The dynamic compressive behavior of beryllium bearing bulk metallic glasses

The dynamic compressive behavior of beryllium bearing bulk

metallic glasses

H. A. Bruck

Idaho National Engineering Labs, Mail Stop 2218, Idaho Falls, Idaho 83415-2218

A. J. Rosakis

Department of Aeronautics, California Institute of Technology, Mail Stop 105-50,

Pasadena, California 91125

W. L. Johnson

Department of Materials Science, California Institute of Technology, Mail Stop 105-50,

Pasadena, California 91125

(Received 14 March 1995; accepted 26 October 1995)

In 1993, a new beryllium bearing bulk metallic glass with the nominal composition

of Zr

41.25

13.75

12.5

22.5

was discovered at Caltech. This metallic glass can be

cast as cylindrical rods as large as 16 mm in diameter, which permitted specimens to be

fabricated with geometries suitable for dynamic testing. For the first time, the dynamic

compressive yield behavior of a metallic glass was characterized at strain rates of 10

s by using the split Hopkinson pressure bar. A high-speed infrared thermal detector

was also used to determine if adiabatic heating occurred during dynamic deformation of

the metallic glass. From these tests it appears that the yield stress of the metallic glass is

insensitive to strain rate and no adiabatic heating occurs before yielding.

I. INTRODUCTION

Many components formed from high strength alloys

experience dynamic mechanical loading during their

fabrication and use, which cause the materials to deform

at very high strain rates. In order to understand the limita-

tions of using high strength alloys in these processes, it is

necessary to quantify the material’s dynamic constitutive

behavior. Insight into this behavior has been customarily

obtained using Taylor anvil tests

or Kolsky bars.

One class of high strength alloys that can be poten-

tially used in many commercial and industrial applica-

tions is known as amorphous metal alloys or metallic

glasses. Previously, cooling rate requirements have lim-

ited the size of metallic glass specimens available for

mechanical testing to cylindrical rods no larger than

2 mm in diameter. Larger specimens are required to

obtain reliable data on the mechanical behavior of these

alloys. Recently, metallic glasses containing beryllium

have been fabricated as ingots up to 16 mm in diame-

ter by directly quenching from the melt.

Mechanical

tests have been conducted on specimens manufactured

from these beryllium bearing bulk metallic glasses.

The

quasistatic constitutive behavior of these bulk metallic

glasses was characterized in these tests.

At that time, all of the constitutive characterization

of metallic glasses was performed in quasistatic tests. No

data are currently available on the dynamic constitutive

behavior of metallic glasses. An attempt was made

by Cline and Reaugh

to determine the dynamic yield

strength of a palladium alloy metallic glass using the

Taylor anvil test; however, they concluded that this was

not appropriate.

The goal of this work is to characterize the dynamic

compressive yield behavior of the Zr

41.25

13.75

12.5

22.5

metallic glass using a Kolsky bar. Ther-

mal measurements were also made using a high speed

infrared temperature sensor

to investigate whether adia-

batic heating occurs during the dynamic deformation of

the glass.

II. KOLSKY BAR THEORY

The basic principle of the Kolsky bar is illustrated

in Fig. 1(a). The setup basically consists of two elastic

pressure bars,

known as the incident or input bar and

known as the transmitter or output bar. A specimen

is placed between the two bars. A striker bar impacts

the input bar at

. This sets up a pressure pulse within

the incident bar with a strain

. When this pulse

reaches

, the end of the incident bar, part of the wave

is reflected with a strain

and part of the wave is

transmitted to the output bar with a strain

. Strain

gauges are placed in the middle of the elastic pressure

bars to provide the time-resolved signals of the incident,

reflected, and transmitted pulses. The pulse is reflected

from the interface of the bar and specimen at

due to

impedance mismatch.

