Int. Z Impact Engng Vol. 5, pp. 463-470, 1987 0734-743X/87 $3.00 + 0.00 Printed in Great Britain Pergamon Journals Ltd.

STRESS MEASUREMENTS IN GLASS USING SHAPED-CHARGE JETS

William Lawrence and Robert E. Franz

Ballistic Research Laboratory Aberdeen Proving Ground, MD 21005-5066

ABSTRACT

S t r e s s e s were measured in g l a s s t a r g e t s i n the v i c i n i t y of a p e n e t r a t i n g s h a p e d - c h a r g e j e t . S t r e s s l e v e l s o f a p p r o x i m a t e l y 0 .3 GPa were measured 12-20mm away from a j e t formed by a 35--. copper l i n e r . High speed f r a m ing camera p h o t o g r a p h s showed t h a t the p e n e t r a t i o n v e l o c i t y in the g l a s s was 2 .57 km/s and the g l a s s f r a c t u r e v e l o c i t y was 2.10 km/s .

INTRODUCTION

I t has been known for ove r 40 y e a r s t h a t g l a s s t a r g e t s a r e u n u s u a l l y e f f e c t i v e i n s t o p p i n g 1 s h a p e d - c h a r g e j e t s . S t u d i e s of t h i s e f f e c t i v e n e s s were made d u r i n g and a f t e r World War I I . These s t u d i e s e s t a b l i s h e d the p r i n c i p l e s of d e f e n s e a g a i n s t s h a p e d - c h a r g e j e t s u s i n g g l a s s . N e v e r t h e l e s s , l i t t l e is known abou t the p h y s i c s and c h e m i s t r y a s s o c i a t e d w i t h the p e n e t r a t i o n p r o c e s s i n g l a s s .

Th is r e p o r t d e s c r i b e s some e x p e r i m e n t s made to measure dynamic s t r e s s e s i n g l a s s i n t he v i c i n i t y of a p e n e t r a t i n g j e t . S t r a l n - c o m p e n s a t e d s t r e s s gages and s i m u l t a n e o u s h l g h - s p e e d f r a m i n g camera pho tog raphs were used f o r t h i s p u r p o s e . These e x p e r i m e n t s a r e p a r t of a l a r g e r e f f o r t t o u n d e r - s t a n d the f u n d a m e n t a l s o f the j e t p e n e t r a t i o n p r o c e s s i n g l a s s and g l a s s - l l k e m a t e r i a l s . The o v e r a l l work a l s o i n c l u d e s t he use of f l a s h r a d i o g r a p h y to o b s e r v e the o n - g o i n g p e n e t r a t i o n , and t a r g e t r e c o v e r y t o o b s e r v e the m a t e r i a l a f t e r p e n e t r a t i o n .

EXPERIMENTAL PROCEDURE

The shaped-charge jets used in these experiments were obtained using a 35 --. diameter conical copper l i n e r w i t h a w a l l t h i c k n e s s of 1 .57 nu and a cone a n g l e of 45 d e g r e e s . The e x p l o s i v e used was Compos i t i on B. When f i r e d a t a s t a n d o f f o f two cone d i a m e t e r s the j e t p e n e t r a t e d fou r cone d i a m e t e r s i n s t a c k e d 25 mm t h i c k r o l l e d s t e e l p l a t e s (Rockwel l h a r d n e s s B81). The j e t t i p v e l o c i t y was 6 .8 km/s .

The t a r g e t s c o n s i s t e d of s t a c k e d l a y e r s of f l o a t g l a s s ( D e n s i t y = 2500 kg /m3) . The g l a s s l a y e r s were e i t h e r 25 .4 --. or 19.1 mm t h i c k and were a p p r o x i m a t e l y 150 --. s q u a r e . They were s t a c k e d e i t h e r p e r p e n d i c u l a r t o the j e t p a t h or p a r a l l e l t o t he j e t p a t h . The l a y e r s were bonded w i t h epoxy cement w h i l e clamped i n a p r e s s . V a r ious cove r p i a t e s were used . The cover p l a t e s were e i t h e r r o l l e d homogeneous armor (RHA) or p o l y m e t h y l - m e t h a c r a l a t e (PMMA), or a c o m b i n a t i o n of the two of d i f f e r e n t t h i c k n e s s e s . Tab le 1 g i v e s d e t a i l s of the v a r i o u s t h i c k n e s s e s , o r i e n t a t i o n s and m a t e r i a l s used i n each e x p e r i m e n t . F i g u r e 1 shows d rawing of t y p i c a l t a r g e t c o n f i g u r a t i o n . The shaped c h a r g e s were f i r e d a t a s t a n d o f f o f two cone d i a m e t e r s above the cover p l a t e s .

