NBSIR 75-810

Semi-annual report on materials research

IN SUPPORT OF superconducting MACHINERY

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

R. P. Mikesell, R. E. Schramm, L. L. Sparks, R. L. Tobler,

and W. F. Weston

/ /

-2

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

m 1975

I

Prepared for

Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209
4H|
NBSIR 75-810

SEMI ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

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

R. P. Mikesell, R. E. Schramm, L. L. Sparks, R. L. Tobler,

and W. F. Weston

Cryogenics Division

Institute for Basic Sandards

National Bureau of Standards

Boulder, Colorado 80302

April 1975

Prepared for

Advanced Research Projects Agency

1400 Wilson Boulevard

Arlington, Virginia 22209

u s DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

Sponsored by

Advanced Research Projects Agency

ARPA Order No. 2569

Program Code 4D10

August 10, 1974 - August 9, 1975

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.

iii
Abstract

Results of six months of study on materials in support of superconductingmachinery (October 1974 through March 1975) are reported to the sponsor, the Advanced

Research Projects Agency of the U.S. Department of Defense. The report is divided into

five sections: Thermal conductivity, magnetothermal conductivity, fatigue and fracturetoughness properties, properties of advanced composites, and elastic properties. The

temperature range 4 to 300 K is covered by the study. Materials studied are either being

used or are candidates for use in superconducting machinery and include: aluminum alloys,

composites, copper, age-hardened nickel-base superalloys, stainless steels, and titanium

alloys.

Special results of the study include: thermal conductivity data for comparison of

the effects of heat treatment on age-hardenable alloys, the first determination of a complete set of elastic constants for a composite at liquid helium temperature, boronaluminum composite tensile data at 4 K, and a summary of fatigue crack-growth rate behavior at 4 K for a number of different structural alloys. These data provide considerable insight into material characteristics at extremely low temperatures, assisting in

material selection and efficient design.

Keywords: Composites; elastic properties; fracture; liquid helium; mechanical properties;

structural materials; superconducting machinery; thermal conductivity.

iv
Report Contents

Page

THERMAL CONDUCTIVITY

J. G. Hust 1

MAGNETOTHERMAL CONDUCTIVITY

L. L. Sparks 11

FATIGUE AND FRACTURE-TOUGHNESS TESTING AT CRYOGENIC TEMPERATURES

R. L. Tobler, R. P. Mikesell, R. L. Durcholz, and R. P. Reed 23

Fracture Testing and Results for a Ti-6A1-4V Alloy at Liquid

Helium Temperature

C. W. Fowlkes and R. L. Tobler 25

Fatigue Crack Growth and J-Integral Fracture Parameters

of Ti-6A1-4V at Ambient and Cryogenic Temperatures

R. L. Tobler 56

Fatigue Crack Growth Rates of Structural Alloys at Four

Kelvin

R. L. Tobler and R. P. Reed 87

The Fracture Toughness and Fatigue Crack Growth Rate of an Fe-Ni-Cr Superalloy at 298, 76 and 4 K

R. P. Reed, R. L. Tobler, and R. P. Mikesell 105

ADVANCED COMPOSITES

R. E. Schramm and M. B. Kasen 123

ELASTIC PROPERTIES OF ENGINEERING MATERIALS AT CRYOGENIC TEMPERATURES

H. M. Ledbetter and W. F. Weston 149

Low-Temperature Elastic Constants of a Superconducting

Coil Composite

W. F. Weston 151

Iron-Molybdenum Alloy

W. F. Weston and H. M. Ledbetter 184

V
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 with 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
NBSIR

Semi-Annual Report on l-Iaterials Research in Support of

Superconducting Machinery

Thermal Conductivity

J. G. Hust

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1975
- ^

Summary; Thermal Conductivity

Thermal conductivity, electrical resistivity, thermopower, and Lorenz ratio data are reported for Inconel X-750 STDA. These data are compared to the previously reported data

for Inconel X-750 ST. Data are presented In tabular and graphical form.

Contents; Thermal Conductivity

Page

1. Introduction . 3

2. Apparatus 3

3. Specimen Characterization 4

4. Results and Discussion 4

5. Acknowledgements 4

6. References 4

List of Figures 5

List of Tables , 5

2
THEBMAL CONDUCTIVITY

J. G. Hust

1. Introduction

Optimum design of superconducting nachinerv 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. It also depends on the micro structure 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) . Thermal conductivity data for particular components are required to limit

heat losses and thermal stresses in machines. rtith 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 nimber 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 is a multi-property apparatus used to simultaneously measure thermal conductivity, electrical resistivity, and thermopower at temperatures between 4 and 300 K. It is based on the longitudinal heat flow method. This apparatus

will be used to measure materials that have not been sufficiently measured and characterized

previously and for accurate temperature dependence determinations.

(b) A fixed point apparatus, capable of measuring only 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 this apparatus is about 10%,

depending mainly on the conductivity of the specimen.

(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

The variable-temperature apparatus was used for the measurements reported for Inconel*

X-750 STDA. The specimen is a rod 23 cm long, with a diameter up to 3 cm depending on its

conductivity. The top of the specimen is thermally connected to a temperature-controlled

floating sink, and the gradient heater is connected at the bottom of the specimen. The

specimen is surrounded with insulation and a temperature-controlled concentric shield.

The longitudinal temperature distribution of the shield is adjusted to match that of the

specimen. Eight equally spaced thermocouples are attached to the specimen to determine

its longitudinal temperature distribution. These thermocouples are calibrated in-place

* Inconel is a tradename of International Nickel Corporation.

3
using accurately calibrated platinum and germanium resistance thermometers. Further

details of this apparatus are documented in an unpublished NBS report available from Hust.

A schematic diagram of the cryostat is shown in a previous semi-annual report to ARPA f3].

3. Specimen Characterization

The material investigated is Inconel X-750 STDA. This specimen is a heat treatment

variation from the previously measured X-750 ST reported in the last ARPA report [4]. The

STDA heat treatment is: ST (1800°F for one hour - air cooled) + ISSCF for eight hours - furnace cooled to IISCF - hold for eight hours - air cooled. The Rockwell hardness and

grain size of the STDA form are C-36 and 0.12 mm. This specimen was measured to determine

the effect of heat treatments on the X-750 alloy. Very little is known about these effects

on such alloys and the latest data will be helpful in predicting the effect on similar

alloys.

This material was measured in the form of a 11.3 mm diameter machined rod, 23 cm long.

The heat treatment was performed prior to the machining.

4. Results and Discussion

Measurements were performed using an ice bath, a liquid nitrogen bath, and a liquid

helium bath. Usually a large number of runs (20-30) are taken to precisely define the

thermal conductivity, electrical resistivity, and thermopower curves at temperatures from

4 to 300 K. However, in this case, because of the similarity of this specimen to the X-750

ST specimen, only a few runs (6) were performed. These runs were set up to match the

conditions of the runs performed on the ST specimen to expedite data intercomparisons.

The resultant experimental data were compared to the X-750 ST data and accurate property

differences were calculated. From these differences and the results reported for X-750 ST we obtained data for X-750 STDA. These results are listed in Table 1 and illustrated in

Figures 1, 2, 3, and 4. The data for X-750 ST are also shown in the figures for convenient

comparison.

It is noted that thermal conductivity is affected very little by the STDA heat treatment. The relative effect is larger at low temperatures. Electrical resistivity has

changed by about 4% over the entire temperature range. However, it is noted that while

thermal conductivity decreased, electrical conductivity (reciprocal of electrical resistivity) increased. This is contrary to expectations but has been observed earlier on a similar alloy, Inconel 718. Because of this contradictory behavior, Lorenz ratio values

are not useful for prediction of heat treatment effects in these alloys. Figure 3 shows

that Lorenz ratio differences are larger than either thermal conductivity or electrical

resistivity differences. For thermal conductivity predictions based on Lorenz ratio to be

accurate, the opposite must be true.

5. Acknowledgements

I express appreciation to Joe Wells of Westinghouse Research Laboratories, Pittsburgh,

Pennsylvania for supplying the Inconel X-750 STDA material.

6. 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

(Aug. 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, (Feb. 1973) 133 pp.

3. Hust, J. G. and Giarratano, P. J., Semi-annual report on materials research in support

of superconducting machinery, pp. 29-43, Unpublished NBS report.

4. Hust, J. G. and Giarratano, P. J., Semi-annual report on materials research in support of

superconducting machinery, pp. 1-35, Unpublished NBS report.

4
List of Figures

Figure Page

1. Thermal conductivity of Inconel X-750 STDA compared

to previously reported data for X-750 6

2. Electrical resistivity of Inconel X-750 STDA compared

to previously reported data for X-750 ST 7

3. Lorenz ratio of Inconel X-750 STDA compared to previously reported data for X-750 ST 8

4. Thermopower of Inconel X-750 STDA compared to previously reported data for X-750 ST 9

List of Tables

Table Page

1. Thermal and electrical properties of Inconel X-750

STDA as calculated by comparing six experimental runs

to similar runs for X-750 ST 10

5
6
1.30 1

\

\ \

I \ i 1

1

\ r

FIGURE 2. Electrical resistivity of Inconel X-750 STDA compared to

previously reported data for X-750 ST^

7
30

25

10

ST

7 f

20

-/

_/

/

15

\

STDA

V

V

50 100 150

TEMPERATURE, K

200 250 300

FIGURE 3. Lorenz ratio of Inconel X-750 STDA compared to previously

reported data for X-750 ST.

8
9
Table 1. - Thermal and electrical properties of Inconel X-750 STDA as calculated by comparinK six experimental runs to similar

runs for X-750 ST.

Temperature A P L X 10^ S

(K) Wm'-'-K"-'- n^^ V^/K^ yv/K

6 0.846 1175 16.57 .57

7 1.03 1175 17.29 .69

8 1.22 1174 17.90 .77

9 1.42 1174 18.52 .84

10 1.61 1174 18.90 .91

12 2.03 1173 19.84 1.06

1^ 2.43 1173 20.36 1.19

16 2.85 1172 20.88 1.32

18 3.22 1172 20.96 1.44

20 3.62 1171 21.20 1.52

25 4.48 1171 20.98 1.73

30 5.24 1171 20.45 1.94

35 5.92 1171 19.80 2.17

40 6.52 1171 19.09 2.40

45 7.05 1172 18.36 2.64

50 7.51 1173 17.62 2.86

60 8.18 1176 16.03 3.34

70 8.66 1179 14.58 3.76

80 8.93 1182 13.19 4.17

90 9.12 1185 11.73 4.58

100 9.27 1188 11.01 4.93

120 9.50 1192 9.44 5.64

140 9.71 1196 8.30 6.23

160 9.92 1201 7.45 6.79

180 10.1 1205 6.76 7.30

200 10.4 1209 6.29 7.71

220 10.6 1214 5.85 8.12

240 11.2 1223 5.27 8.78

280 11.5 1227 5.04 9.09

300 11.8 1232 4.84 9.39

10
NBSIR

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH IN SUPPORT OF

SUPERCONDUCTING MACHINERY

MAGNETOTHERMAL CONDUCTIVITY

L. L. Sparks

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

March 1975
Summary: Magnetothermal Conductivity

The effect of a longitudinal magnetic field on the thermal conductivity of Inconel 718,

AISI 310, and high purity copper (RRR = 1520) are presented. The results Indicate that the

relative change In thermal resistivity (AW/W^) of Inconel 718 Is 0.08 at 5 K and 0.03 at

19 K when an 80 kOe magnetic field Is applied. The corresponding values for AISI 310

stainless steel are 0.28 at 5 K and 0.10 at 19 K. The effect of the magnetic field on the

high purity copper specimen Is much larger since Its thermal conductivity is nearly all

due to electrons. The relative change in thermal resistivity for the high purity copper

specimen is 3.4 at 5 K and 2.8 at 19 K.

Contents : Magnetothermal Conductivity

Page

13

1. Introduction

13

2. Procedures

13

2.1 Apparatus

2.2 Materials . 14

3. Results

14

4. Discussion

5. References

List of Figures 16

12
MAGNETOTHERMAL CONDUCTIVITY

L. L. Sparks

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

1. Introduction

The objective is 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 operating at cryogenic temperatures. The existing world's

literature on magnetothermal conductivity, A(H), is concerned almost exclusively with

scientific materials, e.g., very pure materials and single crystals. A complete bibliography of the subject was given by Sparks and Fickett [1].

The materials studied in this program are being used 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. The broad material categories of

interest include superconductor stabilizing materials such as copper and aluminum, and

structural materials such as nickel alloys, stainless steels, and metallic composites.

2. Procedures

2.1 Apparatus

The experimental determination of A(H) of metals in high magnetic fields is complicated

by the requirement that the specimen be contained in a region of homogeneous field. For

magnets of reasonable size, this restriction necessitates small specimen lengths and

resultant small temperature differences along the specimens. Our X(H) probe is designed

to be used in a superconducting solenoid with a 3.8 cm bore and a 2.5 cm homogeneous (1%)

field sphere. Our specimen length is therefore limited to approximately 2.5 cm.

The principle components of the MH) system are shown in figure 1. A specimen is

shown with its axis mounted parallel to the magnetic field. This configuration is used to determine the longitudinal X(H) . Provision for making transverse A(H) measurements (heat

flow perpendicular to the direction of the field) have been included in the system design.

The basic operation of the system involves balancing electrical power supplied to three heaters with the heat leak to the liquid helium bath via the THERMAL LINKS (capitalized words refer to figure 1) . The electrical heaters are wound one each on the

TEMPERATURE CONTROLLED HEAT SINK (TCHS) , the SPECIMEN, and the TEMPERING POST. The power

supplied to the TCHS determines the approximate temperature of the specimen; the SPECIMEN

HEATER is used to establish a temperature gradient along the specimen; and, the TEMPERING

POST HEATER is used to eliminate any temperature difference between the specimen and the

tempering post. The TEMPERING POST and TCHS heaters are automatically controlled during

all tests, while a constant current is supplied to the SPECIMEN HEATER.

The thermometers used in the probe are three 1/8 watt, 100 ohm Allen Bradley^ carbon

resistors (CRT's) and a single calibrated germanium resistor (GRT) . The CRT's are located,

one each, in the TCHS and the two THERMOMETER BLOCKS, which are clamped to the specimen.

The GRT is located in the TCHS and is used for zero-magnetic-field calibration of the CRT

resistors. The effect of the magnetic field on the resistance of the CRT's is taken to be

that published by Neuringer and Shapira [2]. Resistance measurements on the two specimen

CRT's are made using a lock-in amplifier as both detector and power supply for an AC bridge.

Both absolute and difference resistance measurements are possible using this system.

The thermal conductivity of a specimen is computed from the specimen geometry (Area/

length), the specimen heater power (Q) , and the measured temperature difference along the

Trade name of Allen Bradley Co. 13
specimen (AT) . The relationship of X to these parameters Is given by

A series of measurements of AT and Q at various fields (0 _< H £ 80 kOe) and temperatures

(4 < T < 20 K) result In the data presented in this report.

2.2 Materials

A total of four materials have been tested—Inconel 718^, OFHC' copper, AISI 310

stainless steel, and a high purity copper referred to as NBS-B stock 7. The Inconel 718 was

in the age-hardened condition with a Rockwell hardness of C39 and an average grain diameter

of 0.06 mm. The composition in weight percent for this material is: Nl = 54.57, Cr = 18.06,

Fe = 17.08, Nb + Ta = 5.12, Mo = 3.18, Ti = 0.85, Al = 0.44, Mn = 0.29, Si » 0.24, Cu, C,

and S < 0.1%. The residual resistance ratio (RRR = R^-j^^^e^^ °^ Inconel 718 specimen

is 1.06. The AISI 310 specimen was measured in the cold worked condition; its Rockwell

hardness was B48 and its RRR = 1.27. Chemical analysis and grain size determination of

the AISI 310 specimen are being done. The high purity copper, NBS-B stock 7, was vacuum

annealed at 850''G for one hour. The electrical resistivity of this copper specimen was too low to be measured in the A(H) system; however, extensive work on the electrical resistivity

of NBS-B stock 7 copper by Fickett [3] indicates that RRR = 1520 for our specimen. The

ratio for our particular specimen will be determined shortly.

3. Results

A large magnetic field effect on the thermal conductivity of Inconel 718 was reported

in the previous ARPA semi-annual report [4]. Further analysis shows that the field was

exaggerated. The re-evaluated data are given in figure 2. Data are shown only for 0 and

80 kOe fields; curves for H = 10, 20, and 40 kOe fall between the two curves shown. The

estimated 10% uncertainty of the data would indicate that the data at 0 and 80 kOe are indistinguishable. However, as the curves drawn through the data points show, the precision of the measurements is sufficient to indicate a definite trend toward lower thermal

conductivities at 80 kOe. The zero field data for Inconel 718 is within 10% of the zero field data by Hust, et al. [5] for a similar specimen.

Preliminary data for AISI 310 stainless steel are shown in figure 3. Again, only the

0 and 80 kOe curves are shown.

Preliminary data for NBS-B stock 7 copper are shown in figure 4. The experimental

points at H = 0 represent averages, while the experimental points for H ii^ 0 are single

data points. The extremely high conductivity at zero field is near the limit of what can be measured in the present system. Repeat runs and data averaging were used to increase

the reliability of the zero field results. The origin of the curve representing H = 0

data will be discussed later in this paper.

4 . Discussion

Our data indicate that an 80 kOe magnetic field reduces the thermal conductivity of our Inconel 718 specimen by 8% at 5.5 K and by 3% at 19.5 K. An estimate of the electronic

contribution to the thermal conductivity of this material can be made using Lorenz ratio

data (L = pA/T) given by Hust, et al. [5]. This estimate indicates that the electrons carry

roughly 25% of the heat current at 5 K and 18% at 19 K. The Lorenz numbers for stainless

steels are typically lower than those for the NlCrFe alloys by approximately a factor of 2. This would suggest a larger electronic component and consequently a larger field effect. The

effect of a 80 kOe field on the AISI 310 stainless steel specimen is to reduce the con- ductivity by 20% at 5.25 K and 11% at 19.5 K. These percentages are determined at the

extremes of temperature as shown in figure 3. At intermediate temperatures the conductivity at 80 kOe appears to be higher than at zero field. This effect is probably not real,

but rather the conductivity should parallel the zero field data as was the case for Inconel

718. Further tests will be done on AISI 310 if a similar anomaly appears in the results for

AISI 304.

Trade name of International Nickel Corp.

Trade name of AMAX Corp.

14
I

The very high thermal conductivity of the NBS-B stock 7 copper specimen causes

i experimental difficulties that result in lower accuracy in the zero field runs than was

! the case for the lower conductivity materials. The solid curve shown in figure 4 for

H = 0 was derived using the relationship

1/A = W = AT^ + B/T

I and represents the data within the experimental accuracy. When put in the form

I WT = AT"^^"*" + B, B is the intercept and A is the slope of a WT vs T^"*""*" plot. Further

j details of this procedure, including determination of the constant n, are given by Powell,

—8

et al. [6]. The constants derived from the current zero field data are A = 3.02 x 10 ,

i n = 2.55, and B = 4.7 x 10 ^ with the units of W being mK/W. The effect of a magnetic

! field is included in figure 4. The anomalous decrease shown in this figure for X at

20 kOe and high temperatures is probably not real; the single data point at 21 K appears

to be bad, but no reason can be found to discard it. Figure 5 presents the relative

change in thermal resistivity (AW/Wo = A - X /\ ) as a function of magnetic field.

rl— U H n

: The high temperature, 20 kOe data have been ignored in this figure due to its anomalously

low value. This is unfortunate since the apparent knee in the AW/Wo data shown in figure 5

I occurs in the 20 kOe field range. Although the exact placement and shape of the knee is

somewhat questionable there, there is no doubt a rapid decrease in slope of AW/Wo in the

10 to 40 kOe range. A similar plot of AW/Wo for the previously reported OFHC copper is

shown in figure 6; there is no rapid change in the slope of AW/Wo for this material. A

magnetic field should affect the electronic conductivity strongly if the mean free path

j is long, e.g., lux >^ 1 where oj is the angular frequency and T is the relaxation time.

I oj is proportional to the magnetic field as indicated by the cyclotron relationship

j u) = eH/mc. Further, T (high purity copper) > T (low purity copper), so that lot becomes

large for the high purity stock 7 copper before it does for the OFHC specimen; consequently,

the effect of a magnetic field should be seen at the lower fields for the stock 7 copper

than for the OFHC material. A comparison of the data in figures 5 and 6 show this to

be the case.

In conclusion, the effect of a magnetic field on structural alloys such as the

Inconel 718 and stainless steel reported here is relatively small. The results are not Inconsistent with estimates of the possible field effects using Lorenz ratio data. Good

conductors such as the two copper specimens show greater field affects which are expected

due to the large electronic component of the thermal conductivity.

The effort to detect and eliminate possible sources of error such as spurious

control voltages, inadequate thermal contacts, and unwanted heat flow paths is continuing

and will hopefully result in increased precision and reliability. Materials to be

tested in the remainder of the year include AISI 304 stainless steel, an undesignated

aluminum, and Ti-6A^-4V.

5. References

1. Sparks, L. L. and Fickett, F. R., Materials research in support of superconducting

machinery, National Bureau of Standards, Boulder, Colorado, Cryogenics Division,

March, 1974 NBSIR-74-359 , AD-780 596/3^.

2. Neuringer, L. J. and Shapira, Y., Low temperature thermometry in high magnetic

fields, I. Carbon resistors, RSI 40, No. 10, 1314 (Oct., 1969).

3. Fickett, F. R., A preliminary investigation of the behavior of high purity copper

in high magnetic fields. Annual report to INCRA, (August, 1973)

.

4. Sparks, L. L. and Fickett, F. R. , Materials research in support of superconducting

machinery. National Bureau of Standards, Boulder, Colorado, Cryogenics Division,

October, 1974, NBSIR-74-393

.

5. Hust, J. G., Weitzel, D. H., and Powell, R. L. , Thermal Conductivity, Electrical

Resistivity, and Thermopower of Aerospace Alloys from 4 to 300 K, J. Res. Nat.

Bur. Stand. (U.S.), 75A, No. 6, 269 (July-August, 1971).

15
6. Powell, R. L., Roder, H. M. , and Hall, W. J., Low-temperature Transport Properties of

Copper and Its Dilute Alloys: Pure Copper, Annealed and Cold-Drawn, Phys. Rev. 115 , No. 2, 314 (July 15, 1959).

List of Figures

Page

1. Magnetothernial conductivity probe and magnet 17

2. Thermal conductivity of Inconel 718 as a function of temperature for

H = 0 and 80 kOe 18

3. Thermal conductivity of AISI 310 stainless steel as a function of

temperature for H = 0 and 80 kOe 19

4. Thermal conductivity of high purity copper (RRR = 1520) as a function of temperature for H = 0, 10, 20, 40, and 80 kOe . 20

5. Relative change in thermal resistance of high purity copper as a function

of magnetic field 21

6. Relative change in thermal resistance of oxygen-free copper ae a function

of magnetic field 22

16
Sipport Tikes Li^iil Fill iMbes

Therimeter Biick (carhij

SpeciieR (iiRsitMiinal)

(trMsverse net skiwR

TherniMeter Blfck

SpeciMeR Heater

Gas Aisorbent

Vaciii aii

Electrical Leads

Li^id Heiiii Tenperatire Cap

Tkerial Liiks

Tenperatire CoRtrollei Heat Sink

TeRperlRf Post

Speciaei

CkaMker (Ci}

ii

TenperiRi Post Heater

100 kOe Siperciiiictiii Siieiiii HoMiceReiis Field ii 2.54 en

iiaieter Spkere

Figure 1. Magnetothe rmal conductivity probe and magnet.

17

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•u r^

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(U

(1) H 4J

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W/W 'AlIAIlOnaNOD "i\/Wy3Hi

19

I
cn o ^ N o

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T3

II

C

r> o

<r

d) o aoo o

>^u

•HO ^3 II &, u

•H o

j=

4-1 0) O S-i 3

>^ •u •u •H> OJ •H

•UO

4-1 ^3C M-4 O O a

iH o

CO •H

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LDCO >|iu/M 'AlIAIiOnQNOD 1\/Wb3Hl

20
4.0

T

stock 7 Copper

0 10 20 30 40 50 60 70 80

H, kOe

Figure 5. Relative change in thermal resistance of high purity copper as a function

of magnetic field.

21
20 40 60 80 100

H (kOe)

Figure 6. Relative change in thermal resistance of oxygen-free copper as a function

of magnetic field.

22
NBSIR

SEKI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

FATIGUE ANT) FRACTLTIE TOUGHNESS

TESTING AT CRYOGENIC TEMPERATITIES

R. L. Tobler, R. P. Mikesell, R. L. Durcholz, and R. P. Reed

Cryogsnics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1974
SUMMARY

The report includes four manuscripts. Fracture mechanics design data are presented

for a variety of cryogenic structural alloys having potential applications at 4 K. The

plane strain fracture toughness parameters, K and J-j„, and fatigue crack growth rates,

da/dN, were measured at temperatures from 295 to 4 K using compact specimens and state-ofthe-art test procedures. The results are summarized as follows:

1) Fracture toughness and fatigue crack growth tests lasting several hours were performed using about ten liters of helium per test and specially designed

cryostats.

2) It was observed for the first time that the ELI (extra-low-interstitial)

grade of Ti-6A1-4V exhibits a ductile-to-brittle transition between 125 and

76 K. Despite the transition, the toughness of the ELI grade exceeds that

of the normal grade by a significant margin at all temperatures.

3) The fracture toughness of A 453, a precipitation-hardened austenitic stainless steel, decreased very slightly over the interval 295 to 4 K; its resistance

to fatigue crack propagation was improved at cryogenic temperatures.

4) Fatigue crack growth rate results for ten alloys indicate that stable

face-centered cubic (austenitic) alloys exhibit the best resistance to fatigue

crack propagation at 4 K.

24
FRACTURE TESTING AND RESULTS FOR A

T1-6A1-4V ALLOY AT LIQUID HELIUM TEMPERATUREt

C. W. Fowlkes* and R. L. Tobler

Cryogenics Division

National Bureau of Standards

Boulder, Colorado 80302

t Contribution of NBS, not subject to copyright.

* Present address: Fowlkes Engineering, 12450 W. 82nd Ave.,

Arvada, Colorado 80005

25
ABSTRACT

This paper discusses fracture toughness and fatigue crack growth testing at liquid

helium temperature, 4 K (-452 "F) . The design and performance of a fracture testing cryostat and associated instrumentation are described. Fracture toughness and fatigue crack

growth data for Ti-6A1-4V from room temperature to 4 K are presented.

Key words: Crack propagation; cryostats; fracture tests; low temperature

tests; mechanical tests; titanium alloys.

26
INTRODUCTION

The phenomenon of superconductivity is currently being applied in the design and

construction of motors and generators, allowing a reduction in physical size of machinery

for a given power output. Superconducting components are cooled with liquid helium, and,

since some structural parts must operate at 4 K, a need for mechanical property data at this temperature has developed. Some existing data for structural alloys at 4 K describe

fatigue and tensile properties [1-3]

.

Conventional tensile data do not provide an adequate basis for predicting the load

carrying capability of structures where stresses are concentrated locally at fatigue

cracks or other common flaws. In such cases, a fracture mechanics analysis may be the

best method for determining the safe-operating lifetime of the structure. Fracture

mechanics techniques utilize the concept of the stress intensity factor to characterize

crack-tip stress fields, and this concept fo rms the basis of the ASTM Standard Method of Test for Plane Strain Fracture Toughness of Metallic Materials (ASTM E-399-74) [4]. The

essential design parameters are the plane strain fracture toughness (K^p) of a material

and the fatigue crack growth rate (da/dn). A knowledge of these parameters for materials

at 4 K is relevant to the optim\im design of superconducting machinery since:

1) The investment in machinery is large, and fractures would be costly.

2) At low temperatures the yield strength of materials is increased and ductility

may be decreased, increasing the probability of brittle fracture.

3) The materials in motors and generators are subject to high cycle fatigue; flaws

in a structure, inherent or due to fabrication, may propagate to critical proportions

during long-term operating conditions.

