Incident shocks varying from 9 to 12 GPa and 2 µs duration, impinging on porous pure Mo

(100 µm) powder of distension 1.4, are found to produce compacts of at least 99.4% of

crystal density. Although recovered samples are consolidated and exhibit diamond

pyramid hardness of ~330 to 400, the particles do not appear to be well bonded. Among

several possible models for producing a melt layer on particles vie propose a dynamic

frictional model. The shock pressures required to produce a ~1 µm film of molten

material as a result of dynamic friction varies from 11 to 108 GPa for grain sizes of

100 to 10 µm

Ahrens, Thomas J.

Kasiraj, P.

Kostka, D.

Schwarz, R. B.

Vreeland, T., Jr.

Caltech Authors - Main

Shock Compaction of Molybdenum Powder

Shock recovery experiments which were carried out in the 9 to 12 GPa range on 1.4 distension Mo and appear adequate to compact to full density ( 45 (SIGMA)m) powders were examined. The stress levels, however, are below those calculated to be from 100 to approx. 22 GPa which a frictional heating model predicts are required to consolidate approx. 10 to 50 (SIGMA)m particles. The model predicts that powders that have a distension of m=1.6 shock pressures of 14 to 72 GPa are required to consolidate Mo powders in the 50 to 10 (SIGMA)m range

Ahrens, T. J.

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SHOCK COMPACTION OF MOLYBDENIM POWDER
Thomas J. Ahrens, D. Kostka, T. Vreeland, Jr., R. B. Schwarz*, and P. Kasiraj
California Inbtitute of Technology
Pasadena, CA 91125
*Materials Science and Technology Division
Argonn: N.tional Laboratory
hrgonre, Illinois 60439
September 1983
The submitted manuscript has been autho•ed
by a contractor of the U. S. Government
under contract No W 31 109ENG 78
Accordingly, the U. S Government retains e
nonexclusive, royalty -free license to publish
or reproduce • '.e published form of this
contnbubon, or allow others to do w, for
U. S. Government purposes.
DISCLAIMER
This report was prepared as an account of work sponsored by an agencv of the United States
Government. Neither the United States Government nor any agency thereof nor any of their
employees, makes any warranty, express or implied, or assumes any legal liability or responsi-
bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or
process disclosed, or represents that its use would not infringe privately owned rights. Refer-
ence herein to any specific commercial product, process, or service by trade name, trademark,
manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-
mendation, or favoring by the United States Government or any agency thereof. The views
and opinions of authors expressed herein do not necessarily state or reflect those of the
United States Government or any agency thereof.
SuLmitted to the Proc. of the 3rd APS Conf. on Shock Waves its Solids, Santa
Fe, New Mexico (North Holland, 1983).
,M^
DISTRIBUTWN OF INIS DKU+MENT IS OLIMI1EO
SHOCK COMPACTION OF MOLYBDENUM POWDER
Thomas J. Ahrens, D. Kostka, T. Vreeland, Jr., R. B. Schwarz* and P. Kasira3
California institute of Technology, Pasodena, California 91125
Incident shocks varying from 9 to 12 GPa and 2us duration, impinging on porous pure Mo
(100 um ) powde- of distension 1.4, are found to produce cotn,'icts of at least 99.41 of
c rstal density. Although recovered samples are consolidated and exhibit diamond
pyramid hardness of -33U to 400, the particles do not appear to be well bonded. Among
several possible models for producing a melt layer on particles vie propose a dynamic
frictional model. The shock pressures requirea to produce a -lam film of inol*.en
material as a result of dynamic friction varies from 11 to 108 GPa for grain sizes of
100 to 10 um.
^On leave from MST Div., Argonne National Laboratory, Argonne, IL 60439.
I
1. INTRODUCTION
Tne study of the physics of shock compaction of
refractory metals such as Mo i s interesting in
that it yields insight into the dynamic
compression of porous media in genera! as well
as,	 providing	 tests	 of	 theories	 of
consolidation. Moreover, the compaction 	 and
possible	 consolidation of refractory 	 metal
powders via shock may in the future lead to a
technologically useful process.
	
