Application of Al-Cu-W-Ta graded density impactors in dynamic ramp compression experiments

J. Appl. Phys. 

125

, 145902 (2019); 

https://doi.org/10.1063/1.5055398

125

, 145902

© 2019 Author(s).

Application of Al-Cu-W-Ta graded density

impactors in dynamic ramp compression

experiments

Cite as: J. Appl. Phys. 

125

, 145902 (2019); 

https://doi.org/10.1063/1.5055398

Submitted: 07 September 2018 . Accepted: 26 March 2019 . Published Online: 11 April 2019

James P. Kelly

, Jeffrey H. Nguyen

, Jonathan Lind

, Minta C. Akin

, Brian J. Fix

, Cheng K. Saw

, Elida R.

White

, Waldi O. Greene

, Paul D. Asimow

, and 

Jeffery J. Haslam

Application of Al-Cu-W-Ta graded density

impactors in dynamic ramp compression

experiments

Cite as: J. Appl. Phys.

125

, 145902 (2019);

doi: 10.1063/1.5055398

View Online

Export Citation

CrossMar

Submitted: 7 September 2018 · Accepted: 26 March 2019 ·

Published Online: 11 April 2019

James P. Kelly,

Jeffrey H. Nguyen,

Jonathan Lind,

Minta C. Akin,

Brian J. Fix,

Cheng K. Saw,

Elida R. White,

Waldi O. Greene,

Paul D. Asimow,

and Jeffery J. Haslam

AFFILIATIONS

Lawrence Livermore National Laboratory, Livermore, California 94551, USA

Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA

Author to whom correspondence should be addressed:

kelly70@llnl.gov

ABSTRACT

Graded density impactors (GDIs) are used to dynamically compress materials to extreme conditions. Two modi

cations to a previously devel-

oped Mg-Cu-W GDI are made in this work before using it in a dynamic compression experiment: Mg is replaced with Al and a Ta disk is

glued to the back. The Mg phase is replaced by Al because FCC Al remains solid to higher pressure along its Hugoniot compared to Mg. The

addition of the Ta disk creates a constant particle velocity regime and facilitates a de

nition of peak pressure states. Microstructure analysis,

pro

lometry, and ultrasonic C-scans of the Al-Cu-W GDI all con

rm excellent uniformity. We evaluated signal variation in the radial direc-

tion of a dynamically compressed Al-LiF bilayer target to evaluate the contribution of spatial nonuniformity to errors. Velocity traces from

ve photon Doppler velocimetry (PDV) probes located at di

erent radial distances from the center of the target varied at most by 1.1% with

a root mean square of 0.3% during the compression ramp, demonstrating low PDV measurement error over a relatively large experimental

area. The experimental PDV data also agrees well with 1D simulations that use inputs from predictive characterization models developed for

the material properties resulting from tape casting, laminating, and powder consolidation processes. Low measurement error during quasi-

isentropic compression, leading to better precision, ensures a robust platform to reach extreme compression and low-temperature recovery

states and facilitates discovery via synthesis, quenching, and preservation of new high-pressure phases.

Published under license by AIP Publishing.

https://doi.org/10.1063/1.5055398

I. INTRODUCTION

Dynamic compression experiments are used to study matter at

extreme conditions in

elds as diverse as aerospace, biology, chemistry,

geophysics, and planetary science. The physical state of matter in the

Earth

’

s core or the evolution of matter in a bolide impact target can

be explored.

An overview of the dynamic compression of materials

that includes general considerations, experimental methods to generate

dynamic compression, experimenta

ldiagnosticsathighdynamicpres-

sures, and error propagation is given elsewhere.

Interesting chemistry

and physics that emerge under extreme conditions are of general inter-

est and have also been reviewed elsewhere.

The report from the Basic Research Needs Workshop on

Synthesis Science for Energy Relevant Technology

identi

ed four pri-

ority research directions (PRDs) for realizing the vision of predictive,

science-directed synthesis. Two of the four PRDs are (1) to achieve

mechanistic control of synthesis to access new states of matter and

(2) to accelerate materials discovery by exploiting extreme condi-

tions, complex chemistries and molecules, and interfacial systems.

Many future discoveries are expected to come from relatively unex-

plored parameter spaces that push the boundaries of synthesis

science. The latter PRD speci

cally highlights the ability to synthe-

size matter under extreme conditions, providing access to previously

unknown phase space of new, metastable compounds. Shock

physics and dynamic compression enable access to these extreme

conditions for short periods of time, which may help quench new

metastable phases. Nanosecond synthesis of diamond by shock

compression is one of the most widely known examples of metasta-

ble phase synthesis,

and other examples exist in the literature. Our

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recovery experiments after dynamic compression demonstrate a varying

crystal defect structure evolution with loading paths,

which could

uence phase transitions.

The use of customized loading paths in dynamic compression,

including intervals of quasi-isentropic compression, enables access

to a wider range of extreme pressure and temperature conditions

than can be achieved with traditional static or shock compression

experiments. Compared to conventional shock compression, exper-

iments with designed impedance pro

les and ranges of impact

velocity provide access to periods of quasi-isentropic compression

that, in turn, allow temperature and pressure to be tuned, which

—

among other applications

—

presents an exciting opportunity to

quench new high-pressure phases to ambient conditions by exploit-

ing lower temperatures that inhibit the kinetics of forward or back-

ward transformations. Discovery and characterization of such novel

recovered phases may have implications in condensed-matter

physics, chemistry, materials science, planetary science, and various

applications. Methods for achieving quasi-isentropic loading and

other designed loading paths include gas gun,

–

laser,

–

and

magnetically driven compression.