Programs have been initiated at the National Bureau of Standards to collect the

needed fracture mechanics design data. The first step was to design test apparatus capable

of efficient operation at 4 K. Experience gained during this phase of research is included in this report, which discusses: the optimum design of mechanical testing cryostats, the features and performance of the fatigue and fracture cryostat currently in use

at NBS, and fracture data obtained for a Ti-6A1-4V alloy at 295, 77, and 4 K. CRYOSTAT DESIGN CONSIDERATIONS

Systems Analysis

The cost of mechanical testing at 4 K depends on the amount of liquid helium consumed

in cooling the specimen and cryostat. To insure a uniform temperature, the specimen must

be submerged in the liquid and additional helium must be added to allow for evaporation

during the test. The simple model of a fatigue and fracture testing cryostat shown in

Figure 1 can be used to outline the mechanical and thermal trade-offs involved in cryostat

design. The parameters of interest are the amount of heat to be removed during cool-down,

the steady state heat gain, the load capacity, and the stiffness of the frame.

The initial heat, Q ^ , , that must be removed from the dewar, the enclosed frame

cool-down

and the specimen can be approximated by:

Q , , = (m.c, + m c + 2L.A^p.c^) AT (1) cool-down dd ss ifff

where where m is mass, c is average specific heat, p is density, A is cross-sectional

area, AT = (T ,

, - T ), and the subscripts d, s, and f refer to the dewar, specimen, ambient test and frame respectively. The term is defined in Figure 1. The rate of heat gained by the cryostat during steady state operation can be separated

into heat conducted along the frame', heat leaked into the dewar, q^, and heat generated

during fatigue operation, q^ . . The total steady state rate of heat gain, q . ,

, . , ^fatigue ' ^ ^steady' can be approximated by:

^steady = ^^Vf ' ^ ""d ^ 'Ifatigue

where k^ is the thermal conductivity of the frame members, and is defined in Figure 1. Heat is generated during fatigue due to plastic deformations of the test specimen.

Cyclic operation will also stir and agitate the cryogenic fluid, increasing the heat

27
gained by the cryostat through dissipation and Increased convection. The last term In Eq.

(2), *lf3(.j^gyg» includes these sources of heat. Such heat gains are significant in actual

operation, tending to Increase with the frequency and displacement of the test program,

but for all practical applications they are independent of the cryostat design. For this

reason, ^If^^j^gug will not enter in the optimization equations.

The strength and compliance of the cryostat frame are related to the size of the

frame and therefore affect both cool-down and steady state heat gain. The load capacity,

^max'

°^ tension and compression members of the frame extending into the dewar will be

taken as:

P = a, (3) max ds f where a^^ is a design stress which can be represented as some fraction of the ultimate

tensile stress of the material. The compliance (reciprocal of stiffness) of the load

frame, C^, can be approximated by considering the deflections of both tension and compression members. Neglecting bending, the compliance is given by

L + L,

where is Young's modulus of the frame material. The compliance of the specimen is not

included in Eq. (4); the specimen design is independently fixed, and its compliance will

not affect the optimization of the cryostat.

The compliance of the cryostat is also important because it influences the performance of the fatigue actuator in the testing machine. The displacement-frequency behavior

of the actuator used in these experiments, shown in Fig. 2, indicates that the frequency

and hence the duration of a fatigue test is a strong function of actuator displacement.

Assume for example that the compliance of the system is such that the displacement at

the required fatigue load is 1.27 mm. The corresponding maximum frequency from Fig. 2 is

50 Hz. If the frame is reduced in cross section by a factor of two in an effort to reduce

heat gain and mass, the compliance will be doubled. Figure 2 shows that the maximum

frequency will be reduced to approximately 25 Hz. This lower frequency doubles the test

duration and the steady state heat gain.

Optimization

From the discussion above it can be seen that there is an interdependence among the

design objectives. According to systems analysis procedures, an optimimi design can be

achieved by finding values of the controllable variables which minimize some objective

function [5]. An objective function is a function that relates the design variables in a form such that their effects on optimization can be evaluated.

Case I. High-cycle fatigue cryostat

In a high-cycle fatigue cryostat we seek to minimize cool-down heat loss and steady

state heat gain and simultaneously to maximize the load capacity and stiffness. One

simple objective function which states this goal is:

min z = ^Qcool-down^ ^^steady^ ^^f^ Pmax

(5)

where min z indicates that the group of terms comprising the objective function is to be

minimized subject to other system constraints f5].

The dewar heat gain, the specimen design, the specimen compliance, and the fatigue

heat gain are Independently fixed. Removing these terms from Eqs. (1) and (2) and substituting Eqs. (1) through (4) into Eq. (5) and simplifying yields:

min z =

r \ ^f^'f^f M 2 M ^^e ^i^ ^i

28

(6)
where material properties are grouped separately from geometrical factors.

Clearly, the specific heat, density, and thermal conductivity of the frame should be

minimized whereas the modulus and design strength should be maximized. All of these terms

are linear in Eq. (6) . The temperature difference is important since it is squared, but

it cannot be changed. The total length of the frame (L + L.) is also limited by the

e 1 dimensions of the testing machine, but the internal length, L^, should be minimized and

the external length, L^, maximized. Note that the cross-sectional area of the frame

members does not appear in Eq. (6). In addition to this particular result, it is instructive to briefly consider the

outcome from Eq. (5) for three other cases. Case II. Low-cycle fatigue cryostat

If compliance is removed from Eq. (5) the result is:

mm z = Pf^f^f

^ds

f X (AT) 2)

(7)

showing that the ratio of internal to external lengths is to be minimized. The cross sectional area should also be minimized subject to other constraints, such as the load

capacity of the cryostat. This objective function applies to the design of tensile cryostats and some fatigue cryostats. The low compliance implied by this objective function

may affect some fracture measurements.

Case III. Creep Cryostat

If only the steady state heat gain and load capacity are considered, the objective

function becomes:

ds AT

/ L + L.

' e X

(8)

The only controllable variables are chermal conductivity and frame length. This objective

function would be used to design a cryostat for creep and sustained load crack growth

experiments

.

Case IV. Tensile Cryostat

If the cryostat is not intended for long-term static or fatigue tests, the steady

state heat gain and compliance terms can be removed from the objective function. The

result:

mxn z

'^ds

L.

X AT (9)

suggests the use of a high strength structural material having low density and specific

heat. The Internal length of the frame should be minimized, the cross-sectional area of

the frame members cancels, and there is only a linear dependence on temperature difference.

Cool-down Calculations

Unless the test duration exceeds several hours, the amount of heat removed from an efficient system in cooling from ambient temperature to liquid helium temperature is large

compared to the steady-state heat gain. Particular attention must therefore be given to the details of the cool-down procedures [6]

.

Pertinent data on liquid nitrogen and liquid helium are shown in Tables 1 and 2. Four facts bear directly on design: (a) liquid helium is expensive, (b) liquid nitrogen

is relatively cheap, (c) liquid helium has a relatively low heat of vaporization and (d)

helium gas has a relatively large enthalpy compared to the heat of vaporization. Clearly,

an optimum cool-down procedure should include precooling and cryostat with liquid nitrogen

and effective utilization of the enthalpy of the helium gas.

29
The most efficient use of the enthalpy of the helium gas occurs for an isothermal

cool-down where the vapor exhausted from the dewar is always at a temperature lower than

the current temperature of the cryostat by only an infinitesimal amount. Here the term

"cryostat" refers to the dewar and everything contained in it (the frame, specimen, grips,

etc.). Assuming that the cryostat has been precooled to 77 K using liquid nitrogen, the

subsequent cool-down to 4 K using evaporated helium will be considered.

Let an infinitesimal mass of liquid helium, dm^, be vaporized at one atmosphere and

then brought to a temperature T and an enthalpy H^. The heat required is approximately

dm^H^. If this heat is supplied by the cryostat of mass m^ initially at a temperature T +

dT, the enthalpy of the cryostat will decrease by dH^ during the dT temperature change.

The energy lost by the cryostat is m dH . The subscripts h and c refer to helium and

cryostat, respectively. ^

The equation expressing the heat balance for this ideal cool-down is:

dm^H^ = m^dH^ (10)

To simplify calculations the enthalpies in J/gm can be approximated by [7]:

« 1.8 X

10"^ (T)-^"^^ (11)

and [8]:

20.46 + 5.34 (T-4.2) (12)

where the temperatures are Kelvin.

Taking the mass of the cryostat described in a later section as 9.1 kg, substituting

Eqs. (11) and (12) into Eq. (10), and integrating the result yields:

T

• Am^ = 1.2 X

10"^ [0.34T^*^'^ + 0.187T-'-"^^ + ... (13)

where T^ and T^ are the initial and final temperatures of the cryostat and Am^ is the mass

of liquid helium in kg.

As calculated from Eq. (13), the liquid helium consumed in ideal cooling from various

temperatures to 4 K is shown in Figure 3. The minimum amount of liquid required for ideal

cooling from 77 K is about 1.25 liters. In contrast, 20 liters would be consumed if the

heat of vaporization alone were used for cool-down. Twenty liters represent the upper

limit for extreme inefficiency.

The cryostat can be precooled to about 63 K using liquid nitrogen at a reduced pressure.

Lowering the pressure from 1.0 to 0.18 atm reduces the equilibrium temperature to 63.14 K,

the freezing point of nitrogen [9]. Figure 3 indicates that precooling the cryostat to 63

K will reduce the liquid helium required for subsequent cool-down by half a liter. As

described later, this step can be incorporated in the cool-down procedures. Additional

data for cool-down calculations are given by Jacobs [10].

. .

, J FATIGUE AND FRACTURE CRYOSTAT

Description of Apparatus

The 100 kN capacity cryostat built for these tests, shown in Figures 4, 5, and 6,

tends to minimize the objective function of Eq. (6). The load frame consists of two tubular, composite compression members that are linked at the lower ends with a maraging

steel bridge. The lower sections of the compression members are AISI 304 having a wall

thickness of 3.18 mm; the upper sections are fiberglass reinforced plastic (FRP) having a wall thickness of 6.35 mm. The maraging steel grips conform to ASTM E-399-74 specifications.

The lower grip is pinned into the center of the bridge, while the upper grip is threaded

to a titanium alloy loading rod.

30
A double dewar arrangement is used for tests in liquid helium, but conventional glass

dewars were rejected because of fragility. Instead, an inner helium dewar was fabricated

from fiberglass reinforced plastic. A vacuum is maintained in the space between the walls

of this dewar by periodic mechanical pumping, and five layers of aluminized mylar line the vacuum space for added insulation. The foam insulated outer dewar for liquid nitrogen was

fabricated from fiberglass and epoxy; the flared shape minimizes nitrogen consumption and

facilitates assembly during testing.

Thin copper baffles may be attached along the frame with hose clamps. These baffles

were designed for a close fit with the inner dewar. Staggered openings form a labyrinth

for cold vapor introduced at the bottom of the dewar during helium transfer. Thus, the

baffles direct the vapor flow and also serve as radiation shields.

A vacuum jacketed helium fill tube and a plastic purge tube extend to the bottom of

the inner dewar. Other features include two vents, a carbon resistor liquid level indicator,

a gas cylinder and pressure gage connection, and an instrumentation lead-through. With an 0-ring placed under the cryostat lid and all vents closed, the helium dewar is sealed and

its internal pressure may be raised or lowered.

A conventional double-beam ASTM E-399-74 clip gage was used to measure deflections at

the specimen edge. Commercially available cryogenic strain gage films were bonded to the

gage beams using an epoxy for low temperature applications. The gage films were left

uncoated to reduce the probability of thermal cracking. The body of the clip gage was

enclosed in a protective aluminum cage and tetraf luoroethylene coated lead wires in a woven glass fiber sheath linked the gage to extefial instrumentation. With the clip gage

in liquid heliiim, a low excitation voltage (1.5 vdc) minimized the noise due to local

boiling at the films. Direct calibrations using a dial micrometer verified that the gage

satisfied ASTM E-399-74 linearity requirements and that there was only a small change in

sensitivity with temperature. This clip gage has operated for 10^ fatigue cycles at temperatures from 295 to 4 K, with about 10^ cycles at 4 K. Cryostat Operation and Performance

Liquid helium testing begins by filling both inner and outer dewars with liquid

nitrogen. After reaching equilibrium at 1 atm, the pressure on the inner dewar is reduced

to approximately 0.2 atm. On reaching equilibrium at this new pressure, the cryostat is

pressurized with helium gas to purge the liquid nitrogen. Liquid helium is then slowly

transferred into the dewar. When the required level has been reached, the transfer line

is disconnected and the test begins. The helium transfer takes about thirty minutes and

the entire cool-down procedure takes at least two hours.

An alternative procedure eliminates the use of baffles and the steps involving mechanical

pumping and purging. After precooling the cryostat to 77 K, the inner dewar of liquid

nitrogen can be removed, emptied, and replaced in less than thirty seconds. The outer

dewar is then assembled and helium transfer begins. This reduces considerably the time to accomplish cool-down, at the cost of less than two additional liters of liquid helium.

The volume of liquid required to submerge the specimen in this cryostat is about 4 liters but a reserve of up to 5 additional liters can be added for long-term tests. Assuming ideal cool-down, the lower bound of liquid helium consumption per test is approximately 5.25 liters. In practice, some liquid is used in cooling the transfer lines. The

actual liquid helium consumption per test for Ti-6A1-4V specimens varied between 7 and 11

liters, depending on the amount of reserve fluid added and the rate of helium transfer.

The steady state loss of liquid helium under static load is between 0.05 and 0.1

liter per hour. During the fatigue tests reported here, the loss increased about five

times due to dissipation in the specimen and agitation of the liquid as discussed earlier.

The cryostat accepts specimens of the compact geometry (described below) up to 3.81

3/2 cm-thick, developing a stress intensity factor of 110 MN/m on such a specimen at maximum

load. The ASTM E-399-74 specimen thickness requirement will be satisfied for materials

2 3/2 having a yield strength above 890 MN/m and a K^^ value less than 110 MN/m

The load-deflection behavior of the cryostat frame and load train, shown in Figure 7, was determined by replacing the specimen with a large rigid block. The frame was statically

loaded to 110 kN, and approximately 10^ fatigue cycles were applied at lower loads. The

31
main cantilever resonance of the frame is 17 Hz, but no difficulties are encountered in

practice if the operating frequency during fatigue tests is kept above 19 Hz or below 15

Hz. The entire apparatus, including the 100 kN servo-hydraulic test machine used in these

tests, is shown in Figure 8. In this photograph the helium dewar is in place and the

nitrogen dewar is lowered.

EXPERIMENTAL PROCEDURE

Material

The alloy Ti-6A1-4V was tested in this study. Stock was obtained in the form of a 2.54 cm X 6.40 cm cross-section bar which had been mill annealed at 977 K for two hours,

air-cooled, and descaled. The microstructure consisted of primary alpha and beta, having

a grain size of 0.006 mm. The mill analysis and room temperature mechanical properties of

the material are shown in Tables 3 and 4. Specimen

The crack growth and fracture tests were performed using 2.54 cm-thick compact specimens

that were proportioned in accordance with the ASTM E-399-74 method as shown in Figure 9. The notch was machined in the TL orientation [4], and deflections were measured between

attachable knife edges located at the specimen edge.

The compact specimen was chosen because it has the largest fracture toughness measurement capacity for its size of any of the common fracture specimens [11,12]. A relatively

small load applied to the compact specimen produces a large stress intensity factor. This

allows the mass of the grips, the cryostat frame, and the loading rods to be minimized

which significantly reduces the liquid helium consumption and cost per test. Relationships between load, crack length, stress intensity factor, dimensions, and

deflections for this specimen were given by Roberts [13] and are reproduced in Table 5. The stress intensity factor is given by [4]:

p 1/2 3/2 5/2

K

I = -^77 [29.6 (|) -185.5(f) + 655.7 (J)

BW^/^ WWW

7/2 9/2

-1017.0 ( J

) + 638.9 ( J

) ]

where P is the applied load and a, B, and W are defined in Figure 9. Test Procedures

The test procedure consisted of cooling the specimen and the cryostat. Initiating the

crack, propagating the crack at various ranges of stress intensity, and finally loading

the specimen to fracture. Tests were conducted in ambient air at room temperature, in

alcohol and dry ice at 195 K, in liquid nitrogen at 77 K, and in liquid helium at 4 K. The specimens were allowed at least 20 minutes to reach thermal equilibrium in the cryogenic fluids, and data were not recorded until the crack had advanced at least 1.27 mm

(0.05 in) from the machined notch.

The fatigue tests were performed in load control, using a sinusoidal load cycle. The

loads were measured and controlled during the tests to ± 1% and the ratio, R, of minimum

to maximum stress intensity (K . /K ) was maintained at 0.1 ± 0.05. The test frequency mm max

was 25 ± 5 Hz, except for a few high load tests at 10 Hz. Monitoring the crack length at cryogenic temperatures presents some problems since

the specimen cannot be visually observed without removing the dewars. In this study, the

specimen compliance method [14] in conjunction with fracture surface fatigue marking was successfully employed. The room temperature results showed that experimentally determined

crack length and compliance values for the Ti-6A1-4V specimens were in close agreement

with the theoretical values derived from the data in Table 5. Thus, crack length could be

inferred from compliance measurements made at intervals during the tests. The crack

growth rates were determined by differentiating graphs of crack length versus fatigue

cycles.

32
To translate the room temperature compliance curve to a curve for a different temperature, the changes in the clip gage calibration and in the Young's modulus of the specimen

material must be known. Both variables are linear factors in the compliance relationship.

Between 295 K and 77 K, the clip gage sensitivity changed by only 0.25% while Young's

modulus of Ti-6A1-4V increases by about 9% fl5]. The calibration curve at 77 K was constructed using these corrections and the values in Table 5. A simple alternative can be employed if there is a well defined crack front (such as

the final crack length) on the fracture surface of the specimen. The room temperature

compliance curve can be shifted along the displacement or compliance axis to make it

coincide with the measured value at the reference crack length. This compensates for the

changes in clip gage sensitivity and Young's modulus, as well as automatically including

an operational definition of crack length.

Using corrected compliance calibrations at each temperature, the predicted or inferred

values of crack length were always within ± 1.3% of the values actually measured from the

specimen fracture surfaces. This uncertainty is within the resolution for values of

compliance read from the X-Y recorder. For all these tests, the actual crack length was measured as an average of readings at three points equidistant across the specimen thickness.

Dynamic measurements using representative loads and frequencies showed that no overloads greater than 2% occurred when the machine was turned on or off. Also, when the

stress intensity factor was reduced to lower values the growth rate - aiiowtu to stabilize before any data were considered valid. The criterion used was Irwin's formula for

plastic zone radius, r^ [16]:

""p " ^

(15)

2TTay where o is the yield strength of the specimen material. When the stress intensity factor

was reduced during a test, subsequent crack growth data were ignored until the crack had

grown an increment equal to or greater than the value of r from Eq. (15) . The effects of

load changes were thus excluded from the test results fl7]?

The fracture toughness tests were performed in stroke control subsequent to precracking at the same temperature. The data interpretation followed the standard ASTM E2 399-74 method, and the thickness requirement that B >^ 2.5 ) was amply satisfied by

the 2.54 cm-thick specimens. ^

RESULTS

Crack growth rates

da Crack growth rates, — , are often described by equations of the form:

§=C(AKj)" (16)

where a is crack length, N is the number of fatigue cycles, AK^ is the range of stress

intensity factor (K - K . ), and C and n are empirical constants. As discussed by Paris

max min

and Erdogan fl8], this equation applies to a wide range of data if the stress ratio, R, is

non-negative and relatively constant. Accordingly, log-log plots of da/dN versus AK^

should reveal linear trends, and are appropriate for illustrating the present results.

The room temperature crack growth results are shown in Figure 10 and the results at

77 K and 4 K are shown together in Figure 11. Superimposed on these curves is a shaded

band representing data in the Damage Tolerant Design Handbook [19] and elsewhere [20].

The average values of K shown in these graphs indicate the upper limit of slow growth.

As shown in Figure 10, the present room temperature data fall wichin the range of

currently accepted handbook data. The results at liquid nitrogen and helium temperatures

show that there is not a large change in the crack growth rates at these low temperatures.

33
The 77 K and 4 K data are plotted on the same graph since any variation due to temperature

is of the same magnitude as variations between specimens. In relation to the apparent

temperature Independence of these growth rates, it is significant to note that Wei and

Ritter found the growth rates of a similar Ti-6A1-4V alloy to be temperature independent

over the interval 295 K to 563 K [21].

3/2 The crack growth curves show an increased slope at AK less than about 16.5 MN/m

If this trend is extrapolated another decade in crack growth rate, the intercept of stress

3/2 intensity is about 8.8 MN/m . This value is termed the threshold value of stress intensity, the point below which crack growth rates become diminishingly small. Room temperature measurements [20] report threshold values for a similar Ti-6A1-4V alloy to be

3/2 about 6.6 to 8.8 MN/m . This result compares well with an extrapolation of the present

data.

Crack growth tests of two specimens immersed in a slush mixture of dry ice and alcohol

at 195 K could not be interpreted because the compliance curves were non-linear. Moreover, the crack fronts were irregular, invalidating fracture toughness tests at this

temperature. The dry ice and alcohol environment apparently caused these anomalous results.

Fracture toughness

A typical fracture test record at liquid helium temperature is shown in Figure 12,

test records at 77 K were similar. A very slight departure from linearity during the last

5% of load was the only sign of slow crack growth at low temperatures. At room temperature, a more noticeable "pop-in" (increment of unstable crack extension) preceded fracture

by a few seconds. The room temperature records resembled the Type III record described in

ASTM E-399-74.

The surface appearance of specimens fractured at 295 K and 4 K are shown in Figure

13. The fracture surfaces were predominantly flat, with a gradual reduction in the extent

of shear lips at lower temperatures. The room temperature specimens displayed 2% oblique

fracture, while liquid helium test specimens displayed less than 1%. The flat fracture

surfaces were relatively rough at the higher temperatures, becoming smoother as temperature

was reduced.

The K data are shown in Figure 14 and Table 6. Between 295 and 4 K, there is a

XL* uniform reduction in fracture toughness amounting to approximately 19%. However, the

difference in toughness between 77 and 4 K is negligable for this material.

Also shown in Figure 14 are the results reported by Vishnevsky and Steigerwald [22].

They obtained valid K^^ data from bend specimens at temperatures as low as 77 K. Their

alloy was beta processed Ti-6A1-4V, solution treated at 1227 K (1750°F) for one hour and

aged for two hours at 811 K (1000°F) . Comparing the valid results at 295 and 77 K, the

present data are in excellent agreement with Vishnevsky and Steigerwald ' s data.

There are other cryogenic fracture data for Ti-6A1-4V alloys [23-28], but the variety

of specimen designs and sizes as well as the material condition makes direct comparison

difficult. Some of these data are for thin sheet specimens that do not satisfy the thickness requirement for linear-elastic plane strain, while other results pertain to alloys

having extra-low-interstitial impurity contents. The data in these references are all

higher than the K values shown in Figure 14.

CONCLUSIONS

(1) Fracture toughness and fatigue crack growth tests were performed at 4 K using

approximately 10 liters of helium for each test. Stress intensity factors up to 110

3/2 1/2 MN/m (100.2 ksi • in ) can be produced with the cryostat described, and fatigue tests

spanning several hours are accomplished without refilling.

(2) The conventional clip gage instrumentation can be used for fracture and fatigue

testing in liquid helium if cryogenic strain gages and wiring procedures are used.

(3) The crack length can be inferred to within ± 1% using the compliance method.

Changes in the compliance calibration with temperature can be compensated by shifting the

theoretical calibration curve by an amount determined during the test itself.

34
(4) The crack growth rates of T1-6A1-4V at 77 K and 4 K showed no significant

departure from room temperature results.

3/2

(5) The fracture toughness of Ti-6A1-4V decreased from 47.4 MN/m (43.2 ksi

1/2 3/2 1/2 •in ) at room temperature to 38.5 MN/m (35.1 ksi "in ) at liquid helium temperature. The change in fracture toughness with temperature was monotonic and no anomalies

were observed at 4 K. ACKNOWLEDGMENTS

This work was sponsored by AKPA in cooperation with the Naval Ship Research and

Development Center. The cooperation of Dr. H. V. Vanderveldt of NSRDC is acknowledged.

The authors thank Ralph Trapani for assisting in the experiments and data reduction. The

helium dewar was fabricated by George Wallace.

35
REFERENCES

[1] J. G. Kaufman and E. T. Wanderer, Tensile properties and notch

toughness of some 7XXX alloys at -452 °F, Advances In Cryogenic

Engineering, Vol 16, Ed. K. D. Timmerhaus, 27-36, Plenum Press,

(1970).

[2] A. J. Nachtigall, Strain-cycling fatigue behavior of ten structural

metals tested in liquid helium (4 K) , in liquid nitrogen (78 K)

and in ambient air (300 K) , NASA TN D-7532, National Aeronautics

and Space Administration, (1974).

[3] F. R. Schwartzberg, S. H. Osgood, R. D. Keys, and T. F. Kiefer,

Cryogenic Materials Data Handbook, AFML-TDR-64-280, Martin Marietta

Co., AD 609562, (1964).

[4] Standard method of test for plane-strain fracture toughness of

metallic materials, E 399-74, Annual Book of ASTM Standards, Part

10, 432-451, Amer. Soc. Test. Mater., (1974).

[5] Tung Au and T. E. Stelson, Introduction to Systems Engineering,

Deterministic Models, Addison-Wesley Publishing Co., (1969).

[6] D. N. Lyon, D. B. McWhan, and A. L. Stevens, Cryostat for studies

at 100 kilobars at liquid helium temperatures. Rev. Sci. Instrum.

,

Vol 38, No. 9, 1234-1240, (1967).

[7] V. J. Johnson, ed., A compendium of the properties of materials at

low temperature, (Phase 1) Part II, WADD Tech. Report 60-56, (1960).

[8] R. D. McCarty, Thermodynamic properties of helium 4 from 2 to 1500 K

at pressures to 10 Pa, Jnl. Phys. Chem. Ref. Data, Vol 2, No. 4, (1973).

[9] R. T. Jacobson, R. B. Stewart, R. D. McCarty, and H.J.M. Hanley,

Thermophysical properties of nitrogen from the fusion line to 3500 R

(1944 K) for pressures to 150,000 Psia (10342 x 10^ N/m^) , NBS Tech.

Note. 648, (1973).

[10] R. B. Jacobs, Liquid requirements for the cool-down of cryogenic

equipment. Paper J-6 in Advances in Cryogenic Engineering, Vol 8,

Ed. K. D. Timmerhaus 529-535, Plenum Press, (1963).

fll] J. E. Srawley and W. F. Brown, Jr., Plane Strain Crack Toughness

Testing of High Strength Metallic Materials, ASTM STP 410, Amer.

Soc. Test. Mater., (1969).

[12] J. G. Kaufman, Progress in fracture testing of metallic materials.

Review of Developments in Plain Strain Fracture Toughness Testing,

ASTM STP 463, 3-21, Amer. Soc. Test. Mater., (1970).

[13] E. J. Roberts Jr., Elastic crack-edge displacements for the compact

tension specimen. Materials Research and Standards, MTRSA, Vol 9, No. 2, 27, (1969).

[14] W. F. Brown Jr. and J. E. Srawley, Commentary on present practice.

Review of Developments in Plane Strain Fracture Toughness Testing,

ASTM STP 463, 216-248, Amer. Soc. Test. Mater., (1970).

[15] E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Elastic properties

of two titanium alloys at low temperatures. Cryogenics, Vol 14,

246-249, (1974).
[16] G. R. Irwin, Fracture, Handbuch der Physik, Vol 6, 551-590,

Springer-Verlag, (1958)

.

[17] E. F. J. Von Euw, R. W. Hertzberg, and R. Roberts, Delay effects in

fatigue crack propagation, in Stress Analysis and Growth of Cracks,

ASTM STP 513, 230-259, Amer. Soc. Test. Mater., (1972).

[18] P. C. Paris and F. Erdogan, A critical analysis of crack propagation

laws, Jnl. Basic Eng. Trans., ASME, Series D, Vol 85, No. 4, 528-534,

(1963).

[19] Damage Tolerant Design Handbook - A Compilation of Fracture and

Crack-Growth Data for High Strength Alloys, Metals and Ceramics

Information Center, Battelle Memorial Institute, Columbus, Ohio, (1972).

[20] R. J. Bucci, P. C. Paris, R. W. Hertzberg, R. A. Schmidt, and A. F. Anderson, Fatigue threshold crack propagation in air and dry argon

for a Ti-6A1-4V alloy, in Stress Analysis and Growth of Cracks,

ASTM STP 513, 125-140, Amer, Soc. Test. Mater., (1972).

