is loaded cyclically at a selected load range and at

181
Fig. 7 Capacitance extensometer

assembly for foam specimen

testing.

a frequency of 20 Hz. At intervals ranging from 100 to 20,000

load cycles (N) , the specimen compliance is recorded and used to

obtain the instantaneous crack length. The FCGR is simply the

change in crack length per cycle, which is calculated as the

slope of the a-versus-N curve at a given value of a. The cycle

number is easily monitored by electronic or mechanical counters.

To calibrate this method, crack front striations on specimen

fracture surfaces are created by changes in the minimum fatigue

load. After breaking open the calibration specimen, the values

of a are measured, averaged, and plotted against their compliance

values. The resultant curve is fit using the appropriate polynomial expression, which in turn is used to infer crack lengths

from compliance data recorded during FCGR tests.

The FCGR data are commonly plotted against the cyclic

applied stress intensity factor range (AK) , which is calculated

from load, crack length, and specimen dimensions. Uncertainties

of measurement and material variability may be significant, and

standard deviations of 20 to 40% from the average value of FCGR

at a given AK value are typical for our results. The accuracy of

FCGR data can be degraded if highly variable materials such as welds are tested.

182
Fig. 8 Compliance method for measurement of fatigue crack

growth rate da/dN using the specimen compliance.

USE OF TOUGHNESS AND STRENGTH DATA

A structure can tear and fracture because of inadequate

toughness or inadequate strength. Toughness is required in large

sections with cracks of large absolute size. Strength is a problem in smaller sections with cracks which may be small on an absolute scale but are large relative to the section size. An

estimate of the size scale of interest for cracks can be made

from a fracture mechanics formula for stress intensity. In a material whose yield strength is 850 MPa and whose toughness is

150 MPafm, a crack of large absolute size would be one over about

1 cm in length (through crack) . A large section dimension would

be one greater than 10 cm. In large sections, the critical

stress intensity factor can be reached before the section yields,

producing failure at loads "lower than expected." The greater

the material toughness, the larger the crack that can be tolerated

at a given load. If the material toughness is improved and

permitted cracks get larger, or if the size of the section is

scaled down with crack size held constant, the section containing

a crack can yield before crack extension. Once a section has

reached yield, it will extend at a nearly constant load until the

load is relieved or the section fails. The critical factor in

such a case is the material strength. Higher strength holds off

section yielding to a higher load. Higher toughness will allow

183
slightly more yield-load extension before fracture, but the

amount is small, of the order of millimeters or less. From these

considerations it is clear that inspection for large defects is

necessary to insure fracture prevention in severely loaded structural members.

CONCLUSION

Techniques are described for the measurement of fracture

toughness, tensile properties (including yield and ultimate

strengths, elongation to failure, and reduction of area) and

fatigue crack growth rates at temperatures down to 4 K. Accuracy

is generally limited by specimen-to-specimen variation.

ACKNOWLEDGMENTS

J. Shepic contributed by designing and building the cryogenic

clip gages. This work was supported by the U.S. Department of

Energy, Office of Fusion Energy.

REFERENCES

1. R. P. Reed, "A Cryostat for Tensile Tests in the Temperature

Range 300 to 4 K, " in: Adv. Cryo. Eng., 1_ (1961) 448-454.

2. C. W. Fowlkes and R. L. Tobler, "Fracture Testing and

Results for a Ti-6A1-4V Alloy at Liquid Helium Temperature,"

Eng. Fract. Mechs., 8^ (1976) 487-500.

3. R. L. Tobler, D. T. Read, and R. P. Reed, "Strength and

Toughness Relationship for Interstitially Strengthened

AISI 304 Stainless Steels at 4 K," in: Fracture Mechanics:

Thirteenth Conference, ASTM STP 743, to be published.

4. H. M. Ledbetter, N. V. Frederick, and M. W. Austin, "Elastic

Constant Variability in Stainless Steel 304," J. Appl.

Phys., _51 (1980) 305-309.

5. J. M. Arvidson, "Capacitive Technique for High- Sensitivity

Low Temperature Extension Measurement," to be published.

184
*Published i

PREDICTED SINGLE-CRYSTAL ELASTIC CONSTANTS

OF STAINLESS-STEEL 316*

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

n British Journal of Non-destructive Testing, Vol . 23, 2S6 (1981

)

185

286 BRITISH JOURNAL OF NDT November 1981 Predicted Single-Crystal Elastic

Constants of Stainless-Steel 316

H. M. Ledbetter, B.Sc., M.Sc., Ph.D.

For stainless-steel 316, the author gives an improved prediction of the three CiJ elastic-stiffness constants, which determine the optimum

direction for acoustic beams used to locate and size flaws. The predictive method applies generally to all cubic-crystal-structure anisotropic

materials.

1.

Introduction

Since the late 1800's, single-crystal elastic-stiffness constants have provided considerable understanding of the mechanics, chemistry, and physics of crystals. These constants, the Q/s in Voigt's notation, relate to many fundamental

solid-state phenomena. For example: interatomic potentials,

lattice-defect energies, theoretical strength, diffusion, and

Debye characteristic temperatures.

Technologists, that is, those concerned with technological

materials such as steels, have largely ignored these constants. Most technological materials show macroscopic isotropy.

They are completely characterised elastically by two independent elastic constants: for example, the Young modulus, E, and the Poisson ratio, v, the two constants that arise naturally

in describing a uniaxially loaded rod. Elastic constants appropriate to other loading configurations—shear, torsion,

hydrostatic stress, etc. —can be computed simply from E and v. More recently, technologists are increasingly recognizing

the value of single-crystal elastic constants for revealing

anisotropy-related behaviour of engineering materials. Effects of anisotropy on ultrasonic propagation in solids were re- viewed by Smith and Stephens0 \

Several authors* 2 _4> have emphasized the importance of

the Q/s for studying welds, where elastic anisotropy enters two ways. First, as the anisotropy of individual crystallites, which can be indexed for cubic crystallites by Zener’s aniso- tropy ratio ^=2QV4/(C11-C12)=C44/C’ (1)

Second, as a nonrandom (preferred) distribution of

crystallite orientations. Called ‘texture’, this anisotropy arises from the welding process where heat flow and solidification do not proceed randomly.

Quite recently. Silk, Lidington, and Hammond*4 ’ investi- gated theoretically the propagation of ultrasound in a model

stainless-steel-316 weld, and found it necessary to estimate

this alloy’s C,/s, which remain unmeasured. For cubic symmetry there are three independent Q/s, usually Cllt C12 , and C44 . In this application the Q/s are useful in several ways: (1) as an overall anisotropy indicator—as A approaches

unity, anisotropy effects disappear; (2) for determining the deviation of the directions of wave propagation and energy

flux; (3) to determine the optimum acoustic-beam angle for studying a weld; (4) to allow computation of velocity, slowness, and wave surfaces, which are useful for interpreting nuances of acoustic waves in anisotropic media. Kupperman

and Reimann(3) give many further references that show the importance of the Q/s for ultrasonic weld studies. The present paper gives an improved method for predicting the three stainless-steel-316 single-crystal elastic stiffnesses. Compared with the results of Silk et al., they differ by —9, 0, and +7 per cent for C1X , C12 , and C44, respectively. These

The author is with the Fracture and Deformation Division,

National Bureau of Standards, Boulder, Colorado 80303, USA.

differences are significant for the applications described above. The prediction method uses existing isotropic polycrystalline elastic constants and a theory due to Kroner0 ' for relating the single-crystal and polycrystal elastic-stiffness tensor. The

method is quite general, being applicable to other austenitic

steels, to ferritic steels, and indeed to any material.

2.

Theory

Especially for cubic crystal symmetry, the problem of re- lating the single-crystal elastic constants (CX1 , C12 , C44 ) to the quasi-isotropic polycrystalline elastic constants (B, G) has been studied extensively, both theoretically* 6 ’ and experimentally<7)

. The bulk modulus, B, because it is a rotational in- variant of the elastic-stiffness tensor, is always given by

5=(C11 +2C12)/3, (2)

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

single-crystal inclusion embedded in a corresponding

tropic matrix, and assuming stress equilibrium at the interface. Kroner* 5 ' showed that G

3 +<xG 2 +(3G+y=0 (3)

where

«=(5C11 +4C12)/8 (4) P= — Q^aCn—4C12)/8 (5) and

y = -C44(C 11 -C12) (Cu+2C12)/8. (6)

In the forward case, these relationships permit the calcuia; on

of B and G from the Q/s, the isotropic from the anisotropic, two elastic constants from three. With one additional piece of information, fremeithcr hoo: > or observation, from some single relationship among the Q/s, the reverse-case can be computed also. 1 he c s can be computed from B and G.

3.

The Present Case: Stainless

Steel 316

For a relationship among the Q/s of stainless steel 5 1 6, we

consider the existing Q, measurements on f e e. Fe-Cr-Ni

alloys summarized in Fable I. At leas relationships emerge. First, the elastic anisotrop> ;s re ..: \c > constant, being 3.51/ 0.19. Second, the ' t , Q mco >

relatively constant, being 0.642 0.03". Ledbetter'* showed

that a slightly better y value results if values for c c Fe and

Ni are also included with these four alloys, r ue v=0.635±0.031. Tablet probably contains other Q relationships. But these two are simple and sufficient. For B and G values, we use those reported by Ledbetter 1 *' B=1.575±0.014 and G=0.752±0.0I5.10‘ 1 N nv

:

.

187
November 1981 Predicted Single-Crystal Elastic Constants of Stainless-Steel 316 287

4. Results

Table I contains the results of two calculations of the Q/s

of stainless steel 316. Both calculations involve eqs. (2) and

(3). The first assumes .y =0.635; the second assumes A =3.51. The bottom line of Table I averages the two calculations.

5. Discussion

The present theoretical CtJ results in Table I seem quite

satisfactory on several counts: both cases agree exactly with observed B and G values; both give reasonable A values; both

Cn and C12 agree within one percent; C44 agrees within five per cent. Why A remains relatively constant among these alloys re- mains unexplained. For f.c.c. crystals, in a central-force model, nearest-neighbour-only interactions require that A =2.

Deviations from this indicate significant noncentral forces between (or among) atoms. Excluding as somehow anomalous

those f.c.c. elements where A <2 (Al = 1.22, Ir = 1 .56, Pt =

1.59), we find that the average A for f.c.c. elements is 3.17/r

0.52 (Ni=2.66, Pd=2.81, Au = 2.85, Ag=2.88, Cu = 3.27, Th = 3.62, Pb=4.07). Thus, Fe-Cr-Ni alloys have typical A

values. High A values indicate a high vibrational entropy and

a tendency toward mechanical instability0 3)

. Similarly, the relative constancy of y = C12/C11 remains

unexplained. For an f.c.c. nearest-neighbour-only central- force model, y=0.50. Ledbetter0 ° showed that volumedependent energy terms tend to increase y above this value. In summary, this study focuses on a theoretical method for predicting the single-crystal elastic constants, the Q/s, of

cubic materials. The method requires two polycrystalline

elastic constants and a Cu interrelationship determined either from observation or from theory. We believe the stainless- steel-316 Q/s predicted in this study are the best values now

available. These elastic constants are useful for many purposes, including the ultrasonic nondestructive evaluation of

welds. Future studies by the author will use these results to predict the effects of texture on elastic-wave propagation

through welds.

References

1

Smith, R. T. and Stephens, R. W. B. Effects of anisotropy on ultrasonic propagation in solids. Progress in Applied

Materials Science, Volume 4. National Trade Press, London, 1964, pp. 4-64.

2. Dewey, B. R., Adler, L., King, R. T. and Cook, K. V.

1977. Measurements of anisotropic elastic constants of

type 308 stainless-steel electroslag welds. Exper. Mech.

17, 420^126.

3. Kupperman, D. S. and Reimann, K. J. 1980. Ultrasonic wave propagation and anisotropy in austenitic stainless

steel weld metal. IEEE Trans. Sonics Ultrason. SU-27,

7-15.

4. Silk, M. G., Lidington, B. H. and Hammond, G. F. 1980. A time domain approach to crack location and sizing in austenitic welds. Brit. J. NDT 22, 55-61.

5. Kroner, E. 1958. Berechnung der elastischen Konstanten

des Vielkristalls aus den Konstanten des Einkristalls. Z. Phys. 151, 504-518.

6. Ledbetter, H. M. and Naimon, E. R. 1974. Relationship

between single-crystal and polycrystal elastic constants.

J. Appl. Phys. 45, 66-69.

7. Ledbetter, H. M. 1980. Sound velocities and elastic- constant averaging for polycrystalline copper. J. Phys.

D: Appl. Phys. 13, 1879-1884.

8. Salmutter, K. and Stangler, F. 1960. Elastizitat u. Plastizitat eines austenitischen Chrom-Nickel-Stahls. Z. Metallkde. 51, 1-4.

9. Kikuchi, M. 1971. Elastic anisotropy and its temperature

dependence of single crystals and polycrystal of 18-12

type stainless steel. Japan. Inst. Met. 12, 417^121.

10. Mangalick, M. C. and Fiore, N. F. 1968. Orientation dependence of dislocation damping and elastic constants

in Fe-18Cr-Ni single crystals. Trans. Met. Soc. AIME

242, 2363-2364.

11. Ledbetter, H. M. 1981. Predicted single-crystal elastic constants of stainless steel 304. To be published.

12. Ledbetter, H. M. 1980. Sound velocities and elastic constants of steels 304, 310, and 316. Metal Sci. J., forthcoming.

13. Zener, C. Elasticity and Anelasticity of Metals. Univ.

Chicago Press, Chicago, 1948, p. 37. Acknowledgement

Major support for this study came from the DoE Office of Fusion Energy and the NBS Office of Nondestructive

Evaluation. Dr. C. M. Fortunko of NBS pointed out this application of the Q/s together with several valuable

references.

TABLE I

Single-crystal elastic constants of several face-centred-cubic Fe-Cr-Ni alloys in units of 10 1

N/m 2

, except A and y, which are dimensionless

Alloy Cn Ci, C44 B C’ A y Ref.

Experiment Fe-12Cr-18Ni 2.332 1.626 1.225 1.862 0.353 3.45 0.697 8 Fe-18Cr-12Ni 1.912 1.179 1.386 1.423 0.367 3.78 0.617 9 Fe-18Cr-14Ni 1.98 1.25 1.22 1.49 0.365 3.34 0.631 10 Fe-18Cr-19Ni 1.91 1.19 1.24 1.43 0.360 3.44 0.623 10

Theory

Stainless 316 2.261 1.336 1.114 1.644 0.463 2.41 0.591 4*

Stainless 316 2.08 1.32 1.16 1.575 0.380 3.06 0.635 Present

Stainless 316 2.04 1.34 1.22 1.575 0.348 3.51 0.659 Present-2

Stainless 316 2.06 1.33 1.19 1.575 0.365 3.27 0.647 Present-average

Corrected to a mass density of 7.958 g/cm 3 . 188
Manganese contributions to the elastic

face-centered-cubic Fe-Cr-Ni stainless steels

constants of

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of standards

Boulder, Colorado 80303

USA

Abstract

We determined experimentally the effect of manganese on the elastic

constants of Fe-Cr-Ni alloys. By a pulse-echo-overlap method,

longitudinal and transverse sound-wave velocities were determined

in ten alloys containing up to six percent Mn. All the elastic

stiffnesses decrease linearly with increasing Mn. The bulk modulus

decreases most strongly. Poisson's ratio changes least. We

consider what the elastic constants reveal concerning changes in

chemical bonding.

Key Words: Bulk modulus; chromium alloys; elastic constants; iron

alloys; mechanical properties; nickel alloys; physical properties;

Poisson ratio; shear modulus; sound velocities; stainless steel;

Young modulus.

189

Introduction

Manganese decreases the elastic stiffness of bcc Fe.

1 Studies of

alloys containing up to ten atomic percent Mn show a linear decrease in

both Young's modulus, E, and the shear modulus, G. The decrease

amounts to approximately 0.3 percent per atomic percent Mn. Vegard's

law predicts a 0.06 percent decrease for G and a 0.65 percent decrease

for the bulk modulus, B.

Effects of Mn on the elastic stiffness of fee Fe remain unknown.

Manganese's peculiar elemental properties--a 58-atom unit cell, a bulk

modulus 0.35 that of Fe's, anti ferromagnetic electronic interactions,

negative low-temperature thermal expansivity--preclude any reliable

predictions of such effects. Despite the proximity of Mn and Fe in the

first long row of the periodic table of elements, their properties

differ dramatically; Mn dissolved in Fe may behave very differently

from Mn dissolved in Mn. From available elastic constants of fee Ni

and Mn, Vegard's law predicts that Mn lowers all the elastic stiffnesses and Poisson's ratio, v: B by 0.33 percent, E by 0.18 percent, G

by 0.18 percent, and v by 0.16 percent. Here, we assume that the

unknown elastic constants of fee Fe do not differ significantly from

those of fee Ni; because Fe's atomic volume exceeds Ni's by eight

percent, fee Fe may be slightly softer elastically.

Face-centered-cubic Fe-Cr-Ni alloys provide the basis for commercial stainless steels. Manganese also occurs in such steels, mair v

to improve fabricabil i ty and weldability.

191
Effects of Mn on the elastic properties of Fe-Cr-Ni alloys remain

undetermined. Such knowledge of basic mechanical -physical properties

underlies any modeling of macroscopic mechanical properties such as

strength and toughness.

The present study sought to determine how Mn affects the polycrystalline elastic constants of Fe-Cr-Ni alloys containing up to six

2 percent Mn. Such results would test the conjecture that these alloys

should "show large changes in their elastic moduli as functions of

composition." Complete sets of polycrystalline elastic constants were

determined: Young's modulus, shear modulus, bulk modulus, and

Poisson's ratio. The experimental approach consisted of measuring

longitudinal and transverse sound velocities using a pulse-echo-overlap

method.

One may ask also whether Mn affects chemical bonding in Fe-Cr-Ni

alloys. As described above, Mn is truly a maverick metallic element.

3 In considering chemical bonding in both nonmetals and metals, Pauling

referred to "the anomalous Mn radius" and to Mn's "striking abnormality

in behavior." We know that elastic stiffness depends relatively

-4

sensitively on atomic radius, r, varying as r . Thus, Mn's larger

atomic volume arising from magnetic repulsions explains in part its

lower elastic stiffness.

Experiment

Material

s

All alloys are Mn-modified type-304LN face-centered-cubic stainless steels. Custom-composition alloys were obtained from a commercial

steel company in the form of plates approximately 2.5 cm by 14 cm by

41 cm. 192
Each plate was hot rolled at approximately 1175°C (2150°F), annealed

for 0.5 h at 1 06

5

0 C (1950°F), water quenched, and acid pickled. Table

1 shows chemical composition, hardness, mass density, and grain size.

Grain size was measured in the plane perpendicular to the transverseplate direction.

Methods

Sound velocities were determined by a method described in detail

4 previously. Briefly, 1.5-cm cubes were prepared by grinding so that

opposite faces were flat and parallel within 5 ym. Quartz piezoelectric

crystals with fundamental resonances between 4 and 7 MHz were cemented

with phenyl salicylate to the specimens. An x-cut transducer was used

for longitudinal waves and an ac-cut for transverse waves. Ultrasonic

pulses 1 to 2 cycles long were launched into the specimen by

electrically exciting the transducer. The pulses propagated through

the specimen, reflected from the opposite face, and propagated back and

forth. The pulse echoes were detected by the transducer and displayed

on an oscilloscope equipped with a time delay and a microprocessor for

time-interval measurements. The sound velocity was computed by

v = 2 £/ 1 (1)

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

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

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

cycles. Elastic constants were computed from the general relationship

C = pv

2 (2)

193
where p denotes mass density. The usual engineering elastic constants

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

v by

2 longitudinal modulus = = pv^ (3)

2 shear modulus = G = pv

t (4)

bulk modulus = B = C

£ -(4/3)G (5)

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

X/ (6)

Poisson's ratio = v = ( E/2G) -1 (7)

= (l/2)(C

l

-2G)/(C rG)

Results

Table 2 gives for two alloys the variation of sound velocites and

elastic constants with direction. In this table, n denotes propagation

direction and p denotes polarization direction. Table 3 contains the

principal results of the study: for ten alloys the longitudinal and

transverse sound velocities, v„ and v., and the various elastic

l t constants C , G, B, E, v defined in Eqs. (3)-(7). Figure 1 shows these

constants versus Mn concentration. Table 4 contains the results of

linear least-squares fits to these compositional changes. In this

table, a and b have units of the elastic constants. The dimensionless

ratio a/b gives the quantity (l/y)(dy/dx) at x = o, the fractional

change in the elastic constant due to alloying. Also included in Table

4 are predicted values of b/a based on Vegard's law and handbook

elastic constants for Ni and Mn. (Elastic constants of fee Fe are not

available.

)

194
Discussion

First, we consider the possibility of texture. Results in Table 2 indicate the absence of texture in these alloys. For alloy 10, for

example, in three orthogonal directions (corresponding to the rolling

direction, transverse direction, and through-thickness direction) the

longitudinal modulus varies less than 0.1 percent and the shear modulus

less than 0.4 percent. These results agree with those reported

previously for 304 stainless steel. In these alloys the Zener

anisotropy ratio A = 2C44/(C

11 - C 12 ) is approximately 3.5

5

, that is,

moderately high. Thus, significant texture would evidence itself in

£ the elastic constants. Recent calculations by Ledbetter concerning

the elastic constants of textured aggregates show that for 304

stainless steel along principal axes, fiber textures such as <100>,

<110>, and <111> change an average of 11 percent and 6 an average of

19 percent. These elastic constants can be measured readily within a

fraction of a percent. We ascribe the lack of texture to the

thermomechanical treatment: annealing after hot deformation.

We consider now what the elastic constants reveal concerning

changes in the chemical bond when Mn is alloyed substitutional ly into

the fee Fe-Cr-Ni matrix. Essentially, we look for changes in the

degree of covalent bonding, which manifests itself as a resistance to

bond bending, a manifestation of many-body forces. Koster and Franz

concluded that "Poisson's ratio depends to a much greater extent on the

conditions of bonding than do the other elastic coefficients." This

assertion remains without theoretical basis, probably because theory

does not predict directly the Poisson ratio, which is the negative

ratio of two fourth-rank elastic compliances, -SI ./SI^ .

.

,

where

primes denote rotation of the coordinate system.

195
For quasi-isotropic solids, Poisson's ratio is a scalar that relates

simply to the bulk and shear moduli:

v = (1/2) (3B-2G)/ (3B+G) = (l/2)(3y-2)/(3y+l) (8)

where y is defined to be B/G. Thus, the dependence of v can be studied

parametrically as the dependence of y. For cubic elements, Leibfried and

O Breuer give a graph of B/C^ versus elastic anisotropy, being one of the

usual two cubic-crystal elastic shear moduli. They point out that purely

longitudinal first-neighbor spring interactions require that B/C^ = 4/3. For

Voigt averaging, the equivalent ratio for polycrystals is B/G = 5/3; for Reuss

averaging it is 28/15; thus, the Hill arithmetic average is B/G = 280/159

= 1.76. Departure from this ratio indicates that many-body forces occur in

the solid. In terms of a force-constant model, this means that bond-bending

forces must occur along with more familiar bond-stretching (bond-compressing)

forces. One should note that from Eq.(8) it follows that B/G is a more

sensitive parameter than v because for typical v values dv/v = (1/2) dy/y.

Examination of Table 3 shows that B/G = 2.005 ± 0.014 for all ten alloys.

Thus, the marked departure from a value of 1.76 shows that many-body forces

occur in these alloys. That many-body forces exist in transition-metal alloys

g is already well known. The surprising result is that the ratio is nearly

constant for all alloys, indicating no significant change in the character of

the chemical bonding. Table 3 shows that the Poisson's ratio is also nearly

invariant with Mn content: v = 0.286 ± 0.001, but also different from the

v = 0.261 predicted for longitudinal-force-constant-only bonding. As described above, B/G and v must behave similarly.

1 96
In terms of the single-crystal cubic-symmetry elastic constants C^, C^, and

C^, this means that must be nearly constant. This follows because

the usual crystal -axis Poisson's ratio is

S

12 _

C 12 =

c

1 1+ C-j^ ^

i +y (5)

where y

= C^/C^.

Conclusions

1. Alloying Mn into a stainless-steel -304-type Fe-Cr-Ni alloy decreases

all the elastic stiffness constants and also decreases Poisson's ratio.

2. The bulk modulus decreases most, reflecting the high compressibility

of Mn atoms.

3. Poisson's ratio and the B/G ratio both vary slowly with Mn concentration. This indicates that Mn does not change the nature of the chemical

bonding. Manganese's unusual bonding characteristics lead one to expect

possible changes.

4. By factoring into force constants, the relationship of many-body

forces to elastic constants and bonding becomes more clear.

Acknowledgment

This study was supported in part by the DoE Office of Fusion Energy.

197
Appendix: Force-constant approach

One always profits from considering elastic constants in terms

of force constants, which relate more directly to forces between

pairs of atoms in solids. Many force-constant models exist^

0

. For

11

fee lattices, Leibfried and Breuer consider a three-force-constant

model summarized in Fig. Al. The three parameters consist of a

longitudinal spring, f ^ , and two different transverse springs,

and f^, corresponding to bending along [001] and [110],

respectively. The coupling matrix for this model is

[ 110 ] ij

a 6 0

B a 0

0 0 y

(Al)

[d]

Physically, <|>. 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 i. If the

M.] u r\j displacement vector corresponds to an eigenvector, then -<|>.j corresponds to a

[ 110 ] _ , [ 110 ] spring constant. By symmetry <f> ^J = $

[ 110 ] _ [ 110 ]

22

L [ 110 ]

and 4> [110] _ .[110] _ 12

= <l> 21

23

= 4> 22 • Components such as <(> ^

vanish because force and

displacement are perpendicular, thus no coupling. Diagonal ization of <j>.ij

gives three eigenvalues:

f j - a + B

f2 = y

f

3

= a - S

(A2 )

(A 3 )

(A4 ) Leibfried and Breuer relate the f

1 s to the six eigenvalues of the 6x6 Voigt

C.. matrix:

vJ f

l = I4 (4C + 2C + 3C ) a

1 2 4 f

2 = Y2 (-C - 2 C + 3 C)

a 2 4 f

3

- f

(ZC - 0

where a denotes cubic unit-cell size.

198

(A5 )

(A6)

(A7 )
From the cubic-symmetry invariants,

1C C 11

+ 2C

12 (A8)

2 3 c c c irc

i 2 (A9)

4 5 6 C ~ C C ^44 (A10)

the f's relate to the Voigt C..'s:

f

l =4

( C ll + C 12

+ W (All)

f

2 = 4

(" cn

+ 2 C44) (A12)

f

3 = 4

^ C ll

" C 12

' C44^ (A13)

and vice versa:

C 11 ’ 7

< 2f

l + 2f

3

> (A14)

C

12 7 ( f

l - 2f2

- 3f

3

> (A15)

C44 - 7

(f

l + 2f2 + f

3> (A16)

More-interesting physical C.. combinations are:

1 U (C irC 12)

=

a

^ f

l + 2f2 + 5f

3

^ (A17)

( C H+C

1 2

) = j

(4fj - 4f

2 -4f

3

) (A18)

^ C 12~ C44 ^ = I

' ” 4f

2

“ 4 f 3^ (A19)

A=2C

44/(C n

-C

12 ) = (2f

1 +4f2 +2f3

)/(f

1 +2f2 +5f3

) (A20)

( C

1

1

~ C 12~ 2 C44 ) =

a^

( “ f r

2f

2 +3f3

} (A21 )

Cll~Ci2 1S t *ie 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 ^ , f^, and fg. C^+20^

is three times the bulk modulus (reciprocal compressibility). Since uniform

dilatation changes bond lengths but not bond angles, it may seem surprising

that B depends on f

2 and fg in addition to fj. This occurs because the spring

constants f

2 and fg relate also to many-body forces. (Recall that the third12

order perturbation-theory calculation of Axilrod and Teller for interactions

199
between triplets of atoms contained three interatomic distances--^, r^,

r 13

--and three included angles-^, Y

2

> Y

3 —with y being the angle between r^

and r^).

^i 2”^44 1S t *ie Cauchy (noncentral -force) discrepancy for cubic

crystals. Thus, if accidently f^-f^, then the material will appear to have

central forces by the familiar Cauchy criterion = C^. Thus, this

criterion is necessary but not sufficient. The Zener anisotropy ratio, A,

depends on all three force constants. For vanishing many-body forces, 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

Ci 1 = 2C^ = 2C^ = 4C', where C' = i(C^-C^). Finally, elastic isotropy

demands that C' = or that - 2C^

= 0. In terms of force

constants, isotropy demands that f^ = 3f^ - 2f?, a condition that arises only

accidently.

We now consider the polycrystalline case, which has two independent

13 elastic constants. Following Stokes , we choose to consider B and G, the

elastic constants that represent the two extreme types of deformation--pure

dilatation (volume change without shape

change) and pure shear (shape change without volume change). For

aggregates of cubic crystallites, because the bulk modulus is a

rotational invariant, it is

B = (C n

+2C

12 )/3 (A22)

For the shear modulus, no unique averaging method exists. Many methods

14 using different physical principles have been proposed . A method due

to Hershey,^ Kroner,^ and Eshelby^ is used increasingly. For copper,

18 Ledbetter verified that this method agrees best with observation.

200
For simplicity, we use Voigt's averaging method here. Voigt^

showed that when the aggregate has uniform elastic strain the shear

modulus of cubic aggregates is

G

v

“ ^11 1

2

+ ^^44 ^ ^ ^ (A23)

In terms of force constants:

G V

( f

i +2V2 V < A24 > 20 The Reuss shear modulus, based on constant stress in the aggregate, is

“ 2 ^44^11~^12^^?^ll”^12^ + ^44^ (A25)

and must also depend on all three force constants.

Consider now a typical metal --copper , where C n

=1.696, C 12=1.224,

and C 44

=0.754*10 U

N/m

2

. Thus, f

1 /a=0.9185, f

2 /a=-0.0470 , and

f

2 /a=-0.0705 in the same units. Table A1 shows how the three force

constants contribute to various elastic constants and to the elastic

anisotropy, A. For both A and C^/C we made the very rough approximation that both f

2 and fg are small compared 'with f^. Except for the

Cauchy discrepancy, C

1 2' C44’ dorT11

' nates every elastic constant. As

expected, many-body effects show most strongly in but also

strongly in C', A, and C^/C^. The bulk modulus is least sensitive to

many-body terms. In all cases except C 44the f^ force constant contributes less than the f^ force constant; bending out of the (100)

plane contributes less than bending in the plane. Negative f^ and f^

values apparently imply instabilities with respect to bending. But one

must remember that the bending springs represent many-body, not twobody, 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.

201
Table A1 contains results also for stainless steel. Principal

differences are that f^ and f^ are approximately double those of copper

with the sign on f^ being reversed. This means that the stainless

steel elastic anisotropy is higher (higher negative f^). Except for Th, and

Du, all fee elements exhibit a negative Implications of a positive

remain unclear. Because both Th and Pu are relatively unstable in the fee

structure, a positive fr, may indicate a tendency toward chemical instability.

202
References

1. W. C. Leslie, Iron and its dilute substitutional solid solutions, Metall

.

Trans. 3., 5-25 (1972).

2. J. F. Janak and A. R. Williams, Giant internal magnetic pressure and

compressibility anomalies, Phys. Rev. B 14 , 4199-4204 (1976).

3. L. Pauling, The Nature of the Chemical Bond (Cornell U.P., Ithaca, 1960).

pp. 254, 419“ —

4. H. M. Ledbetter, N. F. Frederick, and M. W. Austin, Elastic-constant

variability in stainless-steel 304, J. Appl . Phys. 51, 305-309 (1980).

5. H. M. Ledbetter, Predicted single-crystal elastic constants of

stainless-steel 304, in NBSIR 81-1645 (1981), pp. 227-236.

6. H. M. Ledbetter, Sound velocity as a texture probe: application to

stainless-steel welds, intended for J. Appl. Phys.

7. W. Koster and H. Franz, Poisson's ratio for metals and alloys, Metall.

Rev. 6, 1-55 (1961).

8. G. Leibfried and N. Breuer, Point Defects in Metals I (Springer-Verlag,

Berlin, 1978), p. 127.

9. C. C. Matthai, P. J. Grout, and N. H. March, Force fields in d-band

metals, Int. J. Quant. Chem. Symp. 1_2, 443-459 (1978).

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. 57, 2053-2065 (1979).

11. Reference 8, p. 42.

12. B. M. Axilrod and E. Teller, Interaction of the van der Waals type

between three atoms, J. Chem. Phys. H_, 299-300 (1943).

13. G. G. Stokes (1845); reported 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. H. M. Ledbetter, Estimation of Debye temperatures by averaging elastic

coefficients, J. Appl. Phys. 44, 1451-1454 (1973).

15. A. V. Hershey, The elasticity of an isotropic aggregate of anisotropic

cubic crystals, J. Appl. Mech. 21_, 236-240 (1954).

16. E. Kroner, Berechnung der elastischen Konstanten des Vi el kristal Is aus den Konstanten des Einkristal 1 s , Z. Phys. 151 , 504-518 (19581.

203
17. J. D. Eshelby, Elastic inclusion and inhomogeneities, in Progress in

Solid Mechanics, Volume II (North-Hoi 1 and , New York, 1961), pp. 87-140.

18. H. M. Ledbetter, Sound velocities and elastic-constant averaging for

polycrystalline copper, J. Phys. D: Appl . Phys. 13>, 1879-1884 (1980).

19. W. Voigt, Ueber die Beziehung zwischen den beiden Elasticitatsconstanten

isotroper Korper, Ann. Phys. 38^, 573-587 (1889).

20. A. Reuss, Berechnung der Fliessgrenze von Mischkri stal 1 en auf Grund der

PI astizi tatshedingung fur Einkristal le, Z. Angew. Math. Mech. 9, 49-58

(1929).

Figure Captions

Fig. 1. Compositional variation of elastic coAstaiUs of Fe-Cr-Ni alloys

containing Mn. Units on E, B, and G are lO^N/m^. v is dimensionless.

Fig. 2. Face-centered-cubic unit cell showing eigenvectors and eigenvalues

of the coupling matrices to the nearest-neighbor atoms at [i 1 0]-type

positions.

204
Table

1.

Chemical

composition

(weight

percent),

hardness,

grain

size,

and

mass

density.

inm^cMCOONNiDr-H

CNJI^CO'Xir^LOCOCNJLOCO

t/i E o^cccocooocococococo ^ Vl u

^ c: ^ Z (D Oi

TD ^

—

O

c z:

•«- <u •3-ioiTLncotcvD^to^-

fD M S s- -r- h- in i/un in id m in id id in Ol/H/lC

CO

CO

co ,—

<Uc <u cvcocc^-^oooo^ "C £ cocococricooicooaico

s-03 U m o

cn

" " OCOCOOOIOIOOOO roc\jcvjroc\joococororo

oooooooooo

o

C\JC\Jr-iCSJr-Hr-lrH*— r-H CO cocococococococococo OOOOOOOOOO o non^-CTuncNjrHCvj^

inioiD'DiniCMntDiD'n

oooooooooo

IS) OOOOOOOOOO

oooooooooo

IS)

c\joor-Hcococ\joo*d-«3-co

C\JC\JC\JC\JC\JC\JCV1C\JCVIC\J oooooooooo

Q_ oooooooooo

rH O) H a> t-H (Jl If) H ID H i—* i—t r-H r—t r—t r-H r-H CVJ r-H 7—1 z OOOOOOOOOO

iruncocMLn^m^rHrH

CNjOsJcvic\Jcv;c\JOoooro(NJ o OOOOOOOOOO

oooooooooo

corHiDOio^rcsjcoaioj

•r— OCOOCOf^COCsJCOOsJO Z

CONCOI^COI^OOr^OOOO

CTilOOLDCMLn^-HOOCSJlO

s- r-imrHfOCVJCsJN«J^O

o oOCT'Coa'Coaicoaiooco

r—1 r-H r-H r-H r-H r-H r-H r—1 r

1 r-H

c\j cr> o »—i in n oi Ch o '—' c OHOOOtOOMOCO

HiHCvJCMfOoo^ininin

rH (M ro ID ID N co oi or-H

205
Table 2. Directional variation of sound velocities and elastic constants

Alloy n P Velocity

(cm/ys) (10

UN/m

2

)

G

(10

n

N/m

2

)

1 100 100 0.576 2.631

010 0.314 0.780

001 0.315 0.784

010 010 0.576 2.628

100 0.314 0.780

001 0.315 0.785

001 001 0.576 2.622

100 0.314 0.783

010 0.314 0.784

10 100 100 0.572 2.579

010 0.314 0.778

001 0.314 0.773

010 010 0.572 2.580

100 0.313 0.771

001 0.313 0.772

010 001 0.572 2.576

100 0.314 0.778

010 0.313 0.773

206
Table

3.

Sound

velocities

and

elastic

constants

for

ten

manganese-alloyed

stainless-steel-304-type

alloys

t CM O CM o CM CO LO LO CO \

C3 r-H CO CTI CM o t—1 CD CT) CO o o O CT O o o O CTi CT O CO CM CM <—l CM CM CM C\J r-H <—1 CM

CT LO CO LO LO LO lo

co CO co co CO co CO CO oo co

CM CM CM CM CM CM CM CM CM CM > • o O O O O O O O O O

^ cmE'

r-^ t-H OO t—H CO LO cm

LxJ t-H r-H o r-H O o CT CT 00 CT 00

r—

1

o o o o o CT CT CT CT CT o • t—H CM CM CM CM C\J t—H t—H r-H t—H !—

1

V ^

^ CME

21 r-» CO CO CO LO CTi CM t—H CT LO

r-H co lo LO LO LO •sd- co ^ CQ t—

•

LO LO LO LO LO LO LO LO LO LO ot-H t—H 1—

H

r-H r-H t—H T 1 t—H r-H 5—1 t-H V—

CME

2T CT CO CO oo LO LO CM LO CM

C3 <-h co co i--. r-- I'-. I"- r-H r^- r-~ i"- r-- r"- r'- or-H o o o o o o o o o o V ^

CME

=* ^ CM r-H r-H CD CM LO t-H CO LO O r-H CM CM O O CT CT 00 r-~- i"-

r-H CO LO LO LO LO LO LO LO LO LO o • r-H CM CM CM CM CM CM CM CM CM CM

U1 LO LO LO LO "3- «Lfr- ^ CO

4-> O- t—H r-H t—H r-H t—H r-H r-H t-H t-H <j—

H

> CO CO CO CO <o CO CO CO CO CO E

(J o o o o o o o o o o

U~) LO r-- 53- LO LO CO CM CM

p- r~- r-- i-"- 1^- l~-. f'- LO LO LO LO LO LO LO LO LO LO > E • <_> o o o o o o o o o o

4-> U CM ct O r-H LO LO co CT O «-H O- o r-H o o oo CO O N CO 00 c r-H t—H CM CM CO CO LO LO LO

s;

o T 1 CM 3 4 LO LO 7 8 CT Ot—H r—

e£
Table 4. Compositional

y

= variation of elastic constants based on

a + bx type relationship.

y a b b/a b/a (Vegard)

G 0.783 -1.77- 10” 3

-2 . 26 • 10

-3

-1.79- 10

-3

B 1.585 -7.43- 10

-3

-4.69-10

-3

-3.31-10" 3

E 2.017 -5.20- 10" 3 -2.58- 10

-3

-1.75- 10' 3

V 0.288 -0.47-10" 3 -1.62- 10~ 3

-1 . 59-10” 3

208
Table Al. For a typical metal, copper, and for stainless steel,

relative contributions of three force constants to various

elastic constants.

Copper

f

2 f

3

Stainless

f

2

Steel

f

3

C 11

1.00 0.00 -0.08 0.00 -0.12

C 12

1.00 0.10 0.23 -0.17 0.36

C 44

1.00 o

f—

H

1 o -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

C 12

" C 44 0.00 -1.00 -1.00 1 oo -1 .00

C 11

" C 12

" 2C

44

-1.00 1 o H o 0.23 0.17 0.36

A 1.00 (0.0)

a (0.31) (0.00) (0.47)

C 12/C

ll

1.00 (0.10) (0.31) (-0.17) (0.47)

a Parentheses indicate the approximation that both fg/fj and iVf

l are sma11

relative to unity.

209
WEIGHT % Mn

Fig. 1. Compositional variation of elastic corLstarrts of Fe-Cr-Ni alloys

containing Mn. Units on E, B, and G are KTN/m^. v is dimensionless.

210
o

crs

211

Face-centered-cubic

unit

cell

showing

eigenvectors

and

eigenvalues

of

the

coupling

matrices

to

the

nearest-neighbor

atoms

at

Ti

i

0]-type

positions

.

