THE EFFECT OF MATERIAL STRENGTH ON THE RELATIONSHIP BETWEEN THE PRINCIPAL HUGONIOT AND QUASI-ISENTROPE OF BERYLLIUM AND 6061-T6 ALUMINUM BELOW 35 GPa

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THE EFFECT OF MATERIAL STRENGTH ON THE RELATIONSHIP BETWEEN THE PRINCIPAL

HUGONIOT AND QUASI-ISENTROPE OF

BERYLLIUM AND 6061-T6 ALUMINUM BELOW 35 GPa

W. Moss

To cite this version:

W. Moss. THE EFFECT OF MATERIAL STRENGTH ON THE RELATIONSHIP BETWEEN THE PRINCIPAL HUGONIOT AND QUASI-ISENTROPE OF BERYLLIUM AND 6061-T6 ALU- MINUM BELOW 35 GPa. Journal de Physique Colloques, 1984, 45 (C8), pp.C8-263-C8-266.

�10.1051/jphyscol:1984849�. �jpa-00224350�

30URNAL DE PHYSIQUE

Colloque C8, supplément au n ° l l , Tome *5, novembre 198* page C8-263

THE EFFECT OF MATERIAL STRENGTH ON THE RELATIONSHIP BETWEEN THE PRINCIPAL HUGONIOT AND QUASI-ISENTROPE OF BERYLLIUM AND 6 0 6 l " T 6 ALUMINUM BELOW 35 GPa

W.C. Moss

University of California, Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A

Résumé - On peut obtenir la compression quasi-isentropique [QI] en appliquant à un matériel une charge qui consiste en une onde de déformation uniaxe avec un faible taux de déformation et un temps d'accroissement élevé. Des résultats expérimentaux récents montrent que la quasi-isentrope de l'aluminium 6061-T6 excède la tension Hugoniot principale de quelques pourcents, et que, par conséquent, pour un volume spécifique donné, la tension QI excède la tension Hugoniot principale. On a proposé que cet effet est du à la résistance du matériel. Par l'intermédiaire des données Hugoniot, des données choc-choc en retour et choc-décharge pour le béryllium et l'aluminium 6061-T6, nous avons construit les quasi-isentropes en fonction du volume spécifique. Nos résultats montrent que la tension QI excède la tension Hugoniot principale pour une tension Hugoniot supérieure à 8.4 GPa dans le béryllium, et pour des tensions Hugoniot comprises entre 3.8 et 21.4 GPa dans l'aluminium. Cet effet est du à la résistance et implique que la limite de la résistance QI peut être élevée. Nos calculs montrent que la limite de la résistance QI est de 0.9 GPa dans l'aluminium avec une tension QI de 9 GPa, et de 5.2 GPa dans le béryllium avec une tension QI de 35 GPa.

Abstract - Quasi-isentropic [QI] compression can be achieved by loading a specimen with a low strain-rate, long rise time uniaxial strain wave. Recent experimental data show that the quasi-isentrope of 6061-T6 aluminum lies a few percent above the principal Hugoniot, that is, at a given specific volume, the QI stress exceeds the principal Hugoniot stress. It has been suggested that this effect is due to material strength.

Using Hugoniot data, shock-reshock, and shock-unload data for beryllium and 6061-T6 aluminum, we have constructed the quasi-isentropes as functions of specific volume.

Our results show that the QI stress exceeds the principal Hugoniot stress above a Hugoniot stress of 8.4 GPa in beryllium, and between Hugoniot stresses of 3.8 and 21.4 GPa in aluminum. The effect is due to strength and implies that the QI yield strength can be large. Our calculations show that the QI yield strength is 0.9 GPa in aluminum at a QI stress of 9 GPa, and 5.2 GPa in beryllium at a QI stress of 35 GPa.

I - INTRODUCTION

A method for generating quasi-isentropic [QI] compression waves in flat plate impact (uniaxial strain) experiments has been developed recently by Barker/1/. The QI waves are generated by impacting a specimen with a projectile whose nose-piece has an impedance that increases monotonically from a low value at the impacting surface, to a high value at the back of the nose-piece. The resulting wave has a long rise time, and produces much lower strain-rates in the specimen than shock loading to the same specific volume reached by the QI compression. Although elastic-plastic effects in the specimen make the loading thermodynamically irreversible, much less heat is generated than by shock compression (to the same specific volume), hence, the loading is referred to as quasi-isentropic.