[21] R. P. Wei and D. L. Ritter, The influence of temperature on fatiguecrack growth in a mill annealed Ti-6A1-4V alloy, NASA-CR-127042,

Lehigh Univ. , (1972)

.

[22] C. Vishnevsky and E. A. Steigerwald, Fracture toughness of some cryogenic materials at room and subzero temperatures. Fracture Toughness

Testing at Cryogenic Temperatures, ASTM STP 496, 3-26, Amer. Soc. Test. Mater. (1970)

.

[23] W. E. Witzell, Fracture data for materials at cryogenic temperatures.

Tech. Report, AFML-TR-67-257 , General Dynamics Convair, AD 825264,

(1967) .

[24] C. F. Tiffany and P. M. Lorenz, An investigation of low cycle fatigue

failure using applied fracture mechanics, Tech. Doc. Report

ML-TDR-64-53, Boeing Co., (1964).

[25] L. R. Hall, Plane-strain cyclic flaw growth in 2014-T62 aluminum

and 6Al-4V(Eli) titanium, N69-20265, NASA-CR-72396, Boeing Co.,

(1968) .

[26] E. T. Wessel, W. G. Clark, and W. K. Wilson, Engineering methods

for the design and selection of materials against fracture, AD 801500,

Westinghouse Research Labs., (1966).

[27] W. D. Bixler, Comparison of flaw growth characteristics under cryogenic

proof and ambient test conditions for apollo titanium pressure vessels,

N70-18309, Boeing Co., (1970).

[28] F. R, Schwartzberg, A review of cryogenic fracture toughness behavior,

paper G-1 in Advances in Cryogenic Engineering, Vol 12, ed. K. D. Timmerhaus 453-472, Plenum Press (1967).

37
m

•O

•-Ia

^.uo

boouu

^1oaP

.a

(i H

a*

•nC

4) -ao• iH

•IH

1^O ^

•S v; o COh00o

as

73a

I—I

00 ifi O rg

00 ^ O fVJ

rf in

tfl

O

in

C

0)00ou

Ba

I—I

<0 X

i-oo

4->

>)

s->

CO

C_)

00I I s

13Ot

r-H

g

00s

00

inuo>a S ^ 00 oo

CO

38
Table 3. Chemical analysis of j.i-6Al-4V alloy (wt%)

Ti Al V 1 Fe C O N H

bal. 6. 24 4. 18 i .174 . 033 . 155 . Oil 14ppm

Table 4. Mechanical properties at 295 K

0. 2% yield stress ultimate strength elongation in 4D reduction in area (MN/m^) 2 fMN/m ) (%) (%)

942 993 16. 3 26. 4

39
Table 5. Dimensionless stress intensity factors and

displacements for the compact specimen .[i 3]; a EBv^

W P P

0. 30 5. 85 25. 1

0. 35 6. 54 30. 1

0. 40 7. 33 36. 0

0. 45 8. 34 43. 4

0. 50 9. 60 53. 0

0. 55 11. 26 66. 4

0. 60 13. 62 85. 8

0. 65 16. 84 115. 4

0. 70 21. 56 162. 8

E is Young's modulus and v is deflection at the specimen

edge.

40
Table 6. Fracture toughness results for Ti-6A1-4V

Specimen Temperature Fracture toughness, Kjq

(No. ) (K) MN/m^^^

A12 295 47. 3 A15 295 46.9

A16 295 49.4^

A18 295 48. 1

avg = 47.

4

b

A13 195 42.2

A14 195 39.8^

avg = 41. 0 A6 77 37.7

A7 77 38. 1 A8 77 40. 8 A9 77 38.7

avg= 38. 8 AlO 4 39.0

All 4 38.2

A21 4 38.2

avg= 38.

5

^ Invalid; fatigue stress intensity exceeded 0. 6 I^^ .

^ Invalid; irregular crack front.

41
Fatigue Actuator

Length External , L Area, A^ .Modulus,

Length Internal, L^ /

Liquid Helium

Specimen

Dewar

ambi en

t

Heat Leak into Dewar,

Figure 1 . Simplified model of fatigue cryostat used in the

optimization analysis.

42
.1 1 10 100

FREQUENCY, Hz

Figure 2. Performance of 100 kN fatigue testing machine

43
4.2 63.14 77

INITIAL TEMPERATURE OF CRYOSTAT, K

Figure 3. Liquid helium consumption for ideal or isothermal . cool-down from various initial temperatures.

44
Pull Rod

Stand Offs

0 2 4

1 I I L_J

SCALE, inches

0 5

I L

10

SCALE, cm

FRP Insulators

Grip -

ASTM

Clip Gage^

Bridge

Fracture Specimen

FRP Helium Dewar, vacuum insulated

FRP Nitrogen Dewar,

foam insulated

FIGURE 4 - Liquid helium fatigue cryostat.

45
Figure 5. Helium fatigue cryostat (with copper baffles).

46
47
100

DISPLACEMENT, mm

Figure 7 . Compliance calibration of cryostat frame at 77 K.
Figure 8. Cryogenic fatigue testing apparatus,
50
STRESS INTENSITY FACTOR RANGE, AK, ksi-in^^^

STRESS INTENSITY FACTOR RANGE, AK, MN/m '

Figure lO. Room temperature growth rate data,

' 51
10'

STRESS INTENSITY FACTOR RANGE, AK, ksi-in

10 100

1/2

T~rT 1 rTT7

10

-1 • 76 IC-6 Specimen-49 points

A 4 K-4 Specimen-40 points

^ 10

E

u

-4

< 10

Oq;

Q.

^ 10'^

c_>

C3

t—

I—

10

-6

Damage Tolerant

Design Handbook

(295 K)

[19]

10

-7

I III J L

10 100

STRESS INTENSITY FACTOR RANGE, AK. MN/m3/2

600

Figure 1 1 . Crack growth data at 76 K and 4 K

52
Figure IZ . Typical load- displacement record

at 4 K for Ti-6A1-4V.

53
54
55
FATIGUE CRACK GROWTH AND J-INTEGRAL FRACTURE PARAMETERS

OF Ti-6A1-4V AT AMBIENT AND CRYOGENIC TEMPERATURES*

R. L. Tobler

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Abstract

Fatigue crack propagation and fracture parameters for 2.030 cm-thick compact speci- mens of an extra-low- interstitial Ti-6A1-4V alloy were measured at temperatures between

295 K and 4 K. The fatigue-crack growth rates (da/dN) were temperature independent at

3/2 3/2 stress intensity ranges (AK) from 10 to 20 MN/m . Above 20 MN/m , the rates increased

with decreasing temperature. Plane-strain linear-elastic and J-integral fracture test results were in good agreement: the fracture toughness of this alloy decreased from about

3/2 3/2 110 MN/m at room temperature to 54 MN/m at 4 K, with a ductile-to-brittle fracture

transition occurring in the range 125 K to 76 K. These fatigue and fracture results are compared with data previously reported for a normal-interstitial Ti-6A1-4V alloy.

Key Words: Fatigue crack propagation; fracture toughness; J-integral; low temperature

tests; titanium alloys.

* This work was sponsored by Kirtland Air Force Base and the Advanced Research Projects

Agency; it is a contribution of NBS, not subject to copyright. ^ 56
Introduction

High ratios of strength-to-density and strength-to-thermal conductivity make titanium6% aluminum-4% vanadium (Ti-6A1-4V) an attractive aerospace and cryogenic structural

material. Often, service temperatures span the ambient to cryogenic range, and the mechanical

properties at low temperatures may be critical in design.

Temperature reductions increase the yield strength and decrease the ductility of

Ti-6A1-4V [1], resulting in flaw-sensitive mechanical behavior. The normally ductile material

may fail in a relatively brittle manner in the presence of a fatigue crack under conditions

of plane strain. A fracture mechanics analysis is often the best means of assuring structural reliability and design efficiency.

The few fracture data for Ti-6A1-4V (ELI) alloys at cryogenic temperatures are insufficient: crack growth rate data at low temperatures are rare [2], fracture toughness

data for thin sheet or plate [3-5] do not provide valid K^^ data over the entire cryogenic

to ambient range, and no data exist below liquid hydrogen temperature. The present paper

provides some needed fracture toughness and crack growth rate parameters with emphasis at

the temperatures 295, 76 and 4 K. Linear-elastic fracture mechanics and J-integral test results are compared, and the existence of a ductile-to-brittle transition in this material

is demonstrated.

Linear Elastic Fracture Mechanics

If a negligible amount of plastic deformation occurs prior to fracture, the ASTM

Method of Test for Plane Strain Fracture Toughness of Metallic Materials (ASTM E-399-74)

can be applied. This method utilizes the stress intensity factor, K, to describe fracture

behavior. For specimens of a standard geometry, K is calculated from the relation:

[f(a/W)] (1) 1/2 BW '

where P is applied load, B is specimen thickness, W is specimen width, a is crack length,

and f(a/W) is a factor dependent on relative crack length. Linear elastic conditions

prevail for thick specimens where the plastic zone at the crack tip is constrained by the

surrounding bulk of elastically loaded material. Under these conditions, materials loaded

in tension exhibit a critical stress intensity K^^ at which failure occurs spontaneously

without significant plastic deformation.

The parameter K^^ is a material property and a useful design criterion. Provided

that specimen size requirements are met, K^^ can be calculated from Eq. (1) using the secant

load Pq, determined from the fracture test record according to ASTM E-399-74. The size

criterion assuring linear elastic behavior and valid K^^ data is:

K 2 a, b, B > 2.5 ( ^ ) (2) y

where is the 0.2% offset yield strength of the material and b is the specimen ligament

(b = W-a) . Subsized specimens yield invalid fracture toughness measurements that are denoted K^.

J-integral Analysis

Specimens that do not satisfy the thickness requirement of Eq. (2) exhibit nonlinear

load-deflection behavior due to plastic deformation at the crack tip. In such a case, elastic stress field descriptors are not relevant, but the path- independent J-integral

formulated by Rice [6] may be used to characterize fracture.

57
For nonlinear-elastic materials, J represents the change of potential energy with

respect to crack extension. Experimentally, the J-integral can be evaluated as an

energy proportional to the area (A) under the load-versus-loadline deflection (6) curve

of a precracked specimen tested in tension or bending. The critical value, J^-p, has been

defined as the value of J required to initiate crack extension. Although a standard test procedure has not yet been developed, experiments by Begley and Landes [7-9] and others

demonstrated that J^^ is a meaningful fracture parameter for linear-elastic, elasticplastic, or fully plastic behavior. Recent applications include tests of Ti-6Al-AV at room temperature [10,11].

For standard compact specimens, J can be calculated using either of two equations.

Assuming the specimen is in a state of pure bending, the following expression was derived [12]:

This equation is conservative to some degree, but it yields adequate results for deeply

cracked specimens where the assumption of pure bending is more appropriate [12]. Merkle

and Corten pursued a more exact solution for the compact specimen, accounting for axial

force as well as bending [13]:

X

Here, is a factor ranging from 2.55 to 2.31, dependent on relative crack length [13].

This expression applies to a wider range of a/W, but data quantifying the scope and

accuracies of Eqs. (3) and (4) are lacking. Therefore, the present paper includes a comparison of critical J values calculated from both equations. The comparison is made

for a range of a/W, in the linear-elastic case, where K data are also calculated using

ASTM E-399-74 methods.

Since the J-integral applies to plane strain, a size criterion is necessary to insure

that results will be independent of specimen dimensions and geometry. A tentative

criterion is [9]: ..

a, b, B > a ( ^ ) (5) y

where a is a factor of 50. The specimen need not be as large as that required for linearelastic tests; yet, the parameter J can be converted to K using the relation [7]:

XL* i. Lj

where E is Young's modulus and v is Poisson's ratio. Thus, it is possible to derive the

linear-elastic fracture toughness value from smaller, plastic J-integral test specimens.

In this paper, the symbol K (J) distinguishes values obtained using Eq. (6) from K data

IC -L*-* determined according to ASTM E-399-7A.

Material and Specimen

Stock of an extra-low-interstitial (ELI) Ti-6A1-4V alloy produced to AMS 4930

specifications was obtained in the form of a 2.54 cm-thick forged ring, 101.6 cm I.D. by

106.7 cm CD. The material was commercially annealed at 977 + 14 K for two hours, aircooled, and descaled. The microstructure, shown in Figure 1, was primary alpha and beta

with an average alpha grain diameter of 0.013 mm. The chemical analysis is listed in

58
Table 1, and mechanical properties at primary temperatures of interest are listed in

Table 2. The tensile properties were measured at room temperature according to ASTM

method E8-69, or estimated at cryogenic temperatures from handbook data fl].

All tests were performed using compact specimens of the geometry shown in Figure 2. The specimen proportions were in general accordance with ASTM E-399-74, but a modified

notch was introduced to enable loadline deflection measurements. The specimen thickness

was 2.030 cm, the width-to-thickness ratio, W/B, was 2.0, and the orientation was LT [14].

Procedure

Young's modulus and Poisson's ratio were measured at room temperature using the

ultrasonic pulse-superposition method. The results were equivalent (+ 1%) to those reported

for a similar heat [15]. Since the elastic properties of Ti-6A1-4V are regular functions

of temperature, Naimon, Weston, and Ledbetters' values of E and V at low temperatures

could be used with good accuracy [15]

.

Fatigue and fracture tests were performed using a 100 kN capacity servo-hydraulic

testing machine and cryostat. As previously described [16], a vacuum insulated dewar con- taining liquid nitrogen or liquid helium encloses the load frame, specimen, and clip gage

during tests at 76 K or 4 K. In this study, intermediate temperatures were obtained by

admitting cold nitrogen vapor to the dewar. A chromel-constantan thermocouple was attached

to the specimen during these tests and a servo-mechanical temperature controller regulated

the vapor flow such that temperatures of 200, 125, and 110 K were maintained within + 3 K. Clip gage calibrations at temperatures from 295 to 4 K verified that the gage sensitivity

changed by only 1.5% and linearity corresponded to ASTM E-399-74 requirements.

Using load control, the specimens were precracked and then fractured at identical

temperatures. The loading rate to fracture corresponded to a stress intensity factor

3/2 increase of about 1.0 MN/m per second. Critical stress intensity factors were calculated using Roberts' [17] solution for f(a/W). The J-integral calculations were performed for the same specimens using Eqs. (3) and (4) where the area. A, was measured with

a planimeter at points of interest, and values were interpolated from the published

solution [13]

.

For low temperature tests, fracture toughness calculations were performed at the load

point Pq, in accordance with ASTM E-399-74, and at other points described in the text. At room temperature, stable crack extension occurred and the J-resistance curve (J versus Aa) was determined following a procedure outlined by Begley and Landes [9]. Six identical

specimens (a/W = 0.578 + 1%) were loaded to cause decreasing amounts of crack extension.

These specimens were then unloaded and heat tinted 15 minutes at 900 K to oxidize the

surfaces where crack extension had taken place. The specimens were finally fractured into

halves and the increments of crack extension, Aa, were measured with a traveling microscope

at locations corresponding to 25, 50 and 75% of specimen thickness.

Most fatigue crack growth data were obtained during precracking of fracture toughness

specimens. The maximum fatigue stress intensity, K^, was maintained within ASTM E-399-74

specifications. At each temperature (295, 76 and 4 K) , one additional specimen was tested

solely for crack growth data at higher stress intensity factors.

Fatigue crack growth was monitored by elastic compliance measurements, an approach

based on the fact that specimen compliance, 6/P, increases with Increasing crack length.

The correlation between crack length and compliance was determined experimentally by

plotting the crack lengths of fractured specimens versus the dimensionless parameter

EB 6/P. Changes in clip gage sensitivity and Young's modulus with temperature were

accounted for in the term EB 6/P, and, as shown in Figure 3, the results were in agreement

with predictions based on Roberts' solution [17].

Crack growth rates were determined by plotting the static compliance with an X-Y

recorder at intervals during the fatigue tests. Using the correlation shown in Figure 3,

the average crack length could be inferred at any time to + 1%. The crack lengths were

59
plotted versus cycles, N, and the growth rates, da/dN, were obtained by graphical differentiation. Stress intensity factor ranges, AK, were calculated as the difference between the

maximum and minimum fatigue stress intensities.

The loads during fatigue were measured to + 1% by means of a digital peak load

indicator. The load cycle was sinusoidal at a frequency of 20 Hz and a minimum/maximum

load ratio of 0.1.

Results

Fatigue Crack Growth

Fatigue crack growth rates are shown in Figure 4. The data define a slightly curved

scatter band that increases in width at higher stress intensity ranges. Below AK = 20

3/2 MN/m the rates at 295, 200, 76 and 4 K are nearly equivalent and no effect of temperature

3/2 can be distinguished from the scatter among specimens. Above 20 MN/m , the data appear

to diverge according to temperature. In this region of high AK, the rates are lower at room

temperature than at 76 K or 4 K.

As shown in Figure 4, the results are best approximated by straight line segments

3/2 intersecting at AK = 20 MN/m . The equations describing these line segments are of the

form suggested by Paris and Erdogan [18,19]

^ = C(AK)'' (7)

where C and n are empirical constants. The C and n values, which govern growth rates for

various conditions of temperature and AK, were determined graphically and are specified

in Table 3.

A single "Paris" equation, integrated, is sometimes preferred to calculate increments

of crack growth over wide ranges of AK. The present data at 4 K could be closely approxi3/2 mated by a single straight line over the range of AK from 10 to 30 MN/m , but other data

in Figure 4 and elsewhere [20-22] do not conform with a single-equation format. Since

growth rates are highly sensitive to AK, practical applications of these data should incorporate duplicate sets of C and n values at each temperature, depending on the stress

intensity factor range, as shown in Table 3.

A band representing data for a normal interstitial grade of Ti-6A1-4V is superimposed

on the present results in Figure 5. Similarly, data for the normal grade were obtained

at 295, 76, and 4 K, but the results were temperature-independent over the range of AK

investigated [16]. The overlap of bands in Figure 5 suggests that a variation in the

level of interstitials does not heavily influence the growth rates of these alloys.

Fracture Toughness

Macroscopic features of specimens loaded directly to failure are shown in Figure 6. The fracture surfaces indicate decreasing toughness at cryogenic temperatures. Slant

and flat fracture modes are evident at each temperature, but the proportion of slant

fracture at specimen edges decreases from 23% at room temperature to 5% at 4 K. Also,

the flat fracture region becomes progressively smoother as temperature is lowered from

295 to 4 K. Similar trends but less noticeable changes were reported for the normal

interstitial alloy [16].

The variety of P-6 behaviors observed is shown in Figure 7. A transition from

elastic-plastic to linear-elastic behavior occurs at about 125 K, and at 110 K the behavior is ideally linear-elastic. At more extreme temperatures, fast fracture terminates

the curves after a series of pop-ins, increments of unstable crack extension. The pop-ins,

which were faint and sometimes barely perceptible, produced small step-like discontinuities

60
beginning at about 0.95 P^. Thus, specimens at 76 K and 4 K failed in linear-elastic planestrain, but deviations from the initial P-6 slopes are evident. Table 4 cites the relationships among P^, P , and the load at the first noticeable pop-in, P . Q max ^ ' p Linear-elastic Fractures

Of all the results summarized in Tables 5-7, the test at 110 K affords the simplest

interpretation. The K and J measurement point at this temperature is unambiguous since

3/2

P = P = P . The linear-elastic K result (78 MN/m ) is in good agreement with the

p y max

3/2 Kj^(J) value (81.4 MN/m ) obtained using Eqs. (4) and (6). The ratio K^^(J)/K^^ is 1.04,

indicating that the results from two test procedures are equivalent within 4% for an ideal

linear-elastic P-6 record.

The K^^ data obtained at 76 and 4 K are shown in Table 5. The J-integral was evaluated

at the K measurement point, P , and the results denoted J are listed in Table 6. In comparison, the ratios of Kq(J)/K^^ ranged from 1.03 to 1.12, indicating wider disagreement

than observed at 110 K. This is due to the effects of pop-ins on J-integral calculations.

Pop-in phenomena at these lower temperatures violate the assumption of monotonic loading

made in the J-integral formulation [6] . Complete agreement between J and K measurements

is expected only if comparison is made at identical points on a perfectly linear P-5 record.

At 76 and 4 K, the K (J) values exceed the values of K because pop-ins prior to P in- crease the area under the test records without proportionate increases in load.

In this study, errors in J-integral calculations at P^ due to slight nonlinearity or pop-in were corrected as shown in Figure 8. According to this procedure, the initial

linear slope of the P-6 record is extrapolated up to a point P^, which is equal in magnitude to Pq, and J is calculated from the triangular area OPq'6':

where 6' is the hypothetical deflection associated with P^, as defined in the figure.

Values of J adjusted by measuring at P^ are labelled J^^ in Table 8. The correction

brings K (J) and K data into agreement within 4%, which is equivalent to the agreement

J-U XL* at 110 K where no correction was necessary. The correction procedure was also applied to the test record at 125 K where nonlinearity was apparently due to stable crack extension.

The J-integral calculations above incorporated the values of X^. Using J = 2A/Bb,

where is replaced by the constant 2, yields underestimates of the fracture parameters.

At 110 K, the critical stress intensity factor converted from J = 2A/Bb underestimated K^^

by 6%. At 76 K and 4 K, similar calculations at P^ yielded conservative errors as high

as 10%, the results varying as a function of a/W as shown in Figure 9. For a/W equivalent

to 0.6 or greater, the disparity amounts to 4 or 5%. Merkle and Corten's expression for J, Eq. (4), appears to be more accurate, leading to critical J and converted K values that overestimate K^^ by an average of about 3% over the range of a/W from 0.45 to 0.70.

Elastic-plastic Fractures

A single test at 200 K did not yield a K^^ datum. The ASTM E-399-74 requirement that

P /P„ < 1.10 was not satisfied at this temperature. Nor could K^^(J) be obtained, since max Q — IC the Jj^ measurement point could not be identified from the test record.

61
At room temperature one specimen was loaded to the point of fast fracture, while six

others were unloaded at points along the P-6 diagram as shown in Figure 10. The corresponding values of J and Aa are listed in Table 7 and the J-resistance curve is shown in Figure 11.

There is some data scatter, but the resistance curve appears to rise steeply over the

initial portion, becoming linear at crack extensions greater than 0.12 mm. Since methods

of defining a discrete J^^ measurement point for such a curve have not been standardized,

several plausible alternatives are considered here:

1. The trend at high Aa may be linearly extrapolated to Aa = 0, identifying J^^ as the interception the J axis [23]. The broken line in Figure 11 indicates in this case that

88 kJ/m .

2. As described elsewhere [9,24], the line J/2o^ may be constructed, its intersection

with the resistance curve representing J-^-^- Applied to Figure 11, this method yields

J^^ = 94 kJ/m^.

3. A significant amount of crack extension, ^a^, may be defined as critical. Since

good results for Ti-6A1-4V alloys were obtained by specifying Aa^ = 1% [11], the same criterion might be applied here. Then, the resistance curve at 1% crack extension yields

J^^ = 108 kJ/m^.

2 Summarizing, the J^^ value at room temperature lies in the range 98 + 10 kJ/m , depending on the method applied to select the measurement point from the resistance curve

of Figure 11. The corresponding values of K (J) given by Eq. (6) are in the range

3/2 110 + 6 MN/m . This range of K^j^(J) is in close agreement with valid room temperature

ASTM E-399 test results for other ELI grade Ti-6A1-4V alloys; K values from 102 to 121

3/2 MN/m have been reported [25,26].

The J-integral specimen thickness criterion was amply satisfied. Using the K^^(J)

value in Eq. (2), it is estimated that a 4.5 cm-thick specimen would be required to produce

linear-elastic fractures in this material at room temperature. Thickness criteria calculations are summarized in Table 8.

Effect of Temperature

The specimen strength ratio, Rg^> is listed for each temperature in Table 5. Defined

according to ASTM E-399-74, R^^ is the ratio of the maximum nominal net-section fracture

stress to the tensile yield strength:

2P (2 W + a)

he = 2 ^ B(W-a) oy Referring to R^^, Section 4.1.3 of ASTM E-399-74 states that: "It is significant

as a comparative measure of material toughness when results are compared from specimens

of the same form and size, and when this size is sufficient that the limit load of the

specimen is a consequence of pronounced crack extension prior to plastic instability

As a qualitative parameter, R^^ can be used here to rank the effect of temperature

on toughness. The observed increase of R^^ between 125 and 295 K implies that J^.^ for this

material at room temperature should exceed 82.5 kJ/m^, the J value at 125 K. Consequently,

2 82.5 kJ/m could be taken as a lower bound for J at room temperature. Critical values

2 from 88 to 108 kJ/m were obtained from Figure 11 and, although these values could vary

62
depending on how the resistance curve is drawn to account for scatter, it appears that

the J-integral results at 295 K are consistent with the linear-elastic results at lower

test temperatures.

The temperature dependence of K_j.^ is shown in Figure 12. The fracture toughness of

the ELI alloy remains at a high shelf level as temperature is reduced from 295 to 125 K,

but an abrupt decline of K^^ occurs in the range 125 to 76 K. Temperature reductions in

this narrow interval decrease K^^ by 45%, while temperature reductions from 76 K to 4 K

decrease K^^ slightly. The abrupt change in behavior between 125 and 76 K constitutes a ductile-to-brittle fracture transition, which, although commonly associated with beta

titanium alloys and other bcc and hep materials, has not previously been documented for

a Ti-6A1-4V alloy.

The fracture mode and R„ parameters also indicate the ductile-to-brittla transition.

Sc Plotted as a function of temperature in Figure 13, the per cent slant fracture displays a trend similar to that of K^„ data. The values also exhibit a step-like decrease

IC Sc between 125 and 110 K, but the effect is subtle. In contrast to the trends of K.^.^ and

slant fracture mode, R^^ does not exhibit a relatively constant "upper shelf" value.

Discussion

Valid ICj.^ data for a normal interstitial grade of Ti-6Al-4V were also shown in

Figure 12. These results were obtained for 2.54 cm-thick compact specimens [16]. The

normal grade had a microstructure similar to the ELI alloy, except that the average alpha

grain diameter was 0.006 mm. In comparison:

1. the normal grade exhibits low toughness at each temperature, and

2. it does not exhibit a ductile-to-brittle fracture transition over the range

of temperatures investigated.

Tests at higher temperatures than represented in this study might have revealed a transition in T:he normal grade. The transition temperature regime should vary with

parameters such as grain size and composition. A finer grain size should tend to lower

the transition temperature, whereas high impurity content tends to raise if [27-29] . Since

the properties of titanium alloys are particularly sensitive to interstitial content [30,31],

it seems possible that the normal grade of Ti-6Al-4V contained a level of embrittling

elements sufficient to raise the transition temperature above 295 K.

A quantitative relationship between interstitial content and K^.^ values has never been

demonstrated, but the difference in toughness between normal and ELI Ti-6A1-4V grades is

large. It may seem surprising that there is little difference in crack gro\^th rates; but

the data for other types of alloys have often led to the conclusion that rates of crack

growth are not highly sensitive to compositional variations [32,33].

Wei and Ritter [20] found the crack growth rates of a normal grade of Ti-6Al-4V to be

equivalent between 295 and 563 K, while Pittinato's data [2] for a normal grade appear

temperature- independent between 145 and 295 K. The rates from these and other sources [21,22]

compare quite closely with the data in Figure 5 , supporting the conclusion that the rates

for Ti-6A1-4V alloys are relatively constant over several hundred kelvins. The temperature

effects' at high AK values for the ELI grade may be related to the marked temperature dependence

of K^^ for this material.

Cryogenic fracture data for ELI grades of Ti-6A1-4V are available from single-edgenotched or part-through-cracked specimens 0.162-0.325 cm-thick [3-5]. The part-throughcracked specimens simulate surface flaws that occur in service, but the results are considered directly applicable only where service conditions match the specifics of specimen

design [34]. Some of these data at 77 K are nearly equivalent to our results for compact

specimens while others are not. In any case, the values quoted for non-standard specimens

63
1

cannot be termed valid K^^ data until their independence of specimen geometry and flaw

shape is proved.

The AMS 4930 specification requires a room temperature K value of at least 60.4

3/2 MN/m , stating that the ELI alloy is useful at temperatures as low as 20 K. The present

alloy amply exceeds this requirement, but the implied limitation to 20 K seems arbitrary.