–

Early quasi-isentropic compression experiments used cylindrical

compression geometries,

–

plane wave compressions with bu

layers,

–

or conversion of a shock impact into a ramp before it

enters the specimen.

The use of a graded density impactor

(GDI) for quasi-isentropic loading began with Barker

in the 1980s.

At that time, the fabrication of high-quality GDIs was recognized as

the major challenge in creating quasi-isentropic compression with a

well-controlled input wave. Tape casting, laminating, binder burnout,

and hot pressing are highly e

ective methods of tailoring GDIs to

control the thermodynamic path during an experiment because the

GDI design can be controlled by the tape-stacking sequence.

–

Such tailored GDIs can be designed to provide unique thermody-

namic paths that include sequential combinations of shock,

quasi-isentropic compression, constant pressure, and controlled

release regimes

—

all in a single experiment

—

enabling mechanistic

control of synthesis to access new states of matter.

The quali

cation of a new GDI design prepared by tape casting

and laminating is lengthy and generally has three aspects.

–

The

rst aspect is tape characterization, which is used to determine the

tape-stacking sequence. As many as 100 tape layers stacked within a

few millimeters may be required by the GDI design, which necessi-

tates several months of characterization. Replication of quali

cation

experiments can reduce common-cause variation (inherent process

variation) and facilitate assigning and reducing special causes of vari-

ation, but at the expense of adding several more months onto the

quali

cation time. GDI variation is of interest because a sensitivity

study has demonstrated that pressure ramp uncertainty from the

impactor is likely to generate more uncertainty in information

extracted from dynamic ramp compression experiments than align-

ment and diagnostic uncertainties.

The second and third aspects of

quali

cation include process veri

cation and deployment to verify

that there are no processing or application-speci

climitations.

High-impedance GDIs have recently been prepared by func-

tionally grading Mg, Cu, and W.

In this work, we describe the

fabrication and quali

cation of new high-impedance GDI prepared

by functionally grading Al, Cu, and W, followed by gluing Ta to

the back of the GDI. One advantage of replacing Mg with Al is that

the FCC Al phase melts at higher pressure along its Hugoniot com-

pared to the HCP Mg phase. Microstructure analysis, ultrasonic

C-scans, and pro

lometry of GDIs alongside photon Doppler

velocimetry (PDV) signals recorded during a dynamic ramp com-

pression experiment all con

rm excellent GDI uniformity.

Velocity traces from

ve PDV probes located at di

erent radial

distances from the center of a dynamically compressed target

varied by less than 1.1% of nominal in the functionally graded

section with a root mean square of 0.3%, indicating low PDV

measurement uncertainty. Low measurement uncertainty during

quasi-isentropic compression, leading to better precision, ensures

a robust experimental platform to facilitate the discovery and syn-

thesis of new high-pressure phases that can be quenched to

ambient conditions by exploiting extreme compression and low-

temperature recovery states.

II. MATERIALS AND METHODS

A. Tape characterization and root cause analysis of

variation

At least 20 nominally two-phase metal composites span-

ning the full composition range of Al-Cu and Mg-Cu systems

were fabricated by tape casting powder mixtures, stacking and

laminating 50 layers of tapes, binder burnout, hot pressing, and

characterization methods tha

t have been described in detail.

–

One of the systems consisted of aluminum (98%, APS 10

–

Alfa Aesar, Ward Hill, MA) and copper (99.9%, 3

–

m, Alfa

Aesar). The other system consisted of magnesium (99.8%,

−

325

mesh, Alfa Aesar) and copper (99%,

−

325 mesh, Alfa Aesar).

The Mg-Cu composites were prepared and characterized for

comparison purposes.

The length of the binder burnout cycle was two days longer and

the

nal temperature was 25 °C higher (i.e., 400 °C) for the Al-Cu

system compared to the binder burnout cycle for the Mg-Cu system.

The extended binder burnout cycle was necessary to prevent compact

defects. All other parameters were controlled to the maximum extent

possible. Samples were hot pressed at 370 °C for 66 min under a uni-

axial stress of 250 MPa using a Carver 30-ton Autoseries press

(Carver, Wabash, IN). Tape layer thicknesses reported are the mean

from measuring 5 blanks with a digital caliper. Consolidated layer

thicknesses and composite densities were measured from the cylindri-

cal geometry and masses of the hot pressed compacts. The 10-MHz

longitudinal acoustic velocities through the height of the compacts

were measured in four approximately equidistant locations around

the compact perimeter and in the center of the compact. A

time-of-

ight cross correlation method was used to calculate acoustic

velocities. Reported values are an average of values obtained at the

ve measurement locations.

Three replicate samples of select Mg-Cu composites (

=3)

were also prepared to evaluate the e

ect of secondary phases by

X-ray di

raction (XRD) analysis and using Jade software (v.9.7,

Materials Data, Inc., Livermore, CA). The XRD data were collected

with a conventional Phillips vertical goniometer, utilizing Cu-K

radiation. Step scans were performed from 20° to 100° 2

with a

step size of 0.02° and an acquisition time of 2 s per step. Rietveld

nement,

a whole pattern

tting technique, was applied to

the XRD data to extract estimates of the weight percentage of each

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phase with better accuracy than typical peak intensity comparison.

The weight percent estimates were converted to volume percent

using the theoretical density of the phases.

B. GDI process veri

fi

cation

An Al-Cu-W GDI was designed and built in two steps

because of di

erent processing requirements for Al-Cu mixtures

compared to Cu-W mixtures, as noted by Yep

et al.

