METROLOGY AND DYNAMIC BEHAVIOUR OF SOLIDS

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METROLOGY AND DYNAMIC BEHAVIOUR OF SOLIDS

M. de Gliniasty

To cite this version:

M. de Gliniasty. METROLOGY AND DYNAMIC BEHAVIOUR OF SOLIDS. Journal de Physique

Colloques, 1984, 45 (C8), pp.C8-245-C8-256. �10.1051/jphyscol:1984847�. �jpa-00224348�

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JOURNAL DE PHYSIQUE

Colloque C8, supplément au n ° l l , Tome 45, novembre 1984 page C8-245

METROLOGY AND DYNAMIC BEHAVIOUR OF SOLIDS

M. de Gliniasty

Commissariat a. I'Energie Atomique, Centre d'Etudes de Vaujours, B.P. n° 7, 77181 Courtry, France

Résumé - La plupart des difficultés rencontrées dans l'étude du comportement dynamique des matériaux sont d'ordre expérimental. Il y a une quarantaine d'années, lorsque débutèrent les études sur les ondes de choc dans les solides, l'expérimentateur ne disposait que de contacts électriques ; seule la mesure de déplacement était possible.

L'apparition dans les années 60 de capteurs capables de mesurer des profils de pression ou de vitesse a permis des progrès considérables dans la compréhension du comportement dynamique des matériaux. Mais aujourd'hui, il devient nécessaire d'explorer l'épaisseur même du front de choc. Heureusememnt le développement de nouvelles techniques optiques (telle la spectro RAMAN) offre de belles perspectives dans cette voie.

Abstract - Dealing with dynamic behaviour of solids mainly involves metrology problems. When the shock wave studies began, forty years ago, only pins were available.

Discrete displacement versus time could be measured. Major improvements came in the sixties with pressure and velocity profile measurements. Since that time, a large amount of data has been gathered and, within the frame of continuum theory, constitutive relations taking into account elastic failure, phase transitions, rate effects, have been proposed. But it has become necessary to get down to the thickness of the shock front. Fortunately, the development of new optical techniques, such as RAMAN spectroscopy, offers potentials for that.

1. INTRODUCTION

To give a review of the dynamic behaviour of materials and of the metrology of high dynamic pressures in forty minutes is a challenge : although shock physics in solids is a rather recent branch, only forty years old, a considerable amount of work has been done and many comprehensive reviews have been published already (see for example [l] , [2] ).

Before getting down to the main part of the talk, I would like to emphasize the tight link between measurement techniques and the modeling of the dynamic behaviour of materials.

Remember that we are dealing with waves propagating at velocities of several km/s and with states persisting for only a few microseconds or even nanoseconds. It is clear then, that our knowledge of what happens is strongly influenced by experiment: we are in fact totally dependant on the images obtained from the various sensors that have been developped. As a direct consequence of this statement, the theory usually follows the experiment.

Because of time limitations and because of my own background, I shall restrict the talk to plane waves of uniaxial strain in materials in which shear stress exists, i.e. mainly solids.

2. GENERATION OF HIGH DYNAMIC PRESSURES

To begin this talk, I would like to say a few words on how to produce high dynamic pressures. The easiest way is to generate shock waves and there are different methods of doing so :

- to detonate an explosive in contact with the sample, - to impact a projectile accelerated by explosive or by a gun,

- to deposit energy inside the sample by means of an electron beam or a laser beam,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984847

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-

t o use nuclear explosion for very high pressures.

T o achieve good quality plane waves, t h e use of guns is more appropriate ; moreover their different types (gas gun, powder gun, t w o s t a g e light g a s gun, e l e c t r i c gun) enable t h e shock physicist t o reach a large pressure scale.

The major disadvantages of using explosive is t h a t t h e pressure pulse is not sustained, and of course special facilities a r e necessary. As for energy deposition, one needs large machines t o achieve high pressures. In this last case, t h e pressure is raised at constant volume, s o t h e ini- t i a l state is different.