Other structural materials such as ferritic steels are seldom used below their ductileto-brittle transition temperatures. If the ELI grade of Ti-6Al-4V is an exception, it

should be considered useful at any cryogenic temperature; there is only a small change

in toughness between 20 and 4 K.

If stable crack extension does not occur and J^^ is strictly defined as the value of

J just prior to crack extension, it seems logical to choose the load point at the first

noticeable pop-in, P , as the J measurement point. For the tests described here at

P J-L< 76 and 4 K, could be considered a possible measurement point. However, the appearance

of load point discontinuities in test records is affected by material and experimental

variables, and the identification of such a measurement point is also dependent on judgment in cases where pop-ins are faint and indistinct. The ASTM E-399-74 procedure

obviates these problems by defining K^^ at P^, which corresponds to an effective crack

extension of 2% [35]. Following the standard procedure in this study, P^ could not be taken

as the K^^ measurement point for tests at 76 and 4 K. Similarly, the 2% point served as a basis for J^^ measurements in the linear-elastic case. Here, it was desirable to maintain

consistency with ASTM E-399-74 results by measuring J^^ at P^ as described in the text.

Summary

1. The ELI grade of Ti-6A1-4V exhibits a ductile-to-brittle transition in the tem- perature interval 125 to 76 K; the fracture toughness significantly exceeds that of a normal grade at all temperatures between 295 and 4 K.

2. The fatigue crack growth rates of the ELI Ti-6A1-4V alloy were temperature

3/2 3/2 independent for AK <_ 20 MN/m ; above 20 MN/m , the rates at 295 K were lower than at

76 and 4 K.

3. The J-integral fracture criterion provided meaningful results for a spectrum of

load-deflection behaviors; J data for the elastic-plastic case were in consistent

agreement with valid K^.^ data for this material.

4. Critical values of the J-integral calculated from the equation J = 2A/Bb led

to converted K^^ values that appeared to underestimate ASTM E-399-74 linear elastic

fracture toughness values by 4 to 10%, depending on a/W; the equation J = A^A/Bb led to modest overestimates of about 3%, independent of a/W.

Acknowledgment

The test material and room temperature tensile data were furnished by Beech Aircraft

Division in Boulder, and the chemical analysis was performed by Titanium West, Reno, Nevada.

The elastic properties at room temperature were measured by Dr. W. Weston of the NBS Cryogenics Division. Earl Balinger, Bea Crockett, and Steve Naranjo also aided in data reduction. All of this assistance is appreciated.

64
References

1. Handbook on Materials for Superconducting Machinery, MCIC-HB-04, Metals and Ceramics

Information Center, Battelle Columbus Laboratories, Ohio, (1974)

.

2. G. F. Pittinato, Hydro gen-enhanced fatigue crack growth in Ti-6A1-4V ELI weldments.

Met. Trans., 3, 235-243 (1972).

3. W. E. Witzell, Fracture data for materials at cryogenic temperatures. Tech. Report,

AFML-TR-67-257, General Dynamics-Convair, AD 825264 (1967).

4. C. F. Tiffany and ?. M. Lorenz, An investigation of low cycle fatigue failure using

applied fracture mechanics, Tech. Doc. Report ^IL-TDR-64-53 , Boeing (1964).

5. L. R. Hall, Plane-strain cycle flaw growth in 2014-T52 aluminum and 6A1-4V (ELI)

titanium, N69-20265, XASA-CR-62396, Boeing (1968).

6. J. R. Rice, A path independent integral and the approximate analysis of strain con- centration by notches and cracks, J. Appl. Mechs., Trans. ASME 35, 379-386 (1968).

7. J. A. Beglej* and J. D. Landes, The J-integral as a fracture criterion, in Fracture

Toughness, Proc. 1971 Nat. Symp. on Frac. Mech. , Part II, ASTM STP 514, pp 1-20

(Amer. Soc. Test. >Iater. , Philadelphia, PA, 1972).

8. J. D. Landes and J. A. Begley, The effect of specimen geometry on J-j-^j ii^ Fracture

Toughness, Proc. 1971 Nat. Symp. on Frac. Mech. , Part II, ASTM STP, pp 24-39 (Amer.

Soc. Test. >Iater., Philadelphia, PA, 1972).

9. J. D. Landes and J. A. Begley, Test results from J-integral studies: an attempt to establish a J^^ test procedure, in Fracture Analysis, ASTJI STP, pp 560 (Amer. Soc. Test. Mater., Philadelphia, PA, 1974).

10. G. R. Yoder and C. A. Griffis, J-integral and the initiation of crack extension in

a titanium alloy, NRL report 7662, Naval Res. Lab., Washington, D.C. (1974), 37pp.

11. G. R. Yoder and C. A. Griffis, Obser\-ations on the use of the J-integral to determine

plane-strain fracture toughness from subsized specimens of a titanium-6Al-4V alloy,

NRL report 7789, Naval Res. Lab., Washington, D.C. (1974), 17pp.

12. J. R. Rice, P. C. Paris, and J. G. Merkle, Some further results on J-integral and

estimates, in Progress in Flaw Growth and Fracture Toughness Testing, ASTM STP 536,

pp 231-244 (Amer. Soc. Test. >!ater. Philadelphia, PA, 1973).

13. J. G. Merkle and H. T. Corten, A J-integral analysis for the compact specimen, con- sidering axial force as well as bending effects. Trans. ASJIE, J. Pressure Vessel

Tech., No. 6, 1-7 (1974).

14. R. J. Goode, Identification of fracture plane orientation. Mater. Res. Stand., 12, No. 9, 31-32 (1972) .

15. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Elastic properties of two titanium

alloys at low temperatures. Cryogenics, 14, 246-249 (1974).

16. C. V. Fowlkes and R. L. Tobler, Fracture testing and results for a Ti-6A1-4V alloy

at liquid helium temperatures, submitted for publication.

17. E. Roberts, Jr., Elastic crack-edge displacements for the compact tension specimen.

Mater. Res. Stand., >fTRSA, 9, No. 2, 27 (1969).

18. P. C. Paris, The fracture mechanics approach to fatigue, in Fracture-An Interdisciplinary

Approach, pp 107-133 (Syracuse Univ. Press, Syracuse, 1964)

.

65
19. P. C. Paris and F. Erdogan, A critical analysis of crack propagation laws, Jnl. Basic

Eng., Trans, ASME, Series D, 85, No. 4, 528-534 (1963).

20. R. P. Wei and D. L. Ritter, The influence of temperature on fatigue-crack growth in a mill annealed Ti-6A1-4V alloy, NASA-CR-127042 , Lehigh Univ. (1972).

21. R. J. Bucci, P. C. Paris, R. W. Hertzberg, R. A. Schmidt, and A. F. Anderson, Fatigue

threshold crack propagation in air and dry argon for a Ti-6A1-4V alloy, in Stress

Analysis and Growth of Cracks, ASTM STP 513, pp 125-14 (Amer. Soc. Test. Mater.

Philadelphia, PA, 1972).

22. A. Yeun, S. W. Hopkins, G. R, Leverant, and C. A. Rau, Correlations between fracture

surface appearance and fracture mechanics parameters for stage II fatigue crack

propagation in Ti-6A1-4V, Met. Trans., 5, 1833-1844 (1974).

23. C. A. Griffis and G. R. Yoder, Application of the J-integral to crack initiation in

a 2024-T351 aluminum alloy, NRL report 7676, Naval Res. Lab., Washington, D.C.

(1974), 17pp.

24. G. A. Clarke, W. R. Andrews, P. C. Paris and D. Schmit, Single specimen tests for J^.^ determination, presented at the Eighth National Symposium on Fracture Mechanics,

Brown University (Aug. 1974).

25. H. I. McHenry and R. E. Key, Brazed titanium fail-safe structures. Welding Journal,

53, 432-439S (1974).

26. R. W. Judy, Jr., R. W. Ruber and R. Goode, Fracture characteristics of Ti-6Al-lMo and

Ti-6A1-4V in 3-inch section, NRL Report MR 2156, Naval Res. Lab., Washington, D.C.

(1970), AD 711-586, 22pp.

27. R. W. Armstrong, The influence of polycrystal grain size on mechanical properties, in

Advances in Materials Research 4_, Ed. H. Herman, pp 101-146 (Interscience, New York,

1970)

.

28. R. W. Armstrong, The polycrystal ductile-brittle transition. Paper 26 in Fracture

1969, pp 314-326, Ed. P. Pratt (Chapman and Hall, London 1969).

29. N. S. Stoloff, Effects of alloying on fracture characteristics, in Fracture-An

Advanced Treatise, 6^, Ed. H. Liebowitz, pp 1-81 (Academic Press, New York, 1969).

30. S. F. Frederick and W. D. Hanna, Fracture toughness and deformation of titanium alloys

at low temperatures. Met. Trans., 1, 347-352 (1970).

31. J. L. Shannon, Jr., and W. F. Brown, Jr., A review of factors influencing the crack

tolerance of titanium alloys, in Applications Related Phenomena in Titanium Alloys,

ASTM STP 432, pp 33-63 (Amer. Soc. Test Mater., Philadelphia, PA, 1968).

32. J. M. Barsom, Fatigue-crack propagation in steels of various yield strengths, Trans. ASME J. Eng. Ind. 93, 1190-1196 (1971).

33. H, H. Johnson and P. C. Paris, Subcritical flaw growth. Eng. Fract. Mech. 1, 3-45

(1968)

.

34. R. M. Ehret, Assessment of fracture mechanics technology for space shuttle applications,

SD-73-SH-0270, Rockwell International (1973), M 7302002.

35. J. E. Srawley, Plane strain fracture toughness. Chap. 2, in Fracture-An Advanced

Treatise, Ed. H. Liebowitz, pp 45-68 (Academic Press, New York, 1969).

66
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86
FATIGUE CRACK GROOTH RATES OF STRUCTURAL ALLOYS AT FOUR KELVIN*

R. L. Tobler and R. P. Reed

National Bureau of Standards

Boulder, Colorado

Abstract

The fatigue crack growth rates of nine structural alloys were tested at 4 K. Growth

-5 -3 rates from 7 x 10 to 2 x 10 nnn/cycle were measured for compact specimens 2.54 to 3.81

cm thick. The materials tested include: Ti-5Al-2 . 5Sn, Ti-6A1-4V, AISI 304, 310, and 316

stainless steels, 5083-0 aliaminum, 9% nickel steel, and two Fe-Ni-Cr superalloys . Results

showed that stable face-centered cubic alloys having high elastic moduli displayed superior

crack growth resistance at 4 K, whereas materials with body-centered cubic, hexagonal-closepacked or martensitic phases exhibited relatively high growth rates at this temperature.

When compared on the basis of the strain intensity factor, AK/E, the growth rates of

alloys having close-packed crystal structures were in close agreement. An equation describing the crack growth rates of four stable fee alloys is:

da , ,AK . dN = ^ )

b

where, depending on the range of Ak/E, the constants A and b have two distinct values.

Key words: Aluminum alloy; crack propagation; fatigue; iron alloys; liquid helium;

stainless steels; steels; superalloys; titanium alloys.

This work was sponsored by the Advanced Research Projects Agency and is a contribution

of NBS, not subject to copyright.

»/
Introduction

Recent developments in applied superconductivity have demonstrated the feasibility

and practicality of constructing electrical machinery to operate at liquid helium temperature. A device such as a rotating superconducting generator contains structural members

that are continually subjected to fatigue during operation at 4 K. The fatigue resistance

of candidate structural materials in this environment is a vital design consideration, and

fatigue studies at extreme cryogenic temperatures are currently of great practical importance .

Experiments at temperatures near absolute zero can provide basic information regarding the mechanical behavior of materials. At extreme cryogenic temperatures thermally

activated deformation processes are suppressed and resistance to slip increases. Since

fatigue is a process involving reversed slip, some early investigations ri~5] at temperatures of 4 K and below contributed to a basic understanding of fatigue in metals.

Fatigue design data at 4 K are not abundant. MacCrone, McCammon and Rosenberg

reported S-N data for several commercially pure metals [1,2], while Nachtigall, Klima,

and Freche [6] reported S-N data for structural alloys. Nachtigall also reported straincycling fatigue data for alloys [7]. The latter paper demonstrated that, with an accuracy equivalent to results at room temperature, the strain-cycling fatigue life

of unnotched specimens at 4 K can be predicted by means of the Manson equation [8]:

- ° n 10 . 100 ^.0.6 .0.6 y^. Ae = 3.5 ^ (Nj-°-^2 ^ (j^^ )] . (Np (1)

t E f

where Ac^ is the total strain range, is the ultimate tensile strength, E is Young's

modulus, Nj is the number of cycles to failure, and RA is the percent reduction in area

from a uniaxial tensile test.

Although conventional S-N data provide valuable design information, the results in

terms of total cycles to failure do not distinguish between the separate stages of crack

initiation and crack growth. Specific knowledge of crack growth rates is needed to apply

current techniques of fracture mechanics analysis. The fracture mechanics approach is

based on the premise that cycle-life capability can be predicted, given the initial and

critical crack sizes and the crack growth rate.

This paper provides crack growth rate data for nine structural alloys tested in a liquid helium environment. The alloys are familiar cryogenic materials that have potential

applications at temperatures approaching absolute zero. These data can be used in a fracture mechanics evaluation of critical components, and the results lead to some generalizations regarding the selection of materials for maximum resistance to fatigue

crack propagation at 4 K.

Materials and Specimens

A summary of the materials tested in this study is contained in Table 1; included

are material condition, chemical analysis, grain size, hardness and tensile properties.

Three alloys have more common designations: ASTM A 453 is A286*, ASTM A553 is Fe-9%Ni

and ASTM A637 is Inconel 750*. All tensile data were obtained in our laboratory. Most

of the alloys were tested in the as-received condition, but the ASTM A453 and A533 specimens

vjere machined from stock and then heat treated prior to testing. Conventional heat treatments were applied. The A453 alloy was solution treated and aged:

1. 1172 K (1650 F) , 2 hrs., oil quench

2. 1005 K (1350 F), 16 hrs., air cool

The use of trade names is for the sake of clarity and does not imply a recommendation

or endorsement by NBS . yy
and the A533 alloy was solution treated and double aged:

1. 1255 K (1800 F), 1 hr . , air cool

2. 1144 K (1600 F), 24 hrs., air cool

3. 977 K (1300 F) , 20 hrs., air cool.

Tests were performed on compact specimens, which are described in ASTM E-399-74 [9].

Specimens machined from plate stock (Ti-6A1-4V, AISI 304, 310 and 316, ASTM A553, and

5083-OAl) were tested in the TL orientation, whereas specimens from forged bar stock

(Ti-5Al-2.5Sn, ASTM A453, and ASTM A637) were tested in the TS orientation [9]. Specimen

thicknesses (B) ranged from 2.54 to 3.81 cm; specimen widths (W) were 7.62 cm except for

a 5.08 cm width for Ti—6A1—4\ . All width to thickness ratios (W/B) were 2.00 except for

ASTM A553 (W/B = 2.5) and 5083-0 (W/B = 2.4). Titanium alloy specimens were provided with

attachable knife edges and deflections were measured at the specimen edge as described in

ASTM standard E-399-74. For other specimens, the notch was slightly modified [10], allowing deflections to be measured at the axis of loading.

Procedure

Fatigue tests were conducted using a 100 kN capacity servo-hydraulic mechanical

testing machine. The machine was equipped with a 100 kX capacity cryostat for fatigue

testing of specimens submerged in liquid helium. Conventional clip gages [9] were attached

directly to the specimens. Calibrations at 4 K remonstrated that clip gage linearity

satisfied ASTM E-399-74 requirements. Detailed descriptions of the low-temperature apparatus

and test procedures are discussed by Fowlkes and Tobler [11].

All tests were performed using load control. Dynamic fatigue loads were measured

and controlled to + 2% by means of a digital peak-load recording device. The load cycle

was sinusoidal at frequencies of 20-28 Hz, and the ratio, R, of minimum/maximum load was constant at 0.1.

Fatigue precracks were usually introduced at 4 or 76 K. ^sTienever precracking was performed at temperatures higher than 4 K, the subsequent growth rate data were discounted

until the crack had propagated beyond the plastic zone created by precracking. Estimates

of the plastic zone radius, r^, were calculated using the relation [12]

1 K

2 r„ = ^ i~) (2) p / i Jy

where K is the stress intensity factor defined by equation (3) and is the yield strength

of the material at the temperature of precracking. Using this criterion, the data from

several specimens of a given material were in good agreement, independent of precracking

temperatures

.

Crack length was monitored during the tests by means of elastic compliance measurements. A correlation between crack length and specimen compliance at 4 K was determined

experimentally for each material, following techniques previously developed [10] . Striations were generated on the crack surfaces when fatigue loads were increased to obtain

data at higher stress intensities. After the specimens were fractured subsequent to fatigue cracking, the distance separating striations was measured and correlated with

compliance data obtained at the time the load changes were made. Crack length was measured as an average of three readings at 25, 50 and 75% of specimen thickness.

At least ten data points were used to define the crack length-compliance correlation

for each material. The compliance correlation obtained for AIST 310 shown in Fig. 1, is

typical, but the agreement between empirical and theoretical curves [13] varied for different

materials

.

To obtain crack growth rates, the crack length, a, was plotted versus the total

number, N, of fatigue cycles. The crack growth rates, da/dN, were determined by graphical

differentiation at points along the a-versus-N curves. Data were obtained from at least

three specimens per material, except as noted.

89
The stress intensity factor, K, which governs the elastic stress distribution ahead

of the crack tip, was calculated from the expression for compact specimens [9]:

p 1/2 3/2 5/2 7/2 9/2

K = [29.6

(J) - 185.5(J) + 655.7

(f) - 1017.0 (|) + 638.9 (|) ] (3) BW where P is the applied load, B is the specimen thickness, and W is the specimen width.

Stress intensity factor ranges, AK, corresponding to various crack growth rates, were calculated from the relation:

AK = K - K . (4) max min

where K and K . are the stress intensity factors at the maximum and minimum fatigue

J max mm ° loads

.

Results and Discussion

The crack growth rate data at 4 K for the Ti-5Al-2.5Sn alloy, as well as the results

previously reported for a mill annealed Ti-6A1-4V alloy [11], are shown in Fig. 2. Metallographic examination indicated that the Ti-6A1-4V alloy had a two-phase microstructure con- sisting of primary alpha (hep) and beta (bcc) , whereas the Ti-5Al-2.5Sn alloy was almost

100% alpha. As Fig. 3 demonstrates, the rates of crack growth are higher for the two-phase

alloy containing beta.

The results for three fee alloys are shown in Fig. 3. Data for the nickel-base alloy

ASTM A637 and the iron-base alloy ASTM A453 show little scatter and nearly equivalent

behavior. Both alloys exhibit a high resistance to crack growth, as evidenced by the fact

3/2 that AK values as high as 30 to 80 Mn/m are required to produce growth rates from

-7 -7 3/2

5 X 10 to 7 X 10 mm/cycle. On the other hand, AK values of only 10 to 20 Mn/m produce similar growth rates in 5083-0 aluminum. The fatigue crack growth resistance of the

aluminum alloy is comparatively low, in proportion to its lower elastic modulus.

The data for several AISI 300-series stainless steels are compared in Fig. 4. The

3/2 3/2 AISI 304 and 316 alloys exhibited similar growth rates at AK ~ 40 Mn/m . Above 40 Mn/m

3/2 the rates are only slightly higher for AISI 304, whereas below 40 Mn/m the converse is true. Significantly, the behavior of AISI 310 is superior over the entire range of stress

intensities investigated.

To varying degrees, depending primarily on alloy composition, the austenitic stainless

steels are metastable. In response to plastic deformation or stress at low temperatures, the

austenitic phase may transform to bcc and hep martensitic structures. Several studies

describe the effects of these transformations on low temperature tensile properties [14-19],

but few discuss the effect of such transformations on fatigue crack growth rates [20].

The bcc martensite product is ferromagnetic while the austenite is paramagnetic. In this study, magnetic measurements [14,16] and metallographic examination confirmed that

cyclic loading of AISI 304 and 316 caused martensite formation in crack-tip plastic zones.

It can be assumed that the martensitic transformation preceded crack extension, and that the

parameter measured in these tests was the rate of crack propagation through partially

transformed austenite.

There was no evidence of transformation in the AISI 310 stainless steel. The data for

this alloy represent crack propagation through stable austenite. A comparison shows that

the rates for AISI 310 are similar to those shown in Fig. 3 for ASTM A637 and A453 alloys,

two stable austenitic superalloys. These findings suggest that the martensitic transformation may have influenced the results for the metastable stainless steels, causing higher

growth rates than observed for stable austenites.

The tests of a quenched and tempered 9% nickel steel (ASTM A553) revealed exceptionally

high crack growth rates at 4 K, as shown in Fig. 5. The rates at 4 K are much higher than

90
the rates at 295 or 76 K, which are included in Fig. 5. To interpret the behavior at 4 K, it is essential to realize that the 9% nickel steel undergoes a ductile-to-brittle fracture

toughness transition at temperatures below 76 K [10] . This transition is reflected in the

crack growth rates, also.

3 /2 Growth rates at IK below 30 Mn/m were not obtained for A553 steel at 4 K, and the

data in Fig. 5 cannot be extrapolated to lower AK without reservations. An A553 steel

3/2 specimen subjected to 30,000 cycles at IK = 20 Mn/m at 4 K exhibited no measureable

crack growth, although an incremental advance of 3.5 mm was expected based on the trend

in Fig. 5. McCammon and Rosenberg f2] reported that the S-N fatigue results of brittle

metals at extreme cryogenic temperatures can be irregular. Their data for iron and zinc

showed that only a narrow stress range existed in which fatigue was observed; moderate

increases in stress levels resulted in immediate fracture, whereas moderate decreases led

to inordinately long testing periods. The fatigue behavior of brittle materials, in

particular the 4 K crack growth resistance of A553 steel at lower stress intensity ranges,

deserves further investigation.

The data of Fig. 2-5 can be approximated by straight lines conforming to Paris'

equation [21,22]:

It - '^^^'^

where C and n are empirical constants. Such linear approximations are shown in Fig. 2-5,

and the corresponding values of C and n are listed in Table 2. Over the range of AK investigated, a single straight line represents the data for each of the stainless steels and

the A553 steel. However, the data for the other alloys extend to lower growth rates and

are best. approximated by two line segments. Such changes in the slope of crack growth data

have been demonstrated by other authors [23-25]

.

The linear approximations in Fig. 6 represent the crack growth rate data plotted

versus -K/E. The values of Young's modulus at 4 K were taken from measurements by Ledbetter,

Naimon, and Weston [26-29], and are listed in Table 1. For ideal elastic behavior, the

stress, z^, normal to the crack plane is proportional to the strain, and

AK = Aa /liaT (6) n

It follows that AK/E is proportional to Ae /2Tra and, by analogy, AK/E may be termed the

"strain intensity factor" [30,31].

When the present results are compared on the basis of AK/E, the A553 steel, nearly_^

100% ferritic, clearly exhibits the highest growth rates. For growth rates from 2 x 10

to 3 X 10 ram/cycle the AK/E values are much lower for this alloy than for the stable fee

alloys having nearly equivalent Young's modulus. Since the titanium alloys and the metastable austenitic stainless steels also have higher crack growth rates than the stable

austenitic alloys (AISI 310, ASTM A453 and A637, 5083-0), all observations are consistent

with the conclusion that the presence of bcc and hep phases are generally deleterious to crack growth resistance at 4 K. Note that the hep Ti-5Al-2.5Sn alloy exhibits better re- sistance to fatigue crack propagation than do alloys containing bcc phases; its crack

growth resistance is surpassed only by the stable fee alloys. In sharp contrast, room

temperature da/dN data versus AK/E show relatively good agreement among alloys regardless

of crystal structure [32,33,34]. Therefore, it is reasonable to assume that the lower crack

growth resistance of bcc and hep materials at 4 K is another aspect of the low temperature

embrittlement phenomenon that is characteristic of their fracture, tensile, and impact

properties. These generalizations hold true for the alloys considered in this study, but

exceptions may exist. For example, a few ferritic alloys retain high fracture toughness

at 4 K [35]; it cannot be assumed that these alloys would exhibit poor resistance to fatigue crack propagation at liquid helium temperature.

The similar behavior observed for alloys having close-packed crystal structures is

emphasized in Fig. 7. The shaded band represents the results obtained for the fee alloys —

5083-0 aluminum, AISI 310, ASTM 453 and ASTM A637. This band is relatively narrow, with

—4 1/2

a transition in slope occurring at about Ak/E = 1.6 x 10 m . Two straight lines re- presenting the data are described by the equation:
da , ,AK.^

dN = ^

25 ir where A = 6.7 x 10 and b = 8 for the upper range of AK/E, and A = 9.3 x 10 and b = 4.3

b/ 2 for the lower range of AK/E. The units of A are (mm/cycle) / (m ) and b is dimensionless.

These equations approximate the growth rates of the four fee alloys within a faetor of

about + 2. Alternatively, a single equation:

i

= 8.6 x 10^5 if (8)

may be used to approximate the data over the entire range of Ak/E investigated, with some saerifice of aecuraey.

The alloys represented in Fig. 7 have widely varying tensile properties that were not

taken into consideration in normalizing the eraek growth data on the basis of AK/E. This

implies that properties sueh as yield and tensile strength are not particularly strong

factors influencing crack growth rates at 4 K, as demonstrated for other alloys at ambient

temperature [36,37]. The present results provide ample evidence that AK, Young's modulus,

crystal structure, and phase stability are the primary factors governing fatigue crack

growth at liquid helium temperature.

Summary

1. Stable fee alloys having high elastic moduli offered maximum resistance to fatigue

crack propagation at liquid helium temperature.

2. Several metastable austenitic alloys and alloys containing bee and hep phases

displayed inferior crack growth resistance at 4 K. AK

3. Tfie 4 K crack growth results for stable fee alloys were a similar function of — . The results for an aluminum-base, a nickel-base, and two iron-base fee alloys

can be approximated within a factor of about + 2 by a single equation:

da/dN = A(AK/E)^

where the constants A and b have values that depend on the range of AK/E.

92
References

1. R. K. MacCrone, R. D. McCammon and H. M. Rosenberg, Phil. Mag., 4_: 267 (1958).

2. R. D. McCammon and H. M. Rosenberg, Proc. Roy. Soc . A, 242 : 203 (1957).

3. D. Hull, J. Inst. Met., 86: 425 (1957).

4. L. P. Andreev and N. V. Novikov, Problems of Strength, No. 11: 45 (1971).

5. I. A. Gindin, Ya. D. Starodubov and M. P. Starolat, Ukrainian J. Phys., 18: No. 11.

1899-1905 (1973).

6. A. J. Nachtigall, S. J. Klima and J. C. Freche, J. Mater. JMLSA 2= ^25 (1968).

7. A. J. Nachtigall, NASA TN D-7532 National Aeronautics and Space Administration,

Lewis Research Center, Cleveland, Ohio (1974).

8. S. S. Manson, Experimental Mech. , ^: 193 (1965).

9. Standard method of test for plane strain fracture toughness of metallic materials,

E-399-74. Annual book of ASTM Standards, Part 10, (ASTM, Philadelphia, Pa., 1974).

10. R. L. Tobler, R. P. Mikesell, R. L. Durcholz and R. P. Reed, "Properties of Materials

for LNG Tankage," ASTM STP 579 (ASTM, Philadelphia, Pa., 1975).

11. C. W. Fowlkes and R. L. Tobler, submitted for publication to Engr. Mech. (1975).

12. G. Irwin, "Fracture," Handbuch der Physik, 6, (Springer-Verlag, Berlin, 1958) p. 551.

13. E. Roberts, Jr., Mater. Res. Stand., 9^: 27 (1969).

14. C. J. Gunter and R. P. Reed, ASM Trans. Quart., 55: 399 (1962).

15. D. C. Larbalestier and H. W. King, Cryogenics, 1_3: 160 (1973).

16. R. P. Reed and C. J. Guntner, Trans. AIME, 230: 1713 (1964).

17. J. F. Watson and J. L. Christian, ASTM STP 287, (ASTM, Philadelphia, Pa., 1960), p. 170

18. J. F. Watson and J. L. Christian, Trans. AIME, 224: 998 (1962).

19. D. Bhandarkar, V. F. Zackay and E. R. Parker, Met. Trans., 3^: 2619 (1972).

20. A. G. Pineau and R. M. Pelloux, Met. Trans., 5^: 1103 (1974).

21. P. C. Paris, "Fracture - An Interdisciplinary Approach," (Syracuse University Press,

Syracuse, 1964), p. 107.

