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1': NBSIR 76-848

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

R. P. Reed, J. G. Must, M. B. Kasen, H. M. Ledbetter, H. I. McHenry,

D. T. Read, R. E. Schramm, L. L. Sparks, and R. L. Tobler

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

Prepared for : Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209

NBSIR 76-848

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

R. P. Reed, J, G. Must, M. B. Kasen, H, M. Ledbetter, H, I. McHenry,

D. T. Read, R.E.Schramm, L. L. Sparks, and R. L. Tobler

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

Prepared for : Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

Sponsored by

Advanced Research Projects Agency

ARPA Order No. 2 569

Program Code 4D10

August 10, 1975 - October 1, 1976

Program Director

Dr. E. C. van Reuth

Materials Sciences

Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209

Program Manager

Dr. R. P. Reed

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The views and conclusions contained in this document are those of the

authors and should not be interpreted as necessarily representing the

official policies, either expressed or implied, of the Advanced Research

Projects Agency or of the U.S. Government.
Abstract

Results are reported of a six-month study, ending September 1976, on candidate materials for superconducting-machinery components. The results

cover five areas--advanced composites, elastic properties, fatigue resistance and fracture toughness, magnetothermal conductivity, and thermal con- ductivity. Material properties were studied over the temperature range 4 to 300 K. Materials studied include: aluminum alloy 5083, copper-0.3

cadmium-0.3 tin, copper-28 nickel, iron-48 nickel, 3.5 Ni and 9 Ni steels,

titanium-4 aluminum-6 vanadium, titanium-5 aluminum-2.5 tin, stainless steel

21-6-9, several austenitic stainless steels of the 300 series, 300-grade

maraging steel, phenolformaldehyde , and the composites boron/aluminum,

boron/epoxy, graphite/epoxy , and niobium-titaniiam/copper . Some notable

results of the study are: anomalous elastic properties of stainless steel

21-6-9 due to a Neel transition; complete sets of elastic constants for two

composites, B/Al and NbTi/Cu; thermal conductivities of Ti-6A1-4V and Fe48Ni are reduced by a magnetic field while those of Cu-0.5 Sn and Cu-28Ni

are unaffected; a screening method for composites of possible cryogenic use;

general trends regarding temperature effects on the fracture toughness and

fatigue-crack-growth resistances of structural alloys are correlated with

crystal structure class; and the tensile-yield-strength and fracturetoughness data for fourteen commercial structural alloys at 4 K and 295 K are compared demonstrating an inverse relationship between these properties

and indicating the optimum combination of properties that are technologically possible. Also, the materials and properties studied experimentally

during the three-year program are summarized.

This work was supported by the Advanced Research Projects Agency of

the U.S. Department of Defense.

Key words: Aluminum alloys; composites; elastic properties; engineering

materials; fatigue; fracture; iron alloys; cryogenic temperatures; maraging

steels; mechanical properties; nickel alloys; phenolformaldehyde ; stainless

steels; superconducting machinery; thermal conductivity; titanium alloys.

iv
Report Contents

Page

ADVANCED COMPOSITES

M. B. Kasen, R. E. Schramm, and D. T. Read 1 ELASTIC PROPERTIES

H. M. Ledbetter and D. T. Read 19

Orthorhombic elastic constants of an NbTi/Cu composite

superconductor

H. M. Ledbetter and D. T. Read 23

Temperature dependence of the elastic constants of an NbTi/Cu superconducting composite

D. T. Read and H. M. Ledbetter 4 8 Low-temperature elastic properties of a 300-grade

maraging steel

H. M. Ledbetter 66

Low- temperature elastic properties of a precipitationhardened copper alloy

H. M. Ledbetter 84

Elastic properties of a boron-aluminum composite at

low temperatures

D. T. Read and H. M. Ledbetter 100

Anomalous low-temperature elastic behavior of a nitrogenstrengthened chromium-manganese stainless steel

H. M. Ledbetter 117

FRACTURE MECHANICS PARAMETERS

R. L. Tobler, H. I, McHenry, R. P. Reed, and R. E. Schramm . . 133

Fracture mechanics parameters for a 5083-0 aluminum

alloy at low temperatures

R. L. Tobler and R. P. Reed 135

Tensile and fracture behavior of a nitrogen-strengthened,

chromium-nickel-manganese stainless steel at cryogenic

temperatures

R. L. Tobler and R. P. Reed 16 2 Cryogenic tensile, fatigue, and fracture parameters

for a solution-annealed maraging steel

R. L. Tobler, R. P. Reed, and R. E. Schramm 188

Cryogenic effects on the fracture mechanics parameters of ferritic nickel-alloy steels

R. L. Tobler 214

Note on the fracture properties of Fe-49Ni

at cryogenic temperatures

H. I. McHenry and R. E. Schramm 244

Fatigue crack growth resistance of structural

alloys at cryogenic temperatures

R. L. Tobler and R. P. Reed 256

Fracture of structural alloys at temperatures

approaching absolute zero

R. L. Tobler 279

MAGNETOTHERMAL CONDUCTIVITY

L. L. Sparks 287

THERMAL CONDUCTIVITY

J. G. Must 305

IT
Disclaimer

Tradenames of equipment and materials are used in this report for

clarity and to conform with standard usage in the scientific and engineering literature. Selection of materials for discussion and examination wit

regard to application in superconducting machinery is based on properties

reported in the literature, and must be regarded as preliminary and tentative. In no case does such selection imply recommendation or endorsement

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

or equipment is necessarily the best available for the purpose.

vi
SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

ADVANCED COMPOSITES

M. B. Kasen, R. E. Schramm, and D. T. Read

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

1
NBS COMPOSITE-MATERIALS STUDIES DURING ARPA-SPONSORED

PROGRAM, SEPTEMBER 197 3 TO SEPTEMBER 1976

Subject .

- .

ARPA Report No.

Literature Review 1, 2, (4), (5)*

Cryostat Construction ' . 1 Tensile Test Procedures 2, 3, 4 Shear Test Procedures . 3, 4 Compression Test Procedures 5 Fatigue Test Procedures 6 Tensile Data, Boron-Epoxy 2, 3, 4 Tensile Data, Boron-Aluminum 3, 4 Tensile Data, Graphite-Epoxy 3, 4 Tensile Data, Glass-Epoxy 4 Tensile Data, Kevlar-Epoxy 4 Shear Data, Boron-Epoxy 4 Shear Data, Boron-Aluminum 3, 4 Shear Data, Graphite-Epoxy 4 Shear Data, Glass-Epoxy 4 Compression Data, Boron-Epoxy 5 Compression Data, Boron-Aluminum 5

Compression Data, Graphite-Epoxy 5

Compression Data, Glass-Epoxy 5

Tensile Fatigue Data, Boron-Epoxy 6

Tensile Fatigue Data, Boron-Aluminum 6

Compression Fatigue Data, Boron-Epoxy 6

*Numbers in parentheses refer to report numbers in which reprint

versions of the manuscripts occur. Other numbers refer to preprint versions.

2
Summary: Advanced Composites

A comparison has been made between the wearout rates of [0/±45/0]s boronepoxy and boron-aluminum composites in low-cycle fatigue at 295 K and 76 K.

Using degradation of modulus as the wearout criterion, these preliminary

data indicate that cryogenic temperatures have a negligible effect on either tensile or compressive fatigue performance of boron-epoxy, A similar

indication was obtained for boron-aluminum in tensile fatigue.

Contents; Advanced Composites

Page

1.0 Review 3 2.0 Phase III: Fatigue of Composites at Cryogenic Temperatures . . 3 2.1 Introduction 3 2.2 Experimental Procedures 4 2.3 Results and Discussion 5 2.4 Conclusions 6 3.0 References 7 Appendix 1: List of Symbols 8

1.0 Review

Work on this project was initiated by preparing state-of-the-art reviews on

the mechanical and thermal properties of structural composites at cryogenic

temperatures (1-3). These reviews suggested that boron-aluminum, boronepoxy, graphite-epoxy , glass-epoxy and Kevlar 49-epoxy composites warranted

further study to characterize key static mechanical properties at cryogenic

temperatures. This work was undertaken in a previous experimental portion

of the ongoing study (9)

.

Phase I of the experimental work involved development of apparatus and procedures for obtaining the required data. Phase II encompassed the static

characterization work. All of the above work has been completed and has

been reported in prior Semi-Annual Reports (see summary table at beginning

of this section) . Phase III addresses the question of the effect that

cryogenic temperatures have on the performance of composite materials under

fatigue loading and is the subject of this report.

2.0 Phase III: Fatigue of Composites at Cryogenic Temperatures

2.1 Introduction

The ability of composite structures to withstand cyclic stresses at cryogenic

temperatures is crucial to their suitability for use in rotating cryogenic

machinery. Very little is presently known on this subject. The few studies

that have been undertaken indicate that the fatigue life of glass-clothepoxy composites is improved by cooling to cryogenic temperatures, although

the overall performance remains unimpressive (4). NBS tests of uniaxial

glass-epoxy straps indicate that they are fit for service as thermal standoffs transitioning from 4 K to 295 K in a superconducting generator (5)

.

The only data known to the authors on the fatigue performance of advanced

composites at cryogenic temperatures is restricted to low-cycle hydrostatic

testing of filament-wound pressure vessles (6-7).

It is unfortunate that there exists no body of theory permitting prediction

of crossply composite fatigue performance from systematically determined

uniaxial properties, as is the case for the static mechanical properties.

Each layup of a particular type composite must therefore be looked upon as

a distinct material having a unique S-N curve. To a large extent, this

3
problem arises due to the differing strain to failure of the fiber and the

matrix. Where the strain capability of the fiber exceeds that of the

matrix and where the fiber is of low modulus as is the case for glassepoxy, the matrix will fracture at relatively low stress levels, even when

stressed in the uniaxial fiber direction. This leads to increased damping,

fiber-matrix debonding and to relatively poor fatigue performance. Conversely,

where the fiber has a low strain capability and high modulus, as with

graphite or boron, the fatigue performance in the uniaxial fiber direction

is excellent, as the matrix remains intact until fiber fracture. Advanced

composites tested in the uniaxial longitudinal direction have almost flat

S-N curves at room temperature. However, when advanced composites are crossplied, the failure mode in fatigue becomes a complex function of the

anisotropy of a particular layup as well as of the constituent properties,

composite quality and other variables.

The above considerations made it evident that the conventional S-N curve approach to studying composite fatigue would be unproductive in the present

program. An alternative approach was to seek to answer the more general

question of the extent to which cryogenic temperatures affect the fatigue

performance of state-of the-art composites developed for service at and

above room temperature. The development of an efficient means of accom- plishing this would permit screening of existing composites for further

cryogenic study and might well pinpoint some composite types so insensitive

to temperature as to allow existing room temperature fatigue data to be

used to predict cryogenic fatigue performance. This report describes the

attempts made to achieve this goal.

2.2 Experimental Procedures

Composites begin to wear out when the magnitude of a cyclic applied stress

exceeds the elastic limit of any component. Wearout is manifested by an increase in damping (increased internal friction) and in a decrease in

modulus. The initial objective of the present work was to determine if

modulus changes could be used as a criterion for assessing the state of

internal damage in a [0/±45/0]g 5.6 mil boron-epoxy specimen subjected to

tensile-tensile and to compressive-compressive low-cycle fatigue at 295 K

and 76 K, and in a similar boron-aluminum composite in tensile-tensile

fatigue.

The selected composites consisted of eight plies of 0.014 cm (5.6 mil)

boron in a matrix of PR-286 epoxy or 6061 aluminum. The commercial suppliers

reported 52.1% and 48.4% nominal fiber volume fraction for the boron-epoxy

and the boron-aluminum, respectively. Loads were always applied along the

0° fiber direction. This layup was selected to provide reasonable fatigue

performance due to the 0° plies while providing wearout by virtue of the

inability of the ± 45° plies to sustain the loads.

Specimen configurations were similar to those previously used for static

tension and compression studies. Table 1. Sufficient thickness to avoid

column bending failure in compression was obtained by removing the scrim

cloth and bonding two thickness of boron-epoxy to give 16 plies.

The tensile specimen gripping system which had proved adequate for static

testing (8) was inadequate for fatigue, as the specimen tended to pull out

of the grips. The 0.16 cm (0.06 in) Ti-6A1-4V serrated gripping plates

were replaced with 0.64 cm (0.25 in) thick Inconel X-750 plates, and the

0.48 cm (0.19 in) stainless steel pressure plates were increased to 0.64 cm

(0.25 in) thickness. Provisions were made for passing a 0.64 cm (0.25 in)

diameter bolt through the grip system and specimen. This bolt was torqued

to 16 N*m (12 ft'lb), while the twelve pressure screws on the sides of each

grip were torqued to 8 N*m (6 ft'lb) each.

The compressive test fixture developed for static use (9) proved adequate

4
for the fatigue program. However, the titanium pull rods failed under

fatigue and were replaced with stainless steel.

As previously in this study, specimen strain was monitored by gages bonded

to the specimen surface. Tensile fatigue specimens had both longitudinal

and Poisson's gages, while only a longitudinal gage was used for the com- pression fatigue specimens. Debonding of the gages was not a problem.

Static mechanical properties of the composite were determined in tension

and compression at 295 K and 76 K using methods previously described (9)

.

Fatigue studies utilized a closed-loop electrohydraulic machine, specially

adapted for cryogenic work. All tests were run at 30 Hz using a sinusoidal

wave form. The experimental procedure was similar to that of Williams, et

al . (10). A static stress-strain curve was initially obtained, after which

a dynamic stress-strain curve was obtained for comparison. To obtain the

dynamic stress-strain curve, we first fatigued (R = 0.1) the specimen for

25, 000 cycles at a maximum stress (-^lajf^ that was a small fraction of the

ultimate strength. Near the end of this fatigue increment a peak-reading

DVM was used to measure the maximum strain (e^i^x^ • After fatigue, a quasistatic loading gave the modulus (Ef ) . The maximum fatigue stress was then

increased for another 25,000 cycles and another set of measurements. These

stress increases were repeated until specimen fracture.

The 295 K tests were run in ambient air. A small temperature increase {'^

10°C) was observed after the first few steps, remaining relatively stable

for the remainder of the step sequence. The 76 K tests were run immersed

in liquid nitrogen.

An attempt was made to measure modulus and damping changes by dynamic

methods during several tensile fatigue tests of the boron-epoxy and boronaluminumi composite materials at 295 K and at 76 K. Piezoelectric transducers were attached to opposite ends of the specimen-grip system; one was driven with an electrical signal of variable frequency, and the voltage

across the other was monitored as the output signal. This allowed the

specimen-grip-load train system to be scanned for mechanical resonances

over a 0.5-15 kHz range between load steps.

2.3 Results and Discussion

Static mechanical properties are given in Table 2. Table 3 compares these

data with values of tensile strength and moduli predicted by the rule of

mixtures, using uniaxial and ± 45° data obtained earlier in this program

from the same type composites. The boron-epoxy properties follow the rule

of mixtures very well in both strength and modulus. Boron-aluminum follows

the rule reasonably well in strength. However, the measured modulus substantially exceeds the predicted value, reflecting the non-linearity between

stress and strain in crossplied boron-aluminum composite materials.

Results of the dynamic stress-strain, low-cycle fatigue program appear in

Table 4 and in s"ummary in Figs. 1-3. In each of these Figures, plot (a)

reflects the strain determined dynamically during a given run, while plot

(b) reflects quasi-static strain determined from the slope of a stress-strain

curve obtained between each fatigue step. If the dynamic tensile modulus

remains unchanged throughout a test, a plot of -niax'^o'''^^ • ^max/etu should

have a slope of 1.0 for a composite with a linear stress-strain curve to

fracture. (See Appendix 1 for definition of symbols.) The same is true for

the dynamic compressive modulus. Likewise, a plot of Ef/E^ vs. e-^g^-^/ ^tu

should have a constant value of 1.0 if the static modulus is unchanging. The

same is true for the static compressive modulus. Therefore, deviations from

these values were considered as indicators of the extent to which damage was

being incurred during the fatigue program.

Fig. 1 (a) indicates that the dynamic tensile modulus of the [0/±45/0]s

5
boron-epoxy was not affected by cyclic loading up to about 76% of its static

ultimate strength at either 295 K or 76 K. However, Fig. 1 (b) indicates

that a small decrease in static tensile modulus did occur at both temperatures.

The compression fatigue data of Fig. 2 show more scatter than does the tensile

data. Nevertheless, Fig. 2 (a) indicates that the dynamic compression modulus

is relatively unaffected by cyclic loading below about 60% of its ultimate

compressive strength. The data suggest that a modulus reduction may occur

at higher stress levels. Test temperature appears irrelevant. Fig. 2 (b)

indicates that the static compressive modulus does decline with cyclic loading; in some specimens, the decline began at very low stress levels. Again,

no temperature dependence of the modulus change was evident.

Most of the compressive data were obtained by cycling at 30 Hz with 25,000

cycles per increment of stress. As reported on Table 5, several runs were

also made at 15 Hz and at 10,000 cycles per increment without a significant

difference in result.

The limited amount of data obtained on [0/±45/0]g boron-aluminum during

dynamic stress-strain, low-cycle fatigue testing in tension is reported on Table 4 and summarized in Fig. 3. The displacement of the data above the

line of slope 1.0 in Fig. 3 (a) does not reflect cyclic stiffening.

Rather, it reflects an increase in the slope of the initial part of the

stress-strain curve due to the initial cycle to the preload limit indicated

on the Figure for the purpose of determining the static modulus. During

the cyclic test, the modulus follows the steeper initial slope up to the

preload limit, after which it continues at a lesser slope of approximately

1.0, causing the observed displacement of the plotted data. This is an illustration of the non-linearity characteristic of cross-plied boronaluminum composites. Fig. 3 (a) therefore suggests that the cyclic tensile

loading up to about 82% of the static ultimate strength had no significant

effect on the dynamic tensile modulus. Fig. 3 (b) indicates that the

tensile modulus was likewise unaffected. The temperature of testing appears

irrelevant.

Attempts to measure modulus and damping changes by resonance methods during

the dynamic stress-strain, low-cycle fatigue program produced inconsistent

results. Several maxima of the amplitude of the output signal voltage,

each corresponding to a mechanical resonance in the specimen-grip-load

train system were observed in the 5-15 KHz range. In most of the tests,

the observed frequencies and amplitudes did not exhibit systematic behavior

as a function of load step number (increasing stress increment) . The

boron-aluminum specimen tested at 76 K (specimen 1-3) did exhibit systematic

behavior. Fig. 4 shows the frequency (x axis) and amplitudes (y axis) of

several resonances after the load step indicated by the numeral at the data

point. These load steps correspond to the increasing stress levels for

specimen 1-3 listed on Table 4. The systematic decrease in resonance

amplitude at those frequencies indicates that damping in this specimen was increased significantly by stress cycling, while the absence of large

systematic changes in resonance frequencies indicates that the modulus

change was not large, in agreement with Fig. 3 (b) . The failure to observe

similar systematic behavior in test at 295 K indicates that the damping in

the specimens before fatiguing, the sensitivity of the apparatus, or both

change significantly on cooling to 76 K.

2.4 Conclusions •

A dynamic stress-strain, low-cycle fatigue method has shown itself capable

of detecting composite wearout as revealed by modulus changes in a [0/+4 5/0]g

boron-epoxy specimen. However, the method was found to lack the sensitivity

required for purposes of screening composite systems for use at cryogenic

temperatures. The data suggest that static and dynamic moduli differ, the

static modulus providing the most sensitivity to composite wearout. It is

6
probable that the method would produce more useful results with a composite

layup less forgiving in fatigue, i.e., a [0/±45] or a [+ 45] orientation.

The wearout rate in boron-epoxy appears to be greater in compression fatigue

than in tension fatigue both at 295 K and 76 K, although the substantially

larger scatter in data in compression tends to obscure this difference.

The wearout rate as measured by modulus decrease in the [0/±4 5/0]g boronepoxy composite used in this study was the same at 76 K as at 295 K. This

suggests that the room temperature fatigue data on boron-epoxy composites

might serve as a criteria for cryogenic service. However, these preliminary

indications must be complimented by additional test work.

Results of the study indicate that [0/±45/0]g boron-aluminum performs well

in low-cycle tensile fatigue. No difference in performance was detected

between tests conducted at 295 K and at 76 K.

Attempts to use an in-situ dynamic resonance method for evaluating com- posite wearout was for the most part unsuccessful. However, partial success with a boron-aluminum specimen fatigued in tension at 76 K suggests

that the method might prove very useful when apparatus and procedures are perfected.

3.0 References

1. Kasen, M. B. , "Properties of Filamentary-Reinforced Composites at

Cryogenic Temperatures," Composite Reliability , ASTM STP 58 0,

American Society for Testing and Materials, 1975, pp. 586-611.

2. Kasen, M. B., "Mechanical and Thermal Properties of FilamentaryReinforced Structural Composites at Cryogenic Temperatures. I: Glass-Reinforced Composites," Cryogenics, 15 (6), 1975, pp. 327-349.

3. Kasen, M. B. , "Mechanical and Thermal Properties of FilamentaryReinforced Structural Composites at Cryogenic Temperatures. II:

Advanced Composites," Cryogenics, 15 (12), 1975, pp. 701-722.

4. Brink, N. 0., "Determination of the Performance of Plastic Laminates

under Cryogenic Temperatures," ASD-TDR-62-794 , Air Force Systems

Command, WPAFB, Ohio (August 1962) AD 288944.

5. Tobler, R. L. and Read, D. T., "Fatigue Resistance of a Uniaxial

S-Glass/Epoxy Composite at Room and Liquid Helium Temperatures,"

J. Compos. Mater. 10, 32 (1976).

6. Hanson, M. P., "Tensile and Cyclic Fatigue Properties of Graphite

Filament-Wound Pressure Vessels at Ambient and Cryogenic Temperatures,"

NASA TN D-5354, National Aeronautics and Space Administration, Lewis

Research Center, Cleveland, Ohio (1969) (N69-31300) (identical to

SAMPE 15, 249)

.

7. Alfring, R. J., Morris, E. E., Landes, R. E., "Cycle-Testing of

Boron Filament-Wound Tanks," NASA CR-72899, National Aeronautics and

Space Administration, Lewis Research Center A(1971) (N71-38023)

.

8. Kasen, M. B. and Schramm, R. E., "Advanced Composites," in Semi-Annual

Technical Reports on Materials Research in Support of Superconducting

Machinery - II ; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.); Nat.

Bur. Stds., Boulder, CO; October 1974; ADA004586.

7
9. Schrainin, R. E. and Kasen, M. B., "Advanced Composites," in Semi-Annual

Technical Reports on Materials Research in Support of Superconducting

Machinery - V ; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.); Nat.

Bur. Stds., Boulder, CO; April 1976.

10. Williams, R. S., Reifsnider, K. L. , Stinchcomb, W. W. , and Turgay,

H. T., "The Effect of Frequency and Strain Amplitude on the Fatigue

Damage of Boron/Epoxy Fiber-Reinforced Composite Materials," AFOSR-TR75-1387, AFOSR, Arlington, VA, April 1975, ADA 015479.

APPENDIX 1; LIST OF SYMBOLS

E Elastic modulus measured from quasi-static loading.

E^ Elastic modulus measured prior to fatigue.

E^ Elastic modulus measured after fatigue. , R Ratio of minimum to maximum stress during fatigue cycle.

cu . . e Maximum strain measured m quasi-static loading (compression)

.

e^^ Maximum strain measured in quasi-static loading (tension)

.

c Maximum strain measured during fatigue, max ^ ^

a^" Maximum stress measured in quasi-static loading (compression)

.

a^^ Maximum stress measured in quasi-static loading (tension)

.

a Maximum stress measured during fatigue, max ^ y

V Poisson's ratio measured in quasi-static loading.

Poisson's ratio measured prior to fatigue.

Poisson's ratio measured after fatigue.

8
Table 1. Nominal specimen dimensions.

Length Width Thickness Gage Length

Specimen cm in cm in cm in cm in

Tension 25.4 10.0 2.54 1.0 0.142 0.056 15.2 6.0

Compression 10.2 4.0 0.406 0.160 0.279 0.110 1.3 0.5

Table 2. Static mechanical properties

Test E Temp. (K)

Q 9 10 N/m" 10^ psi V lO^N/m^ 10^ psi eh

[0/+45/0]g Boron- Epoxy

Tension

295 120 17.4 0. 755 7.62 110 0.65

295 119 17.2 0. 692 7.60 110 0.68*

295 122 17.7 0. 806 8.10 117 0.71

76 117 17.0 0. 551 8.56 124 0.70

76 133 19.3 0. 540 8.61 125 0.70

4 134 19.4 0. 580 ** ** **

4 133 19.3 0. 561 8.87 129 0.71

Compression

295 102 14.8 12.4 180 1.20

295 101 14.7 9.7 141 1.08

[0/i45/0]g Boron-Al uminum

Tension

295 178 25.8 0. 295 7.74 112 0.54*

295 179 26.0 0. 287 8.53 124 0.60*

295 180 26.0 0. 305 7.61 110 0.58

295 159 23.0 0. 415 6.34 92 0.51

76 163 23.6 0. 350 8.14 118 0.68

4 166 24.0 0. 314 8.47 123 0.72*

* Grip Fracture

** No fracture

Underlined values used in calculating data on Figs. 1-3 and Table 5.

9
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Table 4, Results or dynamic o-e tests.

Fatigue Dynamic Static

Cycles a e E v —

z— — — ?=— ^ ^ max max no tu tu E 1° loW I

Boron-Epoxy, specimen 1-8,

76 K, a^u = 8.61 x 10^

N/m^, etu = 0.70%, 30 Hz,

Tension

Boron-Epoxy, specimen 1-3,

295 K, o^^ = 8.10 X 108

N/m^, etu = 0.71%, 30 Hz,

Tension

Boron-Epoxy, specimen F-7,

rCU - 76 K,

Compression

-CU - 12.0 X 10°

0.93%, 30 Hz

Boron-Epox^, specimen F-18,

76 I,

N/m^,

Compression

-CU 12.0 X 0.93%,

10°

30 Hz,

0 — 130 0.578 -- -- 1 00

25 0.50 0. 05 132 0.573 0.06 0 07 1 02

50 1.01 0. 09 132 0.553 0.12 0 13 1 02

75 1.51 0. 13 132 0.563 0.18 0 19 1 02

100 2.02 0. 17 132 0.568 0.23 0 24 1 02

125 2.53 0.21 128 0.563 0.29 0 30 0 98

150 3.03 0. 24 126 0.563 0.35 0 34 0 97

175 3.53 0. 29 126 0.580 0.41 0 41 0 97

0. 33 1 ?R n 47 0u 47 n Qfi 225 4.54 0. 38 124 0.589 0.53 0 54 0 95

250 5.05 0. 41 123 0.593 0.59 0 59 0 95

275 5.56 0. 46 122 0.587 0.65 0 66 0 94

300 6.06 0. 50 120 0.608 0.70 0 71 0 92

325 6.56 0. 52 132 0.641 0.76 0 74 1 02

0

-- 117 0.703 -- - 1 00

25 0.50 0. 05 116 0.712 0.06 0 07 0 99

50 1 .00 0. 09 115 0.698 0.12 0 13 0 98

7R 1 50 0. 13 115 0 1 Q 0 \ o n 100 2.51 0. 23 117 0.715 0.31 0 32 1 00

125 3.51 0. 31 113 0.717 0.43 0 44 0 97

150 4.01 0.36 113 0.713 0.50 0 51 0 .97

175 4.51 0. 40 113 0.728 0.56 0 56 0 97

200 5.01 113 0.740 0.62 -- 0 97

225 5.51 0. 50 110 0.739 0.68 0 70 0 94

250 6.01 0. 55 -- -- 0.74 0 77 --

0

-- 137 -- -- -- 1 00

25 1 .009 0. 07 132 0.08 0 08 0 96

50 2.017 0. 14 140 0.17 0 15 1 02

75 3.026 0. 22 137 0.25 0 24 1 00

100 4.035 0. 28 144 0.34 0 30 1 05

125 5.043 0. 34 148 0.42 0 37 1 08

150 6.052 0. 42 140 0.50 0 45 1 02

175 7.061 0 54 133 0.59 0 68 0 97

200 8.069 0. 75 113 0.67 0 81 0 82

0 156 1 00

25 1.02 0 06 156 0.09 0 06 1 00

50 2.05 0 12 148 0.17 0 13 0 95

75 3.07 0 20 144 0.26 0 21 0 93

100 4.10 0 28 140 0.34 0 30 0 90

125 5.12 0 35 139 0.43 0 38 0 89

150 6.15 0 44 139 0.51 0 47 0 89

175 7.17 0 53 133 0.60 0 57 0 85

185.07 8.19

11
Table 4 . continued

Fatigue Dynamic Static o ^ e ^ ^ T

r- max max f Cycles ^ o e E v —r— —r— t2

'"^x max ^tu ^tu E^

^° loVm^ % loVm^

Boron-Epoxy, specimen Frl5, 0 76 K, = 12.0 X 10^ 10 0.99

N/m2, eCU . o.93%, 30 Hz, 20 1.97

Compression 30 2.96

40 3.94

50 4.93

60 5.91

Boron-Epoxy, specimen Frl6, 25 1.02

76 K, = 12.0 x 10^ 50 2.03

N/m^, e^^ = 0.93%, 15 Hz, 75 3.05

Compression 100 4.06

125 5.07

150 6.09

175 7.10

200 8.12

Boron-Epoxy, specimen F-6, 0 295„K, o^^ = 12.4 X 10^ 25 1.015

N/m^, e^^ = 1.20%, 30 Hz, 50 2.029

Compression 75 3.044

100 4.058

125 5.091

150 6.088

175 7.102

200 8.117

Boron-Epoxy, specimen F-10, 0 295„K, o^^ = 12.4 X 10^ 25 0.99

N/m^, e^^ = 1 .20%, 30 Hz, 50 1 .99

Compression 75 2.98

100 3.97

125 4.96

150 5.95

175 6.95

186.18 7.94

Boron-Epoxy, specimen F-12, 0 295 K, = 12.4 x 10^ 10 1.00

N/m2, eCU = i.20%, 30 Hz, 20 1.99

Compression 30 2.99

40 3.98

50 4.98

60 5.97

70 6.97

80 7.96

90 8.91

152 - -- 1 .00

0.07 150 0..08 0,,08 0.99

0.14 151 0..16 0,,15 0.99

0.21 143 0..25 0.,23 0.94

0.30 130 0,.33 0.,32 0.85

0.37 136 0,.41 0.,39 0.89

0.46 132 0,.49 0,,50 0.87

0.08 — 0..09 0,.08 —

0.15 1 47 0..17 0.,16 1 . 00

0.24 129 0..25 0.,25 0.88

0.31 131 0,.34 0,,34 0.89

0.39 134 0..42 0..42 0.91

0.48 129 0..51 0,,52 0.88

0.57 125 0..59 0..61 0.85

0.64 157 0..68 0,.69 1 .07

134 -- -- 1 .00

0.1

1

145 0..08 0,.09 1 .08

0.20 135 0,,16 0,.17 1 .01 0.24 133 0..25 0..20 0.99

0.33 128 0..33 0.,28 0.96

0.40 128 0..41 0.,33 0.96

0.49 122 0..49 0.,41 0.91

0.57 121 0..57 0,,48 0.96

0.73 106 0,.65 0.,61 0.79

88 1 .00

0.12 93 0..08 0,,10 1 .05

0.23 91 0,.16 0.,19 1 .04

0.31 103 0..24 0,,26 1.16

0.41 104 0..32 0.,34 1.17

0.51 99 0..40 0.,43 1.12

0.63 94 0..48 0.,53 1 .07

0.75 87 0,,56 0..62 0.99

0.95 0.,64 0. 79

107 1.00

0.08 104 0..08 0,,07 1 .02 0.20 107 0,,16 0.,16 0.99

0.31 112 0,,24 0.,26 1 .04

0.38 111 0.,32 0..32 1 .03

0.45 109 0,,40 0.,37 1.01

0.55 107 0.,48 0.,46 1.00

0.68 106 0.,56 0.,56 0.98

0.79 104 0.,64 0.,66 0.97

0.88 103 0,,72 0.,73 0.96

12
Table 4. continued

Fatigue Dynamic Static a e

„ T r max max f Cycles a e E v —:— , ~ max max tu tu E 10°N/m^ % lO^N/m'^

Boron-Epoxy, Specimen E-ll , 0

295-K, a^^ 12.4 x 10^ 25 1.00

N/m^, £cu . -12%, 15 Hz 50 2.00

Compression 75 3.00

100 4.00

125 5.01

Boron-Aluminum, specimen 0 1-3, 76 K, a^^ = 7.61 25 0.56

x 10^ N/m2, etu = o.58%, 50 1.13

30 Hz, Tension 75 1.69

100 2.82

125 3.95

150 5.08

175 6.21

Boron-Aluminum, specimen 0 1-6, 295 K, o}^ = 8.14 25 0.56

x 108 N/m2, = 0.68%, 50 1.11

30 Hz, Tension 75 1 .67

100 2.79

125 3.90

150 4.46

175 5.01

._ 132 _ _ 1

.

00

0.,09 123 0..08 0. 07 0. 94

0.,15 119 0..16 0. 14 0. 91

0.,26 116 0..24 0. 21 0. 88

0.,33 118 0..32 0. 27 0. 90

0,.42 116 0..40 0. 35 0. 88

199 1 .00

0,,03 197 0..07 0 .06 0 .99

0.,07 193 0..15 0 .11 0 .97

0,,10 200 0,.22 0 .18 1 .01

0.,17 199 0..37 0 .30 1 .00

0.,25 200 0,.52 0 .44 1 .01

0,,33 196 0..67 0,.58 0 .98

0.,42 189 0..82 0 .72 0,.95

187 1..00

0.,03 189 0..07 0,.05 1

.

,01

0.,07 188 0. 14 0,.11 1

.

.01

0,.10 188 0.,21 0..15 1

,

,01

0,,18 186 0.,34 0..27 0..99

0,.26 184 0.,48 0,.38 0..98

0..30 183 0. 55 0..44 0..98

0..34 185 0. 62 0..50 0,.99

13
14
E /E

1.1

1.0

0.9

0.8

BORON-EPOXY

COMPRESSION

76 K

295 K

0.8

Fig. 2. Relative stress and relative modulus as a function of relative

strain for boron-epoxy during compressive fatigue. Each point

represents an increment of 25,000 cycles.

15
Ef/Eo 1.0

BORON-ALUMINUM

TENSION

76 K

295 K

0.8

Fig. 3. Relative stress and relative modulus as a function of relative

strain for boron-aluminum during tensile fatigue. Each point

represents an increment of 25,000 cycles.

16
T

^

0.01

0.001

BORON-ALUMINUM

TENSION

76 K

•2

•4

• 3

• 2

4V3

•5

•6

T

»4

>3

6t5

•7

Numerals indicate load step number

500 700 900 1100 1300 1700

FREQUENCY (Hz)

Fig. 4. Frequency and amplitude of three maxima in piezo electric

transducer output after the indicated fatigue-stress steps.

17

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

ELASTIC PROPERTIES

H. M. Ledbetter and D. T. Read

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976
NBS ELASTIC-PROPERTIES STUDIES DURING ARPA-SPONSORED

PROGRAM, SEPTEMBER 1973 TO SEPTEMBER 1976.

rid Lcr 1 a 1 nr\r ARPflM Report No.u A^c 1 1 lllcii La 1 Method(s)

1 Aluminum Alln\/ 1100 p**

2. " 2019 5 P

0 •

II II poic 5 r 4. " 5083 2,(5) P

5. " 7005 2,(5) P

6. " 7075 2,(5) P

7/ • At R P

8. " -lONi 4 R,P

9. " -30Ni 4 R,P

1 n H ,0 R P n. Inconel 600 1,(4) P 12. 718 3,(5) P

^ 13. " X750 1,(4) P

14. Iron-36Ni (Invar) 4 R,P

15. Maraging steel 6 P

16. Nitronic 40(21-6-9) 6 R,P

17. Stainless steel A286 2.(4) P 18. 304 2,(4) P 19. 310 2,(4) P 20. 316 2,(4) P .'

21. Titanium-6A1-4V 1,(2) P 22. -5Al-2.5Sn 1,(2) P

Composites:

23. Boron/aluminum 6 R

24. Fiberglass/epoxy 3,(5) R

25. NbTi/Cu 6 P.R

26. NbTi/Cu/epoxy 3,(5) R

* Numbers in parentheses refer to report numbers in which reprint

versions of the manuscripts occur. Other numbers refer to preprint versions.

**P = pulse, R = resonance.

20
ELASTIC PROPERTIES OF ENGINEERING MATERIALS AT CRYOGENIC TEMPERATURES

H. M. Ledbetter

Six manuscripts on the elastic properties of engineering materials

are included in the present report:

1. "Low temperature elastic properties of a precipitation-hardened

copper alloy." by H. M. Ledbetter. This manuscript on the cryogenic

elastic properties of copper alloy PD 135 complements the manuscript

in the fourth semi-annual report that described the anomalous elastic properties of this alloy at room temperature.

2. "Orthorhombic elastic constants of an NbTi/Cu composite superconductor" by H. M. Ledbetter and D. T. Read. This manuscript

describes the elastic symmetry of a material used in cryogenic

magnets.

3. "Temperature dependence of the elastic constants of an NbTi/Cu

superconducting composite" by D. T. Read and H. M. Ledbetter. This

manuscript complements item (2), giving the low-temperature elastic

constants.

4. "Anomalous low-temperature elastic behavior of a nitrogenstrengthened chromium-manganese stainless steel" by H. M. Ledbetter.

This is the first study of the low-temperature elastic properties

of this steel. It behaves anomalously because of a paramagneticantiferromagnetic transition.

5. "Low-temperature elastic properties of a 300-grade maraging

steel" by H. M. Ledbetter.

6. "Elastic properties of a boron-aluminum composite at low temperatures" by D. T. Read and H. M. Ledbetter.

Since this is the final report of the three-year ARPA-sponsored program on materials research for superconducting machinery, it is appropriate to review briefly the entire elastic-properties effort. The table

on the previous page summarizes the NBS experimental studies on lowtemperature elastic properties. Twenty-six materials were studied in the

temperature region 4-300 K: six aluminum alloys; four copper alloys;

three inconels; an iron-nickel alloy; a maraging steel; a nitrogenstrengthened stainless steel; two titanium alloys; and four composites:

boron/aluminum, fiberglass/epoxy , NbTi/Cu, and NbTi/Cu/epoxy . Some of

the special properties of these materials inclu'de: precipitation

hardening, low thermal expansion, high strength-density ratio, and high

strength-thermal conductivity.

21
NBS PUBLICATIONS ON ELASTIC PROPERTIES, RESULTING FROM

ARPA-SPONSORED PROGRAM, SEPTEMBER 1973 TO SEPTEMBER 1976

1. E. R. Naimon, H. M. Ledbetter, and W. F. Weston, Low-temperature

elastic properties of four wrought and annealed aluminum alloys,

J. Mater. Sci . 10 (1975) 1309-1315.

2. D. T. Read and H. M. Ledbetter, Temperature dependencies of the

elastic constants of precipitation-hardened aluminum alloys 2014

and 2219, submitted for publication.

3. H. M. Ledbetter and W. F. Weston, Low-temperature elastic properties

of some copper-nickel alloys. Ultrasonics Symposium Proc, Cat. No.

75 Ch 8 994-4SU (IEEE, New York, 1975) 623-627.

4. H. M. Ledbetter, Anomalous elastic properties of a precipitationhardened copper alloy, submitted for publication.

5. H. M. Ledbetter, Low-temperature elastic properties of a precipitationhardened copper alloy, submitted for publication.

6. W. F. Weston, H. M. Ledbetter and E. R. Naimon, Dynamic lowtemperature elastic properties of two austenitic nickel -chromiumiron alloys. Mater. Sci. Engg. 20 (1975) 185-194.

7. W. F. Weston and H. M. Ledbetter, Low-temperature elastic properties

of a nickel -chromium-iron-molybdenum alloy, Mater. Sci. Engg. 20

(1975) 287-290.

8. H. M. Ledbetter, E. R. Naimon, and W. F. Weston, Low-temperature

elastic properties of invar, Proc. ICMC, Kingston, Ontario, July

1975 (Plenum, New York, forthcoming).

9. H. M. Ledbetter and D. T. Read, Low-temperature elastic properties

of a 300-grade maraging steel, submitted for publication.

10. H. M. Ledbetter and D. T. Read, Low-temperature elastic properties

of a nitrogen-strengthened chromium-manganese stainless steel,

submitted for publication.

11. H. M. Ledbetter, W. F. Weston, and E. R. Naimon, Low-temperature

elastic properties of four austenitic stainless steels, J. Appl

.

Phys. 46 (1975) 185-194.

12. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Elastic properties

of two titanium alloys at low temperatures. Cryogenics !£ (1974)

246-249.

13. D. T. Read and H. M. Ledbetter, Low-temperature elastic properties

of a boron/aluminum composite, submitted for publication.

14. W. F. Weston, Elastic constants of a superconducting-coil com- posite material, J. Appl Phys. 46 (1975) 4458-4465.

15. H. M. Ledbetter and D. T. Read, Orthorhombic elastic constants

of an NbTi/Cu composite superconductor, submitted for publication.

16. D. T. Read and H. M. Ledbetter, Low-temperature elastic constants

of an NbTi/Cu composite superconductor, submitted for publication.

22
ORTHORHOMBIC ELASTIC CONSTANTS OF AN

NbTi/Cu COMPOSITE SUPERCONDUCTOR*

H. M. Ledbetter and D. T. Read**

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Elastic properties of a niobium-titaniuri -filament, copper-matrix

composite superconductor were studied experimentally. Ultrasonic

pulse and resonance measurements showed the material has orthorhombic

symmetry and, therefore, nine independent elastic constants. With respect

to copper: C^y C^^, and C^^ 3re about seven percent lower; C^^

C^^, and Cgg are about fifteen percent lower; the off-diagonal elastic constants are unchanged; and the bulk modulus is about five percent lower. Deviations from isotropic elastic behavior are small.

Key words: Bulk modulus; composite; compressibility; copper; elastic

constants; niobium-titanium; Poisson's ratio; pulse method; resonance

method; shear modulus; sound velocity; superconductor; Young's modulus.

* Contribution of NBS, not subject to copyright.