One would expect that at a given specific volume, the principal Hugoniot stress (q-i) would be greater (compressive stresses are positive) than the quasi-isentropic stress (chi), due to the increased entropy production in the shock process, but Barker/1/ has determined experimentally that the quasi-isentrope of 6061-T6 aluminum is a few percent above the principal Hugoniot, for Hugoniot stresses less than 9 GPa (the range of the data).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984849

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( a i s t h e longitudinal s t r e s s in a uniaxial s t r a i n configuration, and i s related t o t h e pressure [PI by a = a l + P , where a ' is t h e longitudinal deviatoric stress). I t h a s been suggested t h a t t h i s e f f e c t is d u e t o m a t e r i a l strength. Figure 1 illustrates schematically t h e relationship between t h e stresses, pressures, and deviatoric stresses on t h e principal Hugoniot and quasi-isentrope.

T h e figure also shows how material strength (values of t h e deviatoric stresses) c a n account f o r aqi(V)>q-i(V). T h e dashed lines show t h e Hugoniot s t r e s s and pressure. T h e difference between t h e t w o curves is t h e deviatoric Hugoniot s t r e s s [&(V)]. T h e solid lines show t h e QI s t r e s s a n d pressure. T h e difference between t h e t w o c u r v e s i s t h e deviatoric QI s t r e s s [ Ii(v)]. In t h e figure u q i ( V ) > ~ ( V ) , t o b e consistent with t h e experimental d a t a f o r 6061-T6 3 u m i n u m . In general, theory places no restriction on t h e relationship between aqi a n d ql. Pise(V) [dot-dashed line] is t h e t r u e isentropic pressure, t h a t is, t h e pressure resulting f r o m a reversible adiabatic compression. Theory requires Pise(V) t o b e less t h a n Pqi(V), PH(V), ql(V), and aqi(V). Pqi(V), lies above Pise(V), because t h e h e a t produced by p l a s t ~ c work along t h e quasi- sentr rope ralses t h e pressure above t h e isentropic value. PH(V) must also l i e above Pise(V), d u e t o t h e h e a t produced by plastic work and t h e h e a t generated by t h e shock process.

I t i s not known whether q i ( V ) e x c e e d s Pqi(V), in general, because t h e amount of plastic work t h a t is done along t h e quasi-isentrope differs from t h a t along t h e Hugoniot. Thus, PH(V)>Pqi(V) if t h e sum of t h e h e a t d u e t o plastic work along t h e Hugoniot and t h e h e a t d u e t o t h e shock process exceeds t h e h e a t d u e t o t o plastic work along t h e quasi-isentrope. In t h e figure, w e have chosen arbitrarily t o show PH(V)>Pqi(V).

We should emphasize t h a t t h e d i f f e r e n c e between t h e Pise, Pqi, and P H curves i s small;

t h e figure i s exaggerated, f o r c l a r i t y of presentation.

We conclude our discussion of t h e figure by noting t h a t if U;~(V)>&V) by a sufficient amount, then uqi(V)>q+(V).

Stress

0 Specific volume " 0

FIG. I. T h e relationship between stresses, pressures, and deviatoric s t r e s s e s on t h e principal Hugoniot and quasi-isentrope.

THEORY

In a previous paper/2/, w e showed how material s t r e n g t h a f f e c t s t h e construction of P(V,E) using shock data. In this paper, w e e x t e n d our analysis and show how m a t e r i a l strength a f f e c t s t h e construction of aqi(V) using shock data. We show t h a t t h e experimental observation of a q i , > q c a n b e deduced f r o m shock-reshock and shock-unload d a t a , and t h a t m a t e r ~ a l s t r e n g t h 1s responsible f o r t h e e f f e c t . We s u m m a r i z e briefly t h e procedure t h a t we employ: (i) experimental shock veloc~ty-particle velocity d a t a a n d t h e Rankine-Hugoniot equations a r e used t o c o n s t r u c t aH(V); (ii) U$V) is obtained from t h e results o f a method developed by Asay and Chhabildas/3/ [AC], then PH(V) i s calculated; (iii) a f o r m f o r P(V,E) is assumed (Mie-Griineisen), with t h e restriction t h a t along t h e Hugoniot, PH(V) i s recovered; (iv)

