Experimental Data on Shock Compression and Adiabatic Expansion of Condensed Matter

447 Pages·5.404 MB·English

by  Trunin R.F., Gudarenko L.F., Zhernokletov M.V., Simakov G.V. (Ed.),

EXPERIMENTAL DATA ON SHOCK COMPRESSION
AND ADIABATIC EXPANSION OF CONDENSED
MATTER

Academic publication

Edited by R.F. Trunin, Sc.D. in phys. & math.

RFNC-VNIIEF
SAROV
2001
Experimental Data on Shock Compression and Adiabatic Expansion of
Condensed Matter. – Sarov: RFNC-VNIIEF, 2001, 446 p.
ISBN 5-85165-624-7

Authors: R. F. Trunin, L. F. Gudarenko, M. V. Zhernokletov, G. V. Simakov

The Collection presents results of the experiments on shock compression and adiabatic
expansion of condensed matter and the data on compression of some gases obtained in
Russia from 1949 to 2000.
The Collection includes data on most periodic table elements (including on continuous,
porous and molten metals), oxides, alloys, metal hydrides, carbides and nitrides,
halogenides, solid and liquid organic materials, water and its solid modifications, water
solutions of salts, and a number of other compounds.
The experimental data on continuous sample compression is approximated with simple
interpolation dependencies convenient for using in practice and represented in the graphic
form. A table of cinematic and thermodynamic parameters is presented for each material –
shock and mass velocities, pressure, compression, density, and shock compression energy
(internal energy).
The data presented can be used in many high energy density physics branches – when
considering high-velocity impacts, in issues of planetary astronomy, including internal planet
composition, different aspects of explosion technique and technology (including issues of
prevention of accidents of devices operated under high-pressure conditions), explosive
processing of materials, synthesis of new materials, etc.
The Collection is intended for scientists, engineers, post-graduates, and students who
pursue using shock waves in modern physics, physical astronomy, chemistry, power
engineering, technology, space and defense science, and other disciplines.

(cid:211) Russian Federal Nuclear Center – VNIIEF, 2001
ISBN 5-85165-624-7
FOREWORD
In Russia, the infancy and evolution of the shock-wave methods for material thermo-
dynamic characteristic studies goes back to 1947, when the works on the equation of state
studies were placed on a broad footing under the governmental Atomic Program. The equa-
tions of state that functionally integrate the thermodynamic parameters, i.e. energy (or tem-
perature), pressure, and density, are required to close the continuum motion equation sys-
tem used in mathematical calculations of different structures under action of intense pulsed
loads.
A major information source used when constructing the equations of state is experi-
*
mental data on continuous material shock compression that determines pressure as a func-
tion of density and energy, i.e. shock Hugoniot. It is for this reason that most papers studying
condensed material properties with shock-wave methods measure material compressibility.
However, information from the continuous material shock compression experiments
determines the equation of state only near one line, the continuous material Hugoniot, on the
phase plane. The description of material states in a wider phase diagram region involves
additional data on shock compression of porous samples (with artificially reduced initial den-
sity), adiabats of double compression (by two sequential shock waves), sound speeds, and
adiabatic expansion of materials pre-compressed in shock waves. These data in the aggre-
gate provide information about compressed material high-temperature state thermodynam-
ics in a wide pressure and density range.
The data presented in the Collection is mainly obtained by All-Russian Research Insti-
tute of Experimental Physics from the late 1940's to the end of 2000. Besides the authors,
an appreciable contribution to setting up the studies and conduct of a great number of the
experiments on the material property studies using shock waves was made by L.V. Alt-
shuler, M.A. Podurets, A.A. Bakanova, M.N. Pavlovsky, V.N. Zubarev, Yu.N. Sutulov,
I.P. Dudoladov, L.V. Popov, B.N. Moiseyev.
In the experimental data processing and systematization, much assistance was ren-
dered to the authors by O.N. Gushchina, who developed (jointly with V.D. Trushchin) the
database and prepared the electronic version of the Collection. At different phases of the
Collection preparation, the authors were assisted by M.Yu. Belyakova, V.A. Bugayeva, L.M.
Terskova, N.L. Shaboldina. The authors would like to express their appreciation and grati-
tude to them.
The Collection may be not free of demerits, so the authors welcome any comments
both on the contents and the representation form of the experimental data.