**NRC-NBS Postdoctoral Research Associate, 1 975-6.

23
ORTHORHOMBIC ELASTIC CONSTANTS OF AN

NbTiVCu COMPOSITE SUPERCONDUCTOR*

H. M. Ledbetter and D. T. Read**

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

I. INTRODUCTION

The purpose of this paper is to report an experimental study of

the elastic properties of a composite material, emphasizing elastic

symmetry and the value of applying familiar single-crystal methods to

composites. This composite contains unidirectional niobium-titanium

(NbTi) filaments in a copper (Cu) matrix. It is designed as a superconductor for magnets. Manufacture and morphology suggest that the

filament direction is an elastic symmetry axis. Thus, the macroscopic elastic symmetry is orthorhombic, tetragonal, hexagonal, or

cubic. Oblique axis systems--tricl inic , monoclinic, trigonal --are

excluded.

The present study shows that this composite is orthorhombic.

But, deviations from isotropy are small. Thus, it can

be referred to other co-ordinate axes--for example, hexagonal-- without

introducing large errors. Advantages of this simplification are discussed

below. Nevertheless, a complete set of nine orthorhombic elastic constants was determined.

24
Experimentally, two dynamic methods were used: pulse and

resonance. Most measurements were made by a pulse method; eighteen

ultrasonic wave velocities were measured along the orthorhombic <100>

and <110> directions. Resonance experiments were done to achieve two

ancillary objectives. First, to detect dispersion, the variation of soundvelocity with frequency. Second, to confirm the off-diagonal elastic

constants.

It is emphasized that the elastic constants reported here may differ

from those of apparently identical composites for reasons discussed below

in sections IIIC and VF.

25
II. WAVE MOTION IN ORTHORHOMBIC MEDIA

Usual crystal lographic notations for vectors and elastic constants are used in this report, although all components of the

studied composite material are polycrystal 1 ine. Symmetries discussed here are strictly macroscopic. The filament direction of the composite is designated [001], and the principal directions perpendicular to the

filaments are [100] and [010]. These directions are indicated in Fig. 1.

As stated above, the studied material has orthorhombic symmetry.

Materials with orthorhombic symmetry have nine dependent elastic constants.

These are displayed in Eq. (1) in the Voiqt contracted notation in

matrix form. ^

11 12

'22

^13 0 0 0

^23 0 0 0

^33 0 0 0

0 0

0

^66

(1)

where the matrix is symmetrical about its main diagonal. The Christoffel

equations, which relate the elastic constants to the plane, monochromatic

phase velocities, are:^

(Sjkl"j"k- ^il^Pl

~- ° (2)

where C^jj^i is the fourth-rank elastic stiffness tensor, n is the wavepropagation direction, p is the mass density, v is the wave velocity,

26
is the Kronecker delta, and p is the displacement vector. It is easy to

show that the resulting secular equation is diagonal for the [100], [010],

and [001] directions. Thus, waves traveling along <1UU > directions are pure modes,

Their velocities are determined by C-j^, C^^, Cg^; > C^^, C^^; and C^^^

^44' ^55' "Respectively. Thus, all diagonal elastic constants C^^ can be

determined by propagating waves in < 100 > directions. For each direction,

there is one longitudinal wave and two shear waves; the three are polarized

mutually orthogonally. Thus, checks on each of the three shear elastic

constants C^^, C^^, and Cgg are available. The off-diagonal elastic constants C-j^, C-|25 and C^^ ^^^^ determined by measurements where the n

vectors are oblique to the <100 >directions.

In general, waves traveling along lower- symmetry directions are not

pure modes. For n =<110>, there is a single pure mode whose

velocity is determined by j(C^^ + Cgg), ^(C^^ + Cg^), and j(C^^ + C^^)

for the [Oil], [101], and [110] directions, respectively. These provide

additional checks on the three C^.^ shear constants measured along < 100 >

directions. The two impure modes that propagate along each < 1 10 >direction can be determined from the Christoffel equations.

The < 01 1 > propagation-direction case is now outlined. The KelvinChristoffel elastic stiffnesses

^11 = Sjki"j"k

are for the case n = — [Oil]

27
il

^^55 ^66

0

0

r + f

c + r ^23 ^44

c + r ^23 ^44

^33 ^44

(4)

Thus, one solution is

(5)

a torsion mode. And the remaining two roots are

(6)

2 Experimentally, pv is measured and C23 is unknown. Thus, by rearrangement

(7)

The spurious second value of C23 from this equation can be discarded on

physical grounds. Similarly, [101] and [110] planes can be used to determine Ci3 and C-|2> respectively. For these cases

C,3= il [2fv2- ^(Ci,-C33.2C55)]2- \^'^-^^^

and

C,2= lU2fV^- 5-(Cii+C33+2Cgg)]2- \{Z^^-C^/ (^^^6

Further details on the problem of wave propagation in orthorhombic

3 media were given by Musgrave.

(8)

(9)

28
III. EXPERIMENTAL

A. Material

The samples used in this study were cut from a short section of Kryo

210* superconductor supplied by Magnetics Corporation of America. This

is a copper-matrix, niobium-titanium-filament composite material. The

Cu/NbTi volume ratio is 6:1, and the bar contains 2640 filaments with a

twist each 7.6 cm. The distribution of filaments is shown in Fig. 2.

The sample obtained for this study was about 20 cm

long, 1.0 cm wide, and 0.5 cm thick. Four samples were cut for ultrasonic pulse measurements, one with its surfaces perpendicular to the symmetry axes of the material and three with the largest surface oriented at

45'' to two symmetry axes. Sample geometries are shown in "^ig. 1. Samples were studied in the as-received condition, that is, optimized by the

manufacturer for use as a superconductor. Tne thermal and mechanical

treatments that optimize such superconductors were descri bed by Mclnturff

4

and Chase. The specimen with jlOO [ surfaces was

0.5 cm by 1.0 cm by 1.0 cm,, while the three off-axis specimens had

thicknesses of 5 mm, 3 mm, and 2 mm. All specimens were ground sufficiently flat and parallel for ultrasonic study.

B. Procedures

Eighteen different ultrasonic-wave modes could be studied in

these four specimens. All eighteen were examined at room

temperature using the following procedure. Quartz-crystal transducers

either 9.5 mm or 6.4 mm in diameter with fundamental resonance

*A trade name is used to describe the studied material; its use is not

an NBS endorsement of the product.

29
frequencies between 5 and 10 MHz were bonded to one sample surface with

phenyl sal icylate (salol ) . Ultrasonic pulses were generated and

detected in the transducer using an electronic apparatus described

5 previously. The time interval between the arrival of selected pulses

from the ultrasonic echo train was measured using an oscilloscope with

a delaying time base calibrated against a precision time-mark generator.

The ultrasonic echo patterns obtained in this study were of good quality.

They had three to thirty well-defined echoes.

Using the velocity v of the ultrasonic wave obtained from the

transit time and the path length and the specimen mass density p the

room-temperature elastic constants were calculated using the relationship

C = pv^ (10)

a simplified form of Eq. (2), where C is a combination of the C.^'s

depending on the mode. Results derived from Eq. (2) for the eighteen

modes studied here are given in Table 1.

Resonant-bar elastic-constant measurements were performed on two

other specimens at room temperature. These specimens were 4.8 mm diameter

cylinders with lengths of 1.9 cm and 3.1 cm prepared with filaments

along the specimen axis. In the resonant-bar technique, the sample is excited into longitucfinal or torsional resonance

by an attached quartz-crystal driver of appropriate mode and frequency. Resonance is detected using a quartz gauge crystal attached

to the driver. The driver, gauge, and specimen form a composite oscillator. The appropriate elastic constant of the specimen can be calculated from the resonant frequency of the composite oscillator, the

30
specimen density, and known properties of the driver and gauge crystals.

Since the composite-oscillator resonant frequency is often

tens of kilohertz, this technique is sometimes called a kilohertz technique. But, in the literature it is called a

compos ite-osci 1 lator technique.^

C. Uncertainties

Experimental uncertainties of the elastic constants are discussed in

two parts: imprecision and systematic error. Imprecisions affect many con- clusions of the study. Systematic errors do not; they affect slightly only

the C .

.

' s themsel ves.

^ 3Bounds on the C..'s in Table I are imprecisions expressed as + a,

where a is the standard deviation based on a normal distribution. For

the diagonal C^j's, these imprecisions are based on two to five pure-mode

measurements. Imprecisions of the non-diagonal C^.j's depend both on these

values and on an assumed imprecision of 0.005 in the quasi-transverse

2 values of pv . Sources of imprecision include: deviations of specimens from flat and parallel, specimen-length mismeasurement , specimento-specimen bond variations, transit-time mismeasurement, and, for this

material, specimen imhomogenei ty.

There are two principal systematic errors, one arising from the mass

density and one from the transducer-bond coupling to the specimen. Maximum error in the mass density is estimated

to be less than 0.15 percent. Transit-time error due to the

ultrasonic wave traveling through the transducer and the coupling agent

is estimated to be less than one percent; and, when corrected for, increases

2 the pv values. Thus, the overall uncertainty in the C.. s is estimated

to be less than + 1.5 percent.

31
A possible source of sample-to-sample

variation in the elastic constants of any composite material is its

thermal -mechanical treatment, which may vary considerably for the type

of material reported on here. For example, for copper, elastic-constant

differences up to ten percent have been reported for annealed and

deformed specimens.^ Such variations can also occur in copper-base

composites. Residual stresses of the order of the yield strength may

occur in the composite, but simple computations show that these would

change the elastic constants by less than one percent.

IV. RESULTS

Results of the study are displayed in the first four tables. In

2 Table I, the observed room-temperature values of pv are given for

eighteen measurement modes. This table also contains expres2 sions for the pv in terms of the C .'s. These expressions were derived

from the Christoffel equations. When a + sign occurs, the + sign corresponds to the longitudinal mode, and the - sign corresponds to the

transverse mode. Estimated errors for the derived elastic constants are

also in Table I. The basis for estimating these errors was described

above.

Results of the resonance studies are in Table II. S^^ is the reciprocal Young's modulus along the filament direction, and j

(S^^ + S^^)

is the reciprocal torsion (or shear) modulus around that direction.

The elastic compliances, the S^.j's, are in Table III along with a

summary of the C^.j data. The S^.^.'s were determined by inverting the C^.^

matrix displayed in Eq. (1) and substituting the C. values from Table I.

^ 3 Except for S^^, S^^, and Sgg, which are simple reciprocals of the corresponding C^.j's, errors in the S^.j's are larger than those in the

C.. 's because of error accumulation.

3?
The practical elastic constants (E = Young's modulus, G = shear

modulus, and v = Poisson's ratio) are given in Table IV. These parameters are related to the S^^'s displayed in the matrix equation:

^ij

=

1/E

11 ^21^^22

1/E

22

-^31 /^33 0 0 0

"^32'^^33 0 0 0

1/^33 0 0 0

1/G44 0 0

0

1/G

66

where the Poisson ratios are defined

v.. - -S VS.. (no sum)

and the S.. matrix is symmetrical about its main diagonal.

33
V. DISCUSSION

A. Symmetry

On the basis of its internal and external geometry, the composite

appears to be orthorhombic. If an object has three mutually perpendicular two-fold axes, then it belongs to the orthorhombic symmetry system.

These rotation axes are labeled x, y, and z in Figs. 1 and 2.

Other possible symmetry systems can be excluded. Triclinic has no

symmetry axis. Monoclinic has a single two-fold axis. Trigonal has a

single three-fold axis. Clearly, these three systems are less symmetrical than the composite.

Orthorhombic symmetry includes four other symmetry systems: tetragonal, hexagonal, cubic, and isotropic. Relationships among the C..'s

for these systems are listed in Table V together with tests of the relationships. Clearly, from Table V, none of the higher^ symmetry systems

can be used to describe exactly the observed C. .'s. But the deviations

are small for any of these four symmetry choices. Tetragonal

is a slightly better choice than hexagonal. The advantage of

describing an object by its highest symmetry is that there

are fewer independent elastic constants: six for tetragonal, five for

hexagonal, three for cubic, and two for isotropic. Thus, measurements

and calculations are simplified to various degrees. In Table IV, the

present orthorhombic results are also expressed in higher-symmetry

co-ordinates to facilitate comparisons with other studies. When

necessary, elastic constants were simply averaged.

B. Off-Diagonal Elastic Constants

The off-diagonal (i t ^) elastic constants are more difficult to

determine and almost always have higher uncertainties than

the diagonal ( i = j) elastic constants. This problem is reflected in

34

•I
the present study in Table I. The problem arises because the off-diagonal

elastic constants are not related simply to any pure mode of mechanical

deformation. This is best shown in the S.. matrix displayed in Eq. (11).

All the diagonal S..'s are related reciprocally to either a Young's modulus

or to a shear modulus. But all the off-diagonal terms are related to a

Young's modulus and a Poisson's ratio, which is in turn determined by

two other elastic constants, as shown in Eq. (12).

In the present study, another difficulty arose in determining the

off-diagonal elastic constants. As shown in Table I, different values

of the off-diagonal C^.j's were obtained depending on whether the observed

2 2 pv^ or the observed pv^ were substituted into the C^.j expressions given

in the table. For example, in the [Oil] direction the quasi-transverse

datum gave = 0.715 while the quasi-longitudinal datum gave =

1.041. The and C-j^ cases are similar. On the basis of small imprecisions of the measurements, and on the basis of the correctness of the

value of the third (pure shear) mode, it seemed that the off-diagonal terms

should be less uncertain than this and that one of the two values was

perhaps correct.

To resolve this uncertainty in the off-diagonal elastic constants, an

independent experiment was done. Some of the S. .'s were determined by a

resonance method. Dilatational and shear modes were measured on a cylindrical specimen with filaments along the cylinder axis. Results shown in

Table II for the torsional mode ^

(S^^ + S^g) agree exactly with the value

calculated from the C..'s. (The S..'s are computed from the C..'s by inverting the C. matrix.) Similarly, exact agreement is also obtained for the

dilatational mode, S^^j if the C^.j data from quasi-transverse modes rather

than quasi-longitudinal modes are used. Thus, it was concluded that the

quasi -transverse velocity data are both correct and consistent with other

35
data. However, the quasi-longitudinal wave velocities are low by about

five percent. This slowing can be interpreted as a longer path length in

the specimen due to interactions between the quasi -longitudinal waves and

internal boundaries due to the presence of filaments.

C. Comparison with Copper

It is useful to compare the elastic constants of the composite with

those of the matrix material, unalloyed copper,^ to determine

the effects of the filaments. Comparative data are shown in Table IV. Both

the Young's moduli and the shear moduli of the composite are about fifteen

percent lower than those of copper. The compressibility

K = i L S.. (13)

^ i,j = l,3 ,

of the composite is about five percent higher. The off -diagonal C^^'s

are identical to the value for copper, within one percent. This result

is quite unexpected. And it may be accidental since it has no obvious

physical interpretation.

D. Comparison with Previous Studies

The elastic constants of this composite were measured by Sun and

o Gray using static methods, assuming hexagonal symmetry. Their results

are shown in Table IV. Considering the higher inaccuracies usually associated with static methods, the agreement between the two sets of data is

good. The static Younq's and shear moduli are ud to nine oercent hiahpr

than the values reported here. The largest discrepancy is in and is

due probably to error accumulation in the computed static value. Possibly, the differences in the two data sets are real, but this cannot be

decided without knowing the uncertainties of the static values. A real

36
difference is, however, unlikely because, ignoring dispersion effects,

dynamic elastic moduli are almost always higher than static elastic

moduli, and the opposite effect is observed in this case.

E. Dispersion

No dispersion effects were observed, either in the limited 5-10

MHz region that was studied or in comparing the MHz pulse data with the 60 kHz

resonance data. By dispersion is meant the dependence of sound velocity on

frequency. Dispersive effects have been reported in many composite materials; they are usually due to either relaxation or resonance effects.

Their absence here is attributed to coherent interfaces between the filaments and the matrix and to the small difference in acoustic impedance

between the filaments and the matrix. Absence of dispersion is also consistent with the well-defined echo patterns that were obtained.

F. Relationship to Similar Composites

Elastic-property data have not been reported for NbTi/Cu composites

with different ratios of NbTi or with different thermal -mechanical treatments. The present data can be applied to other NbTi/Cu composites

through predictive schemes that relate the elastic constants of a composite to those of its components. Using the values of the NbTi elastic

g constants given by Sun and Gray and formulas summarized by them, it follows that the present material obeys approximately simple rules of mixtures.

Thus, similar composites would also be expected to follow these rules approximately. The present study is a useful guide to the elastic properties of

any NbTi/Cu composite, but it is a source of exact elastic data only for

the particular material studied. Even when the filament matrix volume

ratio is adjusted for, several other variables remain that can affect

elastic properties. These include: the state of mechanical deformation

37
(the number and distribution of lattice defects), composition of the NbTi

filaments, preferred orientations in either the filaments or the matrix,

and degree of coherency of the filament-matrix interfaces.

G. Low-Temperature Elastic Constants

Since this composite is intended for use as a superconductor, its lowtemperature elastic properties are important. Studies down to liquidhelium temperature are underway in our laboratory, and results will be

reported subsequently. Preliminary results are that the composite behaves

on cooling approximately like unalloyed copper. But the magnitudes of

the elastic constant changes are slightly different, and there are some

anomalous effects that are both reproducible and reversible.

38
VI. CONCLUSIONS

The chief conclusions of this study are:

(1) Ultrasonic (5-10 MHz) waves, both di 1 atational and shear, can

be propagated in an NbTi/Cu composite in directions parallel, perpendicular, and oblique to the filaments.

(2) Except as noted below, usual single-crystal elasticity techniques could be used to establish the complete set of elastic constants

of the composite.

(3) Longitudinal waves propagated obliquely to < 100 >directions had

velocites about five percent lower than expected. Obliquely propagated

shear waves traveled with their expected velocities.

(4) The studied composite has orthorhombic symmetry, and, therefore,

nine independent elastic constants. But the deviations from isotropy are

smal 1

.

(5) Compared to copper, the C.. (i = j) of the composite are lower

by about seven percent for C-j-j, 0^2 » and C^^* and by about fifteen percent for C^^, Cg^, and C^g. But the C^.j (i f j) are about the same. The

composite's compressibility is about five percent higher than copper's.

(6) The present dynamic results agree resonably well with existing

static measurements.

(7) Advantages of combining pulse-echo measurements and resonance

measurements were found.

(8) No dispersion, change of velocity with frequency, was observed.

ACKNOWLEDGMENT

This study was supported by the Advanced Research Projects Agency of

the U.S. Department of Defense. G. A. Miranda of Los Alamos kindly contributed a photomicrograph of the studied material. W. H. Gray of Oak Ridge

National Laboratory contributed a critical reading of the manuscript.

39
REFERENCES .

~

1. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon,

London, 1959), p. 104.

2. J. R. Neighbors and G. E. Schacher, J. Appl . Phys. 38, 5366-5375 (1967).

3. M. J. P. Musgrave, Crystal Acoustics (Holden-Day, San Francisco,

1970), p. 117-123.

4. A. D. Mclnturff and G. G. Chase, J. Appl. Phys. 44, 2378-2384 (1973).

5. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics 21,

246-249 (1974).

6. J. Marx, Rev. Sci. Instrum. 22, 503-509 (1951).

7. H. M. Ledbetter and E. R. Naimon, J. Phys. Chem. Ref. Data 3 897-

935 (1974).

8. C. T. Sun and W. H. Gray, Sixth Symp. Engnrng. Probs. Fusion Res.,

San Diego, CA, Nov. 1975. .

40
i/) __ rw\

/-\ EO I/)

s-O CVJ>

ill 0/ 1 ^ lU

ts •r- f—

4-> 1 ^ oWf-a

+->

O t/) Q. a E E O 0^

(Ju

03 Vii'

O Q-

•p— 1— D

O s- c c o 03 cu M- o

CO MC

+Jcoop

<o

'aj

(Us.3

-M

(tJ S-O)Q.E

O) •MI EOo c ? a;

(/) O) ao

•o

+-> oc

0)

s- . 3 +-> Q. X E OJ i

S- CM 0 E -O C ^ OJ Z 1/5 -M to C I— 3

Oru

SO on M- r-.,- 1 -a

<+-O 00c

1/1 o

-t-> CO

•I- rxj C O) 3 S- >S

O)

T3>o

CM >

Q.

CM >

Q.

0)E S- Oi <u 3 E

1/1 3 a

0)u

O)Q.

1/1

LO o o o O o o o o o o o o t—

J o o o + 1 + 1 " ^ + 1 ' " + 1 + 1 \^ LO LD

CO CO o CO o LO

CO CO 00 o CO

O 00 o

II oII o

II II II i

11

M II fp fT~II II II LO CM CO I • / ty^ \ J CO CM

LO CM oo CM f 1 f ^ (_)

O o C_)

LOLO

c^jt- cvf*^ r 1 t 1 1 1 CNJ LO

LO t "T + 1 T

OO OO C\J

C\J 1 + _1_ "P

CNJ • oo OO CVJ oo oo C\J o o 1CVJ 1

C\J

—

L—

J + 1 1 1 1 I -r 1 oo LD oo LO CM LO

oo LO oo LO CNJ LO O o + + + + + T

LO r—

C\J LO f \ C—3 — ' ' LO CM OO LO C\J CM C\J CM CNJ CNJ CM oo LO o o C_3 o o

oo 00 Q1 CO CD

(—% o O

OOO <^ <^ OO o o o o o o O o C) O O

00

CO CO

it ^<

v.—

o o o o o o o o o o O o o o o o o o o o o o o ' o o o o f—1

r— CM 00 LO LD CO CT>

O I— CM CO LO 00

41
Table II. Elastic compliances of an NbTi/Cu composite measured

-1 1 2 by a resonance method. Units are 10 m /N.

=ij

Observed Calculated from C.

.

s^33 0.873 + 0.009 0.878 + 0.073 from quasi-shear modes

(0.692 from quasi -longitudinal modes)

2.398 + 0.024 2.430 + 0.041

Table III. Room-temperature elastic stiffnesses C.

.

and elastic compliances S. . of an NbTi/Cu composite

'J 11 2

and copper. C.. units are 10 N/m ; S.. units are

-11 2

10 m /N. Values in parentheses are derived from

2^44 = - C^2 ^44 = 2(S^^ - 5^2)-

Composite Copper

ij So S. . ij

11 1 .834 0.924 2.006 0.780

22 1.878 0.894

33 1.880 0.879

44 0.416 2.404 0.477 2.096

55 0.407 2.457

66 0.414 2.415

12 1.056 -0.341 (1.052) (-0.268)

13 1.039 -0.322

23 1.041 -0.307

^ Ref. 7

42
Table IV. Practical elastic constants E = Young's modulus, G = shear modulus, v

= Poisson's ratio for NbTi/Cu composite in different co-ordinate systems at

1 1 2 room temperature. Units are 10 N/m , except v's, which are dimensionless.

Elastic Orthorhombic Tetragonal Hexagonal Isotropic Copper^ Static Results'

Constant Basis Basi

s

Basis Basis Values (Hexagonal Basis)

E^^ 1.082 1.100 1.100 1.112 1.282 1.22

E22 1.119

E33 1.138 1.138 1.138 1.1 9

G^^ 0.416 0.411 0.411 0.412 0.477 0.448

Ggg 0.414 0.414 (0.398)^ (0.431)

0.381 0.381 0.381 (0.415)^

0.365 0.357 0.357 0.347

Voo 0.349

^ Ref. 7

^ Ref. 8

Quantities in parentheses are derived from given data

using G,. = E,,/2(l + v,,).

43
Table V. Checks for various symmetries for NbTi/Cu composite. For hexagonal and

cubic cases, relationships (1), (2), and (3) also hold. For isotropic

case, all eight relationships must hold; either number (4) or (8) is

redundant.

Symmetry System Relationships Ratio of L.H.S./R.H.S. for NbTi/Cu

Tetragonal (1) Z,^^ = C^^ 1.024 + 0.020

(2) C55 = C44 \ 0.978 + 0.014

(3) = C^3 1.002 + 0.040

Hexagonal (4) Cgg = j

(C^^ - 0^2) ^-^^^ t 0-020

Cubic (5) C33 = C^^ ^ 1.025 + 0.007

(6) C^2 " ^13 ^-0^^ t 0-040

(7) Cgg = 1.017 + 0.018

Isotropic (8) C^4 = ^

(C^^ - 0^2^ ^-069 + 0.016

44
LIST OF FIGURES

Fig. 1. Schematic geometries of four pulse specimens. Filaments along

[001] are indicated by striping. The wave-propagation directions

(indicated by dashed lines) and displacement vectors are given

in Table I. The x, y, and z axes are equivalent to the [001],

[010], and [001] axes that are used in the text and tables.

Fig. 2. Photomicrograph showing distribution of filaments. Plane of

photo is perpendicular to filaments. Width shown corresponds

to 4.3 mm in specimen. Vertical direction is x = [100] and

horizontal direction is y = [010].

45
Fig. 1. Schematic geometries of four pulse specimens. Filaments along

[001] are indicated by striping. The wave-propagation directions

(indicated by dashed lines) and displacement vectors are given

in Table I. The x, y, and z axes are equivalent to the [001],

[010], and [001] axes that are used in the text and tables.

46
• 1

Fig. 2. Photomicrograph showing distribution of filaments. Plane of

photo is perpendicular to filaments. Width shown corresponds

to 4.3 mil in specimen. Vertical direction is x = [100] and

horizontal direction is y = [010].

47
TEMPERATURE DEPENDENCE OF THE ELASTIC CONSTANTS OF

AN NbTiVCu SUPERCONDUCTING COMPOSITE*

D. T. Read** and H. M. Ledbetter

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Low- temperature elastic properties are reported for a commercial

superconducting composite consisting of niobium-titanium filaments in

a copper matrix. Both an ultrasonic (10 MHz) pulse-superposition technique and a composite oscillator (100 kHz) technique were used. Seven

of the nine independent elastic constants of this material were determined between 76 and 300 K; and two, the Young's modulus along the filament axis and a shear modulus perpendicular to that axis, were determined

between 4 and 300 K. All these elastic-stiffness constants are about ten

percent lower than the corresponding values for copper. All increase

about ten percent on cooling from 300 to 4 K. And all have anomalous

temperature behavior.

Keywords: Bulk modulus; composite; compressibility; copper; cryogenic

tempeatures; elastic constants; niobium-titanium; Poisson's ratio; shear

modulus; superconductor; Young's modulus.

* Contribution of NBS, not subject to copyright.

**NRC-NBS Postdoctoral Research Associate, 1975-76.

48
INTRODUCTION

Superconducting composites consisting of niobium- titanium filaments in a copper matrix are now available commercially for applications in which high electrical -current density must be obtained in

high magnetic fields. Components containing these conductors are

designed critically. Elastic constants of such conductors are useful

for two reasons: for computing the recoverable deflections due to

applied loads, and for computing thermoelastic stresses due to either

temperature changes or differential thermal contractions. Also, elastic constants provide a valuable characterization of a material. For

composite materials, accurate elastic data provide key tests for theories

that relate macroscopic elastic properties to elastic properties of

constituents.

The particular NbTi/Cu composite reported on here has orthorhombic

symmetry, and the room- temperature values of all nine independent elastic constants, the C.'s, were reported previously.^ ' The temperature

dependencies to 77 K of seven of these nine were determined in the

present study: C^^, 0^2' ^33' ^55' ^66' ^33' ^/(S^^ + S^^), where

is Young's modulus along the filament axis and 2/(S^^ + S^^) is the

torsion modulus about that axis. Two elastic constants, E^^ cind Cgg,

were determined to 4 K. The temperature dependencies of the other

elastic constants, such as C12 and C-j^* were not determined because they

are not measured directly and they have larger errors. Symmetries

discussed here are strictly macroscopic. The filament direction of the

composite is designated [001], and the principal directions perpendicular

to the filaments are [100] and [010]. These directions are indicated in

Fig. 1.

49
EXPERIMENTAL -

; .

A. Material

Specimens were cut from a short section of Kryo 210* superconductor supplied by Magnetics Corporation of America. This is a coppermatrix, niobium-titanium-filament composite material. The Cu/NbTi

volume ratio is 6:1, and the bar contains 2640 filaments with a twist

pitch of 7.6 cm. The section obtained for this study was about 20 cm

long, 1.0 cm wide, and 0.5 cm thick. Four specimens were cut for ultrasonic pulse measurements, one with its surfaces perpendicular to the

symmetry axes of the material and three with their largest surface

oriented at 45° to two symmetry axes. Specimen geometries are shown in

Fig. 1. The material was studied in the as-received condition. The

thermal and mechanical treatments of such superconductors during manufacture were described by Mclnturff and Chase. The specimen with |lOO}

surfaces was 0.5 cm by 1.0 cm by 1.0 cm, while the three off-axis specimens had thicknesses of 5 mm, 3 mm, and 2 mm. All specimens were ground

sufficiently flat and parallel for ultrasonic study.

Two composite-oscillator specimens were prepared. These were

right-circular cylinders 4.8 mm in diameter and 3.1 and 1.9 cm long for

the extensional and torsional measurements, respectively.

* A trade name is used here to characterize the studied material. Its

use is not an NBS endorsement of a particular product.

50
B. Procedures

The room- temperature elastic constants of the specimens used in

this study were reported previously.^ The temperature dependence of

five of these constants, the elastic stiffnesses C-j-j, ^2.v ^33' ^55'

and Cgg, were measured using a pulse-superposition technique in which

the ratio of the ultrasonic velocity, v, at low temperatures to its

value at room temperature was measured every five degrees between room

temperature and the lowest temperature obtained during each cooling.

These ratios of sound velocities were used to calculate the temperature

2

dependence of the appropriate elastic constant, C, from C = pv where

p is the mass density of the specimen. Each sample was cooled by

enclosing it in a sample chamber and lowering it gradually into the

ullage of a dewar containing either liquid nitrogen or liquid helium.

3 The low- temperature apparatus and techniques were described previously.

The temperature dependencies of the Young's modulus and the torsional

modulus were measured using a composite-oscillator technique. Briefly,

the resonant frequency is measured of a composite oscillator consisting

of the specimen, a quartz-crystal driver, and a quartz-crystal gauge.

This composite oscillator is also cooled by putting it in a sample holder

and inserting the specimen end into the ullage of a dewar containing

either liquid nitrogen or liquid helium. The resonant frequency of

the specimen is calculated from the resonant frequency of the composite oscillator, the masses and geometries of the specimen and the sample,

and known properties of the gauge and quartz crystals. Froms its

resonant frequency, the elastic constant of the sample can be calculated easily. The apparatus and techniques used in such measurements

4 were described previously.

51
RESULTS .

-

The measured value of E^^ (Young's modulus along the filament

direction) for the NbTi/Cu composite is shown in Fig. 2. Young's

5 modulus, E, of polycrystal 1 ine copper is shown for comparison.

Young's modulus of the composite is about ten percent lower than that

of copper, and it rises with decreasing temperature to a value at 4 K

about ten percent above its room-temperature value. Irregularities

in the curve for the composite are not observed in copper, and they

are significant deviations from the temperature dependence of Young's

modulus for ordinary materials, of which copper is a good example.

The upturn in the curve below 20 K is believed to be a real effect.

The value of 2/(S^^ + S^^), the modulus of torsion about the fila

ment axis, is shown in Fig. 3. Shown also is the torsional or shear

modulus, G, of copper. It is clear that the temperature behavior of

2/(S^^ + Sgg) is dissimilar to the of E^-^j and that its approximate

relationship to the torsional modulus of copper is nearly the same as

the relationship of E^^ to the Young's modulus of copper. The dashed

part of the curve is an extrapolation based on the usual behavior of

elastic constants at low temperatures and the behavior of the elastic

constants of this composite that were measured to 4 K.

The Poisson ratios of this composite material that relate the

strain along the filament axis (produced by a stress along that axis)

to the strains perpendicular to the axis were found to be 0.366 and

0.349 along the x and y axes respectively at room temperature.^ The

temperature dependencies of these ratios are not easily measured by

dynamic techniques, and they were not measured in this study. However

since Poisson' s ratio for copper decreases by two percent on cooling

52
of the composite are intermediate between those of the two copper moduli.

Based on simple rule-of-mixture arguments it follows from Fig. 6 that

the shear modulus of NbTi must increase with temperature similar to copper, but the longitudinal modulus of NbTi must increase considerably

more than that of copper.

DISCUSSION

In a previous study J it was shown that the room- temperature magnitudes of the elastic constants of this composite can be predicted

approximately from a rule of mixtures from the known elastic constants

of copper and NbTi. It was also shown that the observed values of the

practical elastic constants E^^ and 2/(S^^ + S^^) were consistent with

the measured values of the elastic stiffnesses, the C..'s.

Rules of mixtures could not be used to predict the temperature

dependence of the composite material studied here because the temperature dependencies of the elastic constants of the niobium-titanium

alloy have not been reported. An attempt to obtain such data failed.

Weston^ reported the temperature dependencies of the elastic constants of an NbTiCu/fiberglass-epoxy coil composite. Although that

composite included fiberglass and epoxy, the temperature dependence of

its elastic constants reflects that of the NbTi/Cu part, because the

stiffness of the fiberglass-epoxy is low and it constitutes only about

one-fourth the total volume. The sign and magnitude of the temperature

dependencies observed by Weston were about the same as those observed

in the present study. For most of the elastic constants, Weston reported

very small deviations from the usual temperature behavior of ordinary

materials. But, in the Young's modulus along the filaments, Weston

found a large deviation from usual temperature behavior. However, none

53
of the elastic constants of the coil composite studied by Weston showed

the type of anomaly observed in the present study.

The observed increase in all the elastic stiffnesses of about ten

i

i percent on cooling from 295 K to 4 K is expected for this material.

i Elastic constants of most metals increase between five and fifteen per8

! cent on cooling to zero temperature; the polycrystal 1 ine longitudinal

modulus of copper increases four percent on cooling. Thus, the sign

and magnitude of the observed temperature dependencies of the elastic

constants of the NbTi/Cu composite studied here are not surprising.

As shown in Figs. 2-6, all the measured elastic constants reported

here have irregular temperature dependencies compared to copper.

Experimental evidence for these anomalies is strong: they occur in

seven different measured elastic constants; they were observed on measurements made during both heating and cooling; and they occurred in repeated

experiments. These anomalies are probably insignificant from the viewpoint of engineering design because they change the elastic constants

only a few percent from regular behavior scaled against copper. However, they indicate unexpected behavior of the composite.

The cause of these anomalies is uncertain. Two hypotheses can be

suggested. First, since elastic constants are changed by stress, the

anomalies may arise from internal -stress changes due to differential

thermal contraction during cooling. Second, the anomalies may arise

from similar anomalies in the temperature dependencies of the elastic

constants of the niobium-titanium filaments. Anomalies similar to those

observed here were reported in niobium and in other transition metals,

9 10 where they are ascribed to the electronic structure, ' and in a

niobium-zirconium alloy, where they are attributed to the formation of

omega phase.

54
from 300 to 4 K, a similar change would be expected for Poisson's

ratio of the composite.

Attention is now turned from the practical elastic constants to

the elastic-stiffness coefficients, the C^.j's. Although C-j^, £22^ were all measured, the data for 0^2 Pi^cictical ly coincide with those

for C^^j so only C-ji and C^^, normalized separately to their 300 K

values (given in Table I) are shown in Fig. 4 together with the longitudinal modulus, Cj^, of copper. The dashed curves are extrapolations.

Again, these elastic constants are about seven percent lower than those

of copper, and they increase about five percent on cooling. As in the

previous cases of the practical elastic constants, anomalous changes in

these elastic constants occur during cooling.

The temperature dependence of Cgg, normalized to 300 K, is shown

in Fig. 5. C^^ was measured between 300 and 76 K; the resulting data

nearly coincide with those for Cgg and they are not shown. C^^ and Cgg

for the composite material are about fourteen percent lower than the

value for copper, and they increase about ten percent on cooling.

They also exhibit anomalous temperature behavior. The data point shown

as an open square at 4 K in Fig. 5 represents an absolute, rather than a

relative, elastic-constant measurement; it confirms the overall elasticconstant change due to cooling.

and C^g, a longitudinal and a transverse stiffness of the composite material are shown in Fig. 6 together with and C^, the longitudinal and transverse moduli of polycrystal 1 ine copper. In both copper and the composite, the transverse (shear) moduli have stronger temperature dependencies than the longitudinal moduli. Surprisingly, the

temperature dependencies of both the transverse and longidutinal moduli

55
CONCLUSIONS

-

The following principal results and conclusions emerge from the

present study:

(1) The Young's modulus along the filaments, E^^* increases twelve

percent on cooling from 300 to 4 K, compared to eight percent for copper.

The extrapolated torsional modulus around the filaments, G , increases

II nine percent on cooling, the same as copper.

(2) The extrapolated elastic stiffnesses C-i-j, ^^2^ and increase

five percent on cooling, compared to four percent for copper.

(3) The shear elastic constants C^^ and Cg^ increase ten percent

on cooling, compared to nine percent for copper.

(4) All measured elastic constants are anomalous in their temperature dependencies.

ACKNOWLEDGMENT

This study was supported by the Advanced Research Projects Agency

of the U.S. Department of Defense.

56
REFERENCES

1. H. M. Ledbetter and D. T. Read, submitted for publication.

2. A. D. Mclnturff and G. G. Chase, J. Appl . Phys. 44, 2378-2384 (1973).

3. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics 14, 246-

249 (1974).

4. J. Marx, J. Sci. Instrum. 22, 503-509 (1951).

5. W. C. Overton and J. Gaffney, Phys. Rev. 98,969-977 (1955).

6. C. N. Reid, J. L. Routbort, and R. A. Maynard, J. Appl. Phys. 44,

1398-1399 (1973).

7. W. F. Weston, J. Appl. Phys. 46, 4458-4465 (1975).

8. R. F. S. Hearmon, in Numerical Data and Functional Relationships

in Science and Technology, Group III, Vol. I , K. H. Hellwege and

A. M. Hellwege, Eds. (Springer-Verlag, Berlin, 1969).

9. K. J. Carroll, J. Appl. Phys. 36, 3689-3690 (1965).

10. F. H. Featherston and J. R. Neighbors, Phys. Rev. 130, 1324-1333 (1963).

11. C. Goasdue, P. S. Ho, and S. L. Sass, Acta Met. 20, 725-733 (1972).

57
Table 1. Elastic constants of an NbTi/Cu composite and polycrystal 1 ine

1 1 2 copper at selected temperatures in units of 10 N/m , except V, which is dimensionless; numbers in parentheses

are based on extrapolated data.

300 K 200 K 100 K OK

NbTi/Cu Composite;

E-j, 1.138 1.189 1.238 1.287

33

G|| 0.417 0.427 0.445 (0.454)

v^^ 0.365

0.349

C^^ 1.834 1.865 1.908 (1.915)

C22 1-878 1.911 1.952 (1.957)

C33 1.880 1.919 1.965 (1.983)

C55 0.407 0.418 0.436 (0.442)

C.c 0.414 0.425 0.442 0.456

Do

Polycrystal 1 ine Copper^:

E 1.282 1.329 1.369 1.386

G 0.477 0.496 0.512 0.519

V 0.344 0.341 0.339 0.338

C^ 2.006 2.053 2.093 2.111

C^ 0.477 0.495 0.511 0.518

a Ref. 5, arithmetic average of Hashin-Shtrikman bounds.

58
LIST OF FIGURES

Fig. 1. Schematic geometries of four pulse specimens. Filaments along

[001] are indicated by striping. In specimen A, waves were

propagated along the [100], and [010] directions; in B along

[Oil]; in C along [101]; and in D along [110].

Fig. 2. Young's modulus of the composite along [001] compared to the

Young's modulus of polycrystal 1 ine copper.

Fig. 3. Shear, or torsional, modulus of the composite around the [001],

01- filament, axis compared to the shear modulus of polycrystal

line copper.

Fig. 4. Longitudinal elastic stiffnesses of the composite in the [100]

and [001] directions compared to the longitudinal elastic

modulus of polycrystal line copper.

Fig. 5. A shear modulus of the composite compared to that of polycrystal

line copper. Cgg corresponds to the shear resistance on a (100)

plane in a [010] direction, or vice versa.

Fig. 6. Comparison of a longitudinal and a shear elastic constant of

the composite. C^^ is measured in the [001] direction, along

the filament axis. C^g corresponds to the shear resistance on

a (100) plane in a [001] direction or of a (001) plane in a

[001] direction. Values for copper are shown for comparison.

59
Fig. 1. Schematic geometries of four pulse specimens. Filaments along [001] are indicated by striping. In specimen A, waves were propagated along the

[100], [010], and [001] directions; in B along [001]; in C along [lOlJ;

and in D along [110].

60
1.40

^

1.36

CM

O

CO

a

O

2

b

o

>-

1.32

1.28

1.24

1.20

1.16

1.12

-] 1

1 1 —1 '

1 r — 1 1 I

NbTi/Cu

E for

\ _ \

\

\

\ \

—

1

j 1 1 1 100 200 300

TEMPERATURE (K)

Fig. 2. Young's modulus of the composite along [001] compared to the Young's modulus

of polycrystal 1 ine copper.

61
o

CO

O

O

a:

<

LU

X

CO

4.6

4.5

4.4

4.3

4.2

4.1

4.0

NbTi/Cu

100

5.2

- 4.7

4.6

200 300

TEMPERATURE (K)

Fig. 3. Shear, or torsional, modulus of the composite around the [001], or filament,

axis compared to the shear modulus of polycrystal 1 ine copper.

62
<

UJ

u

(U

s. s_

01 T3 CL

Q. r—

1

oo O

0) i_i "Oc

to re

4-> r—

1

(/I O >, O s~

«J>,o

a.

-l-> C o

Ul

01

-t->

• r—

U1 •o O o

a.EO u

o

4-> to ^ (O

0)

l(-o

03

l/l c

UJ

t/5

1/1 3

01 l-> c

ll- 01

M- o

(->

1/1 u

+->

1-1 00 o

(T3 u

dJ -o

OJS10 <o c Q.E a o

3 u

-t-> 10 01 c

c o

o

_l

Ol

(S6Z)S/(i)0

63
LU

<

(U zz

>— <u 1— c

+-> 1—

01 Q.

• c

o o o

+Jo

Q. 0)

(0 s-

•r- o c T3 o

t-J 1—1

(O 0) o ^ (J o !-> C r—

U_l o +->

(-> 1/) CO

•r- TJ 1/1 C

01 0) •f— S- Sra <u E re O (1) ,—

o ^ Q.

(/I <u '—

o •r- x:

(/) +J o

Q. O

E -M <o o

<J (/> c o o

<u c

o S4-> Cl. o

I/) (f- at o s- c

s- o

</) o

3 O +-> o

(U T3 >£> S- O O

E "5

s_ • 1—

1

CO S- o 0) Ol x: Q. o 1/1 Q. 1 1 o

ITS

in

o>

Li-

{sezi'o/uf'o

64
65
Low-Temperature Elastic Properties of a 300-grade Maraging Steelt

H. M. Ledbetter and D. T. Read*

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Elastic properties of an annealed 300-grade maraging steel (18 Ni, 9

Co, 5 Mo percent by weight) were studied between room temperature

and liquid-helium temperature. Longitudinal and transverse ultrasonic

velocities were determined by a pulse method. The reported elastic

constants are: longitudinal modulus, shear modulus. Young's modulus,

bulk modulus, and Poisson's ratio. Except for the bulk modulus, the roomtemperature elastic constants are all lower than those of iron; and their

temperature dependencies are regular in the studied temperature region.

