Experi. mental Measurements for the Radi al Di stri but! onof a Ba? 1 Sampi e Mater i a? Derisi ty under Expi osi ye

Spherl cal Compress! on

G. Ya. Anischenko, V. N. Koz1ovky, E. A. Kozloy,B. V. Li tvinov, S. V. Samyl ov

Federal Nuci ear Centre , Al1 -Russi an I nsti tute of Techni cal PhysicsChel yabi nsk -70 , P. 0. Box 245 , Russia

ABSTRACT

I n the gi yen paper the procedure for experi mental measuri ng ther adi a? di str i but! on of a bal 1 sampl e mater i a? densi ty under expi osi yespherical compression is presented. Sample materials are Fe, Pb. Thetechni que was devel oped for measur ement conducti ng under mater i al dy—nami c compacti ori Measuri ng was conducted by a pul sed radi ography me—thod. Object simplest open X - raying was applied wi thout use of col -limating elements or equalizer filters.

a . PROCEDURE DESCRI PTI ON.

The mai ri furicti orial procedure el emerits arid thei r mutual I ocati onI n the experi. merits were shown i n Fl g. I . In the speci fi ed moment ofti me after expl osi ye charge a pul sed ' — source I i rradi at.es samp—le 4 - a ball 40 mm in diameter. In the registrating system 5 whichis on the other sample side X - shade sample image is fixed in thepr edeter — mined phase of compressi on.

2 3\6

1-sourceI I 2 — protec ti ye wal I

3 — explosion products/ ____ 4 - sample

1' 6 - registrating system6 6 — reference wedge

Fig. 1. Experiment arrangement scheme.

Next to the object is a stepwise reference wedge (6) which is re-gistrated together with the object on the same film. The distancebetween the wedge and the object is chosen so, that at the moment ofradiographing the explosion products do not reach the wedge. A pulsed

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Fig. 2. Radiogram of experiment.The sample material - Fe, the radiography time t =37ms.

SPIE Vol. 1801 HjghSpeedPh0t0gTaPhYa Photonics (1992)1 929

reference wed

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I ron—free betat,rori2 wi th boundary quanta energy Eb = Hey and1- pul se durati on of about 0. 2 ps was used as -- source. Ampi I fyi ngmetal and fluorescent screens (front and rear) are placed in theregi strati ng system. Fl g. 2 shows radi ogram of one experl ment.

Accor di ng to the r efer ence wedge X —r ay photometr I c r el ati onshi pof a gi yen C materi al exposed thi ckness dependence on fi 1 m densi. ty )and par ameter s char acter I zi ng r egi str ati ng system unshar pness ar e de—ter ml ned . Photometry of compr essed sampl e I mage i s per for med i n I 0 —12 di r ecti ons . Photometry r esul ts pr ocessi ng i s automated and conduc —ted on a computer usi ng a number of programs performi ng resul ts cor —rection for the field nonuniformity of the ' - source, shielding ofmeasured sample by explosion products and the distortion of X - pho-tometric relation at a sample boundary.

The computation of density distribution along axially symmetricbody radius on the base of its radiogram obtained in the directionperpendi cul ar to the axi s presents concrete probi em of radiographictomography. That 's why the sol uti on of thi s probi em resul ts from theI nverted reducti on of Radon9 , which under axi al or spheri cal symmetrypostulating is reduced to the following form:

r) = -:1 x) (1)

where pEr) — density of a body, exposed to external influence in thepoint at a distance r from the axis,

p0 - density of a substance in initial state,

x - variable of integration,t(x) - thickness of reference wedge step which is equivalent by

the radiation attenuation to the body chord located at a distance Xfrom the axis.

Under this formula derivation the mass attenuation factor along Xcoordinate was assumed to be constant.

Radiogram processing cycle contains the following stages:

1. Deter ml nation of dependence parameters D = fCt), where D —optical r adi ogr am dens I ty i n the pol nt under consi der ati on, t — mate-rial thickness corresponding to this density.It is found that for a number of films this dependence is welldescribed by the expression

D=D +D exp(-cxC(3+lg(e)pt)T), (2)0 max

wheret - material thickness,p — attenuation linear factor,

930 / SPIE Vol. 1801 High-Speed Photography and Photonics (1992)

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D — parameter havi ng the sense of fog opt! cal derisi ty,0D — parameter havi ng the sense of inaxi mum opti cal derisi ty

maxwhich is permitted by the film,

, 2' — parameter s deter mi ru rig cur ye l ope,(9 - curve shift parameter depending on film sensitivity.

Film contrast factor in usual understanding (maximum gradient) isexpressed via said parameters in the following way

1—fgcD 11h11 (3)maxl ce J

For dependence (2) parameters calculation we use reference wedgeof the same mater i al as the body under i nvesti gati on . Parameter s arefound on the base of opti cal densi ti es measured at each wedge stageby means of the program using optimization methods.