Anomalous low-temperature elastic-constant behavior of Fe-20Cr-16Ni-6Nln

H. M. Ledbetter and M. W. Austin

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

Abstract

For this high-nickel -content austenitic stainless steel we determined

ul trasonical ly the complete set of polycrystalline elastic constants between

295 and 4 K. A reversible magnetic transition occurs near 54 K. During

cooling, the bulk modulus begins to soften at a much higher temperature, near

150 K. Local moments above the transition temperature may explain this

pecul iarity.

Key Words: Bulk modulus; elastic constants; iron alloy; low temperatures;

magnetic phase transition; Neel transition, Poisson ratio; shear modulus;

stainless steel; ultrasonic waves; Young modulus.

213

Several recent studies^ ^ show that austenitic stainless steels undergo

O magnetic phase transitions at low temperatures. These studies 6 show the

effect of Mn, which raises the transition temperature.

The present study shows the effect of Ni. In selecting a high-Ni stainless steel for study we chose Fe-20Cr-16Ni-6Mn, a Soviet steel intended for

low-temperature weldments. Mechanical properties of this alloy were reported

recently.^

The actual chemical composition by weight percent is 20.31 Cr, 16.42 Ni

,

6.12 Mn, 0.26 Si, 0.21 Mo, 0.19 N, 0.09 Cu, 0.026 S, and 0.025 P. Hardness

was Rockwell B 88, grain size was 39 pm (ASTM No. 6.4), mass density was

3

7.879 g/cm , and the 1.9-cm plate was ferrite free as determined by a magnetic

balance.

Elastic constants were determined by measuring ultrasonic velocities

5 between 300 and 4 K using equipment and procedures described elsewhere. The

key experimental parameters include: orthogonal -pri sm specimen, 1.3 by 1.3 by

1.6 cm; opposite faces flat and parallel within 5 ym; quartz transducers 1 cm

diam, x-cut and ac-cut, rough polished; gold electroplated two sides, 4-MHz

fundamental frequencies; bonding agents phenyl salicylate at room temperature

and a cyanoacrylate adhesive at lower temperatures.

Table 1 gives for selected temperatures the longitudinal and transverse

sound velocities, v and v., which Fig. 1 shows as longitudinal and shear

Xj L modul i

:

C

t

- pv

2t (1)

and,

C t

- PV

2

t (2)

where p denotes mass density. Table 1 and Fig. 2 give derived elastic constants:

215
Shear modulus = G

=

Bulk modulus = B = G

Young modulus = E = 9GB/(G + 3B)

(3)

(4)

(5)

and

Poisson ratio = v = (E/2G) - 1. ( 6 )

Maximum experimental uncertainties are believed to be 1.0 percent for G and E

and 1.5 percent for B and v.

All this steel's elastic constants show anomalies near 54 K, corresponding presumably to its magnetic-transition temperature, T , for critical

temperature.

The bulk-modulus behavior shows that a second and broader transition,

probably also magnetic, occurs at a higher temperature, near 150 K. This

transition does not affect noticeably the shear-dominated elastic constants

such as G, E, and v. The exact nature of this high-temperature transition

remains unknown. Unlike the low-temperature transition, it does not exhibit a

magnetic-susceptibi 1 i ty maximum.

Bulk-modulus softening implies a possible magnetic transition where the

onset of magnetization causes repulsive atom-atom interactions. This repulsive interaction expands the lattice and softens B because, as discussed by

9 -4

Gilman, B varies with atomic radius as r .

The question arises: what bulk-modulus change does a simple model predict? To answer this, we consider a Stoner,^ collective-electron, itinerantelectron, or band, model. In this model, d or f electrons belong to a degenerate band where electrons of + and - spins possess different energies.

Transfer of an electron from the top (antibonding) band to the bottom

(bonding) band increases its kinetic energy (lower wavelength). But the

potential energy decrease, the exchange energy, may offset this. If so, then

216
magnetic ordering occurs. By assuming that the exchange energy depends only

weakly on atomic volume, the bulk modulus will depend only on the kinetic

energy

E = M

2 /2N (7)

where M is magnetic moment in Bohr magnetons per atom and N is the

electronic density of states at the fermi level in Ry . There arises a

magnetic "pressure"

Pm

= ~^ E/8V)

V = V

Q (8)

_ M

2 3N T 3 V

2N

(9)

Heine

11 showed that d-electron bandwidth, W, varies with atomic radius, r, -5 5 as r . Assuming the product NW is constant, then N varies as r and

dN 5 dV

N 3 V

( 10 )

and

P m

= (5/3) E/V

q

(11)

where V denotes atomic volume,

o The bul k modulus is

B m

= V (

3

2 E/ 3 V

2

) = -V(3P

m

/3V) (12)

which becomes after differentiation

Bm

= (65/18) M

2

/NV

0

= (65/9) E/V

0 (13)

3

For iron, M = 2.12 u

B

, N = 27.4 states/atom- Ry, V

Q

= 7.094 cm /g-atom. Thus,

B = 0.303-10 UN/m

2 m For Fe, this amounts to 18 percent of the zero-temperature bulk modulus.

Thus, magnetic effects can be quite large.

The exchange energy, the companion to the kinetic energy, must contribute

more, but negatively, to the bulk modulus since the net result is elastic

217
1

2

softening. However, present theory does not permit the calculation of the

exchange contribution. For this one needs a relationship between the exchange

energy and atomic volume. Figure 2 shows that the bulk modulus softens about

1.5 percent. Thus, the negative exchange term must offset the positive

kinetic-energy term by this amount.

That B, but not 6, softens at higher temperatures suggests a magnetovolume effect akin to spontaneous volume magnetostriction. This effect is

designated aE^, where w = (V - Vp)/Vp is the spontaneous volume magnetostriction, V is the total volume, and Vp is the volume in the paramagnetic state.

13

The effect was first reported by Engler for an Fe-42Ni alloy. It was

14

explained first by Doring using a thermodynamic analysis. Herein, this

phenomenon will be called the Doring effect. Doring reasoned that in the

paramagnetic region the elastic constant is measured at constant

magnetization, M, while in the ferromagnetic or anti ferromagnetic region the

elastic constant is measured at constant magnetic field, H. Doring showed

that the magnitude of the anomaly in the Young's modulus is given by

AE . 1 2 M

— 1 co 1 1 _ 1 3w 3M

E

2 E m E u 9 3H t

3H t M H a,T a,T

4

(14)

where 3w/3H is the forced volume magnetostriction due to the magnetization,

? 3M/3H is the high-field susceptibility x> E is E^E^, and a is the tensile

1

2

stress. An alternative derivation of Eq. (8) was given by Hausch . Wohl1

5

farth stated, without proof, that the factor of 1/9 in Eq. (8) should be

replaced by (1 - 2v) where v is Poisson's ratio. For the present materials

this introduces a factor of approximately 1.6, which is insignificant for

present purposes. It should be noted that the Doring effect always lowers the

moduli (Epj > E^), whether the volume magnetostriction is positive or negative.

This is related to the fact that a relaxation mechanism is involved in going

218
to a magnetic state, and such mechanisms always soften the elastic stiffness.

•• .. I C The Doring effect in iron-nickel alloys was discussed by Koster, who denoted

it as aE rather than as AE . The effect was invoked by several authors to

Y a) explain elastic anomalies in magnetic materials, usually of the invar type.

1

2

Hausch criticized the relevance of the Doring effect in most of these cases.

Schlosser^'

7 discussed the magnetovolume contribution to the compressibility of

1

2

invar, but Hausch showed that an exchange-energy contribution is also

required in this case. The present results for an Fe-Cr-Ni-Mn (stainlesssteel) alloy seem to constitute a clear case of a Doring-type effect.

1

8

Shiga discussed recently that magnetovolume effects in transition-metal

alloys originate in the onset of local moments. His argument is the following: Energy-band polarization increases the kinetic-energy (as described

above). This kinetic energy is offset by volume expansion because kinetic

_5

energy is proportional to 3d bandwidth that varies as r . Shiga concludes

that the volume increase varies as M . Shiga concludes further that the large

19

volume changes predicted theoretically by Janak and Williams do not occur

because 3d-band polarization persists above T

c because of local moments.

We conjecture that local moments above T

c explain the bulk-modulus

anomaly beginning during cooling near 150 K. Since local moments lead to a

magnetovolume effect, this explains why dilatational modes are altered while

shear modes remain unaffected. Volume expansion would explain the softening

of B, which varies as r~

4

. Other physical properties, such as thermal expansivity and specific heat, probably also change less abruptly than expected

because M does not vanish immediately above the apparent T

c (near 54 K for the

present alloy).

219
Finally, we consider the effect of Ni on the elastic properties by

comparing present results with those obtained previously for 304 stainlesssteel, nominally Fe-18Cr-8Ni. Table 2 shows these results together with the

present results corrected for Mn content. One concludes from Table 2 that Ni

increases slightly all the elastic stiffnesses; Poisson's ratio remains

essentially unchanged. One expects this because Ni 1 s elastic stiffnesses

exceed those of Fe-18Cr-8Ni (see Table 2). And, Ni , with lower atomic volume

-4

than Fe, would also lower the elastic stiffness, which varies as r , where r

denotes atomic radius. However, several previous experimental studies imply

an opposite effect. Table 3 contains elastic constants of five stainless21-24 " 25

steel single crystals averaged using Kroner's method. However, these

averaged results remain unconvincing because they disagree significantly with

26

the observed bulk and shear moduli for 304 stainless-steel. Thus, the

effect of Ni on stainless-steel elastic constants remains uncertain.

Acknowledgment

The DoE Office of Fusion Energy and the National Science Foundation

partially supported this study.

220
References

1. H. M. Ledbetter and E. W. Collings, Low-Temperature magnetic and elasticconstant anomalies in three manganese stainless steels, in Metal Science

of Stainless Steels (AIME, New York, 1979), 22-40.

2. E. W. Collings and H. M. Ledbetter, Sound velocity anomalies near the

spin-glass transition in an austenitic stainless steel alloy, Phys.

Lett. 72A, 53-56 (1979).

3.

H. M. Ledbetter, Anomalous low-temperature elastic-constant behavior in

Fe-1 3Cr-l 9Mn , Metall. Trans. ]_1A, 543-544 (1980).

4.

H. M. Ledbetter, Room-temperature elastic constants and low-temperature

sound velocities for six nitrogen-strengthened stainless steels, Metall.

Trans. JMA, 1067-1069 (1980).

5. H. M. Ledbetter, Stainless steel elastic constants at low temperatures,

J. Appl . Phys. 52, 1987-1589 (1981).

6. H. M. Ledbetter, Low-temperature variability of stainless-steel -304

elastic constants, intended for Cryogenics.

7. H. M. Ledbetter and E. W. Collings, Elastic-constant anomalies at the

Ned! transition in Fe-18Cr-3Ni -12Mn , to be published.

8. R. P. Reed, R. L. Tobler, J. W. Elmer, H. I. McHenry, and K. A.

Yushchenko, Strength and toughness of USSR Fe-20Cr-16Ni-6Mn-0.2N weldments at cryogenic temperatures, NBS Boulder Fracture and Deformation

Division (1981), to be published.

9. J. J. Gilman, Micromechanics of Flow in Solids (McGraw-Hill, New York,

1969), p. 29-4TT

10. E. P. Wohlfarth, Iron, cobalt, and nickel, in Ferromagnetic Materials , Volume 1 (North-Hoi land , Amsterdam, 1980), p. 1-70.

11. V. Heine, 5-d interaction in transition metals, Phys. Rev. 153, 673-682

(1967).

12. G. Hausch, Magnetic exchange energy contribution to the elastic constants

and its relation to the anomalous elastic behavior of invar alloys, Phys.

Stat. Sol i d i (a) J_5, 501-510 (1973).

13. 0. Engler, Der El astizitatsmodul ferromagnetischer Stoffe in Abhangigkeit

von der Temperatur und vom Magnetfeld, Ann. Phys. (Leipz.) 3_1_, 145

(1938).

14.

W. Doring, Uber die Temperaturabhangigkeit des Elastizitatsmoduls

ferromagnetischer Substanzen, Ann. Phys. (Leipz.) 32^, 465 (1938).

15.

E. P. Wohlfarth, Contributions to the invar problem, v. the AE effect,

Phys. Stat. Sol i d i (a) K39-K42 (1972).

221
16.

W. Koster, Elastizitatsmodul und AE-Effekt der Eisen-Nickel Legierungen,

Z. Metallke. 35, 194 (1943).

17. F. Schlosser, Magnetic contributions to the compressibility of invar,

Phys. Stat. Sol i d i (a) 1_8, 235-239 (1973).

18. M. Shiga, Magnetovolume effects in ferromagnetic transition metals and

alloys, in Physics of Transition Metals, 1980 (Inst. Phys., Bristol,

1981), p. 241-250.

19. J. F. Janak and A. R. Williams, Giant internal magnetic pressure and

compressibility anomalies, Phys. Rev. B J4-, 4199-4204 (1976).

20. H. M. Ledbetter, Manganese contributions to the elastic constants of

face-centered-cubic Fe-Cr-Ni alloys, to be published.

21. K. Salmutter and F. Stangler, Elastizitat und Plastizitat eines austenitischen Chrom-Nickel -Stahles , Z. Metallke. 5U 544-548 (1960).

22. H.-U. Richter, Zur Ultraschallprung austenitischer Schwei ssverbindungen

(Teil I), die Technik 23, 610-619 (1968).

23. M. Kikuchi, Elastic anisotropy and its temperature dependence of single

crystals of 18-12 type stainless steel, Trans. Jap. Inst. Met. 12,

417-421 (1971).

24. M. C. Mangalick and N. F. Fiore, Orientation dependence of dislocation

damping and elastic constants in Fe-18Cr-Ni single crystals, Trans. Met.

Soc. A I ME 242, 2363-2364 (1968).

25.

E. Kroner, Berechnung der elastischen Konstanten des Vi el kristalls aus

den Konstanten des Einkristal 1 s , Z. Phys. 151 , 504-518 (1958).

26.

H. M. Ledbetter, N. V. Frederick, and M. W. Austin, Elastic-constant

variability in stainless-steel 304, J. Appl . Phys. 51_, 305-309 (1980).

222
Table 1. Elastic constants of Fe-20Cr-16Ni-6Mn at selected temperatures.

T

(K) (cm/ps)

v

t (cm/ps)

E (10 nN/m2

)

G (10 n N/m2

)

B (lO^N/m2

)

V

295 0.5735 0.3134 1.992 0.774 1.560 0.287

285 0.5742 0.3140 1.999 0.777 1.562 0.287

275 0.5751 0.3144 2.004 0.779 1.567 0.287

264 0.5758 0.3152 2.013 0.783 1.568 0.286

255 0.5765 0.3157 2.020 0.785 1.571 0.286

245 0.5771 0.3163 2.027 0.788 1.573 0.285

235 0.5779 0.3169 2.033 0.791 1.576 0.285

225 0.5787 0.3177 2.043 0.795 1.579 0.284

215 0.5793 0.3183 2.049 0.798 1.580 0.284

204 0.5800 0.3188 2.056 0.801 1.583 0.284

194 0.5807 0.3195 2.064 0.805 1.584 0.283

184 0.5810 0.3201 2.070 0.807 1.584 0.282

175 0.5817 0.3206 2.076 0.810 1.586 0.282

165 0.5824 0.3212 2.083 0.813 1.589 0.282

155 0.5830 0.3218 2.090 0.816 1.590 0.281

143 0.5833 0.3222 2.095 0.818 1.590 0.280

133 0.5841 0.3227 2.101 0.821 1.593 0.280

123 0.5844 0.3233 2.107 0.823 1.593 0.280

112 0.5849 0.3239 2.114 0.827 1.594 0.279

103 0.5852 0.3243 2.118 0.828 1.594 0.278

91 0.5853 0.3247 2.122 0.830 1.592 0.278

82 0.5857 0.3250 2.127 0.832 1.593 0.277

71 0.5857 0.3253 2.129 0.834 1.591 0.277

61 0.5855 0.3255 2.131 0.835 1.588 0.276

51 0.5851 0.3253 2.128 0.834 1.586 0.276

39 0.5844 0.3253 2.127 0.834 1.579 0.276

26 0.5844 0.3253 2.127 0.834 1.580 0.276

13 0.5846 0.3252 2.126 0.833 1.582 0.276

4 0.5848 0.3253 2.127 0.834 1.583 0.276

223
Table 2. Room-temperature elastic

constants of two stainless steels and nickel.

Fe-20Crobserved

•16Ni -Mn

corrected6

Fe-18Cr-8Ni Ni

E (10

1

1

N(m

2

) 1.992 2.014 1.996 2.217

G (10

11 N/m2

) 0.774 0.782 0.774 0.851

B (10

11 N/m2

) 1.560 1.592 1.582 1.868

V 0.287 0.289 0.290 0.302

a For Mn content using results of ref. 20.

224
Table 3. Monocrystal and averaqed polycrystal elastic constants of five Fe-Cr-Ni

alloys. All units are 10 11 N/m*, except v, which is dimensionless.

c n

C 12C 44B E G V Ref.

Fe-1 2Cr-18Ni 2.332 1.626 1 .225 1 .861 2.006 0.759 0.320 2

Fe-18Cr-12Ni 2.16 1.45 1.29 1.687 2.037 0.784 0.299 22

Fe-1 8Cr-l 2Ni 1 .912 1.179 1.386 1.423 2.077 0.826 0.257 23

Fe-18Cr-14Ni 1.98 1 .25 1.22 1.493 1 .997 0.763 0.282 24

Fe-18Cr-19Ni 1.91 1.19 1 .24 1.430 1.951 0.777 0.273 24

225
Figure Captions

Fig. 1. Temperature dependence of longitudinal and shear moduli of

Fe-20Cr-16Ni -6Mn

.

Fig. 2. Temperature dependence of three elastic constants of

Fe-20Cr-16Ni-6Mn: Young modulus, bulk modulus, and Poisson ratio.

226
C(T)/C(295)

TEMPERATURE, K

Fig. 1. Temperature dependence of longitudinal and shear moduli of

Fe-20Cr-16Ni-6Mn.

227
POISON’S

RATIO

YOUNG’S

MODULUS,

lO^N/m

2

TEMPERATURE, K

Fig. 2. Temperature dependence of three elastic constants of

Fe-20Cr-16Ni-6Mn: Young modulus, bulk modulus, and Poisson ratio.

228

BULK

MODULUS,

10"N/m
WELD!HO AMP CAST!HO

229

WELDMENTS AND CASTINGS PROGRAM

LEADER: H. I. McHenry, NBS

STAFF: T. A. Whipple, J. W. Elmer, C. M. Fortunko, H. M. Ledbetter, NBS

CONTRACTS: None

OBJECTIVES:

(1) To investigate the metallurgical factors that affect the mechanical

properties of stainless steel weldments and castings at cryogenic

temperatures

.

(2) To contribute to the development of improved filler metals for

welding stainless steels for liquid helium service.

(3) To evaluate the mechanical properties of weldments and castings at

4 K. (4) To develop methods of detecting defects and evaluating their signify

cance in stainless steel weldments.

RESEARCH PAST YEAR (1981):

( 1 )

( 2 )

(3)

(4)

(5)

( 6 )

The tensile properties and fracture toughness of a series of five

CF8M castings with delta-ferrite contents ranging from 0 to

28 percent were measured at 4 K. Work has continued on a study to relate metal lographic observations

of duplex austenite delta-ferrite microstructures to the deformation

and fracture of stainless stpel welds and castings.

The fracture toughness and fatigue crack growth rates of a 25Mn-5CrlNi alloy, plate and welds, were measured at 4 K. Two 316L stainless steel weldments were tested at 4 K in support of

the LCP program.

An improved method of ultrasonic testing of stainless steel weldments was conceived and demonstrated.

The elastic constants of stainless steel weldments have been related

to texture in the weldment.

RESEARCH THIS YEAR (1982):

(1) The five CF8M stainless steel castings with varying nitrogen content

and constant delta-ferrite content will be tested at 4 K. (2) The metallographi'c study on deformed and fractured stainless steels

with duplex structures will continue.

(3) A set of stainless steel weldments will be produced with varying

delta-ferrite morphologies. These weldments will be used to verify

and extend the deformation model for duplex structures to the finer

structures found in weldments.

(4) A set of submerged-arc weldments will be produced with variations in

the delta-ferrite and oxygen contents.

(5) A series of stainless steel weldments with varying austenite stability will be produced and tested with the weld reinforcement left

on.

(6) The elastic properties of the CF8M stainless steel castings will be

measured ul trasonically.

(7) Mechanical property testing at 4 K, in support of superconducting

magnet design and construction, will continue.

231

WELDMENTS AND CASTINGS FOR LIQUID HELIUM SERVICE

T. A. Whipple and H. I. McHenry

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

The FY 81 results of the NBS program to evaluate weldments and castings

for liquid helium service are reviewed. The tensile properties and fracture

toughness of a series of five CF8M castings with delta-ferrite contents

ranging from 0 to 28 percent were measured at 4 K. Work is continuing on a

study to relate metal lographic observations of duplex austenite delta-ferrite

microstructures to the deformation and fracture of stainless steel welds and

castings. The fracture toughness and fatigue crack growth rates of a 25Mn5Cr-lNi alloy, plate and welds, were measured at 4 K. Two 316L stainless

steel weldments were tested at 4 K in support of the LCP program. The elastic

properties of 316L stainless steel welds have been related to the texture in

the weldment. An improved method of ultrasonic testing of stainless steel

weldments was conceived and demonstrated; the method uses electromagnetic

acoustic transducers (EMATs) to inspect the weldments with horizontal shear

(SH) waves that are inherently less sensitive to the anisotropy of stainless

steel welds. The research planned for FY 82 is also described.

233

INTRODUCTION

The evaluation of weldments and castings for structural applications at

4 K [1-4] was continued in FY 81. This program has four objectives:

1. To investigate the metallurgical factors that affect the mechanical

properties of stainless steel weldments and castings at cryogenic

temperatures

.

2. To contribute to the development of improved filler metals for

welding stainless steels for liquid helium service.

3. To evaluate the mechanical properties of weldments and castings at

4 K.

4. To develop methods of detecting defects and of evaluating their

significance in stainless steel weldments.

Work continued on the first three objectives with evaluations of CF8M

stainless steel castings, 316L stainless steel weldments, and 25Mn-5Cr-lNi

austenitic steel weldments. Research was started on the fourth objective with

the development of a new technique for ultrasonic inspection of stainless

steel weldments. This paper briefly summarizes the research completed in

FY 81 and the plans for FY 82. Detailed summaries of the research completed

in FY 81 are given in the other papers of this section.

STAINLESS STEEL WELDMENTS

Austenitic Cr-Ni stainless steels, particularly the nitrogen-strengthened

grades, are the most commonly used alloys for structural applications in

superconducting magnets for fusion energy devices. These steels have the best

combination of strength, stiffness, and toughness at 4 K. However, the

development of a matching-strength filler metal with sufficient toughness and

resistance to microfissuring for welding the nitrogen-strengthened alloys does

235
remain a problem. A new approach to the development of a base metal/weld

metal system with a satisfactory match in properties has been taken by

Japanese investigators [5]. The new alloys are high-manganese austenitic

steels that are not stainless steels owing to their low chromium content. One

such alloy, 25Mn-5Cr-lNi , was evaluated. The results, reported here by

McHenry, Elmer, and Inoue, indicate the base plate and welds have a favorable

combination of strength, toughness, and fatigue crack growth resistance at

4 K. The weld metal properties are particularly encouraging; specifically,

the yield strength (961 MPa) is sufficiently high to match the base metal, the

toughness (157 MPa/m) is satisfactory, and the microfissuring tendencies

appear to be minimal.

Support of the LCP magnet design and construction program has continued

with the testing of a 316L submerged-arc weld (SAW) and a modified 316L

shielded metal-arc weld (SMAW). The results of the tensile, fracture toughness, and fatigue crack growth rate tests at 4 K are presented in Tables 1, 2,

and 3, respectively. The modified 316L weldment has a high nitrogen content

(0.147%), which results in the relatively high strength and moderate fracture

toughness. A good combination of strength and toughness was achieved in the

316L submerged arc weld. It is anticipated that the testing of qualification

and test weldments will be reduced in the future, since the LCP magnets are

now in the final stages of manufacture and there are now additional facilities

for cryogenic fracture toughness testing [6,7].

The inspectabil i ty of stainless steel weldments by ultrasonic methods is

fundamentally limited by the textured columnar grain structure of the weld

metal. The velocity of vertical shear (SV) and longitudinal (L) waves is

strongly anisotropic, resulting in reflections and mode conversions that may

236
clutter the ultrasonic signals received and mask the defect indication. A new

approach to ultrasonic inspection has been developed and demonstrated; it is

reported herein by Fortunko and Moulder. The principal idea is to use horizontally polarized shear (SH) waves whose wave velocities are not as strongly

anisotropic as SV and L waves. In addition, the wave impedances of the weld

and base metal can be matched more readily with SH waves, and therefore, there

is significantly lower scatter and higher sensitivity. The SH waves are

transmitted and received by electromagnetic acoustic transducers (EMATs).

Unlike piezoelectric crystals, EMATs can readily transmit and receive SH

waves

.

Ultrasonic techniques are also being used to study the elastic properties

of a series of 316L stainless steel weldments with ferrite contents ranging

from 0 to 10 percent. Ultrasonic wave velocities, both longitudinal and

transverse, were measured along the weld axis. Preliminary results indicate

that the elastic properties depend only weakly on ferrite content and that

strong elastic anisotropy occurs in the welds. Theoretical calculations by

Ledbetter show that ultrasonic velocity provides a very sensitive probe for

both detecting and measuring the amount of texture in the stainless steel

welds.

STAINLESS STEEL CASTINGS

Research on the mechanical behavior of stainless steel castings is being

conducted to evaluate CF8M castings for liquid helium service and to improve

understanding of the deformation and fracture of duplex austenite/deltaferrite microstructures at 4 K. The improved understanding should be applicable to welds as well as castings because both are duplex structures of

austenite and delta ferrite. Castings were selected for the study because

their coarser microstructure facilitates metal lographic observation of the

237
response of the two phases to deformation. The research was started in

FY 80 [8] and continued this year. The results, reported herein by Whipple

and Brown, include the observation of deformation twinning in delta-ferrite at

4 K and the fractographic examination of the CF8M stainless steel castings

with varying ferrite contents. The fractographic study has revealed that a

relatively low delta-ferrite content causes a high proportion of the fracture

surface to be brittle in nature. The fracture path is completely through the

ferrite phase at about 15 percent delta-ferrite.

The tensile and fracture toughness properties of a series of CF8M stainless steel castings with ferrite contents ranging from 0 to 28 percent were

measured at 4 K. The results, reported herein by Whipple and Brown, are

consistent with two-phase deformation models, which assume that the deltaferrite is a nonplastical ly deforming phase at 4 K. The tensile tests showed

that the effect of del ta-ferrite is to increase the strain-hardening rate in

the low plastic strain region (less than ^2.5 percent). The fracture toughness tests showed a decrease in fracture toughness with increasing deltaferrite content, up to approximately 15 percent; at higher delta-ferrite

contents, the fracture toughness was essentially constant. This has been

attributed to the establishment of a continuous delta-ferrite crack path.

TEST METHOD DEVELOPMENT

In FY 81, the capability for doing single-specimen Jj

c tests at 4 K on

three-point-bend specimens has been developed. This specimen design has

several advantages over the previously used compact-tension (CT) specimen.

These advantages include lower specimen machining costs and greater flexibility in choosing specimen orientation. The test procedures are very similar

to those used for CT specimens, and only minor modifications to the computeraided J-integral test facility were necessary.

238
FUTURE WORK

In FY 82, the study on the deformation and fracture of duplex austenite/

delta-ferrite structures will continue with the objectives outlined below.

Also, new programs designed to evaluate the effects of weld reinforcement and

oxygen content will be initiated. These factors have not been comprehensively

studied to date. Specifically, the FY 82 research will have the following

objectives:

1. The tensile and fracture toughness properties of five CF8M stainless

steel castings with varying nitrogen content and constant deltaferrite content will be measured at 4 K. This work is an extension

of the study on the fracture and deformation of duplex structures.

It is designed to test the effects of changing the austenite matrix

properties

.

2. The metal lographic study on deformed and fractured stainless steels

with duplex structures will continue and will concentrate mainly on

TEM studies of dislocation structures and deformation twinning.

3. A set of stainless steel weldments will be produced with varying

delta-ferrite morphologies. These weldments will be used to verify

and extend the deformation model for duplex structures to the finer

structures found in weldments.

4. A set of submerged-arc weldments will be produced with variations in

the delta-ferrite and^ oxygen contents. Increasing the oxygen

content will cause an increase in the number of nonmetallic inclusions in the weld, which has previously been shown to have an effect

on the properties at 4 K [9]. This study is intended to quantify

the effect.

239
5 . A series of stainless steel weldments with varying austenite stability will be produced and tested with the weld reinforcement left

on. There has been some indication that the combination of weld

reinforcement and austenite stability has an effect on weldment

strength [10].

6. The elastic properties and internal friction of the CF8M stainless

steel castings will be measured ultrasonically.

7. Mechanical property testing at 4 K, in support of superconducting

magnet design and construction, will continue.

8. Elastic-constant studies of stainless-steel weldments will be

completed.

240
REFERENCES

1. H. I. McHenry, "Evaluation of Stainless Steel Weld Metals at Cryogenic

Temperatures," in Materials Studies for Magnetic Fusion Energy Applications at Low Temperatures-I , National Bureau of Standards, Boulder, CO,

NBSIR 78-884 (1978), pp. 159-166.

2. H. I. McHenry, D. T. Read, and P. A. Steinmeyer, "Evaluation of Stainless

Steel Weld Metals at Cryogenic Temperatures," in Materials Studies for

Magnetic Fusion Energy Applications at Low Temperatures-I

I

, National

Bureau of Standards, Boulder, CO, NBSIR 79-1609 (1979), pp. 299-308.

3. H. I. McHenry and T. A. Whipple, "Weldments for Liquid Helium Service,"

in Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures-I II , National Bureau of Standards, Boulder, CO, NBSIR 80-

1627 (1980), pp. 155-165.

4. T. A. Whipple and H. I. McHenry, "Evaluation of Weldments and Castings

for Liquid Helium Service," in Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures-IV , National Bureau of Standards,

Boulder, CO, NBSIR 81-1645 (1981), pp. 273-287.

5. H. Yoshimura, H. Masumoto, and T. Inoue, "Properties of Low Carbon

25Mn-5Cr-lNi Austenitic Steel for Cryogenic Use," in Advances in Cryogenic Engineering-Materials , Vol . 28, Plenum Press, New York (1 982), pp. 115-

125.

6. W. G. Dobson and C. H. Kano, "Mechanical Testing at 4.2 K," Technical

Report Tr-A771-1, Teledyne Engineering Services, Waltham, MA, July 11,

1981.

241
7 . D. Duncan, M. C. Juhas, and R. Streit, "Development of a Facility for

Fatigue and Fracture Testing of Stainless Steel Weldments and Base Metal

at Liquid Helium Temperature," Lawrence Livermore National Laboratory,

Livermore, CA, unpublished, 1981.

8. T. A. Whipple and E. L. Brown, "Deformation and Fracture of Stainless

Steel Castings and Weldments at 4 K," in Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures-IV , National Bureau of

Standards, Boulder, CO, NBSIR 81-1645 (1981), pp. 415-452.

9. T. A. Whipple and D. J. Kotecki , "Weld Process Study for 316L Stainless

Steel Weld Metal for Liquid Helium Service," in Materials Studies for

Magnetic Fusion Energy Applications at Low Temperatures-IV , National

Bureau of Standards, Boulder, CO, NBSIR 81-1645 (1981), pp. 303-322.

10. K. A. Yushchenko and S. A. Voronin, "The Use of Low-Temperature

Strengthening of Steels in Welded Cryogenic Structural Codes," in

Advances in Cryogenic Engineering Materials', Vol . 28, Plenum Press,

New York (1982), pp. 137-145.

242
Table 1. Tensile Properties of Test Weldments at 4 K

Wei d

c MPa

y

*(ksi)

a MPa

u

*(ksi

)

Elongation

,

%

Reduction

in Area, %

316L (SAW) 655 (95.0) 1485 (215) 40.0 29.3

646 (93.7) 1489 (216) 39.6 32.2

662 (96.0) 1485 (215) 41.6 34.9

654 (94.9) 1486 (215) 40.4 32.1

Table 2. Fracture Toughness Properties of Test Weldments at 4 K

Wei d

J lc’

J ,in-lbx m in

K tIc

MPa/m

(J),

(ksi /in)

316L (SAW) 120 (685) 165 (150)

103 (590) 153 (139)

135 (770) 175 (159)

119 (682) 164 (149)

Modified 316L 46.9 (326) 114 (104)

(SMAW) 80.5 (460) 135 (123)

68.7 (393) 125 (114)

243
Table 3. Fatigue Crack Growth Rate Properties of Test Weldments

at 4 K.

Weld n* c*

316L (SAW) 4.08 6.47 x 10' 11

Modified 316L 3.99 6.19 x 10“ U

(SMAW)

Constants fit the equation: da/dN = CaK

p

, with da/dN

in mm/cycle and aK in MPa/m.

244
FRACTURE PROPERTIES OF A 25 MN AUSTENITIC STEEL AND ITS WELDS AT 4 K*

H. I. McHenry, J. W. Elmer

National Bureau of Standards

Fracture and Deformation Divisions

Boulder, Colorado 80303 USA

and

T. Inoue

Nippon Steel Corporation

Fundamental Research Laboratory

Kawasaki , Japan

ABSTRACT

Tensile properties, fracture toughness, and fatigue crack growth rates of

40-mm and 80-mm-thick plates of a 25Mn-5Cr-lNi steel were measured in liquid

helium at 4 K. Similar tests were conducted on 40-mm-thick shielded-metal -arc welds with a composition of 25Mn-2.8Ni-6.5Cr-l.4Mo. The tensile yield strengths

at 4 K were 895 MPa for the base metal and 961 MPa for the weld metal; these

values are much higher than the yield strength at room temperature (282 MPa

for the base metal). Fracture mechanics tests were conducted using

25.4-mm-thick compact tension specimens. The fracture toughness values

measured by the J-integral method were 249 MPa/m for the base metal and 158

MPa/m for the weld. The fatigue crack growth rates of both the base metal and

the weld were similar to the fatigue crack growth rates of 316 stainless steel

plate over the stress intensity range evaluated, 29-80 MPa/m. The results

indicate that the 25Mn-5Cr-lNi alloy has a favorable combination of strength,

toughness, and fatigue crack growth resistance at 4 K. The fracture surface

of representative fracture toughness specimens of the plate and the weld were examined by scanning electron microscopy, transmission electron microscopy,

and magnetic measurements; they were ductile and contained no evidence of a' martensite.

Accepted for presentation at the International Cryogenic Materials Conference

Kobe, Japan 11-14 May, 1982.

245

INTRODUCTION

A low-carbon, 25Mn-5Cr-lNi , austenitic steel has been developed for

cryogenic applications [1,2,3]. Previous work indicates that the 25Mn steel

has excellent strength and ductility to 4 K [1], high Charpy impact toughness

to 23 K (the minimum temperature tested) [1,2], a stable austenite microstructure [1,2], and a low (relative to austenitic stainless steels) thermal

expansion coefficient [3]. A weld metal with nearly matching composition,

25Cr-2.8Ni- 5.5Cr-1.4Mo, has comparable properties (1).

The objective of the present study is to measure the tensile properties,

fracture toughness, and fatigue crack propagation characteristics of 25Mn steel

plates and welds in liquid helium at 4 K. The test results are compared with

the corresponding properties of nitrogen-strengthened, austenitic, stainless

steel s.

TEST MATERIALS

The test plates of 25Mn steel were produced on a trial commercial scale

from a 45-Mg electric furnace heat, heat M2 from Ref. 1. Bottom-poured 14-Mg

ingots were reheated to 1200°C and rolled into 230 mm slabs. The slabs were

reheated to 1200°C and rolled into 40 and 80 mm thick plates. The plates were

solution treated at 1050°C for 90 min., then water quenched. The chemical

composition (ladle analysis) is shown in Table 1. The steel is microalloyed

with niobium (0.04%) to achieve a fine grain size due to precipitation of

niobium carbonitrides. Note that the steel contains only 0.04 percent nitrogen

and thus, nitrogen, a potent solution strengthener , does not contribute

appreciably to the base metal strength.

The test weldments were 40-mm-thick plates welded by the shielded metal arc

(SMA) process using dc reversed polarity. Welding was done in the flat

position at 140 A, 25 v and 2.2 to 3 mm/s. The joint preparation was a 35 mm

247
deep U-groove with a 30° included angle and a 3-mm root radius. This groove

was filled with 39 weld passes. The weld was back-gouged to a depth of 15 mm

and finished with 15 weld passes. The weld was x-ray inspected and no defects

were detected. The chemical composition of the weld metal is given in Table 1.

TEST PROCEDURES

Tensile

Tensile properties were determined for the base metal and the welds using

3.5-mm-diameter, 20-mm-gage-length specimens. Tests were conducted in liquid

helium at 4 K using a cylindrical support cryostat similar to the type

described by Reed [4]. Strain rates ranged from 4.2 x 10"^ to 4.2 x 10~^S~\

Base plate tensile specimens were aligned transverse to the rolling direction

and were taken from the midthickness of the plates. Weld metal tensile specimens were aligned both transverse to and along the centerline of the weld;

specimens were taken from the quarter- and midthickness of the weldment. The

complete test sections of the weld tensile specimens from each location were

located within the weld, as shown in Figure 1. The tensile properties measured

were the 0.2 percent offset yield strength, the ultimate tensile strength, and

the percent elongation in 20 mm.

Fracture Toughness

Fracture toughness was measured by the J-integral method [5] for the base

metal and welds using 25-mm-thick and 51-mm-wide compact tension specimens.

Tests were conducted in liquid helium at 4 K using a cryostat described by

Fowlkes and Tobler [6]. The single-specimen unloading-compliance technique was

used to measure J-Aa resistance curves for the base metal and the weld.

Additional J-integral tests were conducted on the base plate using multiplespecimen procedures, i.e, the specimen was unloaded after an increment of crack

extension, Aa. The Aa value was delineated after unloading by fatigue

248
crack growth, then the specimen was fractured and Aa was measured on the

fracture surface. The base metal specimens were taken from the midthickness of

the plates tested in the LT orientation (loaded transverse to the rolling

direction). The weld metal specimens were oriented as shown in Figure 1.

The J-Aa resistance curves were used to determine the J T values for the

base metal and weld, i.e., Jj is defined as the intersection of the blunting

line (J = aAa, where a is the flow strength) and the tearing line. The plane

strain fracture toughness K Ic

(J) was calculated from Jj using the

relation [5]:

K

lc

2 J IC

E ^

2

( 1 ) where E is Young's modulus and v is Poisson's ratio.

Fatigue Crack Growth Rate

Fatigue crack growth rate tests of the base metal and welds used the same

specimen configuration and orientations and the same cryostat as the fracture

toughness tests. The specimens were initially precracked in liquid nitrogen at

76 K. Final precracking (approximately 2 mm) and testing were conducted in

liquid helium at 4 K. Crack lengths were measured by the compliance technique.

A sinusoidal load cycle with frequencies of 10 to 20 Hz was used.

TEST RESULTS AND DISCUSSION

Tensile

The tensile test results for the base metal and welds are summarized in

Table 2. The base metal tensile properties were essentially the same for the

40-mm- and 80-mm-thick plates. Similarly, the weld metal tensile properties

were similar for the longitudinal and transverse orientations and for the

quarter- and midthickness positions. The yield strength of the weld metal was

about 10 percent greater than that of the base metal, and the tensile strength

of the weld metal was about 10 percent less than that of the base metal. The

249
overmatching yield strength of the weld metal is particularly important because

it avoids strain concentration in the weld.

Fracture Toughness

The results of the fracture toughness tests at 4 K are summarized in

Table 3: Kj

c (J) for the base metal is 242 MPa/m and Kj

c (J) for the weld metal

is 158 MPa/m. Equation (1) was evaluated using elastic constants of the base

metal at 4 K measured by Ledbetter and Austin [7]: E= 190 GPa and v = 0.274.

The yield strength and toughness data for 25Mn steel are compared with Read and

Reed's [8] trend line for austenitic stainless steels in Figure 2. Note that

the combination of yield strength and toughness for the 25Mn base metal

slightly exceeds the trend line. The weld metal properties fall below the

trend line, but the 25Mn welds have a favorable combination of strength and

toughness when compared with austenitic stainless steel [9, 10, 11] weld

metals.