Key words: Bulk modulus; compressibility; iron alloy; maraging steel;

nickel alloy; Poisson ratio; shear modulus; sound velocity; Young's

modulus.

t Contribution of NBS, not subject to copyright.

* NRC-NBS Postdoctoral Research Associate, 1975-6.

66
INTRODUCTION

Elastic properties of a 300-grade maraging steel (18 Ni, 9 Co,

5 Mo) were studied between room temperature and liquid-helium temperature. Elastic constants were determined by measuring the velocities of

both longitudinal and transverse ultrasonic waves in a polycrystalline

aggregate. The following constants are reported here: C^ = longitudinal modulus, G = shear modulus, B = bulk modulus, E = Young's modulus,

and V = Poisson's ratio.

Maraging steels exhibit some of the best available combinations

of high strength and high toughness at room temperaturel Some alloy

steels with high nickel contents also have good toughness at cryogenic

temperatures. However, the usual heat treatment of maraging steels

would probably embrittle them at these temperatures. Thus, maraging

steels would probably be used at low temperatures in their annealed

conditions. An annealed 300-grade maraging steel was studied (300 indicates a yield stress of approximately 300 x 10^ psi). This alloy has a- body-centered-cubic crystal structure, and it is ferromagnetic at room temperature. Other grades of annealed maraging steels are expected to

be similar elastically because of their similar chemical compositions.

Elastic constants are interesting for two principal reasons. First,

elastic constants are related directly to interatomic forces; thus, they

are connected with a variety of solid-state phenomena, including maximum

attainable strengths, phase stabilities, and lattice specific heats.

Second, elastic constants are essential design parameters; the elastic

constants must be known to compute deflections due to applied loads or

stresses due to temperature changes of constrained components.

67
While some data on the temperature dependence of the Young's modulus

2

of a 250-grade maraging steel are available, data on the other elastic

constants (shear modulus, bulk modulus, Poisson's ratio) and on other

grades of maraging steel have not been reported. Furthermore, because

of the many elastic-constant anomalies exhibited by iron-nickel alloys

(both those with higher and lower nickel contents than maraging steels),

and because of the complicated chemistry of maraging steels, their elastic behavior cannot be estimated confidently by usual predictive methods.

Therefore, detailed experimental studies of the elastic behavior of these

alloys are required.

EXPERIMENTAL

Material

The studied material was obtained from a commercial source in the

form of a 10 X 23 x 108 cm ingot. The chemical (mill) analysis of the

material by weight is: 18.41 Ni , 9.27 Co, 4.95 Mo, 0.002 C, 0.12 Al

,

0.01 Mn, 0.006 P, 0.003 S, 0.01 Si, 0.59 Ti , balance Fe. The Rockwell

3

B hardness is 105, and the mass density is 8.188 g/cm as determined by

Archimedes's method using distilled water as a standard.

Room-Temperature Sound Velocities

Room- temperature sound velocities were measured by a pulse tech3

nique. Briefly, a quartz piezoelectric transducer with a fundamental

resonance frequency of 10 MHz was cemented with phenyl salycilate (salol)

to one end of a specimen having flat and parallel faces. The specimen

in this case was a 1.25 x 1.25 x 1.6 cm paral lelpiped with opposite faces

ground flat and parallel within 2.5 ym. Ultrasonic pulses about one ys

in duration were sent into the specimen by electrically exciting the

transducer. The pulses propagated through the specimen, reflected from

68
the end, and propagated back. The echoes were detected by the transducer

and displayed on an oscilloscope. The sound velocity was computed by

V = 2£/t (1)

where £ is the specimen length and t is the transit (round-trip) time.

On the oscilloscope, t was the time between subsequent echoes. The oscilloscope was calibrated against a precision time-mark generator. An x-cut

quartz transducer was used for longitudinal waves, and an ac-cut quartz

transducer was used for transverse waves.

Low-Temperature Sound Velocities

Low-temperature measurements of the sound velocities were made by a

4 pulse-superposition technique. Briefly, the repetition rate of the

pulse was increased so that each pulse coincided with the second echo

of the preceding pulse. Since the excitation voltage was large compared

with the echo voltages, the oscilloscope display consisted of alternating

pulses of excitation voltages and "echo" voltages where the "echo" voltage represented the sum of all odd-numbered echoes of the non-superimposed

case. Because of interference effects, the envelope of the summed oddnumbered echoes is highly sensitive to small changes in the ultrasonic

velocity that are caused, in this case, by cooling.

The transducer-specimen bonding material was a stopcock grease. Temperatures were monitored with a chrome! -constantan thermocouple placed

near the specimen. Cooling rates were about 2 K/min. The specimen holder

5 was described previously. Cooling was achieved by lowering the specimenholder assembly stepwise into the ullage of a helium dewar. No thermal

contraction corrections were made. For this alloy, the maximum thermal

69
contraction correction to the elastic constant, which applies at T

=

0 K, is 0.3 percent. No correction was made for the transducer-cementcoupling phase shift; the McSkimin^ analysis gives a correction of less

than 0.5 percent in the velocity, assuming a maximum phase shift of tt.

The transit time was corrected to allow for the thickness of the transducer; this correction is approximately one cycle at 10 MHz; thus, the

observed longitudinal -wave and transverse-wave transit times were

reduced about 1.0 and 0.5 percent, respectively.

RESULTS

Room-temperature sound velocities are given in Table 1. Velocities

were measured in three orthogonal directions for three orthogonal

polarizations. The experimental uncertainties in these velocities are

estimated to be 0.5%.

Longitudinal and shear elastic constants were computed from the

velocities according to

and

G = = pv^ (3)

where p is the mass density. The uncertainty of these elastic constants

is estimated to be 1%.

The temperature variations of C,^ and are shown in Figs. 1 and 2.

Curves in those figures are least-squares fits of the data to the Varshni

relationship:

exp(t/T) - 1

70
where C is or C^, C°, s, and t are adjustable parameters, and T is

temperature. The value of C at T = 0 K is C°, and -s/t is the hightemperature limit of the temperature derivative dC/dT. By invoking an

Einstein oscillator model, it can be shown that t is the Einstein temperature. Parameters C°, s, and t are given in Table II. Average

differences between measured and curve values are 0.04 and 0.05 percent

for the longitudinal and transverse cases, respectively.

Temperature variations of Young's modulus, the bulk modulus, and

Poisson's ratio are shown in Figs. 3-5. These elastic constants were

computed from Eq. (4) and the parameters in Table II using the relationships

B = - (4/3)G (5)

E = 9GB/(G + 38) (6)

and

V = (E/2G) - 1 (7)

The experimental uncertainties of these elastic constants are estimated to

be ± ^7o. Values of these elastic constants at selected temperatures are

given in Table III, and temperature coefficients of the elastic constants

are given in Table IV.

DISCUSSION

The present study is discussed in two parts: the room-temperature

elastic constants and the changes of the elastic constants due to cooling

to liquid-helium temperature.

As shown in Table III, the Young's and shear moduli of the steel are about twenty percent lower than those of unalloyed iron, the bulk modulus

71
is about the same, and Poisson's ratio is about ten percent higher.

Usually, the elastic-stiffness constants of alloys are lower than those

of their base metal. Two of the three principal alloying

11 12

elements in the steel -- nickel and molybdenum -- lower the elastic

stiffnesses of iron, while cobalt raises them.

Nickel has the largest effect of the three. Thus, it is

appropriate to compare the elastic constants of the steel with those of

the corresponding iron-nickel alloy, and this is done in Table III.

Except for the bulk modulus, the elastic constants of the steel are very

close to those of an iron-18 nickel alloy. Cobalt and molybdenum seem

to have very little effect on Young's modulus, the shear modulus, and

Poisson's ratio, that is, on elastic constants that are determined either

entirely or largely by the resistance of a material to shear deformations.

The bulk modulus is determined by the resistance of a material to

dilatational deformations, and it is surprising that the bulk moduli of

the steel and of unalloyed iron are the same. There appears to be no

simple explanation for the unexpectedly high bulk modulus of the maraging

steel. The usual effects of alloying are that the bulk modulus changes

approximately in the same way as Young's modulus and the shear modulus.

However, there is no a priori requirement that the bulk and shear moduli

change similarly, and the present case is an interesting departure from

usual behavior. Possible explanations for this effect may lie in the

high bulk modulus of molybdenum, which is fifty percent higher than that

of iron. Of all the elastic constants, the bulk modulus would be

13

expected to come closest to a Vegard-law type behavior because it is

the most structure-independent elastic constant, depending much more on

atomic volume than on other factors. Also, the bulk modulus is the elastic constant least affected by the usual magnetic energies that contribute

to the elastic constants of iron-base alloys.

72
As shown in the figures, the temperature behavior of the elastic

constants of maraging steel is quite regular; that is, qualitatively

the same as that exhibited by almost all simple metals and alloys. The

salient features of regular behavior are: zero slope at zero temperature,

as required by the third law of thermodynamics, continuous decrease with

increasing temperature, consistent with the softening of interatomic

bonding forces due to increased thermal vibrations; and a linear slope

at high temperatures.

The regular temperature behavior of the maraging steel is

unexpected. While no low- temperature elastic constants have been reported

previously for body-centered-cubic iron alloys with so high a nickel

content, some data exist for lower nickel content alloys. Weston,

Naimon, and Ledbetter^^ reported the low- temperature elastic constants

of iron-nickel alloys containing 3.5, 5, 6, and 9 percent nickel. These

alloys show regular behavior above about 40 K, but are anomalous at

lower temperatures. The anomalies are due, presumably, to magnetic transitions. But the maraging steel shows no such behavior. It is well known

that iron-nickel alloys containing more than about 30 percent nickel are

face-centered cubic and have very large anomalies in their elastic constants between room temperature and liquid-helium temperature. These

1

5

anomalies are also due to magnetic effects.

The maraging steel has considerably higher temperature coefficients

of Young's modulus and the shear modulus than unalloyed iron, as shown

in Table IV. This suggests that the steel has a considerably lower

Debye temperature than iron, consistent with the Debye temperatures reported for b.c.c. iron-nickel alloys by Weston, Naimon, and

Ledbetter.^^ Practically, this means the elastic stiffness of the steel,

upon cooling, increases more than in the case of iron.

73
CONCLUSIONS

In the present study, several conclusions were reached concerning

the elastic properties of annealed 300-grade maraging steel:

1. The Young's modulus, shear modulus, and Poisson's ratio are

all about 15 percent lower than the corresponding elastic constants of

unalloyed iron. The bulk modulus is the same as that of iron.

2. Except for the bulk modulus, all the elastic constants are

essentially the same as those of an iron-18 nickel alloy, implying that

the effects of cobalt and molybdenum on the elastic constants are

effectively canceled.

3. All the elastic constants show regular behavior over the entire

studied temperature range, 4-300 K, indicating the absence of magnetic

transitions that have been reported at low temperatures in other bodycentered-cubic iron-nickel alloys.

4. Temperature coefficients of Young's modulus and the shear

modulus are about 40 percent higher than those of unalloyed iron. This

implies a lower Debye temperature for the steel.

ACKNOWLEDGMENT

This study was supported by the Advanced Research Projects Agency

of the U.S. Department of Defense.

74
REFERENCES

1. A Maynde, J. M. Drapier, J. Dumont, D. Coutsouradi s and L.

Habraken: Cobalt - Containing High-Strength Steels , 1974, p. 50,

Centre D' Information Du Cobalt, Brussels.

2. F. R. Schwartzberg, S. H. Osgood, and R. Herzog: Cryogenic Materials

Data Handbook , 1968, U.S. Air Force Systems Command (Tech. Doc. Rpt.

No. AFML-TDR-64-280).

3. R. T. Beyer and S. V. Letcher: Physical Ultrasonics , 1969, pp. 79-87,

Academic, New York.

4. H. J. McSkimin: J. Acoust. Soc. Amer. , 1961, Vol. 33, pp. 12-16.

5. E. R. Naimon, W. F. Weston, and H. M. Ledbetter: Cryogenics , 1974,

Vol. 14, pp. 246-49.

6. H. J. McSkimin: IRE Trans. Ultrasonics Engr. , 1957, Vol. 5, pp. 25-43.

7. Y. P. Varshni: Phys. Rev. , 1970, Vol. 2, pp. 3952-3955.

8. J. A. Rayne and B. S. Chandrasekhar : Phys. Rev. , 1961, Vol. 122,

pp. 1714-1716.

9. H. M. Ledbetter and R. P. Reed: J. Phys. Chem. Ref. Data , 1974,

Vol. 2, pp. 531-618.

10. W. F. Weston, E. R. Naimon, and H. M. Ledbetter: in Properties of

Materials for Liquefied Natural Gas Tankage , ASTM STP 579 , 1975,

pp. 397-420, Amer. Soc. Test. Mater., Philadelphia.

11. W. C. Leslie: Metall. Trans., 1972, Vol. 3, pp. 5-26.

12. S. Takeuchi: J. Phys. Soc. Japan, 1969, Vol. 27, pp. 929-940.

13. N. F. Mott: Rep. Prog. Phys., 1962, Vol. 25, pp. 218-243.

14. W. F. Brown: Phys. Rev., 1936, Vol. 50, pp. 1165-1172.

15. G. Hausch: Phys. Status Solidi., 1973, Vol. 15, pp. 501-510.

75
Table I. Room-temperature acoustic-wave velocities

, in units of 10^ cm/s

Propagation v, v. v Direction ^ ^1 ^2

X. , 0.5673 0.2882 0.2879

y 0.5648 0.2881 0.2865

2 0.5589 0.2848 0.2841

Table II. Parameters determined from

the Varshni equation

Longitudinal Transverse

C°, 10^^ N/m^ 2.654 0.7047

s, 10^^ N/m^ 0.1036 0.05959

t, K 221.9 264.4

76
Table III. Elastic constants of a 300-grade maraging steel at selected

temperatures and those of iron and iron-18 nickel at room temperature in units of 10^^ N/m2 except v, which is dimensionless

.

Material Temp. (K) E G B V

Maraging steel

,

300 1 ,756 0. 663

-1

1 .676 0. 325

300-grade

L. U U 1 1 806 ^ \J \j 0. 683 1 .692 0. 322

100 1 ,848 0.,700 1 .708 0.,320

0 1 .859 0,,705 1 .714 0.,319

Iron^ 300 2 .140 0..831 1 .680 0,,288

Iron-18 Ni^ 300 1 .710 0,.653 1 .463 0..309

a. Ref. 8

b. Ref. 9, 10

Table IV. Temperature coefficients (l/C)(dC/dT} at room temperature in units of 10"^ K*'.

Materi al E G B

Maraging steel -2.92 -3.18 -0.98 1 .04

2 Unalloyed iron -2.11 -2.31 -0.90 0.95

a. Computed from data in Ref. 8 using a Voigt-ReussHill arithmetic average.

77
LIST OF FIGURES

2

Fig. 1. Longitudinal modulus = pv^^ for 300-grade maraging steel

as a function of temperature.

2

Fig. 2. Shear modulus G = = pv^ for 300-grade maraging steel.

Fig. 3. Young's modulus for 300-grade maraging steel.

Fig. 4. Bulk modulus for 300-grade maraging steel.

Fig. 5. Poisson's ratio for 300-grade maraging steel.

78
79
0.710

0.660 ' ' ' ^ ^ ' ' 0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 2. Shear modulus G = C = pv for 300-grade maraging steel.

80
0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 3. Young's rodulus for 300-grade r.araging steel.

81
0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 4. Bulk modulus for 300-grade maraging steel.

82
0.328

0.326 -

0.324 -

0.322

0.320 -

0.318

0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 5. Poisson's ratio for 300-grade maraging steel.

83
Low-Temperature Elastic Properties of a Precipitation-Hardened Copper Alloy*

H. M. Ledbetter

Cryogenics Div., Institute for Basic Standards, NBS, Boulder, CO 80302

ABSTRACT

Elastic properties of a copper-cadi um-chromi urn precipitationhardened alloy differ considerably from those of copper. The shear

modulus of the alloy is higher than copper's while the bulk modulus

is lower. The temperature behavior of the alloy's elastic constants

is regular. Despite different second-order elastic constants, the

temperature derivatives of the elastic constants are similar to those

of copper. The alloy's Debye temperature is seven percent higher

than copper's.

Key words: Bulk modulus; compressibility; copper alloy; Debye temperature; elastic constants; Poisson's ratio; shear modulus; sound velocity;

Young' s modulus.

* Contribution of NBS, not subject to copyright.

84
INTRODUCTION

Precipitation is a principal hardening-and-strengthening mechanism

in metals and alloys. Precipitates can significantly raise a material's

yield strength by pinning the dislocations that initiate plastic flow.

Because precipitates occupy a small volume fraction, they usually have

little effect on most physical properties, including the elastic constants.

Ledbetter^ reported recently that a precipitation-hardened copper0.3 cadmium-0.3 chromium alloy has elastic constants that differ about

fifteen percent from copper's. Such large elastic-constant changes in

such a dilute alloy are unusual, but not necessarily anomalous. The

alloy is^ anomalous because its shear modulus is higher than copper's

while its bulk modulus is lower. Most elastic-constant models predict

that the shear and bulk moduli always change in the same direction when

affected by metallurgical variables such as composition, temperature,

or pressure. Usually, only variables that introduce anisotropies --

mechanical deformation or structural phase transformation, for example --

are expected to change the shear and bulk moduli oppositely. But

there are no such anisotropies in a precipitation-hardened alloy;

precipitates are usually equiaxed, and no macroscopic elastic anisotropy was detected in the studied alloy.

Deviation of the Cu-Cd-Cr alloy's Poisson ratio from that of copper

also represents a significant departure from usual behavior. Kdster

2

and Franz pointed out that Poisson' s ratio is quite insensitive to most

metallurgical variables, including alloying. The reason for this is

simple. Poisson' s ratio, v, is given by

85
V

= 1 3B - 2G

2 3B + G

^

' ^

where B and G denote the bulk and shear moduli, respectively. By

di fferentiation

dv ^ 9GB ,dB dGx

V (G + 3B) (3B - 2G) ^ B

" G^

^'^^

which gives for v - 1/3, a typical value for metals, including copper.

dy 4 /dB dGx

V

"

9

^ B

" G^

Thus, the usually parallel changes in B and G tend to cancel and leave

V unaffected. But opposite changes in B and G affect v additively.

Thus, the precipitation-hardened Cu-Cd-Cr alloy is an exceptional case

where a large change in v can occur in a macroscopical ly isotropic

material.

The low- temperature elastic constants of this alloy are of interest

for two reasons. First, how do the alloy's temperature coefficients

compare with copper's? Second, what are the alloy's low-temperature

elastic constants, which are needed for the cryogenic engineering

applications of this material. Because the room-temperature elastic

constants are anomalous, no basis exists for scaling the alloy's temperature dependence against copper's temperature dependence. And there

is neither a model nor a data base for estimating the alloy's lowtemperature elastic constants. In fact, very few low- temperature

elastic-property studies have been reported for precipitation-hardened

materials.

86
The main purpose here is to report the elastic constants of a

precipitation-hardened Cu-Cd-Cr alloy between room temperature and

liquid-helium temperature. Tvjo experimental methods were used:

resonance (60 kHz) and pulse (10 MHz). For most purposes, the differences

between the dynamic elastic constants reported here and the more familiar

static elastic constants determined by stress-strain methods are small;

for the shear modulus they are zero at all temperatures; for dilatationtype elastic constants such as the bulk modulus, they are zero at zero

temperature, and they increase to a few percent at room temperature.

EXPERIMENTAL

A. Material

The studied material is the same as that reported on previously"',

and it is characterized as follows: The weight-percent chemical composition is: 0.31 Cd, 0.33 Or, < 0.01 Pb, < 0.01 Fe, < 0.01 Ni, < 0.01 Mn

,

balance Cu. Mass density determined by hydrostatic weighing is 8.94

3 g/cm . Hardness is 57.5 on a Rockwell 30-T scale. ASTM grain size

number is five. The material was produced by the Phelps Dodge Corporation in the form of a flat extrusion 2.5 cm x 10.8 cm in cross-section.

The extrusion temperature was 1227 K and the subsequent aging temperature was 866 K for 1 h. The commercial designation of this material is

alloy PD 135. (This trade name is used here to identify the material;

it is not an NBS endorsement of a particular product).

B. Specimens

For ultrasonic-pulse measurements, a "cube" was prepared measuring 0.9 X 1.3 X 1.3 cm. Opposite faces were ground flat and parallel

within 3 urn. For torsional resonance measurements, cylindrical specimens were prepared 0.4 cm in diameter and 2.1 cm long. '

87
C. Methods

Experimental methods used in the present study were described pre3 4 viously '

. Thus, only a brief outline is given here.

5 Room- temperature pulse measurements were made using McSkimin's

method. A quartz transducer with a fundamental frequency between 6 and

10 MHz was bonded to a specimen with salol. X-cut transducers were

used for longitudinal waves and ac-cut transducers were used for shear

waves. The pulse length was about one ys. The ultra-sound velocity

was computed from

V = 2£/t (4)

where ^ = specimen length and t = transit (round-trip) time. On an oscilloscope, t was the time between subsequent echoes. The oscilloscope was

calibrated with a precision time-mark generator. Elastic constants are

computed from the velocities by

C = pv^ , (5)

where p = mass density.

Low- temperature pulse measurements were made with a superposition

5 method where the envelope of the sum of the odd-numbered echoes is

maximized by tuning the carrier frequency, f. Neglecting thermal contraction, the change in ultrasonic velocity is

Av/v = Af/f (6)

88
Details of the specimen holder, cooling procedures, and temperature

3

measurements were given previously. Measurements were made at

intervals of 5 K with a cooling rate of about 2 K/min.

The torsional (shear) modulus was also measured with a compositeoscillator method^ during cooling. The oscillator has three components:

a quartz-crystal driver, a quartz-crystal gage, and a specimen. The

resonant frequency of the specimen is

where m = mass, r = radius of cylindrical specimen, and the subscripts

s, 0, and q denote specimen, oscillator, and quartz. For torsional

resonance, the shear modulus is then

where Z = length. During cooling, the frequency f^ is tuned to the

resonance condition, which is determined by a maximum output voltage

across a gage crystal.

Results of the present study are shown in Table 1 and in Figs. 1-5.

Both the C-| and the G = data were least-squares fitted to a relationship due to Varshni^:

^= f 1+ (f n- f^)(m /m )(r /r )^

s 0 ^ 0 q'^^ q' s^^ q s^ (7)

? 7 G = 401 f ft

s s (8)

RESULTS

C(T) = C° - s/[exp(t/T) - 1] (9)

89
where C°, s, and t are adjustable parameters and T is temperature.

The fitting-parameter values are given in Table 2. Average

differences between measured and curve values are 0.07 and 0.06 percent

for the longitudinal and transverse cases, respectively. The elastic

constants B, E, and v were computed from the smoothed results of Eq. (9)

and the relationships :

B = - (4/3)G (10)

E = 9GB/(G + 3B) (11)

and / ,

V = (E/2G) - 1

^"^ (12)

Temperature coefficients of the elastic constants are given in Table 3.

Point-to-point 2a imprecisions in the modulus-temperature data are

estimated to be less than 0.1 percent. Uncertainties in the roomtemperature experimental moduli are given in Table 1. No significant

elastic-constant anisotropy was detected. Resonance results for the

shear modulus agreed exactly with pulse results, and they are not

reported here.

DISCUSSION

The temperature dependencies of the elastic constants of PD 135

o resemble closely those of unalloyed copper, as shown in Figs. 1-5.

Both materials exhibit regular behavior: linearity at high temperatures,

continuously decreasing slope due to cooling, relative flatness at low

90
temperatures, and zero slope at zero temperature in accordance with

9

the third law of thermodynamics. Hiki, Thomas, and Granato showed

that the temperature derivatives dC/dT depend on elastic constants of

second, third, and fourth order. Thus, second-order elastic constants

(which are reported here) of two materials can differ considerably,

but their temperature derivatives dC/dT can be similar.

The Debye temperature 0 is of considerable interest in a variety

of applications, especially at cryogenic temperatures. It can be computed from the elastic constants by

^ k MttVJ ^m

a

where h = Planck's constant, k = Boltzmann's constant, N = Avogadro's

number, = atomic volume, and the mean acoustic-wave velocity is

a

\' - 1

(^^' ' ) (14)

Using elastic data extrapolated to T = 0 K, the Debye 0 of the Cu-Cd-Cr

alloy is 369 K; for copper, 0 = 344 K. The higher Debye 0 of the alloy

follows directly from its higher shear modulus.

CONCLUSIONS

The following principal results and conclusions emerge from the

91
present study:

(1) All the elastic constants of the studied Cu-Cd-Cr precipitationhardened alloy behave regularly during cooling from room temperature to liquid-helium temperature.

(2) Despite the differences in the elastic constants of Cu-CdCr and Cu, the constants change similarly during cooling. This would be

expected if the third-order and fourth-order elastic constants of the

two materials were similar.

(3) The Debye temperature of the Cu-Cd-Cr alloy is seven percent

higher than that of copper, reflecting the higher elastic shear modulus

of the al loy.

ACKNOWLEDGMENTS

This work was supported by the Advanced Research Projects Agency

of the U.S. Department of Defense. The PD 135 alloy was originally

supplied by B. H. Wilson of the Phelps Dodge Copper Products Co. to Dr.

J. M. Wells of the Westinghouse Research Laboratories who provided the

material and its characterization to NBS.

REFERENCES

1. H. M. Ledbetter, submitted for publication.

2. W. Koster and H. Franz, Met. Rev. 6, 1-55 (1961).

3. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics 2i,

246-249 (1974).

4. W. F. Weston, J. Appl . Phys. 46, 4458-4465 (1975).

5. H. J. McSkimin, IRE Trans. Ultrasonics Engr. 5, 25-43 (1957).

6. J. Marx, Rev. Sci. Instrum. 22, 503-509 (1951).

7. Y. P. Varshni, Phys. Rev. 2, 3952-3955 (1970).

8. W. C. Overton and J. Gaffney, Phys. Rev. 98, 969-977 (1955).

9. Y. Hiki, J. F. Thomas, and A. V. Granato, Phys. Rev. 153, 764-771

(1967).

92
Table 1. Elastic constants of a precipitation-hardened

copper-chromium-cadi urn alloy (PD 135) at selected temperatures. C-| = longitudinal modulus, = transverse

modulus, G = shear modulus, E = Young's modulus, B = bulk

1 1 2 modulus, and v = Poisson's ratio. Units are 10 N/m , except V, which is dimensionless. C-j and are the

measured quantities, and their standard deviations are 0.009 and 0.014 based on 12 and 10 measurements, respectively.

T, K ^1 G=C, E B V

300 1.876 0.540 1.402 1.154 0.298

250 1.894 0.550 1.424 1.161 0.296

200 1.913 0.558 1.445 1.169 0.294

150 1.931 0.566 1.464 1.176 0.293

100 1.948 0.573 1.479 1.184 0.292

76 1.953 0.575 1.484 1.188 0.292

4 1.960 0.576 1.487 1.192 0.292

Table 2. Fitting parameters for the Varshni

relationship, Eq. (9).

Longitudinal Transverse

1 1 ? C°, lO" N/m'^ 1. 960 0. 576

s, lO^^N/m^ 0. 0873 0. 0652

t, K 211. 1 313. 0

93
Table 3. Temperature derivatives (1/C) (dC/dT) of the

elastic constants C at room temperature, in units of

10"^ K'^

Cu-Cd-Cr -1.24 -3.20 -3.51 1.34

(PD 135) ,

Copper^ -1.02 -3.31 -3.70 0.85

a. Reference 8 '

LIST OF FIGURES > u

Fig. 1. Temperature dependence of the longitudinal modulus of a

copper-based, cadmium-chromium, precipitation-hardened

alloy (PD 135) compared to that of copper. The longitudinal modulus is defined in terms of the bulk and shear

modulus in Eq. (10). The copper values are higher.

o Copper values were obtained from Overton and Gaffney

using a Voigt-Reuss-Hill averaging method.

Fig. 2. Temperature dependence of the shear, or transverse modulus

of copper alloy PD 135. The copper values are lower.

Fig. 3. Temperature dependence of the Young's modulus of copper

alloy PD 135.

Fig. 4. Temperature dependence of the bulk modulus, or reciprocal

compressibility of copper alloy PD 135. Note that copper

values are higher. Compare with the shear modulus shown

in Fig. 2 where they are lower.

Fig. 5. Temperature dependence of the Poisson's ratio of copper

alloy PD 135. The relatively large difference between

this alloy and copper results because B and G are

affected oppositely by precipitation-hardening.

94
CM

g 1.98

S 1.96 ET-—

CD

I uI

1.94 -

1.92 -

2.12

CM—

E

2.10 ^

2.08 3

--2.06

2.04

--2.02

250 300

H2.00

C9

TEMPERATURE (K)

Temperature dependence of the longitudinal modulus of a copper-based, cadmiumchromium, precipitation-hardened alloy (PD 135) compared to that of copper.

The longitudinal modulus is defined in terms of the bulk and shear modulus in

Eq. (10). Note copper values are higher.

95
0.59 i i

y 1 1 T 0.53

Q 53 I I I I I I I 0.47

0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 2. Temperature dependence of the shear, or transverse»modul us of copper alloy

PD 135. Note that copper values are lower.

96
TEMPERATURE (K)

3. Temperature dependence of the Young's modulus of copper alloy PD 135

97
1.43

CM

E 1.20 —

CO

m

o

3

o

- 1.40

- 1.42

^

E

- 1.39

- 1.38

1.37

CO

TEMPERATURE (K)

Fig. 4. Temperature dependence of the bulk modulus, or reciprocal compressi bi 1 i ty> of

copper alloy PD 135. Note that copper values are higher. Compare with the

shear modulus shown in Fig. 2 where they are lower.

98
0.302

0.300

0.298

0.296 -

0.294 -

1

1 1 r — 1 1 1 1

/ y

/

/ // / / y / ^ /

^ ^XCu-Cd-Cr

1 1 1 1 1

0.292

=

0.290

0.348

0.346

0.344

0.342

0.340

0.338

0.336

50 100 150 200 250 300

TEMPERATURE (K)

Fig. 5. Temperature dependence of the Poisson's ratio of copper alloy PD 135. The

relatively large difference between the alloy and copper is due to B and G being affected oppositely by precipitation-hardening.

99
Elastic Properties of a Boron-Aluminum

Composite at Low Temperatures+

D. T. Read* and H. M. Ledbetter

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Elastic properties of a boron-filament-reinforced, aluminum-matrix

composite were studied experimentally. Assuming transverse-isotropic

elastic symmetry, five independent elastic constants were measured

using a piezoelectric composite-oscillator method. Two constants --

Young's modulus along the filament axis and the torsional modulus

perpendicular to the filament axis -- were determined between 300 and 4

K, The composite's elastic constants are between boron's and aluminum's,

and closer to aluminum's. Along the filament axis. Young's modulus is

2.30 X 10^^ N/m^. Cooling from 300 to 4 K increases all the elastic

stiffnesses up to eleven percent.

Key words: Aluminum; boron; boron-aluminum; bulk modulus; composite;

compressibility; elastic constants; resonance method; shear modulus;

torsional modulus; Young's modulus.

+ Contribution of NBS, not subject to copyright.

* NRC-NBS Postdoctoral Research Associate, 1975-76.

100
INTRODUCTION

Boron-aluminum composites are useful because they have high elasticmodulus/density ratios (specific modulus) and high strength/density

ratios (specific strength). These properties, together with comparatively

high electrical conductivity, make boron-aluminum a candidate material

for various structural applications: aerospace components; leisure

products such as tennis rackets, bicycle frames, and golf shafts;

orthotic and prosthetic devices; truck bodies; etc.

Elastic constants are important parameters in designing such

components because they relate the mechanical load on a component to

its resulting deflection. Elastic constants are also related to the

basic structure of a material, to ultimate strengths, to melting points,

and to phase stabilities. In a composite, elastic constants are due to

both constituent properties and constituent interactions. Thus,

besides describing the average stress-strain response of the composite,

elastic constants provide tests of the mechanical and geometrical

relationships between composite properties and constituent properties and

a basis for improved material development.

EXPERIMENTAL

The studied boron-aluminum composite consisted of 0.14 mm (5.6 x

10 in)-diameter, uniaxial boron filaments in a matrix of aluminum

alloy 6061. The aluminum alloy was in the F-tempered condition (as

diffusion bonded). The composite, containing 48 percent filaments by

volume, was fabricated as a plate measuring about 10 x 10 x 1.1 cm.

The plate contained about 70 plies (as computed from an average ply

thickness of 0.165 mm found by Kasen and Schramm^ for a fifteen-ply

sheet of the same material). This unusually thick composite was required

for the elastic-constant measurements described below.

101
Elastic constants were measured by dynamic techniques. Such

techniques have been used in our laboratory to obtain accurate values

of complete sets of elastic constants of many polycrystal 1 ine materials,

and to measure elastic-constant temperature dependencies between 300

and 4 K. There are two main dynamic techniques: pulse and resonance;

each has many variations. ^ ^

In the present study, a three-component composite-oscillator

2 resonance technique was used principally. A composite oscillator

(consisting of a quartz-crystal driver, an identical quartz gagecrystal, and a specimen) was resonated by applying a sinusoidal voltage

to electrodes plated on the drive crystal. The 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 quartzcrystals' mass, the quartz-crystals' 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, E, of the specimen was

measured. Quartz crystals driven in torsional oscillation were used to

measure the torsional (or shear) modulus, G.

Elastic constants at low temperatures were measured by enclosing

the composite oscillator in a vacuum-tight container and lowering it

gradually into a dewar containing liquid helium. As the composite

oscillator cooled (about 2 K/min), its resonant frequency was measured.

The oscillator temperature was monitored with a thermocouple. Data

were obtained between 300 and 4 K using this technique, which was

102
described previously in more detail.

ANISOTROPIC ELASTICITY

A boron-aluminum composite is macroscopical ly elastically anisotropic because the filaments affect the elastic modulus more strongly

along the filament direction than in other directions. Using the

notation indicated in Fig. 1, the Young's modulus along the filament

direction, E^^, is expected to be larger than either or £22-

Values of E-ji, E22 and the Young's modulus along other directions in

the 1-2 plane may be different. However, if the filaments are oriented

randomly in the 1-2 plane, and if the matrix is elastically isotropic,

then Young's modulus is invariant in the 1-2 plane (transversely isotropic). A hexagonal packing of filaments produces the seme effect.

The aluminum matrix in this composite is almost elastically isotropic.

Based on the filament arrangement shown in Fig. 2, transverse isotropy

was assumed. This assumption is often made for composites of this

type, and it is not expected to introduce significant errors.

Elastic anisotropics of single crystals have been studied exten4

sively; the theory of materials with complete rotational symmetry

about an axis and translational symmetry along that axis is used for

hexagonal single crystals. This formalism also applies to macroscopic

treatments of filament-reinforced composites that are transversely

isotropic. In this theory, such a material has five independent elastic

constants; all other elastic constants can be computed from these. At

least five independent measurements are required to determine these

five values. Four can be obtained by measuring Young's modulus along

the filament direction (£23)5 the torsional modulus about the filament

direction (G^^ = ^55^' '''o^"9's modulus perpendicular to the filament

direction (E,,), and the torsional modulus about an axis perpendicular

103
to the filament direction 2(G^^ + . The fifth elastic constant

must be obtained from specimens oriented obliquely to the filament

axis. Such off-axis specimens often exhibit coupling between the

desired resonance mode and unwanted modes. This problem is analogous

to pure and non-pure modes in transmitting ultrasonic pulses. This

coupling can sometimes be avoided by appropriately choosing the angle

between the filament axis and the specimen axis. Even if this coupling

occurs, however, its'effects can often be alleviated by allowing the

specimen to vibrate unconstrained. . , .

Six specimens were used. Four of these were cut either parallel

or perpendicular to the filament axis. Two oblique specimens were

prepared with filament-axis/specimen-axis angles of 78° and 45°. The

specimen orientations are illustrated in Fig. 1. The 78° specimen was

computed to have zero coupling between the desired resonance mode and

other modes; zero coupling occurs when the elastic compliance S-j^ is

zero in the coordinate system of the specimen. The 78° specimen had

the disadvantage that its Young's modulus was quite insensitive to the

fifth elastic constant, S-j^- Therefore, a 45° specimen was prepared.

For this orientation, Young's modulus is quite sensitive to S-j^- Mode

coupling in this specimen was minimized by allowing the sample to hang

almost freely in resonance.

RESULTS

The six measured modulus values are given in Table 1. The subscripts indicate that the modulus was measured using specimens with

filaments parallel, perpendicular, or at an angle 0 to the specimen

axis. The elastic-compliance matrix S.. was computed from these data

by the relationships:

104
S33 = 1/E„

S44 = = l/G

Sgg = 2/G^ - 1/Gl

(1)

(2)

(3)

(4)

13

(1/Eg) - S^^cos^G - S^^sin^e

2 2 2cos 0 sin 0

2 ^55 (5)

s = s - — s ^12 ^11 2 ^66 (6)

The two off-axis specimens gave slightly different S-i^ values. The

value chosen was that producing the smallest total deviation of the two

calculated and measured values. Room-temperature elastic compliances

are given in Table 2.

The practical elastic constants can be calculated from the compliances using the relationships shown in Eq. (7), which reflects

either transverse-isotropic or hexagonal symmetry:

105
^n^/^n ^12""^12/^ll ^13 "^31^^33 °

^ir""/^!! ^13="^3l/^33 °

S..= V^/^33 0 0 0

^44=1/644 0

S44="'/^44 °

Some other useful relationships are:

S.. =Sj^ (8)

V. . = S. ./S. . (9)

^ZX^^ll ^ ^12^^11 ^^^^

^66 = 2(S„ - 5,2) = (1 + v,2)/Ei, (11)

The practical elastic constants measured in the present study are given

5

in Table 3 together with data of Gieske and All red and of Schramm and

KasenJ The measured room- temperature Young's and shear moduli listed

in Table 1 are estimated to have inaccuracies of less than one percent.

The values listed in Tables 2 and 3 include additional uncertainties

due to propagation of errors and to the assumption of transverse isotropy.

106
The Poisson's ratios v-i^ and v^-j were obtained by indirectly measuring

using two off-axis specimens. The Young's moduli in these specimens

are insensitive to S-j^j and the values of v-j^ and v^-j may have inaccuracies

as high as twenty percent.

The E

II and temperature dependencies were measured between 300

and 4 K; and the results are given in Figs. 2 and 3 and, for selected

temperatures, in Table 4. In these figures, most of the data-point

deviations from the dashed curves are believed to be measurement

artifacts and not real material behavior. However, the deviations in

the region 0-30 K are believed to be real. The dashed curve is a

three-parameter fit to the data using Varshni's^ equation; it represents

typical elastic-stiffness behavior of typical metals. The measured

elastic-constant changes with temperature are believed to be inaccurate

to less than 0.05 percent of the elastic constant.

DISCUSSION

As expected, the composite's room-temperature elastic stiffnesses

are between aluminum's and boron's. Also as expected, the boronfilament contribution to Young's modulus is largest along the filament

axis. But, two of the composite's Poisson's ratios are outside the

boron and aluminum bounds. No reason for this is obvious.

The room- temperature elastic constants measured in the present

study are compared with previously reported values, both dynamic and

static, in Table 3. The two dynamic-study sets of results differ by

five to fourteen percent. This disagreement is not surprising because

different filament volume fractions and different measurement methods

were used in these studies. Poisson's ratios disagree between the two

sets of dynamic measurements; reasons for this are unclear, but they

107
are probably due to Poisson's ratio being measured indirectly, and less

accurately. The two static elastic-stiffness values disagree about

fourteen percent with the dynamic values, and in opposite senses. The

static Poisson's ratios disagree considerably more. Reasons for this

disagreement are unclear.

The composites elastic-constant temperature dependencies are

expected to be between those of boron and aluminum. Aluminum's values

are well known.'' Boron's values have not been reported, but they are

expected to be much lower than aluminum's because boron has a much

O 7 higher Debye temperature (1362 K) than aluminum (430 K). The measured

E

II and G^, temperature dependencies shown in Table 4, are lower than

the temperature dependencies of aluminum, as expected.

The measured stiffness-constant temperature dependencies of boronaluminum shown in Figs. 2 and 3 show regular behavior; that is, the

stiffnesses increase approximately linearly with decreasing temperature

near room temperature, and increase less steeply with decreasing temperature. This regular behavior resembles aluminum's, and it shows that

nothing exceptional occurs during cooling to the stiffnesses, except

for a small rise below about 30 K.

The composite's geometry suggests that E y is the elastic modulus

that behaves most like boron's and least like aluminum's. The high

value of E|| compared to the composite's other moduli shows this is so.

Because E || is most like boron's modulus, it must be the Young's moduli

of boron-aluminum with the weakest temperature dependence because

boron's temperature dependence is probably small. This explains why

the change in En on cooling from 300 to 4 K is only four percent.

108
significantly less than the changes observed in aluminum during cooling

and less than the temperature dependencies of boron-aluminum's other

moduli. Similar considerations indicate that En and Gl must have the

strongest temperature dependencies of boron-aluminum's moduli, and that

G|| should have a slightly weaker temperature dependence than .

Also, Ej^ is expected to increase by ten percent or less upon cooling

from 300 to 4 K. This increase must exceed four percent and is probably

close to ten. Similarly, G|| should increase by up to, and probably

close to, ten percent or less during cooling from 300 to 4 K. Thus,

all the practical stiffness moduli of boron-aluminum increase eleven

percent or less on cooling from 300 to 0 K, and Young's modulus along

the fiber axis increases four percent on cooling.

CONCLUSIONS

The following principal findings and conclusions emerge from the

present study:

1. Single-crystal methods can be used to study the anisotropic

elastic properties of a composite such as boron-aluminum.

2. For dynamic studies of a composite's elastic constants,

resonance methods have some distinct advantages over pulse methods.

For example, the composite reported on here gave very poor, virtually

unusable, pulse-echo patters in the 6-10 MHz region. However, the

resonance peaks were well defined over a broad frequency range.

3. The elastic constants of a uniaxial boron-aluminum composite

(48 percent volume fraction of filaments) are between those of boron

and aluminum, and closer to aluminum's.

4. The composite's elastic stiffnesses increase by eleven percent

or less during cooling from 300 to 4 K; Young's modulus along the

109
filaments increases four percent during this cooling.