* Of initial density equal to crystalline density.
TABLE OF CONTENTS

DYNAMIC METHODS FOR STUDYING MATERIAL PROPERTIES AT HIGH PRESSURES 6

Shock Hugoniot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Double compression (re-compression) Hugoniot . . . . . . . . . . . .. . . . . . . . . . . . . 8
Shock-compressed material expansion adiabats . . . . . . . . . . . . . . . . . . . . . . . . . 9
Sound speed in shock-compressed material . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Reference Hugoniots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
EXPERIMENTAL DATA REPRESENTATION FORMATS . . . . . . . . . . . . . . . . . . . . . . . . 13

Formats of data on shock compression of continuous condensed materials and
gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Formats of data on shock compression of porous materials . . . . . . . . . . . . . . . . 14
Formats of data on double compression (re-compression) of materials . . . . . . . . 15
Formats of data on expansion adiabats of shock-compressed continuous and
porous materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Formats of data on velocity of shock-compressed material expansion to air . . . . 15
Formats of data on sound speed in shock-compressed materials . . . . . . . . . . . . 16

EXPERIMENTAL DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Nitrogen (liquid), 19. Aluminum, 20. Argon (gas), 27. Argon (liquid), 28. Barium, 29. Va-
nadium, 30. Bismuth, 31. Tungsten, 39. Gadolinium, 45. Gallium, 46. Hafnium, 47. Germa-
nium, 48. Holmium, 49. Dysprosium, 50. Europium, 51. Iron, 52. Gold, 60. Indium, 61. Irid-
ium, 62. Ytterbium, 63. Yttrium, 64. Iodine, 65. Cadmium, 66. Potassium, 69. Calcium, 70.
Cobalt, 71. Silicon, 75. Krypton (liquid), 76. Xenon (gas), 77. Xenon (liquid), 78. Lantha-
num, 79. Lithium, 80. Lutecium, 81. Magnesium, 82. Copper, 85. Molybdenum, 99. Sodi-
um, 109. Neodymium, 110. Nickel, 111. Niobium, 123. Tin, 124. Praseodymium, 128. Rhe-
nium, 129. Rhodium, 130. Samarium, 131. Lead, 132. Selenium, 142. Sulfur, 143. Sil-
ver, 144. Scandium, 145. Strontium, 146. Thallium, 147. Tantalum, 148. Titanium, 154. Car-
bon (diamond), 159. Carbon (graphite), 163. Phosphorus (red), 169. Chrom, 170. Ceri-
um, 173. Zinc, 174. Zirconium, 182. Erbium, 183

Alloys and mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Meteorite (1), 184. Meteorite (2), 184. Quartz-aluminum mixture (1), 185. Quartz-
aluminum mixture (2), 186. Quartz-aluminum mixture (3), 187. Quartz (quartzite)-paraffin
mixture, 188. Quartz-fluoroplastic mixture, 189. Copper-carbon (diamond) mixture, 190. Mar-
ble-paraffin mixture, 192. Paraffin-tungsten mixture (1), 193. Paraffin-tungsten mixture (2),
194. Feldspar-paraffin mixture, 195. Calcite-water mixture (wet chalk), 196. Cobalt-nickel
alloy, 197. Iron-copper alloy, 198. Iron-nickel alloy, 199. Magnesium-lithium alloy, 200. Rhe-
nium-molybdenum alloy, 201. Nickel-copper alloy, 202. Titanium-molybdenum alloy, 203.
Titanium-zirconium alloy, 204. Alloy Amg6, 205. Alloy AMts, 206. Alloy VNZh-90, 207. Alloy
VNZh-95, 208. Alloy VNM-3-2, 209. Wood metal, 210. Alloy D-16, 211. Alloy NT30E, 212.
Alloy NT5E, 213. Steel 12Kh18N10T, 214. Steel 25KhGSA, 215. Steel 30Kh13, 216. Steel
35, 217. Steel 40Kh, 218. Steel 45, 219