Figure 1 shows in a Pressure-Speci- ^loo fic volume plane, t h e range of pressures achievable in copper by those different means. The locus of t h e final states produced by a simple shock wave is a ¹⁰ curve : t h e Rankine-Hugoniot curve (R- H).

As i t has been often pointed out, i t is easier t o generate high dynamic pressures with shock waves, than static ones.

But t h e problem is m o r e complicated when one tries t o reach high dynamic pressures off t h e R-H curve. L e t m e s a y o

a f e w words about t h e corresponding ^RCUTIVESPECIFIC VOLUME

V/V.

methods. Fig.

%

¹^:Range of pressures achievable in copper

Investigation of t h e zone at t h e right of t h e R-H curve, c a n be done with porous materials. It was proposed a s early a s 1953 by WALSH and CHRISTIAN [31

,

but t h e interpretation of t h e results is rather complicated. We shall c o m e back t o t h a t when dealing with t h e problem of internal s t a t e variables.

Far more difficult is t h e access t o t h e zone between t h e isentropic cold compression curve and t h e R-H curve. Many a t t e m p t s have been made since 1972 (a complete bibliography is given in [4] ). Good results w e r e obtained up t o nearly 30 GPa, using glass ceramics which present a non linear elastic behaviour, by BENEDICK and ASAY [5] in 1976. In order t o obtain higher pressures, another method must b e used : t h e projectile with varying shock impedance.

The first successful published results a r e due t o BARKER

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with his "pillows". Various r a m p waves up t o 200 C P a have been successfully produced. I shall c o m e back t o t h a t point later on.

3. THE DISPLACEMENT VS TIME MEASUREMENTS PERIOD

This type of diagnostic was t h e first t o be used because of i t s simplicity. Before presenting some examples, l e t m e show you how those measurements could b e used t o obtain equation of s t a t e data.

In t h e most general case of t h e continuum theory, t h e conservation laws may b e written as follows in any specified volume V, of surface S and normal n :

-

mass conservation : d t _I

-

momentum conservation :

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2 - e n e r g y conservation:

1

d v

where

p

is t h e density, u t h e particle velocity, ti. t h e s t r e s s tensor, f i t h e volumic forces, e t h e internal energy, q t h e volumic energy provided by t h e surroundings and Q. t h e surfacic h e a t flux. If t h e r e is a discontinuity surface inside t h e volume, e a c h integral form can b e shared in t w o parts : a volumic integral form and a jump accross t h e discontinuity. In t h e simplest c a s e of a hydrodynamic medium with no internal sources and a n adiabatic transformation in one dimensional plane geometry, t h e jump equations a r e reduced t o t h e well known Hugoniot equations :

with V specific volume, Us shock velocity, u particle velocity, P pressure and E specific

internal energy. P

When t h e shock waves studies began, forty years ago, only pins w e r e available. The measurement of t h e f r e e surface velocity u with t h e assumption t h a t i t is twice

tpc

particle velocity, and of t h e shock velocity US, allows t h e o t h e r quantities t o b e e s t ~ m a t e d . But this is valid only with a very simple picture of a shock wave, such a s t h e one showed in figure 2.

Experimental R-H curves were ob- tained in 1944 (see (31 ) and equations of s t a t e , of t h e Mie-Gruneisen type, w e r e

proposed ^: Fig. 2 : Simple shock wave picture

P

-

Pref = (E

-

iZref), where (Prep Eref) is a r e f e r e n c e curve in t h e P, V, E space.

Note t h a t this 1s not a complete equation of s t a t e , in t h e sense t h a t t h e t h e r m a l p a r a m e t e r s

v.

(T and S) cannot b e explicitly calculated.

S i e W e Coaxla1 with Figure 3 is a s c h e m e of typical pins

Mylar ~nsulator with their power supply. These pins a r e o f different types : one conductor, coaxial or coaxial with a film of insu- lator (usually mylar) a t t h e t o p ; t h e last model is parti.cularly suited t o shock velocity measurements.