The Cu-W

tapes were prepared from Cu (1.5

–

m, ACuPowder International,

Union, NJ) and W (99.9%, 1

–

m, Alfa Aesar) and stacked in a

compositional sequence that varied from 100% Cu to a mixture of

50:50 volume percent Cu:W. This composition has impedance

close to Ta and provides a good impedance match to the Ta disk

that will be bonded to the back of the GDI. The binder burnout

pro

le was similar in length to that of the Al-Cu pro

le, but 50 °C

lower (i.e., 350 °C). The samples were vacuum hot pressed in a

graphite punch and die set for 2 h at 1000 °C and 70 MPa uniaxial

stress (typical vacuum levels 10

−

–

−

Torr). The Al-Cu sequence,

from 100% Al to 100% Cu, was prepared as described in Sec.

II A

and hot pressed together with the

nished Cu-W sequence,

arranged in the die, and hot pressed to bond the Cu-Cu interface.

The Al-Cu-W GDI was characterized by surface pro

lometry

with a wide-area 3D measurement system (VR 3100, KEYENCE

Corporation, Itasca, IL). Ultrasonic testing with an UltraPAC

™

instrument (UPK-T10, MISTRAS Group, Inc., Princeton, NJ) was

conducted in the pulse-echo mode using a 15-MHz transducer

(0.375 in. diameter and 1.50 in. focal length) on a GDI immersed

in mineral oil. The microstructure was also evaluated using stan-

dard microscopy techniques (sectioning, polishing, and imaging).

C. GDI deployment

A Ta disk was bonded to the back of a GDI fabricated by the

procedure outlined in Sec.

II B

with STYCAST® epoxy. The GDI

and the Ta disk were

rmly pressed into contact to squeeze out

excess epoxy. The Ta disk

—

a high-purity, high-impedance metal

standard in shock physics studies

—

provides a constant particle

velocity regime after the ramped compression and prevents a

release wave from interfering with the compression ramp. To assess

the radial uniformity of a nominally 1D impact, one assembled

GDI was mounted on a Lexan sabot and launched on the two-stage

light gas gun facility at the California Institute of Technology (Shot

#530) to dynamically compress an aluminum target backed with

a LiF window and observed by eight PDV probes located at di

erent

radial distances from the target center (1, 2, 3, 4, 5, 6, 7, and 8 mm).

A schematic of the experimental con

guration is illustrated in

Fig. 1

The edges were machined o

the GDI to form a 25 mm diameter.

The measured velocity of the projectile prior to impact by double-

ash X-ray and dual magnetic loop pickups was 3.85 ± 0.04 km/s.

Only PDV probes with response signal-to-noise ratios (S/N) greater

than or equal to 5 were analyzed, corresponding to 5 out of 8 chan-

nels (

=2,3,4,5,6mm),becausesmallerS/Ncreateddiscontinuities

in the PDV trace when transforming the raw signals into particle

velocities. Apparent velocities measured by PDV were corrected to

account for LiF properties and give true velocities.

Complementary simulations were performed to compare to

experimental data and expand the opportunity for expedited GDI

development and quali

cation. Simulations were performed in

ALE3D, a

nite element code developed at the Lawrence Livermore

National Laboratory.

Inputs included model layer thicknesses and

initial densities from tape characterization. A Mie

–

Grüneisen equa-

tion of state was used for all materials in the simulation with material

parameters from Steinberg.

Cubic hexahedral mesh elements were

used with a side length of 200 nm resulting in 2 × 2 × 10

elements.

The time at impact was de

ned as

= 0 ns (shock breakout time and

ramp compression times are relative to the impact time) and simula-

tions continued up to 1

s after impact. Material composition of any

given element was assigned based on probability equal to the volume

fraction of constituents within a given layer in the GDI.

FIG. 1.

(a) Side view schematic of a dynamic compression experiment where a

25-mm diameter GDI impacts a 32.5-mm diameter, 1.5-mm thick Al baseplate

and a 19-mm diameter, 10-mm thick LiF window. (b) Back view schematic of

the LiF window showing PDV probe locations that observe the Al-LiF interface

at positions 1, 2, 3, 4, 5, 6, 7, and 8 mm from the center.

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III. RESULTS AND DISCUSSION

A. Tape characterization and root cause analysis of

variation

Tape characterization for GDI quali

cation has been described

elsewhere.

–

Important characterization metrics include the consol-

idated thickness, density, and acoustic velocity. Layer thickness analy-

sisforAl-Cucompositesisshownin

Fig. 2

. The mean tape thickness

is 81.12 ± 0.06

m based on a 95% con

dence interval [solid line in

Fig. 2(a)

] and the observed thickness range is within ±8.09

mofthe

mean [bound by the dotted lines in

Fig. 2(a)

Figure 2(a)

also dem-

onstrates that the mean thickness, after binder burnout and consoli-

dation, is 48.02 ± 0.05

m based on a 95% con

dence interval and

the observed thickness range is within ±7.99

mofthemean.Similar

thickness variation from mean values (about 8

m) and similar thick-

ness variation patterns of the two data sets observed in

Fig. 2(a)

suggest that the consolidated thickness is correlated with tape thick-

ness; this correlation is linear, as shown in

Fig. 2(b)

.Theconsolidated

layer thickness can be predicted from the original tape thickness to

within ±9% based on this correlation.

Tape and consolidated thicknesses for Mg-Cu composites are

shown in

Fig. 3(a)

. The mean tape thickness is 85.16 ± 0.08

FIG. 2.

(a) Experimental thicknesses of Al-Cu composite tapes (closed circles)

and consolidated thickness (open circles). (b) Correlation between the Al-Cu

tape thickness and the consolidated thickness (R

= 0.56) that enables the pre-

diction of consolidated layer thicknesses from the tape thickness measurements

to within ±9% of experimental observations. Mean thickness values or predic-

tions (solid lines) and observed limits from the mean or predictions (dashed

lines) are superimposed onto the plots.