Minerals and rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Aleurolite, 220. Anhydrite, 221. Barite, 222. Beryl, 223. Brucite, 224. Wollastonite, 225.
Gabbro, 226. Hedenbergite, 227. Hetite, 228. Hypsum, 229. Clay, 230. Granite, 231.
Dolerite, 232. Dolomite, 233. Dunite-1, 234. Dunite-2, 235. Ilmenite, 236. Calcite, 237. Silica
(quartz and quartzite), 240. Silica (coesite), 256. Silica (crystobalite), 259. Cryolite, 260.
Magnesite, 261. Magnetite, 262. Microline, 263. Marble, 264. Nepheline, 265. Olivinite (1),
266. Olivinite (2), 267. Olivine-diabase, 268. Olivine-diallagite, 269. Periclase, 270. Perov-
skite, 271. Pyrite, 272. Pyrolusite, 273. Feldspar, 275. Feldspathic peridotite, 276. Ore oli-
Table of contents 5
olivinite, 277. Rutile, 278. Sellaite, 281. Syenite, 284. Shale, 285. Spodumene, 286. Glass,
287. Sphalerite, 288. Topaz, 289. Tremolite-1, 290. Tremolite-2, 291. Fluorite, 292. Enstatite
rock, 293. Enstatite gabbro, 294

Water and saturated water solutions of salts . . . . . . . . . . . . . . . . . . . . . . . . . 295
Water, 295. Sea water (Barents Sea), 301. Cesium iodine solution, 302. Cesium bromide
solution, 303. Potassium bromide solution, 304. Potassium chloride solution, 305. Potassium
iodide solution, 306. Sodium iodide solution, 307. Sodium thiosulfate solution (1), 308. So-
dium thiosulfate solution (2), 309. Sodium chloride solution, 310. Zinc chloride solution (1),
311. Zinc chloride solution (2), 312. Zinc sulfate solution, 313

Metal halogenides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Barium fluoride, 314. Potassium bromide, 317. Potassium chloride, 318. Lithium fluori-
de, 320. Copper chloride, 321. Copper iodide, 322. Sodium iodide, 323. Sodium chloride,
324. Thallium iodide, 327. Thallium chloride, 328. Cesium bromide, 329. Cesium iodide, 330

Metal hydrides and nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
Aluminum nitride, 332. Vanadium hydride, 334. Potassium hydride, 335. Silicon nitride, 336.
Magnesium hydride, 337. Tantalum hydride, 338. Tantalum nitride, 339. Titanium hydride,
341. Titanium nitride, 342. Zirconium hydride, 343. Zirconium nitride, 344

Metal carbides and oxides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Beryllium carbide, 345. Boron carbide, 346. Tungsten carbide, 347. Cassiterite, 349. Co-
rundum, 350. Silicon carbide, 351. Niobium carbide, 352. Ruby, 354. Tantalum carbide, 355.
Titanium carbide, 356. Carbonic acid, 357. Zirconium carbide, 358

Organic liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Acrylonitrile, 359. Amyl alcohol, 360. Caproic acid anhydride, 361. Butyric acid anhydride,
362. Aniline, 363. Acetone, 364. Acetonitrile, 365. Benzene, 366. Bromoform, 367. Butyl
alcohol, 368. Hexadecane, 369. Hexane, 370. N- Hexane, 371. Hexene-1, 372. Hexene-2,
373. Hexyl alcohol, 374. Hexine, 375. Heptane, 376. Heptene, 377. Heptylic alcohol, 378.
Decane, 379. Caproic acid, 380. Butyric acid, 381. Formic acid, 382. Nitrobenzene, 383.
Nonyl alcohol, 384. Octene, 385. Octyl alcohol, 386. Octine, 387. Styrene, 388. Tetradec-
ane, 389. Tolyene, 390. Trihydrodecafluoroheptanol, 391. Trihydrooctafluoropentanol, 392.
Trihydrotetrafluoropropanol, 393. Tridecane, 394. Acetic acid, 395. Cyclohexane, 396. Cy-
clohexanone, 397. Cyclohexene, 398. Carbon tetrachloride, 399. Ethyl alcohol, 400

Solid organic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Myristic acid anhydride, 401. Tartaric acid, 402. Glutaric acid, 403. Caprolon, 404. Maleic
acid, 406. Palmitic acid, 407. Paraffin, 408. Polyimide plastic foam, 410. Polycarbonate, 413.
Polymethyl methacrylate, 414. Polystyrene, 419. Polytetrafluoroethylene, 424. Polyethylene,
427. Stilbene, 429. Tetracosane, 430. Phenilone, 431. Phthalic acid, 433. Phthalic anhy-
dride, 434. Epoxy compound EK-10, 435. Epoxy compound EK-34, 436. Succinic acid, 437.
Succinic anhydride, 438