I t is interesting t o notice t h a t pins a r e still largely used t o day (see [7] and [8] f o r example) although f a r more precise techniques, such a s t h e Dop- pler Laser Interferometry (DLI), have been developped. This is because a t high velocities (or pressures) t h e precision of e l e c t r i c a l pins is a s good a s DLI's.

As a n example figure 4 describes a r e c e n t pin developped by C.E.A. [9]

.

This is a ^selfgenerating pin, i.e. which does not need any power supply. The signal is t h e flash of light produced by t h e ionization under compression of t h e a i r gap a t t h e t o p of t h e pin.

b

Fig. 3 : Scheme of e l e c t r i c a l pins

a

&

PLATEAU OF CONSTAHT on w o w c r v a a r l m m s u s

P , V , E , U p

olxunlhun

1 SHOCK WONT I

us IATERlEL AT E S T

--

^P*,V^{0 ,}^t.

-

C

X COOROlNATf

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The light is recorded through a n opti- c a l fiber on a n optoelectronic streak came- r a THOMSON TSN 503.

A similar optical probe has been developped at LLNL but t h e a i r is re- placed by Xenon in order t o record t h e signal on a rotating mirror camera.

The next s t e p in t h e development of measurement techniques was t h e continous displacement versus t i m e detectors. In t h a t category w e find t h e DC capacitor gauge (mentionned in 1945 [3] ), but mainly t h e rotating mirror c a m e r a s (BRIXNEL 1952).

d~~~

\

A scheme of a streak rotating mirror

c a m e r a is given in figure 5. Streak and ^---...I.^...--- framing c a m e r a s a r e still largely used t o

day : even if t h e interpretation is some- tmes difficult, nothing c a n replace a good

image of a phenomenon. I must mention _Time_fiducids _Automatic_&ta _mcesvlr also t h e displacement interferometer, but

T~igylLim

i t h a s not been used very o f t e n since t h e

velocity interferometer appeared. Fig. 4 : CEA Optical pin

As I told you a t t h e beginning, t h e theory usually follows t h e experiment, and a s a n illustration of t h a t statement, l e t m e mention t h a t a l l t h e typical features of a shock wave in a solid have been discovered with those simple displacement vs t i m e detectors :

-

t h e elastic behaviour of m e t a l s (PEIRLS and STEIN 1945 [3] )

-

spalling, a t t h e s a m e t i m e [31

-

phase transitions under shock loading (WALSH and CHRISTIAN 1954 [3] )

The evidence of a two waves structure, in t h a t l a s t case, was given in 1954 but t h e theoretical explanation was found in 1956.

In 1959 another s t e p was taken : DC capacitor records showed t h a t t h e concept of sharp elastic and plastic waves had t o be discarded. Finite rise-times were evidenced and t h e question of r a t e e f f e c t s was raised. The shock picture in iron for example could be modelized a s i t is shown in figure 6.

But t o proceed, i.e. t o establish proper models, a new instrumentation was necessary.

Fig. 5 : Streak c a m e r a Fig. 6 ^:Shock picture

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4. CONTINUOUS VELOCITY OR STRESS VS TIME MEASUREMENTS Fortunately new powerful diagnostics appeared early in t h e sixties :

-

t h e electromagnetic velocity gauge EMV (ZAITSEV 1960 Dl]

,

DREMIN 1964 [12] ),

-

t h e quartz piezoelectric gauge, (JONES 1962

-

t h e manganin piezoresistive gauge (FULLER and PRICE 1962,

hg),

-

the velocity interferometer (LAHARRAGUE-DURAND 1969 k5], [16]

-

t h e VISAR (BARKER-HOLLENBACH 1972, D7] ),

-

and many others (see [2]

1).

All those techniques a r e widely used t o day, instead of the displacement devices. It is clear why this is so : t h e displacement vs t i m e data must be differentiated before t h e wave profiles of interest a r e obtained. I shall describe t h e most commonly used techniques.