When the specimen is deforming uniformly, the

strain rate

within the specimen is proportional to the

J. Mater. Res., Vol. 11, No. 2, Feb 1996



1996 Materials Research Society

503

Help

Comments

Welcome

Journal of

MATERIALS RESEARCH

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

(a)

(b)

FIG. 1. (a) Kolsky bar used for dynamic compression tests. ( b) Stress

and strain analysis of homogeneously deformed specimen.

reflected wave’s amplitude. Similarly, the stress within

the sample is proportional to the amplitude of the trans-

mitted wave. This can be shown by the following analy-

sis [Fig. 1( b)]. In this figure,

is the cross-sectional area

of the elastic bars and

is the cross-sectional area of the

specimen. The strain rate in the deforming specimen is

≠

(1)

where

and

are particle velocities at

and

respectively, and

is the length of the specimen. From

characteristic relations for one-dimensional wave propa-

gation, assuming no wave dispersion occurs, one has

≠

(2a)

≠

(2b)

where

≠

is the longitudinal bar wave speed for

the elastic bars,

is Young’s modulus of the elastic bars,

and

is the density of the elastic bars. From Eqs. (1)

and (2):

≠

(3)

The average stress in the specimen is

≠

(4)

where

and

are the forces at the incident

bar/specimen and specimen/transmitter bar interfaces,

respectively. Assuming that no wave dispersion occurs:

≠

(5a)

≠

(5b)

From Eqs. (4) and (5):

≠

(6)

When

the

specimen

deforming

uniformly

(homogeneously), the stress at the incident bar/specimen

interface equals the stress at the transmitter bar/specimen

interface. From Eq. (5):

≠

(7)

which implies that:

≠

(8)

From Eqs. (3), (6), and (8):

≠

(9)

≠

(10)

Integrating Eq. (10), we obtain the time history of the

strain as follows:

≠

(11)

The stress-strain behavior is completely determined by

measuring

and

on the elastic pressure bars

using strain gauges.

III. HIGH-SPEED INFRARED THERMAL

MEASUREMENTS

High-speed, noncontact techniques have been devel-

oped for measuring temperature fields on the surfaces

of deforming objects.

6,7

These techniques use detectors

to measure the infrared thermal signatures generated by

the deforming object. An Offner imaging system first

employed by Zehnder and Rosakis

was used for the

dynamic compression tests to focus the surface of the

compression specimens onto a single infrared detector.

The Offner system has a fixed 1 : 1 magnification, so that

optics were used with a focal length of approximately

160 mm and an object distance of 320 mm in order to

protect the optics by keeping them a sufficient distance

away from the test specimen.

A single EG&G J15D12 HgCdTe infrared detector

with dimensions 100

m square and a temperature range

of approximately 300 to 1000 K was used to detect

the temperature. The HgCdTe detector was cooled with

liquid nitrogen, and the voltage from the detector was

outputted to a preamp with a bandpass of 5 Hz to 1 MHz,

well beyond the detector’s cutoff frequency of 400 kHz.

Because the sensor had a very high signal-to-noise ration,

the preamp was connected to an amplifier set at

and

a filter set at 10 kHz, which in turn was connected to

a Nicolet 440 digital oscilloscope that was connected to

the strain gauges on the Kolsky bars.

504

J. Mater. Res., Vol. 11, No. 2, Feb 1996

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

The HgCdTe detector integrates wavelengths rang-

ing from 2

mto12

m. The voltage produced by the

detectors is related to the energy emitted by the specimen

through an integral, depending upon the emissivity of

the material,

, the spectral responsivity of the

HgCdTe detector,

, and the black body radiation

, as follows

≠

(12)

where the integration variable

is the wavelength of

the radiation,

is the amplification,

is the detector

area, and

is the fraction of energy transmitted to the

detectors by the optical system (related to the aperture).

When evaluated for HgCdTe detectors, this relationship

is nearly linear on a log-log plot of voltage versus

temperatures. In order to determine this relationship for

the Zr

41.25

13.75

12.5

22.5

metallic glass, a 1.5 mm

thick plate specimen with a thermocouple clamped to

its surface was heated in an oven. The voltage output

from the detectors and the thermocouple readings were

then recorded as the specimen cooled. This calibration

datum was then plotted on a log-log plot, and the linear

relationship was determined (Fig. 2). This relationship

was then used to convert the voltage record from the

detector into a temperature measurement.

IV. EXPERIMENTAL PROCEDURE

Kolsky bar specimens were fabricated as cylindrical

rods with the nominal composition Zr

41.25

13.75

12.5

22.5

using commercially pure (

99.5%

) elements.

The rods were cast by injecting the molten alloy into a

copper mold with cylindrical cavities that are 2.5 mm

in diameter and 30 mm long. This geometry was chosen

because of the ease with which it could be fabricated

FIG. 2. Thermal calibration curve for Zr

41.25

13.75

12.5

22.5

and the significant ductility it exhibited in quasistatic

compression tests.