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
DYNAMIC METHODS FOR STUDYING MATERIAL PROPERTIES
AT HIGH PRESSURES
The experimental data presented in the Collection is obtained using plane [1] (pp. 28,
37, 60, 225, 279) and spherical [2] shock waves generated by laboratory explosive devices
as well as powerful shock waves from underground nuclear explosions that act on materials
to be studied [3].
Shock Hugoniot

The experimental determination of Hugoniots requires no direct measurements of the
thermodynamic parameters, i.e. pressure P, density r (or specific volume V ), and specific
internal energy E. The Rankine–Hugoniot relations, which express the laws of conservation

of mass, momentum, and energy at the shock discontinuity, relate the compressed material
pressure, density, and energy to the shock wave cinematic parameters, i.e. shock wave ve-
locity D and material mass velocity U. For medium that is originally in rest the relations are

r D
= – mass conservation law; (1)
r D- U
0
P - P =r UD – momentum conservation law; (2)
0 0
1 (cid:230) 1 1(cid:246)
E- E = (P +P )(cid:231) - (cid:247) – energy conservation law, (3)
0 2 0 Ł r r ł
0

where subscript "0" denotes the initial state parameters before the shock front. The problem
of the compressed material pressure, density and energy estimation thus reduces to ex-
perimental measurements of wave and mass velocities of shock waves with specially devel-
oped methods.
Estimation of wave velocities. Shock wave velocity is estimated most easily and accu-
rately in dynamic experiments. For this purpose it is sufficient to place any wave front pres-
sure jump sensitive sensor type (electrocontact sensors are used most frequently) on the
shock wave propagation path. The sensor closing times are fixed on time sweep traces of
the recorders. The obtained times and known sample thicknesses determine the velocity of
the shock wave propagating through the samples.
Estimation of mass velocities.
Deceleration method. The second cinematic parameter, i.e. material mass velocity
behind the shock front, is harder to estimate. In this case the sensors must “withstand” high
wave front pressures and response to the states following the front. The problem was solved
indirectly. Consider the deceleration method proposed for this purpose.
Being developed by L.V. Altshuler and associates [4] in the Soviet Union in the late
1940's, the method estimates material mass velocity by recorded velocity W of an impactor
Y
driven by explosion products in its impact on a target made of material to be studied. Shock
wave velocity, D, at the target is simultaneously recorded.
For the impactor and the target fabricated from identical materials the impactor decel-
eration against the barrier produces two equal-intensity waves propagating on either side of
the impact surface. By virtue of impact symmetry, U = W /2. The remaining parameters of
Y
the shock wave in the target are found by substitution of mass velocity, U, and shock wave
7
Dynamic methods for studying material properties at high pressures
velocity, D, into equations (1) and (2) of the laws of conservation, the compressed material
energy is determined from equation (3).
By varying the impactor velocity, W , and measuring relevant wave velocities, D, in the
Y
target, one obtains a set of points that in the aggregate determine the material Hugoniot
position.
When the impactor impacts on a
P
target made of another material, the Y
equality of the mass velocity jumps in the
target and the impactor does not hold. B
The seeming difficulty in the estimation of
U is overcome through the impactor fabri-
cation from material of a known Hugoniot.
In this case the mass velocity is estimated P1 1
using the laws of the Riemann problem at P = r DU
0
the impactor-target interface. Consider
the impactor-target impact on the P–U
diagram (Fig. 1). The impactor Hugoniot is
depicted with curve AY going out of the
initial state, P = 0, U = W . The measured A
Y
0
wave velocity in the target determines the U U
1
slope of wave beam 0B that satisfies
equation P =r DU . Point 1 of the wave W
0 y
beam-impactor deceleration curve inter-
Fig. 1. P–U diagram of the deceleration method
section determines the desired pressure,
P , and mass velocity, U , in the material under study. These values and equations of state
1 1
are used to find other compression parameters as well.
The deceleration method was used to determine Hugoniots of iron and aluminum
(copper in part) which serve as reference materials in the reflection method.
Reflection method. The reflection method developed by the authors of ref. [5] jointly
with G.M. Gandelman found a wide application in studies of shock compressibility of various
materials. The method is based on solution to the Riemann problem in shock wave arriving
at interface of two matters.
In this method, the shock wave transfers to the material under study from a base
plate, for which the equation of state or, at least, Hugoniot is known. If the shock wave pa-
rameters in the base plate are determined, then it is sufficient to measure only the shock
wave velocity in the material under study. Fig. 2 shows the shock wave transition from the
base plate to the sample under study in P–U coordinates.
The Riemann problem appearing when the shock wave reflects from the base plate-
sample interface leads to generation of two waves. The shock wave always moves across
the sample, the reflected wave in the base plate can be either shock wave, if the dynamic
“hardness” (impedance) of the studied material is higher than the base plate impedance, or
rarefaction wave otherwise.
Parameters of initial state 1 in the base plate are found by measured wave velocity,
D , in the base plate through intersection of its wave beam with its Hugoniot 0A. When the
BP
shock wave has reflected from the sample, a new state appears in the base plate that lies
either on re-compression Hugoniot 1–2 or on expansion adiabat 1–2l. The experimental re-
cording of the wave velocity D in the sample gives the slope of wave beam P =r DU . The
0
intersection point of the beam and curve
8
Dynamic methods for studying material properties at high pressures
P - 1- P determines shock wave
P HBP SBP
pressure and mass velocity in the sample,
which are equal to those at the base plate-
B sample interface. Strictly speaking, calcula-
tion of rarefaction wave, P , or re-
SBP
compression wave, P , in plane P–U
HBP
P2 2 requires knowledge of the equation of state
of base plate material in the parameter
range of our concern. However, when pres-
P A sure differences in the reflected shock
HBP
waves or rarefaction waves are not very
large relative to the passing wave in the
base plate, the curve P - 1- P is
HBP SBP
P 1
1 approximated by "specular" reflection of the
principal Hugoniot 0A from point 1 with a
P
SBP
sufficient accuracy [6]. The specular ap-
P/ 2 l B l proximation simplifies the process of estima-
2
tion of shock wave parameters in the sample
0 under study. So in practice one seeks to se-
U U U l U
2 1 2 lect the base material such, that its dynamic