S t r a i n - c o m p e n s a t e d s t r e s s gages were used to measure s t r e s s e s d u r i n g j e t p e n e t r a t i o n . These gages c o n s i s t o f two s e p a r a t e i n t e r l a c e d l o l l g r i d s enca sed i n a p o l y l m l d e p l a s t i c f i l m . One of the g r i d s i s made of manganln and i s used to measure s t r e s s . The o t h e r i s made of c o n s t a n t a n and i s used to measure s t r a i n . The measured s t r a i n i s used to c o r r e c t the s t r e s s measu remen t s .

The gages were bonded be tween t he l a y e r s o f g l a s s i n s h a l l o w s l o t s a p p r o x i m a t e l y 0 .38 mm deep . When the g l a s s l a y e r s were p a r a l l e l to t he j e t p a t h t he gage g r i d s were a l s o p a r a l l e l . L i k e w i s e , when the l a y e r s were p e r p e n d i c u l a r the g r i d s were p e r p e n d i c u l a r to the j e t p a t h . Tab le 1 a l s o

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S t r e s s m e a s u r e m e n t s i n g l a s s u s i n g s h a p e d - c h a r g e j e t s 4 6 5

--LIGHT SOURCE / EXPLODING WIRE

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l I

- - F R E S N E L L E N S , - P R T H OF THE I I I

I I I j RHR I ! I I I I I I I I I 1 I I I I I I I I I I -GRGE I I I I I I I

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JET

LENGTH WIDTH THICKNESS (MM) (MM) (MM)

GLRSS 1 5 0 122 2 5 . 4 RHR 1 5 0 122 2 5 . 4

> T O CRMERR

F i g . 1, P a r a l l e l - L a y e r G l a s s T a r g e t . G a g e is a l s o P a r a l l e l

to t he I n c o m i n g J e t .

466 Will iam Lawrence and Robert E. Franz

includes particulars on gage placement in each experiment. Test No. 15 and Test No. 16 were run without slots in the glass and the offset spaces caused by the thickness of the gage were filled with plastic film and epoxy cement. This was done to see if the slots affected the gage signals. Gupta and Gupta 2 have reported such disturbance in very strong materials. The gages were attached to 93 ohm RG-62u coaxial cables which were connected to bridge circuits similar to those used by Rapacki 3. The circuits were modified to be used with the 50 ohm Dynasen gages instead of the 120 ohm gages used by Rapacki. The signals were recorded on digital oscilloscopes.

For some of the experiments simultaneous framing camera photographs were made during jet penetration. The glass targets were back-lit with an exploding tungsten wire placed near the focus of a plastic Fresnel lens.

RESULTS

The data from the two signals obtained from each gage were reduced in a manner similar to that used by Rapacki 3. That is, calibrations were made of each circuit with known dummy gages inserted in the lines instead of the actual gage. Signals from known changes in resistance were then used to determine the circuit constants. These constants along with the known bridge and cable resistances were used to calculate the resistance of each grid at each simultaneous time s t e p o f t h e s i g n a l s .

To calculate the stress in the glass for each time step it was assumed that the resistance of the constantan grid was not affected by the stress field that surrounded both it and the manganin grid. It was further assumed that the strain of the manganin grid was the same as in the constantan grid. Finally, it was assumed that the stress in the glass was the same as that in the manganin.

The strain for each time step was calculated using the equation 4

ST ffi -I + (RC/ROC) 0.5

H e r e ST ffi strain in the constantan grid RC " resistance of the constantan grid ROC = the initial resistance of the constantan grid

To calculate the stress, the resistance change associated with the strain in the manganin must first be subtracted from the total resistance change. In order to do this the strain gage factor for the manganin grid was determined from a separate static experiment. A strain-compensated stress gage was mounted on an aluminum alloy plate along with conventional strain gages. This plate was pulled in an universal testing machine. The data showed that the manganln grid had a gage factor of 0.7 to a strain of 0.5%. Above 0o5Z strain the manganin deformed plastlcally and the gage factor became the same as for the constantan grid, that is, 2+ST. The apparent gage factor G.F., is defined as

G.F. = DRG/(ROG x ST).

Where

and DRG " the change in gage resistance,

ROG = the initial gage resistance.

The resistance change in the manganin due to the strain was, therefore, calculated by using the following equations.

For - 0 . 0 0 5 < ST < 0 , 0 0 5

DRMS ffi 0.7 x ST x ROM.