Recently Murr
et al.	 [1] has reported some optical	 and
electron microscopy and hardness of shock
compacted Mo. They discovered that explosively
compacted (and hardened) Mo retained in excess
of 300 diamond pyramid hardness (DPH) a'_ high
temperatures.
The present report describes the results of some
exploratory compaction experiments carried out
by p.ojectile impact.
	 Optical microscopy and
microhardness
	
measurements of the resulting
samples, were carried out. In addition, we
present a theoretical mdel to predict the onset
of the shock pressure regime over which shock
consolidation is predicted to occur.
2. EXPERIMENTAL DETAILS.
Aliquots of powdered Mo, -325 mesh	 (grains
<45um) (Fig. 1) were pressed into stainless
steel sample containers to a density of 0.7
times crystal density or 7.0 g/cm 3
 corresponding
to a distension, m, of 1.43.
	 The s3mp : ,:s were
evacuated to <50um Hg	 (air	 pressure)	 and
impacted with 304 stainless steel projectiles at
speeds from 1 to 2 km/sec. Only three
experimenta l assemblies (Fig. 2) shocked in the
8.8 to 11.8 GP,-. pressure range (Table 1) yielded
sample ,  which were suitable for m i croscopy and
hardness measurements. Shock pressures in the
samples were calculated using the impedance
match method and
	 of Mo equation of state
parameters [21	 me 'heoretical form for
po rous media of Simons and Legner [3].
50µ
I. Micrograph of • nitial Mo powder (325 mesh).
Table 1. Shock recovery experiments, m= 1.4 powdered Mo.
Shot I
	
Shock Pressure in
Stainless Steel (GPa)
612	 i9.0
613	 20.0
614	 25.0
Initial	 Diamond
Shock Pressure in Pyranid
Sample (GPa)	 Hardness
	
8.3
	
389
	
10.2	 398
	
11.8	 333
Uun CUCOBASE
TARGET RING
AXIAL SPALL
PLATE
2. Cross-section of target recovery assembly.
a sinilar distension rapid solidified 	 steel
powder	 [4]	 which	 demonstrates	 complete
interparticle welding at 18 GPa (Fig. 4).
501
3. RESLLTS
Although some
	 of	 the
	 samples
	 demonstrate
plucking out of particles upon polishing
sections of recovered materials, the post-shock
density of these was 10.15 t 0.04 g/cm 3 which is
close to crystal density of 10.206 g/cm3.
Even the most highly shocked, reco?ered samples
(Fig. 3) demonstrated some grain refinement,
however, the mechar`cal properties were such
that complete interparticle welding had
	 not
taken place.
	 This contrasts to the behavior of
5Oµ
3. Micrograph of 1.4 distension Mo powder shock
compacted to 11 GPa.
4. Micrograph of 9310 steel powder (50um) shock
consolidated to 18 GPa.
4. THFORY
Previously [5], we have modeled the shock
consolidation process as one in which a thin
film of melt is produced by possibly grain
boundary sliding during shock compaction at the
shock gent. A m'nimum shock pressure required
for compaction, as defined by the level of
ultimate tensile strength can correspond	 to
several microscopic processes including:
(1) Production of a zone melt layer via
dynamic friction.
(2) Deformation behavior such that more
irreversible work is near the particle surfaces
rather than in she interior of the particle.
(3) Conduction of heat away from particle
surfaces during shock compression.
(4) The generation of sufficient retal melt
such tha'-
(a) Surface oxide coatings on the grain
are removed and/or ingested in the melt, or,
(b) The melt coats and fills internal
voids and cracks in the compacted metal.
We propose a thecry for describing Process 01
(above).
Process (4) can partially be described with a
simple expression for the mass fraction of nett:
P V o (m-1)
L
2 [C p (Tm - To)	
`in]	 (l)
where, complete melting corresponds to L n 1.
Hera Vo is specific volume of the solid, m is
distension, C 
	