Determination of the fracture toughness of the base metal was complicated

by the steep slope of the J-Aa curve. Originally, Kj

c (J) was to be measured by

the single-specimen J-integral technique. Single-specimen tests were conducted

on specimens from the 40-mm- and 80-mm-thick plates. In both cases, Jj

c could

not be determined because there was not a significant change in slope of the

J-Aa curve upon tearing. Eight additional tests (four specimens from each

plate thickness) were conducted using the multiple-specimen technique. The

results are plotted in Figure 3. In each of these tests, the specimen was

unloaded and Aa was marked after one of the major load drops that characterized

the load-displacement records, as shown in Figure 4. The specimens with small

Aa values were unloaded after one major load drop, the specimens with larger Aa

values were unloaded after two major load drops, etc. Close examination of the

data in Figure 3 indicates that the data occur in four groups separated by gaps

of crack extension. The crack appears to propagate in steps, accompanied by

load drops, rather than in a continuous manner. Each successive drop and

250
increment of crack extension is larger, giving rise to a tearing line with a

lower slope at large crack extensions.

The fracture toughness of the weld metal was determined by the singlespecimen J-integral method. The J-Aa curves for the two specimens, are shown

in Figure 5, did not clearly define tearing lines for determination of Jj

c owing to scatter of about ± 0.1 mm in Aa values. The tearing line for specimen

MW-2 was determined by the ASTM method [5], i.e., linear least squares fit of

valid data points The tearing line for specimen MW-4 could not be determined

by the ASTM procedure because the valid data were clustered within a Aa range

of .25 mm. The position of the tearing line for specimen MW-4 was the best fit

through the valid data plus the data within 0.15 mm of the blunting line. The

measurement problem is due, in part, to the large increments of cracks extension that occur after the initial 0.5 mm of crack extension. The loaddisplacement curves for the weld specimens had numerous small load drops prior

to maximum load, and then one (specimen MW-4) o-r three (specimen MW-2) large

load drops prior to fracture.

Fatigue Crack Propagation

The results of the fatigue crack growth rate tests at 4 K are summarized in

Figure 6 and Table 4. The base metal data for both plate thicknesses fall in

the same scatter band. Similarly, the data for two weld metal specimens fall

in the same scatter band. The crack growth rates in the base metal are

slightly higher than the rates in the weld metal, particularly at the lower aK

levels; however, the difference is not considered to be statistically significant because of the overlapping scatter bands.

The fatigue crack growth rates measured in the 25Mn austenitic steel plates

at 4 K are essentially the same as those observed in AISI grades 310S and 304L,

as reported by Tobler and Reed [12]. The rates measured in the 25Mn steel

251
weldments are significantly lower at low AK values than those observed in 316L

weldments, as reported by Whipple, McHenry, and Read [10].

Fracture Surface Observations

The fracture surfaces of representative fracture toughness and fatigue

crack growth rate specimens of the plate and the weld metal were examined by

scanning electron microscopy (SEM), transmission electron microscopy (TEM), and

magnetic measurements.

Examination of the fracture surface using the SEM revealed that both the

base metal and the weld failed in a tough ductile manner. The fracture surface

of the base metal (Figure 1) has a coarse texture, which is indicative of high

toughness; however, the dimples characteristic of ductile fracture by microvoid

coalescence were not observed. Apparently, the inclusion content of the base

metal was sufficiently low to reduce the formation of dimples, which are

initiated at inclusions. In contrast, the fracture surface of the weld

metal, shown in Figure 7, had many dimples that initiated at fine nonmetal lie

inclusions. This suggests that the weld metal toughness could be improved by

reducing the inclusion content, e„g. by welding with the gas metal arc or the

gas-tungsten-arc processes.

A thin foil was taken near the fracture surface and examined by TEM. No

transformation was observed. In addition, magnetic measurements on the

fracture surfaces did not indicate any ferromagnetism. Consequently, it is

concluded that the austenitic stability of the 25 mn steel is sufficient to

prevent a ' martensite from forming at 4 K even in regions of high deformation,

such as the fracture surfaces.

Visual examination of the fracture surfaces led to two interesting

observations. First, in the base metal, secondary fractures occurred in a

plane at a slight inclination to the fracture plane. These appeared as slivers

252
and may have contributed to the high toughness of the base metal. Second, no

evidence of microfissuring was found on the fracture surfaces of the weld metal

specimens. If microfissures were present in the weld, they would have been

apparent on the fracture surface as small cracks perpendicular to the fracture

surface.

CONCLUSIONS

The tensile properties, fracture toughness, and fatigue crack growth rates

of a 25Mn austenitic steel plates and welds have been determined in liquid

helium at 4 K. The results indicate that

1. The yield strength of the weld metal (961 MPa) overmatches the yield

strength of the base metal 894 MPa.

2. The combination of yield strength and toughness of the base metal

and welds compares favorably with the corresponding properties in

the austenitic stainless steels.

3. The fatigue crack growth rates are similar in the base metal and

welds and fall in the range of behavior observed in the 300-series

austenitic stainless steel.

253
REFERENCES

1. Yoshimura, H., Masumoto, H., and Inoue, T., in Advances in Cryogenic

Engineering , Vol . 28, Plenum Press, New York, ( 1 982 )

.

2. Yoshimura, H., Shimizu, T. , Yada, H., and Kitajima, K. , Transactions of

the Iron and Steel Institute of Japan, 2jD, 187 (1980).

3. Yoshimura, H., Yamada, N., Honma, H., and Ito, T. , Transactions of the

Iron and Steel Institute of Japan, _16, 98 (1976).

4. Reed, R. P., in Advances in Cryogenic Engineering, Vol. 7, Plenum Press,

New York, 448 (1962).

5. "ASTM Designation: E813-81, Standard Test for J, , a Measuare of Fracture

Toughness," in Annual Book of ASTM Standards, vSrt 10, American Society

for Testing and Materials, Philadelphia, PA (1981).

6. Fowlkes, C. W., and Tobler, R. L., Engineering Fracture Mechanics, 8^, 487

(1976).

7. Ledbetter, H. M. and Austin, M. W., Private Communication, National

Bureau of Standards, Boulder, CO (1982).

8. Read, D. T. , Reed, R. P., Cryogenics, 2_1 , 415 (1981).

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

of Fully Austenitic Stainless Steel Filler Metals at 4 K, National Bureau

of Standards, Boulder, CO, NBSIR 81-1645, 289 (1976).

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

Welding Journal Research Supplement^, 104s (1980).

11. Whipple, T. A., McHenry, H. I., and Read, D. T. , Welding Journal Research

Supplement, 60, 72s (1981).

12. Tobler R. L., and Reed, R. P., in Advances in Cryogenic Engineering,

Vol. 24, Plenum Press, New York, 82 (1978).

254
LIST OF TABLES

1. Compositions of 25Mn Austenitic Steel Base Plate and Welds(Ladle

Analysis)

.

2. Tensile Properties of 25Mn Austenitic Steel at 4 K.

3. Fracture Toughness of 25Mn Austenitic Steel at 4 K.

4. Fatigue Crack Growth Rates of 25Mn Austenitic Steel at 4 K.

255
Table

1.

Compositions

of

the

25Mn

Austenitic

Steel

Base

Plate

and

Welds

(Ladle

Analysis).

O

2: O 1 • O

OO

-Q O 1 • O

CT>

1

O 1 • O

r—

t

0 1 «3

- 2: • r“i

r--~ O s- CO lo

<_) • • 'd' to

r-- CT)

•1

cr> I"-. zr * . O CM

1—

1

CO O 0 00

. * O 0

0 CM 1—

l

D. 0 0 . . 0 0

CO 0 C . . lo LO

C\J CM

to CO

•r~ 00 to

CO * . 0 O

LO

CM CO CM t-H C_> . • O 0

„

OJ

+-> fO

r

Q_

QJ X)

to r

fD CD CD 3
Table

2.

Tensile

Properties

of

25Mn

Austenitic

Steel

at4

K

tocn< ocooop LD LO LO kt- ID Cl Oi CO O CTi IT) ro co n n n c\j oo

Cnc

cd

i- to

+-> Q_ do s:

VD OO N Cn <—i LO CO in in in

CD>C

LO

CM

LO

co >—i o o'! «-i o N ID ID W ID ID CM CO CO CO CO oo

CD>

«=C ooco

CO

a)

IDC

cd

cn

cn>

et

CD>c

CD fO

s_ o_ DO

IDCUISH

r— co o i—

i

co co cd cn

*3- Cn

co

cn cm

co co

cn <t>

co co co i . LO LO 00 o cn cn cn cn

CM

LO

cn

CD

o \ i— c -i-> o ro

•i- 4-> +J C

•i- CD CD *i— O S_ o. o

CD

f

c

£Z CD

CD •P“ CD

S- -o &-

CD CD > +-> >

CD S Z Z •l” z = CD c CD C

to c. to s- o s- 1— hHn H« Hn *-*W

CD

in

CDc

CD +J CJ

fO •!— oooo oooooo «3- *3- co co mi- mi- Mtcl. i—

CDQ.

>5

CD

+-> CD

CD

CD

CO CO

to

+-> CD D

CD

257
Table 3. Fracture Toughness of 25Mn Austenitic Steel at 4 K.

Type Test

Method

J T > Ic ’

kJ/m^

K

Ic

(J),

MPa/m

Base Metal Multiple specimen 280 242

Weld Metal Single specimen, MW-2 122 160

Weld Metal Single specimen, MW-4 116 156

258
Table 4. Fatigue Crack Growth Rates of 25Mn Austenitic Steel at 4 K.

Specimen Type C* n* R** AK range,

MPa/m

M40-1 40-mm-thick plate 2.5x10”q° 5.0 0.996 29.9-51.7

M80-1 80-mm-thick plate 4 . 5x10q 4.2 0.998 34.4-69.7

M40-1 , M80-1 Plate 2.6x10”q 4.3 0.994 29.9-69.7

MW-1 Weld 1.6x10

* 1.9x10";;

6.0xl0 _ii

5.5 0.999 36.2-66.1

MW-3 Weld 4.9 0.995 36.2-66.1

MW-1, MW-3 Weld 5.2 0.995 33.0-71.5

* Empirical constants defined by: — = C( AK)

n where: da/dN is in mm/cycle ^ AK is in MPa/m

**R = linear correlation coefficient

259
List of Figures

1. Test specimen locations and orientations.

2. Fracture toughness vs. yield strength for 25Mn austenitic steel at 4 K. The

trend line is for austenitic stainless steels at 4 K [8].

3. J-Aa resistance curve for 25Mn austenitic steel at 4 K.

4. A load-displacement record for a fracture toughness test on 25Mn austenitic

steel at 4 K.

5. J-Aa resistance curve for 25Mn austenitic steel welds at 4 K.

6. Fatigue crack growth rates for 25Mn austenitic steel at 4 K.

7. Scanning electron microscope photographs of fracture surfaces of 25Mn austenitic

steel fracture toughness specimens tested at 4 K.

260
261

Longitudinal

Weld

Tensile
YIELD

STRENGTH,

ksi

50

100

150

200

250

O) u[/msm ‘ssaNHonox aamovaa

O O

uj> edw ‘ssaNHonoi aamovaa

+j

fD

O)

CD

(/) o

CDa

cr> o

IS)

CD

CD -r- S- r—

-t—1 X) u cz 03 CD

S- i_

262

YIELD

STRENGTH,

MPa
-INTEGRAL,

kJ/m

3. J-Aa resistance curve for 25Mn austenitic steel at 4 K.

263
LOAD,

kN

DISPLACEMENT, mm

4. A load-displacement record for a fracture toughness test on 25Mn austenitic

steel at 4 K.

264
800

Z UI/P>J ‘iej6sju|-r

•“3

IT)

265

-Aa

resistance

curve

for

25Mn

austenitic

steel

welds

at4

K.
o

9|dAd/uiui ‘NP/ep

VN <

Fatigue

crack

growth

rates

for

25Mn

austenitic

steel

at4

K.
Plate

Weld

267

Scanning

electron

microscope

photographs

of

fracture

surfaces

of

25Mn

austenitic

steel

fracture

toughness

specimens

tested

at4

K.

DEFORMATION AND FRACTURE BEHAVIOR OF DUPLEX

AUSTENITE/DELTA-FERRITE MATERIALS AT 4 K.

T. A. Whipple

Fracture & Deformation Division

National Bureau of Standards

Boulder, Colorado

E. L. Brown

Department of Metallurgical Engineering

Colorado School of Mines

Golden, Colorado

ABSTRACT

A series of CF8M stainless steel castings, with varying ferrite contents,

that were deformed at 4 K have been examined with optical and electron microscopy. The purpose of this study is to investigate the deformation and

fracture modes in duplex austenite/delta-ferrite materials at 4 K.

It is shown that the typical fracture mechanism in duplex stainless

steels is a brittle fracture in the delta-ferrite, followed by a ductile

failure of the remaining ligaments of austenite. A completely brittle failure

can occur if there is enough delta-ferrite to form a continuous crack path.

It has also been found that the delta-ferrite, which was previously thought to

be nondeforming at 4 K, does deform by a twinning mechanism. The importance

of this deformation twinning in determining the macroscopic mechanical

properties will be the subject of further investigation.

269

INTRODUCTION

To establish specific criteria for the selection of stainless steel weld

filler alloys or casting alloys for cryogenic structural applications, it is

first necessary to establish the effects that alloy variables have on the

cryogenic mechanical properties of these materials. To date, a number of

factors have been established that have an effect on the cryogenic properties

of stainless steel weldments: the delta-ferrite content of the weldment, the

nitrogen concentration in the weld, and the fusion zone grain size of fully

austenitic weldments (1,2, 3, 4). Nevertheless, it still is not possible to

predict the properties of a stainless steel weldment on the basis of these

factors. Apparently there are factors beyond those stated above that cause

the observed wide variations in fracture toughness (2,5,6). This paper is a

continuation of a previous report (7), which presented metal lographic

observations on the fracture and deformation of duplex austenite/delta-ferrite

structures at 4 K. This investigation is on a series of CF8M stainless steel

castings that have been tested at 4 K.

There are currently very few 4-K mechanical property data on castings,

but a few initial tests have shown a wide variation in fracture toughness

similar to weldments (5). This is not surprising because weldments are

actually rapidly solidified castings. Stainless steel castings also generally

contain a certain percentage of delta-ferrite, although on a much coarser

scale than that of weldments, owing to the slower solidification of castings.

Because of the coarser structure and less directional nature of the

delta-ferrite in castings, they provide an excellent model material for the

study of basic deformation and fracture mechanisms in duplex

austenite/delta-ferrite materials. It is anticipated that this study will aid

in understanding the causes of the property variations in weldments and

castings

.

271
MATERIALS

The materials used in this investigation are a series of five CF8M

stainless steel castings. The chemical compositions of these castings are

given in Table 1. The nickel and chromium contents of the castings were

varied to obtain five residual delta-ferrite contents, ranging from 1.1 to

28.5 volume percent. The castings were produced by a commercial vendor; the

procedures used and room temperature mechanical properties have been reported

previously (8). The castings were received in the form of 30.5 cm (12 in)

x 61.0 cm (24 in) x 10.2 cm (4 in) blocks. All specimens were removed from

areas at least 15.2 cm (6 in) from either end and 3.8 cm (1.5 in) from either

surface. This was done to avoid any effects of the columnar grain structure

near the casting surfaces.

Figures 1 and 2 show typical undeformed microstructures of the 1.1 and

28.5 percent delta ferrite castings, respectively.

PROCEDURES

For this investigation a number of sectioning, metallographic and fractographic techniques were employed. Each technique allows the observation of

different phenomena. Macroscopic examination, optical microscopy, and scanning

electron microscopy (SEM) were used for making observations.

For the most part, metallographic specimens were prepared by using

standard mechanical grinding and polishing techniques, but in a few cases

electrolytic polishing was used. A 10 percent oxalic acid electrolytic etch

was used as a general purpose etch to reveal ferrite morphology and grain

boundaries. A 10 N K0H electrolytic etch was used to reveal ferrite structure

only. This is a deposition etch that colors the ferrite light blue to brown.

The main attribute of this etchant is that it does not remove any material;

therefore, it will not round the edges of cracks or produce pitting and other

272
etching artifacts. A boiling solution of 1 part and 2 parts H

3 P04 was

used to reveal strain induced martensite.

RESULTS AND DISCUSSION

Low Temperature Deformation

It is generally true that bcc materials, such as delta-ferrite, go

through a ductile-to-brittle transition at low temperatures, whereas fee

materials, such as austenite, do not. This is due to the difficulty of

operating non -cl ose-packed slip systems at low temperatures. The temperature

at which this transition occurs in steels is influenced mainly by alloy

content and microstructure; a higher nickel content and a smaller grain size

lead to a lower transition temperature. Another factor to consider is the

increase in strength with a reduction in temperature; bcc materials have a

much more dramatic increase in yield strength than fee materials at low

temperatures

.

These general observations lead to some expectations for the behavior of

duplex stainless steels. At higher temperatures, both austenite and ferrite

are ductile and have similar strengths; in this case the amount and morphology

of delta-ferrite is expected to have a much smaller effect on strength and

ductility than at low temperatures where the delta-ferrite is strong and

brittle. The effect of the property transition in the delta-ferrite should be

to increase the strain-hardening rate of the duplex alloy. Data that demonstrate the greater strengthening effect of delta-ferrite at cryogenic temperatures have been presented by Read, McHenry, Steinmeyer, and Thomas (1).

Evidence to date had indicated that delta-ferrite does not deform at 4 K.

However, work on the series of CF8M castings has shown that this is not

strictly true. As can be seen in Figure 3, the delta-ferrite does deform by a

273
twinning mechanism. The jogs in the del ta-ferrite/austenite interface and the

fact that twins are not observed in undeformed structures (Figures 1 and 2)

demonstrate that they are, in fact, deformation twins. Further evidence of

this conclusion is given in Figure 4 in which three twin variants are shown.

A stereographic projection of the angles between the three variants shows that

they are consistent with (112) twin planes, which is typical for deformation

twinning in ferritic materials.

In a macroscopic sense, the deformation associated with twinning in the

delta-ferrite is small; however, it may have some significant secondary

effects. One of these effects can be seen in Figures 5 and 6. These figures

show bands of intense martensite formation in the austenite at the ends of

deformation twins in the delta-ferrite. This intense deformation could create

preferred sites for void nucleation in the austenite.

Low Temperature Fracture

As discussed in the previous report (7), it appears appropriate to

classify duplex austenitic stainless steel at low temperatures as a ductile

matrix composite with hard, brittle discontinuous fibers. This is not an

exact classification, since the delta-ferrite does show some evidence of

deformation and can be either continuous or discontinuous, depending on

solidification and cooling conditions, but this classification does provide a

good starting point for the discussion of fracture mechanisms. There are

three possible mechanisms for the fracture of ductile

matrix/hard-discontinuous fiber composites (8).

1. Brittle fracture of the fibers.

2. Matrix/fiber interface separation.

3. Fiber pull-out.

Brittle fracture of the fibers occurs when the local stress in the fiber

exceeds its fracture strength. The local stress in the fiber is not neces274
sarily the same as the macroscopic stress on the sample, it can be considerably higher owing to inhomogeneous plastic deformation in the matrix. Interface separation is an important consideration with artificial composites and

with metal -matrix/particulate composites; however, the interface between

austenite and delta-ferrite appears to be very strong and no evidence of

interfacial separation has been observed. Fiber pull-out is sometimes

associated with interface separation, but for the purpose of this discussion

it means a ductile failure of the matrix near the matrix/fiber interface.

This occurs when the fiber does not fracture, but the highly inhomogeneous

deformation of the matrix near the fiber results in void nucleation at this

location. The occurrence of one of these mechanisms over the others depends

on fiber strength, content, and morphology.

In the previous study (7), evidence was found for both fiber fracture and

fiber pull-out. Until that investigation there had been no direct observation

of the brittle fracture of ferrite in weldments and castings at 4 K. Although

this had long been assumed to be the cause of the reduction in toughness of

stainless steel weldments with increasing ferrite content, direct observation

was difficult because of the extremely small size of the ferrite in weldments.

From the observations made to date, fiber pull-out appears to be the less

prevalent of the two fracture mechanisms observed. The most commonly observed

mechanism is brittle fracture of the delta-ferrite. If the delta-ferrite is

conti rvuous, the brittle fracture will result in specimen failure. However, in

the case of discontinuous delta-ferrite, the brittle fracture of discrete

particles will cause stress concentrations that will result in ductile failure

of the austenite matrix. An example of this mechanism is shown in Figure 7,

where, brittle fractures in a delta-ferrite particle are shown with ductile

fracture in the austenite between two cracks. This mechanism will result in a

275
fracture surface displaying a mixed mode fracture (shown in Figure 8), which

is commonly observed in these materials.

The deformation twinning in the delta-ferrite does have an effect on the

fracture process. The different orientation of the cleavage planes in the

twins causes the crack to change direction. This can be seen in the

micrograph in Figure 9. The deformation twinning and the change in crack path

can result in additional energy being absorbed in the fracture process, which

could result in a higher fracture toughness. It is not possible, at this

time, to determine the quantitative effect that this has on the fracture

toughness of these materials.

SUMMARY

Samples of stainless steel castings and weldments that had been deformed

and fractured at 4 K were examined. The thrust of the investigation was to

determine the mechanisms by which residual delta-ferrite affects the deformation and fracture of duplex austenite/delta-ferrite structures at cryogenic

temperatures. Evidence was presented indicating that at low temperatures the

delta-ferrite acts as a hard, brittle second phase particle. The manner in

which these particles affect the mechanical properties of the material depends

on the amount, properties and morphology of the second-phase particles. It

was observed that the delta-ferrite reinforces the austenite matrix and causes

the deformation to be inhomogeneous. Evidence was found for two fracture

mechanisms: (1) brittle fracture of the delta-ferrite mixed with ductile

failure of the matrix between delta-ferrite fractures and (2) ductile failure

in the matrix near the austenite/ferrite interface, which was caused by the

highly inhomogeneous deformation in this region. The occurrence of one of

these mechanisms over the other depends on the morphology and properties of

delta-ferrite. It was also observed that delta-ferrite deforms by a twinning

mechanism at 4K. These deformation twins have an effect on the fracture

process

.

276
REFERENCES

1* D. T. Read, H. I. McHenry, P. A. Steinmeyer, and R. D. Thomas,

"Metallurgical Factors Affecting the Toughness of 316L SMA Weldments at

Cryogenic Temperatures," Weld. J. Res. Suppl

.

, 59, 1980, p. 104s.

2. T. A. Whipple, H. I. McHenry, and D. T. Read, "Fracture Behavior of

Ferrite-Free Stainless Steel Welds in Liquid Helium," Weld. J. Res.

Suppl. , 60, (4), 1981, p. 72s.

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

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

Weld. J. Res. Suppl

.

, 57, 1978, p. 325s.

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

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

Weld. J. Res. Suppl , 58, 1979, p. 34s.

5. T. A. Whipple and H. I. McHenry, "Evaluation of Weldments and Castings

for Liquid Helium Service," in Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures-IV, National Bureau of

Standards, Boulder, CO, NBSIR 81-1645, 1981, p. 273.

6. T. A. Whipple and D. J. Kotecki , "Weld Process Study for 316L Stainless

Steel Weld Metal for Liquid Helium Service," in Materials Studies for

Magnetic Fusion Energy Application at Low TemperaturesIV , National

Bureau of Standards, Boulder, CO, NBSIR 81-1645, 1981, p. 303.

7. T. A. Whipple and E. L. Brown, "Deformation and Fracture of Stainless

Steel Castings and Weldments at 4 K," in Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures-IV, National Bureau of

Standards, Boulder, CO, NBSIR 81-1645, 1981, p. 415.

8. A. Kelly, "Particle and Fibre Reinforcement," in Strengthening Methods

in Crystals, Halsted Press Division, John Wiley & Sons, New York, 1971,

pp. 433-484.

277
Table

1.

Chemical

analysis

of

five

heats

of

CF8M

with

variable

ferrite

content.

Heat C

Mn

Si

Cr

Ni

MoN%

Del

ta-Ferrite*

(vol

ume)

f—1CM CM r-H ID e • • © e f-H CO

f-H COCM

00

CM

LO LO LO LD LO O o o O O © • • • • o o o O o

CM CM CO CO CO i—1 f-H f-H fl-H CM • • • • • CM CM CM CM CM

f-H LO CM *3" CM CO CM CM co

CO

r-H of-H CO co* CD

CM CO o x> o CO CM LO c • • • • C3 CO O') CD o CM o

f—1

f-H f-H CM CM <_>

+-> c

•1—o

cd co CO LO f-H Cl

LO r-H l—1

CD f-H • • • • • o o r-H f-H O r-H XT

Q.

CO

s_CD o 00 co LO CD O

r-H CO CO CO CO r— • • • • • f-H o o o o fO

-4-J OlE

CO co CO CO co LO o o o o o >> • • • • • XI o o o o o to

(1) 1-

13CO

co

t—H

CM CO LO 0) *

278
LIST OF FIGURES

Figure 1. A micrograph of the undeformed initial structure of the 1.1

percent delta-ferrite casting.

Figure 2. A micrograph of the undeformed initial structure of the 28.5

percent delta-ferrite casting.

Figure 3. A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing deformation twinning.

Figure 4. A micrograph of a tensile specimen from the 8.2 percent deltaferrite casting, showing three deformation twin variants.

Figure 5. A high magnification micrograph of a tensile specimen from the

8.2 percent delta-ferrite casting, showing the intense deformation in the austenite associated with twinning in the delta

ferri te.

Figure 6. A micrograph of a tensile specimen from the 8.2 percent deltaferrite casting, showing bands of deformation in the austenite

caused by the deformation twinning of the delta ferrite.

Figure 7. A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing ductile failure of austenite between

brittle fracture of delta-ferrite particles.

Figure 8. A SEM fractograph of a fracture toughness specimen of the 8.2

percent delta-ferrite casting, showing the mixed mode fracture.

Figure 9. A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing the effect of deformation twins on the

crack path.

279
Figure 1.

\ / - .<? r

/• - A ,

•

v

f \

H,

200 um

A micrograph of the undeformed initial structure of the 1.1

percent delta-ferrite casting.

280
200 ym

Figure 2. A micrograph of the undeformed initial structure of the 28.5

percent del ta-ferrite casting.

281
Figure 3.

20 ym

A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing deformation twinning.

282
Figure 4.

20 urn

A micrograph of a tensile specimen from the 8.2 percent deltaferrite casting, showing three deformation twin variants.

283
1 0 ym

Figure 5. A high magnification micrograph of

8.2 percent delta-ferrite casting,

tion in the austenite associated

ferrite.

a tensile specimen from the

showing the intense deformawith twinning in the delta

284
Figure 6.

50 ym

A micrograph of a tensile specimen from the 8.2 percent deltaferrite casting, showing bands of deformation in the austenite

caused by the deformation twinning of the delta ferrite.

285
Figure 7.

50 pm

A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing ductile failure of austenite between

brittle fracture of delta-ferrite particles.

286
Figure 8. A SEM fractograph of a fracture toughness specimen of the 8.2

percent delta-ferrite casting, showing the mixed mode fracture.

287
Figure 9.

50 ym

A micrograph of a tensile specimen from the 28.5 percent deltaferrite casting, showing the effect of deformation twins on the

crack path.

288
THE EFFECT OF DELTA-FERRITE ON THE MECHANICAL PROPERTIES

OF CF8M STAINLESS STEEL CASTINGS AT 4 K

T. A. Whipple

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A series of five CF8M stainless steel castings, with varying deltaferrite contents, has been tensile and fracture toughness tested at 4 K.

Tensile tests were conducted in the low strain region to establish the initial

strain hardening behavior for comparison with two phase deformation theory.

It was found that the tensile behavior of the duplex austenite/delta-ferrite

structure fits very well with the two phase deformation theory proposed by

Ashby. The initial strain hardening rate is determined by the mean-free-path

between delta-ferrite particles. Fracture toughness results at 4 K show a

decrease in fracture toughness with increasing delta-ferrite content up to

approximately 15 percent; at this point a continuous delta-ferrite crack path

is established, and the fracture toughness remains constant with increasing

del ta-ferrite.

289

INTRODUCTION

In some cryogenic structural applications it would be advantageous to use stainless steel castings, rather than wrought and welded construction.

Castings have the advantage of a much lower cost of manufacture when complicated shapes are involved. To date, the use of stainless steel castings for

4-K service has been very limited; this may be partially due to the limited

data available on the mechanical properties at 4 K (1).

The most significant data available on the tensile and fracture toughness

properties of stainless steel castings at 4 K came from a series of CF8

centrifugal castings with varying delta-ferrite contents (1,2). There were

six heats from three different vendors with delta-ferrite contents ranging

from 0 to 14.5 percent. The results generally showed an increase in strength

and a decrease in fracture toughness with increasing ferrite content. The

purpose of this testing on CF8 castings was to select a material for use as

the bore tube for a MHD superconducting magnet.

In the present study a series of five CF8M stainless steel castings was

tensile and fracture toughness tested at 4 K. The purpose of this study is

twofold: First, it is intended to develop a data base on the tensile and

fracture toughness properties of CF8M at 4 K. Second, it is intended to aid

in the understanding of the effects of delta-ferrite on the mechanical properties of duplex austenite/delta-ferrite structures at 4 K. It is anticipated

that the description of the fundamental aspects of the deformation behavior

of castings will also be applicable to stainless steel weldments, since they

also generally contain delta-ferrite.

291
MATERIALS

The materials used in this investigation are a series of five CF8M

stainless steel castings. The nickel and chromium contents of the castings

were varied to obtain five residual delta-ferrite contents, ranging from 1.1

to 28.5 percent. The castings were produced by a commercial vendor; the

procedures used and room temperature mechanical properties have been reported

previously (4). The castings were received in the form of 30.5-cm (12-in)

x 61.0 -cm (24-in) x 10.2- cm (4-in) blocks. All specimens were removed from

areas at least 15.2 cm (6 in) from either end and 3.8 cm (1.5 in) from either

surface. This was done to avoid any effects near the casting surfaces.

PROCEDURES

Tensile Tests

The tensile tests at 4 K were conducted with the test apparatus and

cryostat described by Reed (5). The test specimens were 0.635-cm (0.25-in)

smooth bar tensile specimens, with a 2.54-cm (1.0-in) gage length. The

high-sensitivity strain measurements were made using two resistance type

strain gages mounted on the specimens 180° apart. The strain limit for these

gages is usually about 2 percent. A strain gage extensometer was also mounted

on the specimen; this measured up to 10 percent strain with lower sensitivity.

The remainder of the stress-strain curve was obtained from a load-time record

at a known crosshead displacement rate.

Plastic strain measurements in the low strain region (less than 0.5%

plastic strain) were made using the resistance strain gages and signal condi-

-6 tioning equipment capable of resolving 10” strain. A load/unload technique

was used in which the specimen is loaded to a given stress and then unloaded

to zero stress. The residual plastic strain is recorded and the

292
specimen is reloaded to a higher stress and the process is repeated until a

total plastic strain of about 0.5 percent is reached. At this point the

specimen is loaded monotonical ly to failure and the strain is recorded using

the extensometer and load/time record.

Fracture Toughness Tests

For these tests, a new fracture toughness test procedure using threepoint -bend -specimens , rather than the previously used compact- tension (CT)

specimens, has been developed. The single edge notched three point bend

specimens are 2.54-cm (1.0-in) wide, 2.54-cm (1.0-in) thick, and have a span

of 10.2 cm (4.0 in). The main difference in the single-specimen J-integral

test procedure is that with three-point-bend specimens it is necessary to

measure two displacements: the load-line displacement and the crack-mouthopening displacement. With CT specimens, the two displacements are

coincident. A direct measurement of the load-line displacement is made using

the comparison bar method developed by Dawes (6). The load-line displacement

is used to calculate the J-integral and the crack-mouth-opening displacement

is used to calculate the crack length using a standard compliance

function (7).

A three-point-bend fracture-toughness specimen, with the comparison bar

and clip gages attached, is shown in figure 1. The three-point-bend test

fixture used for cryogenic testing is shown in figure 2. The test data are

acquired and reduced by a laboratory minicomputer, as described by Read (8).

Metallography

The volume percent delta-ferrite and the mean free path between deltaferrite particles were measured metal lographical ly, using a computerized image

analyzer. The specimens were electrol itical ly etched using a 10 N KOH solution, which gives good phase contrast. The values reported for volume percent

and mean free path represent the average for 400 fields at 100 times magnification.

293
RESULTS

The results of tensile tests at 4 K are given in table 2 and shown

graphically in figures 3, 4, and 5. All results are the average of two tests.

Figure 3 shows the stress versus plastic strain curves at less than 0.2-

percent plastic strain (yield strain). Note that the proportional limit (the

onset of plastic deformation) occurs at very close to the same stress for all

five delta-ferrite contents. The differences in 0.2-percent offset yield

strength arises from differences in the strain-hardening rate. In this

plastic strain region, the curve for the 17.3-percent delta-ferrite casting

lies below that of the 8.2 percent delta-ferrite casting, however, the higher

delta-ferrite casting has a higher strain hardening rate, and the two curves

intersect at 0.2 percent plastic strain.

Figure 4 shows the complete stress versus plastic strain curves for the

five CF8M castings. As do most materials tested at 4 K, the castings did

display serrated stress/strain curves. For clarity, the serrations are not

shown and the curves are smooth lines drawn through the peak stresses. Also

not shown is the remainder of the curve for the 1.1 percent delta-ferrite

casting, which actually had a total elongation of 49 percent. The important

features to note in figure 4 are that in the low plastic strain region (less

than 5 percent) there is a very large increase in strain hardening rate with

increasing delta-ferrite content and that above this strain level the curves

are approximately parallel.

These observations are shown more clearly in figure 5, which gives the

flow stress as a function of delta-ferrite content at various levels of

plastic strain. At low strains, 10 ^ and 10”^, the stress shows no definite

correlation with the delta-ferrite content; however, as the strain increases,

the flow stress becomes linear with delta-ferrite content. Also note that at

294
0.025 strain and above the lines are parallel, indicating that the strain

hardening rate is independent of delta-ferrite content.

The results of fracture toughness testing at 4 K as a function of deltaferrite content are given in table 3 and shown graphically in figure 6. The

fracture toughness result on the 1.1 percent delta-ferrite casting is invalid

by specimen size requirements and is used here only as an approximate value.

However, it can be said that the fracture toughness of this alloy is much

higher than the other four heats and is comparable to that of wrought

materials of similar compositions. The interesting feature of the fracture

toughness data is that the three high delta-ferrite heats (17.3, 23.1, and

28.5 percent) have approximately the same fracture toughness. Also shown on

figure 6 are the fracture toughness results from Reference 9 on a series of

316L weldments that are similar in composition to CF8M castings. These data

indicate that at a given delta-ferrite content castings have a higher fracture

toughness than weldments.

DISCUSSION

Extensive metal 1 ographic observations on stainless steel weldments and

castings containing delta-ferrite, which have been deformed and fractured at

4 K, has qualitatively shown that these duplex materials can be treated as a

ductile matrix/hard-brittle discontinuous fiber composite (10). The materials

previously examined did not constitute a controlled series on which quantitative analysis could be performed. The present study on the controlled series

of CF8M stainless steel castings with the chromium and nickel contents varied

to change the delta-ferrite content does make this analysis possible. There

are two basic approaches to modeling the deformation and fracture of two phase

materials.

The composite modeling approach attempts to predict the properties based

on the volume fraction of fibers and the properties of the two constituents.

295
This approach is best developed and most applicable to unidirectional continuous fiber composites (11). The composite model in its simplest form is called

the "rule of mixtures," which predicts the total stress to be divided between

the fiber and matrix in proportion to the volume fractions.

a = a x V. + a V > c f f mm ( 1 )

where V r and V are the volume fractions of the fiber and matrix,

respectively. The assumption implicit in the use of this equation is that the

strain in the fiber and matrix are equal. This assumption is good for

unidirectional continuous fiber composites stressed axially with respect to

the fiber orientation. Deviations from this assumption make the rule of

mixtures less valid. Considerable effort has been made to modify this model

for other cases (12,13); these efforts have resulted in varied success and are

generally only applicable to very limited cases.

The results of this study do follow the form predicted by the rule of

mixtures, that is, the stress is linearly related to the volume fraction of

delta ferrite (see figure 5). However, beyond this point the composite

modeling approach cannot do much towards describing the deformation

mechanisms. For these reasons the following model is preferred.

The other approach to modeling the deformation of two phase materials is

the micro-mechanical model. In this model the microscopic deformation

mechanisms are used to predict the effect of second phase particles on the

macroscopic properties. The model is described in detail by Ashby (14), and

only the major points are discussed here. The case described by this model is

that of a ductile matrix with a nonplastical ly deforming second phase. To

describe the plastic deformation of this type of material the concept of two

different types of dislocations is introduced: geometrically necessary and

statistically stored dislocations. Geometrically necessary dislocations are

those that are needed to accommodate the nonuniformity of strain in the matrix

296
when it contains a particle that does not deform. The density of these

dislocations can be calculated as a function of the particle size, shape and

arrangement and the plastic strain in the matrix. The other type of dislocations, statistically stored, are those dislocations that are produced in the

matrix as a result of plastic strain, independent of the presence of a secondphase particle.

Ashby has shown that densities of geometrically necessary and statistically stored dislocations can be related to strain in a general way by

G 4y

p = ~r~

x b

b (2)

and

S _ 4y

P "

A S

b (3)

G S where A is the geometric slip distance, A is the slip distance for statistir cal storage, y is the shear strain, and b is the Burgers vector. A is a

microstructural parameter related to the arrangement of second phase particles

$ and does not vary with strain. A , however, does vary with strain, becoming

smaller as the strain increases.

How these dislocation densities affect the macroscopic stress-strain

properties will now be considered. The general expression relating the flow

stress to the dislocation density is (15).

t

= Tq + CGb/p (4)

where x is the applied shear stress, Tq is the frictional stress, G is the

shear modulus and C is a constant. The dislocation density in this equation

is the sum of the two densities discussed above; therefore the flow stress

will be controlled by the larger of the two dislocation densities. At the

c onset of plastic deformation, A (equation 3) can be taken as the grain size

Q of the matrix. If the microstructural parameter, A , is smaller than the

grain size of the matrix, the geometrically necessary dislocation density will be

297
s larger and will dominate the early stages of deformation. Since x decreases

with strain, the statistically stored dislocation density will increase more

rapidly and eventually overtake the geometrically necessary dislocation

density and dominate the flow stress at higher strains.

To discuss this model with respect to the duplex austenite/delta-ferrite

stainless steel castings of this study the microstructure of the castings was

considered to be the ideal case shown in figure 7. In this ideal microstructure the delta-ferrite occurs as a cubic array of square plates.

Ashby (14) has shown the geometrically necessary dislocation density for this

arrangement to be

where £ is the mean free path between plates. This parameter has been

measured for the five CF8M castings and is given in table 4. The effect of

increasing the delta-ferrite content is to reduce this value.

Based on the Ashby model it is possible to predict, in a qualitative

manner, the differences in stress-strain behavior between the five CF8M

castings. Referring to equation 4, the onset of plastic deformation is only

dependent on the frictional stress, t^, in the matrix and should be independent of delta-ferrite content. At low strain levels the flow stress will be

controlled by the geometrically necessary dislocation density, since the

mean free path between delta-ferrite particles is much smaller than the

austenite grain size. If the geometrically necessary dislocation density is

controlling, equation 5 can be substituted into equation 4

and at a constant strain, the flow stress should be proportional to the

inverse square root of the mean free path. At some higher strain the

G 4y

p = bl (5)

( 6 )

298
statistically stored dislocation density will become controlling and the

increase in flow stress with increasing strain (strain hardening rate) should

be independent of delta-ferrite content. Since the strain at which the

statistically stored dislocation density becomes controlling is dependent on

the difference between the austenite grain size and the delta-ferrite spacing,

it should also increase with increasing delta-ferrite content.

The tensile results, at 4 K, from the CF8M castings, (figures 3,

4, and 5), fit very well with the above predicted behavior. The only

_5 exception was that the onset of plastic strain, taken to be 10 plastic

strain, did not occur at the same stress for all the castings. This means

that Tq is not constant. The exact reason for this has yet to be determined,

however, it could be due to differences in compositions of the austenite or a

number of other factors. To eliminate this factor in the analysis Tq is taken

_5

to be the flow stress at 10 plastic strain and equation 6 is rearranged.

This predicts that the difference between the flow stress at a given strain

of the mean free path between delta-ferrite particles. The data for two

strains are plotted on figure 8 and show a good fit with the theoretical

slope.

The foregoing discussion demonstrates that the duplex structure of CF8M

castings at 4 K behaves as predicted by two-phase deformation theory. This

results in a better understanding of the deformation of duplex structures at

4 K and may lead to the determination of methods of improving the performance

of these materials.

(7)

_5

and the flow stress at 10 strain is proportional to the inverse square root

299
An analytical treatment of the fracture toughness properties of two phase

materials is much more difficult than that of tensile properties. This

analysis will be undertaken in future work. However, a few points can be made

with respect to the fracture toughness results of this study. It is evident

from numerous studies that an increase in the delta-ferrite content of stainless steel weldments and castings decreases the fracture toughness. This

study has shown that at higher delta-ferrite contents the fracture toughness

reaches a constant level. Metal 1 ographic and fractographic evidence has shown

that this is related to the establishment of a continuous delta-ferrite path

through which the crack can propagate, without the necessity of ductile

failure in the austenite. The fracture toughness value at high delta-ferrite

contents is consistent with what would be expected of a ferritic stainless

steel of similar composition.