For ST > 0.005

DRMS " ( 2 + S T - 0 . 0 0 5 ) x ( S T - 0 . 0 0 5 ) x ( 1 ÷ 0 . 7 x 0 . 0 0 5 ) x ROM +

( 0 . 7 x 0 . 0 0 5 ) x ROM

ffi ( 1 . 9 9 5 + S T ) x ( S T - 0 . O 0 5 ) x 1 . 0 0 3 5 x ROM + 0 . 0 0 3 5 x ROH

F o r ST < - . 0 0 5

Stress measurements in glass using shaped-charge jets 467

DRMS " (2.005+ST) x (ST+0.005) x 0 .9965 x ROM - 0.0035 x HOg

Here DRMS = the change in r e s i s t a n c e of the manganin g r i d due to s t r a i n

ROM = the i n i t i a l r e s i s t a n c e of the manganin g r i d .

The s t r e s s i n the mansanln was then c a l c u l a t e d u s i n g a c u b i c f i t to the d a t a of C h a r e s t 5. e q u a t i o n i s

S = 53.19 x (DRM/RO) - 159.91 x (DRM/RO) 2 + 493 .16 x (DRM/RO) 3

Where S = s t r e s s in the manganin (GPa)

DRM = DRMT - DRMS

RO = ROM + DRMS

and DRNT = t he t o t a l r e s i s t a n c e change in the manganln .

F i g u r e 2 shows r e s u l t s o b t a i n e d from one of the t e s t s .

Th is

DISCUSSION

The s t r e s s measurements r e p o r t e d h e r e were o b t a i n e d under p a r t i c u l a r l y a d v e r s e p h y s i c a l c o n d i t i o n s . I t was l e a r n e d in p r e l i m i n a r y e x p e r i m e n t s t h a t t he l o l l gages and t h e i r l e a d s had to be p r o t e c t e d from a h o s t i l e env i ronmen t which i n c l u d e d f r a c t u r i n g g l a s s . The l a y e r s of p o l y t e t r a f l o u r o e t h y l e n e , used fo r t h l s p r o t e c t i o n , r e s t r i c t e d the m e c h a n i c a l r e s p o n s e of the g a s e s e s p e c i a l l y to t he i n i t i a l s h a r p l y r l s i n S shock waves . The r e s p o n s e was f u r t h e r r e s t r i c t e d by the e l e c t r o n i c bandwid th of t he r e c o r d i n g equ ipment so t h a t submic rosecond changes i n e i t h e r s t r e s s or s t r a i n cou ld no t be t r a c k e d .

The gages were a p p r o x i m a t e l y 19 mm to t he s i d e of the j e t p a t h fo r p e r p e n d i c u l a r s h o t s and 12.7 m from the p a t h f o r p a r a l l e l s h o t s . The s t r e s s e s measured d i d no t exceed a p p r o x i m a t e l y 0 .3 GPa u n t i l t h e s a g e s were on t he v e r s e o f d e s t r u c t i o n from the f r a c t u r i n S g l a s s . The s t r a i n i n most o f the s h o t s d id no t c o n t r i b u t e s i g n l f i c a n t l y t o t h e s t r e s s compensa t i on u n t i l 3 t o 4 m i c r o - seconds a f t e r the s t a r t o f the s t r e s s s i g n a l s . The u s u a l s i g n a l showed two c o m p r e s s i v e peaks f o l l o w e d by e i t h e r t e n s i o n or c o m p r e s s i o n . These s i g n a l s a r e shown in F i g s . 2 and 3.

A l though u n s l o t t e d gages d id no t show t h e s e d i s t i n c t peaks t he measured s t r e s s l e v e l s were a p p r o x i m a t e l y the same as f o r s l o t t e d g a g e s . I n most c a s e s t he gages s t a r t e d to f a l l b e f o r e or nea r j e t a r r i v a l , t h a t i s , 15 t o 20 m i c r o s e c o n d s a f t e r the shock a r r i v e d . For two s h o t s t he gages s u r v i v e d fo r l o n g e r t i m e s . No e x t r e m e l y l a r g e s t r e s s e s were measured on t h e s e s h o t s . The p a r a l l e l gages showed lower i n i t i a l s t r e s s l e v e l s t h a n the p e r p e n d i c u l a r g a g e s .

The f r aming camera pho tog r a phs c l e a r l y show t h a t f r a c t u r e o c c u r r e d around the gages b e f o r e the a r r i v a l o f the p e n e t r a t i n g j e t . Th i s was caused by i n t e r a c t i o n w i t h the l e a d i n g shock wave which was formed when the j e t impac ted t he cove r p l a t e . There was a d e l a y of abou t 3 m i c r o s e c o n d s a f t e r shock a r r i v a l b e f o r e c r a c k l n S was seen a t the gage . Data from the f i l m was used to c a l c u l a t e the shock v e l o c i t y , the i n i t i a l p e n e t r a t i o n v e l o c i t y , and the g l a s s f r a c t u r e v e l o c i t y . The measured v a l u e s a r e :

P e n e t r a t i o n Velocity = 2.57 km/s

F r a c t u r e V e l o c i t y = 2.10 km/s

Shock V e l o c i t y = 5 .90 km/s .