impedance be close to similar characteristics
Fig. 2. P–U diagram of the reflection method
of materials to be studied.
The data on shock wave compressibility presented in the Collection was obtained with
the reflection method for essentially all materials, excluding some continuous reference
metals.
Double compression (re-compression) Hugoniot

To acquire information about thermodynamic material properties in the range of densi-
ties higher than single shock compression density, methods are developed for recording
states appearing in shock compression by two successive waves. The presented data on
the material compression by the second shock wave resulted either from using the method
of barriers or from head-on or oblique impact in the shock-wave sample. The experimental
scheme of the re-compression Hugoniot recording with the method of barriers is in essence
a variation of the reflection method.
Revert to Fig. 2. Arrival of the shock wave that initially moved in studied material with
parameters P and U at the interface with the dynamically harder barrier is accompanied
1 1
with generation of two shock waves moving on either side from the interface. As a result, the
material under study is compressed two times, that is by the incident wave up to pressure P
1
and by reflected wave up to pressure P
2
P =P +r D D U . (4)
2 1 1 12 12

In so doing material density increases up to

D
r =r 12 , (5)
2 1 D - D U
12 12

where D is reflected wave velocity relative to material velocity before the wave front and
12
D U is mass velocity jump at the reflected wave front. For practical implementation of the
12
method, single compression Hugoniots both for the material to be studied and for the hard
9
Dynamic methods for studying material properties at high pressures
barrier have to be known. Then it is sufficient to experimentally estimate shock wave veloc-
ity, D , in the material under study and shock wave velocity, D , in the barrier. The value of
1 2
D is used to find P,U ,r , that of D to estimate P and U . Hence,
1 1 1 1 2 2 2