Details of the alloy design and

casting procedure can be found in Ref. 3. Periodically,

disks of approximately 250

m in thickness were ma-

chined from the rods and placed in an Inel CPS-120

x-ray diffractometer to verify that the structure was

amorphous.

After casting the rods, Kolsky bar specimens were

machined with length to diameter

aspect ratios

ranging from 1 : 2 to 2 : 1. The ends of the specimens

were then mechanically polished with 600 grit grinding

paper using a V-block to ensure flat and parallel surfaces.

By measuring the length of the specimen at four different

locations along the specimen’s edge with a Mitutoyo

micrometer, the surfaces were found to be flat and

parallel to within 3

m, the resolution of the micrometer.

The dynamic testing of the Zr

41.25

13.75

12.5

22.5

metallic glass was conducted using a split Hop-

kinson bar with elastic bars made from C350 maraging

steel that has a yield stress of 2.5 GPa. The bars were

1.22 meters in length and 1.27 cm in diameter. Speci-

mens were placed between the elastic bars using a pair

of WC insets coated with “Molygraph Extreme Pressure

Multi-purpose” grease to reduce end effects. The WC

inserts were machined to a diameter of approximately

0.85 cm in order to impedance match them with the

C350 maraging steel. A striker bar was used that was

manufactured from the same material as the elastic

bars and with the same diameter, but only 10 cm in

length. Strain gauges from Micromeasurements Group

were placed midway from the ends of the elastic bars

to measure the strain response on the surface of the

bar from the propagating waves. The strain gauges

were attached to quarter Wheatstone bridges whose

voltage outputs were measured with a Nicolet 440 digital

oscilloscope using a sampling rate of 5 MHz.

Sometimes when the striker bar impacts the incident

bar, there is some misalignment which can cause a

variation in the amplitude of the incident stress pulse

often referred to as “ringing.” Consequently, there is

some dispersion of the stress pulse that is detected by

the strain gauges well after the stress pulse has passed

underneath the strain gage. This makes it extremely

difficult to detect the start of the reflected wave when

it passes through the same strain gage.

In order to reduce dispersion from the incident stress

pulse, a copper insert was placed between the striker

bar and the incident bar as described by Follansbee in

the

Metals Handbook.

The resulting stress pulse gen-

erated by using the copper inserts was a ramp function

instead of the step function generated when the copper

inserts are removed. The period of the stress pulse was

nearly quadrupled by the presence of the copper inserts.

Theoretically, the length of the stress pulse would be

twice the length of the striker bar, which implies that

J. Mater. Res., Vol. 11, No. 2, Feb 1996

505

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

the stress pulse generated using copper inserts would be

eight times the length of the striker bar. A constraint on

the length of the stress pulse is it should be less than the

length of the bar if there is to be no overlap of incident

and reflected signals underneath the strain gage when

it is positioned midway from the ends of the bar. So,

the striker bar should be less than 15 cm in length if the

stress pulse is to be less than the length of the elastic bar,

which dictated that the 10 cm long striker bar be used.

Striker bar velocities varied from 5 m

sto20m

which generated strain rates in the specimen of 300

to 6000

s, depending on the length of the specimen.

One problem with using the copper inserts was the

stress pulses generated by their deformations were of

insufficient amplitude to obtain strain rates in the speci-

men greater than about 2000

s to 3000

s, depending

on the length of the specimen. In order to obtain the

higher strain rates, it was necessary to remove the copper

inserts.

V. EXPERIMENTAL RESULTS AND DISCUSSION

Strain gage data and the thermal measurements from

a typical Kolsky bar test on the Zr

41.25

13.75

12.5

22.5

metallic glass can be seen in Figs. 3 and 4.

The dynamic stress-strain curve and strain-strain rate

curve reduced from these signals can be seen in Figs. 5

and 6. Yield stresses were obtained for a variety of

strain rates and plotted in Fig. 7. Catastrophic failure of

dynamic compression specimens occurred due to shear

banding along a plane oriented 45

to the loading axis as

seen in Fig. 8, which is identical to the failure observed

in quasistatic tests.

Thermal measurements indicated that temperatures

varied dramatically after the specimen failed, reaching

peak values of approximately 500

C. Since the speci-

men failed by shear binding, it is possible that the

variations in the thermal trace are due to the shear band

passing through the detector and that the peak values

correspond to the maximum temperature reached within

FIG. 3. Strain gage signals from dynamic compression test.