5. Except for a non-zero slope at temperatures below 30 K, the

composite's elastic constants show essentially regular behavior during cooling.

ACKNOWLEDGMENTS

This study was supported by the Advanced Research Projects Agency

of the U.S. Department of Defense.

REFERENCES

1. ' R. A. Schramm and M. B. Kasen, in National Bureau of Standards

Report No. NBSIR 75-828, 1975.

2. J. Marx, Rev. Sci . Instrum. 22^, 503-509 (1951 ).

3. W. F. Weston, J. Appl . Phys. 46, 4458-4465 (1975).

4. J. F. Nye, Physical Properties of Crystals (Oxford U. P., Oxford,

1960), p. 141.

5. J. G. Gieske and R. E. Allred, Exper. Mech. 1_4' 158-165 (1974).

6. Y. P. Varshni, Phys. Rev. 2, 3952-3955 (1970).

7. E. R. Naimon, H. M, Ledbetter, and W. F. Weston, J. Mater. Sci.

ig, 1309-1316 (1975).

8. K. A. Gschneider, in Solid State Physics , edited by F. Seitz and

D. Turnbull (Academic, New York, 1964), Vol. 16, p. 370.

110
Table 1. Direct experimental elastic stiffnesses

of a boron-aluminum composite containing 0.48

1 1 2 volume fraction of filaments, in units of 10 N/m .

Constant Value

E 1,

II 2.30

El 1.39

G|| 0.568

0.515

E^go 1.41

^45° 1 .45

Table 2. Elastic-compliance matrix of boron-aluminum

composite at 300 K as displayed in Eq. (7); matrix is

symmetrical about main diagonal; derived from results

-1 1 2

in Table 1; units are 10 m /N.

0.719 0.343 -0.074 0 0 0

0.719 -0.074 0 0 0

0.435 0 0 0

1.755 0 0

1.755 0

2.123

111
Table 3. Practical elastic constants of boron-aluminum (0.48 volume

fraction boron) at T = 295 K.

Gieske, Schramm,

Present Allred^ Kasen'^ Boron^ Al uminum^

n ? E^^do' 'N/m^) 1. 39 1. 34 -- 4 41 0. 703

"22 1. 39 1 19 1 61 4. 41 0. 703

E

" "33 2. 30 2 11 2 00 4. 41 0. 703

0. 569 0 539 0 397 2. 03 0. 259

0. 569 0 542 2. 03 0. 259

^66 0. 471 0. 455 2. 03 0. 259

Vi2(climensionless) 0. 48 0 41 0 086 0 357

0. 17 0 25 0. 086 0. 357

-32

' 0. 17 0 23 0 299 0 086 0 357

a. Linear interpolation of data between 0.34 and 0.54 volume fractions of

boron.

b. Static test results, Ref. 1. c. Ref. 8, polycrystalline, v = (E/2G) - 1. d. Ref. 7, polycrystalline.

112
Table 4. Elastic stiffnesses of boron-aluminum

1 1 2 at selected temperatures; in units of 10 N/m .

300 K 200 K 100 K OK

E|| 2.30 2.33 2.37 2.38

Gj^ 0.515 0.543 0.569 0.578

Fig. 2. Photomicrograph showing distribution of 0. 14-mm-diameter boron

filaments in aluminum matrix. Plane of photo is perpendicular

to filaments.

113
3=filament axis

Fig. 1. Co-ordinate system, specimen geometries, and specimen orientations. Striping

indicates filaments.

114
CM

2.40

2.38

S 2.36

CO

3 2.34

CO

2.32

2.30

2.28

1 1 1

-

1 1

B/AI

V -

1 1 1 V\

0 50 100 150 200 250 300

TEMPERATURE (K)

Fig. 3. Temperature dependence of Young's modulus En = E33 along the

filament axis. Dashed curve is a semi -empirical three-parameter

equation that is typical for most materials. Except for the

rise below 30 K, data scatter are experimental artifacts.

115
Fig. 4. Temperature dependence of the torsional (or shear) modulus

about an axis perpendicular to the filament axis. See caption

of Fig. 3.

116
ANOMALOUS LOW-TEMPERATURE ELASTIC BEHAVIOR OF A

NITROGEN-STRENGTHENED CHROMIUM-MANGANESE STAINLESS STEEL

H. M. Ledbetter

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Elastic constants of an Fe-?1 Cr-6Ni -9Mn stainless steel were

studied experimentally by both pulse and resonance methods. The roomtemperature elastic constants are similar to those of AISI 304. During

cooling to liquid-nitrogen temperature (76 K) , all the elastic constants

behave anomalously below 130 K. As in Fe-Mn alloys, these anomalies are

probably due to a N^el transition. A further anomaly in the compressibility at 190 K suggests a second transition of unknown nature.

Keywords: Bulk modulus; compressibility; elastic constants; Poisson's

ratio; pulse method; resonance method; shear modulus; stainless steel;

sound velocity; Young's modulus.

Contribution of NBS, not subject to copyright.

I

117
ANOMALOUS LOW-TEMPERATURE ELASTIC BEHAVIOR OF A

NITROGEN-STRENGTHENED CHROMIUM-MANGANESE STAINLESS STEEL

H. M. Ledbetter - Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Nitrogen-strengthened chromium-manganese stainless steels containing

other alloying elements such as nickel and molybdenum are promising

alloys for low- temperature applications.^ They have high strength and

toughness at cryogenic temperatures, and they resist stress-induced martensitic transitions that are often accompanied by undesirable property

changes. Some low-temperature mechanical and physical properties of

these materials have been reported.^ And other low- temperature studies

are in progress, including fatigue-crack growth rate and fracture toughness

3 and tensile and strength properties of weldments.

The purpose of the study reported here was to determine the

low- temperature elastic properties of a nitrogen-strengthened steel

containing 21 chromium, 6 nickel, and 9 manganese, percent by weight.

This steel is commonly called 21-6-9. The applicable elastic properties

are: Young's modulus, the shear modulus, the bulk modulus (reciprocal

compressibility), and Poisson's ratio. Besides characterizing

a material, the elastic constants are also essential for computing

either stress-induced deflections or thermo-elastic stresses. Elastic

constants are inherent in fracture mechanics; for example, the planestrain stress-intensity factor, Kj^, is computed from the elasticplastic fracture criterion, Jj^, by using Young's modulus and Poisson's

ratio.

118
In the presently reported study, the elastic constants v;ere determined by measuring the velocities, v, of longitudinal waves and shear

waves in a thin-rod resonance experiment near 60 kHz and in an infiniteplate pulse experiment with a carrier frequency near 10 MHz. Elasticstiffness constants, C, are computed by

C = cv^ (1)

where z is the mass density. Depending on the velocity mode -- longitudinal, shear, extensional, torsional, etc. -- different types of elasticstiffness constants are determined. The dynamic elastic constants were

obtained because the measurements were made at high frequencies. These

differ very little from the more-familiar static elastic constants that

result from stress-strain-type experiments. For the bulk modulus, the

difference is zero at zero temperature, and it increases to a few

percent at room temperature. For the shear modulus, the difference is

zero at all temperatures. Depending on their relative shear and dilatational parts, all other elastic constants fall between these two

behavior bounds. For example, Young's modulus behaves nearly like the

shear modulus because volume is nearly unaffected by uniaxial elastic

deformation.

EXPERIMENTAL

A. Material

The steel was provided by Lawrence Livermore Laboratories in the

form of a 50 X 50 X 3.6 cm plate that was hot-rolled (1356-1089 K)

from a 30.5 x 30.5 x 10 cm slab in twelve steps with 90° rotations of

the slab between rollings. The plate was annealed 1.5 h at 1283 K,

119
air cooled, annealed 1.5 h at 1366 K, and water quenched. This material has a hardness of Rg = 92, an average grain diameter of 0.16 mm,

3

and a mass density of 7.838 g/cm (determined by hydrostatic weighing).

Its chemical composition in weight percent is: 19.75 Cr, 7.16 Ni;

9.46 Mn, 0.019 C, 0.15 Si, 0.004 P, 0.003 S, 0.28 N, balance Fe.

B. Specimens

For ultrasonic-pulse measurements, cylindrical specimens were prepared 1.7 cm in diameter and 0.5 to 1.0 cm long. Opposite faces were

ground flat and parallel within 3 ym.

For resonance measurements, cylindrical specimens were prepared

0.4 cm in diameter and 4.2 and 2.6 cm long for the extensional and torsional modes, respectively.

C. Methods

Experimental methods used in the present study were described pre4 5 viously '

. Thus, only a brief outline is given here.

Room- temperature pulse measurements were made with a McSkimin

method. A quartz transducer with a fundamental frequency between 6 and

10 MHz was bonded to a specimen with phenyl salicylate. X-cut transducers

were used for longitudinal waves and ac-cut transducers were used for

shear waves. The pulse length was about one ys. The ultra-sound velocity

was computed from

V = Zl/t (2)

where I = specimen length and t = transit (round-trip) time. On an oscilloscope, t was the time between subsequent echoes. The oscilloscope was

calibrated with a precision time-mark generator.

120
Low-temperature pulse measurements were made with a superposition

method where the envelope of the sum of the odd-numbered echoes is maximized by tuning the carrier frequency, f. Neglecting thermal contraction, the ultrasonic-velocity change is

Av/v = Af/f (3)

Details of the specimen holder, cooling procedures, and temperature mea4

surements were given previously. Measurements were made at intervals

of 5 K with a cooling rate of about 2 K/min.

Young's modulus and the shear (torsional) modulus were also measured

5 with a composite-oscillator method during cooling. The resonance frequency of the specimen is computed from

f^ = f^ + (f^ - fbm/m^ (4)

s 0 ^ 0 q q s

'

where m = mass and the subscripts s, o, and q denote specimen, oscillator, and quartz. For an extensional resonance. Young's modulus is

E = 4p{il^f^)^ (5)

where p = mass density and i = length.

RESULTS

Room- temperature elastic constants are given in Table I for both

pulse and resonance cases. Resonance values of many of the elastic constants are not shown because they are much more inaccurate than those

obtained by a pulse method.

121
Temperature variations of the two experimentally determined elastic

constants -- the longitudinal and shear moduli are shown in Fig. 1.

The temperature variations of the derived elastic constants -- Young's

modulus, the bulk modulus, and Poisson's ratio -- are shown in Fig. 2.

Resonance-method temperature data are not reported here because they

contain higher inaccuracies than the pulse-method data. The two sets

of data were consistent within a few percent.

Based on several measurements, the 2a uncertainties in the roomtemperature elastic constants are estimated to be + 3%. The point-topoint imprecision in the temperature-dependence measurements is

estimated to be + O.IX.

DISCUSSION :

Results shown in Figs. 1 and 2 are surprising; all the elastic

constants of Fe-21 Cr-6Ni-9Mn behave anomalously during cooling. The

primary purpose of this section, then, is to explain this alloy's

anomalous temperature behavior. Any fundamental model -explanation is

precluded by the alloy's complexity -- four major components, all

transition metals with incomplete d shells that exhibit either ferromagnetism, antiferromagnetism, or both. But several alternative types

of "explanation" are possible. The problem is -- why doesn't 21-6-9

show regular temperature behavior (indicated by the dashed curves in

4

Fig. 1): zero slope at zero temperature, a T dependence at low temperatures; and a decreasing linear behavior at higher, increasing

temperatures? In the simplest models of solids, Debye or harmonic,

elastic constants are temperature independent. But, regular temperature behavior is predicted by a quasi-harmonic approximation,'^ in

which the vibrational energy is volume dependent.

Changes of crystal structure cannot explain the present results.

Both a and e phases can be produced from the y phase in 21-6-9 at low

122
temperatures by mechanical stress. However, the stress used in the

present study was infinitesimal (the strain is typically 10 ), and no

stress-induced phases are possible. Athermal martensitic transition

can also be excluded because such transitions in ferrous alloys are

g always accompanied by large temperature hysteresis. No hysteresis was

observed in the present studies; within experimental error, elasticconstant/temperature curves were identical in heating, in cooling and

9 in successive runs. Available data indicate that the y-e martensitic

transition increases Young's modulus, contrary to present observations.

Thus, the anomalous temperature behavior has no structural origin.

Neither can present results be explained by the familiar lE effect

due to linear magnetostriction, arising from either ferromagneti sm or

antiferromagneti sm. Such effects are not observed in a saturating magnetic field because domain-wall motions are prevented. While no magnetic

field was used in the present study, the high frequencies (10 MHz) that

were used are equivalent in suppressing the l£ effect because the domainwall displacements cannot follow the oscillating stress.

''^

It is useful to compare the present results with studies on morefamiliar stainless steels, Fe-Cr-Ni alloys, which have low-temperature

elastic anomalies due to paramagnetic-antiferromagnetic transitions. For

present purposes, 21-6-9 is an AISI-304-grade stainless steel containing an additional nine percent Mn. The elastic constants of these two

alloys are quite similar, with the Young's and shear moduli of 21-6-9 being

about three percent higher than those of AISI 304. The elastic properties

of AISI 304 were reported between room temperature and liquidhelium temperature by Ledbetter, Weston, and Naimon"'^ together with

similar data for AISI 310, AISI 316, and A286. All these stainless

123
steels have elastic-constant anomalies below about 80 K. These anomalies

were interpreted by invoking the Doring effect. Doring^^ showed thermodynamically that either a paramagnetic-ferromagnetic (Curie) transition

or a paramagnetic-antiferromagnetic (N^el ) transition must be accompanied

by a Young 's-modul us anomaly due to volume magnetostriction, which is

manifested as the difference between Young's modulus at constant magnetic

field and at constant magnetization. However, Doring' s analysis does

not account for an anomalous change in the shear modulus, and it is

inapplicable to 21-6-9. Thus, an important difference exists between

the low- temperature elastic anomalies in Fe-Cr-Ni and Fe-Cr-Ni-Mn

alloys. Fe-Cr-Ni alloys are anomalous in every elastic constant

except the shear modulus . Fe-Cr-Ni-Mn alloys are anomalous in every

elastic constant. This difference is important for developing models

of elastic behavior, and it can be identified only when continuous,

complete sets of elastic constants are available over a wide temperature region.

Since Fe-21 Cr-6Ni -9Mn behaves differently from Fe-Cr-Ni alloys, it

9 12-15

is appropriate to compare it with Fe-Mn alloys. Several authors '

have reported low- temperature elastic constants of these alloys, which

are often called manganese steels. The present alloy compares closely

with Fe-Mn alloys in several respects: (1) all elastic constants are

anomalous; (2) the anomaly consists of a lowering of the elastic stiffnesses during cooling; (3) little or no hysteresis; (4) a wide temperature range of transition; (5) frequency independence; and (6) a maximumminimum-maximum behavior exhibited during cooling. Antiferromagnetism

1 fi in Fe-Mn alloys was demonstrated first by Sedov, who measured the

124
temperature dependence of the magnetic susceptibility of alloys containing 13.0 to 43.9 wt. pet. Mn. Elastic anomalies associated vn'th the

Neel transition in Fe-Mn alloys were reported first by Sokolov and

1

2

Melker, who measured the temperature dependence of Young's modulus of

alloys containing 11.1 to 52.4 wt. pet. Mn. Young's modulus anomalies

were also reported by Bogachev et al.''^'"''^ (13-44 and 14-38 wt. pet.

1 5 Mn). Tanji reported anomalies in both Young's modulus and the shear

modulus of alloys containing 30 to 48 wt. pet. Mn. Tanji also reported

very peculiar behavior of the bulk modulus in the vicinity of the Neel

transition. Young's modulus anomalies were also reported by Lysek et

9 al . , although they were complicated by the -{-z structural transition.

These previous studies can be summarized as follows: Fe-Mn alloys

containing 13-48 pet. Mn undergo a Neel transition during cooling; both

Young's modulus and the shear modulus decrease anomalously because of

the transition; the bulk-modulus behavior during the transition may be

peculiar, and further study is appropriate; no results have been reported

for changes in Poisson's ratio. Thus, it is concluded that in Fe-21Cr6Ni-9Mn the basic magnetic mechanism causing the elastic anomaly is

the same as in Fe-Mn alloys.

Tv/o additional results of the present study deserve mention. First,

as shown in Fig. 2, Poisson's ratio is the most sensitive elastic-constant

indicator of the transition, that is, a locater of the N^el temperature.

Within the paramagnetic region, Poisson's ratio is almost linear over a

wide temperature range. Since Poisson's ratio is not related simply to

interatomic forces in solids, the physical implications of this behavior

are unclear. Second, as also shown in Fig. 2, the bulk modulus has a

maximum at 190 K, about 60 K above the suggested Neel transition. This

125
implies a second transition. The nature of this transition is unknown;

but it also is probably magnetic, and magnetic-susceptibility measurements might elucidate its nature.

Several further studies are suggested by the present results: (1)

Thermal expansion . Elastic-constant/temperature anomalies are often

accompanied by anomalous thermal expansion, particularly in magnetic

materials where they have a common cause --- magnetostriction. A weaker

interatomic bond usually means a higher specific volume and lower elastic stiffnesses. Regions of negative thermal expansion are possible

in this alloy since the magnetic effects may overcompensate for the

usual thermal expansion. Alloys with both low thermal expansion and low

temperature coefficients of the elastic constants are of considerable

technological interest. Also, thermal-expansion data would be useful

for distinguishing among possible magnetic mechanisms. (2) Damping .

Changes in elastic constants are always accompanied by increases in

damping. The possibility of high damping over a temperature region

(determined by Mn content) in a non-ferromagnetic material is an interesting possibility. (3) Compress i bi 1 ity . The variation of the compressibility in the vicinity of the N^el transition needs further, detailed

1

5

study. Tanji's results suggest that the compressibility is discontinous at the N^el temperature, implying a first-order phase transition.

But, Neel transitions are known to be second-order. (4) Additional

al loys . It would be useful to study other 21-6-9-type alloys to

determine the more general validity and utility of the present results.

In particular, effects of manganese content should be determined. (5)

Magnetic susceptibility . Such measurements made continuously versus

temperature would verify the occurrence of a Ndel transition and possibly

elucidate the nature of the transition that lowers the bulk modulus at

190 K.

126
CONCLUSIONS

The following principal results and conclusions emerge from the

present study:

(1) At room temperature, an Fe-21 Cr-6Ni -9Mn alloy has elastic

properties similar to those of AISI 304; all the elastic constants

except Poisson's ratio are slightly higher in 21-6-9.

(2) Upon cooling, all the elastic constants show anomalous behavior,

which is reproducible and reversible, showing no hysteresis.

(3) These anomalies are believed to result from a paramagneticantiferromagnetic (N^el) transition, with a transition temperature near

130 K, as evidenced by drops in the shear modulus and in Young's modulus.

(4) Poisson's ratio is especially sensitive to the N^el transition.

It is almost linear in the paramagnetic region, and the slope dv/dT

reverses sharply at the transition.

(5) This alloy's behavior resembles the Fe-Mn case rather than

the Fe-Cr-Ni case, emphasizing the role of manganese in affecting

properties.

(6) There may be a second transition in this alloy, evidenced

by the drop in the bulk modulus upon cooling below 190 K.

(7) Such alloys may offer exceptional physical properties for nonferromagnets , for example: high damping, low thermal expansion, and a

small elastic-modulus change with temperature.

ACKNOWLEDGMENT

This work was supported by the Advanced Research Projects Agency of

the U.S. Department of Defense.

127
- REFERENCES

1. Handbook on Materials for Superconducting Machinery (Metals and

Ceramics Information Center, Battelle, Columbus, Ohio, Nov. 1975).

2. R. L. Tobler, in National Bureau of Standards Rep. No. NBSIR 76-

848 (1976).

3. J. M. Wells, R. Kossowsky, W. A. Logsdon, and M. R. Daniel, Westinghouse Research Rep. No. 76-9D4-CRYMT-R1 (1976).

4. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics X4,

246-249 (1974).

5. W. F. Weston, J. Appl . Phys. 46, 4458-4465 (1975).

6. H. J. McSkimin, IRE Trans. Ultrasonics Engr. 5, 25-43 (1957).

7. G. Leibfried and W. Ludwig, in Solid State Physics , edited by F.

Seitz and D. Turnbull (Academic, New York, 1961), Vol. 12, p. 383.

8. R. P. Reed and J. F. Breedis, in Behavior of Materials at Cryogenic

Temperatures, ASTM STP 387 (Amer. Soc. Test. Mater., Philadelphia,

1966).

'

9. L. I. Lysek, S. P. Kondratev, Yu. N. Makogon, and B. I. Nikolin,

Soviet Phys.-Doklady 18, 428-429 (1973).

10. R. M. Bozorth, W. P. Mason, and H. J. McSkimin, Bell Syst. Tech. J.

30, 970-989 (1951).

11. H. M. Ledbetter, W. F. Weston, and E. R. Naimon, J. Appl. Phys. 46,

3855-3860 (1975).

12. 0. G. Sokolov and A. I. Melker, Soviet Phys.-Doklady 9, 1019-1021 (1965).

13. I. N. Bogachev, V. F. Egolaev, and B. A. Potekhin, Soviet Phys.-

Doklady U, 377-379 (1967).

14. I. N. Bogachev, V. F. Yegolayev, and T. L. Frolova, Fiz. Metal.

Metal loved 29, 358-363 (1970).

15. Y. Tanji, J. Japan Inst. Met. 35^, 1-5 (1971).

16. V. L. Sedov, Soviet Phys. JETP 15, 88-89 (1962).

17. G. Hausch and W. Warlimont, Z. Metallkd. 64, 152 (1973).

I2«
Table I. Elastic constants of an Fe-21 Cr-6Ni -9Mn alloy at room temperature, compared to those of AISI 304.

Fe-21Cr-6Ni-9Mn AISI 304

Pulse Resonance Pulse

3

: ,g/cm 7 838 7 864

5

V 10 cm/s 0 571 0 563

V , lO^cm/s

t 0 310 0 306

1 1 2

C,;, 10"N/m^ 2 534 2 491

G=C^, lo''^N/m^ 0 755 0.779 0 735

1 1 2 B, 10 N/m^ 1 527 1 506

1 1 2 E, lO' 'N/m^ 1 945 1 .957 1 897

0 288 0 290

LIST OF FIGURES

Fig. 1. Longitudinal and shear moduli variations with temperatures,

as determined by an ultrasonic pulse-superposition method.

Data are shown for a single cooling. Subsequent heatings and

coolings reproduced these data within + 0.1 percent. Dashed

curves represent behavior expected for a typical material.

Fig. 2. Shear modulus (G), Young's modulus (E), Poisson's ratio (v),

and bulk modulus (B) computed from data in Fig. 1 by using

standard formulas. Note that the bulk-modulus anomaly begins

about 60 K higher than the shear-modulus anomaly.

129
1.08

1.07

in

m

^

1.06

u

1.05

<

C/3

Fig. 1

1.04

< 1.03

1.01

1.00

1 r

Fe-21Cr-6Ni-9Mn

1.02 -

Shear Modulus

200

TEMPERATURE (K)

300

Longitudinal and shear moduli variations with temperature, as determined

by an ultrasonic pulse-superposition method. Data are shown for a single

cooling. Subsequent heatings and coolings reproduced these data within

+ 0.1 percent. Dashed curves represent behavior expected for a typical

material. 130
100 200

TEMPERATURE,(K)

Fig. 2. Shear modulus (G), Young's modulus (E), Poisson's ratio (v) , and bulk

modulus (B) computed from data in Fig. 1 by using standard formulas.

Note that the bulk-modulus anomaly begins about 50 K higher than the

shear-modulus anomaly.

131

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

FRACTURE MECHANICS PARAMETERS

R. L. Tobler, H. I. McHenry, R. P. Reed, and R. E. Schramm

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

133
NBS FRACTURE MECHANICS PROPERTIES STUDIES DURING ARPA

SPONSORED PROGRAM, SEPTEMBER 1973 TO SEPTEMBER 1976.

Material Fracture Toughness Fatigue Crack Growth

1. Aluminum alloy 2014-T652 5,6 NA

2. " 2219-T87 5 NA

3. " 5083-0 . 6 6

4. Inconel alloy 718 5 5

5. Inconel alloy 750 2 2

6. Managing steel, 18Ni, 300 grade 6 6

7. Iron-49% Ni 6 6

8. Stainless steel Nitronic 40 (21-6-9) 5,6 6

9. " A 286 3 3,6

10. " AISI 304 1 1,6

11. " AISI 304L NA 6

12. " AISI 310 2 2,6

13. " AISI 316 1 1,6

14. Titanium alloy Ti-6A1-4V, Normal 1,3 1,3

15. " Ti-6A1-4V, ELI 3 3

16. i-5Al-2.5Sn, Normal 2 2

17. " Ti-5Al-2.5Sn, ELI NA 6

134
FRACTURE MECHANICS PARAMETERS FOR A 5083-0

ALUMINUM ALLOY AT LOW TEMPERATURES

t

R. L. Tobler and R. P. Reed

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

The fatigue crack growth ana fracture resistance of a 5083-0

aluminum alloy plate v^ere investigated at four temperatures in the

ambient-to-cryogenic range -- 295, 111, 76, and 4 K. J-integral test

methods were applied using compact specimens 3.17 cm thick, and the

value of J required to initiate crack extension (Jj^) is reported as

an index of fracture toughness. The fracture toughness was orientation

dependent, with anisotropy accounting for J^^ variations of up to a

factor of 2. For specimens having fracture planes parallel to the

rolling direction, J^^ increases progressively from 9 to 25 kJm as

temperature decreases between 295 and 4 K. In contrast, the fatigue

crack growth rates (da/dN) are insensitive to specimen orientation.

The fatigue crack growth rates at cryogenic temperatures are up to 10

times lower than in air at room temperature, but are virtually constant

between 111 and 4 K. These results should be useful in fracture

mechanics analyses of cryogenic structures, including liquified natural

gas tankers.

Key words: Aluminum alloys; cryogenics; crack propagation; fatigue;

fracture; low temperature tests; mechanical properties.

"Contribution of NBS, not subject to copyright.

135
INTRODUCTION

The aluminum alloy designated 5083-0 is strengthened by solid

solution additions of magnesium and used in the annealed condition.

Excellent formability, weldability, toughness, and relatively low cost

are some advantages that make this alloy an attractive low temperature

structural material. Applications include storage and transport tanks

for cryogenic fluids. Currently, thousands of tons of 5083-0 alloy are

destined for use in liquefied natural gas (LNG) tankers at service temperatures as low as 111 K. Emerging applications may include structural

components for superconducting machinery. These structures are costly,

and in the case of LNG tankers, the transported cryogen is flammable.

Design engineers and regulatory agencies therefore require efficient

and fail-safe design.

Extensive mechanical property data exist for 5083-0 aluminum [1-7].

Between room and liquid helium temperatures (295 to 4 K), the yield and

ultimate strengths increase by 25% and 70%, respectively, with most of

the improvement occurring at lower temperatures [2]. Ductility also

improves at low temperatures, and precracked specimens retain the ability

to deform prior to fracture. Nevertheless, quantitative fracture toughness data for this alloy are lacking. Several attempts to measure the

critical stress intensity factor, K^^, have been unsuccessful. As defined

by the ASTM testing method for plane strain fracture toughness of metallic

materials (ASTM E 399-74), the parameter Kj^ applies to linear-elastic

loading behavior. Kaufman, Nelson, and Wygonik [3] showed that 5083-0

alloys in section thicknesses up 20 cm remain sufficiently plastic to

invalidate direct Kt measurements.

136
This study employs an alternative approach to fracture toughness

characterization. The method is based on Rice's formulation of the

J-integral [8], which is the rate of change of potential energy with

respect to crack area. In applications of the J-integral, Begley and

Landes identify a parameter denoted Jj.^ which, unlike Kj^, can be measured under nonlinear-elastic conditions [9,10]. Since experimental

results for aluminum alloys support the hypothesis that Jj^ is a material constant [11,12], the J-resistance curve test method [10] was

applied here to a 5083-0 aluminum plate. The J^^ values and fatigue

crack growth rates reported in this study should assist fracture

mechanics analyses of 5083-0 structures at temperatures in the ambientto-cryogenic range.

PROCEDURES

Material and Specimens

A 4.32 cm thick 5083-0 aluminum alloy plate was obtained from a

commercial source and tested in the as-received condition. The microstructure is shown in Figure 1. The ASTM specification B 209-66 gives

the chemical composition of this alloy in wt'.- as: 4.0-4.9 Mg, 0.3-1.0

Mn, 0.05-0.25 Cr, 0.4 max. Si, 0.4 max. Fe, C.IO max. Cu, 0.25 max. Zn,

0.15 max. Ti , and 0.15 max. of other impurities.

After machining 0.44 cm of metal from each surface of the stock

plate, 3.17 cm thick compact specimens were fabricated with the geometry

shown in Figure 2. The specimen width, W, was 7.62 cm. The width-tothickness ratio, W/B, was 2.4. Knife edges were machined integral to

the notch to enable clip gage attachment and deflection measurements at

the leadline. Most of the specimens were machined in the TL orientation (fracture plane normal to the long transverse direction), but

137
several specimens of the LT orientation (fracture plane normal to the

longitudinal or rolling direction) were also tested.

Tensile tests of unnotched, longitudinally-oriented specimens

were performed at room and liquid nitrogen temperatures, following

ASTM Method E 8-69. Two tests were performed at each temperature. The

yield and ultimate strengths, elongation, and reduction of area results,

shown in Table 1, agree with other data for similar 5083-0 products [13]

Fatigue Crack Growth

A 100 kN servo-hydraulic test machine adaptable for cryogenic

service was used in all fatigue and fracture tests. Room temperature

tests were conducted in unconditioned air at a relative humidity, H, of

approximately 30%. Low temperatures were achieved by enclosing the load

frame, specimen, and clip gage in a dewar of liquid helium (4 K) , liquid

nitrogen (76 K) , or nitrogen gas (111 + 4 K) . The low temperature

apparatus and techniques were previously described [14,15]. The clip

gage satisfied ASTM Method E 399-74 linearity requirements, and its

sensitivity changed by no more than 5% over the temperature range

investigated.

The compact specimens were precracked at their test temperatures

1 II using maximum fatigue stress intensity factors of from 10 to 22 MPa»m

The minimum- to-maximum load ratio, R, was 0.1. Some fatigue crack

growth rates were measured during precracking, but additional rates at

relatively high stress intensity factors or R values were measured

using specimens not intended for J-tests. All precracking and fatigue

crack growth tests used sinusoidal ly-varying loads at a frequency of

20 Hz.

A correlation between crack length (a) and specimen compliance

138
(deflection per unit load, 6/P) was established using measurements

from fractured specimens. Crack length was defined as the average of

three measurements at the middle and quarter points of specimen thickness. The fatigue tests were then interrupted periodically to record

compliance, and the inferred crack length was plotted as a function of

load cycles, N. The fatigue crack growth rates, da/dN, were calculated

by graphical differentiation of a-versus-N curves, while the corresponding stress intensity factor ranges, AK, were calculated from the maximum

and minimum fatigue loads:

According to ASTM Method E 399-74,

f(a/W)=29.6(a/W)l/2.,85.5(3/w)3/2+655.7(a/W)5^2.,(„7.o(a/W)^/2^638.9(a/W)5/2

The uncertainty in crack growth rates is estimated at less than + 25%.

Fracture Toughness

At each test temperature, a series of specimens having similar precrack lengths were loaded to selected deflections at the stroke rate of

0.05 mms'^ . These loadings were sufficient to cause stable crack extensions of up to 0.25 cm. Each specimen was then unloaded and refatigued

using cyclic loads no greater than 70% of the maximum static load. After

the refatigue crack was propagated several millimeters, the specimens

were fractured into halves by a single loading.

The fracture surfaces showed, in succession: (1) a precrack zone,

(2) a crack extension increment due to static loading, and (3) a refatigue

139
crack zone. The relatively coarse and less reflective increment of static

crack extension was measured to the nearest 0.003 cm with a traveling

microscope at the center and quarter points of specimen thickness,

the three-point average being defined as Aa. The corresponding values

of J were calculated for each test, using the approximate solution for

deeply cracked compact specimens [16]:

J = 2A/Bb. ^

' (^)

Here, A is the total area (energy) under the test record up to the point

of unloading, and b is the original ligament depth (b = W - a). The

uncertainty in J measurements was not greater than + 2%.

To obtain critical J values, the resistance curves of J-versus-Aa

were back-extrapolated to Aa = 0.005 cm. In tests of a 2219-T6 aluminum

alloy. Read and Reed [12] suggested that defining Jj^ at 0.005 cm crack

extension leads to reproducible results. The uncertainty in the Jj^

values obtained in this way for 5083-0 aluminum is estimated at + 15%.

RESULTS AND DISCUSSION

Fatigue Crack Growth

Fatigue crack growth data at 4, 76, 111, and 295 K for 5083-0

aluminum specimens of the TL orientation at R = 0.1 are shown in Figure 3.

The results span two orders of magnitude from 5 X 10" mm/cycle to 2.5 X -3

10 mm/cycle. For a given AK value, the rates of crack growth at 111,

76, and 4 K are equivalent within the degree of scatter among replicate

tests. However, the rates at room temperature are up to 10 times faster

than the rates at cryogenic temperatures.

140
As plotted on logarithnic coordinates, the lov; temperature fatigue

crack growth data describe an approximately linear trend over the entire

AK range, wnereas the room temperature data do net. The linear approximation to tne data at 111, 76 and 4 K, shown in Figure 3, is consistent

with a Paris equation of the form:

f =c(:k)"

1 j2_ Here da/dN (mm/cycle) is a power law function of IK (MPa^m ). The

constants C and n correspond to the ordinate intercept at IK = 1 , and

the slope, respectively. A graphical solution for the equation of tne

line drawn through the 111, 76 and 4 K data yields:

^= 1.3 X 10-10(:K)5-2,

The room temperature data fail to conform to a single power-law

equation, due to the appearance of a "shoulder" on the da/dN-versus-lK

1 II

plot at IK values between IC and 15 MPa-m . This shcjlder brings the

room and low temperature crack growth rates into closer agreement at

higher IK values. Consequently, the room temperature fatigue crack

growth resistance is only slightly inferior at stress intensity factor

1 II

ranges greater 'chan 15 MPa^m

Figure 4 shows additional crack growth data for the TL orientation

at 295 and 111 K (R = 0.3), as well as data on specimens of the LT

orientation at 111 K (R = 0.1). Scatterbands representing the data of

Figure 3 are superimposed on Figure 4 for comparison. This comparison

indicates that the change in R from 0.1 to 0.3 had no effect on the

141
room temperature fatigue crack growth rates, whereas, at 111 K, this

change increased the rates by nearly a factor of 2. Also the data

obtained for specimens of the LT orientation at 111 K fall within the

band for TL orientations for the same stress ratio, R = 0.1. Thus,

specimen orientation has no measureable effect on fatigue crack growth

rates. Kaufman and Kelsey [17] also noted relatively isotropic fatigue

crack growth in their tests of a 5083-0 aluminum alloy.

Comparisons of fatigue crack growth data reported in the literature

for compact specimens of 5083-0 aluminum are shown in Figures 5 and 6.

Although these data show considerable variance, most results can be

rationalized in terms of the different test variables and procedures.

Usually, higher R values lead to increased fatigue crack growth rates.

Other significant factors to be considered include the procedure used

to obtain a-versus-N data, and the relative humidity at room temperature

In reference to Figures 5 and 6 note first that the present study

yielded somewhat lower rates at a given AK value as compared with other

investigations [4,17-19]. In our study, the crack length was defined as

an average of measurements at the center and quarter points of thickness

Other studies used measurements of the crack at specimen edges. In our

study the edge crack lengths were typically 5 to 8% shorter than the

average crack lengths. If edge crack lengths had been used, the f{a/W)

values of Eq. (1) would have been reduced, and the AK value for a given

growth rate would have been 10 to 17% lower than actually reported.

This would shift the bands of Figures 5 and 6 into good agreement with

the bulk of previously published results.

As shown in Figure 5, at least three other laboratories report a

shoulder in room temperature fatigue crack growth rates [17-19]. This

142
shoulder occurs at rates near 3 X 10~ mm/cycle, for tests conducted

in air with appreciable moisture contents. Kelsey, Nordmark and

Clark's [4] room temperature results at 90': relative humidity and

R = 0.33 are nearly in agreement with Argy, Paris, and Shaw's [18]

results at 50% relative humidity and R = 0.4. However, as the relative humidity is decreased to less than 10";, the shoulder is eliminated

and fatigue crack propagation resistance at low is improved. Note

in Figure 5 that the overall agreement of data is better at high AK

values where differences in relative humidity are less influential.

Deleterious effects on the fatigue crack growth resistance of this

alloy due to moisture are not surprising in view of the trends exhibited

by other aluminum alloys [20]. Hartman and Schijve's [21] data for a

7075-T6 alloy demonstrate trends analogous to the behavior indicated in

Figure 5. In dry air, their logarithmic plots of da/dN-versus-AK display

-5 -3

a linear trend for growth rates in the range 10 to 10 mm/cycle j in

moist air (relative humidity = ^5%), a shoulder appears in the data

1 /2

at AK ~ 15 MPa'm , and the rates at lower AK are accelerated by up

to a factor of 10. Again, the rates at high AK are not sensitive to

moisture.

Thus, the effects of moisture on the room temperature fatigue crack

growth behavior of 5083-0 and 7075-T6 alloys are remarkably similar.

The trend of the Kelsey et al . [4] data for 5083-0 aluminum in a dry

air environment probably represents the true trend of room temperature

results when moisture effects are practically eliminated. Note from

Figures 5 and 6 that the rates reported by Kelsey et al . [18] for tests

in dry air at 295 K are nearly equivalent to but slightly faster than

their rates at 76 K. Based on these observations, it may be concluded

143
that moisture effects at 295 K are predominant, and temperature variations between 295 K and 4 K intrinsically have little effect on the

fatigue crack propagation resistance of 5083-0 aluminum. This is consistent with results for other face-centered cubic alloys which show

only modest improvements of fatigue crack growth resistance at low

temperatures [22].

Fracture Toughness

Plasticity and stable crack extension caused nonlinearity in the

fracture test records at all temperatures, and unstable cracking was

never observed. As expected, the linearity requirements of sections

9.1.2 and 9.1.5 of ASTM Method E 399-74 could not be satisfied using

our specimens of aluminum alloy 5083-0, so it was appropriate to conduct J-integral tests. Table 2 lists the J-integral test results for

both the LT and TL specimen orientations.

Resistance curves (J-versus-Aa graphs) for the TL orientation are

shown in Figure 7. The results at 295, 111, 76, and 4 K show that

higher J values are required for a given crack extension as temperature

decreases. The Jj^ values obtained at Aa = 0.005 cm progressively

_2 increase from 9 to 25 kJm between 295 and 4 K. Moreover, the rate

of increase of J with respect to Aa is greater at 111, 76, and 4 K

than at room temperature. Thus, greater energy is expended in fracture

initiation and propagation at cryogenic temperatures. Kahn-type tear

and dynamic tear tests render a similar conclusion [5-7, 23].

Figure 8 compares the J-resistance curves for the TL and LT orientations at 111 K, demonstrating the anisotropy of fracture toughness

for this alloy. Based on these curves, Jj^ for the LT orientation is

_2 approximately 39 kJm at 111 K, or twice the value for the TL orientation. The superiority of the LT orientation in comparison with the TL

144
orientation is typical of many alloys, and the tear test results

and projected Kj^ values reported by Kaufman et al . [3,5,6] indicate

a similar orientation dependence for 5083-0 aluminum.

The fracture anisotropy is also evident in Figure 9, which shows

TL and LT specimens that were tested at 111 K. The LT specimen was

fatigue cracked and fractured in a single loading. The TL specimen

was used in a J-test, and it shows an increment of crack extension, Aa,

located between two fatigue cracks. The LT specimen displays shear fracture portions amounting to 30% of specimen thickness; delaminations are

also visible at mid-thickness. In comparison, the TL specimen exhibits

a flat fracture mode requiring less energy for crack extension. The

fracture surface appearance of the TL orientation was not significantly

influenced by test temperature.

The Jt data listed in Table 2 can be used to estimate values

Ic Ic

by using the equation

2 ^^ic

^Ic = 2

1 - V

In this equation, E is Young's modulus of elasticity and v is Poisson's

ratio. The values of E and v at temperatures between 295 and 4 K are

known from Naimon, Weston, and Ledbetter's study [24]. The K^^ estimates

based on these data at 295, 111, 76 and 4 K are plotted in Figure 10,

along with the corresponding Jj^ values.

As shown in Figure 10, the Kj^ estimates converted from J^^ data

range from 27.0 to 60.2 MPa^m^^^, depending on temperature and specimen

orientation. For the TL orientation, the Kj^ estimates at 295 and 76 K

are 27.0 and 43.4 MPa^m^^^, respectively. These are lower than Kaufman

145
and Kelsey's [17] projected Kj^ estimates of 49.5 MPa-m^^^ at 295 K

1 12

and 55 MPa*m at 77 K. Kaufman and Kelsey's K^^ estimates also pertain to specimens of the TL orientation, but their K calculations are

based on the maximum load observed in fracture tests. Their procedure

does not account for the fact that crack extension occurs prior to

maximum load.

'

Finally, it should be noted that Merkle and Corten's method [25]

of J calculation could have been used in this study. When applied to

the 5083-0 aluminum experiments described in the text, that method

amounts to replacing the coefficient 2 in Eq, (3) by higher factors

from 2.2 to 2.3. The Jj^ values would have been increased by about

10%; the Kj^ estimates, by 5%. Read and Reed [12] found from measuring

both Kj^ and Jj^ at 76 K for the aluminum alloy 2219-T87 that Jj^ as

calculated from the measured Kj^ was about 40% greater than the measured Jj^. Thus, the Jj^ data and Kj^ estimates reported here for

5083-0 may be considered conservative.

SUMMARY AND CONCLUSIONS

The fatigue crack growth behavior and J-integral fracture toughness

of a 5083-0 aluminum alloy have been investigated at 295, 111, 76 and

4 K, a wider range of temperatures than previously studied. Specifically

1. Fatigue crack growth resistance at 111 K was insensitive to

specimen orientation, but improves at decreasing R ratios.

2. Although the fatigue crack growth rates in ambient air at room

temperature exceed the rates at cryogenic temperatures by up to a factor of 10, the rates between 111 and 4 K are nearly equivalent. The

high rates in ambient air can be attributed to the presence of moisture,

rather than temperature effects per se.

146
3. Results for the TL orientation at decreasing temperatures

between 295 K and 4 K indicate nearly a three-fold increase of Jj^

from 9 to 25 kJm"^.

4. Anisotropy in rolled plate caused a Jj^ variation of a least

2:1 at the LNG temperature of 111 K.