The principle of t h e EMV gauge is very simple (figure 7) : a loop of a conductive material (usually anodized a1uminum)is embedded inside t h e sample, in a constant magnetic field B. The magnetic field can be produced either by coils or by permanent magnets.If 1 is t h e length of t h e conductor, u i t s velocity, a n electromotive force e appears a t t h e terminals of t h e loop (Faraday's law) :

e = B 1 u

So t h e recorded voltage is directly proportional t o t h e velocity of the conducting loop, that is t o say t o t h e particle velocity of t h e medium.

Note that the medium must be non conductive.

The most widely used piezoelectric quartz gauge, has been designed by GRAHAM [18] : i t is the ring X-cut quartz gauge (fig. 8).

It consists in a mono crystalline piece of X oriented quartz which is metal deposited except on a ring a t i t s back face.

The piezoelectrically produced polarization in a s t a t e of one dimensional strain is proportional t o t h e applied stress, if t h e quartz remains linearly elastic (and dissipationless).

d

MENTAL SET UP.

wtmn SUCH MT RIKI AW NOT MORE THlW b9b OF AREA OF IM

-&+

&EPOSIFO C H ~ ~ , S I L V ~ , O R GOLD L A T E F A -ACES CAREFULLY

TYPICAL STRESS TIME PROFILE FOR OURALUMIN

Fig. 7 : Principle of EMV gauge Fig. 8 : X-cut quartz gauge (from [IS] )

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Then t h e current-time waveform is directly proportional t o t h e interface stress-time profile : G ( 0 , t ) = 1 i(t)/AkV for t 1/V

,

where A is t h e area, 1 t h e thickness of t h e q u a r t z and V i t s

4 q q q

dilatational elastic wave velocity.

Although i t gives a precise measurement with a good t i m e resolution (1 t o 5 ns), t h e q u a r t z gauge presents some disadvantages : pressure limited t o nearly 2 G P a (Hugoniot elastic limit of quartz), and pressure measured inside t h e q u a r t z instead of t h e sample. A review on piezo- electricity is given in n91.

The manganin piezoresistive gauge is more versatile. A typical low impedance gauge f201 is presented in figure 9.

GAUGE FEATURES

Embedded inside t h e material, .Photoetthed trame fmm manoanln f o ~ i of 25 urn

~ r

i t gives t h e pressure inside t h e sam- -P.T.F.E packing thickness of 0 . 6 m b 0,7mrn

ple, up t o 50 t o 60 GPa. -Leads mpper platted with 5pm of copper

The low impedance gauge needs =:~L--I

a constant c u r r e n r power supply and

, LLG:-

t h e voltage is collected at t h e termi-

nals of t h e active p a r t (manganin). 3-

m.7

-TFen The typical resistance of such

IIP(B**IY Y I Ls

gauges is less than 0,l

.

High im-

, -

pedance gauges (25 or 5 0 R ) a r e also

; : 1 ,

' available, but they need a constant

voltage power supply through

a Wheatstone bridge. They a r e limited

-,-

t o I 5

-

20 GPa, maximum pressure. -DIAGNOSTIC ASSEMBLY - -TYPICAL SIGNAL - Fig. 9 : Low impedance Manganin gauge

The main disadvantage of t h e manganin gauge is i t s t i m e resolution due t o t h e thickness of t h e insulation : more t h a n 50 ns.

The manganin gauge, used a s a lagrangian gauge, withstands t h e r a r e f a c t i h waves, s o i t gives useful information on the release behaviour of materials. This is not t h e c a s e for Carbon piezoresistive gauges [21]

.

But these Carbon gauges a r e more recise at low pressures ( < 5 GPa) 1221. Ytterbium piezoresistive gauges have also been used e 3 ] t o a small extent. All t h e piezoresistive gauges have t o b e calibrated.

But t h e major improvement in t h e techniques of high dynamic pressure measurement has been t h e velocity interferometer, by means of Doppler laser interferometry (DLI).