FIG. 4. Temperature and loading recorded from dynamic compres-

sion test.

FIG. 5. Stress-strain curve reduced from strain gage signals in Fig. 5.

the shear band after deformation. This temperature is ap-

proaching the Zr

41.25

13.75

12.5

22.5

metallic glass

melting point

of 663

C, which would imply that the

deformation within the shear band is so intense that

the material within the band could be melting. It has

also been observed that there is a temperature of 100

which is sustained for a period of time after the specimen

has yielded. Since the homogeneous plastic deformation

is too limited to account for this temperature rise, it could

be due to the formation of micro-shear bands.

This is the first time transient thermal measurements

have been made on a metallic glass during a shear band-

ing event. However, more definite conclusions could be

made about the origin of the thermal measurements if an

array of detectors had been used to detect the inhomoge-

neous thermal distribution that would be associated with

shear banding.

Evidence that localized melting may be responsible

for the observed thermal measurements was obtained

from a scanning electron micrograph of the failure

surface, which can be seen in Fig 9. The only mor-

phology that appears on the failure surface are vein-like

506

J. Mater. Res., Vol. 11, No. 2, Feb 1996

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

FIG. 6. Strain-strain rate curve reduced from strain gage signals

in Fig. 5.

patterns. These features are identical to those observed

on the failure surfaces of other metallic glass specimens

tested in compression. An explanation for these features

has been proposed which asserts that the viscosity of

the material within a shear band is reduced consid-

erably because of adiabatic heating generated by the

enormous plastic deformations within the shear band

which preceded catastrophic failure.

As the material

separates, pores are opened up, leaving behind the vein-

like morphology. This hypothesis has been confirmed by

shear experiments performed on a viscous material that

has been placed between glass slides.

After the slides

are sheared apart, a vein-like morphology is revealed on

the separated surfaces.

The dynamic compressive stress-strain response in

Fig. 5 is very similar to the quasistatic compressive

stress-strain response reported in Ref. 4. For the sake

of comparison, the quasistatic compressive stress strain

curve is shown in Fig. 10. The material exhibits an

almost textbook case elastic-perfectly plastic response

with yielding occurring at approximately 2% elastic

FIG. 7. Yield stress versus strain rate from the dynamic compres-

sion tests.

FIG. 8. Orientation of failure surface for 2.5 mm dynamic compres-

sion test specimen.

strain. From Fig. 7, it appears that the dynamic com-

pressive yield stress is within 5% of the quasistatic

value of 1.89 GPa reported in Ref. 4 for strain rates

below 1500

s. However, for strain rates greater than

3000

s, the compressive yield stress

appears

to decrease

monotonically with strain rate (strain rate softening). At

first this was believed to have been due to adiabatic

heating of the specimen; however, thermal measurements

indicated that no heating occurred prior to the onset of

yielding (Fig. 4).

During the dynamic compression tests, it was ob-

served that the WC inserts were failing in tests conducted

at strain rates above 3000

s. If the WC inserts were fail-

ing before the specimens failed, then the observed strain

rate softening could be due to the failure of the inserts.

To test this theory, the WC inserts were removed and the

compression tests repeated. By removing the inserts, the

FIG. 9. Scanning electron micrograph of compressive failure surface.

J. Mater. Res., Vol. 11, No. 2, Feb 1996

507

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

FIG. 10. Stress-strain curve from quasistate compression test.

stress concentrations at the end of the specimen might

not be reduced which may cause permanent failure. The

results from these tests in Fig. 7 indicate that removing

the WC inserts did not alter the observed yield stress of

the specimens at strain rates below 1500

s, while still

exhibiting the same softening behavior above 3000

Therefore, it was decided that the WC inserts should be

removed from the dynamic compression tests since they

were not affecting the test results.

No other observations were made during the dy-

namic compression tests that might explain the apparent

strain rate softening. Therefore, it became necessary to

reassess the conditions under which the dynamic com-

pression tests were performed to rule out any possible

artifacts in the testing system that might be responsible

for the apparent strain rate softening.

There are three basic, underlying assumptions used

in the reduction of split Hopkinson pressure bar test data.

They are as follows: (i) The specimen undergoes ho-

mogeneous deformation during the experiment. (ii) The

various stress pulses (e.g., reflected and transmitted)

encountered in the split Hopkinson bar undergo minimal

dispersion. (iii) The bars remain elastic at all times, and

the ends of the bars in contact with the specimen remain

flat and parallel throughout the experiment.