5. In view of the favorable low temperature effects on tensile,

fatigue, and fracture properties, it is apparent that the structural

reliability of flawed or unflawed 5083-0 alloy components will not be

decreased by cryogenic temperatures.

' ACKNOWLEDGMENTS

This work was sponsored by the Maritime Administration and the

Advanced Research Projects Agency of the U.S. Department of Defense.

The authors gratefully acknowledge the assistance of R. L. Durcholz

and Dr. R. P. Mikesell in conducting the tensile tests. We also wish

to thank Dr. R. A. Kelsey of the Alcoa Technical Center for reviewing

the manuscript.

147
REFERENCES

1. Properties of Materials for Liquefied Natural Gas Tankage, ASTM STP

579, Amer. Soc. Test. Mater., Philadelphia, 1975, pp. 1-204.

2. Rice, L. P., Campbell, J. E., and Simmons, W. P., in Advances in

Cryogenic Engineering, Vol. 8, 1963, pp. 671-677.

3. Kaufman, J. G., Nelson, F, G., and Wygonik, R. H., in Fatigue and

Fracture Toughness -- Cryogenic Behavior, ASTM STP 556, Amer. Soc.

Test. Mater., 1974, pp. 125-158.

4. Kelsey, R. A., Nordmark, G. E., and Clark, J. W., in Fatigue and

Fracture Toughness -- Cryogenic Behavior, ASTM STP 556, Amer. Soc.

Test. Mater., 1974, pp. 159-185.

5. Kaufman, J. G. , Nelson, F. G., and Wanderer, E. T., Mechanical Properties and Fracture Characteristics of 5083-0 Products and 5183

Welds in 5083 Products, Proceedings of the International Congress

of Refrigeration, Washington, D.C., Vol. 1, 1971, pp. 651-658.

6. Nelson, F. G., Kaufman, J. G. , and Wanderer, E. T., Tear Tests of

5083 Plate and of 5183 Welds in 5083 Plate and Extrusions, Paper D-1

in Adv. in Cryo. Eng., K. D. Timmerhaus, Ed., pp. 91-101.

7. Judy, R. J., Jr., and Goode, R. J., Fracture Resistance of Thick

Plate 5083-0 Alloy, Report of NRL Progress, December 1974, pp. 36-38

8. Rice, J. R., J. Appl . Mechs., Trans. ASME, Vol. 35, 1968, pp. 379-386

9. Begley, J. A. and Landes, J. D., in Fracture Toughness, ASTM STP 514,

Amer. Soc. Test. Mater., 1972, pp. 1-39.

10. Landes, J. D. and Begley, J. A., in Fracture Analysis, ASTM STP 560,

Amer. Soc. Test. Mater., 1975, pp. 170-186.

148
11. Griffis, C. A. and Yoder, 6. R. , Application of the J-Integral to

Crack Initiation in a 2024-T351 Aluminum Alloy, Naval Research

Report 7676, 1974, pp. 1-25.

12. Read, D. T. and Reed, R. P., Effects of Specimen Thickness on Fracture Toughness of Some Aluminum Alloys, submitted to Int. J. Fract.

(1976).

13. Bogardus, K. 0. and Malcolm, R. C, in Ref. 1, pp. 190-204.

14. Fowlkes, C. W. and Tobler, R. L., Fracture Testing and Results for

a Ti-6A1-4V Alloy, Eng. Fract. Mechs., to be published.

15. Tobler, R. L., Mikesell, R. P., Durcholz, R. L., and Reed, R. P.,

in Ref. 1, pp. 261-287.

16. Rice, J. R. , Paris, P. C, and Merkle, J. G., in Progress in Flaw

Growth and Fracture Toughness Testing, ASTM STP 536, Amer. Soc.

Test. Mater., 1973, pp. 231-244.

17. Kaufman, J. G. and Kelsey, R. A., in Ref. 1, pp. 138-158.

18. Argy, R., Paris, P. C, and Shaw, F., in Ref. 1, pp. 96-137.

19. Person, N. L. and Wolfer, G. C, in Ref. 1, pp. 80-95.

20. Wei, R. P., Eng. Fract. Mechs., Vol. 4, 1970, pp. 633-651.

21. Hartman, A. and Schijve, NLR Tech Note No. MP 68001 U, 1968; see

also Fig. 11 of Reference 17.

22. Materials Research in Support of Superconducting Machinery, Vols.

Ill, IV, and V, Reed, R. P., Clark, A. F., and van Reuth, E. C,

Eds., National Bureau of Standards, Boulder, CO.

23. Zinkham, R. E. and Ashton, R. F., in ASTM STP 579, Ref. 1, pp. 159-175.

24. Weston, W. F. , Naimon, E. R. , and Ledbetter, H. M. , in Ref. 1,

pp. 397-420.

25. Merkle, J. G. and Corten, H. T. , "A J-Integral Analysis for the Compact

Specimen, Considering Axial Force as Well as Bending Effects," presented at the Pressure Vessels and Piping Conference with Nuclear

Engineering and Mechanical Divisions, American Society of Mechanical

Engineers, Paper No. 74-PVP-33, 1974. - 149
01 U3 o r—

CO 00

4-> OoO)

eel

cn

CD

(J

LO *—

CO ro 0 ^ 00 C\J 0

fO S- •r- 0 4-> E •+- fO

:3 CD

c: LO

•t— O) 0 E :3 

3 ^— LlJ

r

— n3

fO > 0 <L> 1 CD

CO 03 x:

CO i- +-> 0 <U CD^

—

'—'—'—»

un > C T- C\J LT)

s-

— i- 00 CO 0 +J — WD

00

00

C cu

-l-J 0 -l-J 1— -t— fO 3 +-> E ti LD CM

(/) fO •1— Q_ 0 0

O) +-> 4-> 2: CO

s> e ! OJ ZD

>>•>-

-t-> iS- 0

OJQ-r— 0 fO sz

SC +-> Q.-I- CDC '-^

<D 3 OJ -1- <X> 0 r— 4-> S- 00

•1 •! +-> ^ 0 CO CD 00 ' C\J C\J CVJ C C

O) 0 0

1— r—

<u

•p— >- fO 0 to

LO 00

QJ CM

JD 0 fO hO)

s-

—

0 CO CM

13 Ll- r-^ CM LD

4-> 0 00

eo 1 i-<DQ.

LD

OJ ^ CT> 1— C\J

r- CM
Table 2. J-integral test results.

emperature Specimen Orientation

'^fmax

^^''^ "^t K T /o cm cm , , -2 o MD, ,^'/2 kJm , ,-2 MPa-m kJm

295

111

111

76

13 TL 14 .642 .010 10,,3

CO Tl1 u 21 . 647 . 020 1 5 R

q 15 . 647 029 20 • 11 Qo

Tl 21 .620 . 036 22,. 9

31 Tl1 L. 13 .641 .059 27

,

. 5 7 TL 15 .644 .070 30,.5 14 TL 22 .61

1

.109 41 ,.6

LT 16 .622 .033 65

,

, 6

LT 18 .612 . 019 54..2 4 LT 18 .622 .033 60.,8

5 LT 18 .619 .053 76.,0

30 TL 19 .622 .01 0 23.,6

20 TL 13 .630 .023 36,,4

?? TL 14 .617 . 056 59., 1

11 nKJ TL 20 .629 .103 78.,5

1 1 TL 20 .617 .253 122.,4

20 TL 15 .629 .01 0 27.,9

17 TL 14 .623 .01 9 31 ,,2

19 TL 16 .631 .026 40.,5

16 TL 14 .633 .039 54.,7

14 TL 17 .628 .083 72..5 9 TL 21 .632 .093 77,,3

15 TL 19 .602 .003 13.,7

11 TL 18 .597 .003 17.,6

10 TL 20 .608 .010 30.,2

17 TL 19 .602 .019 38.,3

16 TL 18 .602 .030 47.,3

18 TL 18 .597 .056 61 .,4

41

19

21

25

151
St

L-longitudinal or rolling direction

T-long transverse direction

S-short transverse or plate thickness direction

Figure 1. Microstructure of 5083-0 after rolling and annealing, lOOX.

152
|-* .42W ^ W — 1.25W

ure 2. Compact specimen used in fatigue and fracture tests (thickness,

B = 3.17 cm; dimensions are in cm).
2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m'"^

Figure 3. Fatigue crack growth rate results for TL orientations at

295, 111, 76 and 4 K.

154
2 5 10 20 50

STRESS INTENSITY RANGE, AK, MPa m'^

Figure 4. Fatigue crack growth rate results at 295 and 111 K, showing

the effects of orientation and R ratio variations.

155
1—

r

Kaufman [l?]

R=0.33

H=90%

H=10%

Person jg]

R=0, H=?

Argy [is]

HsSO%

R=0.4

R=0.05

Kelsey [4J

R=0.33, H

This Study

5083-0 ALLOY

Room Temperature

I I I I I I I I i_L

2 5 10 20 50 100

STRESS INTENSITY RANGE, AK, MPa m''^

ure 5. Comparison of fatigue crack growth data at 295 K.

156
2 5 10 20 50 1 STRESS INTENSITY RANGE, AK, MPa m''^

Figure 6. Comparison of fatigue crack growth data at low temperatures.

157
I—0.005 cm

.02 .04 .06 .08 .10 .12

AVERAGE CRACK EXTENSION, Aa, cm

Figure 7. J-integral resistance curves for 5083-0 aluminum, showing

the effect of temperature.

T58
.02 .04 .06 .08 .10 .12

AVERAGE CRACK EXTENSION, Aa, cm

Figure 8. J-integral resistance curves for 5083-0 aluminum at

in K, showing the effect of orientation.

159
Figure 9. Fracture appearance of LT (left) and TL (right) specimens

tested at 111 K.

160
1 1 1 1

^LT orientation

p 5083-0 ALLOY

1

LT orientation

TL

5083-0 ALLOY

0 100 200

TEMPERATURE, K

Figure 10. Temperature dependences of Jj^ data and K^^ estimates,

300

161
TENSILE AND FRACTURE BEHAVIOR OF A NITROGEN-STRENGTHENED,

CHROMIUM-NICKEL-MANGANESE STAINLESS STEEL AT CRYOGENIC TEMPERATURES*

R. L. Tobler and R. P. Reed

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

J-integral-fracture and conventional tensile properties are

reported for an Fe-21Cr-6Ni-9Mn austenitic stainless steel that contains

0.28% N as an interstitial strengthening element. Results at room (295

K), liquid-nitrogen (76 K), and liquid-helium (4 K) temperatures demonstrated that the yield strength and fracture toughness of this alloy

are very temperature dependent. Over the investigated temperature

range, the yield strength tripled to 1.24 GPa (180 ksi) at 4 K. The

fracture toughness, as measured using 3.8-cm-thick compact specimens,

decreased considerably between 295 and 4 K. During plastic deformation

at 295 K the alloy undergoes slight martensitic transformation, but at

76 and 4 K it transforms extensively to hep and bcc martensites. The

amount of bcc martensite formed during tensile tests was measured as a

function of elongation.

Key words: Cryogenics; fracture; low temperature tests; martensitic transformations; mechanical properties; stainless steel alloys.

*NBS contribution, not subject to copyright.

162
Introduction

Recently, austenitic stainless steel strengths have been increased

considerably by the substitution of nitrogen and manganese for nickel.

In addition to providing interstitial and solid solution strengthening,

these elements serve to increase austenite stability with respect to

martensitic transformations. Compared to nickel, these elements are

more abundant and less expensive. The alloy studied in this report,

Fe-21Cr-6Ni-9Mn-0. 3N (21-6-9), has a room temperature yield strength

(1-4) nearly twice that of AISI 304. Available tensile and impact data^ '

suggest that 21-6-9 retains good toughness at low temperatures, leading

to consideration of its use for applications benefiting from high

strength and toughness.

Accordingly, 21-6-9 is currently being considered for such critical

components as the coil form for the prototype controlled thermonuclear

reaction superconducting magnets and the torque tube for rotating

superconducting machinery. To insure satisfactory service life and to

compare with other candidate materials it is necessary to evaluate the

fracture resistance of the alloy. This study presents the first

fracture toughness data for this alloy.

Material

The 21-6-9 austenitic stainless steel plate was processed and

donated by Lawrence Livermore Laboratories, Livermore, California.

The chemical composition (in weight percent) of this heat is: 19.75

Cr, 7.16 Ni, 9.46 Mn, 0.019 C, 0.15 Si, 0.004 P, 0.003 S, and 0.28 N.

This steel was hot rolled from 30.5 x 30.5 x 10 cm slabs to 50 x 50 x

3.6 cm plate using the following schedule:

163
soak for 4 hours at 1366 K;

ro from 10 cm to 9.4 cm, screw down (compress) to 9.3 cm;

rol 1 from 9.3 cm to 8,7 cm, screw down to 8.6 cm. rotate 90°;

rol 1 from 8.6 cm to 8.0 cm. screw down to 7.9 cm;

rol 1 from 7.9 cm to 7.4 cm. screw down to 7.3 cm. rotate 90°;

rol 1 from 7.3 cm to 6.9 cm. screw down to 6.7 cm;

rol 1 from 6.7 cm to 6.3 cm. screw down to 6.2 cm. rotate 90°;

rol 1 from 6.2 cm to 5.9 cm. screw down to 5.7 cm;

rol 1 from 5.7 cm to 5.4 cm. screw down to 5.3 cm. rotate 90°;

rol 1 from 5.3 cm to 5.0 cm. screw down to 4.8 cm;

rol 1 from 4.8 cm to 4.5 cm. screw down to 4.3 cm. rotate 90°;

rol 1 from 4.3 cm to 4.2 cm. screw down to 4.0 cm;

rol 1 from 4.0 cm to 3.8 cm. screw down to 3.6 cm.

final plate temperature after this hot rolling was 1089 K Each

plate was then annealed at 1283 K for 1-1/2 hours and air cooled,

followed by an anneal at 1366 K for 1-1/2 hours and a water quench.

The resultant hardness was Rockwell B92 and the average grain diameter

was 0. 16 mm.

Procedure

Tensile

69 (5)

Tensile specimens were machined following ASTM specification E8-

; the reduced section diameter was 0.5 cm and gage length was

2.54 cm. The tensile axis was oriented transverse to the final rolling

-4

direction. Tests were performed at a cross-head rate of 8.3 x 10

cm/s, using a 44.5 kN screw-driven machine that was equipped with the

cryostat assembly designed by Reed.^^^ The tests at 295 K were conducted

in laboratory air, whereas tests at 76 K and 4 K used liquid nitrogen

164
and liquid helium environments, respectively. Load v;as monitored with

a 44.5 kN commercial load cell while specimen strain v/as measured with

a clip-on, double beam, strain gage extensometer . Yield strength was

determined as the stress at 0.2:. offset plastic strain.

Magnetic

To detect the amount of ferromagnetic, body-centered cubic (bcc)

martensitic phase in the paramagnetic, fee austenitic matrix a simple

bar-magnet torsion balance was used.^'^'' Previous measurements on FeCr-Ni austenitic steels established a correlation between the force

required to detach the magnet from the specimen and the percent bcc

martensite .

• The same correlation was used for this study to estimate

the amount of bcc martensite in the Fe-Cr-Ni-Mn alloy.

Fracture

The J-integral specimens were 3.78 cm thick compact specimens of

( 8

)

a geometry described in ASTM E 399-74 ' The specimen width, W, and

width-to-thickness ratio, W/B, were 7.6 cm and 2.0, respectively.

Other dimensions are shown in Figure 1. The notch, machined parallel

to the final rolling direction of the plate, was modified to enable

clip gage attachment in the loadline.

The J-integral specimens were precracked at their test temperatures,

(9) using a 100 kN fatigue testing machine and cryostat^ '

. All fatigue

operations were conducted using load control and a sinusoidal load

cycle at 20 Hz. Maximum fatigue precracking loads (P^) were well below

the maximum load of J tests (P ) , as indicated in Table 1. The max maximum stress intensities during precracking (K^), the final relative

crack lengths (a/W), and the edge-crack-to-average-crack-length ratios

(a /a) at each temperature are also listed in Table 1. After precracking.

165
the specimens were transferred to a 267 kN (60,000 lb) hydraulic tensile machine for fracture testing. Thus, the 76 and 4 K fracture

specimens were warmed to room temperature between precracking and J

testing at 76 and 4 K. This was necessary since the load limitations

of the 20 kN fatigue machine precluded loading this alloy to fracture

at low temperatures.

The J-integral tests followed a resistance curve technique similar

to that described originally by Landes and Begley.

^^^'^ ^

^ A series of

nearly identical specimens was tested at each temperature. Each

specimen was loaded to produce a given amount of crack extension. The

specimens were then unloaded and heat tinted to mark the amount of

crack extension associated with a particular value of J. The oxidized

zone of crack extension could be identified and measured after fracturing

the specimen into halves.

(12) Using the approximation for deeply cracked compact specimens,^ '

J = 2A/B(W-a), (1)

the value of J for each test was calculated from the total area. A,

under the load-versus-record. The values of J obtained at each temperature were plotted versus crack extension, Aa, which was measured at

five locations equidistant across the specimen thickness, and averaged.

The critical value of the J integral, Jj^, defined as the J value

at the initiation of crack extension, was obtained by extrapolating the

best fit J-Aa curve to the point of actual material separation.

Conversion to the plane-strain fracture toughness parameter, Kj^, is

made using:

166
K

2IC

E

2 (2)

where E is Young's modulus and v is Poisson's ratio. At room temperature, E ^ 195 GPa and ^ 0.287; at 76 K and 4 K, E ^ 203 GPa and

(13)

V - 0.278, according to Ledbetter's measurements.^

The yield and tensile strengths, elongation, and reduction of

area were obtained for the 21-6-9 alloy at 295, 76, and 4 K. These

data are summarized in Table 2. The results from this study are

combined in Figures 2-4 with the unpublished results of Landon''''^ for

the same heat, also hot rolled and annealed, and with the results of

Scardigno, Malin,^^^, and Masteller^^^ for annealed bar stock. The

spread of the Mai in data represent results from both the longitudinal

and transverse specimen orientations. Agreement is very good, except

that the ultimate strength data of Masteller are consistently higher

than the average of the other data.

Typical stress-strain curves at each temperature are presented in

Figure 5. The pronounced discontinuous yield behavior at 4 K probably

is associated with adiabatic specimen heating. Significant local

heating is indicated, as the flow stress drops to stress levels less

than sustained at 76 K. Another indication of significant local heating

is the rise of the reduction of area to values higher than obtained

during 76 K tests. Specimens tested at 4 K developed very local areas

of increased plastic deformation, which resulted in sizable specimen

necking prior to fracture. These load drops should not be attributed

to martensitic phase transformations for three reasons: (1) more

Results and Discussion

Tensi 1

167
extensive transformation was detected in this alloy at 76 K than at 4 K

(see later discussion) and no discontinuities in the stress-strain mode

at 76 K were observed, (2) load drops have been observed in both metastable (e.g., AISI/304) and stable (e.g., AISI 310) austenitic stainless steels at 4 K and no distinction is apparent between the two alloy

groups,

^^"^^ and (3) in austenitic steels the amplitude and frequency of

(14) the load drops at 4K are a function of the strain rate^ ' which would

be expected if local heating were responsible.

From the tensile data it is clear that the alloy 21-6-9 has a

significant decrease of ductility below 195 K, and tensile elongation

decreases progressively between 195 and 4 K.

A primary advantage offered by this alloy is its high yield

strength compared to other austenitic alloys. At room temperature the

yield strength of the 21-6-9 alloy is about 0.38 GPa (55 ksi), compared

to AISI 300 series (Fe-Cr-Ni) steel values of 0.21 to 0.25 GPa (30-35

ksi). The yield strength of the 21-6-9 steel approximately triples to

a value of 1.24 GPa (180 ksi) as the temperature is decreased to 4 K.

The Fe-Cr-Ni austenitic alloys achieve values about double or triple

their room temperature values (60-110 ksi) at 4 K. Thus, the strength

advantage offered by the 21-6-9 alloy is greatest at low temperatures.

Fracture :

The load-versus-loadl ine deflection curves for compact specimens

at 295, 76 and 4 K are shown in Figure 6. The curves at 295 K extended

to larger deflections than indicated on the axis of the diagram. The

fracture test data are tabulated in Table 3. There are no ASTM E 399-

74 valid Kj^ data. The 5% secant offset data are denoted Kq because the

ASTM E 399-74 thickness and crack front curvature criteria are not

168
satisfied. Using B > 2.5 (K^/a^) , a specimen thickness of 4.2 cm at 4

K is required, slightly larger than the 3.8 cm thickness tested. The

crack front curvatures shown in Figure 7, are slightly larger than

allowed by ASTM E 399-74. The surface crack lengths are 88 to 89% of

the average of internal crack lengths, while 90% is specified in the

ASTM E 399-74 Method as the minimum deviation.

The J-versus-Aa results at room temperature are plotted in Figure

8. Ductile tearing or slow, stable crack extension occurred at this

temperature. Large apparent crack extensions were observed due to

plastic deformation at the crack tip; only in two specimens at the

highest values of Aa was actual material separation noted. These two

values fall on the same trend line as the specimen data that did not

exhibit material separation. Therefore the response of this extremely

ductile material to J-integral tests at room temperature is inconclusive, with no well-defined break from the linear portion of the plastic deformation curve observable.

According to the tentative size criterion suggested by Landes and

Begley^^^^, the specimen thickness for valid Jj^ measurements should

satisfy the relationship:

B > a(J/a^) (3)

where a is 25 and is the average of the yield and tensile strengths.

In the tests at 295 K, the conditional critical J values are in the

range 925 to 1350 kJm"^. Using the flow stress value of 0.527 GPa

(76.5 ksi), the J-integral results at room temperature are invalid for

the specimen thickness tested here. A specimen thickness of 6.3 cm

(2.5 inches) may be needed to insure valid data, according to Eq. (3).

169
The J-resistance curve at 76 K is also shown in Figure 8. The

data fit a regular trend, with the exception of the point representing

the largest observed crack extension (not shown). The curve drawn

through the remaining data indicates that crack extension initiates at

a Jj^ value of about 340 kJm . The corresponding value of Kj^(J),

estimated using Equation 2, is 275 MPa-m^^^ (250 ksi in^^2), + 5%.

At 4 K, the alloy approached linear-elastic behavior, but the

results of the first three tests failed to satisfy the ASTM validity

criteria^ ' for direct Kj^ measurements. Eight additional J tests were

conducted and these results are included in Figure 8. The J-Aa curve

_2

at 4 K is nearly horizontal, indicating a Jj^ value of about 150 kJm

+ 10; the Kj^ estimate from Eq. (2) is 182 MPa-m^^^ (165 ksi'in^^^).

Phase Transformations

After tensile tests at 76 and 4 K, the deformed specimens were

magnetic. Therefore, these specimens were measured, using bar-magnet

torsion balance equipment, to correlate magnetic attraction with

specimen reduction of area. The magnetic readings were converted to

percent bcc martensite and the reduction of area converted to elongation, assuming constant volume. These data are plotted in Figure 9 and

typical microstructures are shown in Figure 10.

Although not positively identified, it is probable that hep martensite was also formed in the 21-6-9 alloy during low temperature

deformation. The microphotographs after deformation at 4 K (Figure

10) identify transformed regions which are parallel to the (111) slip

band traces. These appear identical to the hep areas identified in

earlier research on AISI 304, an Fe-Cr-Ni alloy. ^^'^^^

170
The amount of bcc martensite fonned is large and only slightly

less than that which is formed in AISI 304 at the same temperatures^^'^^^

Permeability values of the order of 10 were measured in heavily deformed

specimen portions at 76 K, but it is difficult to identify bcc martensite

in the Figure 10 photo-micrographs. Normally, in austenitic stainless

steels the bcc martensitic product has an acicular, plate-like morphology

with the habit plane of the plate not {111}. Examination of specimen

microstructures, typified by Figure 10 indicate that only at {111}

band intersections are the distinctive plate-like microstructures

observed.

There is clear evidence that the amount of the transformation is

suppressed, as a function of either stress or strain, as temperature is

lowered from 76 K to 4 K. This is similar to the Fe-Cr-Ni (AISI 304)

alloy martensitic transformation behavior^ '^'^^^

, where formation of the

hep martensitic phase was suppressed at temperatures between 20 and 4

K. Apparently, in the complicated energy balance affecting martensitic

transformation for these alloy systems at low temperatures, the increase

of flow stress and the decrease of dislocation mobility more than

offset the gradually increasing free energy difference between the

structures.

Finally, it is not clear that martensitic transformations are

deleterious to material application. Normally, the stress levels used

in service are less than the yield strength, and no martensitic transformations should occur. The complexities and concern usually are

discussed when one considers welds and weld techniques. Chemical

segregation and stress concentraions are then more likely, rendering

particular sections less stable and, locally, stressed above the yield

171
strength. In these situations martensitic products will form.

AISI 304 behaves in a similar manner; it is stable on cooling to

low temperatures but transforms to hep and bcc martensitic products

during plastic deformation. But, unlike 21-6-9, the fracture toughness

(15) of AISI 304 remains extremely high at 4 , implying that martensitic transformations are not harmful to the fracture toughness of the

Fe-Cr-Ni stainless steel. This is not clear in the case of the Fe-CrNi-Mn-N alloy, however, as the toughness is rapidly decreasing between

76 and 4 K. For appropriate safety of operation at 4 K, additional

research is necessary to understand the effect of martensitic transformations on fracture toughness. '•

Conci usions

1. The fracture toughness of the 21-6-9 austenitic stainless

steel exhibits a decided temperature dependence between 300 and 4 K,

2 1/2 but retains a toughness of 150 kJ/m (136 ksi»in ) at 4 K. Linearelastic behavior was approached at 4 K.

2. The yield strength of the 21-6-9 alloy is also very temperature dependent, tripling from room temperature to 4 K, and reaching a

value of 1.24 GPa (180 ksi) at 4 K.

3. During plastic deformation at 76 and 4 K, bcc martensite

was identified and correlated with strain. Suppression at 4 K, compared to 76 K, of the amount of bcc martensite was found.

Acknowledgements

The authors thank D. P. Landon, Lawrence Llvennore Laboratories

for supplying the test material. Dr. R. P. Mikesell conducted the

tensile tests, R. L. Durcholz contributed technical assistance to

tensile, fracture, and metal lographic preparation, and Dr. M. B. Kasen

provided the photomicrographs.

172
References

1. P. R. Landon, Unpublished data, Lawrence Livermore Laboratories,

Livermore, CA (1975).

2. P. F. Scardigno, Masters Thesis, Naval Postgraduate School, Monterey,

CA, AD/A-004555 (1974).

3. C. 0. Mai in, NASA SP-5921 (01 ), Technology Utilization Office, NASA,

Washington, D.C. (1970).

4. R. D. Masteller, NASA CR-72638(N70-271 1 4) , Martin Marietta Corp.,

Denver, CO (1970).

5. Standard Methods of Tension Testing of Metallic Materials, ASTM

E8-69, 1976 Annual Book of ASTM Standards, Part 10 (ASTM,

Philadelphia, PA, 1975) p. 120.

6. R. P. Reed, Advances in Cryogenic Engineering , Vol. 7 (Plenum Press,

New York, 1962) p. 448.

7. R. P. Reed and C. J. Guntner, Trans. AIME, 230, (1964) p. 1713.

8. Standard Method of Test for Plane-Strain Fracture Toughness of

Metallic Materials, ASTM E 399-74, 1976 Annual Book of ASTM

Standards, Part 10 (ASTM, Philadelphia, PA 1976) p. 471.

9. R. P. Reed, R. L. Tobler, and R. P. Mikesell, "Advances in Cryogenic

Engineering - ICMC", Vol. 22_ (Plenum Press, New York, 1976), to be

publ ished.

10. J. D. Landes and J. A. Begley, Westinghouse Research Laboratory

Scientific Paper 73-1 E7-FMPWR-P3 , Pittsburgh, PA (1973).

11. J. D. Landes and J. A. Begley, "Fracture Analyses", ASTM STP 560,

(American Society for Testing and Materials, Philadelphia, PA 1974)

p. 170.

12. J. R. Rice, P. C. Paris, and J. G. Merkle, ASTM STP 535 (ASTM,

Philadelphia, PA 1973j p. 231.

13. H. M. Ledbetter, personal communication.

14. C. J. Guntner and R. P. Reed, ASM Trans. 55_, (1 952) p. 399.

15. R. P. Reed, A. F. Clark and E. C. van Reuth, Eds. "Materials Research for

Superconducting Machinery III", AD-AOl 2365/3WM, National Technical

Information Service, Springfield, VA (1975).

173
List of Figures

Figure 1. Compact specimen for fracture testing of Fe-1 9Cr-6Ni-9Mn

alloy.

Figure 2. ' Summary of tensile and yield strength data as a function of

temperature for the Fe-21Cr-6Ni-9Mn alloy.

Figure 3. Summary of tensile elongation as a function of temperature

for the Fe-21Cr-6Ni-9Mn alloy.

Figure 4. Summary of tensile reduction of area as a function of

temperature for the Fe-21 Cr-6Ni -9Mn alloy.

Figure 5. Stress-strain curves for the Fe-21Cr-6Ni-9Mn alloy at

295, 76 and 4 K.

Figure 6. Typical load-deflection curves for compact specimens

at 295, 76 and 4 K for annealed Fe-21 Cr-6Ni-9Mn alloy.

Figure 7. Fracture characteristics of Fe-21Cr-6Ni-9Mn alloy at

295, 76 and 4 K.

Figure 8. The J-integral as a function of crack extension at

295, 76 and 4 K for annealed alloy Fe-21Cr-6Ni-9Mn.

Figure 9. Estimated percent bcc martensite that forms during

tensile tests as a function of tensile elongation.

Figure 10. Microstructures of alloy 21-6-9 after deformation at 4 K. Bands lie on {111} austenite planes and probably represent hep and bcc martensite, (a) 800X, (b) 1200X.

List of Tables

Table 1. Precracking parameters for J-integral specimens.

Table 2. Tensile properties of Fe-21 Cr-6Ni-9Mn alloy.

Table 3. Fracture results for 3.8 cm thick compact specimens of

alloy Fe-21Cr-6Ni-9Mn.

174
Table 1. Precracking parameters for J-integral test specimens.

Test ^f/^ma ^^^"^

"^f Relative Crack a /a

Temperature

(percent) (MPa-m^/^^ ^^"^th, a/W

295 40-45 48-54 0.638 0.90-0.91

76 22-27 52-63 0.640 0.87-0.90

4 30-35 52-63 0.64 to 0.795 0.88-0.89

175
Table 2. Tensile properties of Fe-21 Cr-6Ni -9Mn alloy.

Yield Strength Tensile Strength Elongation

Temperature Q.Z% offset GPa 2.5 cm gage Reduction of

(K) GPa . length {%) Area {%)

295 K 0. 350 0. 696 61 79

0. 357 0 705 61 • 78

Average 0. 353 (51 ksi) 0 701 (102 ksi

)

61 78

76 K 0. 913 1 462 42 32

0. 886 1 485 43 41

Average 0. 899 1 474 (214 ksi

)

43 37

4 K 1. 258 1 633 . 40

1. 224 1 634

Average 1 241 (180 ksi) 1 634 (237 ksi) T6 40

176
Table 3. Fracture results for 3.8 cm thick compact

specimens of alloy Fe-21 Cr-5Ni -9Mn

Temperature

(k)

a/W 1

(MPa TH '

\ \ W U. Ill )

J

J

_?

( kJm ) ^ l\ U 1 1 1 J

Aa

( rm ) i kJm" ) y r\ k-* 1 1 1 J

295 0.638 58 177

2 0.013p

0. 636 61 744 0. 051

0.640 55 905 0. 069? 1 1 30+20%

0. 635 53 1 355 0.097?

0. 642 50 1423 0.112

76 0.612 134 261 0.0

0.634 153 413 0.028

0 640 1 31 499 0 053

0. 637 1 37 674 0. 079 337+1 0%

0 645 1 30 788 0 091

0. 643 1 30 698 0. 1 98

4 0. 645 1 64 NA NA

0. 648 1 62 NA NA

0. 643 159 NA NA

0. 670 NA 1 00 0.0

0. 655 167 147 0. 020

0. 670 158 149 0. 080

0.656 160 162 0.076

0.750 NA 89 0.0 150+10%

0.725 NA 191 0.0313

0.725 NA 274 0.105

0.755 NA 141 0.033

1. Calculated from ASTM E 399-74 Method.

2. Apparent crack extension due to crack tip deformation only.

3. Crack extension due to deformation and material separation.

NOTES: 1 in-lb-in"^=0.175 kJm"^; 1 inch=2.54 cm; 1 ksi •in^^2=l .099 MPa-m

U7
i

3.6cm—

5.7cm

W= 7.6cm — 9.5cm

Figure 1. Compact specimen for fracture testing of

Fe-19Cr-6Ni-9Mn alloy.

178
2.0

1.6

o

O 1.2

t;; 0.8

Tensile

Yield

0 This Report

A Scardigno (1974)

London (1975)

V Mosteller (1970)

1 Molin (1970)

0.4

50 100 150 200

TEMPERATURE, K

250 300

Figure 2. Summary of tensile and yield strength data as a function of temperature for the Fe-21 Cr-6Ni -9Mn alloy.

179
80

60

z

lAJ U

uj 40

20

I

ELONGATION

V Mast«ll«r (1970)

0 This Report

A Scardigno (1974)

Landon (1975)

1 Malin (1970)

50 100 150 200

TEMPERATURE, K

250 300

Figure 3. Suininary of tensile elongation as a function of

temperature for the Fe-21Cr-6Ni-9Mn alloy.

180
0 50 100 150 200 250 300

TEMPERATURE, K

Figure 4. Summary of tensile reduction of area as a function

of temperature for the Fe-21Cr-6Ni-9Mn alloy.

181
Figure 5. Stress-strain curves for the Fe-21Cr-6Ni-9Mn

alloy at 295, 76, and 4 K.

18 2
0 .1 .2 .3 .4 .5

LOADLINE DEFLECTION, cm

Figure 6. Typical load-deflection curves at 295, 76, and

4 K for annealed Fe-21Cr-6Ni-9Mn alloy.

183
29SK 76K 4K

Figure 7. Fracture characteristics of Fe-21Cr-6Ni-9Mn

alloy at 295, 76, and 4 K.

184
1600

Aa, cm

Figure 8. The J-integral as a function of crack extension at 295,

76, and 4 K for annealed alloy Fe-21Cr-6Ni-9Mn.
ELONGATION, percent

Figure 9. Estimated percent bcc martensite that forms during

tensile tests as a function of tensile elongation.

186
(a) (b)

Figure 10. Microstructures of alloy 21-6-9 after deformation at 4 K.

Bands lie on {ill} austenite planes and probably represent

hep and bcc martensite, (a) 800X, (b) 1200X.

187
CRYOGENIC TENSILE, FATIGUE, AND FRACTURE PARAMETERS

FOR A SOLUTION-ANNEALED MARAGING STEEL"^

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

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Contribution of NBS, not subject to copyright.

188
ABSTRACT

The mechanical properties of an eighteen percent nickel, solutionannealed 300-grade maraging steel were measured to assist in the

evaluation of this material for low-temperature structural applications. Tensile, fatigue-crack growth rate, and fracture toughness

tests were performed in ambient air (295 K), liquid nitrogen (76 K),

and liquid helium (4 K) , with the following results: (1) the yield

strength of this material increases from 848 MPa at room temperature

to 1596 MPa at 4 K; (2) the tensile ductility is moderate, with elongation decreasing from 15.5 to 6.7'o for this temperature region; (3) the

1 /2 plane strain fracture toughness (Kj^,) decreases from 165 MPa-m at

1 12. room temperature to 83 MPa^m at 4 K; and (4) the fatigue-crack

propagation resistance at intermediate stress intensity ranges is

relatively insensitive to temperature. These results are compared

with similar data for other cryogenic materials.

Key words: Fatigue; fracture; low temperature tests; maraging steels;

mechanical properties; nickel alloys.

189
INTRODUCTION

The beneficial effect of nickel on the low temperature fracture

resistance of steels is well known [1-2]. Concentrations of from 2 1/4

to 9% Ni are used in the 0.1 to 0.2% carbon ferritic steels that were

specially developed for low temperature service [2]. For these steels,

increasing nickel content correlates with reduced ductile-to-brittle

transition temperatures. For the grade having the highest nickel content,

ASTM A533-72a (9% Ni steel), the transition to low fracture toughness

occurs at temperatures between 76 and 4 K. Emerging applications in the

relatively new field of superconducting machinery would benefit from a

commercially-available ferritic steel that retains high toughness at 4

K. •

With this goal in mind, the 18% Ni maraging steels must be considered. Maraging steels are easily processed and are weldable. High

nickel and low carbon contents 0.003% C, max.) account for the

relatively soft, platelet-like martensite that forms on cooling from the

austenite field. Cobalt, molybdenum, titanium, and aluminum alloying

contributes significantly to strengthening, and the ultra-high strengths

obtained with fully aged 300 grade maraging steels represent an outstanding technological achievement [3,4]. However, low fracture

toughness is often associated with high yield strength [5-8]. Therefore the fracture toughness of this material should be investigated

before considering it a candidate for cryogenic structural applications.

The literature contains numerous plain strain fracture toughness (Kj^)

and fatigue crack growth rate parameters for maraging steels [9-15],

but low temperature studies are less common [10,13-15].

190
This paper describes the mechanical behavior of a solution-annealed

18% Ni, 300 grade maraging steel at temperatures in the ambient-to-extreme

cryogenic range. The conventional tensile properties, fatigue crack

growth rates, and fracture toughness values were measured at 295, 76,

and 4 K, using state-of-the-art techniques. This alloy was tested in

the solution-annealed condition, to maximize the fracture toughness.

Material

The 300 grade maraging steel tested in this study was supplied by

the Morris Steel and Aluminum Corporation. The material was a 5.3 x 15.4 x

58 cm forged bar that had been solution-annealed at 1088 K and air cooled.

The chemical analysis quoted by the supplier is, in weight percent:

18.41 Ni, 0.002 C, 0.01 Mn, 0.006 P, 0.003 S, 0.01 Si, 9.27 Co, 4.95 Mo,

0.59 Ti, 0.12 Al , and balance, Fe. This alloy was tested in the asreceived condition which is a lath martensite having the body-centered

cubic crystal structure and virtually no retained austenite [9].

Procedures

Tensile

Cylindrical tensile specimens having a reduced section 3.8 cm long

and 0.51 cm in diameter were machined in the transverse orientation,

such that the loading-axis/fracture-plane orientation matched that of

the compact specimens described below. The tensile tests were conducted

at a crosshead velocity of 0.008 mms"'' , using the 44.5 kN screw-driven

machine and cryostat previously described [16]. The commercial load

cell and clip-on strain gage extensometer outputs were autographical ly

recorded, and the resultant load-versus-deflection curves were analyzed

following the standard ASTM E8-69 Method [17].

191
Fracture

Compact specimens of the TL orientation [18] (notch plane normal to

the long transverse forging direction) were used in all fatigue and

fracture tests. The specimens were 2.3 cm thick (B) and 5.08 cm wide

(W), The planar dimensions are shown in Figure 1. Knife edges were

machined integral to the notch, permitting clip-gage placement and.

deflection measurements at the loadline.

Room temperature (295 K) tests were conducted in unconditioned

air, using a 100 kN servo-hydraulic test machine and cryostat. Low

temperature tests were performed with the specimen and clip gage completely submerged in liquid nitrogen (76 K) or liquid helium (4 K)

environments. At each temperature, the clip-gage satisfied the ASTM

E-399-74 Method linearity requirements [18]. The apparatus and low temperature techniques are described elsewhere in greater detail [19].

The test procedure involved precracking the specimens at their test

temperatures and subsequently loading them to fracture by increasing the

1/2 -1 stress intensity at a rate of approximately 1 MPa*m ' s . At 76 K and

4 K, the ASTM E 399-74 requirements for valid, linear-elastic fracture

toughness tests were fulfilled. Therefore, Kj^ was calculated directly

using the solution for compact specimens [18]:

' he ^ PQB^W^/^[f(a/W)] ^ . H (1)

The calibration factor, f(a/W), is a function of relative crack length [18]:

f(a/W) = 29.6(a/W)^^^-185.5(a/W)^/^+655.7(a/W)^/^-1017.0(a/W)''/^+638.9(a/W)^

192
The load Pg is derived from the test record using the secant offset

procedure, and crack length is the average value of measurements at 25,

50, and 75% of specimen thickness. The uncertainty in Kj^ values

obtained by this method is estimated at less than 5% [20].

Nonlinearity in the test records at room temperature precluded

using the ASTM E-399-74 method. Therefore, Kj^ was estimated using the

J-integral concept. J is the rate of change of potential energy with

respect to crack area for nonlinear elastic materials, and it is a

measure of the crack-tip strain field intensity for elastic-plastic

fractures. The critical value, Jj^, is the value of J at the onset of

crack extenstion [21].

Since stable crack extension occurred in the solution-annealed

maraging steel at room temperature? the resistance curve technique [21]

was used to measure Jj^. Seven nearly identical specimens (a/W - 0.6)

were loaded to cause crack extension increments of up to 0.4 cm. The

specimens were then unloaded and heat-tinted to oxidize the crack surfaces

The specimens were then cooled to 76 K (to avoid subsequent plastic

deformation) and fractured into halves. The straw/blue crack extension

increments (Aa) created during the initial loading were measured to the

nearest 0.001 cm with a travelling microscope at three points equidistant across the specimen thickness, and averaged. The J values at

points of unloading were calculated using the approximation [22]:

J = 2AB"^(W - a)"^ (3)

The pairs of J and Aa measurements were plotted and extrapolated to

obtain Jj^ with an uncertainty of + 10%. The room temperature Kj^ was

then estimated from:

193
where E, Young's modulus for the material is 175.6 GPA (25.5 x 10^ psi)

and V, Poisson's ratio is 0.325 [23].

Fatigue Crack Growth

Fatigue crack growth rates were measured during the precracking of

fracture toughness specimens, but the maximum stress intensity factor

1 II was restricted to less than 50 MPa-m ' , to insure that the precracking

loads did not influence the fracture toughness test results. To obtain

1 11 da/dN data at stress intensity factors greater than 50 MPa*m , one

additional specimen was tested at each temperature. The fatigue tests

were conducted using controlled loads, a sinusoidal load cycle, a test

frequency (F) of 20 Hz, and a minimum/maximum load ratio, R, of 0.1.