The wave p r o f i l e s d e t e r m i n e d w i t h t he s t r e s s s a g e s were d i f f i c u l t t o i n t e r p r e t when compared to the h i g h speed f r a m ing camera p h o t o g r a p h s . For i n s t a n c e , a t l e a s t two shock waves a r e e v i d e n t i n t he p h o t o g r a p h s of the g l a s s i n T e s t No. 8 where t h e cover p l a t e c o n s i s t e d of 25 .4 ~,~ of ~ and 25.4 mm of F ~ A . The f i r s t wave was caused by t he o r i g i n a l j e t impac t a t t he RHA s u r f a c e and t he second ( p r o b a b l y ) by the impact o f t he j e t r e a c h l n S t he PMPA-glass i n t e r f a c e . I n t he s t e e l , t h e shock v e l o c i t y was h i g h e r t h a n t he p e n e t r a t i o n v e l o c i t y , w h e r e a s , i n t he PMMA t he o p p o s i t e was t r u e . The j e t r eached the g l a s s i n t e r f a c e a p p r o x i m a t e l y 2 .2 m i c r o s e c o n d s a f t e r t h e shock and a c c o u n t s fo r the p h o t o g r a p h i c r e s u l t s . The s t r e s s p r o f i l e a l s o showed a two wave s t r u c t u r e bu t

468 William Lawrence and Robert E. Franz

CO _J <C

(.0 CO <C

[I_ <C LO

LD I ~0 CO W rr F- CO

i.25

1.00

0 . 7 5

O. 50 -

O. 25 -

I I i I I I

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75 80 85 0 . 0 0 ~ ~ ' ~ ~

55 60 65 70 go

TIHE-MICROSECONOS

Fig. 2. S t r e s s M e a s u r e m e n t f rom G a g e in P a r a l l e l

C o n f i g u r a t i o n in T e s t No. 8. G a g e was in the S lo t .

O. 80

O. 70

I I I I

03 _J <C C.) tO <C n <C L3

0 I CO tO W nl F- tO

O. 60

O. 50

0 .40

O. 30 -

O. 20

0.10

O. O0 50 75 55 60 65 70

Stress measurements in glass using shaped-charge jets 469

TIHE-NICROSECONDS

Fig. 3. S t r e s s M e a s u r e m e n t f rom G a g e in P e r p e n d i c u l a r

C o n f i g u r a t i o n in T e s t No. 16. Gage was in the S lo t .

470 William Lawrence and Robert E. Franz

the spacing was 7 microseconds. A cover plate of PMMA 50.8 mm thick was used in Test No. I0. The photographs show a double wave structure but in this case the second shock is much weaker than for Test No. 8. In the PMMA, the penetration velocity was higher than the shock velocity, and the jet tip arrived at the PMMA-glass interface before the shock. The jet impact produced a shock in the glass after which the following shock in the PMMA entered the glass and caused the double wave structure of the photographs. The photographs of Test No. 8 also show a weak third shock which can be ascribed to the same causes.

CONCLUSIONS

The following conclusions were drawn from the experience gained in applying stress gage technology to the measurement of stress during shaped-charge jet penetration in glass, and from the combined photographic and stress results of this study.

First, the stress profiles measured were limited by both the mechanical and electrical response of the instrumentation.

Second, the stress measurements, with their shortcomings, were of sufficient quality to indicate stress levels in the in~nediate vicinity of a penetrating jet.

Third, although higher stress levels than those measured in these experiments must be present at the jet-glass penetration interface, they will be difficult, if not impossible to measure with foll stress gages.

Fourth, the information presented here can be used in analysis or design considerations for armor or antl-armor applications. The stress measurements can be used to verify analysis that can infer stress levels in inaccessible locations in a target.

REFERENCES

Allison, F. E., Defeat of Shaped Charse Weapons, Final Report, Contract No. DA-36-061-ORD-507, Carnegie Institute of Technology, April 1960.

Gupta, S. C. and Oupta, Y. M. Effect of Matrix Properties on the Piezoresistanee Response of Ytterbium and Manganin Foils, Bulletin of the American Ph~slcal Society, Vol. 29, No. 4, 741, April 1984.

Rapacki, Jr., E. J., Instrumentation Techniques for Measuring Large I High Rate Strains with Foll Resistance Strain Gages, Ballistic Research Laboratory Technical Report ARBRL-TR-02573, August 1984.

Franz, R. E., The Measurement of Large Strains with Foll Resistance Strain Gages, Ballistic Research Laboratory Technical Report ARBRL-TR-02519, August 1983. ADA 133686.

Charest, J. A., Characterization of an Encapsulated 50-Ohm Manganin Foll Piezoresistive Gauge, Air Force Weapons Laboratory Report No. AFWL-TR-71-81, August 1972.