For the strain rates above 3000

s, the magnitude

of the incident stress pulse was 400 MPa, well below

the 2.5 GPa yield stress of the elastic bars. Therefore,

assumption (iii) was not violated. Verifying that the

other two assumptions were not violated required using

analyses developed by Ravichandran and Ghatuparthi.

VI. LIMITING STRAIN RATE FOR A METALLIC

GLASS SPECIMEN IN A KOLSKY BAR

Ravichandran used a simple analysis to establish

the conditions under which a specimen must be tested

to obtain homogeneous deformations consistent with

assumption (i).

This analysis assumed that there must

be some minimum time which was required for the

waves reflected back and forth inside a specimen to

equilibrate. For a specimen which exhibits a linearly

elastic material response up to some failure strain

the limiting strain rate

was derived to be:

≠

(13)

where

is the specimen’s longitudinal bar wave velocity,

is the length of the specimen, and

is a nondimen-

sional parameter whose value depends only on the shape

of the incident pulse.

From an analysis of one-dimensional wave propaga-

tion in the elastic bars and specimen using the method

of characteristics,

it was determined that for typical

incident pulses the gradient of stress along the length of

the specimen was within 5% of the mean stress in the

specimen when

≠

. This meant that for the metallic

glass specimens used for the dynamic compression test,

which had lengths of 5 mm or less and a longitudinal bar

wave velocity of 3925 m

s determined from ultrasonic

measurements,

the limiting strain rates were 3925

when the failure strain was at least 2%. Although this

value is larger than the 3000

s strain rate at which the

softening began to occur, it was still close enough that it

was decided to repeat the tests using specimens with

aspect ratios of 0.7 to 1, which would increase the

limiting strain rate to above 8000

s and eliminate any

questions about the homogeneity assumptions.

It has already been observed quasistatically that by

lowering the aspect ratio the yield stress increases be-

cause a plain strain stress state is approached. Therefore,

the conditions appeared encouraging for these tests. In

Fig. 7, it can be seen that the yield stress results from

these tests were identical to the test results for the longer

specimens. Thus, it was concluded that the plane strain

stress state was not being approached as the aspect ratios

of the test specimens were reduced below 1 and that the

inhomogeneity of the stress field was not responsible for

the apparent softening behavior.

VII. EFFECTS OF DISPERSION IN A KOLSKY

BAR AT HIGH STRAIN RATES

Ceramics have exhibited the same apparent strain

rate softening behavior as the Zr

41.25

13.75

12.5

22.5

metallic glass at strain rates above 2700

Dispersion effects were also analyzed by Ravichandran

and Ghatuparthi to determine if they would account for

the apparent softening behavior of ceramics.

Because

of dispersion effects, the amplitude and duration of a

stress pulse changes as it propagates in a bar. The extent

of geometrical dispersion depends on the dominant fre-

quency components contained in the pulse that is being

508

J. Mater. Res., Vol. 11, No. 2, Feb 1996

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

propagated, which is determined by the duration and

shape of the pulse.

13,14

From Ravichandran’s analysis, the effects of dis-

persion are minimized when the dominant frequency

component in the frequency spectrum of the input pulse

in a cylindrical bar is such that

0.1

. Here,

the radius of the bar and

is the wavelength associated

with the dominant frequency component. This condition

can be rewritten as:

√

0.1 ,

(14)

where

is the fundamental frequency associated with

the bar,

is the fundamental frequency of the pulse,

is the characteristic propagation velocity for the given

frequency, and

is the longitudinal bar wave velocity.

The fundamental frequency associated with the bar is

given by:

≠

∂

(15)

The value of

for large wavelengths can be obtained

from the Rayleigh approximation

≠

∂

(16)

where

is Poisson’s ratio.

For the Kolsky bars used in the dynamic compres-

sion experiments,

≠

6.35

mm,

≠

0.3

, and

≠

4970

s. Thus, plugging these values into Eq. (15)

yields

≠

4.92

rad

s. Using the value for

≠

0.1

from Eq. (16), a limiting value of

4.88

rad

s for the fundamental frequency of the pulse

is obtained. The corresponding period of the pulse,

can be calculated as follows:

≠

(17)

Assuming that the time to failure coincides with

the peak of the input pulse, and from symmetry, the time

to failure

will be

. The minimum time to failure

should be at least 6.44

s to minimize dispersion.