FIG. 3.

(a) Experimental thicknesses of Mg-Cu composite tapes (closed circles)

and consolidated thickness (open circles), (b) consolidated shrinkage of Mg-Cu

tapes, and (c) correlation (R

= 0.82) that enables the prediction of the consoli-

dated layer thickness from tape thickness measurements and knowledge of the

tape formulation to within ±9% of experimental observations. A predicted con-

solidation shrinkage line (solid line) and observed limits from the prediction

(dashed lines) are superimposed onto the correlation plot in (c).

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based on a 95% con

dence interval and the observed thickness

range is within ±15.17

m of the mean. The average consolidated

thicknessis34.31±0.06

m based on a 95% con

dence interval

and the observed thickness range is within ±15.95

mofthe

mean. The observed thickness range is about twice as much for

Mg-Cu tapes as it is for Al-Cu tapes, and the consolidated thick-

ness is not correlated with the tape thickness in the Mg-Cu tapes

= 0.06 and not shown for brevity). The absence of correlation

suggests an additional source of variation, which is explored in

the next paragraph.

The calculated shrinkage during hot pressing of each Mg-Cu

tape is shown in

Fig. 3(b)

. The consolidation shrinkages for

Mg-Cu tapes are generally greater than for Al-Cu tapes. Several

factors (e.g., powder characteristics, additives) can cause di

eren-

ces in the powder packing density that result in di

erent consoli-

dation behaviors.

Without establishing individual contributions,

there is a reasonably tight linear correlation (R

= 0.82) between

the volume of polymers in Mg-Cu tapes and the consolidation

shrinkage [

Fig. 3(c)

]. This suggests that the slurry formulation

used to produce the tapes is a root cause for di

erences in the

powder packing density and thus consolidation shrinkage. The

correlation can also be used to predict the consolidated layer

thickness of the Mg-Cu tapes to within ±9% from the tape formu-

lation and tape thickness measurements. It was not necessary to

consider the e

ect of the polymers for Al-Cu tapes because there

was better control over the binder formulation (polymer fraction

within ±5 vol. % for all Al-Cu tapes compared to ±9 vol. % for

Mg-Cu tapes). The thickness data are summarized in

Table I

Consolidated thickness predictions based on the initial tape thick-

ness and polymer content can now be made with ±9% uncertainty

for both tape systems at the current level of process control. The

results suggest that better control over slurry formulations and

tape casting thickness will reduce this aspect of uncertainty.

Density after hot pressing is the second metric for characteriz-

ing the tapes. The measured densities and relative densities of the

composites are shown in

Fig. 4

. The theoretical densities of com-

posites were determined by a rule of mixtures:

¼

(1)

where

is the theoretical density of the composite,

is the

volume fraction of phase

, and

th,i

is the theoretical density of

phase

(e.g., Al, Cu, Mg). Theoretical densities of composites were

used to determine relative densities from measured densities. The

relative densities are measured densities expressed as a percent of

theoretical density. The

th,i

values for Al, Cu, and Mg phases used

in calculations were 2.70, 8.93, and 1.867 g/cm

, respectively.

The

th,i

value used for Mg is intentionally higher than the theoretical

FIG. 4.

Composite density (

) and density relative to theoretical (

rel

)for(a)

Al-Cu composites and (b) Mg-Cu composites. Mean density relative to theoretical

(dotted line), predicted composite density based on the mean relative density (solid

line), and observed density limits (dashed lines) are superimposed onto the plots.

Density can be predicted to be within ±2% of observed values for Al-Cu compos-

ites and ±4% for Mg-Cu composites using a rule of mixtures. (c) Phase estimates

from X-ray diffraction data were used to correct theoretical and relative densities of

Mg-Cu composites in part (b);

fi

ts are superimposed onto the plot to guide the eye

(n.b., no secondary phases were observed in the Al-Cu

system).

TABLE I.

Summary of thickness data and observed limits compared to predictions.

Metric

Al-Cu

Tapes

Consolidated

Al-Cu

Tapes

Mg-Cu

Tapes

Consolidated

Mg-Cu

Tapes

Mean thickness (

m) 81

Observed range (

m) ±9

±8

±15

±16

Mean shrinkage (%) NA

Observed limits (%) NA

±9

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density of Mg (1.74 g/cm

) to account for signi

cant MgO contam-

ination with 3.58 g/cm

theoretical density.

The MgO in Mg

determined by XRD measurements was 13.23 ± 0.12 wt. % based on

a 95% con

dence interval, or 6.92 ± 0.07 vol. % using theoretical

densities. Thus, Eq.

(1)

predicts a density of 1.867 ± 0.001 g/cm

for

the Mg-MgO composite, which is used in place of the pure Mg

density. Although Mg

Cu and MgCu

intermetallic phases were

observed, such intermetallic phases are insigni

cant to the density

because the compound densities are very close to the weighted

density of the pure metals with the same atomic proportions. No

additional phases were found in the Al-Cu system.

The measured and relative densities of Al-Cu composites are

shown in

Fig. 4(a)

. The mean relative density of the Al-Cu compos-

ites is 95.31% ± 0.01% of theoretical density based on a 95% con

dence interval and the observed relative density range is within

±1.79% of the mean. The relative density variation appears nor-

mally distributed around the mean value. The measured and rela-

tive densities of Mg-Cu composites are shown in

Fig. 4(b)

. The

mean relative density of the Mg-Cu composites is 95.85% ± 0.02%

based on a 95% con

dence interval and the observed relative

density range is within ±3.89% of the mean. There is more varia-

tion in the relative density for the Mg-Cu composites compared to

that for the Al-Cu composites. Unlike the Al-Cu system, there is a

systematic variation in the relative densities with composition in

the Mg-Cu system. The relative density is biased toward lower

values with increasing copper, as observed in prior studies.