CONCLUSIONS

1. The tensile behavior of CF8M stainless steel castings at 4 K is

consistent with a two- phase deformation model, which predicts the

relative strain hardening rates as a function of the mean free path

between delta-ferrite particles.

2. Increasing the delta-ferrite content of CF8M castings decreases the

fracture toughness at 4 K, up to a del ta-ferrite content of 17 percent.

Above this point the fracture toughness is constant.

ACKNOWLEDGMENT

This study was supported by the Department of Energy Office of Magnetic

Fusion Energy. The author would like to thank R. J. Fields of NBS for the

quantitative metallography work he performed.

300
REFERENCES

1. D. Dew-Hughes and K. S. Lee, "The Choice of Steel for the Isabelle Magnet

Tubes," Advances in Cryogenic Engineering, Vol . 26, Plenum Press, New

York, (1981), pp. 151-157.

2. E. L. Brown, T. A. Whipple and R. L. Tobler, "Fracture Toughness of CF8

Castings in Liquid Helium," Met. Trans. To be published. Also in

Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures -V , National Bureau of Standards, Boulder, CO, NBSIR 82-

(1982) pp. 107-143.

3. T. A. Whipple and H. I. McHenry, "Evaluation of Weldments and Castings

for Liquid Helium Service," in Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures-IV , National Bureau of Standards,

Boulder, CO, NBSIR 81-1645, (1981), pp. 273-287.

4. L. Finch, "The Influence of Ferrite and Nitrogen on the Mechanical

Properties of CF8M Cast Stainless Steel," in Materials Studies for

Magnetic Fusion Energy Applications at Low Temperatures-IV , National

Bureau of Standards, Boulder, CO, NBSIR 81-1645, (1981) pp. 337-355.

5. R. P. Reed, "A Cryostat for Tensile Tests in the Temperature Range 300 to

4 K," in Advances in Cryogenic Engineering , Vol. 7, K. D. Timmerhaus ed.,

Plenum Press, New York (1961), pp. 448-454.

6. M. G. Dawes, Welding Institute Research Bulletin, 7, (1976), p. 185.

301
7. A. Saxena and S. J. Hudak, Jr., "Review and Extension of Compliance

Information for Common Crack Growth Specimens," Int. J. of Fracture, V\_,

5, (1978), pp. 453-468.

8. D. T. Read, "The Computer-Aided J-Integral Test Facility at NBS," in

Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures-III , National Bureau of Standards, Boulder, CO, NBSIR

80-1127, (1980), p. 205.

9. D. T. Read, H. I. McHenry, P. A. Steinmeyer, and R. D. Thomas, "Metallurgical Factors Affecting the Toughness of 316L SMA Weldments at Cryogenic

Temperatures," Weld. J. Res. Suppl . , 59 , (1980), pp. 104s-113s.

10 T. A. Whipple and E. L. Brown, "Deformation and Fracture of Stainless

Steel Castings and Weldments at 4K," in Materials Studies for Magnetic

Fusion Energy Applications at Low Temperatures-I

V

, National Bureau of

Standards, Boulder, CO, NBSIR 81-1645, (1981), pp. 415-451.

11. A. Kelly, "Particle and Fibre Reinforcement," in Strengthening Methods in

Crystal s

,

Halsted Press Division, John Wiley & Sons, New York, (1971),

pp. 433-484.

12. S. T. Mileiko, "The Tensile Strength and Ductility of Continuous Fibre

Composites," J. of Mat. Sci . , 4, (1969), pp. 974-977.

13. B. W. Rosen, "Mechanics of Composite Strengthening," in Fiber Composite

Materials , ASM, Metals Park, Ohio, (1965), pp 37-75.

302
14. M. F. Ashby, "The Deformation of Plastically Non-Homogeneous Alloys," in

Strengthening Methods in Crystals , Halsted Press Division, John Wiley &

Sons, New York, (1971), pp. 137-192.

15. F. R. N. Nabarro, Z. S. Basinski and D. B. Holt, "The Plasticity of Pure

Crystals" Adv. in Physics, _13, (1964), p. 193.

303
LIST OF TABLES

Table 1

Table 2

Table 3

Table 4

Chemical composition and delta-ferrite contents of CF8M castings.

Tensile properties of CF8M stainless steel castings at 4 K.

Fracture toughness properties of CF8M castings at 4 K.

The mean free path between delta-ferrite particles in the CF8M

castings.

304
Table

1.

Chemical

analysis

of

five

heats

of

CF8M

with

variable

ferrite

content.

305
Table 2. Tensile properties of CF8M stainless steel castings at 4 K.

Heat Flow

ID'

5

Stress at

10“ 3

Given Strain,

2xl0"

3

MPa

10' 2

Ultimate Strength

MPa

Elongation

°l

1 378 556 581 614 1215 49

2 448 613 653 700 986 21

3 308 574 641 779 1143 19

4 376 630 707 855 1221 19

5 410 783 851 962 1164 11

306
Table 3. Fracture toughness properties of CF8M castings at 4K.

Heat J TIc

KJ/m

2

Ki c (0)

MPa/m

1 562.0* 352*

2 99.4 148

3 62.1 117

52.5 108

4 52.5 108

48.1 103

5 49.0 104

49.9 104

* Invalid by specimen size requirements.

307
Table 4. The mean free path between delta-ferrite particles in the

CF8M castings.

Heat Mean Free Path mm

1 1.55

2 0.185

3 0.074

4 0.064

5 0.044

308
LIST OF FIGURES

Figure 1. A three-point-bend fracture toughness specimen with the comparison bar and clip gages.

Figure 2. Test fixture for three-point-bend fracture toughness testing at

cryogenic temperatures.

Figure 3. The stress versus microstrain results for the five CF8M stainless

steel castings at 4 K.

Figure 4. The total stress versus plastic strain curves for the CF8M

castings at 4 K. The load drops and the remaining 24 percent

strain for the 1.1 percent delta-ferrite casting are not shown.

Figure 5. The flow stress as a function of del ta-ferri te content at various

strain levels for the CF8M castings at 4 K.

Figure 6. The plane strain fracture toughness, at 4 K, as a function of

delta-ferrite content for CF8M castings and 316L weldments (8).

Figure 7. An ideal representation of the microstructure of CF8M stainless

steel castings used for modeling the deformation at 4 K. The

delta-ferrite occurs as a cubic array of square plates.

Figure 8. A log-log plot of the flow stress difference, at 4 K, as a function of the mean-free-path between delta-ferrite particles.

The data are compared with the theoretical slope of -0.5.

309
Figure 1. A three-point-bend fracture toughness specimen with the comparison bar and clip gages.

310
Figure 2. Test fixture for three-point-bend fracture toughness testing at

cryogenic temperatures.

311
STRESS,

MPa

Figure 3. The stress versus microstrain results for the five CF8M stainless

steel castings at 4 K.

312
STRESS,

MPa

PLASTIC STRAIN, %

Figure 4. The total stress versus plastic strain curves for the CF8M

castings at 4 K. The load drops and the remaining 24 percent

strain for the 1.1 percent delta-ferrite casting are not shown.

313
STRESS,

MPa

1200

ti i i i 0 10 20 30

PERCENT DELTA FERRITE

Figure 5. The flow stress as a function of delta-ferrite content at various

strain levels for the CF8M castings at 4 K.

314
PERCENT DELTA FERRITE

Figure 6. The plane strain fracture toughness, at 4 K, as a function of

delta-ferrite content for CF8M castings and 316L weldments (8).

315
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Nonhomogeneous

Deformation

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function

of

the

mean

free

path

between

delta-ferrite

particles.

The

data

are

compared

with

the

theoretical

slope

of

-0.5.

ULTRASONIC INSPECTION OF STAINLESS STEEL BUTT WELDS

USING HORIZONTALLY POLARIZED SHEAR WAVES*

C. M. Fortunko and J. C. Moulder

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Inspection of austenitic stainless steel weldments by conventional

ultrasonic means is fundamentally limited by the textured, columnar grain

structure of the weld metal. It is shown that, for selected angles of

incidence, shear waves normally polarized with respect to the columnar grains

can pass through the weld metal-base metal interface without partial

reflection. As a consequence, the inspectability of stainless steel weldments

can be improved. The operation of a low frequency, ultrasonic system for

stainless steel butt weldments is demonstrated.

Key Words: Acoustic waves; elastic anisotropy; nondestructive evaluation;

nondestructive testing; stainless steel; ultrasonic scattering; ultrasonic

waves

.

*Submitted to Ultrasonics for publication.

319

Introduction

It is now recognized that the inspectability of stainless steel

weldments by ultrasonic methods is fundamentally limited by the textured,

columnar grain structure of the weld metal. The grains within each

weld pass grow with the [100] direction along the thermal gradient and

[ 2 ] continue to grow epitaxially from pass to pass. The resultant grain

structure causes large variations in the ultrasonic velocities as a

[3] function of the propagation and polarization directions. Additional

complications are introduced at the weld metal-base metal interface

where the discontinuity in the elastic properties can result in triref ringent

transmission and reflection of the probing ultrasonic signals. As a

result, unless the angles of incidence and polarization of the incident

ultrasonic signals are judiciously selected, many unwanted indications

[3] are produced that mask the defect indications.

321
Conventional ultrasonic techniques for evaluating stainless steel

weldments generally rely on the use of shear or longitudinal wave probing

signals that are polarized in the plane normal to the weldment (i.e.,

the sagittal plane) . The probing signals are generated by fluid-coupled

piezoelectric transducers that can irradiate the material with only

vertically polarized shear (SV) and longitudinal (L) wave vibrations.

Upon incidence at the weld metal-base metal interface, these SV and L

waves are split into reflected and refracted SV, L and horizontally

polarized shear (SH) waves. Because stainless steel weld metals are

elastically anisotropic, the tracing of the SV, L, and SH wave signals

through the weld metal-base interface is generally very difficult, if

[4 5 ] not impossible. 5

Recently, a different approach to the problem of ultrasonic detection

r & 7

1 and sizing of defects in stainless steel weldments has been investigated. L ’

The new approach is different from conventional ultrasonic nondestructive

evaluation (NDE) methods in three respects: 1) the wavelength of the

ultrasonic signals is longer than the typical through-thickness defect

dimension, 2) the ultrasonic probing signals are shear waves polarized

in the plane of the weldment and perpendicular to the columnar grain

direction, and 3) noncontacting, electromagnetic-acoustic transducers

(EMATs) are used to generate and detect these special probing waves.

The principles and operation of electromagnetic-acoustic transducers are

described elsewhere. ^

The new ultrasonic technique is particularly well suited for the

detection and sizing of elongated incomplete fusion (IF), inadequate

penetration (IP), and other crack-like defects in butt weldments. In

322
this application, shear waves polarized parallel to the welding direction

exhibit important advantages over shear waves polarized in the sagittal

plane and longitudinal waves. For example, they do not mode convert

when polarized along the long defect dimension. Furthermore, they can

be generated and detected with equal efficiency at any angle with respect

[9] to the surface normal.

In this paper it is demonstrated that practical ultrasonic techniques,

using shear waves polarized parallel to the welding direction, can be

devised. In particular, it is shown that shear waves polarized parallel to

the welding direction can be completely transmitted through the weld

metal-base metal interface without significant reflection or mode conversion.

As a consequence, the number of unwanted ultrasonic indications can be

minimized. The conditions for complete transmission are determined

theoretically and verified experimentally. In addition, the detection

of real weld defects in a stainless steel weldment is demonstrated.

The subject of sizing elongated defects in anisotropic stainless steel

weld metals is addressed in Ref. 10.

Transmission of SH Waves through the Weld Metal-Base Metal Interface Region

The factors governing the propagation of ultrasonic signals in

stainless steel weldments have been studied extensively. However,

progress has been slow because of an incomplete understanding of the

role of elastic anisotropy and the lack of efficient transducers for shear

waves polarized parallel to the welding direction.

In many multipass stainless steel weld metals, the columnar grains

are aligned uniformly . In such cases, the weld metal exhibits a

transverse-isotropic texture with the plane of transverse isotropy parallel

323
to the plane of the weldment and the propagation properties of ultrasonic

waves within the weld metal exhibit circular symmetry about the normal

[ 12 ] to the plane of the weldment.

The propagation properties of shear waves polarized in the plane of

transverse isotropy are of particular interest here. It can be shown

that such waves propagate as pure shear waves, unlike ultrasonic signals

of other polarizations. In this paper, they are referred to as SH

waves, in contrast to vertically polarized shear (SV) and longitudinal

(L) waves.

The velocity of SH waves within the stainless steel weld metal,

modeled as a transversely isotropic aggregate, is given by:

V

2

(0) - —[1 +

Sin2 e (c ll

“ c 12"2c

44 )

] P —Tc

1

44

where the angle 0 is defined by the axis of the columnar grain growth

and the wave normal. The constants C^, C > and are three of five

elastic moduli needed to describe the ultrasonic wave propagation in

transversely isotropic materials. Because the direction normal to the

axis of grain growth usually coincides with the plane of a weldment, the

pure shear wave is horizontally polarized (an SH wave) . The weldment

geometry is defined in Fig. 1.

To investigate the transmission of SH waves through the weld metal

base metal interface in the geometry of Fig. 1, consider the case of normal

incidence with respect to the welding direction. Since normally incident

324
SH waves are polarized parallel to the plane of the interface and propagate

as pure shear waves in the weld metal, no mode conversion by polarization

coupling to the L and SV waves can occur. The amplitudes and propagation

directions of the transmitted and reflected SH waves can then be completely

determined from a scalar relationship involving only the acoustic

impedances of the SH waves and Snell's law considerations. In fact,

since the densities of the weld and base metals are nearly equal, the

transmission and reflection coefficients are determined only by the

propagation directions and velocites of SH waves propagating in the

sagittal plane.

The SH wave velocity surfaces for type 308 stainless steel weld

metal and type 304 stainless steel base metal are shown in Fig. 2.

The surfaces were calculated using experimental and calculated^ ^

elastic moduli. It is observed that the surfaces intersect for two SH

wave propagation directions. As a consequence, it should be possible to

match the acoustic impedances of SH waves propagating in the sagittal

plane for this particular combination of weld and base metals.

An experimental scattering configuration of considerable practical

importance is illustrated in Fig. 3. In this case, the stainless steel

weld metal is deposited in a "vee— groove" between two stainless steel

plates that are assumed to be isotropic and homogeneous. The columnar

grains are then aligned symmetrically along the normal to the plate.

The direction of alignment is, therefore, tilted with respect to the

weld metal-base metal interface that is illuminated by a beam of SH

waves. The SH waves are excited by an EMAT that is placed on the top

surface of the plate.

The transmission of SH waves through the weld metal-base metal

interface can be investigated by using two coordinate systems: (x,z).

325
which is associated with the weld metal, and (x',z'), which is associated

with the base metal. In the sagittal plane, (x x z or x' x z'), the

(x,z) and (x'

,

z') coordinate systems are rotated by an angle <f> . The

weld metal-base metal interface is then rotated by an angle -0 with

respect to the z- axis. It is then of interest to identify the angle <f>

for which the SH wave is transmitted through the weld metal-base metal

interface without reflection.

The transmission coefficient at the weld metal-base metal interface

for SH waves propagating in the sagittal plane is given by:

in the base and weld metals, respectively, ip is the angle of the transmitted

SH wave normal with respect to the interface normal.

The angle ip can be determined from Snell's law considerations,

and a solution for <j> , for complete transmission (T=l) , can be found by

inverting Eq. 2. However, it is instructive to obtain an approximate

solution by noting that ip = d + (p when the densities of the stainless

steel weld and base metals are equal and T = 1. In this case <p can be

determined from*

T ( 2 )

where and (\p - 0 + 90°) are the acoustic impedances for SH waves

2 r cos <J> = {VI) - 1] [ C 44

(3)

326
A value of 21 ° is obtained for <j> when the elastic constant values

for 304 stainless steel base metal and 316 multipass stainless steel

weld metal are substituted in Eq. 3. The values are:

It is interesting to compare the degree of skewing of SH wave

beams, upon transit through the weld metal-base metal interface, with

that of SV and L wave beams. For SH waves (j> is independent of 0. The

skewing for a 308/304 weld metal-base metal interface, calculated using

the theory of Ref. 15, is shown in Fig. 4 for SH, SV, and L waves.

The flux deviation angle, A, is plotted as a function of the angle of

incidence, 4>, with respect to the columnar grain direction. It is

observed that for near-grazing incidence, ' 70°<4>< 90° , the flux deviation

for SH waves is substantially smaller than for SV waves and is comparable

to that for L waves. For <f> = '70°, the flux deviation angle, A, is 'v -15°,

Thus, SH wave signals should be sensitive to in-plane and normal

defects in stainless steel weld metals. The above results confirm the

[3] experimental observations of Kupperman , which show that SH waves are

more appropriate than SV and L waves for inspecting multipass stainless

steel weldments.

Two experimental configurations, which are useful for detecting defects

in girth welds of stainless steel pipes, are illustrated in Fig. 5.

Figure 5a shows a tandem EMAT ("pitch-catch") configuration that is

useful for sampling SH wave signals backscattered from the weld. Figure

5b shows a different configuration of the two EMATs. The configuration

c44

(W)

Experimental Configurations

327
of Fig. 5b is useful for sampling SH wave signals transmitted through

the weld. Both experimental configurations have been used to inspect

ferritic butt weldments . ^

Figure 6 shows a particular inspection configuration, including a

block diagram of the signal processing system that has been used to

detect crack-like defects in pipe girth welds. The operation of this

system, in the "pitch-catch" configuration of Fig. 5a, is as follows.

The EMATs are located on the outer surface of the pipe wall and are

aimed colinearly along the normal to the weld. The transmitter EMAT is

positioned between the weld and the receiver EMAT. The transmitter EMAT

is bidirectional and, therefore, generates two SH wave signals of equal

amplitude that travel in opposite directions along the normal to the

weld. The ultrasonic signal 1, traveling to the left of the transmitter

EMAT, illuminates the weld region. The ultrasonic signal 2, traveling

to the right of the transmitter EMAT, passes directly beneath the receiver

EMAT. The latter signal is used as a reference for calibrating the

transduction efficiency of the transmitter EMAT. If a defect is present

in the weld, a portion of the ultrasonic signal 1 is backscattered in

the direction of the receiver EMAT.

The backscattered signal 3 arrives after the reference signal 2

because it travels a longer distance. This arrangement of the two EMATs

ensures adequate temporal separation between the reference and defect

signals. The ratio of signals 2 and 3 is used in defect detection and

sizing.^- ^ As a result, the inspection system is less sensitive to

variations in transducer coupling efficiency caused by lift-off.

328
Experimental Results

The experimental inspection system of Fig. 6 was used to examine

the girth weld in a 304 stainless steel pipe specimen that had been

prepared for NDE purposes. The specimen was a 0.9-m-long, 0.273-mdiameter pipe section with a 12.7-mm wall thickness. As shown in Fig. 5,

a counterbore was ground on both sides of the weld. The weld contained

a number of defects that were detected by conventional radiographic and

ultrasonic techniques.

The ultrasonic inspection of the test specimen was carried out

using the two experimental configurations illustrated in Fig. 5. The

transmitter EMAT was driven with a 10-cycle RF tone burst with a 441-kHz

center frequency. To measure the backscattered SH wave signals, the

transmitter EMAT-to-receiver EMAT distance, £, was approximately 0.15 m,

center- to-center. The distance x, between the transmitter EMAT and the

weld, was 0.1 m. In the transmission mode, the transmitter EMAT was

separated by 0.15 m from the receiver EMAT, but the two transducers were

positioned symmetrically on either side of the weld. Measurements were

taken every 12.7 mm along the circumference to ensure complete coverage

of the weld. The ultrasonic (3-dB) beam width at the weld was approximately

25 mm.

Figure 7 shows three sample waveforms that were obtained at different

locations along the circumference of the pipe using the scattering configuration of Fig. 6. In Fig. 7, the first wave packet, extending from 0-

40 ys , is associated with reference signal 1, which is propagated directly

between the transmitter and receiver EMATs. The second wave packet,

329
centered near 75 ys, is associated with the SH wave signals that are

backscattered from the weld region. The oscilloscope signals are displayed

after signal averaging of 256 frames of the data. The averaging was

necessary to improve the signal-to-noise ratio and to inhibit electromagnetic

interferences. The first photo was obtained in a region of the weld

that contained no defects. It is apparent that very little ultrasonic

energy is backscattered from the weld. In this case most of the backscattering

is attributed to the presence of the counterbore ('ul-mm deep) on the

inside of the pipe. The second and third photos in Fig. 7 were obtained

in regions containing a through-thickness crack and an inadequate penetration

(IP) defect. In contrast to the first photo, the amplitudes of the

backscattered signals in the second and third photos are comparable to

the amplitude of the reference signal.

Figure 8 shows the complete ultrasonic inspection record that was

obtained by scanning the stainless steel girth weld from both sides

using the "pitch-catch" inspection configuration of Fig. 5a. In previous

work, the defect detectability levels were determined by reflections

from the weld reinforcement ("crown") and root, rather than by random

[17] electronic noise. In the present case, the defect detectability

limits are established by the presence of a sharp step (counterbore)

on both sides of the weld root. Because of the poor spatial resolution

at 441 kHz, the signals backscattered from the weld could not be distinguished

from reflections from the counterbore. Therefore, a threshold level of

0.1, corresponding to peak counterbore indications, was adopted. This

threshold setting is indicated in Fig. 8 by a horizontal line drawn

across the inspection record.

330
Figure 9 shows the ultrasonic inspection record that was obtained

by scanning the stainless steel girth weld using the transmission mode

inspection configuration of Fig. 5b. In this case, the threshold was

set at 0.71 on the basis of the average amplitude transmitted through

the weld, relative to the average amplitude transmitted directly through

the base material. It is observed that a significant fraction of the

incident power is transmitted through the weld, as expected from the

model

.

A substantial degree of correlation is observed between the inspection

results obtained using the 441-kHz SH wave system, and those obtained

using conventional radiographic and ultrasonic techniques. The results obtained

using conventional radiographic and ultrasonic techniques are indicated

in Fig.s 8 and 9 with horizontal bars. It is observed that in the transmission

mode three of the five defects are positively detected: inadequate

penetration and the two cracks. On the other hand, in the reflection

mode, only the inadequate penetration defect and the through-wall crack

were positively detected. It is believed that the three undetected

defects (slag, lack of fusion, and partial through-wall crack) were

relatively shallow and had reflectivities comparable to or smaller than

that of the counterbore. (The counterbore was separated by only 15 mm

from the center of the weld. As a result, it could not be resolved

using the relatively narrowband 441-kHz SH wave probing signal.)

Conclusions

The operation of a practical ultrasonic inspection system using low

frequency, horizontally polarized shear (SH) waves has been demonstrated

on an austenitic stainless steel weldment. It has been shown that SH

waves can be completely transmitted through the weld metal-base metal

331
interface without mode conversion to longitudinal and vertically polarized

shear waves. This results in a significant increase in sensitivty to

[3] defects in the weld metal. In addition, the use of low frequency

probing signals allows the use of long wavelength inversion algorithms for

defect sizing. As a consequence, automated ultrasonic inspection

systems for stainless steel weldments may be possible.

Acknowledgment

The authors are indebted to the Electric Power Research Institute

for making available the stainless steel weld specimens. Major support

for this work was provided by the Department of Energy, Office of Fusion

Energy.

REFERENCES

1. M. G. Silk, Propagation of Ultrasound in Anisotropic Weldments,

Mater. Eval. 39. (1981) 462-467.

2. B. L. Baikie, A. R. Wagg, M. T. Whittle, and D. Yapp, Ultrasonic

Inspection of Austenitic Welds, J. Br. Nucl. Energy Soc. 15^ (1976)

257-261.

3. D. S. Kupperman and K. J. Reimann, Ultrasonic Wave Propagation and

Anisotropy in Austenitic Stainless Steel Weld Metal, IEEE Trans.

Sonics Ultrasonics 2_7 (1980) 7-15.

4. J. R. Tomlinson, A. R. Wagg, and M. J. Whittle, Ultrasonic Inspection

of Austenitic Welds, Br. J. NDT 24_ (1980) 119-127.

5. M. G. Silk, B. H. Lidington, and G. F. Hammond, A Time Domain

Approach to Crack Location and Sizing in Austenitic Welds, Br. J.

NDT _24 (1980) 55-61.

6. C. M. Fortunko, Ultrasonic Evaluation of Austenitic Stainless Steel

Welds Using Shear Horizontal Waves, Appl. Phys. Lett, (in press).

332
7. C. M. Fortunko, R. B. King, and M. Tan, Nondestructive Evaluation

of Planar Defects in Plates Using Low Frequency Shear Horizontal

Waves (to be published).

8. R. B. Thompson, A Model for the Electromagnetic Generation and

Detection of Rayleigh and Lamb Waves, IEEE Trans. Sonics Ultrasonics

20 (1973) 340-346.

9. C. F. Vasile and R. B. Thompson, Excitation of Horizontally Polarized

Elastic Waves by Electromagnetic Transducers with Periodic Magnets,

J. Appl . Phys. .5(3 (1979) 2583-2588.

10. S. K. Datta, A. H. Shah, and C. M. Fortunko, Diffraction of Medium

and Long Wavelength SH-Waves by Edge Cracks (to be published)

.

11. L. Adler, K. V. Cook, and D. W. Fitting, Ultrasonic Characterization

of Austenitic Welds, in Ultrasonic Materials Characterization, NBS

Special Publication 596 (NBS, Gaithersburg, MD, 1980) 533-540.

12. M. J. P. Musgrave, Crystal Acoustics (Holden Day, San Francisco,

1970) 94-101.

13. H. M. Ledbetter, N. V. Frederick, M. W. Austin, Elastic Constant

Variability in Stainless Steel 304, J. Appl. Phys. jll (1980) 305-

309.

14. H. M. Ledbetter, NBS, Boulder, Colorado, private communication.

15. M. J. P. Musgrave, On the Propagation of Elastic Waves in Aeolotropic

Media, II. Media of Hexagonal Symmetry, Proc. R. Soc. 226 (1954)

356-366.

16. R. J. Hudgell and H. Seed, Ultrasonic Longitudinal Wave Examination

of Austenitic Welds, Br. J. NDT 25_ (1980) 78-85.

333
17. C. M. Fortunko and R. E. Schramm, Nondestructive Evaluation of

Large Diameter Girth Welds Using Electromagnetic-Acoustic Transducers,

in Fitness-f or-Purpose Validation in Welded Constructions (The

Welding Institute, Cambridge, England, 1981) (in press).

334
Figure Captions

1. The weldment geometry.

2. Velocity surfaces for SH waves propagating in the sagittal plane.

3. Configuration for analyzing the propagation of SH waves through the

weld metal-base metal interface.

4. Skewing of SH, SV, and L wave signals as a function of the wave

normal direction in a type 308 stainless steel weld metal.

5. Experimental configurations used in the nondestructive examination

of stainless steel girth welds.

6. Block diagram of the experimental apparatus.

7. Ultrasonic reflections obtained with 441-kHz SH waves in different

regions of the girth weld.

8. Ultrasonic inspection record obtained using the reflection configuration.

9. Ultrasonic inspection record obtained using the transmission

configuration.

335
Sagittal

Plane

<

hyj

336

Figure

1.

The

weldment

geometry.
Figure 2 Velocity surfaces for SH waves propagating in the sagittal plane.

337
338

weld

metal-base

metal

interface.
FLUX

DEVIATION,

A,

DEGREES

80° i

"80° -| 1 1 1 1 1 1 1 1—

0° 20° 40° 60° 80°

WAVE-NORMAL ORIENTATION, <£, DEGREES

308 SS WELD METAL

Figure 4. Skewing of SH, SV, and L wave signals as a function of the wave

normal direction in a type 308 stainless steel weld metal.

339
Reflection

Figure 5

Transmission

(b)

Experimental configurations used in the nondestructive examination

of stainless steel girth welds.

340
Digital

Control

Module

0) N

341

Block

diagram

of

the

experimental

apparatus.
Figure 7

10 /is

n

regions of the girth weld.

342
343

CIRCUMFERENTIAL

POSITION,
O•

• o

3anindWV 3AI1VT3U

344

CIRCUMFERENTIAL

POSITION,

mm
SINGLE-CRYSTAL ELASTIC CONSTANTS IN NONDESTRUCTIVE

EVALUATION OF WELDS

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

345

SINGLE- CRYSTAL ELASTIC CONSTANTS IN NONDESTRUCTIVE

EVALUATION OF HELDS

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado B0303

ABSTRACT

For studying welds nondestructively using elastic waves, we describe the importance of knowing the

material's single-crystal elastic constants, the C^'s. Hhere these are not known, we give some guidelines

for estimating them from polycrystalline elastic constants such as Young's modulus and the shear modulus.

He consider the important case of [100] texture. Being transversely isotropic, this case exhibits five

macroscopic elastic constants, which we relate to the three cubic elastic constants: C,,, C12 , C^.. From these five constants we compute the angular variations of Young's modulus, the torsional modulus, ^nd the

sound velocities.

INTRODUCTION

Optimum ultrasonic inspection of welds requires

knowing and understanding the weld's single-crystal

elastic constants and how these constants relate

to the macroscopic elastic constants of the textured

aggregate. Several recent studies recognize these

requirements [1-7].

The present study describes two basic relationships. First, how single-crystal elastic constants,

the C^'s, can be obtained from polycrystalline

elastic constants. Second, how the C^'s can be

used to calculate the macroscopic elastic constants

of textured aggregates, which occur often in

welds.

of the model. Considering the self-consistent

problem of an anisotropic single-crystal Inclusion

embedded In a corresponding Isotropic matrix, and

assuming stress equilibrium at the interface. Kroner [10] showed that

G

3+aG

2+eG+Y*0 (2)

where

a*[SCu+Ku)/8 (3)

Bc-C44(7Cir4C

12 )/8 (4)

As an example, we consider a stainless-steel

316 weld, which develops a <100> fiber texture. This Fe-Cr-Ni alloy exhibits a face-centered-cubic

crystal structure and, therefore, three independent

single-crystal elastic constants, usually taken to

be C,,, C^ 2

, and C.. in Voigt's contracted notation. A fibir texture being transversely Isotropic has.

macroscopically, hexagonal symmetry with five

Independent elastic constants: C, 3 and C33

In addition to those for cubic syometry. An ideal

<100> fiber texture means that [1001-type directions

are parallel to the unique axis x

3 (the solidification

direction in this case), and thavthe (lOO)-type

planes perpendicular to x3 are distributed randomly

with respect to rotation about x

3

. Figure 1 relates cubic and hexagonal coordinate systems to weld geometry.

THEORY FOR CUBIC-SINGLE-CRYSTAL C^ 's

Especially for cubic crystal symmetry, the

problem of relating the single-crystal elastic constants (C-|i , C, 2

, C..) to the quasi -Isotropic polycrystalllw elastic“onstants (B,G) has been studied

extensively, both theoretically [8] and experimentally

[9]. The bulk modulus, B, because It is a rotational

Invariant of the elastic-stiffness tensor. Is always

given by

B-(C

11 +2c12 )/3. 0)

even for a highly textured material. The expression

for the shear modulus, G, depends on the assumptions

and

|-Ci2 ) (Cn +2 C

1 2

)' 8 (5)

In the forward ease, these relationships permit

the calculation of B and G from the C^'s, the

Isotropic from the anisotropic, two elastic constants from three.

Hlth one additional piece of information,

from either theory or observation, from some single relationship among the C^'s, the reverse case can be computed also. The vj/s can be

computed from B and G.

If B and G are unavailable, then any other

pair of polycrystalline elastic constants will serve. For example. Young's modulus and Poisson's

ratio. This is so because any Isotropic elastic constant can be calculated from any other two Isotropic elastic constants.

For a relationship among the C^'s of stainless

steel 316, we consider the existing c*, measurements on f.c.c. Fe-Cr-Ni alloys summarized in Table 1. At least two approximate relationships emerge. First, the elastic anisotropy is relatively constant,

being 3.51 ± 0.19. Second, the y*C

12/C, ratio Is relatively constant, being 0.642 ± 07037. Ledbetter

[11] showed that a slightly better y value results

If values for f.c.c. Fe and Ni are also included

with these four alloys, the value being y»0.640 ±

347
0.031. Table 1 probably contains other C.,. relationr.xubic aggregates. We used the form given by

ships. But these two are simple and sufficient. Kroner and Wawra [18].

For B and G values, we use those reported by

Ledbetter. [12]: B*1.575 ± 0.014 and G®0.752 ± 0.015 10

1 N/nr

.

THEORY FOR TEXTURED-A6GREGATE C^ 's

One expects that cubic- symmetry crystallites

In welds occur either with random orientations or with a single preferred axis parallel to the

principal heat-flow direction, denoted x. In

Fig. 1. In the x,-x2 plane, crystallites are expected to orient themselves randomly because no preferred heat-flow direction occurs In that

plane. Thus, an effective fiber texture occurs with x

3 being the fiber axis. Uteeroscopieally,

such a^material exhibits transverse- isotropic

symmetry, with five Independent elastic constants.

This is equivalent to hexagonal symmetry. In Voigt's contracted • notation the symmetrical

elastic-stiffness matrix is [13]:

lb] 1 v

c

M

* C + 8C (7) l

12

l

Z C

13

“ C

2

" 4bC

3 C33

“ C

1 + ®eC

3 C

= ^C1 -C

2 )-4BC

3 C66 I

{C irC12 ) 4^Cll"C

12 ) + 2eC

3

festsere 5C| • 3£|| + 2C-J2 +

^^2 * ^11 + ^^12 " 2 ^44 ( 8 )

C

3

“ C

11 ' C

12

’ 2C44 where 8 * 1/20 for the < 100> fiber texture.

problem 7s to express the five hexagonal -symmetry

elastic constants, C?.» in terms of the three

cubic-symmetry elastic constants: , C^, and

C44‘ Present theory does not permit calculation of

the elastic constants of textured polycrystalline

aggregates of cubic-symmetry crystallites. This

is a special and more difficult case of determining

the average elastic constants of a random polycrystalline aggregate. For this latter problem,

Landau and Lifshitz [14] remind us that "there

is... no general relationship between the moduli of

elasticity of a polycrystal and those of a single

crystal of the same substance." The fiber-texture

case involves a two-dimensional, rather than a three-dimensional, average.

However, elastic-constant bounds can be

calculated for textured aggregates. In this study we calculate the Voigt [15] (constant strain) and

Reuss [16] (constant stress) bounds and use Hi Ills

[17] suggestion of an arithmetic average to estimate

the elastic constants. This approach turns out to

be quite reasonable because the Voigt and Reuss bounds do not differ dramatically (a maximum of

37 percent). And for the important <100>-texture

case, the bounds coincide for three elastic constants:

Cj

3

* C,

3

, and CT.. Thus, we know these three

constants unambiguously. Kroner and Wawra [18]

explain the systematlcs of this bounds coincidence.

Several studies [19-22] derive correctly the

relationships for calculating the Voigt bounds of

macroscopic elastic constants of fl ber-textured

Apparently, relationships for the S^.'s,

which give the Reuss bounds by matrix inversion,

do occur in the literature. These are: H

5 n " ?

C3S

11 + S

12 + 8S44 }

s

12 * ?

(S

11 -3S12

8 m (9)

S

H

13

S

12

H^33 * sn

2*44 * 4S44

S

H

) * S

H06

* «S?! * s n+ 2S

i 2 + 8S44

In deriving these relationships, one must remember

that the inverse C7j. , of a fourth-rank elasticity

tensor relates to tne inverse C of its.associated

6x6 matrix by a factor multi pi i$a times C7l. ,

.

This factor Is 4 if both a and 6 exceed 3, J t$ 2 if

either a or 8 exceeds 3, and Is 1 If neither a nor

8 exceeds 3.

RESULTS

Table 1 shows the predicted single-crystal

elastic constants of stainless-steel 316. Other

principal results of the study—elastic-stiffness,

elastic compliance, and sound velocity—occur in Table 1, which shows Voigt and Reuss bounds together

with their arithmetic average for the < 100> ideal

fiber texture. To obtain sound velocities, we

used a mass density of 7.958 g/cm. From these

results, the polar plots shown In Figs. 2-4 were determined using well-known relationships [23].

These figures give the angular variation of Young's

modulus, E, torsional modulus, T, and sound velocities,

both longitudinal, v,, and transverse. v

t

. All curves in Figs. 2-4 represent arlthmetl coverages

of Voigt and Reuss bounds.

DISCUSSION

The tables and figures show several Interesting,

potentially Important, results:

348
1 .

2 .

3.

4.

Texture Induces large elastic-constant changes

(departures from isotropic values).

H H Shear elastic constants, C44 and Cgc, change

ore than longitudinal constants, C?, and

HC^and more than the off-diagonal constants,

plv . pH

C12 and C

1 3‘ UC7. offers the best opportunity for detecting

tlxture and estimating Its amount. C.. corresponds to a shear wave propagated elong

the fiber axis (x

3

) and vibrating in the x,-

x7 plane, which Is elastically isotropic.

U If high attenuation precludes accurate C.. measurement, C33 provides a„good lowerattenuation alternative. C33 corresponds to

a longitudinal wave propagating along the

fiber axis.

3.

4.

5.

6 .

7.

5. For the principal crystallographic directions,

with one exception, if texture Increases v. It decreases v

t

, and vice versa. Hardly

surprising, this means simply that stiffening

In a particular direction corresponds to softening in transverse directions.

Elastic constants affected least by texture

are Cg6 and Sgg . HThis result, at first

surprising since Cgg depends on the difference

between C?, and C?-? arises presumably because

Cfifi rePre»«nts a »near wave both propagated

and polarized In the x,^ plane, an elastically

Isotropic plane with properties determined,

for all textures, by averaging over all directions perpendicular to the fiber axis.

10 .

11 .

7. Finally-the remark concerning the bulk modulus

of the fiDer-textured aggregate. It equals

identically the cubic-symmetry bulk modulus,

(C,, + 2C,»). It is a scalar. Hydrostatic

stress would dilate uniformly the textured

aggregate. This contrasts sharply with a microscopically hexagonal material that

behaves anisotroplcally, altering Its axial

length ratio, in response to hydrostatic

stress. This means that welds of cubicsyumetry alloys do not develop pressureinduced Internal stresses due to texture. Such stresses would occur, of course. In lower-syrnnetry-alloy welds.

12 .

13.

14.

15.

ACKNOWLEDGMENTS

Two agencies supported this study: The DoE Office of Fusion Energy and the NBS Office of

Nondestructive Evaluation. J. Dahnke assisted

with calculations.

REFERENCES

1. B. R. Dewey, L. Adler, R. T. King, and K. V. Cook, Measurements of anisotropic elastic

constants of type 308 stainless-steel electroslag

welds, Exper. Mech. 17, 420-426 (1977).

2. D. S. Kupperman and K. J. Reimann, Effect of

shear-wave polarization on defect detection

In stainless steel weld metal. Ultrasonics

16, 21-27 (1978).

D. S. Kupperman and K. J. Reimann, Ultrasonic wave propagation and anisotropy in austenitic

stainless steel weld metal, IEEE Trans. Sonics Ultrason. SU-27 , 7-15 (1980).

M. G. Silk, B. H. lldington, and G. F. Harrmond,

A time domain approach to crack locations and

sizing In austenitic welds, Brit. J. NDT 22,

55-61 (1980). ~

J. R. Tomlinson, A. R. Magg, and M. J. Whittle,

Ultrasonic inspection of austenitic welds,

Brit. J. NDT 22 119-127 (1980).

M. G. Silk, The propagation of ultrasound in anisotropic weldments. Materials Evaluation

39462-467 (1981).

C. M. Fortunko, Ultrasonic evalution of

austenitic stainless steel welds using SH waves, submitted to J. Appl. Phys.

H. M. Ledbetter end E. R. Naimon, Relationship

between single-crystal and polycrystal elastic

constants, J. Appl. Phys. 45, 66-69 (1974).

H. M. Ledbetter, Sound velocities and elastic- constant averaging for polycrystalline copper,

J. Phys. D; Appl. Phys. 13, 1879-1884 (1980).

E. Kroner, Berechnung der elastischen Konstanten

des Vielkri stalls eus den Konstanten des

Elnkri stalls, Z. Phys. 151, 504-518 (1958).

H. M. Ledbetter, Predicted single-crystal

elastic constants of stainless-steel 304, to

be published.

H. M. Ledbetter, Sound velocities and elastic constants of steels 304, 310, and 316, Metal

Scl. 14, 595-596 (1980).

J. F. Nye, Physical Properties of Crystals:

Their Representation by Tensors and Matrices

(Oxford, London, 1957), p. 141.