Crack length was inferred by elastic compliance or deflection-perunit-load (6/P) measurements. Following techniques previously described

[24], correlations between average crack length and 6/P were obtained

experimentally using data from fractured specimens. The a-versus-N

curves were constructed from compliance readings taken periodically

during the fatigue tests. Using a computer program, the a-versus-N

curves were fitted with a third order polynomial and differentiated,

yielding da/dN with an uncertainty of less than + 20%. The stress

intensity factor ranges were calculated based on Eqs. (1-2) and the

fatigue load range:

AK = K -K . = (P -P . )B"^W"^/^[f(a/W)] (5) max mm ^ max mm' l \ / /j \ i

194
RESULTS AND DISCUSSION

Tensile

The uniaxial tensile property measurements for the solution-annealed

300 grade maraging steel are itemized in Table 1, and the average values

of yield strength, ultimate strength, elongation, and reduction of area

are shown in Figures 2 and 3. The results show that the strength and

ductility parameters exhibit opposite temperature dependences. Between

295 and 4 K, the yield strength increases from 848 MPa to 1596 MPa,

while reduction of area decreases from 70\- to 47\-. The room

temperature yield strength is significantly lower than the 1790 to 2060

MPa range for aged 300 grade maraging steels [9], but ductility is

higher. On the other hand, this solution-annealed 300 grade maraging

steel offers a modest improvement over the yield and ultimate strengths

and reduction of area values for a commercial 9"'; Ni steel in the quenched

and tempered condition [25]. The yield strengths of several nickel alloy

steels are compared in Figure 4.

Fracture Toughness

The fracture surfaces of compact specimens showed sizable shear-lip

regions at room temperature, whereas the fractures at 76 and 4 K were

relatively flat. "Type I" test records [18] having only slight nonlinear

segments near the maximum load were obtained at these low temperatures.

The fracture measurements at each temperature are summarized in Table 2.

Consider the room temperature results. The J-versus-la

curve at room temperature, Figure 5, reveals a linear trend for Aa

greater than 0.5 mm. At smaller la, apparent crack extension is caused

by crack-tip geometry changes due to blunting instead of actual material

195
separation. The J = 2Aaa^^^^ line was constructed to account for this

blunting, as recommended [21]. The Jj^ value taken at the intersection

kJm"

1/2

_2 of the resistance curve and the flow line is 140 kJm , and the corresponding Kj^ estimate from Eq. (4) is 165 MPa^m

The 76 K and 4 K results from the ASTM E 399-74 method satisfy

the linear-elastic size criterion which requires:

a, W-a, B > 2.5 — ^ (6)

The edge-crack-to-average-crack-length ratios were uniform, with values

ranging from 0.96 to 0.98. The P ^ /P^ ratios were also acceptable,

max y

with values below 1.10. The data listed in Table 2 are therefore

valid, and the average K^^ at each temperature is shown in Figure 6.

As expected, there is a substantial improvement in fracture toughness

over the values reported for aged 300 grade maraging steels. The room

1 II

temperature Kj^ value for our solution-annealed material, 165 MPa*m '

,

is nearly threefold greater than values reported for the aged condition

[3,9]. Low temperature data are scarce, but Antolovich [13] reports Kj^

1 /2 values of 115 and 66 MPa«m ' for an aged 300 grade maraging steel at

295 and 77 K, respectively. Thus, the difference in Kj^ for the solutionannealed and aged conditions may be as large as a factor of 2 at liquid

nitrogen temperature.

While it is true that low temperature effects on Kj^ for the maraging

steels are adverse, our data indicate no abrupt fracture transitions such a

usually observed for body-centered cubic materials, as shown in Figure 6.

Nevertheless, there is a 48% reduction of Kj^ for the solution-annealed

maraging steel between 295 and 4 K. At 4 K, the fracture toughness is

196
83 MPa-m^ , slightly higher than the 75 MPa-m^ value reported [25]

for quenched and tempered 9'.- Ni steel. The absence of transitional

behavior in the maraging steel undoubtedly is rela^ced to the favorable

influences of high nickel and low carbon contents on the deformation

characteristics and cleavage resistance of steel ['!].

The present results reinforce the view that plastic deformation and

fracture processes are competitive, and that factors which tend to

increase a material's resistance to slip also tend to enhance the probability of brittle fracture. In their studies of maraging steels at

room temperature, Fischer and Repko [7], Jones and Brown [6], and

Srawley [5] demonstrated decreases in toughness at higher yield strengths.

They illustrated the inverse relationship by varying yield strength

through metallurgical changes in alloying and heat treatment. In the

present study, similar trends are noted on lowering the test temperature.

Fatigue Crack Growth Rates

Fatigue crack growth rates for the solution-annealed 18% Ni maraging

steel are shown in Figure 7. The da/dN data define a scatterband

1 II approximately 10 MPa-m wide. Within this range, the data at 76 K

and 4 K are virtually equivalent, tending to be slightly lower than

rates at room temperature. Since the improvement in rates at cryogenic

temperatures never amounts to more than a factor of 2, all of the

1 II

results at stress intensity factors between 20 and 55 MPa*m can be

specified by an upper bound equation:

^= 6.5 X 10-^AK)^-° (7)

197
1 /2

Here da/dN and AK are given in SI units, mm/cycle and MPaTn '

, respectively.

At AK values greater than 55 MPa^m^'^^, the rates at 295 K and 75 K

remain conservative with respect to Eq. (7), at least for the range of

AK investigated. However, the rates at 4 K are accelerated and the

fatigue crack propagation resistance becomes inferior as AK exceeds

75% of the reported Kj^ value at this temperature. The 4 K rates at

1 11

stress intensity factors greater than 55 MPa*m are not specified by

the upper bound equation, Eq. (7). Rather, the behavior at 4 K can be

described as resulting from a transition in the power-law dependence on

AK, i.e. a transition from an exponent of n = 3 to an exponent of n = 7.6

1 II occurs at AK = 55 MPa^m . Similar transitions to high values of n

are known to occur in other steels as AK approaches Kj^, due to the

influence of static fracture modes on microcracking [25].

Figure 8 compares Eq. (7) for the solution-annealed 300 grade maraging steel with a band representing typical results for other steels at

room temperature. Included in the band are: (1) Barsom's data [26] for

non-nickel ferritic steels of various strengths, (2) our previously

reported data [25] for 3.5, 5, and 9% Ni ferritic steels, and (3) some

data for the 300 grade maraging steels tested by Bathias and Pelloux

[11], and Antolovich, Saxena, and Chanai [12]. All of these sources

report power-law equation exponents in the range 2.5 to 3.5. Evidently,

the present results are typical for steels at room temperature. Bathias

and Pelloux reported that their rates for a solution-annealed 300 grade

maraging steel were indistinguishable from rates for the same alloy in

1 11

the aged condition, for 30 < AK < 50 MPa^m . However, it would be

speculative to assume that this would be true at extreme cryogenic

temperatures, and data at 4 K for the aged condition are unavailable.

198
In Figure 9, the upper bound representation of Eq. (7) is used

again in comparing the behavior of this maraging steel with bands

representing rates for austentic nickel-base superalloys and austenitic

stainless steels tested at temperatures in the range 295 to 4 K.

Included in the band for austenitic stainless steels are results for

AISI types 304, 304L, 310, 310S, and 316 as well as Kromarc 58, A-286,

and an Fe-21 Cr-6Ni -9Mn alloy [27,28]. Included in the band for nickel

base superalloys are data for Inconel alloys 750, 718, 706 and a low

expansion alloy, LEA [29]. The fatigue-crack growth resistance of the

solution-annealed maraging steel is intermediate when compared with

these potential competitor alloys, suggesting that yield strength and

fracture toughness comparisons should be the primary considerations

governing alloy selection for cryogenic purposes.

CONCLUSIONS

Relatively few mechanical properties relevant to the problem of

fracture-resistant design have been measured for maraging steels at low

temperatures. In this study, conventional tensile properties and fracture mechanics parameters were measured for an 18"^: Ni, 300 grade maraging

steel in the solution-annealed condition, since the toughness of aged

alloys at low temperatures is marginal. The fracture toughness of the

solution-annealed alloy is an inverse function of yield strength between

295 K and 4 K, with K^^ decreasing from 165 MPa-m^^^ to 83 MPa-m^^^,

and yield strength increasing from 848 MPa to 1596 MPa. These strengths

compare favorably with some alloys frequently used in cryogenic environments, such as the austenitic stainless steels. The solution-annealed

maraging steel can be considered for cryogenic uses, although the fracture toughness at 4 K is only about 8'^ greater than that of a cormiercial ly

available and less expensive 9% Ni alloy steel (ASTM A 553).

199
- ' ' ACKNOWLEDGMENTS

This study was sponsored by the Advanced Research Projects Agency

of the U.S. Department of Defense. The contributions of Dr. R. P.

Mikesell and R. L. Durcholz in conducting the tensile tests are gratefully acknowledged.

REFERENCES

1. Johnson, R. J., Metals Eng. Quart. 15 (1975) 1.

2. Pense, A. W. and Stout, R. D., in Fracture Toughness and Related

Characteristics of the Cryogenic Nickel Steels, WRC Bulletin 205

reprint (Int. Nickel Co., New York, 1976) 1.

3. Zackay, V. F., in Alloy Design for Fatigue and Fracture Resistance,

Conference Proceedings No. 185, AGARD-CP-185 (North Atlantic Treaty

Organization, 1976) AD A021486.

4. Floreen, S., Metallurgical Reviews 126 (1968) 115.

5. Srawley, J. E., in Fracture, 1969 (Chapman and Hall, London, 1969) 131.

6. Jones, M. H. and Brown, W. F. , in Review of Developments in Plane

Strain Fracture Toughness Testing, ASTM STP 463 (Amer. Soc. Test.

Mater., Philadelphia, 1970) 63.

7. Fischer, D. M. and Repko, A. J., J. Materials, JMLSA 7 (1972) 167.

8. Psioda, J. A. and Low, J. R., NASA Tech. Report No. 7 (Dept. Mater.

Science, Carnegie-Mellon University, 1975) NASA-CR-143501 . 9.

9. 18% Nickel Maraging Steels, Data Bulletin (International Nickel

Co., 1969). : '

10. Cryogenic Materials Data Handbook, AFML-TDR-64-280 (Martin

Marietta Co., 1964).

200
n. Bathias, C. and Pelloux, R. M. , Met. Trans. 4 (1973) 1265.

12. Antolovich, S. D., Saxena, A., and Chanai , G. R., Met. Trans. 5^

(1974) 623.

13. Antolovich, S. D. , private communication.

14. Vishnevsky, C. and Steigerwald, E. A., in Fracture Toughness Testing at Cryogenic Temperatures, ASTM STP 496 (Amer. Soc. Test. Mater.,

Philadelphia, 1970) 3.

15. Shoemaker, A. K. and Rolfe, S. T., J. Basic Eng. Trans. ASME, 91

(1969) 512.

16. Reed, R. P., in Advances in Cryogenic Engineering 1_ (1962) 448.

17. Standard Methods of Tension Testing of Metallic Materials, designation

E8-69, in 1974 Annual Book of ASTM Standards, Part 10 (Amer. Soc.

Test. Mater., Philadelphia, 1974) 90.

18. Standard Method of Test for Plane Strain Fracture Toughness of

Metallic Materials, designation E 399-74, in 1974 Annual Book of

ASTM Standards, Part 10 (Amer. Soc. Test. Mater., Philadelphia,

1974) 432.

19. Fowlkes, C. W. and Tobler, R. L., Eng. Fract. Mechs. 8 (1976) 487.

20. Antolovich, S. D. and Chanai, G. R. , in Third International Conference

on Fracture (Vereiu Deutscher Eisenhuttenleute, Dusseldorf, 1975)

11-242.

21. Landes, J. D. and Begley, J. A., in Fracture Analysis, ASTM STP

560 (Amer. Soc. Test. Mater., Philadelphia, 1974) 170.

22. Rice, J. R. , Paris, P. C, and Merkle, J. G., in Progress in Flaw

Growth and Fracture Toughness Testing, ASTM STP 536 (Amer. Soc. Test.

Mater., Philadelphia, 1973) 231.

23. Ledbetter, H. M., private communication.

201
24. Tobler, R. L., Mikesell, R. P., Durcholz, R. L., and Reed, R. P.,

in Properties of Materials for Liquified Natural Gas Tankage, ASTM

STP 579 (Amer. Soc. Test. Mater., Philadelphia, 1975) 261.

25. Tobler, R. L. and Reed, R. P., to be published.

26. Barsom, J. M. , J. Eng. Industry, Trans. ASME (1971) 1190.

27. Logsdon, W. A., Wells, J. M., and Kossowsky, R. , in Proceedings of

the Second International Conference on Mechanical Behavior of

Materials (Amer. Soc. Metals, Ohio, 1976) 1283.

28. Tobler, R. L., in Proceedings of the Second International Conference

on Mechanical Behavior of Materials (Amer. Soc. Metals, Ohio, 1976)

573.

29. Logsdon, W. A., Wells, J. M. , and Kossowsky, R. , in Materials Research

for Superconducting Machinery; Reed, R. P., Ledbetter, H. M. , and

van Reuth, E. C, Eds. (National Bureau of Standards, Boulder, CO,

1976).

LIST OF FIGURES

Figure 1. Planar dimensions of compact specimens for fatigue and

fracture tests.

Figure 2. Yield and ultimate strengths for solution-annealed 300 grade

maraging steel, showing 88% and 64% increases for the temperature range 295 to 4 K.

Figure 3. Reduction of area and elongation values for solution-annealed

300 grade maraging steel, showing gradually decreasing tensile ductility at low temperatures.

Figure 4. A yield strength comparison of solution-annealed maraging

steel and some ferritic nickel alloy steels.

202
Figure 5. The J resistance curve for solution-annealed maraging steel

at room temperature, showing a typical data trend.

Figure 6. The effect of temperature on K^^ for solution-annealed maraging steel, which does not show the transitional behavior

exhibited by other nickel-alloy steels. (Data for the

3.5, 5, and 9% Ni steels are published elsewhere [24,25]).

Figure 7. Fatigue crack growth rates for the solution-annealed 300

grade maraging steel at 295, 76, and 4 K.

Figure 8. The fatigue crack growth data [Eq. (7)] for solution-annealed

300 grade maraging steel versus room temperature data for

other steels [1 1 ,12,25,26].

Figure 9. The fatigue crack growth data [Eq. (7)] for solution-annealed

300 grade maraging steel versus data for austenitic superalloys and stainless steels tested at 295 and 4 K [27-29].

203
Table 1. Tensile property results for solution-annealed

18% Ni 300 grade maraging steel.

Temperature 0.2% Yield Strength Ultimate Strength Elongation Reduction in Area

(K) MPa (ksi) MPa (ksi) (%) (%)

295 904 1069 15 71.3 791 1068 16 70.,3

848 (123.0) 1068 (155,.0) 15.5 70.,8

76 1295 1569 12.6 60,.4 1302 1552 13.0 59,,7

1299 (188.4) 1560 (226.• 2) 12.8 60,.1

4 1609 1759 5.6 44,.7 1583 1756 7.8 49,,5 1596 (231 .5) 1758 (255,.0) 6.7 47,.1

a. 2.54 cm gage length

Table 2. Fracture toughness results for solution-annealed 18% Ni 300

grade maraging steel (2.3 cm thick compact specimens).

Temperature

(k)

Specimen a/W ^-2

(kJm ^)

Aa

(cm)

1^

kJm~

Ki^(J)^

(MPa'm^/^) (MPa-m^/^)

295 4 0.,612 199 0.166

5 0.,599 68 0.001

6 0.,597 183 0.105

15 0.,660 206 0.126 140110% 165i5% NA

16 0,,595 272 0.392

17 0,.598 129 0.001

19 0,.606 159 0.006

76 2 0,.471 NA NA NA NA 125.5

3 0,.498 131.0

14 0,.542 107.0

18 0,,548 117.5

Avg = 120.2

4 7 0..466 NA NA NA NA 94.1

n 0..514 78.8

20 0,.483 79.1

21 0,.507 80.1

Avg =83.0

a. obtained from extrapolation, see Fig. 4

b. Calculated using Eq. (3)

c. Obtained using the ASTM E 399-74 Method

204
6.1 cm

3.1 cm

.25 cm

1.27 cm dia.

?pr— 1.52 cm

i 3.

.79 cm dia.

)5 cm

^

W=5.08 cm

< 6.35 cm

THICKNESS, B=2.3 cm; W/B=2

Figure 1. Planar dimensions of compact specimens for fatigue and

fracture tests.

205
2500

2000

ce

CO

CO

1500

1000

CO

500

0

—I 1

^ r~

18% Nj, 300 grade

maraging steel, solution annealed

Ultimate strength, o-y

0.2% offset yield strength, o-y

i 1

0 100 200

TEMPERATURE (K)

Figure 2. Yield and ultimate strengths for solution-annealed 300 grade

maraging steel, showing 88% and 64% increases for the temperature range 295 to 4 K.

206
100

^ 80

c

03

40

\ r

18% Ni, 300 grade

maraging steel, solution annealed

Reduction of area

00

20

Elongation in 2.54 cm gage

0 i i

0 100 200

TEMPERATURE (K)

300

Figure 3. Reduction of area and elongation values for solution-annealed

300 grade maraging steel, showing gradually decreasing tensile ductility at low temperature.

207
2500

2000

1500

1000

500

A ASTM A 203E (3.5Ni) steel

o ASTM A 645 (5Ni) steel

V ASTM A 553A (9NI) steel

18% Ni 300 grade maraging steel,

solution annealed

100 200

TEMPERATURE, K

300

Figure 4. A yield strength comparison of solution-annealed maraging

steel and some ferritic nickel alloy steels.

208
EE

CO<

CO eg OJ

cu

cu +^

(/) __

s»fOE

fO

fO co O- o

{/) CT) e>—o

M— o

LO >

13 OJ U s_

OJu n3

S-OJa.

00 E

O)

CO +-> OJ Eoo

S- CD x: -M

03

s-13

C7)

209
u 100 200 300

TEMPERATURE. K

Figure 6. The effect of temperature on Kj^- for solution-annealed

maraging steel, which does not show the transitional

behavior exhibited by other nickel-alloy steels. (Data

for the 3.5, 5, and 9% Ni steels are published elsewhere [24,25].

210
2 5 10 50 100

STRESS INTENSITY FACTOR RANGE.AK, MPa

Figure 7. Fatigue crack growth rates for the solution-annealed

300 grade maraging steel at 295, 75 and 4 K.

211
1

1 Mill

03

O

E

E

Upper bound for 18%Ni maraging

steel, solution annealed (This study)

-a

CD

<

GC

O

QC

CD

<

GC

CD

<

Ferritic structural steels

at room temperature

10-^ —

I I I I I I I 5 10 50

STRESS INTENSITY RANGE, AK (MPa m^/^)

100

Figure 8. The fatigue crack growth data [Eq. (7)] for solution-annealed

300 grade maraging steel versus room temperature data for

other steels [11, 12, 25, 26].

212
10

-3

o

>-

o

E

E

CD

<

o

cc

CD

<

cc

LU

I

10-^

<

Upper bound for 18% Ni

maraging steeL solution annealed

(This study)

Austenitic stainless steels

4K<T<295K

Austenitic

nickel-base alloys

4K<T<295K

3 5 10 50 100

STRESS INTENSITY RANGE, AK (MPa m^/^)

Figure 9. The fatigue crack growth data [Eq. (7)] for solution-annealed

300 grade maraging steel versus data for austenitic superalloys and stainless steels tested at 295 and 4 K [27-29].

213
CRYOGENIC EFFECTS ON THE FRACTURE MECHANICS

PARAMETERS OF FERRITIC NICKEL ALLOY STEELS+

R.L. Tobler

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

+ NBS contribution, not subject to copyright.

214
ABSTRACT

Fracture toughness data (Kjq? Jjq) and fatigue-crack growth rates

(da/dN) are reported here for quenched and tempered low carbon ferritic

3.5 Ni and 9 Ni steels at temperatures between 295 K and 4 K. Such

data are needed for cryogenic fluid containment and superconducting

machinery design. The tests were performed using 25 and 31 mm thick

compact specimens having fracture planes normal to the long transverse

plate dimension. The fracture toughness results for both steels showed

qualitatively similar trends: at decreasing temperatures below 295 K,

Jj-j. increased by about 20%, prior to the onset of classical ductile-tobrittle transitions involving cleavage. The transitions occurred

between 172 K and 100 K for 3.5 Ni steel, and between 76 K and 4 K for

9 Ni steel. The transitional behavior was also evident in fatiguecrack growth resistance. At room temperature, the fatigue crack growth

rates for these nickel steels are typical of many other ferritic materials; however the rates at sub-transition temperatures are drastically

accelerated, due to cleavage. Data comparisons between 3.5 and 9 Ni

steels tested here and other nickel alloy steels are included in discussion.

Key words: Fatigue; fracture; low temperature tests; mechanical properties; nickel alloys; steels.

215
INTRODUCTION

Low-carbon ferritic 2 1/4 to 9% nickel alloy steels were developed

to provide low-cost alternatives to the more heavily-alloyed austenitic

stainless steels which are too expensive for use in many large-tonnage

cryogenic structural applications. Since 1947, the effects of nickel

on the mechanical properties of the ferritic steels have been studied

and reviewed [1-9], one major finding being that increased nickel

content leads to progressively lower ductile-to-brittle transition

temperatures. Construction costs are minimized by selecting the appropriate nickel content for the intended service temperature range. For

example, 3.5 Ni steel (ASTM A 203 grade E) has a minimum use temperature

of 172 K (-150°F), and is used for liquid acetylene, ethelene, and

propane tankage. On the other hand, 9 Ni steel (ASTM A 553 grade A) is

used for liquified natural gas and nitrogen tankage at temperatures as

low as 76 K (-32rF).

The tensile and impact properties of these steels are wel 1 -researched,

but such data are insufficient to insure fail-safe design according to

modern techniques of fracture mechanics analyses. The fracture parameters currently needed for more accurate material selection and design

efficiency are: Kj^, the critical plane-strain stress intensity factor;

Jj^, the critical value of the J-integral; and da/dN, the fatigue-crack

growth rate where a is crack length and N is fatigue cycles. The

parameters Kj^ and Jj^ characterize the magnitude of crack-tip elastic

stresses or plastic strains, during monotonic loading, respectively,

while da/dN governs sub-critical flaw growth cyclic loading. This

paper investigates the temperature dependence of these parameters for

quenched and tempered 3.5 Ni and 9 Ni steels tested at room temperature

and reduced temperatures approaching absolute zero.

216
Materials and Specimens

A 2.54 cm thick plate of ASTM A 203 grade E steel (3.5 Ni), and a

3.2 cm thick plate of ASTM A 553 grade A Type I steel (9 Ni) were

obtained from commercial sources. Both steels were received and tested

in the quenched and tempered conditions. The 3.5 Ni steel had been

tested at 1172 K for 1 h, and water quenched, followed by tempering at

896 K 1 h, and water quenched. The 9 Ni steel was heated at 1064 K for

1.5 h, and water quenched, followed by tempering at 877 K for 1.25 h

and air-cooled. The mill chemical analyses for both steels are listed

in Table 1, and the uniaxial tensile properties at selected test temperatures are listed in Table 2.

Compact specimens for fatigue and fracture tests were machined in

the TL orientation, having planar dimensions proportional to specimen

width, W, according to the ASTM E 399-74 method [10]. The 3.5 Ni steel

specimens were 2.5 cm thick, and the width-to-thickness ratiOs W/B, was

2.0. The 9 Ni steel specimens were (diagrammed elsewhere [11]) were

3.1 cm thick, with W/B = 2.4. Attached to knife edges at the loadline

was a double-cantilever beam-type clip gage that satisfied the ASTM E

399-74 Method linearity requirements at each test temperature.

PROCEDURES

The environments studied here were room temperature air at 295 K,

nitrogen vapor at 111 K or 172 K, liquid nitrogen at 76 K, and liquid

helium at 4 K. Two 3.5 Ni steel fatigue tests were also performed in

an alcohol/dry ice bath at 195 K. The low temperature apparatus

included a 100 kN servo-hydraulic test machine and cryostat previously

described [11,12].

Fracture Toughness

Direct K^p measurements for nickel alloy steels are seldom

217
reported because the ASTM E 399-74 thickness criterion for valid

linear-elastic tests is difficult to satisfy. The specimen thickness

criterion requires that:

B > 2.5 . : (1)

y

where is the yield strength of the material. In this study J- •

integral and ASTM E 399-74 test methods were used alternatively, depending on the type of load-deflection (P-6) behavior encountered. Examples

of P-6 records for 9 Ni steel specimens are shown in Fig. 1.

Nonlinear, Plastic Fractures

Where ductile fractures by stable tearing occurred (9 Ni steel at

295 and 111 K; 3.5 Ni steel at 295 and 172 K), J-resistance curves were

determined using Landes and Begley's method [13]. J as a function of

crack extension was determined by heat-tinting experiments in which a

series of precracked specimens at each material/temperature combination

were loaded to cause crack extensions of between zero and 0.49 cm.

After unloading, tinting, and complete fracturing, crack extension was

measured to the nearest 0.001 cm at three thickness locations, and

averaged. J values were calculated from the approximation:

where A is the total area (energy) under the P-6 curve. Jj^ was then

obtained by extrapolating the J-versus-Aa plots back to the critical

point of material separation, Aa^. (Crack extensions less than Aa^ are

218
apparent crack extensions due only to plastic deformation or blunting.)

Several reasonable extrapolations were examined to account for scatter.

Finally, estimates of Kj^ denoted Kjq(J) were derived from the relation:

EJxp 1/2

K (J) = —^

(3)

Young's modulus (E) and Poisson's ratio (v) for these steels at low

temperatures are known from the work of Weston, Naimon, and Ledbetter [14].

Linear-Elastic or Unstable Fractures

Where fast fracture occurred (9 Ni steel at 76 and 4 K; 3.5 Ni

steel at 111, 76 and 4 K) , conditional fracture toughness values denoted

Kg were calculated according to ASTM E 399-74. Some of the Kg results

approached nearly accurate Kj^ determinations, but none were valid

according to a strict interpretation of ASTM E 399-74.

In the case of 3.5 Ni steel at 76 K and 4 K, excessive crack front

curvature proved unavoidable in combination with the restriction that

the precracking stress intensity factor had to remain below 0.6 Kj^.

For 3.5 Ni steel at 111 K, Eq. (1) was not satisfied, and the Kg data

decidedly invalid. For 9 Ni steel at 76 K, Eq. (1) was not satisfied,

but the P-6 curve was sufficiently linear that Jj^ could be calculated

at maximum load, assuming sub-critical crack growth was negligable. At

4 K, the 9 Ni steel test records exhibit a unique saw-toothed appearance,

as shown in Fig. 1, due to multiple pop-ins (unstable crack extensions)

and arrests. The P /Pn ratios at 4 K exceeded 1.10, but heat-tinting

max V

experiments confirmed that the nonlinearity was due to cracking, not plasticity.

Fatigue-Crack Growth Rates

Fatigue-crack growth was monitored using the compliance method

219
previously described [11,12]. Rates at stress intensity factors, K^,

1 II

as high as 50 MPa-m were measured during the precracking stages of

fracture specimen preparation, while rates at higher stress intensities

were measured with specimens not used for fracture toughness tests. At

least two specimens were tested per temperature.

All tests used a sinusoidal load cycle at 20 Hz, and a R ratio

(Pm-j«/Pm=v) of O'l- The a-versus-N curves were fitted to a third-order

ml n max

polynomial and differentiated by computer, leading to an uncertainty in

da/dN results of less than + 25%. The da/dN data were plotted as a

function of the stress intensity factor ranges which were calculated

using the ASTM E 399-74 solutions for K and f(a/W):

RESULTS

Fracture Toughness

Table 3 lists the fracture toughness results for 3.5 Ni steel at

295, 172, 111, 76, and 4 K. The J-resistance curves at 295 K and 172

-2 -2

K, shown in Figure 2, yield Jj^ values of 163 kJm and 193 kJm ,

respectively. The corresponding Kj^ estimates from Eq. (1) are 190

MPa-m^'^^ at 295 K and 219 MPa-m^^^ at 172 K. Although the ASTM E 399-

74 results for this steel at lower temperatures are invalid, due primarily to excessive crack-front curvature, it appears that Kj^, approaches

1 II

30 to 50 MPa^m near absolute zero.

The fracture toughness results for 9 Ni steel at 295, 111, 76, and

4 K are listed in Table 4. The J-resistance curves for this steel at

295 K and 111 K (Fig. 3) yielded Jj^, values of 117 kJm"^ and 140 kJm"^,

220
respectively, and the Kj^ estimates are 156 MPa»m ' at 295 K and 174

MPa-m^/^ at 111 K. Between 111 K and 76 K, Kj^(J) is reduced slightly

1 II

to 167 MPa*m , and it appears that the ductile-to-brittle fracture

transition is just beginning at 76 K. Below 76 K the fracture toughness rapidly decreases, and at 4 K nearly all of the ASTM E 399-74

criteria for Kj^ measurements are satisfied. The sole criticism that

can be levelled against the 4 K results for 9 Ni steel is that the a/W

ratios of about 0.6 slightly exceed the preferred range of 0.45 to

0.55. The statement "Kq - Kj^" in Table 4 indicates that these 4 K

data are believed to be nearly accurate Kj^ results.

The temperature effects on Kj^, estimates for the 3.5 Ni and 9 Ni

steels are shown in Fig. 4, along with results for a 5 Ni steel [11]

that was tested using compact specimens (3.1 cm thick) and similar

procedures. The 5 Ni steel was in the austenitized, temperized, and

reversion annealed condition, which tends to decrease the transition

temperature slightly compared to the quenched and tempered condition.

In the range 295 to 4 K, all three steels exhibit: (1) an "upper

shelf" temperature region showing an initial enhancement of fracture

resistance at decreasing temperatures, (2) a transition range of abruptly

decreasing toughness, and (3) a temperature-insensitive sub-transition

range. For each steel, absolute zero is a sub-transition temperature.

Within the transition range, Kj^ increases by factors from 2.2 to 3.

An interesting point seldom noted is that each steel exhibits a maximum

fracture resistance within the upper shelf range, just prior to undergoing the fracture transition. The 6 Ni steel tested in a previous

study also showed this type of behavior between 295 K and 76 K [11].

For these materials, the peak Kjj,(J) value is about 10 to 15% higher

than the value at room temperature.

221
Nickel's beneficial effects on fracture resistance in the transition and sub-transition regions are attributed to favorable effects on

the deformation characteristics and cleavage resistance of iron, combined with a tendency to promote the formation of retained austenite

[3,7-9]. As indicated in Figure 4, the transition temperature intervals correlate with nickel content, lying approximately in the ranges:

1. 4 K < T < 76 K for 9 Ni steel

2. ^ 60 K < T < 111 K for 5 Ni steel, and

3. ^ 100 K < T < 172 K for 3.5 Ni steel.

The fracture toughness at sub-transition temperatures also increases

1/2 with nickel content, with the Kj^ values at 4 K ranging from 30 MPa^m '

for 3.5 Ni steel to 80 MPa»m^^^ for 9 Ni steel. On the otherhand, the

upper shelf toughness is apparently more sensitive to heat treatment

and metallurgical factors other than nickel content; 5 Ni steel exhibits

the highest upper shelf fracture toughness, perhaps due to the uniform

distribution of carbides and other benefits [7] associated with austenitizing, temperizing, and reversion annealing [7].

Fatigue-Crack Growth Rates

Over the range of stress intensity factors investigated (20 to 80

1 /2 MPa-m ) the fatigue-crack growth rates for the 3.5 and 9 Ni steels

conform to equations of the type proposed by Paris and Erdogan [15]:

^= C(AK)" (5)

where n and C are material and temperature dependent empirical constants. Log-log plots of the da/dN-vei7Sus-AK were constructed to

reveal linear trends from which the n and C values were determined as

222
the slopes and ordinate intercepts at AK = 1, respectively. Table 5

lists the n and C values for each material /temperature combination.

Consider the room temperature results, shown in Fig. 5. Here,

"Paris equation" equivalents representing the 3.5 Ni and 9 Ni steels of

this study and the 5, 6, and 9 Ni steels of a previous study [11] are

superimposed on a scatterband for commercially available construction

steels where nickel is not a major alloying element [16-20]. The data

spread for the nickel alloy steels is nearly equivalent to that for the

non-nickel steels, with fatigue-crack growth rate variations approaching a factor of 4. However, the data for two 9 Ni steel alloys, show

that heat-to-heat differences can account for fatigue-crack growth rate

variations of at least a factor of 2 or three. It appears that the

fatigue-crack growth resistances of nickel alloy steels at room temperature are typical of ferritic steels in general, and there seems to be

no simple correlation between fatigue-crack growth rates and yield

strength or nickel content.

The results in Fig. 6 reveal no dramatic temperature effects on

the fatigue crack growth resistance of 3.5 Ni steel, as long as the

temperature remains within the upper shelf region identified by the Jj^

tests. The fatigue crack growth rates at 195 K and 172 K are nearly

equivalent or slightly improved compared to the rates for this steel at

room temperature. On the otherhand, further temperature reductions to

76 K greatly accelerate the rates to values well above those at room

temperature. As indicated earlier, 76 K is a sub-transition temperature for this steel; inferior fatigue-crack growth resistance at this

temperature is associated with the appearance of cleavage-type cracking

modes, and a single increase of the Paris equation exponent from n =

3.2 at 295 K to n = 7.6 at 76 K.

223
The fatigue-crack growth behavior of 9 Ni steel is analogous to

that of 3.5 Ni steel in that low temperature effects are moderate until

the sub-transition range is approached. Data for the 9 Ni steel at

295, 111, 76, and 4 K are shown in Fig. 7. The rates decrease as

temperature is lowered from 295 K to 111 K, but between 111 K and 76 K

1 /2 the trend is reversed. Thus, for AK greater than 40 MPa«m ' , the

rates at 76 K exceed those at 295 K. Previous tests of a second, heat

of 9 Ni steel also reveal led higher rates at 76 K than at 295 K [11].

At more extreme cryogenic temperatures, the present data at 4 K confirm

that the fatigue crack propagation resistance continues to deteriorate.

Thus, for the AK range investigated, the fatigue crack growth resistance of 9 Ni steel is at a maximum near 111 K, the same temperature at

which a peak in the static fracture toughness was observed.

-

. DISCUSSION

Strain-rate, section thickness, and notch severity are three

factors that usually influence the transition temperatures. Nevertheless, recent reports indicated the fracture toughness of 5 and 9 Ni

steels to be unimpaired by dynamic loading [9]. Therefore the relatively thick and sharply-cracked compact specimens used for static

fracture tests may provide a more severe test of crack tolerance than

traditional tests based on Charpy impact energies.

Any comparison between the data of this report and the literature

must carefully take into account the differences in measurement procedures. Standard Kj^ determinations from the ASTM E 399-74 Method provide the most reliable comparisons, but valid Kj^ data are rare. Pense

and Stout [9] indicated that most authors reported "K" or "K

L max

224
values. The v/1de variety of test variables and data reduction schemes

makes "K^" data comparisons difficult. In the present study, the Jintegral at initiation of crack extension is reported, rather than a K

value calculated at the maximum load point. Huettich, Pense and Stout

1 n

[4] report a K^^ measurement of 43 MPa«m for a quenched and tempered

3.5 Ni steel tested at 89 K (-300=F). Based on the data trend of Fig.

4, our 3.5 Ni steel indicates 30'.- higher toughness. This difference

could be due to test procedures, since Huettich et al . precracked their

specimens at room temperature.

In reference to 9 Ni steel, Syn, Jin, and Morris [5] reported a

1 II

Kj^ value of 78 MPa-m for a double-normalized and tempered grade at

1 II

6 K, nearly agreeing with the present result of 75 MPa^m for a

quenched and tempered grade tested at 4 K. Our Kj^(J) results for 9 Ni

steel are up to 16-'; lov/er than results for a second heat tested at 295

K and 76 K [11]. The difference in fracture toughness for these two

heats may be attributed to material variability since: (1) the Jintegral test procedures were equivalent, and ^1) the fracture surface

topographies reveal distinctly different features, especially at room

temperature, as shown in Fig. 8.

The 9 Ni steel of this study displayed highly uniform crack fronts,

as compared to results from other studies. As listed in Tables 3 and

4, the edge crack lengths for the 9 Ni steel were typically 97-"; as long

as the average crack lengths at central thickness. Similar values for

5, 6, and 9 Ni steels (see Fig. 8) ranged from 88 to 90-'-- [11]. These

crack-front curvature effects should not greatly influence the da/dN

comparisons, since the compliance method of crack growth measurement is

sensitive to through-the-thi ckness variations.

225
As indicated in Table 5, the Paris equation exponents for most

nickel steels are nearly 3.0 at room temperature, which is expected for

ferritic steels, based on Barsom's findings [16]. The Paris equation

exponents tend to increase, depending on the severity of the temperature reduction. For example, the 9 Ni steel, shows a progressively

increasing exponent from n = 2.7 at room temperature to n = 5.3 at 4 K.

As long as the temperature remains in the upper shelf range, fatigue

crack growth resistance is satisfactory. The rates for 9 Ni steel at

111 K and 76 K, and for 3.5 Ni steel at 195 K and 172 K deviate from

their 295 K trends by margins not greater than observed in the scatterband shown in Fig. 5. Thus, variations in fatigue crack growth resistance due to temperature variations in the upper shelf ranges are of

the same magnitude as variations induced by metallurgical effects in

other ferritic steels at room temperature. It appears that the trend

of decreasing fatigue crack growth resistance with decreasing temperatures is caused by the incidence of brittle cleavage modes which become

predominant as the maximum fatigue stress intensity factor approaches

Kj^ at low test temperatures. Knott and Ritchie correlated high n

values with steels of low fracture toughness, indicating that n is

1 12. likely to exceed 4.0 if Kj^ is 80 MPa»m or lower [21]. Lindley and

Richards also associate high n values with brittle crack propagation

modes such as occur in static fracture tests [22].

SUMMARY

The onset of cleavage fracture modes which account for transitions

to low fracture toughness in ferritic steels also lead to a deterioration of fatigue-crack growth resistance. The quenched and tempered 3.5

226
Ni and 9 Ni steels exhibit low temperature fatigue-crack growth and

fracture toughness data trends that are believed to be representative,

qualitatively, of ferritic steels in general. Initially, the resistance to crack extension under monotonic loading increases at decreasing

temperatures below 295 K, reaching a maximum prior to the ductile-tobrittle transition. The transition for 3.5 Ni steel lies between 172

and 110 K, and the transition for 9 Ni steel lies between 76 and 4 K.

Based on observations for these and previously tested nickel steels,

the ratios of the peak Kj^ values to the minimum Kj^ values exhibited

near absolute zero are between 2.5:1 and 5:1. The fatigue-crack growth

resistance of ferritic steels at room temperature apparently is not

measurably influenced by nickel content. Reduced temperatures in the

upper shelf range may improve the fatigue-crack growth resistance

slightly, but fatigue cracking at sub-transition temperatures is drastically accelerated by cleavage such that the rates at normal temperatures may be exceeded by an order of magnitude.

CONCLUSION

The fracture mechanics properties reported here for familiar

cryogenic tankage steels are of practical design value for existing and

future structural applications. The data clearly illustrate general

behavior trends for ferritic steels tested over the complete ambientto-cryogenic range. In the future, it may be possible to improve the

fracture resistance of the 3.5 Ni and 9 Ni steels by applying heat

treatments analogous to the austenitized, temperized, and reversion

annealing treatment applied to 5 Ni steel [7]. As regards superconducting machinery developments, these steels would not be ideal for use

227
in tensile-loading (Mode I) applications at 4 K, unless they can be

reprocessed to eliminate the fracture transition as discussed by Syn,

Jin, and Morris in reference to 9 Ni steel [5].

ACKNOWLEDGMENTS

Test materials for this program were donated by the Lukens Steel

and Armco Steel Corporations. The program was sponsored by the

National Maritime Administration and the Advanced Research Projects

Agency of the U.S. Department of Defense. The assistance of Dr. R.

P. Mikesell and R. L. Durcholz in conducting tests is gratefully

acknowledged.

REFERENCES

1. Yeo, R. B. G. and Miller, 0. 0., "A History of Nickel Steels from

Meteorites to Maraging," Sorby Centennial Symposium on History of

Metallurgy, ASM, Cleveland, OH, October 21-23, 1963.

2. Properties of Materials for Liquefied Natural Gas Tankage, ASTM

STP 579, (Amer. Soc. Test. Mater., Philadelphia, 1975) 1-420.

3. Floreen, S., Hayden, H. W. , and Devine, T. M. , Cleavage Initiation

in Fe-Ni alloys. Met. Trans. 2 (1971) 1403.

4. Huettich, N. J., Pense, A. W. , and Stout, R. D. , The Toughness

of 2 1/4 and 3 1/2% Nickel Steels at Cryogenic Temperatures, WRC

Bulletin No. 165 (Welding Research Council, 1974) 1.

5. Syn, C. K. , Jin, S. , and Morris, J. W. , Jr., Cryogenic Fracture

Toughness of 9% Ni Steel Enhanced Through Grain Refinement, Met.

Trans., submitted for publication.

6. McHenry, H. I. and Reed, R. P., "Fracture Behavior of the HeatAffected Zone in 5% Ni Steel Weldments," Welding Journal, submitted

for publication.

228
7. Sarno, D. A., Havens, F. E., and Bowley, D. L., Transformations

involved in Developing Notch Toughness in a New 5% Nickel Steel for

Cryogenic Purposes (ASM Technical Report No. C70-39-2, American

Society for Metals, 1970).

8. Johnson, R. J., The Role of Nickel in Carburizing Steels, Metals

Eng. Quart. , ]S_ (1975) 1.

9. Pense, A. W. and Stout, R. D., Fracture Toughness and Related

Characteristics of the Cryogenic Nickel Steels, WRC Bulletin No.

205 (Welding Research Council, 1975) 1.

10. Standard Method of Test for Plane Strain Fracture Toughness of

Metallic Materials, E 399-74 Annual Book of ASTM Standards, Part

10 (Amer. Soc. Test. Mater., Philadelphia, 1976) 471.

11. Tobler, R. L., Mikesell, R. P., Durcholz, R. L. , and Reed, R. P.,

"Low Temperature Fracture Behavior of Iron-Nickel Alloy Steels,"

Ref. 1, 261.

12. Fowlkes, C. W. and Tobler, R. L., Fracture Testing and Results

for a Ti-6A1-4V Alloy at Liquid Helium Temperature, Eng. Fract.

Mechs. 8 (1976) 487.

13. Landes, J. D. and Begley, J. A., Test Results from J-integral

Studies: An Attempt to Establish a Test Procedure, in Fracture

Analyses, ASTM STP 560 (Amer. Soc. Test. Mater., Philadelphia,

1973) 231.