is specific heat, Tm is melting
point, To i„itial temperature and Hm is the heat
of fusion.
Bowden and Tabor [6] have demonstrated that when
metals slide at speeds of >0.5 km/sec, a film of
liquid forms along the contact and the
coefficient of friction, u, drops to -0.1. We
assume that during the process of crush-up of
the porous media for a time, At , of the order
of that required for the free-sur^ace of a grain
to collide with the next grain,	 the	 mean
distance traveled, g, is given by
(m-1)
9'
3	 (2)
where d is the grain size and u fs is the free
surface velocity. Hence
etc - (m- 1 ) d/ ( u fs 3 )	 (3)
The energy deposited per unit mass by grain
boundary friction, E f , is
E f - pP ufs (atc ) 3/[( d+g ) po]	 (4)
where 3/[(d+g) po] is the surface area per unit
mass. If 36/(d+g) is the mass fraction of
material in the surface "friction", or shear,
zone, of thickness, 6, then we can write that
the criterion for shock-induced surface melting
is
uP ufs atc 3/[(d+g)po] >
36/(d+g)[(Tm T o ) C  + Hm] (5)
or
36 [(Tm - To ) C  + Hm] Po
P2
ud(m-1)	 (6)
In addition to requiring a
	 shock	 pressure
greater than specified by Eq. 6, we also require
that the duration of the shock, ts, be greater
than the time required for the melt to solidify
via heat conduction into the solid interior of
the grain. The shock duration to so?idify a
mass fraction of melt specified by Eq. 1 is
given by [5]
12Vo (m-1)] Fin
L Cp [(Tm - To ) Cp + Hm](Tm-
To)]
(7)
where Dm
 is thermal diffusivity.
In the case of iron for which we have found the
onset of shock melting on surfaces to correspond
to P-10 GPa, mn 1.6 for dn50um. We infer a shear
zone thickness of 6 n 1.02 um from Eq. 6.
Using this value of 6 n1un for Mo, to infer a
possible minimum condition for meltin5, yields
using Eq. 6, the values of critical pressure for
different values of m and d are given in Table
2. Notably, the present experiments for d <
451im were conducted slightly below the shock
stress levels required to produce melt, and
hence consolidation. The present model also
requires freezing of the shock melted surface
coating on the grains prior to unloading.
Table 2. Calculated Minimum Shock Pressure
(GPa) for Consolidating Powdered Mo
Distension	 1.4	 1.6
Grain Size (um)
100	 10.8	 7.2
50	 21.6 14.4
10	 107.8 72.0
5. CONCLUSIONS
Shock recovery experiments carried out in the 9
to 12 GPa range on 1.4 distension Mo appear
adequate to compact to full density (< 45wn)
powders. However, the stress levels are below
those calculated to be from 100 to -22 GPa which
a frictional heating model predicts are required
to consolidate -10 to 50 um particles. The
present model predicts that for powders have a
distension of m• 1.6 shock pressures of 14 to 72
GPa are required to consolidate Mo powders in
the 50 to 10 um range.
Acknowledgments:
	 Supported under NASA Grant
NASW3752. R.B. Schwarz partially supported by
D.O.E. P.	 Kasiraj, T. Vreeland, Jr., and D.
Kostka are with the W. Keck Laboratory for
Engineering Materials, Division of Engineering
and Applied Science. T. J. Ahrens is with the
Seismological
	 Laboratory.	 Contribution 3944
Division of Geological and Planetary Sciences.
REFERENCES
[1] Murr, L.E., Tuominen, S.M., Hare, A.W.,
and Wang, S.-H., Structure and hardness of
explosively	 consolidated	 molybdenum,
Materials Science and Engineering
	 57
(1983) 107-.
[2] McQueen, R.G., Marsh, S.P., Taylor, J.W.,
Fritz,
	 J.N., and Carter,	 W.J.,	 The
equation of state of solids from
shock-wave studies, in Kinslow, R. (ed.),
High Velocity Impact Phenomena (Academic
Press, 1970), 294-419.
[3] Simons, G.A. and Legner, H.H., An
analytic model. for shock Hugoniot in
porous materials, J. Appl. Phys. 53
(1982) 943-947.
* d2
teyr	
64Dm
r	 P
[4] Kasiraj, P., Vreeland, T., Jr., Schwarz,
R.B.,	 and	 Ahrens,	 T.J.,	 Shock
consolidation of a 	 rapidly	 solidified
steel powder, submitted for publication
(1983).
[5] Schwarz, ti.8., Kasiraj, P., Vreeland, T.,
Jr., and Mirens, T.J., A theory for the
shock-wave consolidation of powders,
submitted for publication (1983).
[6] Bowden, F.P. and Tabor, D., Part II, The
Friction and Lubrication of Solids (Oxford
Press, 1968), 544 pp.


Shock Compaction of Molybdenum Powder

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