L. D. Landau and E. M. Llfshltz, Theory of

Elasticity (Pergamon, Oxford, 1970), p. 42.

W. Voigt, Ueber die Beziehung zwlschen den

belden Elastizitatsconstanten isotroper

Korper, Ann. Phys. 38, 573-587 (1889).

A. Reuss, Berechnung der Fliessgrenze von

Ml schk'ri stall en auf Grund der PlastlzitatsbedIngung fur Einkristalle, Z. Angew. Math. Mech.

9. 49-58 (1929).

R. Hill, The elastic behavior of a crystalline

aggregate, Proc. Phys. Soc. Lond. A65 , 349-

354 (1952).

E. Kroner and H. H. Wawra, Coincidence of

bounds for some elastic moduli of polycrystals

with fibre texture, Philos. Mag. 38, 433-437

(1978).

G. Bradfield and H. Pursey, The role of

preferred orientation In elasticity Investigations,

Philos. Mag. 44, 437-443 (1953).

349
20. H. Pursey and H. L. Cox, The correction of

elasticity measurements on slightly anisotropic

materials, Philos. Hag. 45, 295-302 (1954).

21. I. P. Talashkevich and K. S. Aleksandrov,

Effect of preferred grain orientation on the

elastic properties of polycrystals, Fiz.

Hetal. Metal loved 14 , 801-805 (1962).

22. G. Kneer, Uber die Berechnung der Elastizitatsmoduln vi el kri stall iner Aggregate mit Textur,

Phys. Stat. Solidl 9, 825-838 (1965).

23. E. Schmid and W. Boas, Plasticity of Crystals

(Hughes, London, 1950), p. 21.

(h«x)

(cub)

weld)

24. K. Salmutter end F. Stangler, Elastizitat u. Plastizit'at eines austenitischen Chrom-NIckel

Stahls, Z. Metal Ikde. 5]_, (I960).

25. M. Klkuchi, Elastic anisotropy and its tem- perature dependence of single crystals and

polycrystal of 18-12 type stainless steel,

Japan Inst. Met. 12., 417-421 (1971).

26. M. C. Manga lick and N. F. Fiore, Orientation

dependence of dislocation damping and elastic

constants In Fe-18Cr-N1 single crystals,

Trans. Met. Soc. AIMS 242, 2363-2364 (1968).

Fig. 1. Relationships between cubic and hexagonal

co-ordinate systems and weld geometry.

Cubic directions x, and x

2 are distributed randomly, perpendicular to x,. Since hexagonal x,-x2 plane Is elastically isotropic, xi (nex) can be any direction perpendicular to x

3 (hex).

Table 1. Single-crystal elastic constants of several face-centered-cubic Fe-Cr-Ni alloys in units of

11 2 10 N/m , except A and y, which are dimensionless.

Alloy

El2 C-4 B e

1 A y Ref. Experiment

Fe-12Cr-18Ni 2.332 1.626 1.225 1.862 0.353 3.45 0.697 24 Fe-18Cr-12Ni 1.912 1.179 1.386 1.423 0.367 3.78 0.617 24 Fe-18Cr-14Ni 1.98 1.25 1.22 1.49 0.365 3.34 0.631 26 Fe-18Cr-19N1 1.91 1.19 1.24 1.43 0.360 3.44 0.623 26

Theory

Stainless 316 2.07 1.33 1.17 1.57 0.373 3.15 0.640 present

Fig. 2. Angular variation of Young's modulus for

stainless-steel 316 for «001» texture.

Vertical direction Is (hex), about

which figure has complete rotational sym- metry. Average denotes simple arithmetic

average of Voigt and Reuss bounds, which

correspond to constant strain and con- stant stress, respectively.

350
Table 2. Elastic stiffnesses, elastic compliances, and souw

velocities for stalness -steel 316 with <100> fiber texture:'

Voigt Reuss Average Isotropic rMhi 2.473 2.265 2.369 2.577

h2 0.926 1.133 1.029 1.073

c

Hh3 1.326 1.326 1.326 1.073

cH°33 2.072 2.072 2.072 2.577

C

H

U44 1.174 1.174 1.174 0.752

C

H^66 0.774 0.566 0.670 0.752

s

H hi 0.617 0.736 0.676 0.514

S

Hh2 -0.029 -0.148 -0.088 -0.151

sHb 13 -0.376 -0.376 -0.376 -0.151

s

Hh3 0.964 0.964 0,f64 0.514

s

H*44 0.852 0.852 0.852 1.330

s

H*66 1.293 1.766 1.530 1.330

\ < x

i> 0.557 0.534 0.546 0.569

v

l

< x

3

} 0.510 0.510 0.510 0.569

«t

(X,) 0.312 0.267 0.289 0.307

vt

(x

3

) 0.384 0.384 0,384 0.307

*Units on C^j, S^, and v are 10^N/®*» 10”^h2/N, and m/v$ t respectively.

Fig. 3. Angular variation of torsional Modulus.

See caption 2.

SOUND VELOCITY, em//ii

Fig. 4. Angular variation of three sound veloclties. See caption 2.

351

Sound velocity as a texture probe: application to stainless-steel-316 welds

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

Texture (nonrandom distribution of crystallites) influences many properties of

welds: for example, the optimum direction for propagating an elastic wave with

minimum loss. We show theoretically that sound velocity provides a sensitive

test for texture. For 316 stainless steel, a face-centered-cubic Fe-Cr-Ni

alloy, we calculate elastic stiffnesses (cT.'s), elastic compliances ( S -

-

' s )

,

' J

1 J and sound velocities for three ideal fiber textures: <100>, <110>, and <1 1 1 >

.

This amounts to modeling the macroscopical ly hexagonal -symmetry weld in terms

of its cubic-symmetry constituents.

Key Words: Elastic-compliance tensor; elastic constants; elastic-stiffness

tensor; iron alloy; sound velocity; stainless steel; texture; weld

353

Introduction

Several recent studies

1-6

emphasize the elastic anisotropy of stainlesssteel welds. This anisotropy reflects texture, which arises during welding,

probably from strongly directional heat flow.

Absence of macroscopic elastic isotropy affects several weld properties:

(1) ultrasonic-wave velocity varies with direction; (2) for a fiber texture,

five independent elastic constants are required to characterize the macroscopic material (only two are required for isotropic symmetry); (3) internal

friction and ultrasonic-wave-amplitude attenuation also vary with direction;

(4) elastic-wave-energy deviations depend strongly on direction; (5) optimum

directions exist for propagating an elastic wave with minimum loss. All these

properties impact on both the materials science of welds and their nondestructive evaluation.

The present study shows that ultrasonic velocity provides a sensitive

test for texture, both qualitatively and quantitatively. For the particular

case of stainless-steel-316 welds, we show that <10Q>, <110>, and <111> fiber

textures have fiber-direction shear-wave velocities that differ +26, -6, and

-14 percent from the shear-wave velocity of the nontextured random aggregate.

Since sound-velocity measurement error seldom exceeds one percent, the amount

of <100> texture, for example, is measurable, in principle, to within about

four percent. This compares favorably with results of more familiar x-ray

diffraction methods for determining texture. It has the advantages of possible in-situ measurements and volume sampling rather than surface sampling.

Theory

One expects that cubic-symmetry crystallites in welds occur either with

random orientations or with a single preferred axis parallel to the principal

355
heat-flow direction, vertical in the figures, denoted x^. In the x^-x^ plane,

crystallites are expected to orient themselves randomly because no preferred

heat-flow direction occurs in that plane. Thus, an effective fiber texture

occurs with x

3

being the fiber axis. Macroscopically , such a material exhibits transverse-isotropic symmetry, with five independent elastic constants.

This is equivalent to hexagonal symmetry. In Voigt's contracted C. . notation,

^ J the symmetrical elastic-stiffness matrix i s

:

C 11C 12C 13

0 0 0

cj

x C^

3 0 0 0

C Hl o 33

"44

"44

0

0

0

.H"66

( 1 )

H H H where Cgg = i(C^ - C^)* Thus, the theoretical problem is to express the

|_| five hexagonal -symmetry elastic constants, C.., in terms of the three cubic-

^ J symmetry elastic constants: C^, C^, and C^.

Present theory does not permit calculation of the elastic constants of

textured polycrystalline aggregates of cubic-symmetry crystallites. This is a

special and more difficult case of determining the average elastic constants

of a random polycrystalline aggregate. For this latter problem, Landau and

g Lifshitz remind us that "there is ... no general relationship between the

moduli of elasticity of a polycrystal and those of a single crystal of the

same substance." The fiber-texture case involves a two-dimensional, rather

than a three-dimensional, average.

356
However, elastic-constant bounds can be calculated for textured

• aggregates. In this study we calculate the Voigt (constant strain) and

Reuss

1 ^ (constant stress) bounds and use Hill's** suggestion of an arithmetic

average to estimate the elastic constants. This approach turns out to be

quite reasonable because the Voigt and Reuss bounds do not differ dramatically

(a maximum of 37 percent). And for the important <100>-texture case, the

bounds coincide for three elastic constants: C^> C 33 , and Thus, we know

12 these three constants unambiguously. Kroner and Wawra explain the

systematics of this bounds coincidence.

1 3 - 1

6

Several studies ” derive correctly the relationships for calculating

the Voigt bounds of the macroscopic elastic constants of fiber-textured cubic

12

aggregates. We used the form given by Kroner and Wawra:

.H = C

x + 33C 11 3

,H12

13

,H

13

,H

'44

,H

C?. + ^3

C

2

- 48C

3

C

1 + 83 C

3

i(c r

c

2 )-4ec3

C 66 i(C irC

12 } + 2BC

3

( 2 )

where

5 C

i 3C^ + 2C^

2 + 4C^

5

C

2

= + 4C

12 - 2C^

( 3 )

C

3

C 11

‘ C 12' 2C

44

357
where 6 = 1/20, -1/80, and -1/30 for the respective <100>, <110>, and <1 1 1>

fiber textures.

Apparently, relationships for the S..'s, which give the Reuss bounds by

matrix inversion, do not occur in the literature. These are:

S

S

S

S

S

S

H11

H12

H13

H33

H44

H66

= £(35^ + S 12

= i(S n - 3S

12

S 11

= 4S

= 2(S

44

H11 ) =

+ 8S44

8S44

)

)

*11 + 2S

12 + 8S44

(4)

In deriving these relationships, one must remember that the inverse CT^ of a

fourth-rank elasticity tensor relates to the inverse C

_1

of its associated

6x6 matrix by a factor multiplied times CT^ . This factor is 4 if both a

and B exceed 3, is 2 if either a or B exceeds 3, and is 1 if neither a nor B

exceeds 3.

Results

Input information for the calculations came from the author's previous

publications: = 2.06, = 1.33, = 1.19*10^N/m^, and p =

3

7.958 g/cm . Isotropic values in the tables were calculated using Kroner's

method.

17

Principal results of the study--elastic stiffness, elastic compliance, and sound velocity--occur in tables 1-3, which show Voigt and Reuss

bounds together with their arithmetic average for three ideal fiber textures:

<100>, <110>, and < 1 1 1 > . Table 1 shows the C^.'s, table 2 the S^.'s, and

3 table 3 the sound velocities based on a mass density of 7.958 g/cm . From

358
these results, the polar plots shown in Figs. 1-4 were determined. For all

three textures, these figures give the angular variation of Young's modulus,

E, torsional modulus, T, and sound velocities, both longitudinal, v , and

transverse, v^. All curves in Figs. 1-4 represent arithmetic averages of

Voigt and Reuss bounds.

Discussion

The tables and figures show several interesting, potentially important,

resul ts

:

1. Texture induces large elastic-constant changes (departures from

isotropic values), up to 58 percent.

H H

2. Shear elastic constants, and Cgg, change more than longitudinal

H H H H constants, and C^, and more than the off-diagonal constants, and Cjg

|_| 3. offers the best opportunity for detecting texture and estimating

its amount. corresponds to a shear wave propagated along the fiber axis

(x

3

) and vibrating in the x^-x^ plane, which is elastically isotropic.

H H

4. If high attenuation precludes accurate measurement, C 33 provides

U

a good lower-attenuation alternative. C 33 corresponds to a longitudinal wave

propagating along the fiber axis.

5. For the principal crystallographic directions, with one exception, if

texture increases v it decreases v., and vice versa. Hardly surprising, this

X/ L means simply that stiffening in a particular direction corresponds to softening in transverse directions.

6. For all three textures, the longitudinal constants and either

both increase or both decrease. Surprisingly, there is no mixed behavior. In

terms of the S..'s, where the principal -axis Young's moduli are = S.j,

texture decreases E. for <100> texture but increases E^. for <1 1 1 > texture.

359
Figures 1 and 2 show polar plots of Young's modulus and the torsional modulus

H 18

computed from the S..'s using standard relationships.

^ 0 H H

7. Elastic constants affected least by texture are and This

H H result, at first surprising since C 66 depends on the difference between

H H and C.^, arises presumably because Cgg represents a shear wave both propagated

and polarized in the x-^-x^ plane, an elastically isotropic plane with properties determined, for all textures, by averaging over all directions perpendicular to the fiber axis.

8. Along two directions oblique to x^, both E(110) and E( 111 ) equal the

isotropic value. For these two textures, this amounts effectively to an

elastic-constant invariant. Along two different directions, the torsional

modulus shows a similar invariance for these two textures. Invariance properties are quite important. For example, isotropic Young's and torsional moduli

can be determined directly from anisotropic textured aggregates by making

measurements in special directions.

9. The bulk modulus of the f iber-textured cubic-crystallite aggregate

equals identically the cubic-symmetry bulk modulus, (C^ + 2C^)/3. It is a

scalar. Hydrostatic stress would dilate uniformly the textured aggregate.

This contrasts sharply with a microscopically hexagonal material that behaves

anisotropical ly , altering its axial length ratio, in response to hydrostatic

stress. This means that welds of cubic-symmetry alloys do not develop

pressure-induced internal stresses due to texture. Such stresses would occur,

of course, in lower-symmetry-alloy welds.

Acknowledgment

Two agencies supported this study: the DoE Office of Fusion Energy and

the NBS Office of Nondestructive Evaluation. J. Dahnke assisted with calculations.

360
References

1. B. R. Dewey, L. Adler, R. T. King, and K. V. Cook, Measurements of

anisotropic elastic constants of type 308 stainless-steel electroslag

welds, Exper. Mech. 17, 420-426 (1977).

2. D. S. Kupperman and K. J. Reimann, Ultrasonic wave propagation and

anisotropy in austenitic stainless steel weld metal, IEEE Trans. Sonics

Ultrason. SU-27 , 7-15 (1980).

3. M. G. Silk, B. H. Lidington, and G. F. Hammond, A time domain approach to

crack location and sizing in austenitic welds, Brit. J. NDT 2^2, 55-61

(1980).

4. J. R. Tomlinson, A. R. Wagg, and M. J. Whittle, Ultrasonic inspection of

austenitic welds, Brit. J. NDT 2_2, 119-127 (1980).

5. M. G. Silk, The propagation of ultrasound in anisotropic weldments,

Materials Evaluation 39., 462-467 (1981).

6. C. M. Fortunko, Ultrasonic evaluation of austenitic stainless steel welds

using shear horizontal waves, Appl . Phys. Lett. 39, 699-700 (1981).

7. J. F. Nye, Physical Properties of Crystals: Their Representation by

Tensors and Matrices (Oxford, England, 1957), p. 141.

8. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, Oxford,

1970), p. 42.

9. W. Voigt, Ueber die Beziehung zwischen den beiden Elastizitatsconstanten

isotroper Korper, Ann. Phys. 38^, 573-587 (1889).

10. A. Reuss, Berechnung der Fliessgrenze von Mischkristallen auf Grund der

Plastizitatsbedingung fur Einkristalle, Z. Angew. Math. Mech. 9_, 49-58

(1929).

11. R. Hill, The elastic behavior of a crystalline aggregate, Proc. Phys.

Soc. Long. AEL5, 349-354 (1952).

361
12. E. Kroner and H. H. Wawra, Coincidence of bounds for some elastic moduli

of polycrystals with fibre texture, Philos. Mag. 38^ 433-437 (1978).

13. G. Bradfield and H. Pursey, The role of preferred orientation in elasticity investigations, Philos. Mag. 44, 437-443 (1953).

14. H. Pursey and H. L. Cox, The correction of elasticity measurements on

slightly anisotropic materials, Philos. Mag. 45^, 295-302 (1954).

15. J. P. Talashkevich and K. S. Aleksandrov, Effect of preferred grain

orientations on the elastic properties of polycrystals, Fiz. Metal.

Metalloved. 14, 801-805 (1962).

16. G. Kneer, Uber die Berechnung der Elastizitatsmoduln viel kristal 1 iner

Aggregate mit Textur, Phys. Stat. Sol i di 9., 825-838 (1965).

17. E. Kroner, Berechnung der elastischen Konstanten des Vielkristalls aus

den Konstanten des Einkri stal 1 s , Z. Physik 151 , 504-518 (1958).

18. E. Schmid and W. Boas, Plasticity of Crystals (Hughes, London, 1950),

p. 21.

362
Table I. Predi cted C .

.

'

11 2

1

J

10 N/nr

's for textured stainless'-steel 316, in units of

Texture Bound c nC 12C 13

r 33

C44

C66

[100] Voigt 2.473 0.926 1.326 2.072 1.174 0.774

Reuss 2.265 1.133 1.326 2.072 1.174 1.566

Avg 2.369 1.029 1.326 2.072 1.174 0.670

[110] Voigt 2.773 1.016 0.926 2.873 0.774 0.874

Reuss 2.480 1.179 1.065 2.593 0.566 0.650

Avg 2.626 1.102 0.906 2.733 0.670 1.762

[111] Voigt 2.873 1.059 0.792 3.140 0.640 0.970

Reuss 2.650 1.282 0.792 3.140 0.483 0.684

Avg 2.762 1.170 0.792 3.140 0.561 0.796

Isotropic 2.577 1.073 1.073 1.577 0.752 0.752

363
Table II. Predicted S.. 1 -11 2

'•J 10

11 m /N

1 s for ‘textured stainless'-steel 316, in units of

Texture Bound S 11

S 12S 13

s j3

s^44 S 66

[100] Voigt 0.617 -0.029 -0.376 0.964 0.852 1.293

Reuss 0.736 -0.148 -0.376 0.964 0.852 1.766

Avg 0.676 -0.088 -0.376 0.964 0.852 1.530

[110] Voigt 0.442 -0.130 -0.101 0.413 1.293 1.145

Reuss 0.564 -0.205 -0.148 0.507 1.766 1.538

Avg 0.503 -0.167 -0.124 0.460 1.530 1.341

[111] Voigt 0.417 -0.134 -0.071 0.355 0.563 1.103

Reuss 0.507 -0.224 -0.071 0.355 2.071 1.462

Avg 0.462 -0.179 -0.071 0.355 1.817 1.287

Isotropic 0.514 -0.151 -0.151 0.514 1.330 1.330

364
Table III. Predicted sound velocities for textured stainless-steel 316,

in units of cm/ys.

Texture Bound V 11V 33

V 44V 66

[100] Voigt 0.5574 0.5103 0.3841 0.3118

Reuss 0.5335 0.5103 0.3841 0.2667

Avg 0.5455 0.5103 0.3841 0.2892

[110] Voi gt 0.5903 0.6008 0.3118 0.3313

Reuss 0.5882 0.5708 0.2667 0.2859

Avg 0.5742 0.5858 0.2892 0.3086

[111] Voigt 0.6008 0.6281 0.2836 0.3376

Reuss 0.5771 0.6281 0.2463 0.2932

Avg 0.5890 0.6281 0.2649 0.3156

Isotropi

c

0.5691 0.5691 0.3074 0.3074

365
List 'Of Figures

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Angular variation of Young's modulus for three ideal fiber textures.

All curves represent arithmetic average of Voigt and Reuss bounds.

Units are 10^ N/m^.

11 2 Angular variation of torsional modulus. Units are 10 N/m .

Angular variation of longitudinal sound velocity. Units are cm/ys.

Angular variation of first transverse sound velocity. Units are

cm/ys.

Angular variation of second transverse sound velocity. Units are

cm/ys.

366
YOUNG’S MODULUS

Fig. 1. Angular variation of Young's modulus for three ideal fiber textures.

All curves represent arithmetic average of Voigt and Reuss bounds.

Units are 10** N/m^.

367
TORSIONAL MODULUS

Fig. 2. Angular variation of torsional modulus. Units are 10

11

N/m

2

.

368
LONGITUDINAL VELOCITY

Fig. 3. Angular variation of longitudinal sound velocity. Units are cm/ps.

369
TRANSVERSE VELOCITY

Fig. 4. Angular variation of first transverse sound velocity. Units are

cm/ys.

370
Fig. 5

TRANSVERSE VELOCITY

Angular variation of second transverse sound velocity. Units are

cm/ys.

371

NONM E TALUCS

373

NONMETALL ICS PROGRAM

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

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

CONTRACTS: S. K. Datta, U. Colorado; J. G. Hust, Division 773, NBS

OBJECTIVES:

( 1 )

( 2 )

RESEARCH

( 1 )

( 2 )

(3)

(4)

(5)

( 6 )

(7)

(8)

(9)

RESEARCH

( 1 )

( 2 )

(3)

(4)

(5)

( 6 )

To measure, model, and understand the properties of composites that

enter essentially into the conception, design, construction, operation, and performance of magnetic-fusion-energy equipment.

To cooperate with industry to establish and refine cryogenic-grade

specifications for insulating laminates and coding systems for

laminates.

PAST YEAR (1981):

Ledbetter. Review of NBS studies of anisotropic elastic constants

and internal friction of fiber-reinforced composites.

Datta, Ledbetter, Kinra. Theoretical -experimental study of wave propagation and elastic constants in particulate and fibrous com- posites . Datta, Ledbetter. A critical comparison of observation and theory

of the elastic constants of fiber-reinforced boron-aluminum.

Kriz. Effects of absorbed moisture on stress-wave propagation in

graphite/epoxy.

Kriz. A monitoring device for elastic-stiffness degradation in

graphite/epoxy.

Kriz. Ply cracks and fracture strengths of graphite/epoxy laminates

at 76 K. Kasen, Schramm. Measurement of mechanical properties down to 4 K of

a polyimide-matrix variant of G-10CR.

Kasen, Schramm. Screening, down to 76 K, of samples of G-10CR

produced by two new manufacturers of this product.

Hust. Measurements of thermal conductivity at cryogenic temperatures for two glass-fabric-reinforced epoxy-matrix laminates with

different reinforcement-to-resin ratios.

THIS YEAR (1982):

Kriz, Ledbetter. Ultrasonic measurement of the complete ninecomponent elastic-constant tensor of a woven glass-fiber/epoxy com- posite.

Kriz. Calculated stress distributions in a woven composite by a finite-element model.

Datta, Ledbetter, Kriz. Predicted elastic constants of transversely

isotropic composites containing anisotropic fibers.

Ledbetter, Kriz. Elastic-wave surfaces in fiber-reinforced com- posites.

Datta, Ledbetter, Austin, Kriz. Longitudinal wave propagation in an elastic composite thin rod.

Kasen. Continuation of a program on the standardization of cryogenic grades of insulating and structural laminates in cooperation

with industry.

375
DISCUSSION:

The following discussion gives some details of the studies listed above.

(1) Kriz, Ledbetter. By inspection, a cloth-reinforced composite has

three mutually orthogonal mirror planes and, therefore, orthotropic

(or orthorhombic) symmetry. The point group is mm = 2m. Any of the

three diad axes formed by intersecting mirror planes could be chosen

as the z axis. Since z usually denotes the physically most unique

axis, we chose z to be perpendicular to the cloth layers. Materials

with this symmetry exhibit nine independent elastic constants.

Contracting the fourth-rank tensor, C to

i jkl

notation , C ^ , and representing C^. by a 6x6

orthotropic symmetry and the above coordinate

a two-index (Voigt)

matrix, we have for

system:

C 12

rL 13

0 0 0

C 22

rl

23

0 0 0

rl

33

0 0 0

C44

0 0

symmetrical C 550

By ultrasonic methods, we will determine this elastic-stiffness

tensor by measuring the elastic compliances, S.., and using the

matrix equation

[Sij] . [£„]

-1

No one has done this. The results will provide valuable material

characterization, a valid test for any proposed macroscopicmicroscopic theory of material properties, and key design information. We intend to study a G-lOCR-type material.

(2) Kriz. For the purpose of establishing a universal design system, a plane-weave fiber-reinforced composite can be geometrically modeled

as a combination of structural "unit cells." Investigation of the

stress distributions within a unit cell when loaded in tension,

compression, or shear provides an explanation of fracture, which

initiates in high-stress regions. The fracture process in a woven composite can then be modeled as a sequence of related unit-cell

376
failures. The elastic and fracture behavior of a three-ply fiberreinforced plate subjected to bending has been modeled by Hirai and

Senba [1] using a unit-cell structural model. The approach to be

taken in this study is to classify analytically the elastic response

and fracture process of a unit cell when loaded in tension shear, or compression, or any combination thereof. This classification will

be accomplished by a fine-mesh finite-element model of the unit

cell. On the basis of these results, one can construct an idealized, simpler structural unit cell with appropriate elastic and

fracture characteristics; this simpler cell can then be used to

predict the mechanical response of a woven composite structure.

This analysis has high technological consequences and transcends

significantly the existing so-called laminate theory.

(3) Datta, Ledbetter, Kriz. We will derive dispersion relationships for waves propagating perpendicular to continuous fibers that are oriented unidirectional ly. In the long-wavelength limit we will

obtain relationships that predict the composite's effective static

moduli. We will compare these relationships with others derived by

energy methods to obtain upper and lower bounds of the effective

static moduli. We will demonstrate this comparison graphically by

plotting for graphite-epoxy the predicted composite moduli over the

full range of fiber volume fractions. We will consider the fibers

to be anisotropic, but transversely isotropic. We will consider the

relationship between our results and the upper and lower bounds of

Hashin. The static properties are, of course, special cases of the more general dispersion relationships.

(4) Ledbetter, Kriz. As explained above, -one can describe completely

the elastic constants of a woven fabric composite by either the

[C..] L or the [S. .] matrix. However, for understanding the elastic

ij J L ij J constants, no substitute exists for graphical representation sur- faces of quantities, such as Young's modulus, torsional modulus,

Poisson's ratio, linear compressibility, et cetera. This study will

develop and interpret these surfaces.

(5) Datta, Ledbetter, Austin, Kriz. Longitudinal wave propagation in a thin, circular, composite rod has many applications. This

theoretical -experimental study will start with a Mind! in-Herrmann

type of theory to derive the approximate equations of motion. We

anticipate solving a seven-unknown eigenvalue problem to determine

the variation of phase and group velocities with frequency. The

immediate application is to a NbTi/Cu superconductive wire. Longitudinal wave velocity in the wire will be measured by a kHz-region

standing-wave method.

L 1 J Hirai, T. and Senba, T., An Analytical Approach to Interseparation

Behavior of Woven-Fabric Reinforced Plastic Subjected to Bending Displacement," in Composite Materials; Mechanics, Mechanical Properties, and

Fabri cation , Japan Society for Composite Materials, Tokyo (1981).

3 77
(6) Kasen, Schramm. The nonmetallic materials characterization program

continued with the determination of the cryogenic mechanical performance of a variant of G-10CR that contained a polyimide matrix in

place of the conventional epoxy matrix. Studies at the Oak Ridge

National Laboratories had shown that this variant had much higher

tolerance to gamma irradiation at 5 K than did the conventional

laminate. Unfortunately, the NBS studies showed the tensile,

compression, and interlaminar shear properties of the polyimidematrix laminate to be distinctly inferior to the epoxy laminate at

all temperatures. These data, combined with the 5-8 times higher

cost of the polyimide laminate as compared with that of the epoxy

laminate, raise questions as to the viability of the laminate in

magnet construction. Fractographic analysis of the failure modes in

the polyimide laminate are currently underway to increase our understanding of its poor cryogenic performance. Discussions are also underway with industry to assess ways of improving basic

mechanical performance while maintaining radiation resistance. The

use of an epoxy-polyimide "alloy" has been suggested. Characterization studies also included screening of the cryogenic performance of

G-10CR produced by two new manufacturers. Samples of G-10CR from a third manufacturer have also been received for screening. These

studies will be of value in establishing performance variability

among manufacturers.

(7) Hust. Studies on factors controlling thermal conductivity of

laminates at cryogenic temperature have continued, recognizing the

importance of such data to the efficient design of refrigeration

systems for superconducting magnets. Measurements were carried out

on specimens of G-10 laminate containing different proportions of

glass and resin in an attempt to distinguish the contribution of

each to conductivity. As discussed elsewhere in this report, the

results were somewhat ambiguous, although analysis is not yet

complete. The thermal conductivity program also involved characterization of a G-10CR material produced by a different manufacturer to

provide information on the variability that might be expected in

materials produced to the specification.

(8) Kasen. The nonmetal lies program has continued to emphasize development of standard cryogenic grades of insulating and structural

laminates. The objective is to provide magnet builders with com- mercial sources of reliable, characterized materials and to provide

the basis for a systematic materials development program in response

to the needs of the magnetic fusion industry. As manufacturers

worked with the existing specification for the cryogenic grade of

glass-fabric reinforced industrial laminate G-10CR, it became

apparent that the specification was unnecessarily restrictive in some respects and deficient in specificity in other respects. The

specification was therefore revised on the basis of industry recom- mendations and copies of the revision were submitted to the manufacturers for comment. Primary changes were a provision for utilization of several alternative chemically equivalent epoxy resins and

alternative equivalent glass finishes, guidance in establishing the

required cure cycle, and a statement of required minimums in mechanical and physical properties.

378
The standardization program continues to attract the interest of the

U.S. laminating industry; two additional corporations have undertaken production of G-10CR. Three manufacturers are already established in the market.

Substantial progress has been made in working with the laboratory of

another manufacturer on the development of a standard specification

for a discontinuous glass-mat-reinforced epoxy laminate that could

perform most of the functions of G-10CR at a substantially reduced

cost. It is hoped that this specification will be completed in

FY82.

Progress in the standardization program was reviewed in an invited

paper "Current Status of Standardized Nonmetallic Cryogenic Laminates" at the ICMC/ICEC conference in San Diego on August 10-14,

1981. The subject was also reviewed in a session on nonmetal lies

chaired by M. B. Kasen at the NBS-DoE Vail Workshop, October 6-8,

1981.

The subject of nonmetallic materials standardization was also

addressed in the context of a committee discussion on Codes and

Standards for MFE Low Temperature Materials held as part of the Vail

Conference. It was agreed that the initial effort in nonmetallics

should be development of standard test methods. A committee was set

up for this purpose.

379

CURRENT STATUS OF STANDARDIZED

NONMETALLIC CRYOGENIC LAMINATES*

M. B. Kasen and R. E. Schramm

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

The MFE, MHD, and rotating cryogenic machinery technologies are making

increasingly severe demands on materials technology. This is particularly

acute in nonmetallic structural and insulating materials required for superconducting magnet construction. Unlike metals technology, the available

nonmetallic materials have not been standardized, which creates problems in

reliability. This paper is a progress report of the efforts to meet the

industrial needs for such materials while laying the groundwork for systematic

materials development to meet future needs.

*To be published in Advances in Cryogenic Engineering-Materials, Vol . 28,

R. P. Reed and A. F, Clark, Eds., Plenum Press, New York (1982).

381

INTRODUCTION

National Bureau of Standards personnel are continuing to work

with magnet fabricators and with representatives of the U.S. laminating industry to establish standard grades of nonmetallic insulator and structural support materials for use in critical parts of

magnetic fusion energy (MFE) cryogenic systems. Standardized materials are required for several reasons: (1) excessive variability

in the 4-K mechanical properties among nonmetallic laminates purchased to present industrial generic designations, (2) the impracticality of establishing performance specifications for retention

of properties after neutron and gamma irradiation at 4 K, and (3)

lack of knowledge of the significant elements in a laminate that

determine such performance.

The objective of the program is to assist designers in materials selection by establishing commercial sources of standard

materials for which a cryogenic data base has been established.

Achievement of this objective will simplify communication between

designer and laminate producer, enabling a balance to be achieved

between performance and cost, and laying a sound foundation for

systematic materials development in response to demonstrated need.

This is, of course, an open-ended task—there will always be a desire for better material performance at lower cost and there will

always be avenues for improvement. But the program recognizes that

designers require assistance in materials selection for current

designs as well as improved materials for future designs. The

overall approach is illustrated by the flow sheet of Fig. 1. We

*Invited paper.

383
dal-2

start by assessing current materials needs and by consulting with

industry on existing laminate systems best capable of meeting these

needs. A common specification for a high-grade laminate of the

defined type is then established by the laminating industry. At

this point, the standard laminates differ from those of a generic

designation primarily in the restrictions placed on the components

used in their manufacture and on the manufacturing procedure.

These restrictions are intended to be sufficiently stringent to

insure commercially available products whose cryogenic performance

can be meaningfully characterized and whose performance variability

is minimal. Deficiencies that are subsequently revealed through

experience or additional testing can then be systematically addressed since they are associated with defined materials systems.

This paper reviews progress in this effort during the past

several years, discusses the present activity, and offers suggestions for future work.

Fig. 1. Flow chart depicting a proposed approach to meeting immediate needs of nonmetallic laminate development for the

cryogenic industry. Dashed lines indicate the present

state of development of the G-10CR and G-11CR grades of

industrial laminates.

384
dal-3

PROGRESS TO DATE

A survey of proposed MFE designs 1 revealed that high-pressure

glass-cloth-reinforced epoxy laminates of the NEMA G-10 or G-ll

type were likely to be widely used for electrical insulation and

structural support for superconducting magnet windings. It was

known, however, that the cryogenic mechanical properties of such

material produced by different manufacturers could differ as much

as 40% at 4 K. This stimulated a series of discussions with representatives of the laminating industry, culminating in the establishment of tentative specifications for controlled grades of

G-10CR and G-11CR. These materials are currently being manufactured by four U.S. firms and have been well received by the cryogenic industry. The effect of cryogenic temperatures on the

mechanical, electrical, and thermal performance of these materials

has been reported in the literature, and characterization work is

continuing at NBS and other laboratories. The specifications are currently undergoing revision to provide the fabricators with maximum discretion in fabrication while maintaining minimum product

variability.

As anticipated, the G-10CR and G-11CR products have served as baseline materials for the study of several variants. An early

variant replaced the conventional boron-containing type E glass

reinforcement with a boron-free type in expectation of improved

radiation resistance; however, no substantial improvement was observed. 3 Another variant, tentatively designated G-10CR-L,

replaced the conventional glass reinforcement with a lightweight

type having less thickness per layer for the same volume fraction

of glass. This variant is useful in fabricating parts with small

radii of curvature and thin sections where it is desirable to maximize the number of layers of reinforcement. Cryogenic tests have

thus far indicated performance very similar to that of the original

CR grade except for some decrease in compressive strength. It is

probable that this variant will become a standard grade.

Radiation studies conducted at Oak Ridge National Laboratory3 have indicated substantial degradation in mechanical properties of

G-10CR and G-11CR after exposure to neutron and gamma irradiation

at 4 K under fluences at levels expected in the superconducting

magnets of working MFE systems. These results led to the investigation of a G-10CR variant in which the epoxy matrix was replaced

by a polyimide resin. Subsequent tests at Oak Ridge National

Laboratory4 indicated a much improved radiation resistance for this

variant, suggesting that it might be a candidate for insulators and

structural supports in MFE magnets.

Unfortunately, the polyimide variant, tentatively designated

PG-10CR, has several disadvantages of potential significance. One

is high cost—six to eight times that of G-10CR. Another is

385
dal-4

relatively low cryogenic mechanical strength compared with that of

G-10CR. As illustrated in Figs. 2 and 3, the polyimide variant

develops significantly lower tensile, compressive, and interlaminar

shear strengths at all temperatures, with the difference increasing

notably at cryogenic temperatures. The 30-40% lower interlaminar

shear strength of the polyimide variant is potentially the most

significant deficit, because many nonmetallic magnet components are loaded in shear. Young's modulus is the only property in which the

polyimide variant excells.

POSSIBILITIES FOR THE FUTURE

In the near term, it will be necessary to continue the development of standard laminate grades for use in radiation environments. Results described above suggest that radiation resistance

and cost may go hand in hand, in which case it would be desirable

to provide designers with a series of laminate types so that material selection could be made on a cost-versus-performance basis.

Ideally, the series would include laminates reinforced with glass

mat as well as glass fabric and material that could be fabricated

by low- as well as high-pressure molding techniques. Discussions

are being held to determine the feasibility of such development.

Because so little is known of the factors affecting degradation of laminate propeties due to irradiation at 4 K, the achievement of this goal will require close cooperation between

researchers in industry and several scientific disciplines. A

successful program must work with extremely well-characterized

lOOOr

800

<0 Q.

600

400

200

L

D

n

Tensile Strength

(warp)

1000

800

(0 Q.

2 600

3

O

4 K 76 K 295 K

400

200

Compressive Strength

(warp)

4 K 76 K 295 K

G-10CR

PG-10CR

Fig. 2. Comparison of the effect of cryogenic temperature on the

tensile and compressive strength of G-10CR and the polyimide-matrix variant tentatively designated PG-10CR. Preliminary data for two PG-10CR specimens of each condition

tested edgewise (warp direction).

386
42

38

CO _ . q, 34

O

uT

30

26

22

Young’s Modulus

(warp)

0

c=i

85

75

JP 65

CL

co 55

4 K 76 K 295 K

45

35

Shear Strength

“1 (warp)

4 K 76 K 295 K

g-iqcr

PG-10CR

dal-5

Fig. 3. Comparison of the effect of cryogenic temperature on Young's modulus and interlaminar shear strength (guillotine method) of G-10CR and the polyimide-matrix variant

tentatively designated PG-10CR. Preliminary data for two

PG-10CR specimens of each condition tested edgewise (warp

direction) .

materials and would probably require an iterative research cycle of

the type illustrated in Fig. 4. As the cryogenic radiation resistance of a polymer is likely to be a strong function of the exact

molecular structure, 5 an essential part of the cycle is a cor- relation of molecular level damage with radiation level and property change. Only in this way will the required scientific basis

be established.

The need for standardization largely reflects the absence of a nonmetallic materials classification system in which material performance is associated with a coding system. In the long run, it

will be necessary to develop a system for composite laminates that

is the equivalent of the systems developed for metals by AISI, the

Aluminum Association, and other similar voluntary standard bodies.

Although composites are indisputedly more complex than metals,

there seems no a priori reason why such an approach would not be

feasible for composite laminates, recognizing that the significant

engineering properties of a laminate at any temperature are largely

defined by a few parameters. For example, the intrinsic mechanical, elastic, thermal, and electrical properties of a high quality

laminate should be defined within relatively narrow limits by a numerical classification system that establishes the type and

flexibility of the matrix, the type and configuration of the reinforcement, and the reinforcement volume fraction. At the very

least, it should be possible to establish meaningful lower bounds

387
dal-6

Fig. A. Proposed flow chart for development of radiation-resistant

nonmetallic laminate insulators.

on such properties. The basic elements of such a coding system

have been considered in a previous publication. 6

CONCLUSIONS

The author has reviewed ongoing efforts to provide a commercial supply of standardized, controlled-performance laminates

required to meet the short-term needs of the cryogenic industry for

critical components in MFE superconducting magnet design and con- struction. The approach provides a basis for systematic development of material variants and for new materials as required to meet

the needs of future designs. The approach recognizes that development of nonmetallic insulators and structural supports in magnets

subjected to intense irradiation at A K will require a much better

understanding of the factors affecting material performance in this

environment and that this will be achieved only by an interdisciplinary approach.

The lack of terminology allowing a designer to specify non- metallic laminate materials by a performance criteria is a

388
dal-7

continuing problem. The ongoing standardization effort is designed

to meet immediate technical needs; however, a long-range effort to

establish an accepted standards notation system for nonmetallics

comparable to that used in the metals industry is worthy of con- sideration.

ACKNOWLEDGMENTS

This work was supported by the Office of Magnet Fusion Energy,

United States Department of Energy.

REFERENCES

1. R. P. Reed, F. R. Fickett, M. B. Kasen, and H. I. McHenry,

"MFE Low Temperature Materials Program: A Survey,"

National Bureau of Standards, Institute for Basic Standards, Boulder, Colorado (1977).

2. M. B. Kasen, G. R. MacDonald, D. H. Beekman, and

R. E. Schramm, in: Mechanical, electrical, and thermal

characterization of G-10CR and G-11CR glass-cloth/epoxy

laminates between room temperature and 4 K, in: "Advances

in Cryogenic Engineering - Materials," Vol. 26, Plenum

Press, New York (1980), p. 235.

3. R. R. Coltman, Jr., C. E. Klabunde, R. H. Kernohan, and

C. J. Long, "Radiation Effects on Organic Insulators for

Superconducting Magnets," 0RNL/TM-7077, Oak Ridge National

Laboratory, Oak Ridge, Tennessee (1979).