22. P. C. Paris and F. Erdogan, J. Basic Eng. Trans. ASME, D 85: 528 (1963).

23. T. W. Crooker, Report NRL Prog. 25 (Naval Research Laboratory, Washington, D.C., 1970)

.

24. J. A. Feeney, J. C. McMillan and R. P. Wei, Met. Trans., 1: 1741 (1970).

25. L. A. James and E. B. Schwenk, Jr., Met. Trans., 2: 491 (1971).

26. E. R. Naimon, W. F. Weston and H. M. Ledbetter, Cryogenics, 14^: 274 (1974).

27. W. F. Weston, H. M. Ledbetter and E. R. Naimon, Mat. Sci. Engr., to be published (1975)

28. W. F. Weston, E. R. Naimon and H. M. Ledbetter, "Properties of Materials for LNG

Tankage," ASTM STP 579 (ASTM, Philadelphia, Pa., 1975).

93
29. H. M. Ledbetter, W. F. Weston and E. R. Naimon, J. Appl. Phys., to be published (1975).

30. A. I. McEvily, Proc. Conf. on Fatigue and Fracture of Aircraft Structures and

Materials, AFFDL-TR-7 0-144 , Wright-Patterson Air Force Base, Ohio, AD 719756 (1973).

31. G. T. Hahn, A. R. Rosenfield and M. Sarrate, Tech. Report AFML-TR-67-143,

Wright-Patterson Air Force Base, Ohio (1969).

32. R. C. Bates and W. G. Clark, Jr., Trans. ASM, 62^: 380 (1969).

33. N. E. Frost, L. P. Pook and K. Denton, Eng. Frac. Mech. , 3^: 109 (1971).

34. "Materials Research for Superconducting Machinery", National Bureau of Standards,

Boulder, CO., AD 780-596 and AD/A 004586, National Technical Information Service,

Springfield, VA (1974).

35. S. Jin, J. W. Morris, Jr. and V. F. Zackay, Advances in Cryogenic Engineering 19 , Ed. K. D. Timmerhaus, (Plenum Press, New York, 1972) p. 379.

36. J. M. Barsom, Trans. ASME J. Eng. Ind. , 93: 1190 (1971).

37. H. H. Johnson and P. C. Paris, Eng. Fract. Mech., 1: 3 (1968).

94
List of Tables

1. Alloy conditions, chemical compositions, and selected properties,

2. Crack growth rate parameters for alloys at 4 K.

List of Figures

1. Crack length — compliance curves for AISI 310 at 4 K.

2. Crack growth rates of titanium alloys at 4 K.

3. Crack growth rates of face-centered cubic alloys at 4 K.

-t. Crack growth rates of austenitic stainless steels at 4 K.

5. Crack growth rates of ASTM A553 at 300, 76 and 4 K.

6. Comparison of crack growth rates, normalized to Young's modulus.

7. Normalized crack growth rate scatterband of stable face-centered cubic alloys.
—I c

mp

ess o c

o Tj

>-i « ni

UJ 1

jCO pe

yj 0 5

O a Qlj c

X) < 0) .nd u 6

o

a,

d

o

d

. U ^ O !^

fva O

.o ^

O

O

O

Mo, inMo, Mo, U

o" o m 00 S ^ o Ni O o o u cn o• o o

(M

00 d d d o' o d o

o _ d

d

d •1-1 oo c

CT-' io CO W

CO

CO w S >

Cr,

ITl O

U

o i-l in o

(M O

in m o d d in d o' U d d ^ d o'

ro oo

oo" 2

a

00

t-' Oh" ^" w

r-H O

H CJ o E-i o o U( rt' d d Ui o

COo

a o

S d

^ P. O O

•ri O

^d

O 00 ; - o

^ d d

CO

I—

I

CO H

<;

o

00

p

o

CM

t

o

0) o

00 o

H

- J' U CO U

- Tt< in cr^ ^ O (M 00 d d d

• -f

in H ^ <

—( O 00

. in o

o

t>

d

- j2 O fvj

5 in in in O -4

3 C d 0)

. N U

4i>- -1-^ nj

(1) d <U

ni

ealed

ation

t

aged

nched ipered

ation

t

aged

c 1—

<

a

1—1 T!

cl 0 c4J 0 C

ni 01 10 ni

2; 00 d d <; d d d

T3

ni

XI

(UV

a

a

ni

<:

o

96
Table 2. Crack growth rate parameters for alloys at 4 K.

Alloy n C Crack growth region,

-3/2 MN • m

__

Ti-5Al-2. 5Sn 4.89 3.85x 10 18 < ^ ^ 29

9.56 3.04x 10""^'^15 < AK ^ 18

Ti-6A1-4V 4.08 7.49x 10"'^° 16 < ^ < 29

10. 0 6. 72x 10"'^'^ 12 < ^ < 16

AISI 304 3.78 2. 04xlO'-^° 23 < AK < 71

AISI 310 3.68 1.16x 10"'^° 28 < AK < 88

AISI 316 2.92 5,36xl0"^ 18 < AK < 77

ASTM A453 3.84 5.34x 10""^"^ 38 < AK < 88

8.87 3.33x 10"'^'^ 33 < AK <38

ASTMA553 5.31 1.72xl0"'^^ 21<AK<33

ASTM A637 4.16 1.77x 10""^^ 34<AK<93

7.43 1.06x10""^^ 29 < AK < 34

5083-0 4.5 6.76x 10""^° 13 < AK < 28

-14

8. 1 4. 59x 10 9. 8 < AK < 13

97
Fig. 1. Crack length -- compliance curves for AISI 3 J. 0 at 4 K.

98
1

\—I I I

I I

2 5 10 50

STRESS INTENSITY FACTOR RANGE, AK, m/u?^^

Fig. 2. Crack growth rates of titanium alloys at 4 K.

99

5 10 50 100

STRESS INTENSITY FACTOR RANGE, LK, m/m-" ^

Fig. 4. Crack growth rates of austenitic stainless steels at 4 K,

101
1 I—I I I I I

2

STRESS INTENSITY FACTOR RANGE, AK, m/m^'"^

ig. 5, Crack growth rates of ASTM A553 at 300, 76 and 4 K.

102
Fig. 6. Comparison of crack growth rates, normalized

to Young's modulus.

103
0.2 0.5 1 5 10x10

STRAIN INTENSITY FACTOR RANGE, AK/E, m^'^^

Fig. 7. Normalized crack growth rate scatterband of stable

face-centered cubic alloys.

104
The Fracture Toughness and Fatigue Crack Growth Rate of an Fe-Ni-Cr Superalloy at 298, 76 and 4 K*

R. P. Reed, R. L. Tobler, and R. P. Jlilcesell

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

ABSTRACT

Fatigue crack growth rate and fracture toughness data at 298,

76, and 4 K are presented for a precipitation hardenable, Fe-Ni-Cr

superalloy, ASTM A 453. Linear-elastic plane strain and J-integral

test techniques were applied using compact specimens. The crack

growth rate was significantly lower at low temperatures than at room

temperature. The toughness parameter, K^, and the critical value

of the J-integral, J-j-^-j were determined. K^^CJ), as converted from

J^^, decreased slightly with decreasing temperature. These results

represent the first low temperature fatigue crack growth rate and

fracture toughness data published for this alloy.

Key Words: Fatigue crack growth rate; J-integral; plane strain;

stainless steel; tensile strength.

IXTRODUCTIOy

Superconductivity is currently being exploited in prototype design and construction

of motors and generators. Since superconducting components are cooled with liquid helium,

a need exists for mechanical property data in this environment. One alloy that has ex- hibited high strength at low temperature is a precipitation hardenable, iron base (Fe-NiCr) superalloy, designated ASTM A 453. Until this time, no fracture data for this alloy

have been reported at 4 K. Therefore, this alloy was included in a program sponsored by the

Advanced Research Projects Agency ^'^^ to determine the fracture toughness and fatigue crack

growth rate of structural materials at 298, 76, and 4 K. At all test temperatures, valid

data were not obtained using standard compact specimen ASTM E-399-74 procedures and

validity criteria. Therefore, it was necessary to employ J-integral test techniques to obtain useful fracture toughness data. These techniques and data are discussed in this

paper.

The alloy A 453 is normally employed at elevated temperatures because it has ex- cellent high temperature strength, creep resistance and oxidation resistance. Applications include fasteners, turbine wheels and blades, after burner parts for jet engines,

and generator retaining rings. The alloy has been employed for cryogenic applications

related to aerospace. Face-centered cubic metals are excellent low temperature materials,

and this alloy contains sufficient Ni to stabilize the austenitic phase at cryogenic

temperatures. As a result, the alloy has been considered for nuclear rocket structures

requiring excellent mechanical properties in both the cryogenic and elevated temperature

regimes. The alloy has potential applications at 4 K. The austenitic 300 series stainless

steels are already in use in prototype superconducting machinery, and A 453 is a possible

alternative to these materials where a higher yield strength, alloy is required.

* This work is a contribution of NBS, not subject to copyright.

105
Cryogenic mechanical property data for this Fe-Nl-Cr commercial alloy have been

previously reported^''' These references provide conventional uniaxial tensile properties to temperatures as low as 4 K and some Charpy impact data to 20 K. Fracture

mechanics data have not been reported at cryogenic temperatures.

The mechanical properties of this alloy can be widely varied, depending on heat

treatment and cold working. At room temperature, the yield strength of solution treated

(3) material may be as low as 50,000 psi ; for 40% cold worked and aged material, yield

Strengths as high as 183,000 psi are obtained . At 20 K, the yield strength for these

conditions increases to values of 92,000 and 240,000 psi, respectively. As expected, the

ductility and impact energy decrease markedly for cold-worked material.

MATERIAL

The chemical composition of the Fe-Ni-Cr alloy, normally referred to as A-286* and

designated AISI 660 and ASTM A 453, is 24.97 Ni, 13.96 Cr, 2.23 Ti, 1.52 Mn, 1.30 Mo,

0.30 V, 0.19 Al, 0.05 C, 0.54 Si, 0.016 P, 0.007 S, 0.004 B, and balance Fe. This alloy

is paramagnetic, has an austenitic microstructure, and is strengthened by precipitation

hardening, he austenitic structure has sufficient nickel to remain stable, with respect

to martensite transformation, on cooling to 4 K. The aging process produces various

Intermetallic compounds, such as Ni^CTijAl), Ni^Mo (Fe,Cr)Ti, and those containing trace

impurities (e.g., Cr-Sn, Cr-Fe-C)

.

In fig. 1 the typical microstructure is shown. The austenitic grain size corresponds

to ASTM grain size number 6 (average grain diameter = 0.0507 mm). The average hardness is

(2) R^31, which is slightly less than the expected hardness of R^34 for the annealed and

aged heat treatment.

The alloy was received as a forged 11.4 cm square bar, which had been mill solution

treated at 1650°F for 2 hours and oil quenched. Subsequently, the individual tensile and

compact tensile fracture specimens were annealed (1650°F, 2 hours, oil quenched) and aged

(1350°F, 16 hours, air cooled).

EXPERIMENTAL PROCEDURES

Tensile Tests

(9) All tensile specimens were machined according to ASTM specification E8-69 . Each

specimen had a reduced section, 0.25-inch diameter (0.635 cm) by 1.5-inch long (3.81 cm).

The axis of each specimen was transverse to the original forging direction.

Tests were performed with a 10,000 lb (44.5 kN) testing machine at a crosshead rate

of 0.02 inch (5 cm) per minute, using a stainless steel cryostat as previously described

by Reed^''"^\ Testing in liquid nitrogen (76 K) was accomplished by immersion of the

specimen and cryostat in a single metal dewar containing the cryogen. Testing in liquid

helium (4 K) was accomplished with a double glass dewar arrangement, the outer dewar con- taining liquid nitrogen. Load was monitored with a 10,000 lb (44.5 kN) commercial load

cell. Specimen extension was measured with a standard clip-on, double beam extensometer

.

Fatigue and Fracture Specimens

Standard 1.50-inch (3.8 cm) thick compact specimens were machined in the TS orientation with respect to the original forging axis. The geometry and dimensional tolerances were according to ASTM standard E 399-72 but the notch configuration was modified to enable measurement of deflections at the loadline. The depth of the machined notch was

such that a/W =0.45.

* Tradenames are used in this report for clarity and in no way imply endorsement or recommendation by NBS

.

106
Low Temperature Fatigue Tests

Fatigue crack growth tests were conducted at 298, 76, and 4 K using a 20,000 lb (89

kN) servo-hydraulic test machine in the load control mode. The load was varied sinusoidally,

and the ratio of minimum to maximum load was maintained at R = 0.1. Cycling was conducted

at rates of 24 ± 4 Hz. No variation in crack growth rate was detected due to frequency

change in this range. Loads were measured to within 1% during dynamic testing by means of

a digital peak load recording device.

A fiberglass reinforced plastic dewar was used for testing at 76 K, and a double

dewar arrangement was employed for tests at 4 K. The inner helium dewar was fabricated

from vacuum insulated fiberglass reinforced plastic; the space between the walls contains

thin layers of aluminized mylar to reduce heat transfer by radiation. The outer dewar was constructed of foam insulated fiberglass and epoxy. The load frame is composed of two tubular stand off compression members. To minimize heat transfer by conduction, the upper

section of thermal gradient from 4 to 76 K was made of fiberglass reinforced plastic; AISI

304 stainless steel was used for the lower sections. The lower specimen grip of maraging

steel is pinned into the center of the bridge. The upper specimen grip, also of maraging

steel, is threaded and attached directly to a titanium alloy pull rod.

Specimens tested solely for fatigue crack growth rate data were subjected to a range

of stress intensities approaching K^. The majority of specimens were intended for subsequent fracture tests. On these specimens, crack growth rates were obtained between a/W

= 0.47 and a/W = 0.60, and the maximum fatigue stress intensity (K^) was limited to 0.6

Kq. During the final 3% of crack growth, the stress intensity factor was no greater than

0.36 K , thus the fatigue precracking procedure should not have influenced the fracture

data.

The change in crack length during crack growth rate tests was monitored by compliance

measurements. Direct measurement of crack lengths was not possible since the specimens

were inaccessible during cryogenic tests. The compliance method is advantageous for re- latively thick specimens because it is sensitive to crack length variations through the

thickness. Experimental crack length-compliance correlations were obtained at each temperature. The specimen compliance was determined experimentally and plotted for a variety

of crack lengths. Fatigue load changes were used to generate striations so that several

crack length-compliance observations could be obtained from each fractured specimen.

(12) Theoretical compliance curves, based on the solution given by Roberts , were not in

complete agreement with experimental findings. For a given load and crack length, the

compliance depends linearly on Young's modulus. Young's modulus and clip gage sensitivity

are both temperature dependent. The change in clip gage sensitivity as a function of

temperature was negligible, so that the shift in the compliance curve between 298 and 76 K

(13) can be attributed to a change in Young's modulus of 7% . There was not a measurable

change in the compliance curves between 76 and 4 K since the change in Young's modulus

(0.3%) is negligible over this temperature interval.

Crack growth rates were measured by plotting compliance on an X-Y recorder at intervals during the fatigue test. At the same time, the total number, N, of fatigue cycles

sustained by the specimen was noted. Using the experimental crack length compliance

correlation, crack length (a) could then be obtained to ± 1,5%. The crack growth rate,

da/dN, was determined by graphical differentiation of the "a" versus "N" curve. Since

crack growth rates may be temporarily retarded in going from a higher to a lower applied

load. Whenever such a change was made, the crack growth rate was allowed to stabilize

before data were considered valid.

(14) J-integral tests were performed using the procedure outlined by Landes and Begley

Three or more nearly identical specimens (having equivalent average crack lengths) were

tested at each temperature. The specimens were loaded to various increments of stable crack

extension and the tests interrupted. Specimens were pulled apart for analysis after a heat tinting treatment oxidized the exposed crack surfaces. Each value of J, as derived

107
from the area under the load-displacement curve, was plotted as a function of the measured

crack extension, Aa. The critical J integral, J-j-^j was obtained by extrapolation of the

J versus Aa plot to zero extension.

For the compact specimens described in this report, J was calculated from the

(14,15) relation:

J

= 2A

Bb '

where A is the area under the load-displacement curve to a particular value of extension,

B is specimen thickness, and b is the ligament length, W-a. The area A was measured

using a planimeter.

RESULTS AND DISCUSSION

Tensile

The yield and tensile strengths of this alloy and of other age-hardened^''"^ '^^^ and

(3) annealed conditions are shown in fig. 2 and Table 1. Notice that the strengths of the

alloy reported in this paper are on the low side. This is substantiated by comparison of

(2) hardness and yield strength values with producer data ; for 1350°F-16 hour aging, a hardness of R 34 and a yield strength of 110 ksi are reported. However, the yield and tensile

^ (19 23) strengths meet the minimum AMS specifications ' for the aged condition of bar stock,

which lists a minimum yield strength of 85 ksi and a minimum tensile strength of 130 ksi

for room temperature.

The data of fig. 2 are from five independent investigations, yet all conditions have

a similar temperature dependence. This leads to the conclusion that for this alloy, within

the limitations of conventional measurement accuracy, the temperature dependence of the

yield and tensile strength is independent of heat treated condition. The low temperature

yield and tensile strengths are predictable if the room temperature strength is known.

Fatigue

The fatigue crack growth rate results for the Fe-Ni-Cr alloy are presented in fig. 3. The crack growth rates are significantly lower at cryogenic temperatures than at room

temperature. However, there is essentially no difference in the rates at 76 and 4 K. The

crack growth rates at 4 K are relatively low, in comparison with other similar alloys

The A 453 alloy has an equivalent rate to AISI 310 and slower rates than the metastable

AISI 300 series austenitic steel grades. The reduced crack growth rates at low temperatures, compared to room temperature, seem to be typical of stable austenitic structures.

Reduced crack growth rates might be expected to result from increased work hardening

rates, yield strength. Young's modulus, and ductility, which these steels exhibit at lower

/ 1 £ \ temperatures . Additional discussion on low temperature crack growth rate characteristics

is found in the paper by Tobler and Reed^^^\

Fracture

Figure 4 shows typical load-displacement curves at 298, 76, and 4 K. At 76 K, the

first drop in load was accompanied by a barely audible "pop"; the load then continued at the same level until fracture occurred. The other two tests at 76 K were terminated

before an audible pop occurred, although displacement did take place fairly rapidly once

the maximum load of the curve was reached. At all the temperatures, the load-displacement curves were nonlinear. At 4 K, the load-displacement record was linear to about 0.8 P^,

but then curved slightly before reaching the maximum load. As indicated by heat tinting,

the nonlinearity was associated with stable crack growth.

108
The AST>! recommended criteria to establish the validity of potential K_ data (K data)

0 2 is the relation of specimen thickness and crack length to the ratio 2.5(-^^^) ; if this ratio

ys

is smaller th^n the dimensions 3 and a, then can be assumed to represent K^^. As Table 2 illustrates, the ratio is larger than the dimensions at all temperatures, thus these tests

cannot be used to obtain Therefore, to obtain K^^ data for this alloy with the available thicknesses, it was necessary to use J-integral test procedures.

The J-integral at 298, 76, and 4 K, as a function of the crack extension, is shown in

fig. 5. Each value of the crack extension represents an average of fifteen measurements with a traveling microscope, five measurements at the crack front center, and five

measurements at each of the two points midway between the center and edge of the crack

front. Macrophotographs of the three specimens used for measurements at 4 K are shown in

fig. 6. Crack extension was measured on the heat tinted part of the fracture surface.

J-j.^, the critical value of the J-integral just prior to crack extension, was calculated

from a best fit of the data points. These limits were determined by drawing straight

lines through the data points representing both maximum and minimun values at each temperature. It is obvious that for a more rigorous J^ characterization, additional data points ° IC are needed. Unfortunately the quantity of material was limited, allowing for the manufacture of only 10 specimens.

Table 3 tabulates the values of J, la, J-^p, and K_ ( J) , as converted from the critical

(15 21) value of the J-integral. Conversion was vxade according to the relation '

K,,(J) = ^ • J E_

1-v "IC

where E is Young's modulus and is Poisson's ratio. The values of t and from 300 to 4 K

(1 "^^ were determined for the as-received material and are summarized in Table 1. The limits

of J,^ were derived according to the manner just described; the limits of K_j.^(J) were obtained from the J^^ limits.

The values of J at each of the temperatures can be considered to be valid, according

(14,27)

to a tentative criterion proposed by Begley and Landes ; ir

a, B, D ^ a ^—^ , "^f low

where b is the ligament or uncracked length, i is between 25 and 50, and -^Tq^. the

average of the yield and tensile strengths. If J^, the parameter derived from the J-la

curve, does meet the above requirements, then it represents a valid J-j-^- Table 2 shows

that the dimensional requirements are easily met.

Plots of Kq and K_j.^(J), converted from Jj-^> as a fimction of temperature are shown

in fig. 7. The parameter Increases with a temperature decrease to 76 K and then

decreases between 76 and 4 K. K^^(J) changes little between 298 and 4 K. Note that the

Kq curve approaches the curve of K_j.^(J) as the temperature decreases from 76 to 4 K. This

trend is noted in the two ASTM validity criteria, also, (Table 2) as these ratios

P K max Q 2 {—— and 2.5 ( ^

) ) approach acceptable values at 4 K.

109
\

^

SUMMARY

Fracture toughness and fatigue crack growth rate data have been obtained for A 453

Fe-Ni-Cr alloy. The results may be summarized as follows:

(1) The crack growth rate of A 453 is lower at 76 and 4 K than at 298 K

and compares favorably with other austenitic stainless steel grades.

(2) The parameter K (J) , obtained from J-integral tests, showed a toughness

of about 110 ksi /in at all temperatures, decreasing very slightly at lower temperatures.

ACKNOWLEDGEMENT

The authors wish to thank R. L. Durcholz who assisted in testing and cryostat con- struction and improvement for the fatigue and fracture tests at 4 K. NOMENCLATURE

K.IC

J-integral

Aa

a

B;aW

b

A

N

da/dN

AK

a

ys

'^flow

EV

Critical plane strain fracture toughness as defined in ASTM E 399-74.

Load on load-displacement curve corresponding to the intercept of the 5%

secant line, as defined in ASTM E 399-74.

Stress intensity factor corresponding to P^.

Parameter proportional to the amount of energy required to extend a crack.

Crack extension.

Critical value of J meeting size requirements, derived from J vs. Aa curve. Candidate J^^ value subject to evaluation of size requirements.

Dimensionless factor used to evaluate J^.

Thickness of compact specimen.

Average value fatigue crack length of specimen measured from load line.

Width of specimen, measured from the load line, W = (a+b)

,

Uncracked ligament of specimen.

Area under load-displacement curve, to point where test was terminated.

Number of fatigue cycles.

Crack growth rate in fatigue test. Stress intensity range in fatigue cycle.

0.2% offset yield strength in tensile test. Tensile flow stress; the average of the 0.2% offset yield strength and

the tensile strength.

Young's modulus.

Poisson's ratio.

110
References

1. A. F. Clark, R. P. Reed, and E. C. van Reuth, "Materials Research for Superconducting

Machinery, I and II," AD 780-596 National Technical Information System, Springfield,

Va. (1974).

2. Armco Steel Corp., "Product Data - Armco A286", SA-1, Armco Steel Corp., Middletown,

Ohio (1966)

.

2. R. D. Masteller, NASA CR-72638 (N70-27114) Martin Marietta Corp., Denver, Colo.

(May, 1970)

.

4. C. J. Slunder, A. F. Hoenie, and A. M. Hall, NASA Tech. Memo TM-X-53578 (Feb. 20, 1967).

5. C. A. Schwanbeck, Topical Report to NASA by Lockheed Nuclear Products, Lockheed-Georgia

Co. LAC ER-10008 (1968).

6. J. W. Montano, Report IN-P and VE-M64-1, Marshall Space Flight Center, Huntsville, Ala.,

(Feb. 25, 1964).

D. A. Roberts, D. B. Roach, and A. M. Hall, Defense Metals Information Center Report

112, Battelle Memorial Inst., Columbus, Ohio (May 1, 1959).

8. J. W. Montano, "An Evaluation of the Mechanical and Stress Corrosion Properties of

Cold Worked A-286 Alloy," NASA-TM-X-64569 , (Feb. 12, 1971).

9. "Tension Testing of Metallic Materials", E8-72, Annual Book of ASTM Standards,

Part 31, (ASTM, Philadelphia, Pa. 1973).

10. R. P. Reed, Advances in Cryogenic Engineering , Vol. 1_ (Plenum Press, Inc., New York,

1962, Edited by K. D. Timmerhaus) p. 448.

11. "Standard Method of Test for Plane-strain Fracture Toughness of Metallic Materials,"

E 399-74, Annual Book of ASTM Standards, Part 10 (ASTM, Philadelphia, Pa. 1974).

12. E. Roberts, Jr., Materials Res, and Standards , 9^: 27 (1969).

13. E. R. Naimon, H. M. Ledbetter, and W. I. Weston, from Semi-Annual Report on Materials

Research for Superconducting Machinery AD 780-596, National Technical Information

Service, Springfield, Va (1974)

.

14. J. D. Landes, and J. A. Begley, Private Communication from J. A. Begley to R. P. Reed,

Cryogenics Division, NBS , Boulder, Colorado (1973).

15. J. R. Rice, P. C. Paris, and J. G. Merkle, ASTM STP 536, (ASTM, Philadelphia, Pa.,

1973) p. 231.

16. K. A. Warren, and R. P. Reed, "Tensile and Impact Properties of Selected Materials

from 20 to 300 K", National Bureau of Standards Monograph 63, (June 28, 1963).

17. J. F. Watson, J. L. Christian, and A. Hurlich, AD 276-148, Convair Astronautics

Rept. MRG-132-1, San Diego, Calif. (Feb., 1960).

18. Malin, C. 0. as reported in NASA SP-5921 (01), Technology Utilization Office, NASA,

Washington, D.C. (1970).

19. Aerospace Structural Metals Handbook, Vol. I., (Syracuse Univ. Press, March, 1963).

20. R. L. Tobler, and R. P. Reed, "Fatigue Crack Growth Rates of Structural Alloys at Four Kelvin" to be published in International Cryogenic Materials Conference Proceedings

(Plenum Press, New York, 1976).

ill
\

21. J. D. Landes, and J. A. Begley, Proc. of the 1971 National Sjrmposium on Fracture

Mechanics, Part II, ASTM STP 514, (ASTM, Philadelphia, Pa., 1972) p. 24. .

22. J. A. Begley, and J. D. Landes, Fracture Toughness , Proc. of the 1971 National

Symposium on Fracture Mechanics, Part II, ASTM STP 514, (ASTM, Philadelphia,

Pa., 1972) p. 1.

23. R. F. Muraca and J. S. Whittick, "Materials Data Handbook. Stainless Steel Alloy

A-286", N72-30463, Marshall Space Flight Center, Alabama (June, 1972).

112
Figure Captions

1. Mlcrostructure of annealed and aged A 453 alloy. Magnification = 200 x.

2. Tensile and yield strength as function of temperature for a number of similar

aged conditions for A 453 precipitation hardened alloy.

Curves A - 1800°F, 1.5 hr. Oil Q; 1350°F, 16 hr. Air cool, bar, ref. 16. Curves B - 1800°F, 0.5 hr. Oil Q; 1325°F, 16 hr. Air cool, sheet, ref. 17.

Curves C - 1800°F, 2.0 hr, Oil Q; 1350°F, 16 hr. Air cool, bar, this report.

Curves D - 1800°F, 1.0 hr. Oil Q; 1350°F, 16 hr. Air cool, bar, ref. 18.

Curves E - Solution treated, ref. 3.

3. Fatigue crack growth rate at 298, 76 and 4 K.

4. Load-displacement curves at 298, 76 and 4 K,

5. The J-integral as a function of crack extension at 298, 76 and 4 K.

6. Macrophotograph of the fracture surfaces of specimens tested at 4 K.

7. The toughness parameters, and K^^(J), plotted as a function of temperature.

List of Tables

1. Tensile properties of A 453 superalloy.

2. Dimensional criteria for valid K^^ and J^^^ of A 453 superalloy.

3. J-integral and converted K (J) of A 453 superalloy.

113
c o O -H

to CO - 3

(JO .H C 3

60o o

00 oo

<Ti cr\

m ^ m <T <}

in a\ vD vo

CN CM CO

a) <U

0)

M •H

•H c CO o o o O OO CO

CO <u ^ to

pi )_i 1

lO CN o IT) o^ to

0) 4-J <- CTN r-l r-~

O CO o H CO rH CNl rH CN CN c

(U 13C

'i CUo.