Two types of velocimeter a r e in use t o day : t h e DL1 device with a Fabry-Perot interferometer and t h e

VISAR with a Michelson in- OPlOtLLCTIIONIC CAMIRb

terferometer. A schematic view of a Fabry-Perot velocity interferometer is shown in figure 10.

h+ -iue--h+

The velocity V of t h e ^F' t a r g e t i s proportional t o t h e space between t h e fringes

(cf. fig. 10) SURFALE AT R ~ S ~

";LA-(~+

dd-D;-)

A p r e t t y good surface ^4~ D;-d,

finish of t h e t a r g e t is neces-

MOVING SU)HCE

sary t o g e t clear recordings on t h e streak camera.

Fig. 10 : Doppler Laser Interferometer

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The velocity resolution depends on t h e space between t h e mirrors of t h e Fabry-Perot. A few m e t e r s per second is a typical value. Time resolution may be estimated a t 1 t o 5 ns.Now DL1 devices with beam transportation through optical fibers a r e currently developped [24j

.

The VISAR is slightly more complicated a s i t appears in figure 11. The delay leg of t h e Michelson may be a glass cylinder or simply air. The results a r e recorded on photo-multiplier tubes.

H I I ^LASER 1 1 I I I I 1 I

LTALON SPLITTER OELAY LLG

O A T l i l v ' & N'"

DATA2

-

¹

Figure I I : VISAR

Two fringe signals, which a r e 90' o u t of phase, a r e simultaneously recorded t o improve accuracy and t o distinguish acceleration from deceleration. The t i m e resolution of t h e VISAR is also 1 t o 5 ns.

Figure 12 is a n illustration of a DL1 record. The experimental s e t up is shown in t h e figure and t w o different measurements a r e recorded : t h e copper buffer plate velocit and t h e sample (steel) velocity 651.

CU 15mm

On such a record, t h e following events a r e d e t e c t e d :

-

A = elastic precursor

-

B = reflection on t h e plastic I wave C o f t h e reflected elastic wave on the f r e e sur- f a c e

-

C = plastic I wave -+PI~s~,c n wave I

-

D = reflection on t h e plastic I1 wave E of t h e reflected plastic wave I on t h e f r e e surface

,- E = plastic I1 wave _efleckn_{on P}_l_wave

-

F = PIR wave [26]

Figure 12 : Typical DL1 experiment

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With some simple assumptions, such a s centered compression wave [26], t h e following quantities may b e derived : elastic wave velocity C, Hugoniot elastic limit HEL, Poisson r a t i o 3

,

plastic yield

Y ,

pressure of t h e phase transition<+ &

,

and reverse E +&. If spalling had occured, the spall-te%sion could have been measured.

All t h e techniques described above have been improved since their f i r s t appearance. T o illustrate t h a t point, l e t m e present t o you t h e electromagnetic stress and velocity gauge EMSVG [27]

,

1281

.

PLANE WAVE LENS

-

^.^.^.^.^.^.^.^.^.^.^.^.^.^.^.

9, 8AUGE

Figure 1 3 is a schematic drawing of a similar gauge, designed by CEA.

I t consists of a loop, of a special shape, made of anodized aluminium embedded inside t h e material. A magnetic field is produced, a s in t h e c a s e of t h e EMV gauge. I t allows recording of :

-

t h e shock velocity Us,

-

t h e particle velocity u

-

t h e pressure P. P'

A typical record is presented figure 13.

Note t h a t t h e EMSV gauge must b e used in non conductive materials.

I have t o mention a very powerful d a t a analysis which was first proposed by FOWLES and WILLIAMS @9] improved by COWPERTHWAITE

DOI,

and which is now widely used : t h e Lagrangian Analysis.

Fig. 1 3 : EMSV gauge

When you integrate, along lines of constant lagrangian coordinate h, over a short time interval (tl,t2), t h e conservation laws (1) written in I D plane geometry, yo2 g e t :

rt.. PROJECTILE

\%.