4. R. R. Coltman, Jr., C. E. Klabunde, and C. J. Long, "The

Effect of a 100 MGy (10 10 Rads) Gamma-Ray Dose at 5 K on

the Strength of Polyimide Insulators," Report SSD No.

81-10, Oak Ridge National Laboratory, Oak Ridge, Tennessee

(1981).

5. B. S. Brown, Radiation effects in superconducting fusionmagnet materials, J. Nucl. Mater. 98:1 (1981).

6. M. B. Kasen, Standardizing nonmetallic composite materials for

cryogenic applications, in: "Fundamentals and Applications

of Nonmetallic Materials at Low Temperatures," G. Hartwig

and D. Evans, eds., Plenum Press, New York (1981) (in

press)

.

389

Effect of Cryogenic Temperatures on the Mechanical

Performance of Glass-Fabric-Reinforced Laminates

R. E. Schramm and M. B. Kasen

Fracture and Deformation Division

National Bureau of Standards

Boulder, CO 80303

ABSTRACT

This study continues the mechanical testing of glass-fabric/epoxy

composites from several producers using the same specifications. In addition

to the G-10CR and G-11CR standards, two more variants were made to achieve

particular qualities: one contained a lightweight cloth to improve drapability

and the second substituted polyimide for the epoxy matrix to achieve greater

radiation resistance. From these tests, it appears that: (1) various

manufacturers produce a consistent product, (2) the lightweight variant has

properties similar to the standards, and (3) the polyimide variant has

mechanical properties inferior to its epoxy counterpart.

391

INTRODUCTION

Previously we reported on the complete mechanical characterization of one

manufacturer's CR-grade glass-cloth/epoxy composites and the screening of

1-3

those from another company. This report contains screening data on similar

laminates and two variants from two other sources.

MATERIALS

Through NBS-industry cooperation, there are industry-wide specifications

for G-10CR and G- 1 ICR. The basis for both laminates is the same glass fabric

(style 7628) of silane-finished E glass. It has an unbalanced plain weave

with a fiber-bundle density in the warp/fill direction of 42/32 per 25 mm.

The G-10CR matrix is a heat-activated, amine-catalyzed, bisphenol-A,

solid-type epoxy resin. The G- 1 ICR matrix is an aromatic-amine-hardened,

bisphenol-A, liquid-type epoxy resin. Resin weight fraction is 32-36% for G10CR and 28-33% for G-11CR.

4

In addition to standard G-10CR and G-11CR, the producers have provided

several variants as possible solutions to particular problems. The first ones

2 3 tested were a G-10CR and a G-11CR made with boron-free glass. ’ This report

includes two additional variants. One was a G-lOCR-type but made with a

lightweight glass cloth (style 1165 with thinner fibers and a 60/52 warp/fill

ratio) to increase the ability to drape around small -radius curves while still

retaining the same glass content; its identification here is G-10CR-L. The

other was also a G-10CR type but it had a matrix of aromatic polyimide rather

5 6

than epoxy; * its identification here is PG-10CR. Gamma radiation tests on

393
this composite have shown it retained a substantial portion of its initial

strength even after 100 MGy (10^ rads) at 5 K.

^

METHODS

Previous reports have documented our test methods and specimen configuraO O tions, but a brief summary is in order here. All specimens were cut from

flat sheets. Tensile tests used friction grips but no tabs. Specimen gage

length was 54-mm (2.125-in) long, 12.7-mm (0.5-in) wide, and 1.27-mm (0.05-in)

thick. Tensile measurements included Young's modulus, Poisson's ratio, and

strain and strength at failure. Compression specimens had a gage length of

19 mm (0.75 in), a width of 7.9 mm (0.31 in), and a thickness of 3.8 mm

(0.15 in). In the guillotine interlaminar shear tests (ASTM D 2733-70), we

changed the separation between saw cuts to 9.5 mm (0.375 in). Fracture

strength was the only measurement in both compression and shear tests.

The original characterization data were the results of at least three

tests at each temperature, 295 K, 76 K, and 4 K (room temperature, in liquid

nitrogen, and in liquid helium), and in both of the cloth directions (warp and

fill). Our screening process involved only two tests at each of two temperatures, 295 K and 76 K, in the warp direction only. With these values it was

possible to check for any major deviations among batches. Since the polyimide

matrix represented a major change, we extended its screening to include 4-K

measurements and both directions.

Flexural tests are often useful as a method of comparison. We ran a few

such tests on three batches of G-10CR at 295 K and 76 K in four-point loading

(ASTM D 790-71, Method II, Procedure B). Specimens were nominally 25 mm x

76 mm x 4 mm.

394
Conditioning of all specimens prior to testing (ASTM D 3039-71) was at

least 40 h at 22 ± 2°C and 50 ± 10% relative humidity.

RESULTS

Screening data for several epoxy-matrix laminates are in Table 1. Since

the pilot-plant material from Manufacturer A received the most extensive

1 2 examination, * all comparisons for the standard composites should look back

to this data base. With this reference point, it appears there are no

statistically outstanding mechanical variations in the G-10CR from Manufacturer C or D or the G-11CR from Manufacturer D. The inevitable variations

that do exist among the six properties measured appear to be randomly positive

and negative. Most of them are less than 10%, and a few reach the 20% rangevalues quite understandable solely on the basis of small sample size.

Comparing Manufacturer C's lightweight variant and standard G-10CR shows

that the differences again tend to be minor. There is, however, a possible

trend: all of the properties of the variant are somewhat lower at room

temperature but at 76 K they are almost the same or slightly greater, except

for slightly lower shear strength. To maintain the same glass density, the

G-10CR-L contained more layers of cloth per unit thickness and so the epoxy

layers between were necessarily thinner. This could possibly allow for some

relief of residual stresses caused by cooling. Since the lightweight 1165

cloth is less unbalanced than the 7628 style, it has proportionately less

glass oriented in the warp direction and more in the fill direction. This

could explain the trend to lower values at 295 K and also amplify the 76-K

increase. The change in fiber balance would also lead to more balanced

mechanical properties, but we did not test for this.

The PG-10CR data are in Table 2. To determine the effect of changing to a

polyimide matrix, it is necessary to compare its test results with those from

395
the standard laminate. For this purpose. Table 3 lists the average values of

1 2 both pilot plant and production runs of G-10CR from the same manufacturer. *

Figure 1 shows the range of warp measurements for the two composites, and the

mechanical differences due to the matrices are evident. All parameters

increased as the temperature decreased, as is usual. Except for the Young's

modulus and compressive strength, there was little increase between 76 K and

4 K.

A method of comparing the two composites is to calculate ratios of their

properties taken in various pairs. Table 4 collects three sets of such

ratios: (1) the value of each PG-10CR parameter divided by the corresponding

value for G-10CR, (2) each 4-K parameter divided by the 295-K value, and (3)

the fill parameter divided by the warp value.

These room temperature ratios show that all three warp direction

strengths, tensile, compressive, and shear, were about 10% lower for the

polyimide material. At cryogenic temperatures, the ratio of tensile

strengths, dominated by fiber properties but dependent on the matrix for load

transfer, underwent about a 25% decrease. However, the ratios of compressive

and shear strengths, dominated by matrix properties, dropped a significant 40%

at low temperatures. The change in resin also lowered the strain-to-failure

ratios about 20-35% throughout the range of test temperatures. For the filldirection ratios, the tensile and compressive strengths, as well as the

failure strain, were less divergent between the two materials. The order of

the elastic property ratios, on the other hand, showed a reversal. Poisson's

ratio for both was generally the same or possibly somewhat higher for the

polyimide composite. The Young's modulus was 10-15% higher for PG-10CR at all

temperatures in the warp direction and about 20% higher in the fill direction.

396
The ratio of cryogenic to room temperature properties indicates that, in

almost all circumstances, the PG-10CR was less sensitive to low temperatures

than was G-10CR. The one possible exception was the warp direction Poisson's

ratio, but this may simply have been the result of scatter in the small number

of tests. It is interesting to speculate whether there is any relationship

between the polyimide's smaller temperature sensitivity and its greater

radiation resistance.

The number of glass fibers in the fill direction is about 75% of that in

the warp direction in the glass cloth used in G10-CR and PG-10CR. As a first

guess, this would seem to determine the ratio of properties measured along

these two main axes. The last section of Table 4 indicates that the fill/warp

ratio actually varied considerably from this estimate. These values for all

parameters except the tensile strength ran higher than 0.75. Since the

interlaminar shear strength is almost totally a function of matrix material

and fiber bonding, its ratio was about unity. In most instances, the PG-10CR

ratios were greater than those of the G-10CR, indicating less mechanical

inhomogeneity in the cloth plane.

The flexural strengths in Table 5 indicate somewhat low values for the

fill tests of Manufacturer A, but these are most likely due to statistical

fluctuations. The ratio of 76-K to 295-K values ran slightly over two which

is similar to the tension and compression strengths; the fill/warp ratio is

also very similar. Since flexure involves a complicated mix of tension,

compression and shear, the results are not easy to interpret.

397
CONCLUSIONS

Production standards for G-10CR and G-11CR glass cloth/epoxy laminates

are available to all interested U.S. manufacturers. Thus far, five producers

have supplied us with one or both composites as well as several variants.

After testing material from four of these sources, our mechanical data showed

reasonable agreement and the products seemed consistent; this, of course, was

the reason for all the effort in establishing and disseminating the specifications .

A G-10CR-L variant made with lightweight cloth offers some possible

advantages. Its properties would be somewhat less anisotropic as evidenced by

its slightly lower room temperature properties, while its 76-K properties show

a possible slight improvement.

A PG-10CR variant with a polyimide matrix rather than epoxy demonstrated

a higher stiffness but reduced strength, particularly at low temperatures.

This decreased load capacity and its much higher cost necessitate a very

careful analysis of its radiation resistance necessary before this composite

could be a candidate for large-scale use.

ACKNOWLEDGMENT

We would like to thank Mr. N. J. Armendariz for conducting the flexural

tests and analyzing the data.

REFERENCES

1. M. B. Kasen, "Mechanical Properties, Thermal Contraction, and Electrical

Properties of G-10CR and G-11CR," in Materials Studies for Magnetic Fusion

Energy Applications at Low Temperatures - II , Eds. F. R. Fickett and R. P.

Reed, NBSIR 79-1609, National Bureau of Standards, Boulder, Colorado, 407-416

(1979).

398
2. R. E. Schramm and M. B. Kasen, "Mechanical Properties of G-10CR and G11CR," in Materials Studies for Magnetic Fusion Energy Applications at Low

Temperatures - III , Ed. R. P. Reed, NBSIR 80-1627, National Bureau of Standards, Boulder, Colorado, 335-366 (1980).

3. 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-Cloth/Epoxy Laminates between Room Temperatures and 4 K," in Advances in

Cryogenic Engineering , Vol . 26, Eds. A. F. Clark and R. P. Reed, Plenum Press,

New York, 235-244 (1980).

4. J. R. Benzinger, "Manufacturing Capabilities of CR-Grade Laminates," in

Advances in Cryogenic Engineering , Vol. 26, Eds. A. F. Clark and R. P. Reed,

Plenum Press, New York, 252-258 (1980).

5. J. R. Benzinger, "The Manufacture of Radiation Resistant Laminates" in

Materials Studies for Magnetic Fusion Energy Applications at Low Temperatures -

IV , Eds. R. P. Reed and N. J, Simon, NBSIR 81-1645, National Bureau of Standards, Boulder, Colorado, 615-638 (1981).

6. R. P. Reed, R. E. Schramm, and A. F. Clark, "Mechanical, Thermal, and

Electrical Properties of Selected Polymers," Cryogenics _1_3> 66-87 (1973).

7. R. R. Coltman, C. E. Klabunde, and C. J. Long, "The Effect of a 100 MGy

(10

10

rads) Gamma-Ray Dose at 5K on the Strength of Polyimide Insulators,"

Report SSD No. 81-10, Oak Ridge National Laboratory, Oak Ridge, Tennessee

(1981).

8. R. E. Schramm and M. B. Kasen, "Cryogenic Mechanical Peoperties of

Boron-, Graphite-, and Glass-Reinforced Composites," Mater. Sci . Eng. 3(3, 197-

204 (1977).

399
LIST OF TABLES

Table 1. Mechanical Properties of Glass-Cloth/Epoxy Composites.

Table 2. Mechanical Properties of PG-10 CR (Manufacturer A).

Table 3. Average Mechanical Properties of G-l OCR (Manufacturer A, Pilot

Plant and Production).

Table 4. Mechanical Property Ratios.

Table 5. Flexural Strength of G-10CR.

400
Table

1.

Mechanical

Properties

of

Glass-Cloth/Epoxy

Composites

O

or- c

t 3

4_,0

uo

_1 03 _ —. Q_ o

* *

«

CM LO o o

o ^r D ojrr-^| r

-K * O CO LO KO A A

* *

.

A A

^r c\j r— CD

r^. vo n co in o o o

LO VO N

or CO coo

*3- r^

LO CO O LO CO Oi CO

LO VD N

LO LO It— r— CD LO COlCvJ CO O

VO VO O CD

co LO co CO O CM CO o LO LO o CO o

&) o

> D

CM NlO CO LO Oi co

ro

co Iwco

CO VO

lo|vo p

o c\j |i— rsvo is O *3* CM CO CD ||

CO CO I CO ISVO N

LO O 00 envois

CO CO CO

00 ^ VO

cd or ta- co r^|r^

o oolo o cm vo

CM N in I—I C\J PO CO I CO VO vo I VO

-C r4-j in o>

0) *

S- -I

CO- S-OS LO CO

' o o

N O Oi O'— o

co <3- o cm o vo

co co co vokr

co co|co r>* r^|r^

lo cd n cm n

LO vo vo CM CM CM

«3- r^lco c-. cn|co in n vo n co in

*3- <3*ta" co co Ico

co vo

lo vo

O O LO rs vo vo

*3- <3-ta

r- CO O CM »— CM

LO VO LO

CO r— KM

CO CO CO

CtL oo cd lo

i— lo

CO r— r—

r— pO CD

CM CO CM

-

CO oK CO Oi CO

- P

c

o •*

O 03 O- OC

O lf)N

cj- oi <3

- o ojo o o

r— CO o o

*3- CM

CM Oi CD O O O

CO 00 LO

VO r—

CM CM

Oi CM

CM CM o do

CM CO

co 3

“Oo

"

r^. co

oo *3- «3-

CO CM

CO o

CM O CM r—

<3" LO O Oi

*=T *3* *3- LO

03 Q-O

CM O CO CMPO PO CM CM

PO PO LO O O CM CM O CO *3" cm ro co

— po |r^ p>* cm Ilo d co Ico <3 *3 ta M CM [CM PO PO |PO

<D 0) CD CD CD CD CD CD

LO 03 03 LO 03 03 Oi s- LO S- Oi S. vo s- CM <D <D CM CD C

D

> > > >

<C <c «=c <c

CD CD CD CD CD CD CD CD

<o 03 LO 03 03

S~ LO S- CD S- LO $-

(D P>» CD CM CD r*«» CD > > > > C <C <

401

*Minimum

value,

specimen

broke

in

tension.
Table

2.

Mechanical

Properties

of

PG-10CR

(Manufacturer

A)

CO—Ifl3 ct> cn or r— co LO CT» to <3- LO CM CM o

to to to CO LO «3* "3* LO C-* to LO LO LO LO

co co co <3- CO CO CO «3- ^ *3- *3-

„lo to

lo r^. to

to to •o

CO

lo

tO

<3- to

co r^

CM

CO

CM C'-llO

r^» co Ilo co co co

r- W N lo <3

-

1 *3

- *3- *3- H- O O LO

CO CO LD

LO LO LO

CM O I tO to nKo

«3- or>-

LO «3" LO

CO CO CO

CO CO|CO

r^. oo Ico I— CO

to to |to

•<3- o

<T> <T>

*3

" CM CO

LO CM CO

LO to|to

I— O'* LO

r— lo I to

CM CM CM

CM LO CT* co n co co co

to cm

CTi O|0

CO kf

CD- c: s_ CO to CM CO CO tO LO to i— <*3- CO to <3

- LO "3-

•r- =3 co «3- r— *3- co to CM «3- ^3- *3- "3- lo cn CM CO o =3- 03 r— * . . • . • • « S- t- ZD

-t-> 03 1—

CO Li_ U)

1 — CM CM CvJ CM CM CM CM r— CM 1— CO CM

CO - > c 'd- CTi LO LO o tO r— *3- O CM i

LO co p". Or CTi cn o ~ to to to CTi CM i

CO LO *3" LO LO LO cn co to 00

CO O 1— r— r— CM CM CM CM CM i— ii— i

1— 1— 1— 1—

CO -r- • • e • o o • • • • r- 4-> O <T3 CL C£ o o O O O O O O O o o O o o o o o |o

CO

Z3 to CM *3- CO CO 00 <=3* CO , CP) LO CM CO 00 , <3- r- ^ to r- CM 1— 00 LO O r— i

LO CO r\ CTi O o

-a S "3- '3- *3- LO LO LO LO LO LO «3- ^ ^3- «?3- *3- *3* *3- LO LO

'— -

I s— - r-" >—w

CO LU

cnc

O

*

CO to <3- o r^. CO LO <3- CM tO *3- co LO co n- LO £ ‘T; CM CM CM LO to LO O CO* cn 00 co’ 00 r— CO CM *3" *3" *3- >- co CO CO co CO CO CO *3- oo co CM CM CM CO CO CO CO CO CO

CD

S- a> cd a) CD CD CD

=J cn cn CD cn cn CD

-M LO ra 03 03 LO rd ra ra

03 cn to s- %- cn s- to S- s_

t- ^ CM CD 05 ^3" CD CM CD r^. <D '3" CD

CD > > > > > >

CL < c <X. < <c c

402
Table

3.

Average

Mechanical

Properties

of

G-10CR

(Manufacturer

A,

Pilot

Plant

and

Production) * • <U -c c

4-> CSJ CSJ VO av 0 C o <G • • • • • a> <— cl to VO CSJ CSJ 00 U r- ^ 4-> -r- CO 3 . CD

&. >—

55 CO

a> _j

.c ^D

JZ

*-> CPc

a>

s- 4JVO -4- *3 IT) 00 CSJ CO CO « a= 1^ vo co to O'* co co CSI to to

ess cu 1 °

CD• -C

4-> cnc0) s- +

-*-> *3 OV VO CSJ NOICO

00 a. •— ^ VO to to Or z «a* CO 00 CSJ ^ ^

4» ZD Cl r—

*— 1— i. r—

to •p— CO 3 Ll c

a> H-O4-> * CO to to CO

O c i. r~- <-0 to to

-T“ ~T P

ra

ili TU r— CO CO r— CSJ CVJ

4-> 03 (*) t/3 u_

CO - > OCOr- CO CO

O c VO O r- 00 1— 0 • 1— csi csj «— f—» CSJ CO O

to t- t- 4-> 000 000 O

CL QC

CO33

“OO + 0 0 ^ «aO

— S * *3 CO CSJ to CVJ CP

CO CD CSI CO CO CVJ CSI CSJ CPc3O

>-

0>L.3

4-> to vo «d* to VO ^

cp ov

a; CSJ CSI a.Es

4-

VO0 CO

i/I Q)m

t»m>

too 3* X

toB

«C

iSk 03+

403
Table 4

Mechanical Property Ratios*

Temperature

,

K

E V £

tu °TU a

CU

a

ILS

PG-1 OCR/G-1 OCR

Warp

295 1.17 1.04 0.80 0.92 0.95 0.82

76 1.09 1.03 0.67 0.75 0.57 0.67

4 1.10 1.16 0.67 0.74 0.64 0.62

Fill

295 1.27 1.06 0.92 1.03 1.12 - 76 1.20 1.02 0.89 0.83 0.84 0.63

4 1.19 0.85 0.90 0.81 0.95 0.57

4 K/ 295 K G- 10CR, Warp

1.28 1.32 2.05 2.06 2.36 1.61

G- 10CR, Fill

1.30 1.47 1.74 1.93 2.11 -

PG -10CR, Warp

1.20 1.46 1.73 1.66 1.56 1.22

PG -10CR, Fill

1.21 1.19 1.71 1.52 1.80 1.23

Fill /Warp

G-10CR

295 0.80 0.89 0.87 0.61 0.75 - 76 0.82 0.90 0.73 0.54 0.72 1.10

4 0.81 1.00 0.74 0.58 0.69 1.09

PG-10CR

295 0.87 0.90 1.01 0.69 0.89 0.99

76 0.91 0.89 0.97 0.60 1.04 1.03

4 0.88 0.73 0.99 0.63 1.03 1.00

Calculated from average values in Tables 2 and 3.

404
Table 5.

Flexural Strength of G-10CR

295 K 76 K

Warp Fill Warp Fill

MPa (ksi

)

MPa (ksi) MPa (ksi) MPa (ksi)

Manufacturer A (P roduction Plant)

486 (70.7) 283 (41.1) 1120 (163) 745 (108)

540 (78.3) 333 (48.3) 1100 (159) 745 (108)

Avg 514 (74.5) 308 (44.7) 1110 (161) 745 (108)

Manufact,urer B

382 (55.4) 800 (116)

394 (57.2) 807 (117)

383 (55.6) 793 (115)

366 (53.0) 786 (114)

Avg 381 (55.3) 800 (116)

Manufact.urer C

512 (74.3 383 (55.5) 1100 (159) 834 (121)

531 (77.0) 397 (57.6) 1110 (161) 862 (125)

Avg 522 (75.7) 390 (56.6) 1100 (160) 848 (123)

405
lOOOr Tensile Strength

(warp)

(0 a

800

600

D

400-

200

CD

4 K 76 K 295 K

lOOOr

800

<0 EL2 600

3

o

400

200

Compressive Strength

(warp)

4 K 76 K 295 K

42

38 -

Young’s Modulus

(warp)

2 34

o

llT 30

26

22

4 K 76 K 295 K

85r

75

ro 65

a

j 55

b“

45

35

Shear Strength

(warp)

4 K 76 K 295 K

0.3 Poisson’s Ratio

(warp)

^ 0.2

0.1

4 K 76 K 295 K

- 3

£

W

2

-

Strain to Failure

(warp)

i i

4 K 76K 295 K

G-10CR

PG-1 OCR

Figure 1. Comparison of the measurements on two glasscloth composites. The height of the bar

indicates the data spread. For the G- 1 OCR

there were 3-6 tests and, at most, two for the

PG-1 OCR

.

406
*Publ i shed in

MECHANICAL PROPERTIES OF PLASTIC COMPOSITES

UNDER LOW TEMPERATURE CONDITIONS*

M. B. Kasen

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

Composites

,

Vol . 12, 107 (1981).

407

Letters

Mechanical properties of plastic composites

under low temperature conditions

Dear Sir,

It was with interest that I noted in a recent issue of your

journal a contribution 1 describing the low temperature

mechanical properties of plastic composites. The author’s conclusion that composites fabricated with a highly flexibilized epoxy matrix provide better cryogenic properties

than those fabricated with nonflexibilized systems may be

valid for laminates containing 32% by volume reinforce- ment, but it is not valid for the higher volume fractions

typical of laminates in industrial usage. Literature reviews

and work in our laboratory2-4 indicate that residual stresses created by the large thermal contraction of highly flexibilized systems negates any advantage provided by the intrinsically

higher strain capability of the matrix when fiber contents approach 50-60% by volume in glass, graphite or aramid

laminates. We find, for example, that the flexible Resin 2

formulation 5 decreases the 4 K uniaxial longitudinal tensile strength of an S-901 glass-reinforced laminate to a level about

equal to that of a non-flexibilized matrix laminate at 295 K. The transverse strength of a uniaxial graphite-reinforced

laminate at 4 K is reduced by about 60% by a higher flexibilized matrix, while the transverse failure strain is reduced

by about 90%. When used with aramid fiber, the flexibilized matrix reduces the uniaxial transverse strength to an extent

rendering the laminate almost useless for structural applications.

Additionally, the intrinsic weakness of highly flexibilized

resin sysytems near room temperature has resulted in the

catastrophic failure of several structures designed for cryogenic use but necessarily subjected to moderate stresses at room

or slightly elevated temperatures.

The author quite correctly points out the limitation imposed on the effective cryogenic strength of glass-reinforced laminates due to the strain limitations of conventional bisphenol

A epoxies at such temperatures (the *knee point’ in the stress/ strain curve). But the solution requires a resin system providing reasonably high room temperature strength and reasonably

low thermal contraction as well as cryogenic toughness.

Possible approached have been discussed in the recent literat- ure.* Until such systems are developed and proven, it appears most prudent to utilize conventional resin systems

for cryogenic laminates. M. B. Kasen

Fracture Deformation Division, National Bureau of Standards,

Boulder, CO 80303

references

1

Kadotani, K. ‘Mechanical properties of plastic composites under

low temperature conditions’ Composites 11 (April 1980) pp

87-94 2 Kasen, M. B. ‘Mechanical and thermal properties of filamentary- reinforced structural composites at cryogenic temperatures’

Part I: glass reinforced structural composites, Cryogenics, 15 No 6 (June 1975) pp 327-349 Part II: advanced composites,

Cryogenics 15 No 12 (December 1975) pp 701-719

3 Kasen, M. fe.'Cryogenic properties of filamentary-reinforced

composites: An update’ (In preparation) 4 Schramm, R, E. and Kasen, M. B. ‘Cryogenic mechanical

properties of boron-, graphite-, and glass-reinforced composites’ Mater Sd and Eng 30 (1977) pp 197-204

5 Softer, L. N. and Molho, R. ‘Cryogenic resins for glass-fila- ment-wound composites’ NASA CR-72114 (Final) 6 NonmetalUc Materials and Composites at low Temperatures

(Plenum Press, 1979)

Author’s reply

Dear sir,

I would like to thank Dr Kasen for his interest in my paper

1

and to express general agreement with his comments. However, I would like to enlarge upon the published paper and

try to explain further the aims of the work reported. It was my intention to select reinforced-plastics materials for use

as electrical insulation in superconducting magnet coils utilized in fusion reactors and rotating machines. For such

applications glass-fibre reinforced plastics with low fibre volume are preferred in order to match the thermal contraction characteristics of the copper-clad superconductors

and the stainless steel used to fabricate the structural components. The grp components, together with the resin moulded superconducting coils are immersed in liquid

helium so that the operating temperature, at which

electromagnetic stress is applied is always of the order of 4K. Thus it is not expected that the grp components

should have higher mechanical strength at room temperature.

However, assembly of the magnet coils is sometimes carried out at higher temperatures, and resins having adequate

(medium) flexibility have been used in these instances. For

the manufacture of components such as support rods, pressure

vessels and torque tubes, high performance composites such

as boron, carbon or aramid fibre-reinforced plastics with

higher volume fractions and using conventional resin systems

(with Tg in the range 100°C - 200° C) are desirable.

K. Kadotani

Hitachi Raaaarch laboratory. Ibaragi Prefactura, Japan

COMPOSITES. APRIL 1981

409 107

THERMAL CONDUCTIVITY OF G-IOCR AND G-11CR INDUSTRIAL LAMINATES

AND THEIR COMPONENT PARTS AT LOW TEMPERATURES

J. G. Hust

Thermophysical Properties Division

Center for Chemical Engineering

National Bureau of Standards

Boulder, Colorado

ABSTRACT

Thermal conductivity measurements and comparisons with literature data are presented on cryogenic grade composites G-IOCR and G- 1 ICR and their component

parts, resin and glass fibers. The measurements were made in the 2 to 300 K range for heat flow both normal to the fabric and in the warp direction.

Material variability from lot-to-lot and the effect of strain is described.

The relationship of composite conductivity to the conductivities of the resin

and glass components is discussed.

411

INTRODUCTION

As part of the continuing cryogenic materials program, NBS, in cooperation

with the U.S. laminating industry, has arranged for commercial production of

component-specified NEMA/ASTM type G- 10 and G-ll industrial laminates for cryogenic insulation and structural applications. This action was taken because

conventionally produced proprietary G- 10 and G-ll laminates did not meet the

demanding specifications of superconducting magnets for magnetic fusion energy

applications. The cryogenic variability in G- 10 and G-ll laminates occurs because the room temperature NEMA specifications can be met by different glass

rei nforcements, weaves of the fabric, types of epoxy, and cure agents as well

as the fabrication procedures. The component-specified laminates investigated

are designated as G-10CR and G-11CR.

This report summarizes the thermal conductivity measurements of this project and compares the results with literature data. In addition, the relationship of the composite conductivity to the conductivities of the resin and glass

components is discussed.

MATERIAL AND SPECIMEN CHARACTERIZATION

G-10CR and G- 1 ICR are composites of fiberglass fabric and epoxy. The

fabric is woven from type E glass threads with 17 threads per cm (43 per in) in

the warp direction and 12 threads per cm (32 per in) in the fill direction.

The thread is composed of 75 filaments each of 0.00046 cm (0.00018 in) diameter. The density of E glass is 2.58 g/cnA G-10CR resin is a heat-activated

amine catalyzed bisphenol A, solid type, epoxy resin. G- 1 ICR resin is an aro- matic amine bisphenol A liquid type epoxy resin. The G-10CR resin has an uncured density of 1.10 ± 0.01 g/cm^ and the G-ll CR resin has uncured density

of 1.04 ± 0.01 g/cm^. The cured resin density is highly uncertain and is

discussed later.

The G-10CR laminate is specified to contain 33-35% resin by weight and the

weight fraction of resin in G- 1 ICR is specified to be 27-31% by weight.

The dimensions, weights, and densities at 280 K of the specimens measured

are given in table 1. The specimens were generally fabricated from single

blocks of the designated material; however, in some instances layered specimens were used.

Specimens G-10C1, G-10C4, G-10C7, and G-11C1 were measured to establish

baseline values and to study material variability between manufacturers. Specimen G-10C3 was measured to determine the difference between G-10CR and stock

G-10.

The specimen designated as G-10C2 was prepared to study the effect of

strain. A thin strip (2-cm wide, 0.4-cm thick, and about 30-cm long) was cut

from a sheet and strained in a tensile apparatus to 90% of ultimate (1.44%''.

This strip was then cut into squares, and the pieces were bonded under pressure

to form the thermal conductivity specimen. To obtain a control specimen,

G-10C4 was fabricated in the same manner from an unstrained strip.

413
Table 1. Dimensions, Weights, and Densities of the Thermal Conductivity Speci- mens. For the composites, the dimension denotes the direction

normal to the fabric, X 2 denotes the warp direction, and X 3 the fill

direction. All specimens were cut from single blocks supplied by the

manufacturer except as indicated in the footnotes.

Material

Designation

Specimen

Identification

Specimen

Dimensions (cm)

Wei ght

(g)

Density

(g/cm 3

) Xl X2 X3

G-10CR G- IOC

1*

1.910 1.890 1.919 13.188 1.904

G-10C2

+,d 1.913 1.911 1.916 12.767 1.824

G-10C3** 1.882 1.908 1.873 11.717 1.741

G-10C4+ ,d 1.916 1.819 1.824 11.608 1.825

G-10C5

++ 0.373 1.951 1.911 2.385 1.71

G-10C6

3 0.318 1.808 1.885 2.152 1.98

G-10C7 C 0.646 1.910 1.870 3.964 1.72

G- 1 ICR G- 1 1 Cl* 1.915 1.913 1.910 13.684 1.956

G-10CR resin G-10R1 1.915 1.913 1.781 7.698 1.180

G-10R1A 1.915 0.652 1.781 2.615 1.18

G-10R1B 1.915 1.041 1.781 4.175 1.18

G- 1 ICR resin G-11R1 1.915 1.915 1.915 8.620 1.228

E Glass EGL1 0.955 1.905 1.905 8.924 2.58

Vetronite d

VETC1 1.778 0.197 1.765 1.189 1.92

VETC2d

1.780 0.393 1.766 2.328 1.92

VETC4

d

1.780 0.792 1.766 4.770 1.91

VETC12d

1.778 2.378 1.765 14.282 1.91

Mi carta MICR0De 1.915 2.504

*-Manufacturer A

**-Fabricated by bonding two 0. 952-cm-thick pieces (glue plane parallel to

fabric). This is stock G-10 material, not G-10CR.

+-Manufacturer B, G-10C2 measured after 1.44% strain, G-10C4 = control specimen.

++-This material was produced with a higher resin content than normal G-10CR (40%

weight fraction resin compared with 34%).

a-This material was produced with a lower resin content (24% weight fraction

resin)

.

b-This is a European glass fiber/epoxy composite.

c-Manufacturer C. d-These specimens were fabricated by bonding several pieces cut from single

sheets.

e-This specimen is a right circular cylinder, X^ = diameter and X£ = length.

414
Specimens G-10C5 and G-10C6 as well as the pure resin and pure glass specimen were measured to determine the variation of conductivity with resin con- tent .

To study thickness effects and inhomogeneities through the thickness of

the material, specimen G-10R1 was cut normal to the heat flow direction (after

measurement of its thermal conductivity) to produce specimens of approximate!

y

one-third and two-thirds the original thickness. The latter specimens are designated as G-10R1A and G-10R2A, respectively.

A sheet of the Vetronite* material, previously measured at CERN [1], was obtained and 12 square specimens were cut from it. These were fabricated by

cutting two 1.9-cm-wide strips from the supplied sheet. Each of the two strips were further sectioned into six equal pieces. The 12 resulting pieces were machined to their final dimensions. Measurements were performed on selected

groups of these specimens to obtain thermal conductivity values as a function

of specimen thickness. These specimens are designated as VETC1 through VETC12.

The number in the designation indicates the number of pieces within each speci- men. These measurements were performed for comparison with the data reported

by CERN along with numerous other data that were suspiciously low.

The Micarta* rod (MICROD) specimen was measured as part of the apparatus

calibration procedure.

SPECIMEN DENSITIES

The specimen densities have been measured (see table 1) because they are a useful indication of resin content or void content variations. These variations can significantly affect the thermal conductivity of the specimens.

From the measured bulk resin and glass densities, p r and p g (table 1),

and the specified weight fractions, WF, one can calculate the composite density, p, using eq (1).

p -1

+ ( 1 )

These densities are compared with the measured densities in table 2.

The agreement between measured and calculated values is within the specified composition variation except for G-10C1 and G-10C7. It is suspected that

G-10C7 is actually a stock G-10 grade, i.e., not the G-10CR grade. The density

of G-10C3, which is stock G-10, compares well with G-10C7. The reason for the

G-10C1 difference is not known.

It is also noted that the densities of bulk glass and resin may be different from the actual densities within the composites. Void fractions are not

known with sufficient accuracy to correct the calculated values. They are estimated to be less than 2%.

*Trade names are used in this report for a proper understanding of the materials investigated. The use of these trade names in no way implies endorsement

or disapproval of the product.

415
Table 2. Comparison of Measured and Calculated Densities for the Indicated

Specimens. Density of glass = 2.58 g/cm 3

, density of G-10 resin

= 1.18 g/cm 3

, density of G-ll resin = 1.23 g/cm 3

.

Specimen

Identi fication

Weight Fraction Resin

Den si ty (g/cm 3

) Measured Calcul ated

G-10C1 0.34 ± 0.01 1.904 1.84 ± 0.002

G-10C2 0.34 ± 0.01 1.824 1.84 ± 0.002

G-10C4 0.34 ± 0.01 1.825 1.84 ± 0.002

G-10C5 0.40 1.71 1.75

G-10C6 0.24 1.98 2.01

G-10C7 0.34 ± 0.01 1.72 1.84 ± 0.02

G-11CR 0.29 ± 0.02 1.956 1.92 ± 0.04

EXPERIMENTAL PROCEDURE AND DATA ANALYSIS

The thermal conductivity of the test block is determined in a thermal con- ductivity integral apparatus. This apparatus, described by Hust and Arvidson

[2], can be used to perform measurements at temperatures from 2 to 300 K.

Further details of the experimental setup, the thermal conductivity integral (TCI) method, thermocouple calibration, and the operating procedure are described in the report by Hust and Arvidson [2]. A calibration measurement on

a NBS standard reference material is also included in the report. The measurements on the standard reference material (SRM 735)' indicate an overall system

accuracy of about ± 3% up to 100 K and ± 6% above 100 K. A Micarta rod (along

with Vetronite and G-10CR specimens) was used to calibrate the heat leak

between the heat source and heat sink in the cell. The uncertainty of this

heat leak is ± 10% and is the major source of uncertainty in the final results.

RESULTS AND DISCUSSION

The direct experimental data for each specimen are available from the

author. These data were analyzed by both the difference method and the TCI

method. The function chosen to represent x(T) in the TCI method is

6

A(T) = Yi a^nlm)]' (2)

i+1

Thermal conductivities by the difference method are calculated from eq (3)

X(T

2

,T

x

) = Qax/A(T

2 -T1

) (3)

where X(T2 ,Ti) denotes the average value of x(T) from T2 to J\ (the hot and

cold faces, respectively), Q is the heat flow through the specimen with crosssectional area. A, and length, ax. The value of x(T2,Tj) is normally associated with the mean temperature, T = (T£ + T-^)/2, but since large temperature

416
differences are used here, these values are slightly in error due to the curvature of the x(T) function.

Thermal conductivities by the TCI method are determined by fitting the

coefficients in eq (4)

TCI

0 bs

= J

xdT = 1 ntegral of eq. (2) = g^,^, ^ , a 2

,...a

6

) (4)

T

1 The thermal conductivity integral data for each of the specimens are sum- marized in table 3. Each of the data sets spanning the range from helium temperatures to room temperature were represented by eqs. (2) and (4). The coefficients, a-j , were determined via a least squares fit of the observed TCI

values. The relative rms deviation and the maximum deviation, % Dev. =

( TCI obs~TCI calc) 10°/ TCI obs » °f each fit is given in table 3. The coefficients,

a-j, for each least squares fit are listed in table 4.

Values of thermal conductivity as calculated from eq (2) for G-10CR and

G-11CR are plotted in figure 1. Values obtained for the G-10 high resin con- tent and G-10 low resin content are plotted in figure 2 along with the pure

resin and pure glass data. The values for Vetronite and Micarta are plotted in

figure 3. The data reported from CERN [1] for Vetronite (same sheet of material) are also shown in figure 3.

From figure 1 it is clear that the values for the warp direction of G-10CR

and G- 1 ICR are about 20% greater than the values for the normal direction.

This to be expected since the glass fibers represent a parallel high conductivity path through the resin in either the warp or fill direction. However

within the material variability, G10-CR and G-11CR for a given direction have

equal conductivities. Figure 2 shows that the glass conductivity is about 4

times higher than the resin conductivity. Figure 4 compares available literature data [3-6] on G-10 and G-ll to the values obtained in this research.

Comparison of the data in figures 1 and 4 indicates that the CR grade of G-10

has a slightly higher conductivity than the stock G-10 grade. Although material variability data is quite limited, it appears that 10% variability in con- ductivity should be expected.

The resin conductivities plotted in figure 2 reveal considerable differences. Specimen G-10R1 is the original, approximately 2-cm, cube. Because

this specimen is relatively transparent, it was cut into two specimens proportioned approximately one-third and two-thirds of the original thickness, for

additional measurements to detect the effect of radiant heat transfer through

the specimens. The presence of radiant heat transfer results in a decrease in

the apparent conductivity with decreasing thickness. Although a decrease was observed, the magnitude of the decrease was surprisingly large. Further, since

the curves are relatively parallel, the difference cannot be caused by radiation. Radiation heat transfer increases with temperature as T'\ The Vetronite results, discussed later, indicate that this thickness dependence is not

an apparatus error.

To investigate the possibility of inhomogeneities in the two specimens,

due to poor mixing of the ingredients or varying degrees of cure, the glass

transition temperature of each piece was measured along with various other

417
Table 3. Summary of Thermal Conductivity Integral Data and Calculated

Value of X at 280 K for Each Set of Measurements.

Specimen Identi- Number of Temperature Deviation {%) X( 280 K)

f ication/Heat Data Points Range

(W»m

_1

-K”

1 Flow Direction (K) RMS Max. )

G-lOCl/Norm 22 2-302 1.4 2.7 0.50

G-lOCl/Warp 24 2-302 1.2 3.3 0.79

G-10C2/Warp 17 4-305 1.5 3.1 0.61

G-10C3/Norm 1 288 — — 0.42

G-10C4/Warp 2 88,282 — — 0.60

G-10C5/Norm 19 4-308 0.7 1.2 0.37

G-10C6/Norm 17 3-310 0.6 1.1 0.52

G-10C7/Warp 26 4-318 0.4 0.9 0.57

G-llCl/Norm 16 2-297 1.2 2.2 0.53

G-llCl/Warp 15 2-302 1.4 2.1 0.65

G-10R1 21 2-304 1.7 5.0 0.29

G-10R1A 23 4-298 1.6 4.0 0.23

G-10R1B 2 280 — — 0.24

G-11R1 18 4-304 1.6 4.1 0.27

EGL1 20 4-309 0.5 0.9 1.14

V ETCl/Norm 4 289

VETC2/Norm 22 4-308 L 2.1 6.0 0.44 VETC4/Norm 22 4-310 r

VETC12/Norm 23 4-306 J

MICROD/axial 24 2-287 2.7 5.0 0.60

specimens. The results indicate very little difference between the G-10CR

resin specimens, Tg = 85 ± 5°C for the thin specimen and 93 ± 5°C for the thick

specimen. The Tg of specimen G-10C4 is 97 ± 5°C, which is in reasonable agreement with the resin specimen values. The G-10C5 and G-10C6 specimens had a slightly higher glass transition temperature, 103 ± 5°C. The glass transition

temperature of the G-11CR resin specimen was considerably higher, 166 ± 10°C.