0) •d

tJO c

^s (U •H

CM

u to rt u CN <f 0^ H CO -d- CM M

O C/5 0) 00 00 00 iH d u-i O Q. T3 CO o rH CM CO U-1 B

iH iH .H

HH rH CU

0) •u •H H

(Uu3M

•H 00 OO U-) o Uh o\ o> 0^ CM

H CN CM rH 13C

ta

Id

8" ? rd 1 JS 60

O vO

d

CD' <:

H 0) o « CM 1 M • M [1, M x: r-l o CO

C 1 O 1 0 CM iH rH LO E 13

•H 1 1 1 CO rH

rH <U •H o o 0 O 'ri •H •a O O o -a CO CJ\ t>> a u-i u-i o m 00 0 \D CO 00 00 u B o .H iH iH < (Si >x> oM

II H -d

CO dl

M ,;<i

u 0

0< •a so rH %

(UH •H

M ts 4-1 o to CO 13 cu Pd U 4) 4-1 0 1 K o

)-l taex3

CO1

13C o

rH

a

O MH -H o

(TV

O CN

r~. CN o H

i:
+1

CM

+1 +1O

00

OINO

in00

<]

imoo mocNi in^cN I^OiHm omr-( ro<rcsl Or-HOO OOO OiHO

OOOO OOO OOO

un vO r~ O O CM

r-~ 00 lT) m

i£) 00in ^

m vD -dCM n ro o r«. <f in fO

o m 00

fO

cN <r in m vO 00 ro ON

B in o 1^

<a- H

in

II CN

XI

II <N d a • •H •H

r-t

o

1-4Xo

B ^ o

BO 00o

vD O

OO •

• O

—

CO C O

•H

CO

a.eH

00 00 00 00

On ON ON On

CNJ CNI CNl

VD O vD ^

r-^

115
41

Figure 1. Microstructure of annealed and aged A 453 alloy. Magnification = 200 x.

116
STRESS, Ksi

H-" ro u> o o o

o o

e 2. Tensile and yield strength as function of temperature for a number of similar

aged conditions for A 453 precipitation hardened alloy.

Curves A - 1800'F, 1.5 hr. Oil Q; 1350 "F, 16 hr. Air cool, bar, ref. 16.

Curves B - 1800**F, 0.5 hr. Oil Q; 1325 °F, 16 hr. Air cool, sheet, ref. 17.

Curves C - ISOO'F, 2.0 hr. Oil Q; 1350°F, 16 hr. Air cool, bar, this report.

Curves D - ISOO'F, 1.0 hr. Oil Q; 1350°F, 16 hr. Air cool, bar, ref. 18.

Curves E - Solution treated, ref. 3.

117
STRESS INTENSITY FACTOR RANGE, AK (N/m'^-m^)

5x10

-4

^ 10"^

o

<a.o

:^<;

a:o

UJ

10

-6

10

-7

5 10

T 1 I I I I I

5 10

1

1 Mill

8

1

1 I I M I

{ T 1 I 1 It I I •a -I

A -

ASTM A-453

• 298 K - 4 Specimens ^ 76 K - 3 Specimens

4 K - 3 Specimens

J i I I J \ i I I I I I

10

-4

10

-5

10

-6

u

>>u

to •a

cm

<

<

Q.Oa:

o.o

<:

a:

ot—

I

I—

<:

10 100

STRESS INTENSITY FACTOR RANGE, AK (ksi-in^)

Figure 3. Fatigue crack growth rate at 298, 76 and 4 K.

lis
DISPLACEMENT, cm

0 0.02 0.04 0.06 0.08

DISPLACEMENT, in

- Figure 4. Load-displacement curves at 298, 76 and 4 K.

119

121
(AoI—

I

00

UJ

CDo

a:

ZD

\—O

100 200

TEMPERATURE, K

Figure 7. The toughness parameters, K and K (J) , plotted as a function of temperature;

Q 1

122
NBSIR

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH IN SUPPORT OF SUPERCONDUCTING MACHINERY

ADVANCED COMPOSITES

R. E. Schramm and M. B. Kasen

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April, 1975
Contents : Advanced Composites

Page

1.0 Review 126

2.0 Phase I: Preliminary Work

2.1 Materials 126

2.2 Procedures 126

2.3 Results 127

2.4 Discussion 128

2.5 Conclusions 129

3.0 Phase II: Characterization of the Mechanical

Properties of Uniaxial Composites

at Cryogenic Temperatures

3.1 Introduction 129

3.2 Material 129

3.3 Procedures 129

3.4 Results 130

3.5 Discussion 1^0

3.6 Future Work 1^1

1 oi 4.0 Appendix I: Symbols

5.0 Appendix II: Parameters Calculated from Test Results

6.0 References '^^^

7.0 List of Figures ^-^^

8.0 List of Tables 1^^

124
Stmnnary: Advanced Composites

The experimental work in this program is being conducted in two phases. Phase I was devoted to a check of the instrumentation and procedures to be used for tensile-mechanical

property testing of uniaxial composites and included a preliminary evaluation of commercial,

state-of-the-art boron-epoxy and graphite-epoxy composites. Phase I has now been completed.

In Phase II (now under way) we will measure basic tensile and compressive properties of

five selected composites: boron-aluminum, boron-epoxy, and glass, graphite, and Kevlar-49*

in a NASA Resin 2 matrix. These data will be determined at 4 K, 76 K, and 295 K and will

be useful in the design of complex composite structures using luacromechanical analytical

methods. This report presents the detailed results of Phase I and includes some initial

data obtained with a boron-aluminum composite in Phase II.

* The use of trade names in this paper in no way implies endorsement or approval by

NBS and is included only to define the material.

125
1 . 0 Review

Comprehensive literature reviews in previous ARPA reports ' have covered the

mechanical and thermal properties of glass-filament- and advanced-fiber-reinforced

structural composites at cryogenic temperatures. These reviews indicated there were few

low temperature data - almost none at 4 K - but they did make it possible to select for our experimental program the most promising composites for cryogenic use. We arranged for

commercial suppliers to fabricate the following composites:

,5.6 mil Boron-6061 Aluminum

5.6 mil Boron-Epoxy

S-901 Glass-NASA Resin 2 Kevlar-49-NASA Resin 2 Type A Graphite-NASA Resin 2.

We will measure various mechanical properties (static tensile and compressive) for longitudinal (0°), transverse (90°), and crossply (+45°) filament layups. Other investigators

will measure dynamic mechanical and thermal properties. With these sorts of data, it will

be possible to compute design values for complex structures using macromechanical analytical

methods.

Phase I of the experimental program was preparatory in nature. After construction of

the cryostat came the assembly and testing of the electronics. The development of a workable grip system and simple specimen configuration was essential to allow us to perform a large number of tests within our time and money restrictions. The tensile testing system

that evolved consists of a straight-sided coupon with the ends wrapped in stainless steel screen and sandwiched between serrated titanium grip plates; pressure plates hold the

assembly together. Two commercial producers supplied us with some material so we could

both test the apparatus and obtain some preliminary values while awaiting the arrival of

(2) the composites listed above. The last report included the results of the first few tests.

2.0 Phase I: Preliminary Work

2.1 Materials

The graphite- and boron-epoxy composites evaluated in Phase I were state-of-the-art

products, not optimized for cryogenic service. They were obtained as uniaxial panels

from commercial suppliers, and radiography indicated they were of excellent quality. The

nominal fiber volume fractions were reported by the manufacturers to be 50% for the boronepoxy and 60% for the graphite-epoxy . The void content is less than 2%, typical of good

commercial production.

Material Supplier Plies Test Orientation

5.6 mil Boron-Epoxy A 4 longitudinal (0°)

5 . 6 mil Boron-Epoxy A 11 transverse (90°)

4.0 mil Boron-Epoxy B 6 longitudinal (0°)

Graphite-Epoxy A 6 longitudinal (0°)

Graphite-Epoxy A 15 transverse (90°)

2.2 Procedures

All tensile specimens were straight-sided coupons cut by a diamond circular saw, lubricated and cooled by a stream of water-soluble oil. Although the as-cut edges were

already very smooth, light hand buffing with emery paper was added to further minimize

edge imperfections that might cause premature failure. The longitudinal (0°) Specimens were 27.9 cm (11 in.) long by 1.3 cm (0.5 in.) wide by a nominal 0.076 cm (0.030 in.)

thick; the transverse (90°) specimens were about 15.2 cm (6 in.) long by 2.5 cm (1 in.)

wide by a nominal 0.203 cm (0.080 in.) thick. No end tabs were used.

126
Resistance strain gages monitored longitudinal and transverse strains. Before

mounting the gages, the specimen surface was lightly sanded and carefully degreased.

After application of a commercial cement recommended for cryogenic use, the strain gages were aligned with the center line of the specimen, clamped between pressure pads, and

cured overnight at about 345 K, well below the temperature at which the epoxy matrices had

been cured. A second gage, perpendicular to the first, was added whenever Poisson's ratio

was to be determined. For these preliminary tests, the atmospheric conditioning specified

by ASTM D3039-71T, Method of Test of Tensile Properties of Oriented-Fiber Composites , was

not strictly observed; however, all materials were exposed to 293-296 K at 30-40% relative

humidity for at least two days between the strain-gage cement cure and the tensile testing.

Just prior to the test, the grips were attached to each specimen in a separate alignment fixture. The resulting gage length was 15.2 cm (6 in.) for the longitudinal (0°)

specimens and 5.0 cm (2 in.) for the transverse (90°) specimens. This assembly was then

suspended in the test fixture by a pin and clevis at the upper and lower pull rods, and

the cryostat support system was enclosed by a dewar containing either liquid nitrogen

(76 K) or liquid helium (4 K) , the latter being shielded by an outer liquid nitrogen dewar.

Three different crosshead speeds produced strain rates of 0.01-0.03 min in the longitudinal

(0°) specimens and 0.02-0.04 min in the transverse (90°) specimens. Within this small

range and limited number of tests, no strain rate sensitivity was noted in either composite

type. For this set of measurements, the specimens were initially stress cycled in tension

to about 25-75% of their anticipated ultimate loads several times before loading to fracture.

In this way we could determine the repeatability of the elastic portion of the stress-strain

curve for each material.

2.3 Results

The results of each test and their group averages are presented in Tables 1-4. The

elastic moduli for both boron- and graphite-epoxy materials indicate a tendency to increase

as the temperature decreases; however, the data scatter is sufficiently large as to render

this effect uncertain. The highest modulus was obtained with the longitudinal (0°) 5.6

mil boron-epoxy, while the 4 mil boron-fiber composite had a modulus almost 19% lower at both 76 K and 4 K. The modulus of the longitudinal (0°) graphite-epoxy material was about

60% of the boron-epoxy of similar orientation.

The Poisson's ratios are significantly higher in the graphite-epoxy than in either of

the boron composites. Of the two sizes of boron fiber, specimens fabricated with the

larger 5.6 mil fiber produced slightly higher ratios.

The ultimate tensile strength data illustrate the large anisotropy of these materials.

Rotating the tensile axis of the composite from longitudinal (0°) to transverse (90°) changes

the ultimate strength by more than a factor of 20. Longitudinal (0°) properties primarily

reflect the properties of the fiber reinforcement, while the transverse (90°) properties

are mainly a function of the matrix and the fiber-matrix interface. Tensile strengths in

8 2 the fiber direction are very high, approximately 17.4 x 10 N/m (253 ksi) for the boron8 2 epoxy and approximately 13.1 x 10 N/m (190 ksi) for the graphite-epoxy materials at 76 K

and 4 K. Slightly higher strength values were obtained with the 5.6 mil boron-epoxy than

for the 4.0 mil fiber. Room temperature tests were not taken to fracture in Phase I; how-g

ever, the typical room temperature strength of the 4.0 mil boron-epoxy is about 13.0 x 10

N/m^ (188 ksi)^^^ and about 14.5 x 10^ N/m^ (210 ksi) for the 5.6 mill product (manufacturer's data), suggesting a significant strength increase in this material on cooling. The

(2) latter result was unexpected, since the results of the earlier survey indicated little

temperature sensitivity of strength properties for boron-epoxy in the cryogenic range.

Further testing of this material in Phase II will clarify the temperature dependence question. The manufacturer reports typical room temperature tensile strengths of about 14.7 x

8 2 10 N/m (213 ksi) for the graphite-epoxy materials used in Phase I, suggesting that this

material decreases in strength somewhat upon cooling. The latter is consistent with the

(2) results published in the literature survey.

127
The elongation at fracture is very small (< 1%) for both materials. Again it was substantially less in the transverse (90°) than in the longitudinal (0°) direction.

2.4 Discussion

As frequently is observed with composites, a small hysteresis loop appeared on the

initial loading cycle and disappeared on subsequent cycling in tension. This initial

hysteresis is usually attributed to isolated failure of some of the filaments, perhaps

at filament kinks. Except for the small hysteresis, these tests indicated complete

elasticity (no evidence of plasticity).

Figure 1 presents a schematic of the stress-strain characteristics of the two composite

types included in this program. With one exception, both materials and all configurations

displayed a simple straight line, as exemplified by the longitudinal (0°) boron-epoxy in

Figure 1. However, the longitudinal (0°) graphite-epoxy produced an initial slope, followed

by a second and higher slope. There is not a large difference between these slopes, but

they are distinct and reproducible. The change of slope occurs at about 20-30% of the

ultimate stress. This does not represent plastic yielding, as unloading of the specimens

at any point on the curve resulted in retracing of the curves back to the origin. The

authors do not presently understand the mechanism reflected by these two slopes. Primary

and secondary moduli have been noted previously in crossplied glass-polymeric composites

(3) where the knee between the two slopes is attributed to cracking of the epoxy matrix.

However, we know of no previous reports of double moduli in longitudinal (0°) composites.

Furthermore, when observed in glass-reinforced composites, the second slope is always

lower than the first, contrary to the present results. Clearly, the present phenomenon

is of different origin. One possibility is that the increase in slope (increased stiffness) reflects the straightening out of graphite filaments in the yarn bundles. Additional

information on this phenomenon will be obtained during further testing of graphite-epoxy

specimens during Phase II of the current program.

Tensile testing of uniaxial longitudinal (0°) composites is complicated by the necessity of gradually transferring the tensile load from the grips into the fiber reinforcement,

thus minimizing localized stress concentrations that cause premature failure of the specimen

outside the gage length. An "acceptable" fracture is defined as one in which the tensile

break initiates at least one specimen thickness away from the grips (ASTM D3039-71T) . Using

this criterion, there was only one unacceptable fracture among the thirty tests conducted

in Phase I. These results were very rewarding, as available information had suggested

that a 50-70% acceptable fracture rate might be expected, and this would have been prohibitively expensive at cryogenic temperatures. One other fracture was not included in the

averages, as noted on Table 3. The latter specimen inexplicably failed within the gage

length during the third cycle of the preliminary test sequence, failure occurring at a lower

load than the specimen had sustained in the two previous cycles.

The "good break" criterion was difficult to apply to the longitudinal (0°) graphiteepoxy specimens. This material failed catastrophically over the entire gage length, making

it impossible to accurately determine the location of the initial point of failure. Conversely, the longitudinal (0°) boron-epoxy fractures were irregular, but well defined. In all boron-epoxy specimens, one or more splits along the length of the specimen propagated

from the fracture site toward the specimen grips, frequently stopping before reaching the

grip. In these tests, no spurious transverse fractures branched from the longitudinal

splits. All transverse (90°) fractures were straight and sharp, indicating brittle fracture

of the epoxy matrix.

The experimental data of Tables 1-4 are reported as recommended by ASTM D3039-71T. The

coefficient of variation (CV) is the standard deviation stated as a percentage of the

average value. These values for the elastic properties in Tables 1 and 3 indicate both a very good instrumental precision and good material consistency after a few mechanical cycles,

i.e., the results indicate that the fiber-matrix bond had not degraded and that very few,

if any, of the fibers had broken. The spread in values from the separate tests itemized

in Tables 2 and 4 are reasonably consistent with that expected during tensile testing of

other structural materials.

123
2.5 Conclusions

This series of tests has shown that tensile tests can be performed on composites at cryogenic temperatures with a high rate of success. The simple, straight-edged specimen

without tabs in the grip system is acceptable. The mechanical and electronic instrumentation have been debugged and have proven to have sufficient reliability and more than

adequate sensitivity. The data of Phase I will aid in planning the Phase II tests and

have pointed to the interesting phenomenon of two elastic regions in graphite-epoxy

.

3.0 Phase II: Characterization of the Mechanical Properties

of Uniaxial Composites at Cryogenic Temperatures

3.1 Introduction

The five composites selected for the main body of this work are being fabricated by

two commercial companies so that they will be representative of the best production

techniques. Table 5 itemizes the final test materials for this program. This list is

(2) essentially that reported in the last report, modified at the request of the producing

company for their convenience in supplying the materials. The test matrix presented in

the last report remains essentially the same, altered only by a reduction from five to three in the number of specimens to be run for each combination of composite type, test

type, and temperatures. The latter is necessitated by delay in delivery of some composite

materials due to fabricating problems. If time permits, additional tests will be performed

at 4 K.

The fabricator of the three composites using the NASA Resin 2 matrix found extremely

low inter laminate integrity in the first set of composites produced, eventually tracing the

problem to incorrect preparation of the resin. This necessitated a complete remanuf acture

of the three sets of composite samples and inadvertently delayed the program. However, no problems were encountered with the boron-aluminum, which has been delivered and has now been

extensively tensile tested. The boron-epoxy material has also arrived and work has begun on

this material. The fabricator indicates all material will be delivered by the end of April.

The Phase II mechanical characterization data reported here are restricted to the boron

aluminum composite.

3.2 Material

Boron-aluminum is a high strength, high modulus composite. However, unlike polymermatrix composites, boron-aluminum has high thermal and electrical conductivities. Consequently, application of this composite in superconducting machinery will be very specializ

ed; possibly this composite may be used for the eddy current shield.

The boron-aluminum material was supplied in an F temper (as fabricated) . Nominal

thickness of the three orientations selected for tensile testing are noted below. The

nominal fiber volume fraction is 50%. The manufacturer will measure the volume fraction

and provide fabrication details later. Radiography did not reveal any voids.

Orientation P lies Nominal Thickness

(cm) (in)

0.109 0.043

0.246 0.097

0.178 0.070

3.3 Procedures

As in the Phase I work, all test specimens were straight-sided coupons; however, the

overall length of the boron-aluminum was reduced to 15.2 cm (6 in.) with the gage length

reduced to 5.0 cm (2 in.) for all configurations. These reductions are acceptable in view

of the higher strength and ductility of the aluminum matrix as compared to epoxy. Specimen

;1 width was 1.3 cm (0.5 in.) for the longitudinal (0°) tests and 2.5 cm (1 in.) for the

129

Longitudinal (0°) 6 Transverse (90°) 15

Crossply (+ 45°) 10
transverse (90°) and crossply (+ 45°) tests. The edge preparation and gage mounting were

as previously described. The aluminum matrix required no humidity or temperature conditioning before testing. A constant strain rate of 0.01 mln ^ was used for all boronaluminum tests.

3.4 Results

The results of the Individual tests and the group averages are presented In Tables 6 and 7. The Polsson's ratios and Intralamlnar (In-plane) shear moduli, calculated from

the test results, are presented In Table 8. Figures 2-4 are representative tensile stressstrain diagrams of the three orientations of boron-aluminum tested In this program.. There

was Insufficient yielding in the longitudinal (0°) specimens to permit determination of a meaningful proportional limit.

A particularly intriguing phenomenon is the repeated appearance of serrations as evidence of discontinuous yielding during testing of the transverse (90°) and crossply

(+ 45°) specimens at room temperature and at 4 K, and the complete absence of serrations

at 76 K. An additional peculiarity of this phenomenon is that the serrations are caused

by sudden elongation without appreciable load drop, in direct contrast to the serrated

yielding phenomenon in metals and alloys where the primary characteristic is the load drop.

The serrated yielding phenomenon will be investigated further.

The variations in elastic properties with temperature are illustrated in Figures 5-7.

Statistically there appear to be no differences between the 295 K and 4 K values. However, at 76 K there does appear to be a rather consistent minimum in all of the elastic

parameters. The and G values have been calculated from tensile data obtained from the

(5) crossply (+ 45°) specimens using the method of Petit (see Appendix 2).

The temperature dependences of the proportional limit, 0.2% offset yield strength,

ultimate tensile strength, and fracture strain for the boron-aluminum are presented in

Figures 8-11, respectively. The large scatter in the proportional limit data reflects the

difficulty in determining the point at which the stress-strain curves first deviate from

linearity. The 0.2% offset yield strength is much better defined.

In general, the ultimate and yield strength increase with a decrease in temperature.

The ultimate elongation of the crossply (+ 45°) shows a significant decrease as temperature

is lowered; however, the longitudinal (0°) and transverse (90°) orientations displayed a small increase in fracture strain on cooling.

3.5 Discussion

Reflecting the ductility of aluminum, this composite developed' a distinct yield point,

followed by plastic deformation in all but the longitudinal (0°) orientation. Because

of this, each test consisted of only one loading, to fracture. The crossply specimens displayed considerable necking at all temperatures. Since the strain gages failed at about

1% strain, to continue observing the stress-strain behavior and to determine elongation at fracture, the load-cell output fed a constant-speed strip-chart recorder and a two-pen

strain-gage recorder in parallel. Knowledge of chart speed, crosshead speed, and gage

length allowed estimation of strain over the entire stress range. The ultimate elongation

was also checked by displacement of lightly scribed gage marks on the specimen surface.

The gripping method described earlier worked well for all specimens, but a slight

modification was required for the longitudinal (0°) tests at room temperature. Here, the

specimen began to slip from the grips just before reaching the ultimate load. This problem- was solved by removing the stainless steel screen so the specimen was in direct contact with

the serrated titanium grip plates. Table 7 shows that the tensile coupon broke Immediately

adjacent to the specimen grip in three of the four longitudinal (0°) room temperature tests

and in one 76 K test; however, values obtained from the latter were equal or 1ft excess of

values obtained with "acceptable" fractures away from the grips. Conversely, the one transverse (90°) fracture immediately at the grip did appear to result in a low tensile

value. No failures at the grips were observed at 4 K.

130
3 . 6 Future Work

All of the material required for the mechanical property testing of boron-epoxy composite has been received, the test coupons have been cut, and the strain gages mounted. Testing of this material has begun. Shipment of the remainder of the boron-epoxy required for

thermal characterization and the three NASA Resin 2 matrix composites has been promised by

the end of April.

A fixture for compression tests is now completed, but has not yet been tested. Some

additional work will be required to determine the best specimen configuration and the best

gripping method.

4.0 Appendix I: Symbols

E^^ = longitudinal (0°) elastic modulus

~ transverse (90°) elastic modulus

= crossply (+ 45°) elastic modulus

v^2 ~ longitudinal (0°) Poisson's ratio

v^-j^ = transverse (90°) Poisson's ratio

= crossply (+ 45°) Poisson's ratio

G = intralaminar shear modulus

a^"*" = proportional limit; stress at which a stress-strain curve deviates

from elasticity, i.e., is no longer a straight line

ty

a = 0.2% tensile yield strength; stress at the intersection of the

stress-strain curve with a straight line having the same slope

as the elastic modulus and offset by 0.2% along the strain scale

a^^ = ultimate strength; highest stress attained on the stress-strain curve

e*"^ = ultimate elongation; highest strain attained on the stress-strain curve

Superscript 1 and 2 on E and V indicate the primary and secondary values calculated

from the first and second parts of the stress-strain curve for those materials that exhibit

a two-part elastic zone.

5.0 Appendix II: Parameters Calculated from Test Results

By combining the parameters measured for the three configurations (0°, 90° + 45°),

it is possible to calculate the transverse Poisson's ratio and the intralaminar (in-plane)

shear modulus

^22

^21 = ^12 ^ ^^'^ 2UE

G 8U-E

x where „ . „ . „ EU + E22 ^ ^^2Al

8(1-V^2^2l)

131
6.0 References

1) Kasen, M. B., "Advanced Composites," Seml-Annual Technical Reports on Materials

Research In Support of Superconducting Machinery , (1 Sept., 1973 to 1 March, 1974)

National Bureau of Standards - Advanced Research Projects Agency.

2) Kasen, M. B. and Schramm, R. E., "Advanced Composites," Seml-Annual Technical Reports

on Materials Research In Support of Superconducting Machinery - II , (1 March, 1974 to

1 Sept., 1974) National Bureau of Standards - Advanced Research Projects Agency.

3) Broutman, L. J. and Krock, R. H., Modern Composite Materials , Addlson-Wesley, Reading,

Mass., 1967, p. 375.

4) Advanced Composites Design Guide, 3rd Edition, Vol IV, Materials, Air Force Materials

Laboratory, Wright-Patterson Air Force Base, Ohio, January, 1973.

5) Petit, P. H. , "A Simplified Method of Determining the In-plane Shear Stress-Strain

Response of Unidirectional Composites," ASTM STP 460, Composite Materials; Testing

and Design , American Society for Testing and Materials, 1969, pp. 83-93.

i.

132
7.0 List of Figures

1. Typical stress-strain curves for boron-epoxy and graphite-epoxy composites. Note

deviations from linearity in the graphite-epoxy.

2. Typical stress-strain curves for longitudinal (0°) boron-aluminum at various

temperatures.

3. Typical stress-strain curves for transverse (90") boron-aluminum at various

temperatures

.

4. Typical stress-strain curves for crossply (+ 45°) boron-aluminum at various

temperatures.

5. Elastic moduli of boron-aluminum. Error bars reflect + one standard deviation.

6. Poisson's ratio of boron-aluminum. Error bars reflect + one standard deviation.

7. Intralaminar (in-plane) shear modulus of boron-aluminum calculated from the crossply

(+ 45°) stress-strain curve. Error bars reflect + one standard deviation.

8. Proportional limit of boron-aluminum. Error bars reflect + one standard deviation.

9. Yield strength (0.2% offset) of boron-aluminum. Error bars reflect + one standard

deviation.

10. Ultimate tensile strength of boron-aluminum. Error bars reflect + one standard

deviation.

11. Ultimate elongation of boron-aluminum. Error bars reflect + one standard deviation.

133
- Longitudinal (0°

)

'

Boron/ Epoxy / Graphite/Epoxy

// /-^

/y

j/y

y^

yy

//y/y

//^

STRAIN {%)

Figure 1. Typical stress-strain curves for boron-epoxy and graphite-epoxy

composites. Note deviations from linearity in the graphite-epoxy.

134
250

200

150

100

50

to

I—

).4 -0.3 -0.2 -0.1 0 (Perpindicular to Axis)

0.2 0.3 0.4 0.5

(Parallel to Axis]

STRAIN [%)

0.6 0.7 0.8 0.9

0

Figure 2. Typical stres s -strain curves for longitudinal (0°) boron-alunainum at

various temperatures.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

STRAIN (%) (Parallel to Axis)

Figure 3. Typical stress-strain curves for transverse (90°) boron-aluminum at

various temperatures.

135
00o

LU

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

1 1 I 1 I 1 1 1 1 1 1 — ~ 76 ~ 4 k4\ A4 K /

^ 76 K

295 K'*A 1 ^'''^ 295 K —

— \

Boron/Aluminum —

— ' Crossply [t 45°) —

i 1 1 1 ! i 1 1

—

- 70

60

50

40

COo

30

IX.

20

10

0

-6 -4 -2 0 2 4 6 8 10 12 14 16 18 (Perpindicular to Axis) (Parallel to Axis)

. . .. STRAIN (%)

Figure 4. Typical stress-strain curves for crossply (± 45°) boron-aluminum at

various temperatures.

O

l>0

100 150 200

TEMPERATURE (K)

Figure 5. Elastic moduli of boron-alumihum. Error bars reflect ± one standard

deviation.
0.50

0.45

0.40

0.35

0.20 i

0. 15

0.10

Boron/AI umi num A Longitudinal (0°) Transverse (90°

O Crossply (1 45°

21 (Calculated) —

1

50 200 250 300 100 150

TEMPERATURE (K)

Figure 6. Poisson's ratio of boron-aluminum. Error bars reflect ± one standard

deviation.