2. Radiogram scanning in 10. . . 15 directions via centre with obligatory capture of EP zone ring 8. . . 12 mm wide around investigatedmass. Scanning is performed in optical densities with constant step.

3. Optical densities conversion into thicknesses is performed bymeans of expression (2) solved relatively to t value.

4 . X—r ay sour ce fi el d sI ope and mi sal I gnment cor r ecti on.Thicknesses data file is subjected to the correction. By data fi-

Ie of thi cknesses t whi ch are I n ER zone ri ng pol ynomi al of seconddegree I s constr ucted for each secti on by I east—square method. Thenits ordinates are subtracted from all ordinates of thicknesses datafile. Thicknesses which are in EP zone region thus became close tozero.

5. Symmetry centre determination.Symmetry centre is defined as centre of gravity of figure limited

by tCx) after field correction.6. t(x) data file symmet,rization.All ordinates having the same abscissas relative to found centre

are averaged in pairs relative to the found centre of symmetry.7. t(x) data file differentiation by the formulae of numerical

differentiation.

8. Unsharpness zone correction.For the cases when there is a priori Inforrnation on the presence

of sharp outer boundary C step type) of considered mass the followingoperations are performed:

8. 1. Edge dissipation function is found by the optical densitydrop at the wedge boundary after Its differentiation we have linedissipation function. Root—mean—square width o or the latter is adop-ted as unsharpness degree.

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3. SOME RESULTS OF THE PROCEDURE.

Procedure checking was performed by preliminary radiograms (takenbefore explosion) . Fig. 3 shows processing results • according to thisprocedure of a prel I ml nary radi ogram I n the experi merit wi th Fe C steel3OXCA) . mls r adi ogram i I 1 ustr ates wel 1 the cor recti on IX t) I nfl uence in outer boundary unsharpness zone on calculation result p(r).

As densi ty distribution at preliminary radi ogram is well knownit is possible to estimate square—mean--root errors pitch for each dc-pendence point p(r).

Typical distribution of avaraged set ordinates errors is shown atFig. 3a. Errors In centre region are high, but they quickly drop withradius increasing.

It will be incorrect to consider that said errors are characte—ri sti c of this procedure. They depend on information amount in radio—gram. For r adi ogr ams which par ti ci pate i n processi ng, si grial —nol seratio changed in the range 26 40.

Figures 4, 6, 6 show processing results of 3 explosion radio—grams and table I — brief data on experiments.

Table I

Experiment Sample material t jnsI23

PbPb

Fe (steel 30XCA)

2636.237

Due to low accuracy of determination p( r) in sample centre(r< 6mm), p( r) data are not presented for this region. Outer boundarycorrection was performed in experiment I. During experiments 2, 3 wecouldn't satisfactorily describe density change in outer boundaryblurring zone by simple step-wise model -

Presented results are characterized by measurement high error insample centre. This is connected mainly with high level of scatteredradiation, which is natural consequence of open X — raying.

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P9/cm3

50

0

F! g. 3a. Cal cul ated val ues devi at! on pC r) Fig. 3 from thereference density p average value.

934 ISPIE Vol. 1801 High-Speed Photography and Photonics (1992)

9/cm3

5 /0 /5 27 /'fl7I77Fig. 3. Distribution of a sample material density beforethe experiment C according to preliminary radiography )The sample material Fe.I — radiogram processing without correction In outerboundary blurring zone. 2 — radiogram processing withcorrection.

5 /0 20/5

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P9/cr,,3

7.0

6.0 -

4.0

3.0-

2.0-

1.0

p9/cm3

2.0

1.0

0

Fig. 6. Sample density di stributi on in experiment 2.The material - Pb.The radiography time - 36.2 Ins.

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Fig. 4. Sample density distribution in experiment 1.The material - Pb.The radiography time - 2 )ns.

20 30 rmm

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p9/CT!?'3

3.0

2.0

1.0

0

Fi g. 6. Sampl e derisi ty di str I buti on Ini exper i merit 3.The material - Fe (steel 3OXCA)The radiography time - 37

4. REFERENCES

1 . E. A. Kozi ov, H. A. Lebedev, B. V. Li tvi nov "Explosion arrange-merits for a dynamic compaction arid syntheses of Materials". Procee-dings of the international symposium on intense dynamic loading aridits effects, CHENGDU, CHINA, June 9 - 12, 1992.

2. A.I. Pavlovsky, G.D. Kuleshov, "High accuracy iron—free beta—troris", Dokl ady Akademi a Nauk, 160, NI, 68 (1966).

3. G. Hermen "Imag'e reconstrtLc t on by project 1ons Creconstruc t —on toraoraphy bc.sts)", Mir, Moscow, 1983.

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