This is an important point because uncertainties in mean density

values propagate to uncertainty in using and modeling Mg-Cu

GDIs. The volume fractions of the additional phases calculated

from XRD measurements of the weight fractions are given in

Fig. 4(c)

for reference.

The compact density,

, can be estimated from the mean rela-

tive density,

rel

, and the theoretical density:

¼



rel

:

(2)

All measured density data for Al-Cu composites are within ±2%

of values predicted using Eq.

(2)

, whereas measured density data

for Mg-Cu composites vary from the predictions by about twice

as much, ± 4%. The higher uncertainty for Mg-Cu composites is

most likely due to the relative density bias discussed previously.

Copper cannot be directly implicated for the bias toward lower

density with increasing copper because the bias is not observed in

the Al-Cu system. Factors like initial powder packing density and

reactions can in

uence densi

cation.

A lower powder packing

density due to a higher volume of polymers in the tape formula-

tion [see Fig.

] can contribute to the bias. Alternatively, reac-

tions forming the additional phases [see

Fig. 4(c)

] can contribute

to the enhanced densi

cation in the Mg-rich compositions. The

formation of secondary phases involves temperature-dependent

reaction kinetics and so hot pressing thermal parameters

(e.g., heating/cooling rates, hold temperatures, hold times) are root

causes that can impact the quantities of additional phases and con-

tribute to additional uncertainty for the Mg-Cu system. Better

control over the slurry formulations and the hot pressing parame-

ters could reduce this aspect of modeling uncertainty. A summary

of the density data is provided in

Table II

The third metric is acoustic velocity through the hot pressed

compacts. A model of longitudinal acoustic velocity based on the

Reuss approximation of aggregate elastic moduli has been described

in detail and works quite well despite being considered a lower

limit.

The Reuss model assumption of stress continuity among

phases appears to describe the aggregate elastic behavior of GDIs

more closely than the alternative Voigt model assumption of equal

strain in both phases. The model for acoustic velocity of a two-

phase composite is given by

¼

(3)

and

¼

(

þ

)

(4)

where

is the elastic modulus,

is the density,

is the acoustic

velocity,

is the elastic modulus of a two-phase composite

made from phase 1 and phase 2,

is the elastic modulus of

phase 1,

is the elastic modulus of phase 2,

is the volume

fraction of phase 1, and

isthevolumefractionofphase2.

and

are usually determined from Eq.

(3)

with density and

acoustic velocity data on the pure phases, prepared under suit-

able processing conditions. Then,

is estimated from Eq.

(4)

and, with the measured density of the two-phase composite,

Eq.

(3)

yields a model prediction for the acoustic velocity of the

two-phase composite,

.Wewillmakeaslightmodi

cation

to this approach to account for process variation by replacing

measured density and acoustic velocity values of phase 1 and

phase 2 with values that correspond to the mean relative

density. Approximating acoustic velocity at the mean relative

density requires elaboration.

Relative density is lower than theoretical because of porosity.

Accounting for the e

ect of porosity on the model is not straight-

forward because there is no universal equation relating porosity to

elastic modulus; neither stress nor strain compatibility between the

matrix and the voids applies, and the aggregate properties depend

on pore morphology and spatial distribution in addition to volume

fraction. MacKenzie

derived an equation to estimate the elastic

modulus of a solid with a given radii distribution of spherical

pores. Other studies have con

rmed a complex dependence on

pore morphology parameters that may be unknown

–

and on a

residual stress state, which can a

ect acoustic velocity by up to

30%.

MacKenzie

noted that an empirical approach incorpo-

rating experimentally determined values enables reliable estimates

of porosity corrections in the presence of such combined e

ects.

TABLE II.

Summary of composite densities and observed limits compared to

predictions.

Metric

Al-Cu

Composites

Mg-Cu

Composites

Mean relative density (%)

95.31

95.85

Observed limits (%)

±2

±4

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The dependence of acoustic velocity on porosity can be

described generically as

(

)

¼

(

(5)

where

(

) is the acoustic velocity as a function of porosity,

the acoustic velocity without porosity, and

(

) is a porosity func-

tion that corrects the acoustic velocities to the appropriate mean

relative density, 1

−

avg

, where

avg

is the mean pore fraction.

(

)

is calibrated at the measured porosity level,

exp

(e.g., 1

−

rel

¼

(

exp

)

(

exp

)

(6)

and substituting

from Eq.

(6)

into Eq.

(5)

gives the following

expression:

(

avg

)

¼

(

exp

)

(

avg

)

(

exp

)

:

(7)

Equation

(7)

yields the acoustic velocity of the two phases at the

mean relative density once the experimental and mean relative densi-

ties of the two phases are known. Equations

(5)

and

(7)

are written

generically so that any porosity function can be applied. In the

absence of a universal porous elasticity model, the porosity function

used here is derived from Kingery

’

ssimpli

cation

of MacKenzie

’

derivation and the following expression for density:

(

)

¼

:

þ

:

(8)

and

(

)

¼

(9)

where

(

) is the elastic modulus as a function of pore fraction,

the elastic modulus without porosity, and

(

) is the density as a

function of pore fraction. Using Eqs.

(8)

and

(9)

to derive the acous-

tic velocity model from Eqs.

(3)

and

(4)

and comparing to Eq.