O

I

50

45

40

35

20

15

10

0

Boron/Al umi num

50 250

— 7

300

Figure 7.

100 150 200

TEMPERATURE (K)

Intralaminar (in-plane) shear modulus of boron-aluminum calculated from

the crossply (± 45°) stres s -strain curve. Error bars reflect ± one

standard deviation.

137
TEMPERATURE (K)

Figure 8. Proportional limit of boron-aluminum. Error bars reflect ± one standard

deviation. . .......
0 50 100 150 200 250 300

TEMPERATURE (K) Figure 10. Ultimate tensile strength of boron-aluminum. Error bars reflect ± one

standard deviation.

14

12 —

10 —

o

t—o

T T T

TEMPERATURE (K)

Figure 11. Ultimate elongation of boron-aluminum. Error bars reflect ± one

standard deviation.

139
8. 0 List of Tables

1. Tensile propierties of boron-epoxy composites (individual specinnens),

2. Tensile properties of boron-epoxy composites (averages of all tested

specimens).

3. Tensile properties of graphite-epoxy composite, Supplier A (individual

specimens).

4. Tensile properties of graphite-epoxy composite, Supplier A (average

of all tested specimens).

5. Selected composite test materials.

6. Tensile properties of boron-aluminum composites (individual specimens),

7. Tensile properties of boron-aluminum composites (averages of specimens

tested).

8. Pois son's ratios and intralaminar shear moduli calculated from tensile

prope rty data.

140
Table 1

Tensile Properties of Boron-Epoxy Composites

(Individual Specimens )

Elastic Modulus, E

(lo'^N'm^) no^psi)

Poisson's Ratio

CV(%)t ICV(%)

Ultimate Strength, a (10^N'm^)|(10^psi)

lu Ultimate

Elongation

(%)

238(0. 5)

249(0, 4f

229(0, 6)

228(0. 6)

237(0, 0)

252(0. 6)* 243(0. 6)

237(0. 7)

222(0. 6)

219(0. 5) 220(0. 6)

226(0. 7)

224(1. 8)

216(0. 8)

39(1. 0) 41 (1, 0)

39(1.2)

46

43

46(0, 3)

34. 5(0. 06)

36. 2(0. 07)

33. 2(0. 10)

33. 1(0. 09)

34. 2(0. 00)

36. 6(0. 10) 35. 2(0. 10)

34. 3(0. 10)

32. 2(0. 08)

31, 7(0. 08)

31. 9(0. oa)

32. 8(0. 09)

32. 5(0. 25)

31. 4(0. 11)

5. 6(0. 10)

5. 9(0. 08)

5. 6(0. 17)

6. 7

6. 2

6. 7(0. 05)

Longitudinal (OP ) Supplier A

0. 2

0.2

0. 3

0. 3

0. 0

0. 3

0. 3

0. 3

0. 236 (0. 001)

0. 256 (0. 010)

0, 249 (0. 002)

0. 250 (0, 001)

0. 261 (0. 006)

£

0. 248 (0. 002)

0. 255 (0. 004)

0. 5

4. 1 0. 7

0. 4

2. 2

0. 6

1. 6

Longitudinal (CP ) Suppl

0. 2 0.3

0, 3

0, 3

0, 8

0. 4

0. 243 (0, 001)

0. 254 (0, 001)

0.'239 (0. 002)

0. 231 (0. 001)

0. 230 (0. 008)

0. 238 (0. 001)

0. 2

0. 4

0. 7

0. 5

3. 5

0. 5

( 5. 6 mil fibers

)

b

17. 7 18. 0

16. 9

18. 8

17, 8

17. 9

256 0. 78

261 0. 79

245 0. 73

273 0. 74

258 0. 74

259 0. 7 6

ier B (4. 0 mil fiberj)

17. 6

16. 4

15. 6

18, 7 17. 4

17, 2

255

237

227

270

253

250

0. 81

0. 75

0. 84

0. 83

0. 78

0. 80

Transverse (9(f ) Supplier A (5. 6 mil fibers)

0. 7

0, 82

0. 72

0. 78

0. 52

0. 43

0. 65

|l2. 0 0. 19

10. 4 0. 15

11. 2 0. 19

7. 5 0. 12

6. 2 0. 14

9. 5 0. 14

^Standard deviations (in parentheses) and coefficients of variation (CV) given

for data from three or more loading -unloading cycles

^ Specimen not fractured

Previously cycled at 295 K

d Fractured in grip

® Previously cycled at 295 K, then at 76 K

^ Transverse strain gage malfwuictioned

^ Fractured during first loading

141
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iH 3 4-1 •H 03 •3 O

0) c c ^—\ o •3

!-i •H

U

1—1 .-1 rH iH

H 4-1 CO 03

g

C CO iHa s a) •H (31 CO •H a3 6 U iH

TJ CO a. 3 iH e 0) u > CO o i

•Hw c

csi 03a

03 tsS tn \CO a^

.H -;) 00

1-i CO O .-I 0^ > I O ^1

>> • cH m o

vO ~c s O 3

iH

C

O -H a e3

r-l rH

•H < e

•H 03 ^4

O 4-1 60 C C CO O M

l-l 4-1

CO CO X X

CO CO c c P S3

C r-l •H CO3

•H

0) -o 3 3

CO 4-1 r-i -H o. oc 1 3 d o d 0) H 03 33 <U4-1 > H 03 M C J ^

03 S3

145
Table 6

Tensile Properties of Boron -Aluminum Composites

(Individual Specimens)

Temperature

(K)

Elastic Moc

9 2 (10 N/m )

ulus, E

(lO^psi)

Poisson'

s

Ratio, V Proportion Lin

(lO^N/m^)

lit, rf

(lO^psi)

0. 2% Yielc Stre

(lO^N/m^)

1 ty

ngth, CT

(lO^psi)

Ultimate

Streni

(lO^N/m^)

tu

!th, a

3 (10 psi)

Ultimate

„, tu Elongation, e

(%)

Longi tudinal ((3°)

1295^ 195 28. 3 0. 320 12. 4 180 0. 6 295 194 28. 1 0. 280 12. 7 184 0. 6 295^ 1 94 28. 2 0. 275 13.2 191 0. 6 295a 217 31.4 0. 320 12. 5 175 0.6

76 186 27. 0 0. 345 16. 9 245 0. 8 76 196 28. 4 0. 344 15. 8 230 0. 7 76 2 08 30. 1 0. 335 16. 5 239 0. 8 76^ 196 28. 4 0. 351 16. 0 233 0. 8

4 211 30. 6 0. 313 14. 9 217 0. 7 4 207 30. 0 0. 358 16. 9 245 0. 8 4 191 27. 7 0. 343 16. 0 231 0. 8 4 206 29. 9 0. 360 16. 4 238 0. 8

Transverse (90°)

295 165 24. 0 0. 67 9. 7 1. 38 20. 1 1. 74 25. 3 0. 8 295 177 25. 7 0. 54 7. 8 1. 80 26. 1 295 142 20. 6 0. 67 9. 7 l'. 29 18. 7 1. 46 21. 1 0. 6

76a 101 14. 6 0. 92 13. 3 1. 86 27. 0 2. 29 33. 2 0. 8 76 155 22. 5 0. 75 10. 9 1. 67 24. 3 2. 57 37. 3 0. 8 76 138 20. 1 0. 65 9. 4 1. 94 28. 2 2. 47 35. 9 0. 8 76 116 16. 8 0. 72 10. 5 1. 66 24. 1 2. 42 35. 1 0. 9

4 180 26. 2 0. 50 7. 3 1. 97 28. 6 2. 79 40. 5 0. 9 4 152 22. 1 0. 80 11. 6 2. 05 29. 7 2. 73 39.6 0. 8 4 118 17. 1 0. 86 12. 5 1. 87 27. 1 2. 76 40. 0 0. 9

Crossply (± 45°

295 1 12 16. 2 0. 27 3. 9 0. 90 13. 0 3. 62 52. 4 13, 6 295 100 14. 5 0. 417 0. 68 9. 9 1. 01 14. 6 3. 92 56. 9 295 120 17. 3 0. 375 0. 17 2. 4 0. 92 13. 3 3. 32 48. 2 10. 6

76 61. 8 9. 0 0. 313 0. 08 1. 2 1. 52 22. 0 4. 11 59. 6 4. 6 76 71. 8 10. 5 0. 361 0. 20 2. 8 1. 44 20. 9 4. 64 67. 2 8. 8 75 99. 0 14. 4 0. 325 0. 16 2. 3 1. 09 15. 8 3. 66 53. 1

4 109 15. 9 0. 405 0. 48 6. 9 1. 40 20. 3 4. 25 61. 7 3. 2 4 1 1

1

16. 0 0. 378 0. 26 3. 7 1. 20 17. 4 4. 06 58. 9 4. 1 4 84 12. 1 0. 337 0. 18 2. 7 1. 41 20. 5 4. 02 58. 4 5. 2

Fractured at or in grip

r46
3 i

ao

3.17.7

14. 3

7.2

6.4

12. 4

31. 3

23.8

Ultimate

Elongatii

IOI.\~ o o o o o I!^ ^

' sx>oooo r-Qoo^ -^r*-tvj

O* O O O O O OJ sO

> ^ro o^^^ pncoo

ro in o m ^ od f*i

Strength,

(

(10^psi)( <-< in --H 00 —. (M fsj -4* o Tf' r-" ^' 00^ -^.^ -

— — rg^o inorCOflfO 00 m ...vO O f\)00 ...

—'(Mp^j cvjro^ insDin

0) —

6 1

S 2

D o

— .— oooom ocr-(Nj o o o o o o' o o

—< r^cT^NO (Nj *^—

1

... so -H -H

t—t —H (Nl r\J CO...^ ^

^ >

00 sD (NJ CO

<*i r- ^ nD no' c3o"

Id

Strength o ro cr- fo O iM ^ O rO

lD sO

in 00* m <> (T- ^ (M {NJ ^ ^ ^

v —

>< E ^ 2

d o

in rji m (vj O —< O O f\J -H o o o o o o

00 so in

rO O O fn ro

<=>... ^ . ^ <r-.-iLnNO,jirooo

C t/i S D.

c

aJ^soco^ooorg

•"ti ^ ^ (SJ ^ O fM* f

n „ o ir 2 ^_ -

-' ,*^a~-^o'^«n(M'^* H ^ ^ U

0 _

§- 2

00

a. o

X r-H a- r- sO O ^ ^ (NJ o ^

o o* o o o o

fo ^0 f\i in —

I

^ fo —i o" o o o o* o

? g

o" >

(Nj ^ fO CO in rg CO ^ vO in (7-

Poisson's

Ra

(M O f\J (M fvj to o o o o o o

o' o o o o o

<y^ —* rf vO rO fO

ro

rg ro fO CO ro fO o o O O* O* O

" Si

^sOrO Ot^QC OCOO^

^ in Tji .-H 00 o" V .-H « fVj (M ^

lie

Modulus (lO^psi) o rn >£)in^ ^ootM

^ ^ ^ ro cn' (Nj (\j otnso ^inoo Ofor^

cr^GOO^ roco-—' ^ r-t rsjrjfM <\j'-H(Nj

W (M JS E " 2o

o

—^^o^ <—1„ co^<-t ooin f-^rjro or-Tf ooo i-Hooo ^00^ o<Njin -""r-o fM"-irsj —.-^^ ^ _

Temperature

(K) inso^ inxo-* in^o-^

rvj (NJ rg

4J M

C9 -fct

I 147
Table 8

and Intralaminar Shear Moduli of Boron- Aluminum Composite

Calculated from Tensile Property Data

Temperature Poisson's Rat

CV(%)

Intralaminar

9 2 10 N/m

Shear Mo

lO^psi

dulus, G

CV(%)

295

76

4

0.241

0.222

0.253

14.9

19.6

22.2

35.8

23.6

31.6

5.15

3.43

4.61

17.4

31.6

26.6

148
NBSIR

SEMI-ANNUAL REPORT ON MATERIALS RESEARCH

IN SUPPORT OF SUPERCONDUCTING MACHINERY

ELASTIC PROPERTIES OF ENGINEERING MATERIALS

AT CRYOGENIC TEMPERATURES

H. M. Ledbetter and W. F. Weston

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1975
1 Summary; Elastic Properties

During the current year, the elastic properties of a variety of materials are being

studied between room temperature and liquid-helium temperature. Studies on some materials

are now complete; others are in progress. Two accompanying manuscripts describe some of

the completed studies. The status of all current studies is briefly as follows:

(1) Oxygen-free copper . Experimental work and data analysis are complete. Present

results agree well with those of previous studies. This data is essential for analyzing

the behavior of copper-base alloys; two alloy systems are discussed below — copper-nickel

and copper-tin — and the results for oxygen-free copper will be included in the reports

on these alloy systems.

(2) Composite materials . Because composite materials are candidates for components

in superconducting machinery, a study of the elastic properties of composite materials

is needed. Because of the conspicuous lack of elastic data on composite materials, the ^ goal this year was to determine the feasibility of measuring the elastic properties of a composite material using a resonance method. Because of acoustic attenuation and dispersion,

pulse-echo methods are unusable. Conventional static tests have the disadvantages of

large specimen sizes, high refrigeration costs, and less accurate results. The material

selected for this first study was a copper-stabilized niobium-titanium wire embedded in a

f iberglass-epoxy matrix. This material has five independent elastic constants. (Polycrystalline aggregates have only two independent elastic constants.) This attempt

succeeded, and the results are described in the accompanying manuscript: "Elastic constants

of a superconducting-coil composite material." This study represents one of the few determinations of the elastic constants of a composite material by a resonance method. It is

the first determination of the complete set of elastic constants of such a material at

liquid-helium temperature.

(3) Inconel 718 . All work on this material is complete. Results are described in

the accompanying manuscript: "Low-temperature elastic properties of a nickel-chromiumiron-molybdenum alloy." This material is similar elastically to Inconel X-750, which was described in a previous report in this series. It is slightly softer elastically than

Inconel X-750. At least above liquid-nitrogen temperature, it does not undergo a magnetic

transition like those that occur in both Inconel 600 and Inconel X-750.

(4) Copper-nickel alloys . Most of the experimental work on these alloys — commercialgrade copper-10 nickel and copper-30 nickel — is complete. Most results were obtained by

a resonance method, although some pulse-echo results were also obtained. Surprisingly,

both materials are magnetic, due presumably to trace impurities of iron. Basically, both

materials are regularly behaved elastically, but they do show some peculiarities.

(5) Titanium-niobium alloys . These alloys were supplied by F. Jelenik at Battelle;

they have compositions of 5, 10, 20, 22, and 25 at. pet. niobium. While the experimental

results are still preliminary, these alloys show abnormal elastic behavior. The Young's

modulus varies strongly with composition in the low-niobium region. The change in elastic

constants between room-temperature and liquid-helium temperature is unusually large.

(6) Copper-tin alloys . Experimental studies have not yet begun on this system.

(7) Invar . Invar was studied in last year's program using a pulse-echo technique, and

the results were given in a previous report in this series. To better understand the very

unusual elastic behavior of this material, some additional studies were made — resonance measurements between room temperature and liquid-helium temperature. A manuscript describing

these results and reviewing previous elastic studies on invar is in progress and should

appear in the next report in this series. Note: Because of a wrong mass density, the values

of C^, E, G, and B reported previously for Invar are all too high by a factor of 1.1045. The

values of V reported are correct since they do not depend on the mass density .

150
Low-Temperature Elastic Constants of a Superconducting Coil Composite*

W. F. Weston**

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Abstract

A resonant piezoelectric oscillator method for measuring elastic

moduli was applied to composite materials. The complete set of elastic

compliances of a superconducting coil composite was determined semicontinously between 4 and 300 K. Also, two moduli of a layered fiberglass-epoxy composite were determined; this composite is essentially

the matrix material of the coil composite. The Young's moduli, shear

moduli, Poisson ratios, and elastic stiffness coefficients are also

reported. Results agree closely with elastic data obtained by conventional

testing methods.

Key Words: Bulk modulus; composite; compressibility; elastic compliance;

elastic stiffness; piezoelectric oscillator; Poisson's ratio;

shear modulus; Young's modulus.

^Contribution of NBS , not subject to copyright.

**NRC-NBS Postdoctoral Research Associate, 1974-5.

151
Low-Temperature Elastic Constants of a Superconducting Coil Composite

I. Introduction I

The elastic properties of composite materials are currently of considerable

interest. Many composites, because they have high mechanical strength and a higl:

modulus-to-density ratio, are useful as strong, lightweight structural materials.

Some composites have been designed for use at low temperatures, for example as

superconducting coils for high-field magnets. However, few elastic data are

available for composite materials, particularly at low temperatures. To the

author's knowledge, no complete sets of elastic data are available for composite

materials at 4 K. Such data are useful as design parameters, and elastic

constants are among the most accurately known fundamental physical properties

of solids.

Because composite materials are usually highly anisotropic, the determination of their elastic constants is much more difficult than for the more

usual quasi-isotropic engineering materials. Conventional methods of measuring the elastic properties of solids have been applied to composites with only

limited success. These methods usually require relatively large specimens

and considerable time and effort, especially if a complete set of elastic

constants is required. These methods, as applied to composites, include

- 2,3 ^ 4,5,6 . 1,7,8 vibrating or resonant-beam tests, tensile or compressive tests,

19 1 10 11 12 13 torsion tests, ' bending tests, ' and pressure tests ' ' . Generally,

the elastic constants measured by these methods are less accurate than those

acquired by ultrasonic tests.

152
Ultrasonic pulse techniques are limited by the necessity of using wave-lengths

that are large compared with fiber diameters and at the same time sufficiently

small compared with the dimensions of the specimen so that true plane-wave conditions can exist. Since ultrasonic pulse methods are typically perfomed at megahertz frequencies, this condition cannot be met for many composites. If the wavelength is not larger than the fiber diameter, the wave is attenuated and scattered.

Ultrasonic pulse-echo methods have been applied to some metal-matrix composites

with extremely small f ibers . ''"^ ' ''"^ '"^^ Even in these cases the pulse-echo trains

are poor because of high attenuation and dispersion''"^. In fact, Achenbach and

Herrman''"^ predicted large dispersive effects for shear waves propagated in the

fiber direction, even when the wavelength is much larger than fiber diameters.

18 Zimmer and Cost verified this prediction by measuring sound velocities in a

unidirectional glass-reinforced epoxy-fiber composite. For wavelength-to-fiber

diameter ratios of roughly 50, dispersion increased some phase velocities by a

factor of 2. Elastic constants of some carbon-fiber-reinforced plastics have

19 20 21 also been measured by ultrasonic pulse-echo techniques. '

'

Attempts to use 10 MHz pulse echo techniques on the composite studied herein

were unsuccessful. Both longitudinal and shear waves were propagated along all

orientations and produced no detectable echoes. This is understandable since the

filament sizes for this composite, as described in the text, are larger than

the sound wavelength. Larger specimens than are currently available would be

needed for 1-5 MHz pulses, although it is doubtful that even these frequencies

would produce useable echo patterns for this material.

22

The ultrasonic immersion technique, as described by Markham, is fast and

accurate and offers the possibility of measuring all the elastic properties

on one specimen. However, this technique is also limited by fiber size and by

23 24 sample dimensions. ' The choice of ultrasonic modes that can be propagated

in a given direction in a specimen is also limited, and the technique is

inapplicable to low-temperature measurements.

153
25

Zecca and Hay avoided the problems encountered with megahertz frequencies

by using electrostatic transducers to generate and to detect resonant kilohertz frequencies of a metal-matrix composite. Electrostatic transducers,

however, cannot be used with non-metallic materials.

The most widely used ultrasonic technique, using kilohertz frequencies,

is the resonant piezoelectric oscillator. This method is due principally to

2 6 Quimby and associates. Quimby thoroughly analyzed the vibrations of solid

27

rods driven by a piezoelectric crystal, and Balamuth first employed drivers

' '

'

' " ' 28

and specimens of matching fundamental frequencies. Rose extended this method

to torsional oscillators. Basically, the piezoelectric properties of quartz

are used to generate and to detect resonant frequencies of an oscillator consisting of one or two quartz crystals, a specimen, and perhaps a dummy rod, all

cemented together. This method has been used to measure elastic moduli at both

29 30 27 28 30 31 high ' and low ' ' ' temperatures, and has worked well with both

32 33 27-31 ^ metals ' and non-metals. Thus, this technique is well understood both

theoretically and practically, and it would seem to be well suited for testing

composites. The long wavelengths used (typically on the order of centimeters

in the kilohertz region) are much larger than fiber diameters, and, since the

technique employs standing waves rather than traveling waves, specimen sizes

can still be kept small.

In the present paper it is described how this resonance technique was used

to measure the complete set of elastic compliances of a superconducting coil

composite, which was essentially composed of an epoxy matrix and unidirectional

copper-niobium-titanium fibers. The compliances were measured semi-continuously

from 300 to 4 K. Results are given also for an epoxy-f iberglass layered composite.

The results generally agreed closely with the few existing static measurements

on the same composite. - -

154
2 . Experimental Procedure

A. Resonant Piezoelectric Oscillator

The three-component resonant piezoelectric oscillator technique was

34 35 originally described by Marx , and was discussed in detail by Fine . The

technique consists of bonding quartz-driver and quartz-gauge piezoelectric

crystals to a specimen to produce and to detect a standing longitudinal (or

torsional) resonant wave. Each component's length is adjusted so that its

resonant frequency is closely matched to that of the other components. The

system is then driven by the driver transducer at its resonant frequency, which

is monitored by the gauge crystal.

Longitudinal waves are excited by a-quartz bars of square cross section,

excited into longitudinal vibration by an ac signal applied to full-length,

adherent electrodes (see Fig. 1). The driver quartz was fully gold plated on

two parallel sides (z-faces) with a shallow notch cut in the center of each

electrode. Fine, gold-plated tungsten wires, seated in these notches, served

to suspend the resonator assembly at displacement nodes and provided the

necessary electrical contact. The gauge quartz was gold-plated only over the

center third of the two parallel faces and electrical contact was made through

fine wires adhered into the notches with silver conducting paint. The electric

axes of the driver and the gauge crystals were perpendicular to reduce electrical

i pickup.

The longitudinal oscillator apparatus is illustrated in Figure 1. The

(j driver-quartz crystal was suspended by 0.003 in gold-plated tungsten wires.

The driver mounts, which were aluminum, were removed during the torsional

measurements, since the torsional driver crystal was suspended between the

bakelite posts by nylon threads. The specimens were cylindrical for all measure-

' ments. The chromel-constantan thermocouple was placed near,, but not touching, the

specimen. The entire apparatus was sealed in a thin-walled stainless-steel can.

The can was partially evacuated, placed in the ullage of a helium dewar and

lowered stepwise to achieve cooling.

155
The torsional quartz crystals were circular cylinders with their length

in the x-direction and with four gold-plated electrodes running the length of

36

the crystal. Opposite pairs of electrodes were electrically connected. The

driver quartz was suspended vertically by means of fine nylon treads attached

with varnish to opposite sides of the quartz near a displacement node of vibratioi

The quartz crystals were bonded together with a semi-permanent adhesive,

37

Eastman 910. The specimens were right-circular cylinders and were also bonded

to the gauge quartz with the same adhesive. For some torsional experiments, this

cement occasionally failed at low temperatures; such experiments were repeated

vmtil successful. Other materials such as vacuum grease and epoxy resin have

38

been used as low-temperature bonding agents.

The quartz crystals used had resonant frequencies of 60 and 100 kHz. Most

of the measurements were done with the 60 kHz quartz crystals (3/16 in square

cross for longitudinal, and 3/16 in diameter for torsional), but some were

done with the 100 kHz crystals (1/8 in diameter) . The mass of each driver-gauge

combination was noted and the resonant frequencies were monitored from 300 to

4 K. The length of each specimen was determined such that its resonant

frequency for the entire temperature range was within approximately 5% of the

oscillator assembly although in some cases the specimen frequency differed by

as much as 10%. The mass, length, and diameter of each specimen were noted

and its mass density was determined by Archimedes' method 'using distilled water

as a standard. The specimen was then cemented to the quartz crystals and the

resonant frequency of the oscillator was monitored from 300 to 4 K. No thermal

conLi action corrections were made; for the coil composite described below this

39 Introduces a maximum error (over a 300 K range) of about 0.5%. Maximum

uncertainties in the frequency measurements are estimated to be about one

part in^lO^.

156
B. Electronics

Most workers who have used the piezoelectric oscillator technique have

34

employed electronics similar to those described by Marx. This system requires

manual adjustment of the input frequency to the driver crystal to keep the

oscillator at resonance. A less time-consuming and more accurate system is

40 41

the regenerative system designed by Gerk and slightly modified by Johnson.

Gerk's system consists primarily of a closed loop containing an amplifier

and the driver-gauge combination of piezoelectric crystals, which act as a

resonant element, with a feedback circuit to control the gain of the amplifier.

This system is based on the principles of an oscillator; that is, the output

of an amplifier is fed into the input through a frequency-selective network

(the quartz crystals) . The phase shifts are corrected with a variable phase

40 shifter. A more complete description of the system was given by Gerk.

This system locks onto the resonant frequency and automatically stays at the

resonant frequency if this frequency changes, due to a change of the specimen's

environment, for example.

157
C. Specimens

The superconducting coil composite is fully described in reference 39.

Basically, the coil is composed of a copper-stabilized niobium-titanium wire

(0.56 mm by 0.72 mm cross section) coil impregnated with epbxy. The wire

layers are separated by layers of dry fiberglass cloth (0.1 mm thick). The

copper-to-superconductor volume ratio of the wire is 1.8 to 1. The wire-toepoxy cross-sectional area fraction is about 3 to 1. The coil dimensions

were approximately 19 cm I.D., 24 cm CD., and 10 cm long.

Coordinate axes were chosen to coincide with the specimen axes. The

longitudinal axis (3-axis) coincides with the axis of the wire, which was

assumed to have zero helix angle. The 1- and 2-axes lie along the radius and

coil axes, respectively, and form an orthogonal set with the 3-axis. The

symmetry of the coil (orthorhombic) requires nine elastic constants to

characterize the material. By assuming the material to be transversely

isotropic, by neglecting the effects of curvature, the number of independent

elastic constants is reduced to five. An orthotropic body with transverse

isotropy has the same symmetry as close-packed hexagonal crystals such as

magnesium and zinc. Justification for equating the 1- and 2-axes is given

in reference 39, and further experimental data show that the effect of curvature on the moduli is minor

The masses, lengths, and angles between the specimen axis and the 3-axis

are given in Table I. The density of the coil composite was found to be

3

6.000 gm/cm .

Besides the superconducting coil, some specimens composed only of fiberglass

cloth and epoxy were made available. The f iberglass-to-epoxy volume ratio in

158
these samples was approximately the same as in the coil composite. Measurements

were made on two specimens of this material. Dimensions and orientations of

these specimens are also reported in Table I, with the angle 0 corresponding

to the angle between the specimen axis and the direction parallel to the layers

3

of fiberglass cloth. The density of this material was found to be 1.931 gm/cm .

This material can also be considered transversely isotropic, if the fiberglass

is considered transversely isotropic. Thus, five constants are again needed

to completely characterize the material elastically. Cylindrical specimens of

only one orientation were available; thus, only two elastic constants of the

f iberglass-epoxy matrix material were determined.

3 . Results

The directly measured quantity in these measurements is , the frequency

of the three-component piezoelectric resonator. For longitudinal resonance

the frequency of the specimen (/g ) can be found from ^, the frequency of the

driver-gauge quartz assembly (/ ), the mass of the specimen (m ), and the mass

q s of the quartz (niq) :

/

^ = /^ + (/ ^ -/ /m . (1) ^s o o q qs

This formula is more exact than the approximation

/=/+(/-/ )m /m , (2)

s o o qqs

34 which is usually quoted and used for resonant oscillators

The formula for the torsional oscillator is somewhat more complicated

since the moments of inertia (rather than the masses) of the components are

involved

:

159
fJ' = C + (f ^ - f r /(m r (3) s o o q qq ss

Here, is the radius of the quartz and r is the radius of the specimen.

q s

The Young's modulus, E, or shear modulus, G, for the particular orientation of the specimen is given by:

E or G = 4 J^^p. (4)

E is found from the longitudinal-mode fundamental frequency and G is found

from the torsional-mode fundamental frequency. In Eq. 4, L is the specimen

length and p is the mass density.