P - P
D = 2 1 and D U =U - U .
12 r D U 12 1 2
1 12

Substitute these values into relations (4) and (5) to find pressure and density of doubly
compressed material. By using different dynamic hardness barriers and recording P, U that
appear therewith, one can determine the Hugoniot run for re-compression to different pres-
sure levels. Equations (4) and (5) are also valid in determination of re-compression states
that occur under the shock wave head-on or oblique impacts. The incident wave parameters
should be known in either case. The experiments on the head-on impact of two shock waves
of equal amplitude are simplest in interpretation. In this case material density following the
shock front is used as an experimentally measured value; this can be measured either with
pulsed radiography method [7] or other methods, in particular, electromagnetic method [8].
As material is in rest in the impact region, mass velocity jump, D U =U , can be also
12 1
evaluated. This value is used to find reflection pressure and double compression density.
Given the oblique wave impact, it is necessary to know, besides the incident wave pa-
rameters, angle of incidence, a , and angle of reflection, b , to obtain the re-compression
characteristics. The angle of incidence is given by experimental conditions. To estimate the
angle of reflection, ref. [7] uses the pulsed radiography method detecting prompt shock front
positions inside the X-rayed sample. By giving these values in the form of simple trigonomet-
ric relations presented in ref. [7], one can estimate the reflected wave velocity, D , and the
12
mass velocity jump, D U ,
12
sinb
D =D +U cosa (a +b );
12 1 sina 1
cosa
D U =U ,
12 1 cosb

by which P and r are found using equations (4) and (5).
2 2

Shock-compressed material expansion adiabats

The adiabatic expansion of materials on their compression by shock waves are stud-
ied in two options of setting up the experiments. In the first option, the states on the expan-
sion adiabats are determined by recording expansion velocity, W, of the materials under
study. In the second option known as the method of barriers mentioned in the previous sec-
tion, one determines not only final, but also intermediate states that occur during the matter
expansion to the materials, whose Hugoniots in P–U coordinates are located between the
Hugoniots of the material under study and air. As "soft" barriers materials of known Hugoni-
ots are used: light metals, plexiglas, polyethylene, fluoroplastic, plastic foams of various po-
rosity, inert gases – argon and xenon (at different initial pressure), and other materials. Em-
ployment of different-intensity shock wave generators and initial density variation in the sam-
ples to be studied allow us to obtain different expansion adiabats that cover the material
phase diagram from Hugoniot states to supercritical two-phase states.
10
Dynamic methods for studying material properties at high pressures
Sound speed in shock-compressed material

(cid:230) ¶ P (cid:246)
Sound speed, C2 =(cid:231) (cid:247) determines the Poisson adiabat slope on the shock
Ł ¶ r ł
S
Hugoniot or isentropic compressibility of material. In other words, sound speed characterizes
velocity of propagation of small perturbations, i.e. weak shock waves and unloading waves,
through compressed material. The sound
Shock front speed data presented in the Collection
is obtained with three techniques using
optical, electrocontact and electromag-
1
netic methods as well as manganin
a
gauges.
2
Side unloading method. The
h d method was developed in Russia by the
3 authors of ref. [9]. The scheme of the
experiments using the method appears
*
d in Fig. 3.
3 l The unloading wave source is the
4 contact point of the cylindrical sample
side surface and the base plate surface.
By the time of the shock wave arrival at
5
the sample end the expansion waves
cover the peripheral zone S =htga
wide. Sound speed is therewith deter-
Fig. 3. Scheme of the side unloading method: 1 – mined as
base plate; 2 – sample; 3 – thin light material layer
expanding from the surface of the indicating material
under study; 3l – the same layer in flight; 4 – trans- C =D tg2a +(cid:231)(cid:230) D- U (cid:247)(cid:246) 2 .
parent plexiglas barrier; 5 – schematic streak camera Ł D ł
image recording the time difference in the indicating

material impact on the plexiglas barrier; h, d – sam-
ple height and diameter, respectively; d* – diameter
of the non-unloaded portion of the sample
d - d*
Non-unloaded sample diameter, d *, and hence, tga = are found by the
2h
change in the sample free surface velocity. Actually, this reduces to the streak camera re-
cording of the time difference in the impact on a transparent barrier of flying-off thin light ma-
terial layer pre-applied on the sample (or the sample itself).
Method of overtaking unloading. The method implies the shock wave path recording
[9] in the path (x) – time (t) plane. The relevant phenomena are depicted in Fig. 4. For sim-
plicity consider the case, where the impactor and the target are fabricated from the same
material.
Shock waves OA and OB move from impactor-target impact point O across both the
samples. When the shock wave has arrived at the rear plate side, at point B a rarefaction
wave forms which moves across the material at velocity U+C >D and overtakes the shock
front at point A. From that time on, the shock front amplitude decreases and the wave de-
cays. From the diagram it is easy to obtain the sound speed in the material under study as a
function of shock wave parameters, impactor thickness D , and distance l, at which the first
characteristic arrives at the front trajectory:

l+D
C =(D- U)
l- D