(5)

results in the following porosity function:

(

)

¼

:

þ

:

:

(10)

Table III

shows the data and results of the application of these

equations to obtain the mean density and mean acoustic velocity

of phase 1 (Mg or Al) and phase 2 (Cu), to be used as the

Reuss-derived model inputs for acoustic velocity of the composites

[see Eqs.

(3)

and

(4)

The measured and predicted acoustic velocities of Al-Cu com-

posites are shown in

Fig. 5(a)

; values agree within ±3%.

Corresponding values of Mg-Cu composites [

Fig. 5(b)

] agree

within ±4%. Like the density predictions from which the acoustic

velocity model is derived, acoustic velocity prediction errors for

Mg-Cu composites are higher than for Al-Cu composites, most

likely because of the same root causes. Thus, better control over the

slurry formulations and hot pressing parameters is likely to reduce

acoustic velocity prediction uncertainty. A summary of the

observed acoustic velocity prediction limits is given in

Table IV

The purpose of characterizing density and acoustic velocity

is to calculate acoustic impedance. The acoustic impedance,

FIG. 5.

Longitudinal acoustic velocities through (a) Al-Cu composites and (b)

Mg-Cu composites. Acoustic velocity predictions (solid lines) can be made to

within ±3% of experimental observations (open circles) and within ±4% for

Mg-Cu composites using a Reuss-bound model (observed limits from predic-

tions are given as dashed lines).

TABLE III.

Measured and mean densities, porosity fractions, and acoustic velocities

used to predict acoustic velocities of composites.

System Phase

Data

rel

(%)

(g/cm

)

(km/s)

Al-Cu

Al Measured 94.37 0.0563 2.55

5.83

Mean

95.31 0.0469 2.57

5.85

Cu Measured 95.44 0.0456 8.52

3.87

Mean

95.31 0.0469 8.51

3.86

Mg-Cu Mg Measured 94.53 0.0547 1.77

5.41

Mean

95.85 0.0415 1.79

5.44

Cu Measured 93.45 0.0655 8.35

4.13

Mean

95.85 0.0415 8.56

4.17

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is given by

–

¼

:

(11)

Acoustic impedance predictions can be made using density predic-

tions [Eq.

(2)

] and acoustic velocity predictions [Eq.

(7)

] as inputs

to Eq.

(11)

. Impedance values calculated from experimental data

and from this prediction scheme are shown in

Fig. 6

; impedance

predictions are accurate to ±4% for Al-Cu composites and ±6% for

Mg-Cu composites. These observed limits are consistent with the

propagation of the errors on density and acoustic velocity and so,

again, better control over slurry formulations and hot pressing

parameters should reduce acoustic impedance prediction uncer-

tainty. All aspects of tape characterization are now complete. The

second step of GDI quali

cation is process veri

cation.

B. GDI process veri

fi

cation

Section

III A

focused on a comparison between the Al-Cu and

Mg-Cu systems because we are substituting Al for Mg in previously

developed Mg-Cu-W GDIs.

We applied a similar analysis to the

Cu-W system to establish uncertainties, which is only summa-

rized here for brevity (

Table V

). The uncertainty in predicting

thickness, density, and acoustic velocity was 12%, 1%, and 1%,

respectively. There is greater uncertainty in thickness arising from

the tape casting process and lesser uncertainty in density and

acoustic velocity arising from both tape casting and thermal pro-

cessing compared to those in the Al-Cu and Mg-Cu composites.

However, these limits were inferred from a more limited data set

(only 8 composite samples compared to at least 20 in each of the

Al-Cu and Mg-Cu systems).

The prediction methods that have been developed in this work

can be used to model the acoustic impedance pro

le of any GDI

tape-stacking sequence, which is typically done via a lengthy

process (months of e

ort) that determines the thickness and acous-

tic impedance of each individual layer.

–

The predicted imped-

ance pro

le (with calculated uncertainty) of a 52-layer Al-Cu-W

GDI are compared to data from the traditional experimental tape

characterization process in

Fig. 7

. The limits shown are extreme

limits for GDI-to-GDI impedance pro

le variation (e.g., the upper

limit assumes that each consolidated layer has the minimum pre-

dicted thickness and the maximum predicted impedance). The

modeled and measured impedance pro

les agree to within ±4%.

This agreement represents a major progress in the practical applica-

tion of new GDI designs, reducing the time for the

rst stage of

GDI quali

cation from months to weeks since only tape thick-

nesses and full characterization of the pure phases are required

(as opposed to full characterization of each individual compositional

layer), which reduces the number of tapes to characterize by 90%.

The predicted thickness of a GDI having the impedance

pro

le depicted in

Fig. 7

is 2.40 ± 0.23 mm. This corresponds to an

estimated 10% uncertainty in the length or rate of the compression

ramp that will result from the use of the GDI in a dynamic com-

pression experiment.

This level of uncertainty is comparable to

the reported current input accuracy of Sandia

’

s Z machine.

Although the input wave may therefore vary from one GDI to

another, the thickness of each GDI is known before it is used in a

given experiment and the input wave (i.e., drive) for each experi-

ment is directly measured. Hence, the selection of a subset of

TABLE IV.

Observed limits for acoustic velocity compared to predictions.

System

Observed limits (%)

Al-Cu

Mg-Cu

TABLE V.

Observed limits compared to predictions for thickness, density, acoustic

velocity, and acoustic impedance for Cu-W composites.

Parameter

Observed limits (%)

Thickness

Density

Acoustic velocity

Acoustic impedance

FIG. 6.

Acoustic impedance of (a) Al-Cu composites and (b) Mg-Cu compos-

ites. Acoustic impedance predictions (solid lines) can be made to within ±4% of

experimental observations (open circles) for Al-Cu composites and within ±6%

for Mg-Cu composites using the density and acoustic velocity models (observed

limits from predictions are given as dashed lines).