Thus, the measured quantities are the Young's and shear moduli, which

are directly related to the elastic compliances, However, if the

wavelength is not much larger than the sample dimensions, a correction

for the Poisson contraction (or lateral motion) must be applied to Young's

35

modulus. When the length-to-dlameter ratio is 10 to 1, this correction

amounts to about one part in a thousand.

The value of Young's modulus for an arbitrary direction in a specimen

44 with transverse isotropy is given in terms of the elastic compliances by

1€0
^

= S^^sin^e + S^^cos^e + (2 S^^ + S^^)sin^e cos^0, (5)

where 0 is the angle between the specimen axis and the unique axis.

Similarly, the shear modulus is

^

= S^^ + (S^^-S^2-'^S^^)sin^0 + 2(S^^+S^2-2S^2-S44)sin^e cos^B. (6)

Most measurements were made during cooling. All experiments were performed

at least twice, and any unusual behavior was examined on heating as well as

cooling, for reversibility.

A. Superconducting Coil Composite

Measurements made on the coil composite are listed in Table II. Again, 0

is the angle between the specimen axis and the 3-axis (longitudinal axis) . The

mode specifies either longitudinal or torsional oscillations. The subscripts

on E and G designate the direction of the force and the plane on which the force

is applied, respectively. The compliances S^^, S^^' found directly

from experiments 1, 2, and 3, respectively. From experiment 4, S^2 found

using the relation 2(S,, - S^„) = S^,, and the value of S, , from experiment 3.

11 IZ bo 44

Either specimen 5 or 6 can be used to determine S^^^* This compliance must be

determined from a measurement on a specimen with its axis at an angle to the

longitudinal direction. As can be seen from Table 2, however, the Young's or

shear modulus measured on specimens with 0° < 0 < 90°, is Only partly dependent

on S^2' Thus, S^^ will be the least accurately determined compliance. The

measurement of this compliance corresponds to the measurement of the elastic

stiffness C^^ megahertz ultrasonic techniques. Zimmer and Cost"*"^ encountered

difficulty in measuring C^^ ^ composite material and their estimated uncertainty is this elastic constant (100%) was ascribed to dispersion as well

as to the relatively high inaccuracy.

161
The experimental data are presented in Figures 2-7 , The smooth curves

represent regular temperature behavior as given by a theoretical relationship

45

suggested by Varshni, that has been used successfully to represent the

45 45 46

temperature dependences of metals, ionic solids, and several alloys.

The overall fit of this function to these data is not nearly as good as for

other materials, and the data for E^^, could not be fitted to the Varshni

function because of its concave-upWards curvature. A smooth curve was drawn

through the data points and the actual point values were used in calculations.

This modulus was measured several times to check its behavior and the data

from the different measurements were in excellent agreement. This data

is completely reversible.

The shear modulus corresponding to shearing the axial planes in the

radial direction G^^^ or vice-versa is shown in Figure 8. This modulus was

calculated from the curve values of G, „ and G', since G, ^ = l/S->.

13 12 66

Because of the difficulty in machining the specimens to small radii,

the ratios of lengths to diameters were in some cases on the order of four

or five to one. The estimated correction to the Young's moduli in these

cases is still only about one percent.

The elastic compliances as functions of temperature are given in Table III.

The compliances S^^^, S^^j ^nd S^^ are just reciprocals of E^^^, E^^j and G^^*

as mentioned previously. The error in the directly measured moduli is estimated

to be about i%, thus these compliances should be accurate to 1%, also. The

compliance S^^ is found from combining the results of three measurements.

Thus, be less accurately known. It was found that in solving for S-j^^

from either Eq. 5 or 6, a 1% error in the measured modulus led to a 10-20%

error in S^^' Thus, the error associated with S^^ is considerable, perhaps

as much as 100%. The values reported for S^^^ average of the values

162
found from experiments 5 and 6, which are -0.110 and -0.058, respectively.

From the material available, it was not possible to machine specimens with

9 < 60° for other determinations of S^^* expected, the material was

found to be highly anisotropic with s^^^ ^^33*

It is emphasized that the data reported here are dynamic (adiabatic)

rather than static (isothermal) and apply to rapid, rather than slow,

47 loading. Conversion formulas are given in Landau and Litschitz , for

example, and in most cases the differences between adiabatic and isothermal

elastic constants are small. These formulas involve the thermal expansion

coefficients and the specific heat. The thermal expansion coefficients are

39 known for this composite , but the specific heat has not yet been determined.

If an estimate of the specific heat of the composite is made from the specific

heats of the components, the difference between the adiabatic and isothermal

Young's moduli is at most 0.5%. The adiabatic and isothermal shear moduli

are, of course, equal.

B. Epoxy-Fiberlgass Composite

Measurements were also made on the epoxy-f iberglass specimens listed in

Table I. These specimens were oriented with the layers of fiberglass cloth

running the length of the specimen; these were the only orientations available.

The Young's modulus and shear modulus are shown in Figures 9. and 10. The shear

modulus is well represented by the Varshni function, and is seen to have normal

temperature behavior. A smooth curve was drawn through the Young's modulus data,

which could not be fitted to the Varshni function because of the low-temperature

maximum.

l€3
4. Discussion

Some elastic data, taken by conventional static methods, were available

40 48

for the superconducting coil composite and the epoxy-f iberglass composite. '

These data generally compared very favorably with the resonance data. For

example, resonance values of E^^ at room temperature and 4 K are 12% and 1%

larger than the static data taken at these temperatures. The inaccuracy of

the static values is given as about 10%. Also, resonance values of E^^ compare

to within 5 - 7% of the static data, and resonance values of G^^ ^g^^e within

6 - 11% of the static values.

Other elastic constants of interest include the Poisson ratios:

and

^12 ' -hi'hv

^13 = -=13/=33'

where v., represents the negative ratio of strain in the i -direction to strain

in the i-direction.

The value of V-j^2 room temperature is 0.304. The reported ^static

value is 0.335, with the inaccuracy again believed to be about 10%. Thus, this

result gives added confidence to the resonance value of S^2' However, the

Poisson ratio V^^* involves the compliance S^^* which has already been noted

to be much more inaccurate than the other four compliances. In fact, if the

room-temperature values of S^^ and S^^ used, v^^ ~ 0.683, whereas the

39 static value is 0.333. Since the other elastic constants are all in relatively

good agreement with the static values, it is reasonable to expect that V^^

should be also. Thus, the value of S^^ is highly suspect, especially since a value near 1/3 seems more realistic for Poisson' s ratio.

164
It is also of interest to consider the compressibilities. For a material

with transverse isotropy, the linear compressibilities are

^1 " ^11 ^12 ^13'

and (9)

^3 " ^^13 ^33'

where the subscripts designate the axis. Also, the volume compressibility is

K = 2k^ + k^. (10)

If the room temperature values of the compliances, as given in Table III,

-10 2 -in?

are used, then k^ = 0.136 x 10 m /N, k^ = -0.045 x 10 m /N and

-10 2 K = 0.027 x 10 m /N. However, if the Poisson ratio v^^ is taken as 1/3, then

-10 2 -10 2 = -0.041 X 10 m /N at room temperature, and k^ = 0.179 x 10 m /N

-10 2 -10 2 k^ = 0.041 X 10 m /N, and the volume compressibility K = 0.399 x 10 m /N.

The relatively large value for v^^ the negative k^ which result from the

resonance S^^' be unreasonable, considering the multi-component material,

The elastic stiffness coefficients, however, can be calculated from the compliances, and indicate that the resonance value of S^^ error.

The elastic stiffnesses (C . . ) can be directly calculated by inverting

the S_j^_. matrix if all the compliances are known. The explicit relationships

49 are :

165
hi

=12

=13

C33

^11^33 " ^13

(=11 - Sl2>^

'

2

=13 " =12 33

(=11 - =12>=

-hi

s

^11 ^12

(12)

and

^44 -'^^44'

^66 '-''^66'

where S = S^^CS^^ + 8^2^ " ^^13^' Except for C^^ and C^^, these relationships

depend strongly on S^^. Using the resonance value of S^^' elastic stiffnesses

which depend on S^^ found to increase with increasing temperature, which is

contrary to normal behavior. Since the Young's moduli and shear moduli all behave

fairly regularly with temperature, the resonance value of S^^ seems unreasonable. '

In calculating the elastic stiffnesses, then, a value of 1/3 for V^^ was used,

39 and this Poisson's ratio was taken as constant with temperature. It is

believed that the eleastic stiffnesses obtained this way are more accurate than

chose obtained using the resonance value of S^-j* elastic stiffnesses are

given in Table IV. V

'

As expected, the elastic properties of this composite are highly anisotropic

The anisotropy is best described by considering the percent elastic anistropy

as discussed by Chung and Buessem. For transversely isotropic symmetry,

this scheme involves using the conventional anisotropy ratios (the linear

compressibility ratio = k^/k^, and the shear anisotropy A^ =

^UU^-^Sb^ ^°

calculate anisotropy parameters A and A * with the following properties:

166
A* Is zero for materials that are elastically isotropic, i.e., A = 1; A* is

always positive and a single valued measure of the elastic anisotropy of a

material regardless of whether A< 1 or A>1; and A* gives the relative magnitude

of the elastic anisotropy present in the material. For this composite A^- 0.23,

A * - 8.4%, A - 0.61, and A * - 12.3%. For comparison, A * - 9.9% and

c s s c 49

A * - 13.7% for zinc, which is one of the most anisotropic hexagonal metals,

s The static value of Young's modulus of the f iberglass-epoxy is also

40 available. This Young's modulus was measured on a specimen oriented like

the one used for the resonance measurements. The resonance and static values

differ by 4 - 10%. There was no evidence of a maximum in the static data, but

it is believed that the maximum is real. This maximum was observed during

several measurements and was completely reversible. No explanation for this

behavior can be given at this time.

y 5 . Conclusions

The resonant piezoelectric oscillator method used in this work is generally

suitable for measuring the elastic properties of composite materials. This

method is accurate, fast, and requires only small specimens. It is suitable for

measurements at all temperatures from 0 K to greater than lOOO^C. ^^'"^'^ The

general techniques and theory of this method are well understood. This method

does not appear to have the limitations of static and ultrasonic techniques.

The elastic compliance data presented in this work agree well with

existing data taken by conventional static methods. These data can be used

to calculate other elastic properties, such as the elastic stiffness coefficients

and compressibilities.

167
The superconducting coil composite was highly anisotropic, with elastic

anisotropies similar to those of zinc. This high anisotropy, characteristic

of many composite materials, necessitates careful measurements of elastic

properties of these materials.

The measured elastic moduli of the composite are not as well represented

by the Varshni function as they are for most metals and alloys; i.e., the

elastic moduli of the superconducting coil composite are less regularly

behaved with respect to temperature.

6. Acknowledgments

The author would like to express his graditude to D. L. Johnson for his

considerable assistance with the piezoelectric oscillator techniques. He

would also like to thank A. F. Clark for supplying the specimens and the

static data on the coil composite, and H. Dickinson, who aided in the

experiments.

The author is also indebted to H. M. Ledbetter for many helpful discussions

on elastic properties in general and for a critical reading of the manuscript.

168

I
References

1. P. R. Goggin, J. Mater. Sci. 8, 233 (1973).

2. T. J. Dudek, J. Compos. Mater. 232 (1970).

3. T. Hirai and D. E. Kline, J. Compos. Mater. 7^, 160 (1973).

4. Albert B. Schultz and Stephen W. Tsai, J. Compos. Mater. _2, 368 (1968).

5. R. C. Rossi, J. R. Cost, and K. R. Janowski, J. Amer. Ceramic Soc. 55

,

234 (1972).

6. G. C. Wright, J. Sound Vibr. 21, 205 (1972).

7. R. E. Allred and W. R. Hoover, J. Compos. Mater. 8^, 15 (197/4).

8. L. J. Cohen and 0. Ishai, J. Compos. Mater. 1, 1030 (1967).

9. N. L. Hancox, J. Mater. Sci. 1030 (1972).

10. T. R. Tauchert, J. Compos. Mater. _5, 456 (1971).

11. A. Smith, J. Phys. E. Sci. Instrum. 5, 274 (1972).

12. A. Smith, W. N. Reynolds, and N. L. Hancox, J. Compos. Mater. ]_, 138 (1973).

13. A. Smith, S. J. Wilkinson, and W. N. Reynolds, J. Mater. Sci. % 547 (1974).

14. J. V. Grabel and J. R. Cost, Metall. Trans. 2, 1973 (1972).

15. A. E. Lord and D. Robert Hay, J. Compos. Mater. 6^, 278 (1972).

16. W. Sachse, J. Compos. Mater. 378 (1974).

17. J. 0. Achenbach and G. Hermann, AIAA J. i6, 1832 (1968).

18. J. E. Zimmer and J. R. Cost, J. Acoust. Soc. Amer. 47, 795 (1970).

19. W. N. Reynolds and S. J. Wilkinson, Ultrasonics 12, 109 (1974).

20. S. J. Wilkinson and W. N. Reynolds, J. Phys. D: Appl. Phys. 50 (1974).

21. T. R. Tauchert and A. N. Guzelsu, J. Appl. Mech. , Trans. ASME 39.. 98 (1972)

22. M. F. Markham, Composites 145 (1970).

23. G. D. Dean and P. Turner, Composites, July 174 (1973).

169
24 Robert S. Smith, J. Appl. Phys. 43, 2555 (1972).

• A. R. Zecca and D. R. Hay, J. Compos. Mater. ^, 556 (1970).

26 S. L. Quimby, Phys. Rev. 25, 558 (1925).

27 L. Balamuth, Phys. Rev. 45,715 (1934).

28 F. C. Rose, Phys. Rev. _49, 50 (1936).

L. Hunter and S. Siegel, Phys. Rev. 61, 84 (1942).

30. J. W. Marx and J. M. Silvertsen, J, Appl. Phys. 24, 81 (1953).

31. M. E. Fine, Rev. Sci. Instrum. 25,1188 (1954).

32 S. Siegel and S. L. Quimby, Phys. Rev. 49, 663 (1936).

33. J. Zacarias, Phys. Rev. 44, 116 (1933).

34 i. J. Marx, Rev. Sci. Instrum. 2_2, 503 (1951).

35, M. E. Fine, ASTM Special Tech. Publ. No. 129, 48 (1952).

36. ¥. H. Robinson, S. H. Carpenter and J. L.. Tallon, J. Appl. Phys. 45,

1975 (1974).

37. The use in this paper of trade names of specific products is essential

to a proper understanding of the work presented. Their use in no way

implies any approval, endorsement, on recommendation by NBS.

38. A. J. Matheson, J. Phys. E. (Sci. Instru.) 4^, 796 (1971).

39. C. W. Fowles, P. E. Angerhofer, R. N. Newton, and A. F. Clark,

NBSIR 73-349 (1973).

40. A. P. Gerk, Rev. Sci. Instrum. 43, 1786 (1972).

41. D. L. Johnson, University of Illinois, private communication.

42. A. F. Clark, National Bureau of Standards, private communication.

43. W, N. Robinson and At Edgar, IEEE Ttans. Sonics and Ultrasonics 21 , 98 (1974). '

'" ^

'

44. W. Voigt, Lehrbuch der Kristallphysik , (Teubner, Berlin, 1928), p. 746-7.

45. Y. P. Varshni, Phys. Rev. B2, 3952 (1970).

46. E. R. Naimon, W. F. Weston, and H. M. Ledbetter, Cryogenics 14 ,- 721 (1973).

170
47. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (pergamon,

London 1959) p. 17.

48. M. B. Kasen, National Bureau of Standards, private communication.

49. R. F. S. Hearmon, Rev. Mod. Phys. 18, 409 (1946).

50. D. H. Chung and W. R. Buessem, Anisotropy in Single-Crystal Compounds

(Edited by F. W. Vahldiek and S. A. Mersol, Plenum, N. Y., Vol. 2_,

p. 217, 1968).

171
Table I. Dimens ions and orientations of specimens

Specimen Diameter Mass Length Q

N^^ber (inches) (gm) (cm) (degrees)

Superconducting Coil Composite Specimens

1 0.1250 0.540 1.1128 90

2 0.1250 0.925 1.9439 0

3 . 0.1863 1.081 1.0818 0

^ 0.1890 1.248 1.1481 90

5 0.1875 1.874 1.7600 60

6 0.1851 1.327 1.2555 60

Epoxy-Fiberglass Composite Specimens

1 0.1875 0.885 2.5387 0

2 0.1878 0.520 1.4862 0

Table II. Experiments performed on Superconducting coil composite

Exp. No. Spec. No. Mode 0 Measured Quantity

1 1 L 90 E = ^

2 2 L 0 E^^ = -r^

^33

3 3 T 0 G.o =

90

60

60

T _ ^44 + ^66

16

=60° 9S,i + S__ + 6S,_ + 3S., 11 33 13 44

'6=60° 3S,, + 3S„„ - 6Si^ + 2S,, + 3S,.^ 11 33 13 44 66

172
Table III. Elastic compliances of the

superconducting coil composite at selected temperatures (lO"-'-^ m^/N)

T(K)

11

S 1 0 1/

S 1 T IJ 44

S

1bo

0 0.242 0.074 0.061 0.112 0.910 0 .631

50 0.242 0.074 0.061 0.113 0.910 0 .632

100 0.248 0.076 0.066 0.115 0.920 0 .648

150 0.260 0.083 0.073 0.118 0.964 0 .684

200 0.275 0.089 0.079 0.119 1.046 0 .728

250 0. 294 0.094 0.082 0.121 1.170 0 .776

300 0.316 0.096 0.084 0.123 1.350 0 .823

Table IV. Elastic stiffnesses of the superconducting

coil composite at selected temperatures (10'^^ N/

TCK; ^11 ^12 S3 S3 66

0 5.10 1.94 2.39 10.59 1.10 1 .58

50 5.10 1.93 2.39 10.46 1.10 1 .58

100 4.99 1.90 2.34 10.27 1.09 1 .54

150 4.80 1.87 2.27 10.05 1.04 1 .46

200 4.54 1.79 2.15 9.86 0.96 1 .37

250 4.21 1.63 1.99 9.64 0.85 1 .29

300 3.82 1.39 1.77 9.35 0.74 1 .22

173
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182
183
LOW-TEMPERATURE liLASTIC PROPERTIES OE A

NICKEL-CHROMIUM-IRON-MOLYBDENUM ALLOY

W. F. Weston and H. M, Ledbetter

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

V Abstract

The elastic properties of a nickel-chromium-iron-molybdenum

alloy were determined between room temperature and liquid-helium

temperature by measuring both the longitudinal and transverse sound-wave

velocities in a polycrystalline material. These properties include:

the longitudinal modulus. Young's modulus, the shear modulus, the

bulk modulus (reciprocal compressibility), and PoissOn's ratio.

Except for a small anomaly in the bulk modulus, this material

exhibits regular elastic -constant/temperature behavior.

Key words: Bulk modulus; compressibility; Debye temperature;

elastic constants; nickel-base alloys; Poisson's ratio;

shear modulus; sound velocity; Young's modulus.

184
Low-temperature Elastic Properties of a Nickel-Chromium-Iron -Molybdenum Alloy

W.F. "Weston"^ and H. M. Ledbetter

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

The low-temperature elastic properties of two nickel-chromium-iron

1 alloys, Inconel 600 and Inconel X-750, were reported recently. The

same properties- -the longitudinal modulus, Young's modulus, the shear

modulus, the bulk modulus (reciprocal compressibility), and Poisson's

ratio- -are reported here for a nickel-chromium-iron-molybdenum alloy,

Inconel 718. Except for being slightly softer elastically, it resembles

Inconel X-750.

The low-temperature elastic properties of Inconel 718 are of interest

mainly because it is a candidate material for cryogenic structural applic?

2

tions. The elastic properties are important both for the design of

structural components and for understanding the basic physical propertie

of a material. From the temperature -dependent elastic constants, deflections can be predicted for any combination of stress and temperature.

Also, the Debye characteristic temperature can be calculated from the

_

Contribution of NBS, not subject to copyright.

+ NRC-NBS Postdoctoral Research Associate, 1973-74.

Tradenames are used to identify the materials tested; they are not NBS

endorsements of particular products.

185
elastic constants. The Debye temperature relates in turn to a wide

3

variety of solid-state phenomena.

Inconel 718 is made precipitation hardenable by its niobium-plus

tantalum content. (Inconel X-750 is made precipitation hardenable by its

aluminum-plus -titanium content. ) It differs from the nickel-chromiumiron alloys in having superior mechanical properties such as yield,

2

creep, rupture, and fatigue strengths. Its sluggish response to precipitation hardening permits annealing and welding without significant

property changes.

Experimental Methods

Ultrasonic (10 MHz) longitudinal and transverse sound-wave velocities were measured between room temperature and liquid-helium tempera4

ture (4 K) using a pulse-echo-superposition method. Experimental

procedures were identical to those reported previously except that the

material was obtained from a commercial source in the form of 3/4-inch

(1. 9 -cm) rods. Chemical and physical data on the material are given

in Table 1. , ;< ,-

Results *

;

The longitudinal modulus

versus temperature

C^-P.j (1)

is shown in Fig. 1, where p is the mass density and v is the longitudinal sound-wave velocity. The transverse modulus

. C = pv^ := G .

186
is shown versus temperature in Fig. 2, where is the transverse

sound-wave velocity and G is the shear modulus. Young's modulus E,

the bulk modulus B, and Poisson's ratio v were calculated from the

formulas^:

E = 3C^(C^- |-C^)/(C^- C^), (3)

B -C^-|.C^, (4)

V =(1/2XC^- 2C^)/(C^- C^); (5)

and these elastic constants are shown versus temperature in Figs.

3-5. For comparison, Figs. 1-5 also show as dashed lines the elastic

constants of Inconel X-750, which were reported previously.

The temperature dependences of both C ^ and were fitted to a

6

theoretical relationship suggested by Varshni;

J / rp C = C - s/(e - 1) (6) o where C , s, and t are adjustable parameters and T is temperature.

The average difference between curve values and measured values was

0. 06 and 0. 05 pet. for the transverse and the longitudinal modes,

respectively.

The elastic Debye temperature was cialculated from C , and C ^ ^ it

using standard formulas^ and was found to be P= 446 K at absolute zero.

For comparison, 0 (nickel) = 476 K and 9 (Irconel X-750) = 474 K.

Discus sion

Basically, the low-temperature elastic properties of Inconel 718

are very similar to those of Inconel X -75 0. The higher-iron, lowernickel content of Inconel 718 accounts for its slightly lower elastic

187
Debye temperature. Inconel 718 is also Similar to Inconel X-750 in the

temperature dependences of its elastic constants for the cases of E, G,

and C , whj.ch show regular behavior. By regular behavior is meant:

continuously decreasing with increasing temperature, linear behavior at

higher temperatures, relative flatness at low temperatures, and zero slope

at T = 0 K, Both materials show slight anomalies in the temperature dependence of the bulk modulus. While Inconel X-75 0 shows a concavity

upwards in the B(T) curve, Inconel 718, as shown in Fig. 4, shows a maximum near 100 K in its B(T) curve. Based on the previous experience

of this laboratory, it is believed in this case that the imprecisions in both

4 and are a few parts in 10 ^ Thus, this anomaly (though small) is

believed to be real and not a measurement-computational artifact.

The interpretation of the maximum iti the B{T) curve of Inconel 718 can

only be speculative. Unlike Inconel X-750, it was verified during the present

study that Inconel 718 is non-magnetic between rbom temperature and liquidnitrogen temperature (77 K). In some respects, the low-temperature behavior of

the bulk modulus of Inconel 718 resemtales that of Stainless steels AISI

7

304, 310, and 316 reported previously. In those cases, the anomalous

behavior was interpreted in terms of the Doring effect that results from

j

I a large volume magnetostriction accompanying a paramagnetic -toantiferromagnetic transition. However, no evidence of a low-temperature

magnetic transition in Inconel 718 seems to exist; and neither the longitudinal modulus nor Young's modulus show any evidence of a dilatational

anomaly. Thus, the nature of this anomsily, its magnitude, and perhaps

even the question of its existence deserve further study.

188
g Comparisons with some previous results show reasonable agreement for both the room-temperature elastic constants and the temperature

derivatives of E and G. It is easy to verify that the temperature

derivative of v reported here is more reasonable than that obtained from

data in ref. 8. Differentiation of the standard relationship

/i

^ _ IdG \

I E dT GdT 1

gives

dV _ E_

V dT " E-2G I E dT GdT I . (8)

The present data satisfy eqn, (8) exactly, while the data from ref. 8

give a L. H. S. /R. H. S. ratio of 2. 6. Temperature derivatives of B have

apparently not been reported previously. The only previously reported

2

elastic constant at 4 K is Young's modulus; this value,

11 2

2. 11 X 10 N/m , is identical to the present value.

This work was supported in part by the Advanced Research Projects

Agency of the U. S. Department of Defense. Dr. E. R. Naimon of Dow

Chemical (Rocky Flats Division) commented on the manuscript.

189
References

1. W. F. Weston, H. M, Ledbettet, and E. R. Naimon, Mater. Sci. Engg. , forthcoming.

2. Handbook on Materials for Superconducting Machinery, Battelle

Metals and Ceramics Information Center, Columbus, Ohio, 1974.

3. F. H. Herbstein, Adv. Phys . 10(1961) 313.

4. H. J.. McSkimin, J. Acoust. Soc. Amer. 33 (1961) 12.

5. H. M. Ledbetter and R. P. Reed, J. Phys. Chem. Ref. Data , 2 (1974) 531.

6. Y. P. Varshni, Phys. Rev. B2 (1970) 3952.

7. H. M. Ledbetter, W. F. Weston, and E. R. Naimon, J. Appl.

Phys . , forthcoming.

8. Huntington Alloys: Inconel Alloy 718 , Internat. Nickel Co. , Huntington, West Virginia.

Table 1. Composition and properties of the alloy

Mass Density

Chemical Composition, Hardness at 294 K

Mill Analysis (wt. pet. ) (DPH No. , 1 kg load) (g/cm^)

Ni Cr Fe Nb+Ta Mo Ti 425 8. 229

53. 73 18.49 17. 62 5. 17 2. 98 1.01

Al C Mn Si S Cu Condition: As •'received; hot-rolled

0. 58 0. 05 0. 08 0. 17 0. 007 0. 04

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NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. 1 . PU B LIC ATION OR R E PORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA No. SHEET NBSIR 75-810

3. Recipient's Accession No.

4. Tl I'LE AND SUBTl l Ll-; Semi- Annual Report on ^Materials Research,

in Support of Superconducting Machinery

5. Publication Date April 1975

6. Performing Organization Code

275.03

7. AurHOR(S)R, p.Reed, J. G.Hust, M.B. K^sen, H . M. Ledbetter, R.P.Mikesell, R.E.Schramm, L.L. Sparks, R . L. ToDler,

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS and W . F . WestOn.

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2756530

11. Contract/Grant No. ARPA Order No. 2569

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Advanced Research Projects Agency

Department of Defense

Washington, D.C.

13. Type of Report & Period Covered

14. Sponsoring Agency Code

ARPA

1 J. oL. I K 1. C [VICIN lAlxliNLJtO

16. ABSTRACT (A 200-word or less (actual summary of most signidcant information. If document includes a significant

bibliography or literature survey, mention it here.) Results of SIX months of study on materials m support of superconducting

machinery (October 1974 through March 1975) are reported to the sponsor, the

Advanced Research Projects Agency of the U.S. Department of Defense. The re- port is divided into five sections: thermal conductivity, magnetothermal conductivity, fatigue and fracture-toughness properties, properties of advanced composites, and elastic properties. The temperature range 4 to 300 K is covered by the study.

Materials studied are either being used or are candidates for use in superconducting machinery and include: aluminum alloys, composites, copper, age-hardened,

nickel-base superalloys, stainless steels, and titanium alloys

.

Special results of the study include: thermal conductivity data for comparison of

the effects of heat treatment on age-hardenable alloys, the first determination of a complete set of elastic constants for a composite at liquid helium temperature,

boron- aluminum composite tensile data at 4 K, and a summary of fatigue crackgrowth rate behavior at 4 K for a number of different structural alloys. These data

provide considerable insight into material characteristics at extremely low temperatures, assisting in material selection and efficient design.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Composites; elastic properties; fracture; liquid helium; mechanical properties;

structural materials; superconducting machinery; thermal conductivity.

18. AVAILABILITY [X Unlimited

1 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

Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

21. NO. OF PAGES

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

23. Price

USCOMM tRL USCOMM-DC ^fjO^i-H- 74