The above unexplained conductivity dependence on thickness suggests that the

effective conductivity of both the resin and the glass, in the normal direction

within a composite, will be lower than that measured for the bulk specimens.

This is because the distance from fiber-to-fiber within the composite is very

small and the fibers themselves are small. In the warp or fill directions,

conversely, the effective conductivity of the components should correspond more closely to the measured bulk values.

Figure 2 is plotted to illustrate the progression of conductivities from

pure resin to pure glass. Figure 5 is a plot of conductivity as a function of

the volume fraction of resin for various temperatures

.

The model frequently adopted for heat flow normal to the fabric in a com- posite is one in which the glass and resin thermal resistances are added in

proportion to their volume fractions, VF

q and VF

r

. Equation (5) is derived

from this model. y

418
Table 4. The Coefficients, a-j from Eq. (2), for Each Set of Measurements.

a-j x 10 6

i G-lOCl/Norm G-lOCl/Warp G-10C2/Warp G-10C5/Norm G-10C6/Norm

1 -103516.92 -41908.943 -169739.97 -152148.13 -230890.44

2 205526.47 97685.284 325116.43 274868.65 369725.03

3 -112281.75 -30664.161 -182492.29 -158528.27 -193542.14

4 29353.211 1025.1003 47592.068 43456.245 48129.142

5 -3503.0441 1119.1669 -5623.2036 -5605.3277 -5578.9960

6 154.74522 -124.32478 245.58291 277.81952 246.05951

a-j x 10 6

i G-10C7/Warp G-llCl/Norm G-llCl/Warp G-10R1 G-10R1A

1 -160714.93 -52921.090 2506.2012 20818.210 31664.248

2 248829.47 115620.83 109.99048 69419.464 25316.908

3 -107919.63 -53039.929 45194.871 -66383.246 -34696.162

4 19681.969 11279.983 -26205.233 23957.970 14411.594

5 -1148.8081 -894.90446 5593.4980 -3678.6599 -2426.5035

6 -13.425492 11.268249 -400.25814 205.94405 147.08945

a, x 106

i G-11R1 EGL1 VETC*/Norm MICROD

1 183281.88 -1354404.2 -35556.453 22175.004

2 -183347.00 2097015.2 60035.153 -13691.739

3 82596.626 -1101425.2 -11965.605 9957.7037

4 -18103.335 267915.51 -2862.1565 -1485.7131

5 2047.0262 -30401.701 1300.5061 300.72406

6 -96.644046 1307.5164 -113.28850 -51.532623

*A1 1 of the VETC data were represented with a single fit.

41 9
X (5)

X VF +

g r

X r VF

g

where VF-j = WF-jp/pj.

Using the measured thermal conductivities of the pure resin and glass, x r and Xg, the solid curves in figure 5 were calculated. As can be seen, good

agreement between this model and the experimental data exists.

As mentioned earlier, Vetronite was measured as a function of thickness to

determine if apparatus errors are dependent on the thickness. A range of

thickness covering a factor of 12 was investigated. These results, not shown

in figure 3, are plotted in figure 6 for a temperature of 280 K.

Although a slight dependence on thickness in the same direction as for the

G-10CR resin specimens is evident in figure 6, it is considerably reduced. The

increase for the resin was 25% for a factor of 2 increase in thickness, while

for the Vetronite the increase was about 4% for a factor of 12 increase in

thickness. Clearly the source of the increase for the resin specimens is not

in the apparatus or the method of measurement. Thus the large difference in

conductivity between the G-10CR resin specimens remains a mystery.

ACKNOWLEDGMENTS

The author expresses appreciation for the assistance of Rich Boscardin for

performing some of the measurements and aiding in the analysis of the data.

REFERENCES

1. K. Dahl erup-Peterson and A. Perrot , "Properties of Organic Composite

Materials at Cryogenic Temperatures ," I SR-BOM/ 79-39 , CERN, Geneva,

Switzerland (1979).

2. J. G. Hust and J. Arvidson, "Thermal Conductivity of Glass Fiber/Epoxy

Composite Support Bands for Cryogenic Dewars," Unpublished report

available from author. National Bureau of Standards, Boulder, CO (1978).

3. F. J. Walker and A. C. Anderson, "Thermal Conductivity and Specific Heat

of a Glass-Epoxy Composite at Temperatures Below 4 K," Review of

Scientific Instruments 52(3), 471 (1981).

4. J. A. Barclay, S. S. Rosenblum, and W. A. Steyert , "Low temperature

thermal conductivity of some composite materials," Cryogenics _16, 539

(1976), Note: Figures 6 and 8 in this paper are interchanged. The

thermal conductivity of G-10 appears in figure 8.

5. M. Kuchnir, "Apparatus to Measure Thermal Conductance," Cryogenics 20, 203

(1980).

6. Y. S. Touloukian and C. Y. Ho, eds., "Thermophysical Properties of

Selected Aerospace Materials, Part II. Thermophysical Properties of Seven

Materials," Purdue University, TEPIAC/CINDAS, Lafayette, IN (1977).

420
Figure Captions

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Thermal conductivity values of various G- 10 and G-ll specimens from

this research. Legend:

G-llCl/Norm =

, G-llCl/Warp = _, G-lOCl/Norm = O, G-lOCl/Warp - 0,

G-10C2/Warp = •, G-10C3/Norm = ,

G-10C4/Warp = a, G-10C7/Warp = 7.

Thermal conductivity of pure resins, pure glass and two resin/glass

composites of differing resin content.

Thermal conductivity of Micarta and Vetronite. Legend:

MICROD = , VETC (all specimens) =

, VETC (CERN) = 0.

Thermal conductivity of G-10 and G-ll as reported in the literature

compared with the results of this research. Legend:

G-IOCR/Norm (this research) = , G-IOCR/Warp (this research) = G-10/Norm (Kuchnir [5]) = A, G-ll/ Norm (Kuchnir) = 0,

resin/glass composites (Average of values tabulated by Touloukian

and Ho [6]) = •, G-10 (Barclay, Rosenblum, and Steyert [4]) = v, G-lOCR/paral 1 el to fabric (Walker and Anderson [3]) = .

Thermal conductivity variation with resin content of G-10CR normal

to the fibers. The circles indicate the experimental values, and

the solid curves are calculated from the series resin-glass model.

Observed thermal conductivity of Vetronite at 280 K as a function of

thickness.

421
I

_sr oo

s~

naO) Qto 4-

0) «3

to »—1 •r* U

-C o 4-3 T-H8 S u i S- * 4-0 II

to II CL c $- O) E Jt» E S~ 3 •i— o - o 3 r-. 0)^.0

Q. t—i c IflUH O I '—1 i—H CD

r—t B I cd •> CD < oc

<D crI t I

II

II Q.

£_03

cd CL'dc. o

to to o 3 3 <-• O ''V. I r-HO

C- oto «-HI * >hQI t|_ CD II O

*> E

to i s- d) I o I to 00

II oo

>> E ' +J S- • r O CD O CD

^3 .—I II o<-* c I CL O CD S- <D 03

to "O ECO S_ O) o

<JJ CO'—I

-C aj i I— _l CD

a)

C-3

CO

422
|

i

i I i—i—i r

i.i j j i i -Li L

‘x

CM

o

o

423

Figure

2.

Thermal

conductivity

of

pure

resins,

pure

glass

and

two

resin/glass

composites

of

differing

resin

content.
o

II

X.

424

Figure

3.

Thermal

conductivity

of

Micarta

and

Vetronite.

Legend:

MICROD

VETC

(all

specimens)

=

,

VETC

(CERN)

=

0.
o t _>l- u-M ‘x

+-> '5 ii

XJ

a>

4.

<T3 CL

1—1 COO

CJ II < -OO

qj .—s II 4- -C

ra 3 O ** • 0

4_> 4- 1 1 fO /a fa co

s_ oj 1—

JJJ. QJ co 3

4-> QJ 4-

O

•r 4- •(- r— 9 r- C 3 1 co -C O 1 OJ ‘i— CJ 1— 1 JC -C 3 1 +-> -t-> >0 • >— -Q II ^ e

•'“EE £ 4. •a o o

<d z 2: +J

swcl: o O O 1—

0-0 I OI

cr

a<u

+-> ra I 1 o_o = £> C

-Q

O

(t5 II 00

4-> 4.

0) CJ CO 1—I'D

co « 0) «a- c

fO • • 3 1 K r—

r—

-0 fO 4-> TC

r—

0 > 4.

O 1 QJ QJ fO O 00 4- >,

03

O (U s. -O —

4-> 0) c QJ C/0 -SL 03 . 1 DO 1—

fO "D fO

O .c » 4-

C 3 r—

<j .— 0 (1) I 4- sz O a3<u 4- co o a>

s_ >1

4-3 00 • 1— *r— > .c • 1- 4->

+-5 a 4- 3 o

-o

SZ CO O -M

CJ -

3 ,— CO

03 a> E 4.

QJ Qj

U II < • cj

4- ««- fO

qj 1—

C0 LO

0) 1 1 4-

iC0 •!-

•I- c

-C JO

•1-3 CJ3

CL

4.fO E

C. o

oc z: 0 \ O 1-t

—H i—

1 1 cr o 3 4. CO I— jQ

QJ -O fO

4->C 4-

•r- OJ

c/o co o O O -M CLQC E — O « cu u >>.—

K3 1—

fO

4.fOCL

CO

CO

u

fO 4- .— 03 C70 CC ~-~- o o •r- O C

co <—' r—

qj 1 1 4. e: o a

s_3

DO

425
CM

• "O

co Q)

$- 4-> <V fO -O r—

•r- 3

*+ O

0) 03 .c u

+-> a> o $-

T3 S- C CO O) O <11 CO O I

a a> i— s- -C

<T3 t- 4-> E <->

a> oj o r r s.

CO

CD

$-CD

U_

426

VOLUME

FRACTION

OF

RESIN
427

Figure

6.

Observed

thermal

conductivity

of

Vetronite

at

280 K

as

a

function

of

thickness.

WAVE PROPAGATION AND ELASTIC CONSTANTS IN PARTICULATE

AND FIBROUS COMPOSITES*

S. K. Datta and V. K. Kinra

Department of Mechanical Engineering

University of Colorado

Boulder, Colorado

and

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

*Published in Composite Materials; Mechanics, Mechanical Properties and

Fabrication, Japan-U.S. Conf., Tokyo, 1981, Eds. Kawata, K. , Akasaka, T.

,

Japan Society for Composite Materials, Tokyo, Japan (1981).

429

"Composite Materials,” K.Kawata 6 T.Akasaka, Ed., Proc. Japan-U.S. Conference., Tokyo, 1981.

Wave Propagation and Elastic Constants in

Particulate and Fibrous Composites

S. K. Datta*, H. M. Ledbetter**, and V. K. Kinra*

* Department of Mechanical Engineering, University of Colorado,

Boulder, Colorado 80309, USA.

* *Fracture and Deformation Division, National Bureau of Standards,

Boulder, Colorado 80303, USA.

ABSTRACT

For two types of composites—particulate and fiber-reinforced—dynamic elastic properties were studied both theoretically and experimentally. The two composites contained, respectively, randomly distributed spherical inclusions

and aligned continuous fibers, both in a homogeneous matrix. The theory describes

aligned, identical ellipsoidal inclusions. As special cases, the theory comprises both spherical inclusions and short fibers. Bose and Mai presented previously a similar theory for continuous fibers. The theories estimate the effective propagation speed of a plane harmonic wave; the theories average the scattered

field by the Waterman-Truell procedure and use the Lax quasi-crystalline approximation. Theory and observation agree quite well. Particulate composites were

studied in a through-transmission water-immersion tank, while the fiber composite was studied by both pulse-echo-overlap and resonance methods.

NOMENCLATURE

A

WV

, BVV

mn mn

3

iwv’• Cj

A .

, c imn imn

a, b,, c

radius of spherical inclusions coefficients describing coordinate change

coefficients in wave-function expansions of incident field coefficients in wave-function expansions of scattered field

three principal semiaxes of ellipsoid (c>b>a)

cr

c

2 <0^, <C

2

>

?iJ

L(3)

' im (x.

volume concentration of ellipsoids

longitudinal and shear wave speeds in matrix effective principal-axis longitudinal and shear wave speeds wave number

spherical vector wave function of first kind referred to the center of the ith ellipsoid; a longitudinal wave regular near x^

spherical vector outlying longitudinal wave function

30

431
n, n Nf 1} tx, x ) _ inn - - 1

N f 3 )

_ imn

Tmn

ij

V

x

X . _ 1 X, y. z a

e

Pp'

a

Tm

number density

spherical vector wave function of first kind; represents shear-wave polarization in an individual plane and is regular

near x

i spherical vector outying shear wave function

time transition-matrix coefficients displacement field volume of an ellipsoidal inclusion; 4nabc/3

position vector of a point

position vector of center of ith ellipsoid Cartesian coordinates of a point measured parallel to a, b, c m/

c^ m/C

2 Kronecker delta

aC, assumed small density of matrix

density of inclusion Poisson ratio of matrix

C

l /C2 angular frequency

INTRODUCTION

Recently, b'oth particulate and fiber-reinforced composites have been studied

extensively. Excellent reviews include that of experiment by Bert (IJ and of theory by Sendeckyj ( 2)

.

In fiber-reinforced composites, two types occur: continuous-fiber and short (chopped)-f iber . The former have been studied extensively, and some recent studies have been reported on the latter (3)

.

Contrasted with the large literature on fiber composites, few particulatecomposite studies have been reported, and most of these focus on spherical in- clusions .

Relatively few of the reported theoretical studies consider wave propagation

in a composite consisting of a random distribution of either particles or fibers. Most studies consider only the static case.

This paper has three objectives: (1) describe a theory for a composite's

effective wave speeds and, therefore, the elastic constants; (2) present some experimental results for particulate and fiber composites; and (3) compare observation and theory. The theory predicts effective wave speeds in a medium

containing a random homogenous distribution of aligned ellipsoidal inclusions.

Bose and Mai (4) used a similar theory for a random distribution of aligned

continuous fibers.

THEORY

The theory of effective wave speeds given here follows closely that of Mai

and Bose ( 5) for spheres and of Datta (6J for ellipsoids, which was confined to very low inclusion concentration. To obtain the effective wave speeds in a com31

432
posice with random inclusion distribution, one must take the ensemble average of the scattered field due to N ellipsoids with aligned axes and centers at x.. Suppressing the time factor exp(-imt) , the scattered field is (6):

/

s > = e 3 N E

i=l

2 E

n=0

{A. L^

3

) (x,x.) xmn _ lmn _ . 1 tC. N^ 3 -1 (x,x.)} + 0(e

4

) xmn-xmn _ „x

( 1 )

where the A. and C. coefficients depend on the material and geometrical

properties o?

11 each ellipsoid, and on the incident harmonic-wave disturbance. In

(1) the Cartesian reference axes are parallel to the ellipsoid's principal akes, and we assume the wavelength is much longer than the ellipsoid.

If the ellipsoids have the same size and properties, then (7)

l i00 iV

4itc 3 my

T v T00

(a. , + 3t

2 c. xy v xy 'v

)

iV

Tu'v (a, , + 3t

2 c. iy v xy -J

ip2 , 3

4ttc TP2

= iV

4irc 3 T

U 2 p2

(a. , + 3 t^c.

iy v iy v>

x01

= iV T01

01

(a. _ + 2xc . „ ) xOv xOv

4irc

3

iV

Tu'i (a . , + 2 tc

.

ipl iy v iy 'J

”

4ttc 3 Tpl

v = 0,2; y' = 0,2, -2; | y

' |<v (2)

P = 0,2, -2; v = 0,2; y ' = 0, 2 ,-2 ;

| y

'

| <v

p

= -1,1; v = 2; y' = -1,1

v = 1

p = -1,1; v = 1; y' = -1,1

where summation is over the repeated indices y' and v over the integers indicated. Elements are defined in the appendix. Note that

Ciyl t

3A. . and C. 0 = t 3A. ./

2

lyl iy2 iy2 (3)

Furthermore, the coefficients a. and c. are the coefficients in the expansion

of the exciting field near the l^K scattelrer, that is.

u (x . x. ;x . , . .

,

_ _i'.l _i x ) = E

~N n=0 m=-n 2 [a. L^ 33 (x,x.) imn.xmn _ _i + tc . N^ 33 (x,x, ) ] (4) xmn_xmn _ „i

If a plane wave is incident along one of the ellipsoid axes, say the c axis (= z axis) , then

.n-1 laz . .

•3 „ a. = x e x (2n+l)o + c imn mo

; e V: r

jf± \^U y-v

A. A

yV jyv ran

and c =

Xn 1 (2n+l)

ciBz

i

(6 ml - n(n+l)6

nij _1

) + £ 3 E) E E C

j vv

B

, imn 2n(n+l)

(5) j^i v=0 y=-v where A

WV and BUV are defined in (5). Note that these depend on the position of the cen¥er of tfte j th ellipsoid relative to that of the ith ellipsoid. Equation

(5) assumes that the incident wave is

,(i) _ e + e i$z

( 6 ) _ z ~x

the sum of a P wave and a shear wave polarized along x, both propagating along

32

433
To obtain an equation for the averaged field within the composite, we assume a uniform distribution of density n^. Furthermore, for simplicity, the conditional number density n(x.

~ 3 n (Xj|xi) “ n

Q

x. - x. | > 2 c

- j -i

= 0 " ?i | < 2 c

(7)

Equation (7) means that an ellipsoid is enclosed by a sphere of radius c and the condition of noninterpenetration of spheres is satisfied. From (2) and (5) for an incident P wave.

<A. >

Iran i iV

4irc'

[T*JV {iv —

1

iaz.

i ( 2 v+l )6 PO

+ e \f<A . , jp v 1J dx . } +

-1

T.PV J-..V-1,

2v (v+1)

6 (n) T

h v

{

i

v i

( 2v+l )(6 _ - v (v +1 ) 6 _} + £ A(v)n„ f<A. , B

P V dx.] ( 8 ) mn _______ Pi P»-l 0 J jp v 13 pv v '

where the integrals are over |x. - x.|>2c. Note that the summations over p and

V are restricted to the values' Indicated in (2). Also,

A (v) = t

2

; v=l

= t

3 /2; v=0,

2

6 (n) = 3 t 2

; n=0,2

= 2 x; n=l.

One now obtains an integral equation for <A. >. by assuming imn i

<A. , ,>. . = <A. , ,>. jp'v’ lj JP v J (9)

which is known as the quasi-crystalline approximation. This integral equation

is solved by assuming a plane-wave solution

<A. > imn

ikz

.

( 10 )

where k is the effective wave number. After some tedious algebra, it results

that for a P wave in the z direction the effective wave speed is

<C

1

> 2 /C

1

2 - [1 - c (5 tJ

2 (1 +

(5T

° 2 + T^° + 5T

*32

' T^cJl/Kl +

00 02 00 02 /J/U

°

2 T00

T02 (1 + 3B

2 /2a2 )}].

For an S wave propagating along

T°°) " T02 (1 + 3b2/2“ 2) - (

3c T°*){(1 + c T°°)(l + c T°

2 (l + 30

2 /2a2 )) -

z and polarized along x, the wave speed is

<C

2 >2/C2 = [l-c(T

32 + 6 T

j

2 ){(9B 2 /4a

2

) - 1} ] / [ (1 + 3c T^){1 + c(T32 + 6 T

22

)

(1 + 30

2 /2a

2 )}]. (12)

Expressions for waves moving along x and y can be obtained similarly. Effective

wave speeds in a continous fiber-reinforced composite can be calculated similarly,

as done in (4J

.

33

434
MATERIALS

For the particulate composite, the matrix consisted of an epoxy. The solid spherical inclusions consisted either of glass or lead. For any particular

specimen, inclusions of nearly the same diameter (2a) were used: for glass 0.3 mm <_ 2a <_ 3 mm; for lead 0.5 mm 2a <1.3 mm. The volume fraction of inclusions,

c, was varied over the range 0.05 1 c £ 0.53. This range of particle size was

chosen to allow examination of all three regions of interest:

A<<a, X 3 a, and A>>a where X is a characteristic wavelength.

The fiber-reinforced composite consisted of 0. 14-mm-diameter fibers in an aluminum—alloy—6061 matrix in an F-tempered condition. The composite, containing

48 percent fibers by volume, was fabricated as a 10 x 10 x 1.1 cm plate containing

about 70 plies. Mass density measured hydrostatically was 2.534 g/cm

3

. Table 1 gives the mass densities and elastic constants of both constituents.

MEASUREMENTS

Through-transmission Water- immersion All measurements on particulate composites were made in a water-immersion

through-transmission ultrasonic apparatus described in detail in (8); only a brief description follows here. The heart of this apparatus is a pair of accu- rately matched broad-band immersion transducers. A pulse-generator/functiongenerator combination was used to produce a tone burst (10 to 30 cycles) of desired center frequency, n, where 0.3 <n<_ 5 MHz. A radio-frequency power amplifier was used to boost the signal to about 300 volts peak-to-peak. This signal was applied to the transmitter, a P wave was launched in water, the wave was transmitted through the specimen, and was detected by the receiving transducer; the total time of flight was measured by a universal counter-timer with

1-ns resolution. The phase velocity of the P wave in the specimen, <C^>, was measured as follows. The arrival time of a specific peak at the receiver was measured twice: once with specimen in place and once with specimen removed. Together with the specimen width, this information was enough to calculate

<C.>. The shear phase velocity, <C2 > . was measured similarly with the following

difference: the specimen was inclined to the sound beam at a critical angle at which the amplitude of the mode-converted P wave was minimized. Velocity error was estimated to be one percent.

Pulse-echo-overlap

Elastic stiffness constants, C, , of the fiber composite ^ere determined from sound velocities, v, and the familiar relationship C = pv , where p denotes mass density. Eighteen sound velocities were measured by propagating elastic waves with three polarizations in three <100> and six <110> directions, where

[001] denotes the fiber direction and [100] denotes the ply-normal direction. A modified pulse-echo-overlap ultrasonic-velocity system provided the necessary measurement capability (S[). Modifications consisted mainly of narrower pulses

(0.2 us» or two cycles at 10 MHz) and wider bandwidths. Echo patterns contained sufficient quality to permit cycle-by-cycle measurements of transit time between leading edges of adjacent echoes. For this we used a dual-delayed-sweep oscillo- scope equipped with a microprocessor for precise time-interval measurements

(resolution 0.2 ns, typical transit time 5 ys). Other experimental details

include: specimen thickness 3-10 mm; opposite specimen faces flat and parallel

within 5 ym; quartz piezoelectric transducers 1 cm in diameter, x-cut and ac-cut, rough polished, gold electroplated two sides, 10-MHz fundamental frequencies;

phenyl salicylate bonding agent; pulse width near 0.3 ys; pulse height near 20

V.

Resonance Elastic-compliance constants, S , .

,

of the fiber composite were determined from standing—wave sound velocities determined by a three-component compositeoscillator resonance technique. A composite oscillator (consisting of a quartzcrystal driver, an identical quartz gage crystal, and a specimen) was resonated by applying a sinusoidal voltage to electrodes plated on the drive crystal. The

34

435
resulting oscillation amplitude was monitored by observing the voltage developed between electrodes plated on the gage crystal. The drive-signal frequency was varied until a sharp maximum indicating resonance was observed in the gage voltage amplitude. The elastic constant was computed from the composite-oscillator resonant frequency, the specimen mass, the quartz-crystals' mass, the quartzcrystals' resonant frequency with no specimen attached, and the specimen's mass

density and length. By using quartz crystals with orientations and electrode configurations appropriate for extensional oscillation, the Young's modulus of the specimen was measured. Quartz crystals driven in torsional oscillation were

used to measure the torsional modulus. Further details and references on this technique are given elsewhere ( 10 , 11). Specimens consisted of cylinders 5 mm

in diameter with lengths between 2.5 and 5 cm. Nominal resonance frequency was

60 kHz.

RESULTS AND DISCUSSION

Elastic wave speeds along principal axes were calculated from (11) and (12) and are shown in Figs. 1 and 2 for a particular glass-reinforced epoxy- matrix

composite. This composite was modeled as a distribution of thin prolate spheroids

(aspect ratio c/a >1) with fibers parallel to the z direction. From symmetry,

the composite should behave transversely isotropic. Thus, wave speeds parallel

and perpendicular to the fibers (longitudinal and shear) give four of the five independent elastic constants. Figure 1 shows that cC^-* increases rapidly with increasing fiber volume concentration, c, as well as with increasing aspect

ratio, c/a. On the other hand, the < C.

1 > elastic-stiffness change with c/a is not rapid. The shear moduli <C^> aad <C,.g> also change slowly with c/a. Theory predicts a surprising change for < C,,> that is not immediately understood:

<C,,> becomes infinite at low c, 0.17 for the composite considered here. For all other elastic moduli, the present theory agrees with results of other studies

( 3 ).

For spherical (c/a=l) inclusions, present theory predicts bulk and shear moduli that coincide with the lower-bound predictions of Hashin and Shtrikman

(12)

. Figures 3 and 4 compare theory and observation for two particulate composites. Agreement is excellent when wavelength far exceeds the particle size. Interestingly for the lead-epoxy composite, the observed <C^> /C^ is nearly

constant for short wavelengths. To explain this behavior, a model was proposed

( 13 ) that considered lead balls as fluid spheres in a matrix with a small shear- wave speed.

Theory outlined in this paper was also used to obtain expressions for the bulk properties of continuous fiber-reinforced composites. These expressions

coincide with the lower bounds of (14) Table 2 shows results of theory and observation; agreement is excellent, even for the troublesome, error-prone off-diagonal elastic constants.

From the above observations, we see that the theoretical model considered

here predicts accurately the elastic-constant behavior of certain composites.

(However, further studies are required on short-fiber composites) The theoretical model considers the scattering of harmonic waves from obstacles; the waves are averaged in the far field by the quasi-crystalline approximation.

ACKNOWLEDGMENTS

The research studies of S.K.D. and V.K.K. reported here were supported in part by grants ENG-76-09613, ENG-76-04328, and CME 78-24179 from the National

Science Foundation to the University of Colorado. Principal support for studies

by H.M.L. comes from the Department of Defense Office of Fusion Energy and the NBS Office of Nondestructive Evaluation; Defense Advanced Research Projects

Agency sponsored the early experimental studies of boron-aluminum.

35

436
REFERENCES

1 Bert, C. W. , "Experimental Characterization of Composites", Composite

Materials, Volume 8 , Academic, New York, 1975, pp. 73-133.

2 Sendeckyj, G. P., "Elastic Behavior of Composites", Composite Materials , Volume 2 , Academic, New York, 1974, pp. 45-83.

3 Chou, T.-W. , Nomura, S. , and Taya, M. , "A Self-Consistent Approach to the Elastic Stiffness of Short-fiber Composites", Modern Developments in Composite Materials and Structures , Ed. J. R. Vinson, ASME, New York, 1979,

pp. 149-164.

4 Bose, S. K. and Mai, A. K. , "Elastic Waves in Fiber-reinforced Composites", Journal of the Mechanics and Physics of Solids , Vol. 22, 1974, pp. 217-229.

5 Mai, A. K. and Bose, S. K. , "Dynamic Elastic Moduli of a Suspension of Imperfectly Bonded Spheres", Proceedings of the Cambridge Philosophical Society

Vol. 76, 1974, pp. 587-600.

6 Datta, S. K. , "A Self-consistent Approach to Multiple Scattering by Elastic Ellipsoidal Inclusions", Journal of Applied Mechanics , Vol. 44, 1977,

pp. 657-662.

7 Datta, S. K. , "Diffraction of Plane Elastic Waves by Ellipsoidal Inclusions", Journal of the Acoustical Society of America , Vol. 61, 1977, pp. 1432-

1437.

8 Kinra, V. K., Petraitis, M. S., and Datta, S. K. , "Ultrasonic Wave Propagation in a Random Particulate Composite", International Journal of Solids and Structures , Vol. 16, 1980, pp. 301-312.

9 Ledbetter, H. M. , Frederick, N. F. , and Austin, M. W. , "Elastic- Constant Variability in Stainless-steel 304", Journal of Applied Physics , Vol. 51, 1980, pp. 305-309.

10 Weston, W. F., "Low-temperature Elastic Constants of a Superconducting

Coil Composite", Journal of Applied Physics , Vol. 46, 1975, pp. 4458-4465.

11 Read, D. T. and Ledbetter, H. M. , "Elastic Properties of a Boron- aluminum Composite at Low Temperatures," Journal of Applied Physics , Vol. 48, 1977, pp. 2827-2831.

12 Ha shin, Z. and Shtrikman, S. , "A Variational Approach to the Theory of the Elastic Behavior of Multiphase Materials", Journal of the Mechanics and Physics of Solids , Vol. 11, 1963, pp. 127-140.

13 Datta, S. K. , "Wave Propagation in the Presence of a Random Distribution

of Inclusions", to appear In the Proc. 3rd Symposium on Continuum Model of Discrete Systems, Univ. of Waterloo Press, Waterloo, Canada. 14 Hashin, Z. and Rosen, B. W. , "The Elastic Moduli of Fiber-reinforced

Materials", Journal of Applied Mechanics , Vol. 31, 1964, pp. 223-232.

15 Eshelby, J. D. , "The Determination of the Elastic Field of an Ellip- soidal Inclusion and Related Problems," Proceedings of the Royal Society, London , Vol. 241, 1957, pp. 376-396.

APPENDIX

Relevant expressions for T^| needed to calculate <C^> and <C

2

> are:

l-2o 00 , 1+g =. „02

i 00 9(l-a) mmnn’ 00

1+a

, IT-

,00 45 (1-a) 1 '‘'mmnn ^ Tmm33^ ’ T02

. [T - 3T,. ] , 9 (1-a) mmnn 33nn

T01_l,,, . 02= l-2a

T01 3

P 1 ’ X02

- 3T - — fT -3T ) 1 . 15 (1-a) L '*’33nn 3333 3 ' mmnn mm33

T& - ol X +

12 15 (1-c)

li 3131

T3232 ] ’ and T [T 3131

" T3232 ] -12 (l-2o)

12 ' 45(l-a)

— T — A T where T. is defined by the relationship e - T, j. ekl’ where e

ij is the transformation .strain in the equivalent ellipsoidal J Inclusion due to J a uniform

strain field e^ at infinity (15)

.

36

437
or <

C

c c

Figs. 1 and 2. Effective elastic constants <C. > and <C_~> and <C.,> and

11 33 44 <C,.> for short-fiber particulate composites for different aspect ratios,

bb

<c,>

“c7

Figs. 3 and 4. Comparisons of theory and observation for longitudinal

and shear-wave speeds in spherical-particle composites.

37

438
Table 1. Properties of constituent materials.

P 3 E P B V k. X (g/cm ) (GPa) (GPa) (GPa) - (GPa) (GPa)

Boron 2.532 397.9 176.3 178.5 0.129 238.3 59.0

Aluminum alloy 2.702 71.5 26.7 75.1 0.341 84.0 57.3

Epoxy 1.180 4.31 1.57 5.64 0.370 6.16 4.59

Glass 2.492 62.8 26.17 34.85 0.200 43.59 17.42

Epoxy 1.202 4.69 1.71 6.08 0.372 6.65 4.94

Lead 11.300 23.57 8.35 44.32 0.411 47.11 38.76

Table

(SiJ>

2. Observed and predicted elastic stiffnesses (C..) and elastic

of a boron-aluminum unidirectionally fiber-reinforced composite.

compliance:

C

i

j ' s (GPa) S ij

's (TPa-1

)

ij Observation Theory Observation From '

s

Theory

11 185.2 179,0 7.08 6.84 6.99

22 179.7 179.0 7.08 7.07 6.99

33 245.0 256.0 4.38 4.61 4.36

44 56.6 55.9 17.55 IT. 67 17.88

55 56.9 55.9 17.55 17.57 17.88

66 52.6 52.3 21.23 19.01 19.13

12 77.9 74.5 -3.53 -2.61 -2.58

13 60.6 58.3 -1.06 -1.05 -1.00

23 60.4 58.3 1.06 1.10 1.00

38

439

Elastic constants and internal friction of fiber-reinforced composites*

H. M. Ledbetter

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303, USA

We review recent experimental studies at NBS on the anisotropic elastic

constants and internal friction of fiber-reinforced composites. Materials that were studied include: boron-aluminum, boron-epoxy, graphiteepoxy, glass-epoxy, and aramid-epoxy. In all cases, elastic-constant

direction dependence could be described by relationships developed for

single crystals of homogeneous materials. Elastic stiffness and internal friction were found to vary inversely.

Key Words: Boron-aluminum; elastic constants; glass-epoxy; graphiteepoxy; Internal friction; shear modulus; sound velocity;

ultrasonic wave; Young modulus

Published in "Composite Materials; Mechanics, Mechanical Properties and Fabrication," Proc. Japan - U.S. Conf., Tokyo, 1981, Eds. Kawata, K.,

Akasaka, T., Japan Society for Composite Materials, Tokyo (1981).

441

ABSTRACT

We review recent experimental studies at NBS on the anisotropic elastic constants and internal friction of fiber-reinforced composites. Materials that were studied include: boron-aluminum, boron-epoxy, graphite-epoxy, glass-epoxy,

and aramid-epoxy. In all cases, elastic-constant direction dependence could be

described by relationships developed for single crystals of homogeneous materials. Elastic stiffness and internal friction were found to vary inversely.

NOMENCLATURE

C

ij " Cijkl

E

Sij ‘ S ijkl

ij

elastic-stiffness tensor

Young's modulus

internal friction

elastic-compliance tensor

direction cosines in co-ordinate transformation

mass density

INTRODUCTION

Here, we highlight recent experimental studies at NBS on the elastic con- stants and internal friction of several fiber-reinforced composites. Materials

that were studied include: boron-aluminum, boron-epoxy, glass-cloth-epoxy,

graphite epoxy, and aramid-epoxy. Fiber geometries included: uniaxial, crossply, and cloth. Uniaxial materials were studied both parallel and perpendicular

to the fibers. In two cases, boron-aluminum and glass-cloth-epoxy, the complete

elastic-constant tensor was determined together with the directional dependence

of the companion property, internal friction. Internal friction can, of course, be considered as the imaginary elastic modulus, that component ninety degrees

out of phase with stress. All studies described here will be described elsewhere in greater detail.

In our laboratory, elastic constants of composites can be measured at low

( Hz), moderate <- kHz), and^tigh <- MHz) frequencies.

443
The low-frequency apparatus is a forced-vibration system that has been used

so far both in torsion and bending and can be adapted to the extension mode.

Internal friction, Q , in forced vibration is reflected in the width of a resonance peak. In a free-decay mode, Q follows from the exponential time

decay of the strain amplitude. For high damping materials, this apparatus gives

Q as the phase lag of the strain wave behind the harmonic stress wave. Not

yet operating, this apparatus has capabilities of determining Q from the area

of the stress-strain loop. Further details on thin apparatus will be described

elsewhere (1)

.

Our middle-frequency apparatus consists of a Marx three-component composite

oscillator. Most measurements reported here arose from this apparatus, but, for

brevity, we omit details that are given elsewhere (2). This experimental method

yields directly the S...

, 's, the elastic compliances, and was used to study

boron-aluminum (3) . J

At high frequencies we use a pulse-echo-overlap method (4) . This technique was used to determine the complete set of C.-.’s, the elastic-stiffness tensor,

for boron-aluminum (5) and NbTi-copper (6) . ^

RESULTS

Room-temperature Young's modulus and internal

with various fiber orientations are given in Table

with Young's modulus determined statically (2.-9.) • material-characterizations.

friction of twelve materials

1, where they are contrasted

These references also contain

Figure 1 shows the Young modulus versus internal friction for the materials

in Table 1.

Figures 2 and 3 show the variation with direction of the Young modulus and

internal friction for G-10CR glass-cloth-epoxy.

Figure 4 shows for boron-aluminum the variation with direction of the

elastic-wave phase velocity. A companion Figure 5 shows the deviation of the group-velocity vector from the energy-flux vector.

DISCUSSION

Concerning Figure 1, studies on homogeneous materials show an inverse

relationship between modulus and damping ( 10 ) . However, composites could behave

differently since modulus and damping may arise from separate properties. Fiber

volume fraction may control modulus while fiber-matrix interfacial area may

control damping. The preliminary empirical relationship established in Figure 1 clearly needs further study, but it suggests quite useful guidelines for understanding and controlling composite properties. Models should be studied to explain the slope of 0.8, which means a nearly hyperbolic relationship between

Young's modulus, E, and internal friction, Q

Figures 2 and 3 show an inverse E-versus-Q ^ relationship with direction

within a single material, in this case glass-cloth-epoxy. For an arbitrary

direction in a material. Young's modulus is

1/E' S il

q

^Ull “li “lj “lk “lit S ijkl‘ ( 1 )

Letting x., x„, and x^ correspond to warp, fill, and normal directions, respectively, then in the warp-fill, x

1“X

2

» plane

S

’ « b ll a

l

S ll + a

3

S 33 + a

la

2

s 13 ( 2 )

The curve in Figure 2 represents a fit to observation of equation (2). The good

agreement validates the application to composites of relationships developed

nearly a century ago for single crystals of homogeneous materials. And it

emphasizes the validity of point-group theory not only for the properties of

crystals, but for properties of macroscopic bodies also.

444
Directional variation of internal friction has been studied only slightly. But we recognize that, like the elastic stiffness, Q~ also has tensor properties

because elastic stiffness has two components:

=«

- C

iJ iCij' (3)

one real and one imaginary. The latter, being ninety degrees out of phase with

relate to that of C. given by the point group, forbid iC*^ being maximum when

The same symnetry does not

is a min imum , and vice versa.

Finally, we discuss Figure 4, which arose from calculations after Musgrave (11) for representation surfaces of phase velocity, slowness, and group velocity together with a determination for the departure of the energy-flux vector from the wave-propagation vector. For input, these calculations require

the C ’s and the mass density, p. The smaller shear-wave velocity, denoted Tl, is nearly perfectly isotropic. The higher shear-wave velocity, denoted T2,

shows maxima at 9 (the angle to x^) of about forty-five degrees. This difference

between the two shear waves appears also in Figure 5, which shows that A, the

angle between energy-propagation and wave-propagation vectors, can be quite

large, nearly twenty degrees for the T2 wave. Both the T2 wave and the longitudinal wave, L, behave as pure modes in nonprincipal-axis directions near fifty

and seventy degrees, respectively. Other, more-anisotropic composites may show

dramatic differences between phase and group velocities arising purely from the

elastic constants themselves.

ACKNOWLEDGMENTS

Principal support for this study came from the DoD Office of Fusion Energy

and the NBS Office of Nondestructive Evaluation. Defense Advanced Research

Projects Agency sponsored the early experimental studies on boron-aluminum.

REFERENCES

1 Austin, M. W. , Frederick, N. V., Ledbetter, H. M., and Moulder, J. C.

,

"Low-frequency apparatus for elastic modulus and internal friction of solids",

to be published.

2 Ledbetter, H. M., "Dynamic elastic modulus and internal friction in G-10CR and G-11CR fibreglass-cloth-epoxy composites", Cryogenics , Vol. 20, 1980,

pp. 637-640.

3 Read, D. T. and Ledbetter, H. M. , "Elastic properties of a boron-aluminum

composite at low temperatures", Journal of Applied Physics , Vol. 48, 1977,

pp. 2827-2831.

4 Ledbetter, H. M. , Frederick, N. V., and Austin, M. W. , Elastic-constant

variability in stainless-steel 304, Journal of Applied Physics , Vol. 51, 1980,

pp. 305-309.

5 Ledbetter, H. M. , "Orthotropic elastic stiffnesses of a boron-aluminum

composite", Journal of Applied Physics , Vol. 50, 1979, pp. 8247-8248.

6 Ledbetter, H. M. and Read, D. T., "Orthorhombic elastic constants of an NbTi/Cu composite superconductor", Journal of Applied Physics , Vol. 48, 1977,

pp. 1874-1879.

7 Schramm, R. E. and Kasen, M. B., "Cryogenic mechanical properties of boron-, graphite-, and glass-reinforced composites". Materials Science and

Engineering , Vol. 30, 1977, pp. 197-204.