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nished GDIs with a narrower thickness range allows a series of

experiments with nearly identical compression ramps.

We have fabricated 13 GDIs with the nominal impedance

pro

le demonstrated in

Fig. 7

to demonstrate the bene

t of GDI

selection criteria. The mean thickness of the 13 GDIs is 2.42 ± 0.06

mm (95% con

dence interval) and ranged from 2.21 to 2.59 mm.

The measured range is in excellent agreement with the predicted

limits (2.40 ± 0.23 mm). Selecting a subset of 5 GDIs from the orig-

inal 13 yields a thickness range from 2.42 to 2.45 mm and reduces

variations in pressure ramp uncertainty to 1%.

We so far focused on GDI-to-GDI variation, but the unifor-

mity of a given GDI is also important for dynamic compression

experiments. Each fabricated GDI is a cylinder with 31.75 mm

diameter and the microstructure should be as uniform as possible

over the entire area of the GDI to allow

exible placement of mea-

surement probes. Next, we explore the microstructure and compo-

sition gradient on a full-depth, full-radius cross section of a GDI,

pro

lometry to check surface height variation, and ultrasonic

testing to con

rm uniformity.

Figure 8

shows a representative microstructure cross section of

an Al-Cu-W GDI. It is di

ffi

cult to decipher the original tape layer

boundaries, demonstrating a smooth compositional gradient.

Overall, the Al-Cu-W GDI appears to have good microstructure

uniformity. There are rare instances of abnormally large Al grains

in the microstructure, which could be eliminated by better control

of the Al particle size distribution.

Height images of two Al-Cu-W GDIs are shown in

Fig. 9

. The

white arrow across the height image in

Fig. 9(a)

depicts the direc-

tion of maximum side-to-side thickness variation across the

surface, which causes the maximum convex bow height (closed

circle) to shift from the center (open circle). The mean side-to-side

thickness variation from measurements on seven GDIs was 20 ± 10

m (95% con

dence interval) and ranged from 0 to 40

m. The

mean bowing height from measurements on seven GDIs was 30 ±

m (95% con

dence interval) and ranged from 20 to 40

The extent of bowing and side-to-side thickness variation is com-

parable to previously developed GDIs.

Bowing and side-to-side

thickness variation cause local compression or dilation of the

impedance pro

le at di

erent points on the impacting surface that

can contribute to PDV measurement variation.

The extent of side-to-side thickness variation or bowing

(

≤

m) compared to the thickness of the GDI (

≥

2.17 mm) sug-

gests that these factors may contribute up to about 1.8% to PDV

measurement uncertainty at di

erent probe locations. However, this

may be an overly conservative limit because the e

ects of bowing

and side-to-side thickness variation can be partially mitigated by

strategic selection of probe locations. For example,

Fig. 9(b)

demon-

strates a GDI that is bowed, but without a signi

cant side-to-side

thickness variation. For this GDI, probes located at the same radial

distance from the center (e.g., at the positions of the arrows along

the dotted curve) would be minimally a

ected by GDI side-to-side

thickness variation and bowing due to symmetry.

Nondestructive evaluation of each GDI with ultrasonic testing

is performed before it is considered for use in a dynamic compres-

sion experiment.

Such an evaluation is demonstrated by the A-,

B-, and C-scans in

Fig. 10

. An A-scan records the amplitude of

echoes returned to the transducer as a function of time; the front-

side and backside re

ections can be picked and yield a transit time

through the GDI. This can be compared to a prediction from the

tape characterization data. The waveform of an Al-Cu-W GDI is

depicted in

Fig. 10(a)

. The time between the peak amplitudes of

the re

ections from the front Al surface and the back Cu/W

surface is 0.90

s. This precisely matches the acoustic time-of-

ight

expected from thickness and acoustic velocity data (0.90

s for the

2.36 mm thickness of this GDI).

A B-scan is given in

Fig. 10(b)

, which represents the waveform

(A-scan) as a function of position as the transducer is scanned

FIG. 7.

Impedance pro

fi

le of an Al-Cu-W GDI as a function of thickness deter-

mined by predictions and experimental validation (open circles). The predicted

impedance pro

fi

le is given as a solid line and limits derived from thickness and

impedance prediction limits are given as dashed lines. The predicted GDI thick-

ness based on the speci

fi

c tape-stacking sequence is 2.40 ± 0.23 mm when

considering the prediction limits, which agrees well with the observed thick-

nesses of 13 of these GDIs (the mean thickness of 13 GDIs is 2.42 ± 0.06

based on a 95% con

fi

dence interval and ranged from 2.21 to 2.59 mm).

FIG. 8.

Optical micrograph of the graded section of an Al-Cu-W GDI, which

demonstrates the transformation of a series of discrete compositional layers into

a smoothly graded structure as well as good microstructure uniformity.

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along a line, in this case a 31.75 mm grand diameter of the GDI.

The color scale in the B-scan represents the echo amplitudes

returned to the transducer as a function of time (the waveform

from an A-scan is drawn in the center of the B-scan to help clarify

this visualization). The uniformity of the color bands over the

inner 29 mm of the scan length shows that the waveform is

uniform across the scan length except where there are edge e

ects

(i.e., about 1

–

2 mm from each edge). There are no major re

ections

between the signals from the front and back surfaces anywhere

along the scan length, and both the position and the intensity of

the re

ections are uniform. The parallel dotted lines drawn in

Fig. 10(b)

show that deviations from surface parallelism are too

small to be observed by this method.