~ $ 4 ) is obtained f r o m a n analysis of t h e shock-reshock and shock-unload A C data; (v) P .(V) i s calculated f r o m P(V,E); t h e n a i(V) is calculated and compared t o q+(V). T h e c o m p l e t e r e t a i l s of how qi(V) may b e obtained B o m shock d a t a a r e given by Moss/4/. H e r e w e present only t h e results.

RESULTS

Figure 2 shows our calculation of aqi (thin soiid line) a n d UH (dashed line), a s functions of specific volume, f o r aluminum. The e x p e r ~ m e n t a l quasi-isentrope/l/ (thick solid line) and Hugoniot d a t a (solid circles/3/, open circles/5/) a r e also shown in t h e figure. For 3.8

< %<21.4 G P a , aqi , although t h e d i f f e r e n c e i s small, a s shown in t h e figure. The

-

range of t h e data.

FIG. 21 Calculated principal Hugoniot and quasi-isentrope, and experimental quasi- isentrope and Hugoniot d a t a a s functions of specific volume, f o r aluminum.

T h e i i g u r e shows t h a t our approximation of a(i is a n underestimate of t h e a c t u a l value, which may b e approximated b e t t e r using t h e experimental a . and our calculated P . T h e r e i s a difference of a f a c t o r of approximately two. This i n d i c a g s t h a t t h e quasi-isen?:bpic yield s t r e n g t h of 6061-T6 aluminum c a n b e l a r g e [Y/uqix 0.10 a t aqi=9 GPa].

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Figure 3 shows our calculation of oqi (solid line) and q (dashed line), a s functions o f specific volume f o r beryllium. Experimental Hugoniot data161 a r e also shown in t h e figure.

F o r Hugoniot stresses g r e a t e r than 8.4 GPa, o .> T h e maximum relative difference i s 0.023, at 0 ~ ~ 2 7 . 2 GPa. Our calculation yields P E > p : > P i s e throughout t h e r a n g e of t h e d a t a (OzoHoH_05 GPa). The relative difference between P$ and Pise i s negligible. The r e l a t i v e d i f f e r e n c e between P H and P q i increases monotonically t o 0.01, a t 35 GPa. Material s t r e n g t h is responsible f o r u q i > o ~ , because

4 2 1

FIG. 3. Calculated principal Hugoniot and quasi-isentrope, and experimental Hugoniot d a t a a s functions of specific volume, f o r beryllium.

ACKNOWLEDGMENTS

T h e author would like t o thank L. M. Barker a n d 3. R. Asay f o r useful discussions, and w e thank L. M. Barker f o r sending us his quasi-isentropic compression data. T h e computational assistance of J. Sayer i s also acknowledged. This work was performed under t h e auspices of t h e U.S. Department of Energy a t Lawrence Livermore National Laboratory under c o n t r a c t C W-7405-Eng-48.

REFERENCES

I. BARKER, L. M., Shock Waves in Condensed Matter - 1983 (Eds., J . R. Asay, R. A.

Graham, and G. K. Straub, Amer. Inst. of Physics, New York, 1984) 217.

2. MOSS, W. C., J. Appl. Phys., 2 (1984) 2741.

3. ASAY, J. R., and L. C. CHHABIL'DAS, Shock Waves and High Strain R a t e Phenomena in Metals (Eds., M. A. Meyers and L. E. Murr, Plenum, New York, 1981) 417.

4. MOSS, W. C., Lawrence Livermore National Laboratory, Livermore, CA, UCRL-9 110 1 (1984).

5. WALLACE, D. C., Phys. Rev., 822 (1980) 1495.

6 . WISE, 3. L., L. C. CHHABILDAS, and J. R. ASAY, Shock Waves in Condensed M a t t e r

- 1981 (Eds., W. J. Nellis, L. Seaman, and R. A. Graham, Amer. Inst. of Physics, New York, 1982) 417.