8 Schramm, R. E. and Kasen, M. B., "Static tensile properties of boronaluminum and boron-epoxy composites at cryogenic temperatures", in Advances in Cryogenic Engineering, Volume 22 , Plenum, New York, 1977, pp. 205—213.

9 Kasen, M. B., MacDonald, G. R. , Beekman, D. H., and Schramm, R. E., "Mechanical, electrical, and thermal characterization of G-10CR and G-11CR

glass-cloth/epoxy laminates between room temperature and 4 K" , in Advances in

Cryogenic Engineering. Volume 24 , Plenum, New York, 1981, pp. 235-244.^ 10 Read, T. A., "The internal friction of single metal crystals", Physical

Review , Vol. 58, 1940, pp. 371-380.

11 Mus grave, M. J. P., Crystal Acoustics. Introduction to the Study of Elastic Waves and Vibrations in Crystals, Holden-Day, San Francisco, 1970.

445
Table 1. Young's modulus and Internal friction of several fibrous composites at room temperature

Fiber orientation.

Material degrees

Static Young's modulus,*

GPa Dynamic Young's modulus, GPa

Internal , friction, Q“ 10-4

First- harmonic

frequency, Tension Compression kHz

Boron- 0 200 ± 1 257 4 51 226.2 4 0.2 5.6 4 0.4 50 aluminum 90 161 ± 18 148 4 40 139.2 4 0.2 17.0 4 0.5 80

Boron-epoxy 0 231 ± 4 212 4 42 226 4 4 17.6 4 1.4 55 90 17 ± 1 19 4 4 22.7 4 0.2 400.8 4 20.6 35

0, t 45, 0 120 ± 2 102 4 1 121 .4 4 0.8 79.9 4 3.3 70

Glass cloth- woof 26 i 2 24 4 1 30.6 4 0.6 62.1 4 8.2 40 epoxy 1

Glass cloth- woof 28 t 1 27 4 3 29.6 4 0.2 64.9 4 7.5 40 epoxy 2

Glass cloth- woof 45 ± 10 --- 44.3 4 0.5 5.4 4 0.3 30 epoxy 3

G-10CR warp 28.1 29.4 ± 1.0 68.7 4 6.6 40-70

fill 22.4 — 26.3 4 1.0 100.1 4 7.8 45-90

normal — — 14.0t> 228.6 55

G-11CR warp 31.8 31.4 4 0.4 114.5 4 13.9 45-80

fill 25.5 — 27.7 221 .6 4 85.3 40-70

normal — — 15.6 4 0.6 406.5 60

Graphite- 0 118 ± 7 129 4 7 133.5 11.1 90 epoxy 1 90

i 45 7.8 i 1 15.6 4 2 9.7 4 1 10.0 164.2 45

Graphite- 0 323 4 12 368 4 22 300.5 4 0.4 17.9 4 0.4 65 epoxy 2 90 6.7 ± 0.1 7.8 4 1.0 7.3 4 0.5 258.8 4 1.8 45

± 45 21 ± 0.5 — — — —

0, 4 45, 90 — — 120.0 4 4.0 44.2 4 4.0 50

Graphite- 0 186 ± 7 --- 177 4 4 15.0 4 3.8 50 epoxy 3 90 8.6 4 0.4 — 8.5 218.0 4 11.7 30

0, ± 45, 90 — — 70 4 1 49.8 4 2.1 40

Graphite- 0 115 4 6 — 130.4 4 1 2.8 4 0.4 60 epoxy 4

Aramld- o 71 4 1 — 66.1 4 0.5 114.8 4 6.1 60 epoxy

*A11 static values are from Schramn and Kasen.

7 *®

Uncertainties are not given for some cases because only one specimen was measured.

446
Fig. 1. Young's modulus versus internal friction for

materials in Table 1. A least-squares fit to (Q-l)n £ = c gives C = 14.2 when E is in units

10^N/m2 and Q-l in units of 10-4.

Warp Warp

Fill

Figs. 2 and 3. Directional variation of Young's modulus and internal

friction of G-10CR composite in warp-fill plane, in units of GPa. Curve through points in Fig. 2 represents equation (2).

447
z

D

Fig. 4. For boron-aluminum, the directional variation of

phase velocity in units of (C44 / p)l /2 . Longitudinal (L) and shear (T2 and T1 ) velocities are

shown. For isotropic materials these representation surfaces would be spheres.

Fig. 5. Angular deviation. A, of energy-propagation and wave-propagation vectors. Theta denotes angle

between wave vector and fiber direction.

448
ELASTIC CONSTANTS OF FIBER-REINFORCED BORON-ALUMINUM:

A CRITICAL COMPARISON OF OBSERVATION AND THEORY

S. K. Datta

Department of Mechanical Engineering, University

of Colorado, Boulder, Colorado, 80309 USA

and Department of Applied Mathematics,

University College of Science,

92 Acharya Prafulla Chandra Road,

Calcutta 700009, India

H. M. Ledbetter

Fracture and Deformation Division,

National Bureau of Standards,

Boulder, Colorado, 80303 USA

Abstract

Elastic constants, both the C - .

1 s and the S-.'s, were measured and

J ® vJ calculated for a laminated, uniaxially fiber-reinforced boron-aluminum

composite. Three theoretical models were considered: square-array,

hexagonal -array, and random-distribution. By combining several existing

theoretical studies on randomly distributed fibers, a full set of elastic

constants can be predicted for this model. The random-distribution

model agrees best with observation, especially for off-diagonal elastic

constants. Considering all nine elastic constants, observation and

theory differ on the average by six percent. These discrepancies arise

from two sources: experimental -error propagation and the limited

applicability of a transverse-isotropic model to a laminated composite.

Key Words: Boron-aluminum; composite; elastic constants; fiber reinforcement; sound velocity.

449

1 . Introduction

Fiber-reinforced composites have been studied extensively, both

experimentally and theoretically. Recent reviews on this subject

include that of experiment by Bert (1975) and of theory by Sendeckyj

(1974).

Two types of fiber-reinforced composites occur in practice:

continuous-fiber and short (chopped)-fi ber . The former type has been

studied more thoroughly and constitutes the object of this study.

Boron-fiber-reinforced aluminum, a so-called advanced-technology

composite, was the particular material that was studied. The principal

purpose of the study was to evaluate various models for predicting the

composite's macroscopic elastic constants from those of its constituents.

Three models, shown schematically in Fig. 1, were considered: squarearray, hexagaonal -array, and random-distribution. The composite's

elastic constants were measured two ways: by ultrasonic-velocity measurements,

which yield the C..'s, the elastic stiffnesses; and by standing-wave

^ J resonance, which yields the S..'s, the elastic compliances. These

1 J macroscopic elastic constants define for most cases the mechanical

response of the composite to an applied force.

2. Material

The studied composite consisted of 0.14-mm-diameter boron fibers in

an aluminum-alloy-6061 matrix. The alloy was in the F-tempered condition. The composite, containing 48 percent fibers by volume, was fabricated

as a 10 x 10 x 1.1 cm plate containing about seventy plies. Figure 1

451
is a photomicrograph showing the distribution of fibers in the transverse

plane. Cracks in the boron fibers developed during specimen preparation

and do not exist in the bulk material. Mass density, measured hydrostatical ly,

3 was 2.534 g/cm .

Throughout this study we adopt the following co-ordinate system:

is the fiber direction, x-j is normal to the laminae plane, and x

2 is

orthogonal to x-j and x

3

(See Figure 2.). Thus, x-j and x

2 are equivalent

directions from the viewpoint of all three theoretical models considered

here.

3. Experimental Methods

Our experimental methods were chosen to provide the advantages of

small specimens and low inaccuracy.

For brevity, experimental details are omitted here; they were

described previously for both the ultrasonic-velocity method (Ledbetter,

Frederick, and Austin, 1980) and the resonance method (Ledbetter, 1979).

Briefly, the ultrasonic-velocity method consisted of a pulse-echo

technique using gold-plated piezoelectric crystals at frequencies

near 10 MHz with specimen thickness varying from 0.2 to 1.0 cm. Except

for an improved velocity-measurement system used in this study, it

proceeded similarly to that described by Ledbetter and Read (1977).

Reproducibility of measured sound velocities was typically within one

to two percent.

The resonance method used a three-component (Marx) oscillator.

Specimens were rod-shaped, about 0.4 cm in either circular or square

cross section, and 4 to 1 0 cm long. Frequencies ranged from 30 to

50 kHz.

452
4. Experimental Results

Results of the experimental studies are given in Table 1 and in

Table 2 for the C - -

' s and the S..'s, respectively. The nine C -

.

' s are

TJ iJ ij

based on a least-squares fit to eighteen separate wave-velocity propagation directions and polarizations. For details, see Ledbetter and

5 Read . The five S-.'s are based on extensional -mode and torsional -mode

* J measurements on cylindrical specimens whose axes were in the x^-x^

plane, as described by Read and Ledbetter (1977). The plate thickness

of the studied material was too short to permit S. . measurements along x,

.

* J Thus, the measured S^.'s are incomplete since they do not reflect the

full orthotropic symmetry of the composite. However, as shown in Table 2,

except for and S-^, this incomplete set of S^.'s differs only

slightly from those derived from the observed C. .'s, which do contain

" J the full orthotropic symmetry.

Table 3 shows the elastic constants of the constituent materials,

both being assumed isotropic. In this Table, p denotes mass density, E

Young's modulus, y shear modulus, B bulk modulus (reciprocal compressibility), k plane-strain bulk modulus for lateral dilatation without

longitudinal extension, and x the Lame constant. For aluminum these

parameters were determined ul trasonically, as described above, on a bulk

specimen; their uncertainty is less than one percent. Boron's elastic

constants are less certain, a wide range of values being reported in the

literature. The boron values in Table 3 arose from fitting a linear

rul e-of-mixtures to our observed value combined with Gschneidner ' s

(1964) recommended values for boron's bulk modulus.

453
5. Square-array Model

For a periodic square-lattice array of long, parallel, circular

fibers, using a homogeneous continuum model, Achenbach (1976) derived

three relationships for plane, harmonic wave-propagation velocities

2 expressed as pv . Simplified and modified for present purposes, and

with obvious notational correspondences, these are as follows.

For a longitudinal wave propagating along x

3

, parallel to the

fibers,

pv

2

= C 33 = a

1 - a|

# (!)

a

2

where

a-| - c(A

f + 2uf

) + ( 1 -c ) (Am

+ 2um),

a^ = 4c(A

f + uf

) , and

a

3

= 2cA^..

For a longitudial wave propagating along x-j , perpendicular to the

fibers,

pv

2 = C n

- C22 = um

/4H. (2)

454
where

M = c[cD - (1-c) B] + (1-c) f (1-c) A - cB ]

,

4 (AD-B

2

)

A = a

2 p - (1-c)

2 a2

^ d 1_ t c t q um

B = (1-c) a 23

a 23

d 1_ f m q V

D

=

[

cl o o ~ ^ ^ o o ^ I

d

q

c (1-c)

2 a + c

2 a 22

f

22m

a 22 = c (A f + 2u

f

),

a 23

f

cX

f’

a 22m

=0-O + 2um

) + ^c Um + 1(1)7 -2

and

Ea„ = (1-c) + .Jl— c •*

7T 23-

' ''~ w ""

=^7f-sy

' ^

m

455

=4|o
For a transverse wave propagating along x

3

, parallel to the fibers,

and polarized along x-j , perpendicular to the fibers,

pv C 55C 44

d

l (3)

where

a

] = c uf + (1-c) um

,

a

2

= c (u f

- um), and

c

2

a 3c u

f

+ 1-c u

m*

The Lam£ constants, X and u, of the fiber and matrix are denoted by

subscripts f and m; c denotes the volume fraction of fibers, 0.48 for

2 2 the present case, and equals -nr /d , where r denotes fiber radius and d

distance between fiber centers in a square lattice. Clearly, r/d = 0.3909,

or d/r = 2.5583. The constants a^ , a

2

, a^, etc. arise from the strainenergy density in Achenbach's derivation.

Results predicted using these relationships based on Achenbach's

square-array model are shown in Table 1.

6. Hexagonal-array Model

In calculations similar to Achenbach's, the five independent

elastic constants for a composite consisting of parallel fibers arranged

456
hexagonally were derived by Hlavacek (1975). His relationships, rearranged for present purposes, are as follows.

For a longitudinal wave propagating along x-j , perpendicular to the

fibers,

2 2 2 pv C

-j i - C 22 ~ 3

-j - ^®7^g^23~^22 ^ a

7 ^ 7 7

’ a 22

a 23

where

a

l = ( 3V + 1) Am

+ ( 7 V + 2) um

,

a

7

= - V < 3Xm

+ 7um>>

a 8

= - V <\n

+ UJ>

a 22

= -c (A

f + 2u

f

) - (3V-c) Am

- (7V-2c) um

,

a 23

= “ c X

f

- (V “ C) Xm

- VV and

For a longitudinal wave propagating along x

3

» parallel to the

fibers.

457
(5)

2a

C. p pv = C 33

a 15

+

a 18

22

+ a 23

where

a

l 5 = c(A

f + 2uf

) + (1-c) (Am

+ 2um

) and

a

l 8

c ( A f

" V*

For a transverse wave propagating along x-j , perpendicular to the

fibers, and polarized along x^, parallel to the fibers,

2

a io

pv C 44

C 55

a

3 +a

( 6 ) 28

where

a 3 cu

f + um

’

a 10

= c ^ u f

" u

m^ ’ and

a 28

= * cu

f

* < 4V - C

> V

For a transverse wave propagating along x-j

, perpendicular to the

fibers, and polarized along' x^, perpendicular to the fibers.

458
(7)

pv

c = C 66

2 2 -a 0 +

2a

8

a 9

a 26

" a 25 ^ a 8 + a 9^

2 2 a 25

" a 26

where

a

9 _ VA + (5V + 1) um , 2 m

'

3q - -V(A + 5u ) 9 m m

a 25

= -cu

f

- VAm

- ( 5V-c ) um

, and

a 26

= - cu

f

- V \n ' (V - C) V

For the fifth independent elastic constant, Hlavacek derived an

expression for + C^, which is related to the propagation of a

transverse wave:

a

5 a 28

+ d

10

a

l 9

a 18 ^ a

7 * a 8^ f

a 0 o (a 22 + a,,)

~ L 44, ‘28 23‘

( 8 )

where

a c5mm - A + u_

and

a

l 9

= - 4Vu

m'

In Hlavacek' s model, the fiber volume concentration, c, equals r-j/r,,,

the ratio of the fiber radius to that of the circle radius that equals

459
the hexagonal "unit-cell" area. Constants a^ , a^, a^, etc. arise from

Hlavacek's equations of motion.

Results from Hlavacek's hexagonal -array model are shown in Table 1.

7. Random-distribution Model

Considering the propagation of time-harmonic elastic waves in a

composite of circular-cross-section , parallel fibers distributed randomly in a matrix, Bose and Mai (1973, 1974) derived expressions for

three elastic moduli.

For a longitudial wave propagating along x-j , perpendicular to the

fibers.

pv ^11 ^22

[1 - c (1-c

2

) P

2

- 2c

2

P

0

P

2

] (Am

+ 2uJ

(1 + cP

Q

) [1 + c (1 + c

2

) P

2

]

(9)

where P =

o

A m+ u m

- A f

- u

f

A f + Uf + U|])

and

Pn = um

(u m

- u

f>

2 Uj: (A + 3u ) + u [A + u ) f

v m m' m

v m m

'

For a tranverse wavQ propagating along x-j , perpendicular to the

fibers, and polarized along x

3

, parallel to the fibers.

pV C 44

C

55

_ [

2c (Uf ' “m) ]

L

u

f + um

- c < u

f

- um>J

V ( 10 )

For a transverse wave propagating along x

3

» perpendicular to the

fibers, and polarized along x-j

, perpendicular to the fibers,

460
( 11 )

Results from the Bose-Mal random-distribution model are shown in

Table 1.

In this section we show that combining the Bose-Mal relationships

with previously derived relationships for other elastic constants leads

to a full set of five independent elastic constants for the randomdistribution case. For this, a new notation (Sendeckyj, 1974) is

useful, which will be described as it is introduced.

Hashin and Rosen (1964) derived relationships for the effective

moduli of a continuous-fiber-reinforced composite where the fibers are

distributed randomly and homogeneously. Hashin (1970) gave these

relationships in essentially the form

Here, k denotes the two-dimensional, plane-strain bulk modulus, which is

X + vi in an isotropic material. Subscript T denotes deformation in the

x l"

x

2 P^ ane ’ perpendicular to the fibers. Subscript LT denotes shear

deformation in any plane containing the axis, that is, the fiber

axis. Equations (12) and (13) were also derived by Hill (1964) for a

single fiber placed concentrically in a cylindrical matrix.

8. Full Random-distribution Model

( 12 )

and

(13)

461
Hermans (1967) obtained them also by considering Hill's assembly to be

embedded in an unbounded solid having the effective elastic moduli of

the composite. In this model, the fiber: matrix-cylinder radius ratio

1 /2

is r-j/r^ = c . In the limit r-j = 0, Hermans' model becomes the

"self-consistent" model of Hill (1965).

Knowing k^, one can derive the Young's modulus (along x^) and

the Poisson's ratio = -z^/zy where uniaxial stress is along x

3

and

e denotes strain. This derivation requires some exact relationships

given by Hill (1964)

:

1 1 1 - 1 =

kT m =

- 1

k.m

V

LT

" V

f

V, T" LT m f m

4 v, T = vm - c(v* -vm ) LT m f m

E, - E m

- c(E, - E ) L m ' f m

(14)

Solving for E^ and Vp, using Eq. (12), one finds

4c (l-c)(v

f

- v ) 2

E, = (1 -c)E + cE f + —n t !, m

L

v m f 1 - c + c +1

km

um

(15)

and

LT

c(l-c)(v - v )(^

(l-c)v

m

+ cv

f +

km

1 - 1

(T-c) + c +1

m m

(16)

Of course, both of these relationships represent a simple, linear "rule

of mixtures" plus a higher-order correction term. The advantages of

Eqs. (12)-(13) are clear: they give simple, explicit relationships for

four of the composite's elastic constants in terms of the isotropic

462
elastic constants of the constituent materials, the fiber and the

matrix. On the other hand, self-consistent approaches lead to implicit

relationships.

Bose and rial (1973, 1974) also obtained Eqs. (12) and (13), but by

a different approach: by considering the effective velocity for longwavelength plane waves propagating perpendicular to the fibers, for both

a longitudial wave and for a shear wave polarized along x^, the fiber

axis. By a similar approach, examining a shear wave propagating and

polarized in a plane transverse to the fibers, Bose and Mai (1973)

also derived an expression for the shear modulus u-j-j-:

uTT

2c(km + um )(y f

- um ) m m f

*k + (k + 2)[cum + (l-c)u fJ m m

L m ' t

(17)

Previous studies (Hashin and Rosen, 1964; Hill, 1964) did not obtain

this explicit expression, but bounds instead. In fact, Eq. (17)

corresponds to their lower bound. Equations (12), (13), (15), and

(16) are also identical to the lower-bound results. Thus, the "quasicystalline" approximation used by Bose and Mai (1963, 1964) to derive

Eqs. (12), (13), and (16) leads to the lower-bound results, which these

authors believe to be "nearer to the actual value if correlations are

ignored." Equation (17) coincides also with Hermans' (1967) result, which

he points out "lies between the bounds derived by Hashin and Rosen.

From the above relationships, one obtains for the boron-aluminum composite,

using results in Table 3:

463
E

l

= 2.292 • 1

O

1

1

N/m

2

,

kT

= 1 . 267 • 1

O

1

1

N/m

2

,

u LT

= 0.559 • 1

0

1

1

N/m

2

,

uTT = 0.523 * 1

0

1

1

N/m

2

* and

= 0.230 .

If the composite behaves transversely isotropic with the unique

symmetry axis along x

3

, then the C— elastic-stiffness constants can be

computed from

^22 ^T

U

TT * (18)

= e

l + 2vlt

C ]3j (19)

= C 55

= U

LT

(20)

=

2

^ C

ll

“ C

1 2^ = U

TT’

(21)

= k T

- Uj

T

, and (22)

= C 23

= 2v

lt

kT>(23)

These results are given in the final column of Table 1

464
9. Discussion

Here we consider principally the correspondence between observed

C.

j

' s and their counterparts predicted by three models: square-array,

hexagonal -array, and random-distribution.

C 33is predicted reasonably well by all three models, although all

are slightly high, perhaps reflecting the slight uncertainty in Young's

modulus of the boron fibers.

C-j

1 is predicted best by the lattice models, and C22

is predicted

best by the random model. As shown in Fig. 3, this probably reflects

the different imperfections in fiber distributions along the x-| and x

2 directions

.

C44

and C55 , which represent shears with the force parallel to the

fibers, are not predicted accurately by the square-array model; but they

are predicted by both the hexagonal -array and the random models. Thus,

these elastic constants permit one to distinguish fiber arrays that are

transversely anisotropic (tetragonal, orthorhombic) from those that are

transversely isotropic (hexagonal, random).

Cgg, which represents shears with a force perpendicular to the

fibers, is predicted well only by the random model. Since represents also the velocity of a plane wave both propagated and polarized in

the transverse plane, of all elastic constants it should be most sensitive to the fiber distribution. Thus, the different predictions for the

hexagonal and random models, both of which are transversely isotropic,

are not too surprising. Furthermore, Fig. 1 shows little evidence of

either three-fold or six-fold symmetry around the fiber axis.

465
C-j ^

» ar> d ^23’ so “ ca ^ ec* off-diagonal elastic constants,

are predicted surprisingly well by the random model. Since these

constants are always determined indirectly, whether experimentally or

theoretical ly, one expects larger errors than for the diagonal elastic

constants, the C^.'s, discussed above. Absence of large discrepancies

between observation and theory for these three elastic constants gives

one simultaneous confidences in the experimental measurements and in the

random-distribution model for this particular composite.

Finally, we remark that similar observations hold also for the

S.jj's, as shown in Table 2. However, these comparisons are less useful

because only five S..'s were determined experimentally, compared with

1 J nine C^.'s. Also, the experimental is inconsistent with that

predicted or that computed by inverting the C. . matrix; this reflects

J also in the experimental S-j ^ value and is believed to be an experimental

artifact, related perhaps to impure torsional modes about the x^ axis.

Except for this discrepancy, there are no differences between the

30-kHz S. . results and the 10-MHz results; thus, dispersion does not

occur in this material in this frequency range. This absence of dispersion is especially interesting for the higher frequencies where the

wavelength is not much larger than the fiber spacing or the fiber

diameter.

466
ACKNOWLEDGMENT

This study was supported by the NBS Office of Nondestructive

Evaluation. Most of the sound-velocity measurements were made by

M. W. Austin. A first draft of the manuscript was completed while

H. M. L. visited the Institute for Theoretical and Applied Physics at

the University of Stuttgart. J. Dahnke contributed valuably to constructing the manuscript.

467
REFERENCES

Achenbach,J. D. 1976 Arch. Mech. 28, 257.

Bert, C. W. 1975 Composite Materials, Volume 8,

Ch. 9., Academic, New York.

Bose, S. K. and Mai , A. K. 1973 Int. J. Solids Struct. 9_, 1075.

Bose, S. K. and Mai , A. K. 1974 J. Mech. Phys. Solids 22_, 217.

Gschneidner, K. A. 1964 Solid State Physics, Volume 16,

p.370, Academic, New York.

Has hi n, Z. 1970 Mechanics of Composite Material

p. 201, Pergamon, New York.

Hashin, Z. and Rosen, B. W. 1964 J. Appl . Mech. 31_, 223.

Hermans, J. J. 1967 Proc. K. ned. Akad. wet. B70, 1

Hill, R. 1965 J. Mech. Phys. Solids 1_3, 189.

Hlavacek, M. 1975 Int. J. Solids Struct. 11_, 199.

Ledbetter, H. M. 1979 Nonmetal lie Materials and

Composites at Low Temperatures,

p. 267, Plenum, New York.

Ledbetter, H. M., Frederick,

N. V. and Austin, M. W.

1980 J. Appl . Phys . , 51_, 305.

Ledbetter, H. M. and

Read, D. T. 1977 J. Appl. Phys. 48, 1874.

Read, D. T. and

Ledbetter, H. M.

1977 J. Appl. Phys. 48, 2827.

Sendeckyj, G. P. 1974 Composite Materials, Volume 2,

Ch.3., Academic, New York.

468
Table 1. Observed and predicted C-. elastic stiffnesses of a boron-aluminum

1 J

1

1

2 unidirectional ly fiber-reinforced composite, in units of 10 N/m .

ij Observed Square

Model

3

Hexagonal

Model

b

Random

Model

0

Full

Random

Model

11 1.852 1 .856 1 .872 1.790 1.790

22 1.797 1 .856 1.872 1.790 1.790

33 2.450 2.480 2.551 - 2.560

44 0.566 0.451 0.561 0.559 0.559

55 0.569 0.451 0.561 0.559 0.559

66 0.526 - 0.606 0.523 0.523

12 0.779 - 0.661 - 0.745

13 0.606 - 0.578 - 0.583

23 0.604 - 0.578 - 0.583

3 After Achenbach (1976).

°After Hlavacek (1975).

cAfter Bose and Mai (1974).

469
Table 2. Observed and predicted S • . elastic compliances of a boron-

' J aluminum unidirectional ly fiber-reinforced composite, in

units of 10'^m^/N.

ij Observed3From

C

' s b L

ij

S

Predicted, Full

Random Model

11 0.708 0.684 0.699

22 0.708 0.707 0.699

33 0.438 0.461 0.436

44 1.755 1.767 1.788

55 1.755 1 .757 1.788

66 2.123 1.901 1.913

12 -0.353 -0.261 -0.258

13 -0.106 -0.105 -0.100

23 -0.106 -0.110 -0.100

^Assumed tranverse-i sotropic symmetry.

°Based on orthotropic symmetry.

470
Table 3. Properties of constituent materials.

P E u B V k A

(g/cm

3

) (1

1

N/m

2

) ( 1

1

N/m2

) (10^N/m2

) (10

1] N/m 2

) (10

1

Boron 2.352 3.979 1.763 1.785 0.129 2.383 0.5?

Aluminum alloy 2.702 0.715 0.267 0.751 0.341 0.840 0 . 5 :

471
Figure Captions

Fig. 1. Schematic diagram of fiber distribution for three models

considered in this study: square-array, hexagonal -array, and

random-distribution. Diagram shows intersection of fibers,

parallel to x^, with x^x^ plane.

Fig. 2. Co-ordinate system adopted in this study. Fibers are parallel

to x^. Laminae lie in the x

2 -x3 plane.

Fig. 3. Photomicrograph showing distribution of 0.14-mm diameter boron

fibers in an aluminum alloy matrix. Plane of photo is perpendicular to fibers, which are parallel to x^ axis.

472
Q O "O O

I

i

cj) O O <j)

I I 6—o—o—

6

t

I—O O- —

i

$ °

i o o

6 o 6

* o* o—1

I

I o

I o

o

P o o til 9

Fig. 1. Schematic diagram of fiber distribution for three models

considered in this study: square-array, hexagonal -array, and

random-distribution. Diagram shows intersection of fibers,

parallel to x

3

, with x-|-x 2 plane.

473
Fig. 2 Co-ordinate system adopted in this study. Fibers are parallel

to x

3

. Laminae lie in the x

2 -x

3 plane.

474
Fig. 3. Photomicrograph showing distribution of 0.14-mm diameter boron

fibers in an aluminum alloy matrix. Plane of photo is perpendicular to fibers, which are parallel to x

3

axis.

475

TECHNOLOGY TRANSFER

477

TECHNOLOGY TRANSFER PROGRAM

LEADER: N. J. Simon, NBS

OBJECTIVES:

(1) To hold an annual workshop in October of each year. Major topics

include design overviews of fusion energy projects with respect to

material needs and reviews and data on structural alloys, composites, and weldments.

(2) To produce and distribute an annual report. In addition, monthly

reports are furnished to OFE/DoE.

(3) To prepare 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 will form a part of the annual report.

The pages will also be presented for inclusion in the Materials

Handbook for Fusion Energy Systems.

ACTIVITIES PAST YEAR (1981):

(1) The NBS-DoE Workshop on Materials at Low Temperatures was held

October 6-8, 1981 in Vail, Colorado. The program and a description

of the topics covered follows.

(2) "Materials Studies for Magnetic Fusion Energy Appl ications-IV,"

NBS IP. 81-1645, 648 pages (April 1981), Eds. R. P. Reed and N. J. Simon, has been sent to the Technology Information Center, ORNL, and

copies have been made available to other interested persons.

(3) Handbook pages and supporting documentation covering mechanical and

physical properties of AISI 316 stainless alloys are published as an addendum to this report.

ACTIVITIES THIS YEAR (1982):

(1) Current plans are to hold the annual workshop again in October of

1982.

(2) "Materials Studies for Magnetic Fusion Energy Appl ications-V,"

NBSIR 82-1 667 , 490 pages (1982), Eds. R. P. Reed and N. J. Simon, is

the current edition of the annual report.

(3) Production of handbook pages and supporting documentation on mechanical and physical properties of 21-6-9 and AISI 304 stainless stee 1 will be a major effort this year. Also, the AISI 316 handbook page

will go through the review process for the Materials Handbook for

Fusion Energy Systems.

479

</>

</>

NBS-DoE WORKSHOP: MATERIALS AT LOW TEMPERATURES

October 6-8, 1981, Vail, Colorado

N. J. Simon

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado

ABSTRACT

A brief summary of the topics discussed at this annual workshop is

presented. The program and the list of registered participants follow this

summary.

481

The structural and insulating materials used in the superconducting

magnets of fusion energy systems are the subject of this annual workshop.

Current methods of plasma confinement for fusion reactors necessitate the use

of high-field superconducting magnets that operate at temperatures near 4 K.

A major purpose of the workshop is to bring together representatives from the

community of users and suppliers of materials for low temperature magnet

applications with those engaged in development and characterization of these

materials. Participants this year came from industry, the national laboratories, the magnetic fusion energy programs, NBS, DoE, and several

universities. The technical presentations were informal, with opportunities

for comments and questions. The proceedings of the workshop are not

published, but abstracts or short summaries of all the presentations are

provided to those who attend. Some highlights of the sessions are given

below:

Large Scale Magnet Programs :

Don Beard of the DoE Office of Fusion Energy gave examples of large

superconducting magnets that have recently undergone testing as well as a

worldwide overview of large scale magnet programs being conducted to support

fusion programs. Ed Dalder reported on problems that the Mirror Fusion Test

Facility has had with low yield strength and ductility at 4 K of some 304LN

stainless steels in 9- to 14-cm-thick plates. Other presentations covered

requirements for the Fusion Engineering Device magnets and gave details of

Large Coil and other superconducting magnet projects at General Dynamics.

Westinghouse, and the Japan Atomic Energy Research Institute.

Inspection of Magnet Systems :

This was the first year that this type of session has been held.

M. J. Buckley of Rockwell International reported advances in nondestructive

483
evaluation (NDE) capabilities and strongly suggested that NDE be considered at

the design stage of magnets. D. T. Read of NBS explained the fitness-forservice approach. Fracture mechanics is needed for this type of assessment.

C. M. Fortunko of NBS described a new technique for inspecting stainless steel

welds using shear waves polarized in the plane of the weldment, generated and

detected with noncontacting, electromagnetic-acoustic transducers. Other

presentations dealt with the specifics of some NDE systems that have been

successfully used in magnet inspection. Committee meetings on the development

of codes and standards for superconducting magnet design and construction took

place in informal sessions during the conference.

Structural Alloys, Welds and Castings :

R. P. Reed reviewed NBS low-temperature research on alloys, including the

inverse relationship found between yield strength and fracture toughness at

4 K. Reprocessing of the alloy can increase both parameters. R. L. Tobler

discussed improved mechanical property test methods developed at NBS and

recent results for austenitic stainless steels. R. Ogawa of Kobe Steel, Ltd.,

and H. Masumoto of Nippon Steel considered the new, high-manganese stainless

steels that are being developed for cryogenic use because of higher yield

strengths and greater austenite stability than the AISI 304 and 316 stainless

steels. A progress report on a new handbook effort to collect and disseminate

data on structural materials for magnets was given by N. J. Simon of NBS.

Nonmetal lies :

The presentation of M. B. Kasen reviewed the NBS/DoE program on cryogenic

nonmetallic materials development. Of particular interest were recent

measurements of the interlaminar shear strength and other properties of

PG-10CR, a polyimide variant of G-10CR. G-10CR is a cryogenic-grade laminate

484
for which specifications have been established by cooperation between NBS and

industry. PG-10CR has shown relatively good resistance to degradation in the

radiation environment to which superconducting magnet insulating materials

will be exposed, but its mechanical strengths are low. Other proposed

cryogenic neutron irradiation studies of various nonmetal lies were described

by G. F. Hurley of Los Alamos National Laboratory.

The low temperature thermal conductivities of G-10CR, G-10CR variants,

and other nonmetallics were reported by L. L. Sparks of NBS for J. G. Hust.

H. M. Ledbetter of NBS summarized results of studies that indicate a surprisingly close correspondence between dynamic and static measurements of the

Young's modulus of fiber-reinforced composites, in view of theoretically

predicted differences.

485
PROGRAM

NBS/DoE Workshop on Materials at Low Temperatures

October 6-8, 1981

Vail, Colorado

Tuesday, October 6

Session 1 (9:00-12:00 a.m.) Large Scale Magnet Programs

R. P. Reed, Chairman

Introduction

Overview - DoE Office of Fusion Energy

Design and Construction of Mirror Fusion Test Facilities

Large Coil Project (cancelled)

R & D Requirements for the FED Magnet

20 MJ Poloidal Magnet Coil

Magnet Development at General Dynamics

R. P. Reed, NBS

D. S. Beard, DoE

E. N.C. Dalder LLNL

A. J. Moorhead, ORNL

R. Derby, ORNL

M. Attaar, Westinghouse

J. L. Christian, GD

Photograph of the entire group - 12:00 NOON

Session 2 (2:00-5:00 p.m.) Inspection of Magnet Systems

C. M. Fortunko, Chairman

Building in Improved NDE Through Design

Large Coil Project Solder Bond Inspection System

Stainless Steel Weld Inspection

NDE of Magnet and Enclosure

Fitness-for-Service

Codes and Standards - Introduction

M. Buckley, Rockwell

S. W. Gill, GD-Convair

C. M. Fortunko, NBS

B. W. Maxfield, LLNL

D. T. Read, NBS

R. P. Reed, M. B. Kasen

NBS

COCKTAIL PARTY 6 - 8 p.m Cabin Lounge

Wednesday, October 7 Session 3 (9:00-12:00 a.m.) Structural Alloys, Welds and Castings

J. W. Morris, Chairman

Review of Structural Alloys

Spontaneous Martensitic Transformations in Type 304

Austenitic Stainless Steels

Deformation and Fracture of Structural Alloys

High Strength/High Mn Steels for Cryogenic Steels

Weld Fillers for Austenitic Stainless Steels

Cryogenic Research at the Lawrence Berkeley Laboratory

25 Mn Steel

R. P. Reed, NBS

D. Larbalestier, Univ.

of Wisconsin

R. L. Tobler, NBS

R. Ogawa, Kobe Steel

K. Crooks, Armco

J. W. Morris, Univ. of

California

H. Masumoto, Nippon Steel

Wednesday Afternoon FREE FOR ACTIVITIES OR COMMITTEE MEETINGS

486
Wednesday, October 7

Session 4 (5:00-7:30 p.m.) Nonmetallics

M. B. Kasen, Chairman

Review of Composite Properties

Radiation Research on Candidate Organic Insulators

Thermal Conductivities of Composites

Cryogenic Performance of Glass-mat Reinforced Epoxy

Laminates

Dynamic and Static Young's Moduli of Fiber-Reinforced

Composites

Thursday, October 8

Session 5 (9:00-11:30 a.m. ) Structures and Materials

D. S. Beard, Chairman

Structural Materials for Superconducting Tokamaks

The Effect of Ferrite on the Mechanical Properties of

CF8M Stainless Steel Castings at 4K

Handbook on Structural Materials for Magnets

Codes and Standards

M. B. Kasen, NBS

G. F. Hurley, LASL

J. G. Hust, NBS

J. Gauchel, Owens-Corning

H. M. Ledbetter, NBS

H. Tsuji, JAERI

T. A. Whipple, NBS

N. J. Simon, NBS

Committee Discussion

487
NAME

Albertson, S

Attaar, M . Arvidson, J. Baysinger, B Beard, D. Benzinger, J

Buckley, M. Chow, G. Christian, J Conder, R. Crooks, K. Dalder, E. Derby, R. Dobson, W.

Fortunko, C.

Fultz, B. Gaines, A.

Gauchel , J. Gill, S.

Hanson, D. Hassenzahl ,

l Hooper, R. Horvath, J. Kasen, M. Kim, H. Kotecki, D. Kriz, R. Larbalestier,

Ledbetter, H. Masumoto, H. Markley, F. Maxfield, B. Morris, J.

Ogawa, R. Peters, C. Read, D. Reed, R. Rensberger, K Roden, W.

Shul 1 , G.

Simon, N. Tobler, R. Tsujo, H. Whipple, T.

Wille, J. Witherel 1 , C.

Zbasnik, J.

NBS/DOE WORKSHOP

October 6-8, 1981

Vail, Colorado

AFFILIATION

Lawrence Livermore Lab.

Westinghouse

National Bureau of Standards

Welk Bros.

U,S, Department of Energy

Spaulding Fiber Co.

Rockwell Science Center

Brookhaven National Lab.

General Dynamics Convair

Beech Aircraft

Armco

Lawrence Livermore National Lab

MIT

Teledyne

National Bureau of Standards

U.C. Berkeley

Owens Corning Fiberglas

General Dynamics Convair

Welk Bros.

Lawrence Berkeley Lab.

General Electric

General Dynamics Convair

National Bureau of Standards

U.C. Berkeley

Teledyne

National Bureau of Standards

D. University of Wisconsin

National Bureau of Standards

Nippon Steel Corp.

Fermi lab

Lawrence Livermore National Lab

Lawrence Berkeley Lab.

Kobe Steel

Lawrence Berkeley Lab.

National Bureau of Standards

National Bureau of Standards

Cryogenic Energy Co.

General Dynamics Convair

Beech Aircraft

National Bureau of Standards

National Bureau of Standards

JAERI

National Bureau of Standards

McDonnel 1 -Douglas

Lawrence Livermore National Lab

Lawrence Livermore National Lab

488
489
ACKNOWLEDGMENT

The editors wish to express their appreciation to JoAnne Wilken and

Carole Montgomery for their work in preparing the manuscript.

Marilyn Stieg removed many of the inconsistencies, grammatical errors,

and awkward usages of language. The editors are responsible for those that

rema i n

.

490
NSS-1 14A (REV. 2-80

U.S. DEPT. OF COMM. 1. BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR 2 REPORT NO.

. Performing Organ. Report No. NBSIR 82- 1667

3. Publication Date May 1982

4. TITLE AND SUBTITLE

Materials Studies for Magnetic Fusion Energy Applications a‘ Temperatures - V

t Low

5. AUTHOR(S)

R. P. Reed and N. J, Simon, Editors

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Department of Energy

Office of Fusion Energy

Washington, DC 20545

10. SUPPLEMENTARY NOTES

Related earlier reports: NBSIR 81-1645, NBSIR 80-1627, NBSIR 79-1609,

NBSIR 78-884

_ Document describes a computer program; SF- 185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnifi cant bibliography or literature survey, mention it here) This report contains results of a research program to

Droduce 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 conceived and developed jointly by the staffs of the National

Bureau of Standards and the Office of Fusion Energy of the Department of Energy; it is

lanaged by NBS and sponsored by DoE. Research is conducted at NBS and at various other

laboratories through subcontracts with NBS.

The reports presented here summarize the fifth year of work on the low temperature

materials research program. Highlights of the results are presented first. Research

'esults are given for the four main program areas: structural alloys, weldings and castings, nonmetallics, and technology transfer. Objectives, approaches, and achievements

are summarized in an introduction to each program area. The major portion of the program has been the evaluation of the low temperature me- chanical and physical properties of stainless steel base metals, welds, and castings, with

articular emphasis on the nitrogen-strengthened stainless steels. Stainless steels with

manganese additions and other high manganese steels have also been investigated. Work has

>een done on the production and standardization of nonmetallics, primarily industrial

aminates, for low temperature' appl ications and on the measurement of their DroDerties

at cryogenic temperatures. A brief summary is qiven of the fifth NBS/DoE Vail Workshop

teld in October 1981

.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words :y sc - co ons alloys; castings; composites; cryogenic properties; Vow temperature; mechanical propertied

nonmetallics; physical properties; stainless steels; structural alloys; welding.

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

| XI Unlimited For Official Distribution. Do Not Release to NTIS 452

| | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

15. Price

2Q402.

fcl Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $33.00

USCOMM-PC

U.S. GOVERNMENT PRINTING OFFICE: 1982-578-925/274 REGION No. 8