Using the failure strain of 2% for the Zr

41.25

13.75

12.5

22.5

metallic glass, the limiting strain rate

would be 3100

s. This is approximately the strain rate

at which the apparent strain rate softening begins. Since

the reflected pulse is also affected by dispersion, it is

not unreasonable to believe that the strain rates, like the

stresses, are also underestimated. So, the true strain rates

are probably much higher than 3000

s, which would

mean that the strain rate softening occurs well beyond

the calculated limiting strain rate.

There are two methods to correct the dispersion

problem. The first is to directly correct for the dispersion

in the signal.

This requires that a sufficient number

of data points be sampled so that the contribution of

each significant frequency component can be extracted

by means of a Fourier transform. At the sampling

rates used in the dynamic compression experiments,

approximately 80 data points could be obtained for strain

rates above 3000

s. Unfortunately, this is not enough

data to characterized properly the signal in terms of its

significant frequency components. Therefore, dispersion

in the signal cannot be corrected directly.

The second method involves placing a strain gage

on the surface of the specimen to measure directly the

specimen strain.

In order to interpret the corresponding

stresses, a linearly elastic material response must be as-

sumed using a Young’s modulus

of 93 GPa to compute

the stresses. This assumption appears to be reasonable

given that the Zr

41.25

13.75

12.5

22.5

metallic glass

exhibits linearly elastic behavior up to yield and that the

ductility of the specimen is very limited.

A strain gage from JP Technologies was placed on

the surface of a dynamic compression test specimen,

and tests were repeated for strain rates above 3000

and at approximately 230

s. For strain rates of 230

the specimen did not fail and the deformation was

purely elastic, as evidenced by a stress-strain response

identical to the linear portion of the curve in Fig. 5. The

strains were recorded from the specimen strain gage and

compared with the strain derived from the transmitted

pulse, assuming a linearly elastic response (Fig. 11).

From these low strain rate results, it appears that the

strains from the specimen strain gage are within 5% of

the strains derived from the transmitted pulse with the

greatest deviation occurring at the peak strain level. This

is not unexpected since strain gage signals are rarely

accurate to within 10% of the actual strain depending

on the strength of the adhesion between the gage and

the specimen surface. The strain rate was computed by

curve fitting the linear portion of the strain signal from

the specimen strain gage.

FIG. 11. Dynamic strain response from the specimen strain gage and

derived from the transmitted signal for a strain rate of 230

J. Mater. Res., Vol. 11, No. 2, Feb 1996

509

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

After elastically loading the specimen at low strain

rates, the specimen was reloaded at a strain rate above

3000

s. A typical result can be seen in Fig. 12 where the

strain rate was determined to be approximately 3400

From these results it is obvious that the strain derived

from the transmitted signal does not correlate with the

strain from the specimen strain gage. In fact, the strain

from the strain gage has a bandwidth of approximately

s, while the strain derived from the transmitted

signal has a bandwidth of about 14

s. This difference

in bandwidths was also observed in high strain rate

compression tests conducted on ceramics and attributed

to dispersion effects.

The strain response from the specimen strain gage

shows a dramatic increase in strain rate at approximately

2.0% strain, which is most likely due to the initiation of

shear banding. Therefore, this was taken to be the yield

strain of the specimen. The peak strain derived from the

transmitted bar is approximately 1.3%, a value 35% be-

low the yield strain. The differences in peak strain were

also observed in the high strain rate experiments con-

ducted on ceramics and attributed to dispersion effects.

The yield stress was therefore calculated to be

approximately 1.9 GPa, which is within 5% of the value

derived from the transmitted signal at strain rates below

3000

s. This yield stress can be seen in Fig. 13 plotted

against the data from Fig. 7 along with another data point

obtained using a strain gage on a specimen tested at a

strain rate of approximately 4400

s that had not been

prestrained. The data points obtained using specimen

strain gauges are larger than any of the yield stresses

derived from the transmitted signal at strain rates above

3000

s, clearly indicating that dispersion effects are

responsible for the apparent softening behavior observed

at strain rates above 3000

Although peak strains of 3.5% were measured from

the specimen strain gage, it is difficult to interpret the

corresponding load levels. Obviously, if shear banding

FIG. 12. Dynamic strain response from the specimen strain gage and

derived from the transmitted signal for a strain rate of 3400

FIG. 13. Data from Fig. 9 plotted against specimen strain gage data.

has occurred, the stresses cannot be derived assuming a

linearly elastic behavior. Furthermore, the strain would

appear to be accumulated at local rates within the shear

bands of approximately 30,000

s. It has been postulated

that strain rates of this order or higher might occur inside

a shear band during dynamic deformation. Although it is

unreasonable to assume that the strain gage could resolve

strains inside a shear band, it does indicate that there is

some type of post-yield behavior such as shear band

deformation occurring.