,

^',

,,ME

I t is clear t h a t t h e knowledge of

6

(h,t) and i t s ^{- -}^.^-.^A>?..2

..

- - . -

derivatives is sufficient t o calculate all t h e o t h e r

.,

- - - - ?+ *_c_-_..

% ^'*e

parameters (u,E,V), without any information o r as- %

sumption about t h e equation of state. The s a m e is

t r u e with u(h,t) and i t s derivatives, but i t is slightly o,

more difficult. T o day, nearly all t h e lagrangian

experimental d a t a (manganin or carbon gauges, EMV

11 a

gauge, DLI) a r e s o processed.

-

HI

Figure 14 shows a typical experiment with t h e pressure records by means of manganin gauges and t h e resulting thermodynamic pathes at different lagrangian coordinate location, in a P-V plane. The

detailed rocedure of t h e lagrangian analysis may b e

J

^LLATIM^{S ~ A C}^W ^L ^~ ^~ ^~

found in el]

.

Fig. 14 : Lagrangian analysis

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The introduction of time resolved velocity and stress measurements has also considerably changed t h e classical constitutive relations representing t h e behaviour of specific materials.

For instance, complete experimental models for plastic yield surface have been built, using the experimental determination of deviatoric stress. There a r e several methods :

-

t h e comparison of t h e Hugoniot curve with t h e hydrostat, which is no longer used,

-

t h e unloading and reloading waves method

p2] ,

- t h e combined compression and shear loading [?33

, -

t h e use of anisotropic crystals 1341

.

I shall describe here a method u- s sing manganin gauges [35]

.

The principle ^e

5

is t o measure simultaneously t h e longi- tudinal stress GK and t h e lateral stressC7

.

The sample is arranged a s shown in figure 15. A full description of ^=zGAu t h e method is given in [36]. In figure 1 5 t h e 6

,6 ,

vs t i m e results a r e shown in ^uy t h e czse 8f PMMA.

Time resolved stress and velocity measurements have also allowed t h e development of r a t e e f f e c t s models. Now they a r e taken into account, in t h e fra-

me the continuum by means ?ig. 15 : Deviatoric stress measurement (from 1361 ) internal s t a t e variables.

Roughly speaking, a new parameter is introduced in t h e conservation laws or in t h e equation of s t a t e , and a new relation, usually t i m e dependant and experimentally derived, is added. As examples, one c a n mention HERRMANN1s oc internal variable (which separates t h e volume variation due t o t h e matrix compression from t h e void closure, in porous materials) p7] or t h e burnt mass fraction in models for t h e initiation of explosives [38], or t h e density of dislocations in metals b9]. A complete review of t h e internal s t a t e variables problem is given in [40]

.

5. MISCELLANEOUS MEASUREMENTS M'I L't

$1

^{L I} ^{M I}

A large e f f o r t has been d e v o t e d ' b y shock physicists t o t e m p e r a t u r e measurements. As early a s 1946 [3] a t t e m p t s were

made using thermocouples, but unsuccess- ^\^\ ^/^/

fully because of response t i m e problems. ^{\ \}_\

I

_j _/^//

Since then o t h e r methods have been tried \ \ ;

/

(GIBSON (411

,

KATO [42]

,

VON HOLLE \ : /

,

^{: ,}

[433

,

ROSENBERG [44). But, a s a tran- ^I^{: \}

/ / \

sition towards future w0rk.s on optical diag- / i^. ^\\

nostics, I shall only mention t h e method of _/^// ^f ^\

BOISARD and DELPUECH [45], [46]. ^/ ^\^\

They use RAMAN spectroscopy. If qo is t h e RAYLEIGH frequency and $

+ 9.

t h e RAMAN frequencies t h e intensitigs- o i t h e M Z

Stokes and anti-Stokes lines may be expres- sed a s :

4 - h S i / k ~ ) -1

IS = Ci 1 ~ ( ? ~ - 3 ~ ) (1-e D O U ~ I ~

+ h ? i / k ~

c

I ( 3 +3i)4 (e

-

1) 'AS= i o o

Where I. is t h e incident intensity, and _Opticalspectrum

ci

a parameter including cross sections, ^onolyaeur

medium density, optical apertures.