A C-scan represents the spatial uniformity over the entire GDI

surface, typically by plotting either the acoustic time-of-

ight or

the amplitude of the largest re

ection in a speci

ed time frame as a

function of scan position. For example, the C-scan in

Fig. 10(c)

depicts the amplitude of the back Cu-W surface re

ection from the

GDI across the scan area. Any abnormalities in the GDI that cause

excessive acoustic scattering or re

ection would decrease the ampli-

tude of the back surface re

ection. However, the amplitude of the

back surface re

ection is about 57% ± 1% over the entire surface

and demonstrates excellent radial uniformity of the GDI.

C. GDI deployment

Experimental diagnostics have rarely been used to explore the

uniformity of a dynamic compression response in the radial direc-

tion because such measurements are easily a

ected by lateral

release waves.

Here, we carefully designed an experiment to evalu-

ate radial uniformity using a large-diameter, thin target that keeps

lateral release waves away from the probed region. The results can

be used to evaluate the intrinsic uniformity of the drive provided

by the GDI. As noted above, the GDI used was typical of the

selected group of most uniform GDIs, with 30

m bowing, 30

side-to-side thickness variation, and 2.36 mm thickness, implying

thickness variations of up to 1.3% of the total GDI thickness. The

GDI diameter is turned down before mounting into the sabot; the

diameter reduction of about 20% suggests up to 1.1% thickness var-

iation across the

nal

yer plate.

The plot in

Fig. 11

shows the apparent particle velocity traces

from

ve PDV probes located at 2, 3, 4, 5, and 6 mm from the

center of an Al-LiF target (see

Fig. 1

). All particle velocity traces

show the shock breakout, followed by velocity stabilization at about

2500m/s for about 200 ns because of the constant impedance Al

section at the front of the GDI. The particle velocity then rises to

about 3600m/s over another 200 ns. There is a minor release due to

the slight separation between the Al-Cu-W GDI and the Ta

backing, where there is a glue line, followed by a rise back to about

3700m/s. The particle velocity stabilized to a plateau for about

300 ns due to the constant impedance of the Ta plate glued onto

the back of the GDI, followed

nally by target decompression. The

release wave from the glue layer is acceptable if the goal of the

experiment is achieved before the release occurs or if the release

does not directly a

ect data of interest beyond the release.

However, in some applications, the glue release could a

ect the

thermodynamic path and path-dependent variables. In such cases,

the release wave may be eliminated by di

usion bonding rather

than gluing the constant impedance backing to the GDI (this

method has been used in other GDIs, not shown here). Since the

primary goal of this experiment is to test radial uniformity of the

compression ramp, it was not necessary to eliminate this release

wave from this shot.

Bastea

et al.

suggested that properly diagnosed PDV measure-

ment variations can be minimized by time corrections to the

FIG. 9.

(a) Height image of the back surface of an Al-Cu-W GDI with a 31.75

mm diameter, a side-to-side thickness variation of about 20

m, and a bow

height of about 30

m [the white arrow depicts the direction of maximum

side-to-side thickness variation, which causes the maximum convex bow height

(closed circle) to shift from the center (open circle)]. (b) A height image of a

GDI without a side-to-side thickness variation, but with a similar bow height,

shows that strategically placed probes at a constant radial distance from the

center could exploit the symmetry of this GDI to minimize geometric

trace-to-trace differences in PDV pro

fi

les.

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particle velocity traces.

Time shifts between PDV traces might be

due to GDI factors (nonuniform impedance, bowing, side-to-side

thickness variation, and tilt between projectile and target surfaces

due to sabot mounting or in-

ight rotation), target factors (varia-

tions in thickness, nonplanarity), or diagnostic factors (cables car-

rying current to the recording oscilloscopes, etc.). Diagnostics are

designed or calibrated to minimize the timing o

set and the target

thickness is usually controlled to be within 1

m, so GDI and pro-

jectile factors are most likely responsible for timing o

sets.

The maximum timing o

set of the shock breakout between

the di

erent particle velocity traces is 65 ns. This corresponds to a

linear distance of 250

m based on the projectile velocity (3.85 km/s).

This distance is greater than the extent of side-to-side thickness varia-

tion or bowing within the GDI, which can account only for o

sets of

about ±4 ns and indicates that tilt between the projectile and the

target surfaces due to sabot mounting and/or in-

ight rotation is

most likely responsible for the timing o

sets.

Figure 12(a)

depicts results from an analysis of projectile tilt.

Two of the probes yielded equal shock breakout times, each o

set

by +10 ns from the average shock breakout time. We therefore

developed a model for tilt of a planar projectile with a tilt rotation

axis parallel to the line between these two probe locations.

Assuming that the timing o

sets are due to a simple tilt of a planar

projectile only, we obtain the timing o

set for each other point by

projecting parallel timing o

set contours through those points (red

lines).

Figure 12(b)

shows that the measured timing o

sets are

linear when plotted against the distance between the o

set contours

in the assumed tilt direction. The strong correlation of the linear

= 0.998) suggests that indeed tilt is the primary cause for shock

breakout timing di

erences. The slope of 5.37 ns/mm, for a

FIG. 10.

Ultrasonic (a) A-scan, (b)

B-scan, and (c) C-scan of an Al-Cu-W

GDI. The A-scan waveform measures

the acoustic time-of-

fl

ight between the

front and back surface re

fl

ections

(0.90

s), which is consistent with the

expected transit time for the 2.36 mm

thick GDI. The B-scan demonstrates

that the waveform is consistent across

a grand diameter of the GDI with no

major internal re

fl

ections. The C-scan

plots the back surface re

fl

ected ampli-

tude in two dimensions, showing no

major internal scattering or re

fl

ections

from defects.

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