While the strain derived from the transmitted sig-

nal is affected by dispersion, the strain derived from

the reflected signal does not appear to be as sensitive

(Fig. 14). In fact, up to yielding the two signals appear

to be identical. This would indicate that although the

yield stresses in Figs. 7 and 13 might be affected by

dispersion at strain rates above 3000

s, the strain rates

should be reasonably accurate. Given that the typical

reflected signal is similar to the incident signal, as seen

in Fig. 3, with a period twice as large as that of the

transmitted signal, it appears reasonable that the reflected

signal would be insensitive to dispersion.

FIG. 14. Dynamic strain response from the specimen strain gage and

derived from the reflected signal for a strain rate of 3200

510

J. Mater. Res., Vol. 11, No. 2, Feb 1996

H. A. Bruck

et al.:

The dynamic compressive behavior of beryllium bearing bulk metallic glasses

VIII. CONCLUSIONS

For the first time, dynamic tests have been conducted

on a metallic glass at strain rates on the order of

–10

s. From these tests, it appears that the metallic

glasses retain their elastic-perfectly plastic material be-

havior at high strain rates. Furthermore, the yield stress

of the Zr

41.25

13.75

12.5

22.5

metallic glass was

not found to depend on strain rate. This result is not

unexpected since the micromechanisms for yielding in

metallic glasses are much different than in conventional

polycrystalline metals and ceramics, where the growth

and motion of defects like dislocations and microcracks

are sensitive to strain rate.

Thermal measurements of shear banding processes

in metallic glasses have been made for the first time.

These measurements indicate that temperature increases

due to adiabatic heating occur only after the onset of

inhomogeneous deformation. Furthermore, temperatures

near the melting point of the Zr

41.25

13.75

12.5

22.5

metallic glass may be approached within shear bands af-

ter the specimen has failed. This is consistent with SEM

observations of a vein-like morphology on the failure

surface which is attributed to localized melting during

shear banding failure. Since only a single detector was

used for the thermal measurements, it was impossible to

identify the detailed nature of the thermal distribution

near the shear band.

REFERENCES

1. G. I. Taylor, Proc. R. Soc. London

A194,

289 (1948).

2. H. Kolsky, Proc. R. Soc. London

B62,

676 (1949).

3. A. Peker and W. L. Johnson, Appl. Phys. Lett.

63,

2342 (1993).

4. H. A. Bruck, T. Christman, A. J. Rosakis, and W. L. Johnson,

Scripta Metall. Mater.

30,

429 (1994).

5. C. F. Cline and J. E. Reaugh, J. de Phys. IV

139 (1991).

6. A. T. Zehnder and A. J. Rosakis, J. Mech. Phys. Solids

39,

385

(1991).

7. A. J. Rosakis, J. J. Mason, and G. Ravichandran, unpublished.

8. P. S. Follansbee,

Metals Handbook

(American Society of Metals,

Metals Park, OH, 1985), Vol. 8, p. 198.

9. H. J. Leamy. H. S. Chen, and T. T. Wang, Metall. Trans.

699

(1972).

10. C. A. Pampillo and A. C. Reimschuessel, J. Mater. Sci.

718

(1974).

11. G. Ravichandran and S. Ghatuparthi, J. Am. Ceram. Soc.

77,

263

(1994).

12. J. M. Staehler, W. W. Predebon, B. J. Pletka, and J. Lankford,

J. Am. Ceram. Soc.

76,

536 (1993).

13. R. A. Davies, Philos. Trans. R. Soc. London

A240,

375 (1948).

14. P. S. Follansbee and C. Frantz, J. Eng. Mater. Technol.

105,

(1983).

15. H. Kolsky,

Stress Waves in Solids

(Dover Publications, New York,

1963).

J. Mater. Res., Vol. 11, No. 2, Feb 1996

511