14. Weston, W. F. , Naimon, E. R. , and Ledbetter, H. M. , "Low Temperature

Elastic Properties of Aluminum 5083-0 and Four Ferritic Nickel

Steels," Ref. 1 , 397.

15. Paris, P. C. and Erdogan, F., A Critical Analysis of Crack Propagation Laws, Trans ASME, J. Basic Eng., 85_ (1963) 528.

229
16. Barsom, J. M., Fracture-Crack Propagation in Steels of Various

Yield Strengths, Trans. ASME, J. Eng. Ind. (1971) 1190.

17. Barsom, J. M. , Imhof, E. J., and Rolfe, S. T., Fatigue Crack

Propagation in High Yield Strength Steels, Eng. Fract. Mechs. 2

(1971 ) 301.

18. Wei, R. P., Talda, P. M., and Che-Yu Li, Fatigue Crack Propagation

in Some Ultra-High Strength Steels, in Fatigue Crack Propagation,

ASM STP 415 (Amer. Soc. Test. Mater., Philadelphia, 1967) 460.

19. Brothers, A. J. and Yukawa, S., Fatigue Crack Propagation in Low

Alloy Heat Treated Steels, Trans. ASME, J. Basic Eng., 89 (1967)

19.

20. Miller, G. A., The Dependence of Fatigue-Crack Growth Rate on the

Stress Intensity Factor and Mechanical Properties of Some High

Strength Steels, Trans. ASM, 61 (1968) 442.

21. Ritchie, R. 0. and Knott, J. F., Mechanisms of Fatigue Crack

Growth in Low Alloy Steel, Acta Met., 21 (1973) 639.

22. Richards, C. E. and Lindley, T. C, The Influence of Stress

Intensity and Microstructure on Fatigue Crack Propagation in

Ferritic Materials, Eng. Fract. Mechs., 4 (1972) 951.

LIST OF TABLES

Table 1. Mill chemical analyses of test materials.

Table 2. Tensile properties of test materials.

Table 3. Fracture toughness results for ASTM A 203 E (3.5% Ni ) steel

(specimen thickness = 2.54 cm).

Table 4. Fracture toughness results for ASTM A 553 A (9% Ni) steel

(specimen thickness = 3.1 cm).

Table 5. Comparison of Paris equation parameters for nickel alloy

steels.

230
Table 1. Mill chemical analyses of test materials, wt%.

Material Fe Ni C Mn P S Si

fo.STM A203-E (3.5 Ni steel) bal . 3.62 0.10 0.46 0.015 0.013 0.2

quenched and tempered

lASTM A553-A (9 Ni steel ) bal. 8.99 0.08 0.62 0.010 0.010 0.1

quenched and tempered

I

231
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CM CM CO C\J

CM r-^ V£)

(Ti 00 CO 00 CM CM CO CM o o o o o o o o

/-\

*~ 3 . 1 CxJ p~~ CnJ

I^J ) CNJ C\J CSJ CnJ H~ CvJ CvJ C\J

OO

O fO 1 itj 1 n \ w ^ 0\ • rf" Ki^^ rf* «^ rf" «i4^ <cC LO

/1 1 (j rv

(/)

fO

•r—<^

"1— QJ T—

O )

«U

err • err "4*. rf* rf* to w CO i.O c—}-

n \ CO CO CO CsJ

4-^

O LO

l4_o 1 1 1

t/^

/1 1

S- r—

Q. t/^ O

S- ir> CO 1^ 1— 1 xJ r—

*nJ LO [ 1^ ^NJ \ > to ^ ' ' ' c= +-' 1

.

cu "O

r— fO

fO CM P** CO Li 1 LO " > 1

•r— 4-^ rO cn CO ^ c J rw cu o»

CO ^ r— CM CM LO Ui "J

CD CO _-

LO 1

LO 1— LD ^ CTi 1

CTi 1

CD CM r— CM r—

Q.t—

c= 1

^ ^

O)

LlJ cu <S. i— 1 -t-> 1 CU r— CO to ro <U o IT) -M CM •!- LO </l ^

sC •.-

4-) LO

5: . s:

s: 1— CT> — OO<

cu

to OJ

+-> to

CU CU

+-> _l

cu -o

+-> fO fO CJ

•r- c

Q. o 13 E T3

fO Eo

s- M- o to +j

<U to

13 cu 3 > E

CU

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5~ to

s_ ro

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03
CSJ

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CDE

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in

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to -M

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t—> Q.

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c:OJu

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+-> to

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<<<:-<<:<; cc <=c <: < ct

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ro CO LT) cn <x> CO oo in un o 00 >—

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in cn o o VO l£ l>0 l>0 VO 1^

o o o o o

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to CO CM CTi O 00 00 00 CX) CTi

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to CM O ^ CO CO

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in CX3 to LO

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LD

cnCM

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233

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+->

s- S-o

+j 4-> cn U

c to cu <4->>

4-> (J 'r— rC to

S- C u <1> -M

to (U to CJ) •r— OJ (T3 c S- to

to a > OJ

i. sz 1 -M CO -M O O to -M c 4-) CD

<u ^ C

cr E S- U

LU •r— fO U cn- u tn Ln

CD O) Q- (J fO to CTl CTl C CIL 1 S- f-^ CM

•r— to u

V) men cu +J 4-> +J 3 +-> S- to to ro C Cl. <u a. -o OJ x> -a T3

O) •r— (V cu cu -M O > > > ^

(O •1— •r- •p- u a o

H- 00 to to ro (O to ^- to to to i_ S- s~ O 3 O) <u a o o

to o U a cu cu (U (O e X X X s- s- s- o »—

LU LlJ uj ex. a.

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to

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un <^ CM o r-- CO

00 CO r-~-

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00 1^ LO CM CTl CD

CM r— CM ^ 1— CO

I— 1^ C3^ I— LT) CTi O O O I— ^ o

AAA A A A A A A

LDcoi— cococn r>-cooor^cocD cocmi— cooor^

1— Or- OOO 1— 1— "^Or— O I— ^r— OOi—

COCOCOCOCOCO VOCOCOCDCOCO CO CO CO CD CD CD oooooo oooooo

CO CO CO CO

01 CT) CT> CTi CTt CTi OOOOOO

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00 CO

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CO CO 1— c— CO CM

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CO r-. I— CM CO 1— CM CM CM

CO CO cn I— CM cn

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1— CO CO ^ CO

^cocj^cncDoo I— or-~ ^cmld

CO • 00

CO

• <u CT C • \jj ^

o

Cr>'r- CO

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4-> 03 -a

cu

4-) 03

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cu

13 C(_

cn

cn

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234

03 X3 U
Table 5. Comparison of Paris equation parameters

for nickel alloy steels (da/dN in mm/cycle)

Material Temperature C n AK Region

K MPa-m'/2

ASTM A 203-E 295 1 .3x10

(3.5 Ni steel) 195 1.3x10

This study. 172 1.0x10

76 1 .6x10

ASTM A 645 O A n 295 1 . 1x10

(5 Ni steel ) [11

111 1 .1x10

76 2.0x10

N-TUF Cr-196 295 3.7x10

(5.5 Ni steel) [11] 111 3.7x10

76 4.2x10

ASTM A 553-A 295 2.3x10

(9 Ni steel) [11] 76 3.1x10

ASTM A 553-A 295 2.0x10

(9 Ni steel) 111 1 .0x10

This study. 76 4.8x10

4 1.4x10

-8

-8

-9

-14

-8

-8

-10

-9

-9

-9

-7

-9

-8

-9

-11

-11

3.2 18 to 60

3.2 30 to 70

3.2 30 to 60

7.6 20 to 30

1.1 25 to 90

1.1 25 to 60

4.0 27 to 80

3.0 22 to 85

3.0 22 to 85

3.2 25 to 75

2.0 27 to 100

3.3 27 to 100

2.7 16 to 70

3.4 17 to 80

4.4 17 to 64

5.3 25 to 35

235
LOADLINE DEFLECTION, 8. mm

Figure 1. Load-versus-loadl ine deflection curves for 9 Ni steel.

236
S-3

+J

ns

s-Q)Q.E •

+-> ii^ E c\j OO r— s+J CU

fO sZ3 r— -(-> OJ 03

O) S-

+-> 0) CO Q.E

•r- O)

S- E o 3

to c

O) -r- > E

i-3 O) u

4-> <uU T3 C C

fO ro

+-> CO ^-^

•r-to

OJ LO I C\J

>-0

—

OJ

S237

Figure 4. Temperature dependence of Kjq estimates obtained for the 3.5

Ni and 9 Ni steels of this study and the 5 Ni steel of a previous study [11].

239
10-3 —

-

10

1—I—I

I I I I

a) 3.5 Ni Steel, This Study

b) 5 Ni Steel

)

c) 6 Ni Steel [14]

d) 9 Ni Steel ) e) 9 Ni Steel, This Study

'd

a

Other structural steels

without nickel

10

-5

b

1

2 5 10 50

STRESS INTENSITY FACTOR RANGE, AK, MN/m

100

3/2

Figure 5. Room temperature fatigue crack growth data for the 3.5 Ni

and 9 Ni steels of this study, the 5, 6, and 9 Ni steels of a previous study [11], compared to data for other ferritic

structural steels without nickel [16-20].

240
1 1

\—Mill

2 5 10 50 100

STRESS INTENSITY FACTOR RANGE.M, MPa m^

Figure 6. Fatigue-crack growth rates for 3.5 Ni steel at room and

cryogenic temperatures.

241
E

-3

O

OE

C9

u

<

ee

u

LU

C9

10

10

ASTM A553A

(9Ni) steel

4K

o 76K

A 111K

• 295K

R = 0.1

f = 20Hz

B = 3.1 cm

I I I I I I I I 2 5 10 50 100

STRESS INTENSITY FACTOR RANGE.AK, MPa

Figure 7. Fatigue-crack growth rates for 9 Ni steel at room and

cryogenic temperatures.

242
Figure 8. A comparison of the fracture surfaces of two different heats of

9 Ni steel fractured at 295 K (Top) and 76 K (Bottom) reveals

heat-to-heat variability. The quenched and tempered 9 Ni steel

of a previous study (left) displays a greater proportion of

shear fracture at specimen edges, as well as a more pronounced

degree of crack-front curvature.

243
NOTE ON THE FRACTURE PROPERTIES OF Fe-49Ni AT CRYOGENIC TEMPERATURES

H. I. McHenry and R. E. Schramm

The tensile, fatigue crack growth and fracture toughness properties

of Fe-49 Ni were determined at room temperature, 76 K and 4 K. Tensile

properties were determined with 25 mm gage length, 6.4 mm diameter specimens using the methods described previously by Reed [1]. Fatigue crack

growth rates were determined with 25 mm thick, 51 mm wide compact tension specimens using the compliance method for crack length determinations;

the test procedures and equipment were described previously by Fowlkes

and Tobler [2]. Fracture toughness was determined with 25 mm thick, 51

mm wide compact tension specimens using the J-integral test procedures

of Landes and Begley [3] and the cryogenic testing procedures and equipment described previously by Tobler et al. [4].

The results of the tensile tests are summarized in Table 1. The

tensile and yield strengths at room temperature and 76 K are essentially

the same as those obtained by Reed [5]. However, at 4 K the strength

values obtained in this investigation are approximately 20% higher than

those obtained by Reed [5].

The results of the fatigue crack growth tests are summarized in

Figs. 1, 2 and 3. For each temperature, the line drawn through the

data points has the form

m

= c(AK)" (1)

where da/dN is the fatigue crack growth rate in mm/cycle, AK is the stress

1 /2 intensity range in MPa«m '

, and C and n are emperical constants. The

244
values for the intercept, C, the slope, n, and the coeficient of

determination, R, were determined by least-squares regression analysis:

Temperature C n R

Room Temp 7.7xlO'L 3.0 .977

76 K 8.4x10"^ 3.5 .981

4 K 1.6x10^ ^ 3.9 .995

A comparison of the data indicate that over the range of crack growth

rates measured, the data at 4 K and 76 K are essentially the same and

the growth rate at room temperature ranges from 1.4 to 2.5 times faster

than the growth rate at the cryogenic temperatures.

The results of the fracture toughness tests are summarized in Table

2 and plotted in Figs. 4, 5 and 6. The J-integral value (J) for each

test is calculated using the approximation of Rice, Paris and Merkle [6]

where A is the area under the load displacement curve, B is the specimen

thickness, W is the width and a is the crack length. For each temperature

a curve of J vs Aa (crack extension) is constructed. On the same graph,

the line defined by Eq. (3) is drawn:

J = 2a^Aa (3)

where = (a^^ + = .2% offset yield strength and z^^ =

ultimate tensile strength. The intersection of the J-Aa plot and the

J/2a^ line is defined as Jj^, the value of J at the onset of crack

245
2 2

extension. The values for Jj^ are 1000 KJ/m at 76 K and 870 KJ/m at

4 K. At room temperature, Jj^ was not defined because the curves did

not intersect. It is reasonable to say that the room temperature

2

toughness exceeds the J value for zero crack extension, i.e. 281 KJ/m .

Specimen size requirements for valid Jj^ measurements have not yet

been agreed upon by ASTM, however, Landes and Begley [3] suggest use

of the following size criteria:

By these criteria, the measurement capacity of a 2.5 cm thick (W = 5 cm)

compact tension specimen precracked to a/W = 0.62 would be determined

by the ligament size, W-a = 1.9 cm. The calculated measurement capa2 cities are 275, 464 and 568 KJ/m at room temperature, 76 K and 4 K,

respectively. At all temperatures, the measured Jj^ values exceeded

these limits. Thus, the specimen is not sufficiently large to assume

that J characterizes the crack-tip field. If in fact the toughness

does exceed the measurement capacity of the specimen, the toughness

of Fe-49Ni is very high and not an important consideration in structural

design.

Begley and Landes [7] have proposed that the plane strain fracture

toughness, K,p, is related to J^p as follows:

where E is Young's modulus and v is Poisson's ratio. The values for E and

a, B, W-a > 25 Jxp/a (4)

(5)

246
V for Fe-49Ni were obtained from Ledbetter [8]: at 76 K E = 1.562 x 10

N/m^ (22.6 X 10^ psi) and v = .343; at 4 K E = 1.569 x 10^^ N/m^ (22.8 x

10^ psi) and v = .343. The values calculated for Kj^(J) are 423 MPaTn^^^

(382 ksi/Tn) at 76 K and 396 MPa-m^/^ (396 ksi/Tn) at 4 K. These levels of

toughness virtually preclude the possibility of brittle fracture in Fe-49Ni.

1. R. P. Reed, Advances in Cryogenic Engineering , Vol. 7 (Plenum Press,

New York, 1962) p. 448.

2. C. W. Fowlkes and R. L. Tobler, Eng. Fract. Mechs. 8 (1976) 487.

3. J. D. Landes and J. A. Begley, "Test Results for J-Integral Studies --

An Attempt to Establish a Jj^ Testing Procedure," Westinghouse

Research Laboratory Scientific Paper 73-1E-7-FMPWR-P3, 1973.

4. R. L. Tobler, R. P. Mikesell, R. L. Durcholz and R. P. Reed, ASTM

STP 579, 1975, p. 261.

5. R. P. Reed, National Bureau of Standards, Boulder, CO, to be

publ ished.

6. J. R. Rice, P. C. Paris and J. G. Merkle, ASTM STP 536, 1973, p. 231.

7. J. A. Begley and J. D. Landes, ASTM STP 514, 1972, p. 1.

8. H. M. Ledbetter, National Bureau of Standards, Boulder, CO, to be

published.

247
Table 1. Tensile property results for Fe-49Ni

Temperature Yield Strength Ultimate Strength Elongation Reduction of Area

K MPa (ksi) MPa (ksi) % in 25 mm %

298 194 28.2 495 71.9 49 70

298 233 33.8 499 72.5 47 74

Average 214 31.0

' 497 72.2 . 48 72

76 351 51.0 841 122 57 72

76 365 53.0 845 123 56 72

Average 358 52.0 843 122 56 72

4 507 73.6 977 142 50 60

4 : 473 68.7 980 142 49 60

Average 490 71.1 978 142 49 60

248
c

o

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+->

<_3 •!— %- 1—1 CO «J5^

0) CM CO

(/) 0) O (O T3

I—1 Q- C

IQ

1 >>

C\JC

(U »—1 r— c "-3 • «r

(U "O

4-> O

C_5 \ z 1—1 "-z ^ :^

o o o o !!q 1—

CO IT) cji o t ^ f— CM CO c

c\e cn r— CTi Ln

00 1— o

00 c^j Ln

CVJ 1— U3 CM O

o o o

(U

o

(0

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CO

CM

O

in

ooo

in CM

LD O CM CTi o o o

cn Ln 00 I— CM CM I—

00 Ln 1— O r— .— O

m cn cn cn

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o>

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ro CO

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o >— cr> CM CM CM r—

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ra- LD r~~.

E

E

X X

CM 00

<Ti 00 O

+JoOJ T3

fOO

O)

So

4-> T3

OJ T3O

<U

iCl.

COLn

CO

C31 CO

o

O

CO

o o o o c o 1— ^ ^ <^ LD P^ LD

"d- r>« "d- ^

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CO O O O rr-^ 00 00 CO 00

CO XJ CM Ln

(Ti o 1^ <Ti O P-^ CM CO 1— o o o o o

Ln r-- oo o CM c7> Ln cTi Ln o r- o o o

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249
10

"i

E

CO

104

o

QC

<

CC

u

UJ

CD

<

10

— / :

—

— da/dN = 7.7x10 5 AK^"

—

Pe - 49IMI

Room Temp. —

R = 0.1

A Soec 21 —

o Spec 14

1 1 1 1 1 1 1 1 10 20 40 60 100

STRESS INTENiSITY RANGE, AK (MPa m'/^)

1. Fatigue crack growth rates in Fe-49 Ni at room temperature

250
10-3

J2

u

S

= 10-^

o

oc

CD

CJ

<

oc

CJ

LU

C9

10

10

da/dN=8.4x10-^°AK^^

Fe-49Ni

76K

R = 0.1

Spec 1 o Spec 4

A Spec 20

20 40 60 100

STRESS INTENSITY RANGE, AK (MPa m^^j

2. Fatigue crack growth rates in Fe-49 Ni at 76 K.

251
10

U

>-u

E

10

-4

CD

CJ

<

CD

<

10

da/dN=1.6x10 ^°AK

10 20 40 60

STRESS INTENSITY RANGE, AK (MPa m^')

100

3. Fatigue crack growth rates in Fe-49 Ni at 4 K.

2B2
CRACK EXTENSION, Aa (in)

0 0.02 0.04 0.06

Fe-49Ni

Room Temp.

10,000

8000

6000^5

4000 C9

2000

0.04 0.08 0.12 0.16 0.20

CRACK EXTENSION, AK (cm)

J-Aa fracture toughness curve for Fe-49 Ni at room temperature.

253
1800

CRACK EXTENSION, Aa (in)

0.02 0.04 0.06

1400

1000

600

200

1 Fe-49Ni

/Dl\

/

•

/ —

—

y/^^\z = lOOOkJ/m^

y

^Aa = J/2o-f

— O data use for J- Aa curve

/ • / 1

A a estimated from obliteratei

, fracture surface ,

1 1 1

10,000

8000

6000

4000

0.04 0.08 0.12 0.16

CRACK EXTENSION, Aa (cm)

0.20

J-Aa fracture toughness curve for Fe-49 Ni at 76 K.

254
1800

1400

1000

600

200

CRACK EXTENSION, Aa (in)

0.02 0.04 0.06

Fe-49Ni

4K

Jic = 870 kJ/m^

Aa = J/2o-f

o data used for J- Aa curve • Specimens (2) overloaded

prior to test

0.05 0.10 0.15

CRACK EXTENSION, Aa (cm)

10,000

8000

6000

4000

2000

0.20

6. J-Aa fracture toughness curve for Fe-49 Ni at 4 K.

255
FATIGUE CRACK GROWTH RESISTANCE OF STRUCTURAL

ALLOYS AT CRYOGENIC TEMPERATURES*

R. L. Tobler and R. P. Reed

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Fatigue crack growth rate data at selected temperatures including

295, 76, and 4 K are presented for a variety of titanium alloys, stainless steels, and Fe-Ni alloys. The results correlate well with crystal

structure. Compared to their behavior in a room temperature air environ

ment, stable austenitic face-centered cubic alloys exhibit improved

fatigue crack growth resistance at low temperatures. Hexagonal closepacked titanium alloys show temperature-insensitive behavior. Temperature effects on the fatigue crack growth resistance of body-centered

cubic Fe-Ni alloy steels are moderate, except below the fracture transition temperature range where fatigue crack growth rates are drasticall

accelerated.

Key words: Crack propagation; fatigue; low temperature tests; nickel

alloys; stainless steels; steels; superalloys; titanium alloys.

*NBS contribution, not subject to copyright.

256
INTRODUCTION

Fatigue failure is a process of crack initiation, crack propagation, and fracture. Fracture occurs when the crack propagates to a

critical size, and the structural component is no longer able to support the applied stress. The critical crack size is a function of the

fracture toughness of the material and the component geometry, and can

be calculated from a fracture mechanics analysis. The fatigue life is

determined by the time required to initiate and propagate a crack to

critical size.

Fatigue design data are essential to avoid catastrophic failure,

overdesign, and inefficient selection of materials. Conventional

stress-controlled S-N test data for several alloys at 295, 76, and 4 K

are available from the work of Schwartzberg and Kiefer [1] and Nachtigall,

Klima and Freche [2]. Nachtigall [3] also reports strain-controlled SN test data at low temperatures. Such data pertain to smooth or notched

bar specimens where the crack initiation phase is important and may

account for up to 90% of the total fatigue lifetime, depending on the

stress level. However, in many large engineering structures cracks

already exist, or are assumed to exist, due to manufacturing and fabrication defects. In such cases, the life of the structure is determined

solely by the crack growth rate, and a specific knowledge of fatigue

crack growth rates (da/dN) is essential for accurate fatigue life

predictions.

This paper summarizes our experimental results on the fatigue

crack growth resistance of 14 commercial structural alloys tested at

selected temperatures between 295 and 4 K. The data presented are

257
directly applicable to design. Many of the results are reported here

for the first time, although some data alloys were previously tested

and individually discussed in prior reports []. This collection and

comparison of data leads to generalizations showing that temperature

effects on da/dN-versus-AK behavior correlate well with alloy crystal

structure.

EXPERIMENTAL '^'-^

A list of alloys for which fatigue crack growth rates were measured is shown in Table 1. Included are the material forms, chemical

analyses, heat treatments, and specimen orientations according to the

ASTM E 399-74 notation [4]. The compact specimen geometry was chosen

because it is standardized and much experience with it has been accumulated. Constant amplitude fatigue tests were performed using specimens

20 to 38 mm thick, a sinusoidal load cycle, test frequencies between 20

and 28 Hz, and a constant minimum- to-maximum load ratio, R, of 0.1.

The compliance method of crack growth measurement was employed, using

apparatus and techniques that were previously described in detail

[5,6], producing fatigue crack growth rate data with uncertainties

typically no greater than + 20%.

RESULTS AND CONCLUSIONS

Fatigue crack growth rates at intermediate stress intensity factor

ranges, AK, usually conform to Paris equations having the form [7]:

^= C(AK)" (1)

where C and n are empirical constants that depend on material and test

variables. Logarithmic plots of da/dN-versus-AK data that are in agree

ment with Eq. (1) reveal linear trends, n and C being the slope and

258
ordinate intercept at AK = 1, respectively. Room temperature and

cryogenic fatigue crack growth rate data for the alloys tested in this

study are plotted in Figs. 1-13, and Paris equation parameters for each

material/temperature combination are listed in Table 2. There are three

distinct alloy groups:

I. HCP Titanium Alloys

Of all the alloys having mainly close-packed hexagonal crystal

structures, the Ti-5Al-2.5Sn (single phase, HCP) and Ti-6A1-4V (two

phase, HCP and some BCC) alloys are the most common for cryogenic service.

These alloys offer high strength-to-weight ratios, while retaining

adequate low temperature ductility and fracture toughness. As shown in

Figs. 1 and 2, the fatigue crack growth data for annealed normal and

low-interstitial grade Ti-5Al-2.5Sn alloys demonstrate temperature

independent behavior between 295 K and 4 K. The Paris equation exponents

for these alloys range from 4.0 to 4.8. Other results for the millannealed normal-interstitial and recrystallization-annealled, extra-lowinterstitial Ti-6A1-4V alloys described in previous reports [9] also

show temperature insensitive behavior. The results for those Ti-6A1-

4V alloys are compared with the Ti-5Al-2.5Sn alloys in Fig. 3. Over

most of the stress intensity range investigated, the fatigue crack

growth resistances offered by the Ti-5Al-2.5Sn alloys are slightly

superior to the Ti-6A1-4V alloys.

II . BCC Ferritic Steels

Fatigue crack growth rates for three ferritic steels containing

3.5, 5, or 9% nickel are shown in Figs. 4-6. Low temperature effects on

this group of alloys are insignificant or slightly beneficial as long as

259
temperature reductions remain in the "upper shelf" range, which is

defined as the region where dimpled rupture or fibrous fractures occur

during static fracture toughness tests. However, these ferritic steels

exhibit abrupt transitions to low fracture toughness involving cleavage

at temperatures determined primarily by the nickel content. Cleavage

cracking also leads to a drastic acceleration of fatigue crack growth

rates at temperatures in the sub-transition ranges. Accelerated fatigue

crack growth rates were observed for 3.5 Ni steel at 76 K (Fig. 4), and

for 9 Ni steel at 4 K (Fig. 6). A reduced fatigue crack growth resistance is also evident in the data for 5 Ni steel (Fig. 5) between 111

and 76 K. Due to such adverse trends, ferritic or BCC alloys are of

limited use in low temperature tensile applications, and are usually

restricted to service temperatures in their upper shelf ranges. Of all

alloys tested, the ferritic steels exhibit the most dramatic Paris

equation exponent transitions, with the room temperature values near

3.0 increasing to as high as 7.6 at sub-transition temperatures.

III. FCC Austenitic Alloys

Although more expensive than the less alloyed ferritic steels,

austenitic superalloys and stainless steels offer high fracture toughness and constitute the most important class of cryogenic materials.

Extensive alloying is possible in austenitic alloys, and a large number

of commercially available compositions exist. However, the structures

of some alloys are unstable at low temperatures; stress-induced bcc and

hep martensitic phase transformations can occur, affecting fatigue

crack growth resistance and other mechanical properties.

Figs. 7-9 illustrate fatigue crack propagation results for Inconel

260
750* (ASTM A 637), A-286 (ASTM A 453) and AISI 310 stainless steel,

three austenitic alloys that remain stable with respect to martensitic

transformations during fatigue tests at room and low temperatures.

These alloys exhibit similar behavior: the fatigue crack growth rates

at a given stress intensity factor are lower at 76 K and 4 K than at

room temperature, but there is no measureable difference in the rates at

the two cryogenic temperatures. Other stable FCC alloys such as 5083-

0 aluminum and Inconel 718 show similar trends [9]. Logsdon, Wells, and

Kossowsky [8] also reported improved rates at 4 K compared to room

temperature, in tests of the stable austenitic alloys Kromarc 58 and A286.

The AISI 304, 304L, and 316 stainless steels and the Fe-21Cr-6Ni9Mn stainless steel are unstable, undergoing significant martensitic

phase transformations during fatigue tests at 76 K and 4 K. Evidence of

martensite in crack-tip plastic zones was obtained metal 1 ographi cal ly,

and by detection with a magnetometer. In comparison, the small amounts

of martensite formed at 295 K are negligable. It can be assumed that

transformations precede crack growth at 76 and 4 K, and that fatigue

crack growth at these temperatures represents crack propagation through

partially transformed austenite.

It is difficult to generalize regarding the effect of martensitic

transformations on fatigue crack growth resistance. The results for

AISI 316 and 304 stainless steels, shown in Figs. 10 and 11, reveal no

pronounced temperature effects on fatigue crack propagation resistance,

*Tradenames are used for the sake of clarity, and do not imply

endorsement or recomnendation by NBS.

261
except perhaps at high rates approaching 2.5 x 10" mm/cycle. The AISI

304L stainless steel, having lower carbon content than AISI 304 (0.026C

compared to 0.05C), shows behavior analogous to that observed for stable

alloys. As shown in Fig. 12, there is a significant decrease in the

rates for AISI 304L at cryogenic temperatures compared to room temperature, but and the data at 76 K and 4 K are equivalent. The lower

carbon content should reduce the stability of AISI 304L relative to

AISI 304. Thus, the dissimilar temperature dependences for these

alloys may be due to differences in the quantity and properties of the

marten sites formed. -

The fatigue crack growth rates for the Fe-21Cr-6Ni-9Mn alloy are

shown in Fig. 13. The rates at 295 K and 76 K are equivalent despite

appreciable martensitic transformations occurring at 76 K. This behavior

is similar to that observed for AISI 304 and AISI 316. On the other

hand, the rates at 4 K are definitely higher than at 295 K and 76 K.

Pronounced cleavage-like facets were observed under magnification of the

4 K fatigue surfaces, so that the decreased fatigue crack propagation

resistance at 4 K can be attributed to a transition in the fracture mode

accompanying the martensitic transformation at this temperature. The

results for this alloy represent the only case where the fatigue crack

propagation resistance of an (initially) austenitic alloy decreases at

cryogenic temperatures. j.c t.'-

SUMMARY . .

Temperature effects on the fatigue crack growth resistance of

alloys correlate well with crystal structure:

1. HCP titanium alloys exhibit temperature-insensitive behavior

between 295 K and 4 K. ; . . . v252
2. BCC ferritic steels exhibit weak temperature dependences at

in their upper shelf temperature ranges, whereas at sub-transition

temperatures fatigue crack growth resistance is markedly decreased,

being associated with cleavage microfracture modes.

3. Stable FCC alloys exhibit improved fatigue crack growth

resistances at cryogenic temperatures, as compared to their behavior

in room temperature air. It is difficult to generalize on the trends

for metastable FCC alloys since favorable, adverse, or temperatureinsensitive behaviors are observed depending on alloy composition.

REFERENCES

1. F. R. Schwartzberg and T. Kiefer, "A Study of Fracture Behavior of

Metals for Superconducting Applications," MCR-74-89 (Issue 4), in

Materials Research for Superconducting Machinery, IV, R. P. Reed,

A. F. Clark, E. C. van Reuth, Eds., (National Bureau of Standards,

Boulder, Colorado, October 1975).

2. A. J. Nachtigall, S. J. Klima, and J. C. Freche, J. Mater. JMLSA

3 (1968) 425.

3. A. J. Nachtigall, in Properties of Materials for Liquified Natural

Gas Tankage, ASTM STP 579 (Amer. Soc. Test. Mater., Philadelphia,

1975) 378.

4. Standard Method of Test for Plane Strain Fracture Toughness of

Metallic Materials, ASTM E 399-74, in 1976 Annual Book of ASTM

Standards, Part 10 (Amer. Soc. Test. Mater., Philadelphia, 1976) 471.

5. C. W. Fowlkes and R. L. Tobler, Eng. Fract. Mechs. 8 (1976) 487.

6. R. L. Tobler and R. P. Reed, in Advances in Cryogenic Engineering

22, R. P. Reed, Ed. (Plenum, New York, 1976) 35.

7. P. C. Paris and F. Erdogan, Trans. ASME, J. Basic Eng. 85 (1963) 528.

8. W. A. Logsdon, J. M. Wells, and R. Kossowsky, in Proceedings of the

Second International Conference on Mechanical Behavior of Materials

(Amer. Soc. Metals, Ohio, 1976) 1283.

9. Materials Research for Superconducting Machinery, Vols. I to V,

R. P. Reed, A. F. Clark, H. M. Ledbetter, and E. C. van Reuth, Eds.,

(National Bureau of Standards, Boulder, Colorado, March 1974 to

March 1976) AD780596, ADA004586, ADA012365, ADA019230, ADA030170.

263
Table 1. Fatigue crack growth rate test materials for the

ARPA sponsored program ending September 30, 1976.

Material Form and Condition Specimen Thickness Mill Chemical Analyses, wt%

(mm), & orientation

Ti-5Al-2.5Sn, normal -interstitial 38, TS

annealed bar

Ti-5Al-2.5Sn, low-interstitial, 32, TL

annealed bar

Ti-6A1-4V, normal-interstitial, 25, TL

mill-annealed bar

Ti-6A1-4V, extra-low-interstitial, 20 to 25, TL

recrystal 1 ization-annealed bar

ASTM A 203 E (3.5 Ni steel), 25, TL

quenched and tempered, 25 mm

thick plate

ASTM A 645 (5 Ni steel), aus- 31, TL

tenized, temperized and

reversion-annealed, 32 mm

thick plate

ASTM A 553A (9 Ni steel, 31 , TL

quenched and tempered, 32 mm

thick plate

5083-0 aluminum alloy, annealed 32, TL

43 mm thick plate

Inconel 718, solution treated 31 , TS

and double-aged forging

Inconel 750, solution treated 38, TS

and double-aged forging

A-286, solution treated and 38, TS

aged forging

AISI 310, annealed 38 mm 38, TL

thick plate

AISI 316, annealed 38 mm 38, TL

thick plate

AISI 304, annealed 38 mm

' 38, TL

thick plate

AISI 304L, annealed 38 mm \ ., J 38, TL

thick plate

Fe-21Cr-6Ni-9Mn, annealed 38, TL

38 mm thick plate

Ti-5.28A1, 2.46Sn, 0.327Fe, O.OIC,

O.OIN, 0.1740, 40 ppm H.

Ti-5.25A1, 2.53Sn, 0.045Fe, 0.012C,

0.009N, 0.1160, 173 ppm H.

Ti-6.24A1, 4.18V, 0.174Fe, 0.035C,

O.OllN, 0.1550, 14 ppm H.

Ti-5.91A1, 3.94V, 0.103Fe, 0.018C,

0.014N, 0.110, 52 ppm H.

Fe-O.lOC, 3.62Ni, 0.46Mn, 0.013S,

0.015P, 0.20Si.

Fe-0.08C, 5.03Ni, 0.6Mn, 0.3Mo,

0.08A1, 0.009S, O.OIP, 0.25Si,

O.OION.

Fe-0.08C, 8.99Ni, 0.62Mn, O.OIS,

O.OIP, 0.19Si.

Al-4.0 to 4.9Mg, 0.3 to 1.0 Mn,

0.05 to 0.25Cr, O.lOCu max,

0.25Zn max, 0.15Ti max, 0.40Si max,

0.40Fe max, 0.15 others, max.

Ni-18.1Cr, 18.5Fe, 0.90Ti, 0.05C,

O.lOMn, 0.002S, O.OIP, O.lOSi,

0.003B, O.lOCu, 0.49A1, 0.17Co,

2.95MO, 5.24 Nb+Ta.

Ni-15.16Cr, 6.58Fe, 2.51Ti, 0.04C,

0.20Mn, 0.007S, 0.25Si, 0.04Cu,

0.78A1, 0.89 Nb+Ta.

Fe-0.05C, 13.96Cr, 24.97Ni, 1.52Mn,

0.54Si, 0.007S, 0.016P, 1.30Mo,

2.23Ti, 0.004B, 0.30V, 0.19A1.

Fe-0.038C, 24.65Cr, 20.4Ni, 1.41Mn,

0.72Si, 0.016S, 0.023P, 0.13Mo, 0.14Cu.

Fe-0.04C, 17.8Cr, 13.10Ni, 1.72Mn,

0.51Si, 0.019S, 0.019P, 2.18Mo.

Fe-0.052C, 18.33Cr, 9.82Ni, 1.6Mn,

0.75Si, 0.015S, 0.028P, 0.20Mo, 0.13Cu.

Fe-0.026C, 18.84Cr, lO.lSNi, 1.65Mn,

0.82Si, O.OIS, 0.022P, 0.27Mo, 0.28Cu.

Fe-0.019C, 19.75Cr, 7.16Ni, 9.46Mn,

0.15Si, 0.003S, 0.004P, 0.28N

264
Table 2. Paris equation parameters for alloys at room and cryogenic

temperatures (da/dN in mm/cycle and AK in MPa^m^^^).

Material Temperature, K n C AK region investigat

Ti-5Al-2.5Sn, annealed

1. normal -interstitial

2. low-interstitial

295, 76, and 4

295, 76, and 4

4.8

4.0

5.1xlo]n

4.9xl0'^

14

10

to

to

30

60

Ti-6A1-4V

1. normal -int., mil 1 -annealed,

2. ELI, recrystal 1 ization-annealed

295, 76, and 4

295, 76, and 4

?QS and 7R

6.0

7.0

o • u

-12

3.1x10^

1.9x1 Op

O A 1 U

14

10

70

to

to

30

20

ASTM A 203 E (3.5 Ni steel)

quenched and tempered

295

195

172

/D

3.2

3.2

3.2

/ . 0

1.3x1 Op

1.3x10q

l.OxlOi,

1 . DX 1

u

18

30

30

90cU

to

to

to

UU

60

70

60

ASTM A 645 (5 Ni steel)

dUS uen 1 1 1 ZcQ , LcMipci IZtiU, rcVtirilUri

anneal ed

295

1 1

1

1 1 1 76

2.7

7 7

4.0

I.IxIOq

1 ixin^

2.0xl0'^

25

25

27

to

to

to

90

60

80

Mo In M jDj m \y IN I s tee 1 ) quenched and tempered in

76

A

9 7

3.4

4.4

o . o

7 DxlO^

1.0x10^.

4.8x10

1 4xin

16

17

17

25

to

to

to

to

70

80

64

35

5083-0 aluminum

annea i eo

111, 76, and 4 5.2 1.3x10^0 8 to 28

Inconel 718

solution treated, double-aged

295

4

4.0

4.0

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20

25

to

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70

90

Inconel 750

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35

25

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to

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60

80

AISI 316, quenched 295 to 4 3.8 2.1x10^° 19 to 60

AISI 304, quenched 295 to 4 3.0 2.7x10^ 22 to 80

AISI 304L, annealed 295

76 and 4

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22

26

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Fe-21Cr-6Ni-9Mn, annealed 295 and 76

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3.7

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25

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80

70

265
03

10-3

E

E

CO

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GC

CD

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Ti"5AI-2.5Sn, Normal purity

295K

A- 76K

»- 4K

1

\—I I I I I

da/dN=5.1x10-ii(AK)

J \ I I I I I I I I i I I I I 2 5 10 50 100

STRESS INTENSITY RANGE, AK (MPa.m^/^)

Figure 1. Fatigue crack growth data for a normal interstitial Ti-5Al-2.5 Sn alloy at

295, 76, and 4 K, showing temperature independent behavior.

266
2 5 10 50 100

STRESS INTENSITY RANGE, AK (MPa m'/^)

Figure 2. Fatigue crack growth data for a low-interstitial Ti-5Al-2.5Sn alloy at 295,

76 and 4 K, showing temperature independent behavior.

267
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295K

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Ti-5AI-2.5Sn

4<T<295K

Normal

ELI

J L I I I 5 10 50

STRESS INTENSITY RANGE, AK (MPa.m^/^)

100

Figure 3. A comparison of fatigue crack growth results for Ti-5Al-2.5Sn and Ti-6A1-4V

alloys indicating the slight superiority of Ti-5Al-2.5Sn alloys over most

of the AK regions investigated.
2 5 10 50 100

STRESS INTENSITY FACTOR RANGE.AK, MPa m''^'

Figure 4. Fatigue crack growth data for a ferritic 3.5 Ni alloy steel at

selected temperatures.

269
2 5 10 50 100

STRESS INTENSITY FACTOR RANGE.AK, MPa

Figure 5. Fatigue crack growth data for a ferritic 5 Ni alloy steel at

selected temperatures.

270
E

E

CO

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R = 0.1

f = 20Hz

B = 3.1 cm

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selected temperatures.

27]
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in

1 i J I L-L

5 10 50 100

STRESS INTENSITY RANGE, AK (MPa-m'/^)

Figure 7. Fatigue crack growth data for a stable nickel-base austenitic

superalloy at 295, 76 and 4 K.

272
1 I

I I M I

1 1 1 1

I I I I

5 10 50 100

STRESS INTENSITY RANGE,AK (MPa m'/^)

Figure 8. Fatigue crack growth data for a stable iron-base austenitic

superalloy and stainless steel at 295, 76 and 4 K.
Figure 9. Fatigue crack growth data for a stable AISI 310 austenitic

stainless steel at 295, 76 and 4 K.

274
Q3

I

10-3

-a

<

cc

CD

<

CD

I—<

10

-4

1—r-TT 1 r 1—'

^

AISI 316

(annealed)

• T=295K

o T=76K

T=4K

1 J I l—L

5 10 50

STRESS INTENSITY RANGE, AK(MPa-ni'/2)

100

Figure 10. Fatigue crack growth data for a metastable AISI 316 stainless steel which

exhibits martensitic transformations during fatigue loading at 76 and 4 K.

275
1—I I I I

1

1

1 1 1 1—I—I I I

5 10 50 100

STRESS INTENSITY RANGE, AK (MPa . m'/2)

Figure 1 1 . Fatigue crack growth data for a metastable AISI 304 stainless steel which

exhibits martensitic transformations during fatigue loading at 76 and 4 K.

276
T

1 1—I—I—r-TT

Figure 12. Fatigue crack growth data for a metastable AISI 304L stainless steel which

exnibits martensitic transformations at 76 K and 4 K.

277
_i I I

» I I I

I I I I I I I I 5 10 50 100

STRESS INTENSITY RANGE, aK (MPa-m'^^)

Figure 13. Fatigue crack growth data for a metastable Fe-21Cr-6Ni-9Mn stainless steel

which exhibits martensitic transformations at 76 K and 4 K.

278
FRACTURE OF STRUCTURAL ALLOYS AT TEMPERATURES

APPROACHING ABSOLUTE ZERO*

R. L. Tobler+

INTRODUCTION

Plastic deformation and fracture are often viewed as competitive processes.

Factors that increase an alloy's resistance to slip usually tend to enhance

the probability of brittle fracture. Temperature reductions can lead to

pronounced increases in yield strength, while ductility may be decreased,

resulting in flaw sensitive mechanical behavior. For this reason, alloys

employed at normal temperatures may be unusable at low temperatures, and

the fracture toughness of candidate alloys for extreme cryogenic service

is a vital design consideration.

With the advent of superconducting electrical machinery we face for the

first time a demand for fail-safe, efficiently designed structures that

must be cooled with liquid helium to temperatures as low as 4 K. Fracture

data are urgently needed to enable judicious material selection for a temperature extreme that previously was rarely experienced. Due to its

inertness and proximity to absolute zero, liquid helium at 4 K provides a unique environment where the thermally-activated deformation processes of

materials are suppressed, and lattice friction stresses are nearly maximized. Therefore, fracture tests in this environment should provide information of current scientific interest as well as data of engineering utility.