Rstroctabk mirror

Fig. 16 : Experimental s e t up for RAMAN spectroscopy

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( )

~h'i"' The ratio IAS/IS gives t h e temperature : R =

-

The experimental s e t u p is pictured in figure 16. On t h e right side t h e RAMAN frequencies shifts due t o shock compression of t h e medium a r e measured. On t h e l e f t side t h e Stokes and anti-Stokes intensities a r e recorded with photomultiplier tubes.

Before concluding, I would like t o say a f e w words about specific volume measurements : measuring V is difficult t o c a r r y o u t and, t o my knowledge, t h e only technique is flash radiography. A special collimation method has been developped by GAUTHIER and GUIX [471.

The main disadvantage of this technique is t h a t large radiographic machines a r e necessary.

6. CONCLUSION

To conclude with t h e measurement techniques appropriate t o t h e continuum assumption, I must say t h a t I have not compared t h e different sensors t h a t c a n be used. This is on purpose : firstly because i t would have been a very hard job, and secondly because t h e search for t h e best precision or t i m e resolution is not necessarily t h e best aim. For example, although t h e velocity interferometer is t o day t h e most precise technique, in some cases i t may not b e appropri2te : as a m a t t e r of f a c t t h e measure is worked o u t o n a very small a r e a (typically 0,05 mm ) and grain s i z e e f f e c t s may a l t e r t h e qual9y of t h e measure. In t h a t case, a manganin gauge, t h e a c t i v e surface of which is a few mm

,

may be more satisfactory.

A f t e r t h a t review, one may think t h a t everything has been done, from a n experimental point of view, except measuring t h e entropy. But, of course t h a t is not true. T o illustrate t h a t s t a t e m e n t I shall briefly summarize results obtained by L. BARKER [6] on 6061T6 Aluminum with i t s llpillow'l technique.

Comparing t h e stress-strain lo I I I I

loading path determined from t h e quasi-isentropic wave profiles, t o

t h e Hugoniot points, he finds t h a t 8

-

a t a given strain, t h e isentropic MEASURED loading produces a higher stress,

which is totally unexpected.

This strange result appears y)

t o be a manifestation of hetero- geneous yielding and thermal trapping e f f e c t s [4]: t h e very ra- pid localized deformation in Hu- goniot experiments can cause lo-

calized heating on t h e shear pla-

- -

nes with a resultant temporary loss of yield strength, which does not happen in t h e c a s e of t h e 0

slower deformation process of t h e 0.00 0-02 0.04 0.06 0.08 0.10

quasi-isentropic experiment. STRAIN

So t h e simple continuum as- _{Fig. 17}: Quasi-isentropic compression results (from ( 6

1 )

sumption is no longer valid : i t has

t o b e completed by internal s t a t e variables taking into account t h e microstructural defor- mations, t h e chemical transformation

...

during dynamic loading.

More and more has been done in t h a t field since a f e w years [48]

.

The usual technique is t h e recovery experiment, where a post-shock analysis of t h e sample is made a f t e r recovery (see for example [49]

,

[50] ). But i t is very difficult t o define precisely t h e thermodynamic path followed by t h e sample during t h e whole experiment : i t experiences release waves a f t e r compresssion. So i t becomes necessary t o carry on measurements within t h e shock front in a material.

T o finish I shall say t h a t w e have already entered a new e r a in shock physics : t h e e r a of microstructural o r even molecular comprehension of t h e dynamic behaviour of solids. Fortuna- tely t h e development of optical sensors, such a s RAMAN spectroscopy, offers potentials for achieving good measurements with t h e required spatial and temporal resolutions (

<

l / U m ,

C 100 ps).

(12)

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