Previous studies of low temperature fracture were hampered by the lack of a quantitative parameter that could be applied to a broad range of material/

temperature combinations. The traditional notched tensile and Charpy tests

provide only qualitative indications of crack tolerance, while the Kj^ test

applies only to high strength alloys which fail in the elastic range. None

of these parameters are well suited for characterizing the ductile and tough

austenitic alloys, which, as this paper demonstrates, offer maximum fracture

resistance at cryogenic temperatures.

In this study, J-integral and Kj^ tests were used to characterize the fracture behavior of 14 alloys at temperatures from 295 to 4 K. The parameters

measured, K^^ and Jj^, are complementary, being related in the linearelastic case by the equation:

K,2 = J,^E(l - v2)-l (1)

where E is Young's modulus and v is Poisson's ratio.

* Contribution of NBS, not subject to copyright.

+ Cryogenics Division, National Bureau of Standards, Boulder, CO 80302.

279
Jj^ is believed to be a material constant, applicable to either elastic

or elastic-plastic fractures. Thus, the Jj^ criterion offers a new

method for comparing low, medium, and high strength alloys -- a task that

was problemmatic in the past.

EXPERIMENTAL PROCEDURES

The commercial alloys listed in Table 1 were tested using compact specimens

20 to 38 mm thick. Where possible, Kjp was measured and Jx^ was calculated

by Eq. (1). Otherwise, Jj^ was obtained directly using the resistance

curve method, which required back extrapolation of J-vs-Aa data for a series

of specimens [1]. Crack extension, Aa, was averaged at 25, 50, and 75% of

specimen thickness, and the J = 2A/Bb approximation was used. Although

special cryostats were required to retain liquid helium, the test procedure at 4 K was similar to that at room (295 K) and intermediate temperatures.

The tensile properties of the alloys were also measured, following ASTM

Method E8-69, and the elastic constants were obtained by Ledbetter et al .

,

using ultrasonic methods [2]. The chemical analyses of these alloys and

other procedural details are available in comprehensive reports [2].

RESULTS

Strength Level and Fracture Mode

Table 1 lists selected mechanical property results at 4 K. Following

Tetelman and McEvily [3], it is convenient to classify these materials as

a a a low < 0.003), medium (0.003 < ^ < 0.006) and high strength (-^ > 0.006)

alloys. Decreasing the temperature from 295 K to 4 K serves to increase

the strength level, with a^/E increasing by amounts ranging from 17% for

5083-0 aluminum to 245% for 21-6-9 stainless steel. Most of these alloys were plastic when fractured at 295 K in the thickness stated, necessitating

J tests. However, at 4 K, the majority of alloys (all of the ferritic

steels and titanium alloys, as well as several precipitation-hardened

fee alloys) were linear-elastic. It was noted that alloys having

> 0.006 usually satisfied the ASTM E-399-74 specimen thickness requirement; exceptions were the ELI Ti-6A1-4V alloy at 295 K and the 21-6-9

stainless steel at 4 K.

Strength Versus Fracture Toughness

Although a combination of high yield strength and high fracture toughness

would be ideal, in reality these properties are antithetical. It appears

that designers must seek an alloy with the optimum combination of strength

and toughness for a given application. An inverse relationship between

280
2

-T

1 \ 1 1 1 1 1 1 1 1

1 1 ' 1 ' _ —

\ T = 295 4K

— o • 1 1 Alloys _ A A Al Alloys —

A.

V T INC Alloys

\

Steels - \ —

\ —

- \

-

^rintimiim PrnnprtiP? ~

|J L 1 1 M U 1 1 1 r 1 u p C 1 U C o V °\

A A

—

ASo

• \

• \ _ A

1 1 1 1 1 1 1 1 1 l\ 1 III"

10''^ 10-2

STRENGTH LEVEL.o-./E

ure 1. Fracture toughness-versus-:: /E for commercial structural alloys

tested at 295 K and 4 K. ^

281
and Kj^ at room temperature has been demonstrated for steel, aluminum,

and titanium alloys [4]. It must be appreciated that a similar trade-off

exists for alloys at cryogenic temperatures, and for elastic-plastic

fractures as wel 1

.

The Jrp and a /E data at 295 and 4 K are plotted on logarithmic coordinates

in Figure 1. These results show that the low strength alloys exhibit a wide variation in toughness, but the spread of observed Jj^ values decreases

with increasing o^/E, following a trend that holds for two orders of magnitude in Jyp. The empirical results for these technologically important

materials support the following conclusion: relatively low fracture toughness values are possible at any strength level, but the maximum toughness

attainable with commercial alloys is an inverse function of strength throughout the elastic and elastic-plastic ranges.

The Temperature Dependence of J.p

Temperature effects on Jj^ correlate well with crystal structure. Figure 2

illustrates three distinct trends for alloys having the fee, bcc, and hep

structures. The data presented in this figure are representative in that

fee alloys typically exhibit high toughness throughout the ambient-tocryogenic range, while the hep alloys are noted for low toughness, and bee

alloys show abrupt transitions to brittle fracture modes involving cleavage.

Secondary metallurgical factors such as composition, purity, heat treatment can modify the fracture toughness of alloys within each crystal

structure class considerably, as indicated by the following.

I. The fee alloys form three sub-groups:

1. Stable, annealed fee alloys show sizable increases in toughness

as temperature is reduced from 295 to 4 K. The AISI 310 stainless steel and

5083-0 aluminum alloys tested in this study showed Jxp increases amounting

to 55% and 175%, respectively.

2. Precipitation-hardened alloys show mild temperature dependences.

Included here are Ineonel 750*, Ineonel 718, A-286, and 2014-T652 aluminum.

The toughness of these alloys either increased, decreased, or remained constant, but the change in Jj^ between 295 and 4 K never exceeded 30%.

3. Metastable austenitic alloys undergo martensitic phase transformations during tests at low temperatures. Two such alloys, AISI 316 and

21-6-9 stainless steels, were studied here. Martensitic phases were detected

at the fracture surfaces of specimens tested at 4 K, but there was no evidence of transformations at 295 K. AISI 316 shows an increase in J^r

* Tradenames are used for the sake of clarity, and do not imply recommendation or endorsement by NBS.

282
300

AISI 310

TEMPERATURE, K

Figure 2. The temperature dependence of fracture toughness for alloys

having three different crystal structures.

283
between 295 and 4 K, whereas 21-6-9 exhibits a sizable decrease. Thus it

is difficult to generalize on the effects of phase transformations since

favorable as well as adverse effects are possible.

II. The bcc alloys including ferritic steels are of limited use due to

their transitional behavior. As a class, the 3.5, 5, and 9% Ni steels

exhibited the largest Jj^ decreases observed in this study. The transition

for 9% Ni steel occurs between 76 K and 4 K, where Jjp is reduced by 82%.

However, note that J^p actually increases by 20% as the temperature is

decreased from 295 to 111 K, just prior to the transition. Similar increases

of in the "upper shelf" regions were observed for 3.5 and 5 Ni steels,

but, due to lower Ni content, the transition temperature ranges for these

steels were higher in comparison with 9% Ni steel.

III. Although the toughness attainable with hep alloys is relatively low

in comparison with austenitic alloys, some hep titanium alloys offer unique

physical properties, such as superior strength-to-weight and strength-to

thermal conductivity ratios, which guarantee their use in many applications.

As indicated in Figure 2, a mildly adverse temperature dependence is

accepted as the general trend for the Ti-5Al-2.5Sn and Ti-6A1-4V alloys

which are most favored for cryogenic service. Nevertheless, many unalloyed

hep metals (Cd, Zn) display ductile-to-brittle transitions, and tests of

an extra-low-interstitial, recrystal 1 ization-annealed Ti-6A1-4V alloy

revealled a sharp decline of Kj^ in the relatively narrow interval 76 <

T < 125 K. A comparison of data for the ELI and normal Ti-6A1-4V grades

(Table 1) confirms that fracture results for these alloys are particularly

sensitive to material condition and purity.

CONCLUSION

The J-integral was used to evaluate and compare the low temperature fracture behavior of 14 commercial structural alloys. These data can be

used in fracture mechanics evaluations, and they suggest several generalizations that should aid in predicting the behavior of untested alloys.

However, many factors affect fracture behavior, and exceptions to the

general trends undoubtedly exist. Moreover, rankings of fracture toughness

based on J^p, a fracture initiation parameter, may not be equivalent to

rankings based on initiation/propagation parameters as measured, for

example, in dynamic tear tests.

REFERENCES

1. LANDES, J. D., and BEGLEY, J. A., in Fracture Analysis, ASTM STP 560,

Amer. Soc. Test. Mater., 1974, p. 170.

2. Materials Research in Support of Superconducting Machinery, Vol. 5 (and

previous volumes). Reed, R. P., Ledbetter, H. M., and van Reuth, E. C,

Eds., Nat. Bur. Stds., Boulder, CO.

3. TETELMAN, A. S., and McEVILY, A. J., Fracture of Structural Materials,

Wiley, NY, 1967.

4. WOOD, H. A., in Fracture Mechanics of Aircraft Structures, AGARDograph

No. 176, Liebowitz, H., Ed., North Atlantic Treaty Organization, 1974,

p. 18, AD-777-641.

284
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SEiMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

MAGNETOTHERI^L CONDUCTIVITY

L. L. Sparks

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

287
MAGNETOTHERMAL-CONDUCTIVITY

SPONSORED PROGRAM, SEPTEMBER

STUDIES

1973 TO

DURING ARPASEPTEMBER 1976

Material Unified Numbering

System Designation

ARPA Report

Number

Inconel 718 N07718 3

AISI 304 S30400 4

AISI 310 S31000 3

Fe-47.5% Ni 6

Cu-28% Ni C71500 6

Cu-0.5% Sn 6

OFHC-Cu C10200 2

Hi Purity Cu 3

Al 1100-0 A91100 5 Ti-6A1-4V 6

288
Siommary: Magnetothermal Conductivity

The magnetothermal conductivities have been determined for four alloys

Fe-47.47 wt % Ni, Ti-6A1-4V (ELI), Cu-0.5 at % Sn, and Cu-28 at % Ni . Data

are presented in the temperature range 4 to 20 K and for magnetic fields up

to 6366 kA/m (80 kOe) . The effect of the magnetic field is to reduce the

thermal conductivity of the Fe-Ni alloy and the Ti-Al-V alloy. The reduction due to 6366 kA/m field is 4.1% for the Fe-Ni specimen at 5 K and 2.2%

at 20 K. The corresponding reductions for the Ti-Al-V specimen are 16% at

K and 1.6% at 20 K. Any magnetic field effect on the thermal conductivity

of the two copper specimens was below the detectable limits of the system

for temperatures below 20 K.

Contents: Magnetothermal Conductivity

Page

1. Introduction 290

2. Procedures 290

2.1 Apparatus , 290

2.2 Materials 290

3. Results and Discussion 291

4. References 292

List of Figures 293

289
1. Introduction

The objective of the magnetothermal conductivity project has been to

determine the effect of magnetic fields on the thermal conductivity of

technically important metals. The need for this information arises from the

development of rotating machinery which operates at cryogenic temperatures.

The existing literature on magnetothermal conductivity, A (H) , deals almost

exclusively with pure materials and single crystals. A complete bibliography

of the subject was given by Sparks and Fickett in a previous ARPA report [1]

,

The materials studied in this program are being used or are candidates

for use in superconducting motors and generators. Optimum design of these

machines, which must operate at low temperatures while in magnetic fields,

requires a detailed knowledge of how the thermal properties of the constituent

materials are affected by a magnetic field. Test specimens were chosen so that broad categories of materials were represented. The categories and the

particular materials tested during the course of the ARPA work were:

(1) structural alloys — UNS-N07718, UNS-S30400, UNS-S31000, Fe-47.47

wt % Ni, and Ti-6A1-4V;

(2) superconductor stabilizing materials — oxygen-free copper, UNSA91100, and high purity copper;

(3) superconductor cable constituents — Cu-0.5 at % Sn and Cu-28 at

% Ni.

Based on these data the magnitude of the magnetic field effect on the thermal

conductivity can be estimated for similar materials.

Four specimens, Cu-0.5 at % Sn, Cu-28 at % Ni, Ti-6A1-4V, and Fe-47.47

wt % Ni, have been tested during this reporting period. Results for these

materials are included in this report.

2 . Procedures

2.1 Apparatus

The principal components of the X(H) system are shown schematically in

Figure 1. The conventional longitudinal heat flow method of determining thermal conductivity [2] is utilized. A specimen is shown mounted with its axis

parallel to the direction of the magnetic field. The longitudinal field

effect is determined when the heat current and magnetic field are parallel.

The basic operation of the system has been described in previous

reports [1,3], and the details of several system modifications were given in [4]

2 . 2 Materials

An extra low interstitial (ELI) form of Ti-6A1-4V was used for the A(H)

specimen. This alloy was produced to AMS 4930 specifications; it was commercially annealed at 977 K for 2 hours, air cooled and descaled. The microstructure of this stock of material was primary alpha and beta with the average

alpha grain diameter being 0.013 mm [5]. The chemical composition of the

alloy in weight percent was: Al , 5.91; V, 3.94; Fe, 0.103; 0, 0.110; C, 0.018;

N, 0.014; H, 52 ppm; Ti, balance. The ratio of the electrical resistivity at

the ice point to the electrical resistivity determined at a temperature just

above the superconducting critical temperature was 1.16 ± 0.02. The ratio of

area to length (A/1) for this specimen was 0.89 ± 0.01 mm.

290
A ferromagnetic specimen, Fe-47.47 wt % Ni, with an A/1 equal to 0.852 ±

0.003 mm was tested in the hot rolled condition. Mill analysis of this alloy

indicated the following composition in weight percent: C, 0.012; Mn, 0.33;

Si, 0.25; P, 0.002; S, 0.004; Ni, 47.47; Fe , balance. Grain size, as determined using the intercept method was 0.12 mm, Rockwell hardness was B75, and

the specimen density was 8.19 x 10-^ kg/m^ [6j. The ratio (RRR) of the electrical resistivity at the ice point to that at liquid helium temperature was

2.40 ± 0.002 for this specimen.

Two copper alloys were made at NBS-Boulder using the drop casting technique described by Ekin and Deason [7] . The melting was done in a flowing

hydrogen-argon atmosphere. Copper stock used in both alloys was from a 1.9

cm bar of oxygen-free copper (UNS-C10200) . The tin content of the Cu-Sn

alloy was 0.49 at % and A/1 = 0.87 ± 0.01 mm. After machining, the specimen

was annealed at 650°C for 2.5 hours at pressures not exceeding 6.4 x

10"-^

Pa. The ratio of electrical resistivity at 295 K to the electrical resistivity at 4.2 K was 1.10 ± 0.01.

3 . Results and Discussion

The Ti-6A1-4V specimen exhibited a superconducting phase in its electrical resistivity. The onset of superconducting behavior at zero magnetic

field occurs when 5.2K<T<5.5Kas shown in Figure 2. The critical transition temiperature is lowered as the magnetic field is increased until at

6366 kA/m (80 kOe) no transition is observed. Within the limits of precision of the measurement, the normal resistivity of the specimen was 1.43

± 0.02 yf^*m and was independent of both temperature (T < 20 K) and magnetic

field. Figure 3 shows the resistance of the specimen at 4.2 K as a function

of magnetic field. The imprecision of the measurements at H = 0 is quite

high as indicated by the scatter shown in the figure. It appears that the

critical field is less than 3183 kA/m (40 kOe) when T = 4.2 K.

The thermal conductivity of Ti-6A1-4V is shown in Figure 4 as a function

of temperature with magnetic field as a parameter. The relative change in

thermal resistivity (AW/Wj^_q) is given by (Wjj - Wjj=q)/Wh=o. When H = 6366

kA/m (80 kOe) , ^W/W^^O 19.8% at 5 K and 1.5% at 20 K. The normal to

superconducting change is not evident in the thermal conductivity data since

the primary mode of heat conduction in this material is due to phonons rather

than the electrons. A marked decrease in conductivity would have been

expected below the critical temperature (T,^) if the primary conduction mode

were electronic. Electrons in the superconducting state have zero heat

capacity and can, therefore, not carry thermal energy.

The thermal conductivity of the Fe-Ni alloy is shown in Figure 5 as a function of temperature with magnetic field as a parameter. As seen in this

figure, essentially all of the reduction in conductivity due to magnetic field

occurs when H ^ 1592 kA/m (20 kOe) . This saturating tendency is shown in

Figure 6. A field of 6366 kA/m (80 kOe) causes Z\W/Wjj=o = 4.79% at 5 K and

AW/Wh=o = 2.27% at T = 20 K. Hust [8] measured the thermal conductivity of

a similar Fe-Ni specimen at zero magnetic field and T = 7.42 K. His data

indicate a conductivity of 1.47 W/m*K which is nearly identical to the data

taken in the magnetothermal apparatus.

The thermal conductivities of the Cu-0.5 at % Sn and Cu-28 at % Ni at

zero field are shown in Figures 7 and 8 respectively. The effect of magnetic

field on the conductivity of these specimens is too small to be detected in

the present system. Differences between the zero field thermal conductivity

291
data and the H = 3183 kA/ra (40 kOe) and H = 6366 kA/m (80 kOe) data are

shown in Figures 9 and 10. The differences in thermal conductivity used in

these curves were obtained by subtracting the experimental thermal conductivities for H 7^ 0 from the values read from the smooth curves shown in

Figures 7 and 8. The electrical resistivity for these copper alloys did

not change as a function of magnetic field or temperature for H 1 6366

kA/m (80 kOe) and T ^ 20 K. This field independence has been observed

previously at 4.2 K [9] on specimens from the same melts used for the A(H)

specimens

.

4. References

1. L. L. Sparks and F. R. Fickett; in Materials Research in Support of Super

conducting Machinery-I ; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.);

Nat. Bur. Stds . , Boulder, CO; March 1974; AD780596.

2. White, G. K. , in Measurement of Solid Conductors at Low Temperatures , Tye, R. P. (Ed.), pages 88-94 (Academic Press, NY, 1969).

3. L. L. Sparks and F. R, Fickett; in Materials Research in Support of Super

conducting Machinery-II; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.);

Nat. Bur. Stds., Boulder, CO; October 1974; ADA004586.

4. L. L. Sparks; in Materials Research in Support of Superconducting

Machinery-IV; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.); Nat. Bur.

Stds., Boulder, CO; October 1975; ADA019230.

5. R. L. Tobler; in Materials Research in Support of Superconducting

Machinery-Ill; R. P. Reed, A. F. Clark, E. C. van Reuth (Eds.); Nat. Bur.

Stds., Boulder, CO; April 1975; ADA012365.

6. H. M. Ledbetter and D. T. Read; in Materials Research in Support of Super

conducting Machinery-V; R. P. Reed, H. M. Ledbetter, E. C. van Reuth (Eds

Nat. Bur. Stds., Boulder, CO; April 1976.

7. J. W. Ekin and V. A. Deason, Technique for Preparing Homogeneous Bulk

Samples of Concentrated Alloys, Rev. Sci. Instrum. 4_6, No. 3, pp. 327

(March 1975)

.

8. J. G. Hust; in Materials Research in Support of Superconducting Machinery

VI; R. P. Reed, H. M. Ledbetter, E. C. van Reuth (Eds.); Nat. Bur. Stds.,

Boulder, CO; to be published.

9. F. R. Fickett, Nat. Bur. Stds., Boulder, CO, personal communication.

292
List of Figures

Figure 1. Schematic of raagnetothermal conductivity probe and magnet.

Figure 2. Electrical resistivity as a function of temperature for Ti-6A1-4V

(ELI)

Figure 3. Electrical resistance of Ti-6A1-4V (ELI) as a function of magnetic

field at 4.2 K.

Figure 4. Therm.al conductivity of Ti-6A1-4V (ELI) as a function of temperature

with magnetic field as a parameter.

Figure 5. Thermal conductivity of Fe-47.47 wt % Ni as a function of temperature with magnetic field as a parameter.

Figure 6. Thermal conductivity of Fe-47.47 wt % Ni as a function of magnetic

field with temperature as a parameter.

Figure 7. Thermal conductivity of Cu-0.5 at % Sn as a function of temperature

at zero magnetic field.

Figure 8. Thermal conductivity of Cu-28 at % Ni as a function of temperature

at zero magnetic field.

Figure 9. Deviation of thermal conductivities found in the zero and nonzero field tests on Cu-0.5 at % Sn.

Figure 10. Deviation of the thermal conductivities found in the zero and nonzero field tests on Cu-28 at % Ni.

293
Vaciii aii

Electrical Leads

Fill Tibes

TherMiMeter llsck (carbsi)

SpeciRei (leieitidiial)

(trais^erse lit shiwi

TkerRiMiter Blick

(carbii)

Speciiei Heater

6 as Aisirbeit

VaciiM aii

^^3;^ Electrical Leais

Li^ii NeliiR Teiperatire Cap

Iberial Liiks

Tenpiratire Ciitrilled Heat Silk

Teiiperiis Pist

Speci^ei

Cbaaber (Cij

Tenperiis fist Heater

7958 kA/n SipercNiictiie Sileiiii HiRiieieiis Field ii 2.54 cr

iiaRiter Spkere

igure 1. Schei,iatic of magnetothermal conductivity probe and magnet.

2 94 -
10-6 -

|j

10

-7

10

-8

E

d

10

10

10

11

10Q_

1.43x10 ^n m for all fields

and T < 20K

Ti - 6AI - 4V (ELI)

o 0 kA/m

O 796 kA/m (10 kOe)

A 3183 kA/m (40 kOe)

6366 kA/m (80 kOe)

8 10 12 14 16 18

T (K)

Figure 2. Electrical resistivity as a function of temperature

for Ti-6A1-4V (ELI)

295
10

10

10

9 10 5

1592

H (kA/m)

3183 4775

Ti - 6AI-4V (ELI)

T = 4.2K

6366

10 6-

10

10

20 40

H (kOe)

60 80

Figure 3. Electrical resistance of Ti-6A1-4V (ELI) as a function

of magnetic field at 4.2 K.

296
c0

-H

+J • Oc 0) p -Pe

fd fd w fd

fd

(d

M

w

pa fd

Cl) 1 -H

iH <4-l <: O 1 •H H +J

OJc

Cn 0 fd6

>1 H +J > H

•H :5 u 0) D

=3

4-> 0 fd U ua

(0 e g (U +j

Q) ^ M-l0

(U H

fa

(>| iu/M)X

297
O o

09

I

An

EES

E<<2

< «NJ CO *g

09 OO ^

O «— CO C&

o O <

CO

eN4

oo

CO

If) CNi

(>| iu/AA) \

298
H (kA/m)

0 1592 3183 4775 6366

4.0

1 1 ' 1 ' 1 1 1 1

Fe - 47.47 wt. % Ni

1 I

1

^Ul\ -

3.0

10 1\

—

cs

^2.0

10K _

1.0

-

1 I , I , I

5K _

1 1 % 20 40 60 80

H (kOe)

igure 6. Thermal conductivity of Fe-47.47 wt % Ni as a function

of magnetic field with temperature as a parameter.

299
oco

•H

-POCP

CO

fOC

o\o . 'a

•H

in

m 0 u 1 -H D -U U <DC O ffl e

>i

-p o

•H 5^ > (D •H N U -P

^3Cooe

0)

03uD

to

0)e

Q) -p

0)

•H

CO

(M-iu/M)

X

300
301
-Oo

u

N

QJ

in

as 09 O O

^ CO

E ^

LO 00 2

O CO CP

c

o ^

LD

•H •

13o

-P

rd w

0) in

•rH . 4-1 •H>H

u

o

u

o

I u

C

O

M

-PW

Q)

(13

QJ (U ^ -H

M-lO

o

•H

-P

fO •H> n3

(U Q

CNJ

Q)

CP •H

P4

0=Hy ^(Hy -0 = Hy

j

302
1—

CM

< y

<_

o o

o o ^ CO

< o

< Ln

OO QQ

CO

csn

CO CD

(U

JJ

•H

^3

o

CO

QJ -H

+J •H>H

4JU

C

Ou

cu

o

5-1 OJN

Ic

o

C

O 13 •H C

o

0) a; Q N

- o O <

I I ^ I L J L 00

0 = Hy ^(Hy .0 = Hy

J

0

•H

303

SEMI-ANXUAL REPORT OX MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

THER2-1AL CONDUCTIVITY

J. G. Rust

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1976

305
THERMAL-CONDUCTIVITY MEASUREMENTS DURING ARPASPONSORED PROGRAM, SEPTEMBER 197 3 TO SEPTEMBER 197 6

Material ARPA Report

No^. Experimental Apparatus

OFHC Copper 2 variable temperature

Inconel X-750 (ST) 2 variable temperature

Inconel X-750 (STDA) 3 variable temperature

INCO LEA 2 variable temperature

Stainless Steel 310-S 2 fixed-point

Stainless Kromarc 58 2 fixed-point

Maraging Steel 300 6 fixed-point

Carpenter 49 Steel 6 fixed-point

Phenol formal dehyde 6 fixed-point .

Graphi te-epoxy 6 fixed-point

Boron-al uminum 6 fixed-point

Boron-epoxy 4,6 both

306
Summary; Thermal Conductivity

Thermal conductivity values are reported for those materia]s measured

during the current reporting period. Specimens were measured of a high permeability steel (Fe-47.5Ni), maraging steel 300 (Fe-18Ni-9Co-5Mo) , both in

the rolling direction and perpendicular to the rolled plate, boron-aluminum,

boron-epoxy, phenolformaldehyde , and graphite-epoxy composites. These data

are compared to literature data for similar materials. A new thermal conductivity apparatus is also described. It is a fixed-Doint aooaratus utilizing

compressive thermal contacts to circumvent problems encountered with bonded

thermal contacts.

307
THERMAL CONDUCTIVITY

J. G. Hust

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Introduction

Optimum design of superconducting machinery requires a knowledge of

thermal properties of technically important materials at low temperatures.

But, often, components extend from ambient temperatures to low temperatures,

and, therefore, data are needed from 4 K to 300 K. Thermal conductivity of

metals is a function of the host metal and its constituent elements and temperature; but it also depends on the microstructure of the material, strain,

fatigue, and heat treatment; and in some cases environmental effects are

important (e.g. in the case of superconducting machinery, magnetic field

intensities may produce significant changes) . Specific thermal conductivity

data for particular components are required to limit heat losses and thermal

stresses in machines. With such a myriad of parameters it is difficult (at

best) to determine accurately, by experiment, the thermal conductivity of

each machine component. Instead, we often rely on a limited number of measurements on specific types of materials, characterized according to the

above parameters. Due to material variability effects these values are generally considered accurate to only about 10%.

It should be noted that accurate thermal conductivity measurements are

much more expensive and time consuming relative to many other property measurements. The ease with which high accuracy can be obtained is primarily a function of temperature and the conductivity itself. The extremes of conductivity (both very high, such as in pure metals, and very low, such as in

insulating materials) promote inaccuracies in measurement. Generally, low

temperature data (below about 100 K) are more readily obtained with accuracy

because radiation errors can be minimized.

For the above reasons, various methods of obtaining thermal conductivity

data are used. The method used depends primarily on the accuracy dictated

by the application. Usually accuracies of 10% are sufficient; in other

cases values accurate to 50% suffice. The present state-of-the-art in thermal conductivity measurements is about 1% accuracy, but seldom is this required

except in theoretical or standardization work.

In this laboratory three methods of data determination are used:

(a) A variable-temperature apparatus, capable of measuring at any

temperature from 4 to 300 K, with an accuracy of about 2%. This

apparatus also simultaneously measures electrical resistivity and

thermopower for additional specimen characterization and subsequent

predictions of similar materials. This apparatus is used to measure materials that have not been sufficiently measured and

characterized previously and for accurate temperature dependence

determinations

.

(b) Two fixed point apparatus, capable of measuring near the fixed

temperatures of various boiling fluids (such as liquid helium and

liquid nitrogen) and melting or subliming solids (such as ice and

CO2) • The accuracy of these apparatus is about 10%, depending

mainly on the conductivity of the specimen.

308
(c) Predictive methods such as those described by Hust and Clark [1]

and Hust and Sparks [2] . The latter paper also contains data for

many metals and alloys, necessary to carry out such predictions.

2 . Apparatus

During the current reporting period the fixed-point apparatus were used

to determine thermal conductivity near the fxxed-point temperatures of various

cryogenic baths. As explained in a later section, difficulty was encountered

in accurately measuring composite specimens using the fixed-point apparatus

described in a previous report of this series [3] . The difficulty was caused

by the differential thermal expansion between the composite specimens and

the copper end pieces glued to the specimens for thermal contact. These

epoxied bonds apparently cracked during cooldown and resulted in poor thermal

contacts. During the last such run with a composite involving NASA resin 2 the end pieces actually fell off during the run. Because of these difficulties a new fixed-point probe was built in which the thermal contact to the

specimen was obtained through a compressed indium contact. Otherwise, the

operation was identical to the older probe. Figure 1 illustrates this compression type fixed-point apparatus.

The operation of this apparatus is the same as that previously described

[3] . Prior to measuring any specimens several calibration runs were conducted

to determine the amount of heat conducted by the compression bolts and the

measuring wires which pass from the top block to the bottom block. These

calibration runs, however, could not be conducted with an empty chamber, as before, because the thermal resistance between the two blocks is dependent

on the existence of a force on the compression bolts. Therefore, the system

was calibrated using three specimens of phenolformaldehyde rods of decreasing

cross-sectional areas. The first was a solid rod of 1.91 cm diameter. The

second was of the same outside diameter with a 1.27 cm holfe through the center.

The third was drilled with a 1.75 cm hole. For each of these specimens, curves

of heat flow versus temperature gradient were experimentally determined.

These curves were cross-plotted to obtain curves of heat flow versus crosssectional area at constant gradient. The intersections of these curves

(straight lines) with the A = 0 axis were used to determine the heat flow

versus temperature gradient of the "empty" chamber. These data, given in

Table 1, were used to correct the measured heat flow to obtain the heat flow

actually conducted by the specimen at a given gradient.

Table 1. Heat flow of the empty chamber as

a function heater block temperature at fixed

upper block temperatures, i.e. the bath

temperature

Bath (temp) (;^(mW) T(K)

liquid helium 0.00 4.0

(4 K) 0.44 6.5

1.32 9.0

2.89 12. 0

5.70 16.0

9.05 20.0

liquid nitrogen 0.0 76

(76 K) 36.0 87

77.7 99

dry ice and alcohol 0.0 192

(192 K) 83.5 204

176.7 216

ice and water 0.0 273

(273.15 K) 149.0 285

307 .0 297

309
4^

To Vacuum Pump

and Electronics

Copper Tempering Tube

Vacuum Chamber

Differential

Thermocouple

Specimen

High Strength Steel

Compression Bolts (3)

Bottom Block

(copper)

Thermal Insulator

Jop Plate

Top Block (copper)

Indium Junctions

Block Heater

High Modulus

Spring Washers

Figure 1. Compressive thermal contact fixed-point

thermal conductivity apparatus.

- 'I ^310
Table 2. Thermal conductivity values for the materials

measured during the current reporting period.

Specimen Identification T } Specimen Identification T _} _-, (K) (W.m'.R^ (K) (W-m'.K')

High Perm 49 Fe-47.5 Ni

(in rolling direction)

SAME (perpendicular to

plate)

Maraging Steel -300

(in rolling direction)

SAME (perpendicular to

plate)

Boron-aluminum composite (longitudinal)

SAME (transverse)

7.41

84.0

200

280

1.24

10.4

15.1

16.9

Phenol formaldehyde Composite

7 AO 1 /1

1.4/

0/1 1 XC.O

1 yy XO.C

280 20.0

85.2 6.93

199 11.8

279 14.4

7.45 0.712

84.5 7.33

199 12.5

280 15.4

7.59 17.7

78.4 75.1

195 82.2

276 89.6

7.60 11.3

78.3 51.3

195 55.7

276 60.6

- V

These data obtained using bonded thermal

contact apparatus.

Boron-epoxy (longitudinal )

SAME (transverse)

Graphite-epoxy (longi

tudinal deformed)

Graphite-epoxy (longitudinal) (high-temp,

resin)

6 0.055

8 0.070

10 0.083

80 0.33

0 58

3on 0.54

5.98 0.248

7.67 0.380

1 r\ o /I 10.84 n C 7 Q 80.3 2.14

198 2.24

277 2.24

5.96 0.128

80.3 0.612

196 0.940

276 0.905

6.07 0.0388

80.2 0.702

196 2.36

277 3.43

5.97 0.0466

10.82 0.0724

80.2 0.920

195 3.19

276 4.64

J V

These data obtained using compressive thermal

contact apparatus.

311
TEMPERATURE, K

Figure 2. Thermal conductivity of High Perm 49 and Maraging Steel

300 compared to literature data [5] for fee iron alloys.

312
IDO

o

o

<:

100

50

20

10

2 -

1

1 I I I I

\ •

o-^

I- / /

,o

I I I I I I

Longi tudinal

O Transverse

J I I I I I I 10 20 50

TEMPERATURE, K

100 200

Figure 3. Thermal conductivity of boron-aluminum composite

313
0.2 -

0.05

20 50

TEMPERATURE, K

100

Figure 4. Thermal conductivity of phenol formaldehyde composite

314
ZDo

o

UJ

1

0.8

0.6

0.4

0.2 -

Longitudinal (Variable Temperature

Apparatus

0.

J \ L_L

O Longitudinal

A Transverse

(Fixed Point Apparatus!

8 10 20 40 60 80 100

TEMPERATURE, K

200 300

Figure 5. Thermal conductivity of longitudinal and transverse

boron-epoxy composite specimens.

315
I I I I I I \ I I

I I I I I I L_

5 10 20 50 100 200

TEMPERATURE, K

Figure 6. Thermal conductivity of two graphite-epoxy

composite specimens (longitudinal).

316
3 . Specimen Characterization

During the current reporting period specimens of high permeability

steel (Fe-47.5Ni), maraging steel 300 (Fe-18Ni-9Co-5Mo) , phenolformaldehyde

boron-epoxy, graphite-epoxy , and boron-aluminum composites were measured.

High Perm 49 (Fe-47 . 5Ni) ; The chemical composition by weight percent of this material is Fe(bal),

Ni(47.47), Mn(0.33), Si(0.25), C(0.012), S(0.004), and P(0.002). The material was hot rolled and ground to a size of 9" X 4" X 20" long. The specimens measured were cut and ground from this plate. The density of the

material is 8.19 ± 0.02 g/cm^ and its Rockwell hardness is B73.

Maraging Steel 300 : The chemical composition is Fe{bal), Ni(18.41), Co(9.27), Mo(4.95),

Ti(0.59), Al(0.12), Mn(O.Ol), Si(O.Ol), P(0.06), S(0.003), and C(0.002).

Its density is 8.06 ± 0.02 g/cm^ and its Rockwell hardness is B105.

Boron-Aluminum Composite ; This composite was fabricated with 5.6 mil boron fibers and 6061-F

aluminum. The aluminum content by voJume is 53% with a void content of

less than 2%.

Phenolformaldehyde Composite ; This material is uncharacterized rod stock used for apparatus calibration

as described earlier.

Boron-Epoxy Composite ; This is the same material as described in an earlier report of this

series [4]. It was remeasured because of the aforementioned thermal contact problems.

Graphite-Epoxy Composite ; Measurements were performed on two graphite-epoxy formulations. One,

designated as SP-288-T300, is composed of continuous graphite fibers

with a PR-288 resin content of 50% by volume. The other is fabricated with

NASA resin 2, also 50% by volume. The latter composite contains a highly

flexibilized resin and was difficult to measure, as discussed later.

4 . Results and Discussion

The results of the measurements conducted during the current reporting

period are listed in Table 2 and illustrated in Figures 2 through 6. The uncertainty of these data is estimated to be ± 10%. The data obtained with poor

thermal contacts are not listed. However, it may be interesting to note

that the discrepancies resulted in values as small as one-third of the correct values. This illustrates the magnitude of the errors which can readily

enter into thermal conductivity measurements and emphasizes the care which

must be exercised to avoid them.

317
High Perm 49 (Fe-47 . 5Ni) and Maraging Steel 300 ; The results of these measurements are plotted in Figure 2. For comparison a shaded area is included which represents the range of reported values

for fee iron alloys [5]. The High Perm 49 values lie at the upper end of

this range and the maraging steel values are near the middle. The differences

between the longitudinal and transverse High Perm 49 specimens are slightly

larger than measurement uncertainty while for maraging steel the differences

are within measurement uncertainty. In either case, however, the differences

are comparable to that one would expect from material variability.

Boron-Aluminum Composite : The measured values of thermal conductivity for the longitudinal and

transverse specimens of boron-aluminum composites are shown in Figure 3. An

attempt was made to correlate these data with the pure component data. However, no data for aluminum 6061 in the F condition and boron fiber have been

reported in the literature. Estimates could be made for both of these, but

because of the high uncertainty of such estimates the resulting correlation

would be of questionable value. Suffice it to say that the measured values

are in reasonable correspondence for a similar aluminum alloy and the results

estimated for boron fibers as reported previously in this series [4].

Phenolformaldehye Composite ; This material was not measured directly as part of this ARPA program but

rather as a calibration material. However, because of its common usage,

the results, illustrated in Figure 4, are considered useful. A. V. Luikov,

L. L. Vasiliev and A. G. Shashkov [6] measured a similar material; their

results are included in Figure 4. The agreement is considered good in view

of the uncharacter ized nature of these specimens. These results and the following were obtained with the compressive fixed-point apparatus. A smooth

(dashed line) has been drawn through the present data, however, the data of

Luikov et al [6] indicate there xs a phase transition at 150 K. The point

spacing of the present data would not reveal this transition but does not

conflict with its potential existence.

Boron-Epoxy Composite ; This material was remeasured with the compressive thermal contact apparatus after the bonded thermal contact problem was discovered. The new results

are illustrated in Figure 5 along with the previously reported values for

the longitudinal specimen using the variable temperature apparatus. Contrary

to the previously reported results using the bonded thermal contact fixedpoint apparatus, the two longitudinal specimens are in reasonably good agreement. The poor thermal contacts reduced the apparent thermal conductivity by

about 50%. The thermal contact to the transverse specimen was apparently

also not good since the previously reported values are low by about 20-30%.

The present values are slightly higher than the literature data for both

specimen directions.

Graphite-Epoxy Composite ;

-

As mentioned earlier , considerable difficulty was encountered in measuring this material. The first attempt to measure this material using the

bonded thermal contact apparatus resulted in broken thermal contacts. The

compressive thermal contact apparatus was then built and measurements

attempted. Again, the results were questionable because of the deformation

of the highly plasticized resin. Another specimen was fabricated using a less flexible resin and these results are considered reliable. The latter

two sets of data are illustrated in Figure 6.

318
References

1. Hust, J. G. and Clark, A. F., The Lorenz ratio as a tool for predicting

the thermal conductivity of metals and alloys. Materials Research and

Standards 11, (No. 8) , 22-4 (August 1971)

2. Hust, J. G. and Sparks, L. L., Lorenz ratios of technically important

metals and alloys, Nat. Bur. Stand. (U.S.) Tech. Note 634, (February 1973)

133 pp.

3. Hust, J. G. , in Semi-annual report on materials research in support of

superconducting machinery, NBSIR 74-359 (1974) 308 pp; available from

NTIS, AD 780-596/3WM.

4. Hust, J. G. , in Semi-annual report on materials research in support

of superconducting machinery, NBSIR 75-828 (1975) 186 pp.

5. Childs, G.E., Bricks, L.J., and Powell, R.L., Thermal conductivity of

solids at room temperature and below, a review and compilation of the

literature, Nat. Bur. Stand. (U.S.) Monograph 131, (1973) 608 pp.

6. Luikov, A.V. , Vasiliev, L.L., and Shashkov, A.G., A method for the simultaneous determination of all thermal properties of poor heat conductors

over the temperature range 80 to 500 K, Proceedings of the 3rd Symposium

on Thermophysical Properties, Purdue University (1965) pp. 314-319.

319 USCOMM - ERL

NBS-1 14A IREV. 7-731

J .5. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 75-8482. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLF

Semi-Annual Report on Materials Research in Support of

Superconducting Machinery

5. Publication Date October 1976

6. Performing Organization Code

275.03

7. AUTHOR^S' K.P. Keed, J.G. Must, M.B. Kasen, H.M. Ledbetter,

H.I. McHenry, D.T. Read, R.E. Schramm, L.L. Sparks, R.L. Tobler

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project Taskwork Unit No. 2750131

11. Contract/Grant No.

12. Sponsoring Organizacion Name and Complete Address (Street, City, State. ZIP)

Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less [actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Results are reported of a six-month study, ending September 1976, on candidate materials for superconducting-machinery components. The results

cover five areas--advanced composites, elastic properties, fatigue resistance and fracture toughness, magnetothermal conductivity, and thermal con- ductivity. Material properties were studied over the temperature range 4 to 300 K. Materials studied include: aluminum alloy 5083, copper-0.3

cadmium-0.3 tin, copper-28 nickel, iron-48 nickel, 3.5 Ni and 9 Ni steels,

titanium-4 alurainuiii-6 vanadium, titanium-5 aluminum-2.5 tin, stainless steel

21-6-9, several austenitic stainless steels of the 300 series, 300-grade

maraging steel, phenolformaldehyde , and the composites boron/aluminum,

boron/epoxy, graphite/epoxy , and niobium- titanium/copper . Some notable

results of the study are: anomalous elastic properties of stainless steel

21-6-9 due to a Neel transition; complete sets of elastic constants for two

composites, B/Al and NbTi./Cu; thermal conductivities of Ti-6A1-4V and Fe48Ni are reduced by a magnetic field while those of Cu-0.5 Sn and Cu-28Ni

are unaffected; a screening method for composites of possible cryogenic use; general trends regarding temperature effects on the fracture toughness and

fatigue-crack-growth resistances of structural alloys are correlated with

crystal structure class; and the tensile-yield-strength and fracturetoughness data for fourteen commercial structural alloys at 4 K and 295 K are compared demionstrating an inverse relationship between these properties

and indicating the optimiom combination of properties that are technologically possible. Also, the materials and properties studied experimentally

during the three-year program are summarized.

This work was supported by the Advanced Research Projects Agency of

the U.S. Department of Defense.'

17. KEY U'ORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key nord unless a proper name; separated by semicolons) Aluminum alloysi composites; elastic Droperties; engineering

materials; fatigue; fracture; iron alloys; cryogenic temperatures; maraging steels;

mechanical properties; nickel alloys; phenol formal dehyde • stainless steels; superconducting machinery: thermal conductivity: titanium alloys

' 19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

18. AVAILABILITY Unlimited

For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13

1 Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

320

22. Price $9.75

USCOMM-DC 29042-P74