THE RESPONSE OF VARIOUS POLYMERS TO UNIAXIAL COMPRESSIVE LOADING AT VERY HIGH RATES OF STRAIN

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THE RESPONSE OF VARIOUS POLYMERS TO UNIAXIAL COMPRESSIVE LOADING AT VERY

HIGH RATES OF STRAIN

S. Walley, John Field, G. Swallowe, S. Mentha

To cite this version:

S. Walley, John Field, G. Swallowe, S. Mentha. THE RESPONSE OF VARIOUS POLYMERS TO

UNIAXIAL COMPRESSIVE LOADING AT VERY HIGH RATES OF STRAIN. Journal de Physique

Colloques, 1985, 46 (C5), pp.C5-607-C5-616. �10.1051/jphyscol:1985578�. �jpa-00224812�

JOURNAL DE PHYSIQUE

Colloque C5, supplement a u nos, Tome 46, aoQt 1985 page C5-607

THE RESPONSE OF VARIOUS POLYMERS TO U N I A X I A L COMPRESSIVE LOADING A T VERY H I G H RATES OF S T R A I N

S.M. Walley, J.E. F i e l d , G.M. Swallowe and S.N. Mentha

P h y s i c s and C h e m i s t r y o f S o l i d s , C a v e n d i s h Laboratory, Madingley Road, Cambridge CB3 OHE, U.K.

Resume - Une b a r r e de Kolsky B choc d i r e c t a 6% u t i l i s e e pour o b t e n i r des courbes contrainte-deformation 3 v i t e s s e de dgformation de 2 x 10' s-' dans un e s s a i de compression s u r polymSres. De p l u s , l a deformation de disques de polymbres imposee par l a chute d l u n poids a Bt6 6 t u d i e e par photographie u l t r a r a p i d e ; l ' i n t e r v a l l e e n t r e chaque image d t a i t de 7 u s e t l a v i t e s s e de deformation de 5 x l o 3 s-'. E n f i n , une nouvelle technique bas6e s u r l t u t i l i s a t i o n de f i l m s e n s i b l e 3 l a chaleur a Bt6 dkveloppde a f i n d'kvaluer l'accroissement de temperature a s s o c i e B une deformation r a p i d e .

Abstract - A d i r e c t impact Kolsky bar has been used t o o b t a i n s t r e s s - s t r a i n curves f o r polymers a t compressive s t r a i n r a t e s of 2 x 10' s-'. High speed photography with an interframe time of 7 ps has been used t o study t h e deformation of s o l i d polymer d i s c s i n a drop-weight machine a t s t r a i n r a t e s of ca. 5 x l o 3 s-'. ^A novel technique using h e a t s e n s i t i v e f i l m has been developed t o e s t i m a t e t h e temperature r i s e s a s s o c i a t e d with r a p i d deforma- t i o n .

I - INTRODUCTION

Although t h e p r o p e r t i e s of polymers a t high s t r a i n r a t e s have been i n v e s t i g a t e d from t h e e a r l i e s t days of S p l i t Hopkinson Pressure Bar (SHPB) t e s t i n g / I / , l i t t l e d a t a on t h e s e m a t e r i a l s e x i s t compared t o metals /2/. A oomprehensive t a b l e of r e f e r e n c e s t o work on t h i s t o p i c up t o 1980 may be found i n / 3 / . Since t h e n , a number of p u b l i c a t i o n s have appeared: on u n i a x i a l compression / 4 / , / 5 / , on t o r s i o n / 6 / , / 7 / , on Taylor Impact / 8 / , and on f r i c t i o n a l e f f e c t s / 9 / .

A s p a r t of a programme t o s t u d y t h e impact behaviour of c e r t a i n polymers, we have obtained: ( i ) values f o r flow s t r e s s e s a t s t r a i n r a t e s of ca. 2 x 10' s-'; ( i i ) h i g h speed photographic sequences of deformation a t s t r a i n r a t e s of ca.5 x ?03s-';

( i i i ) e s t i m a t e s of t h e temperature r i s e s a s s o c i a t e d with bulk flow and shear cracking i n t h e s e m a t e r i a l s a t high s t r a i n r a t e s .

I1 - STRESS-STRAIN ANALYSIS AT HIGH STRAIN RATES

The apparatus used i n t h i s work was t h e d i r e c t impact Kolsky bar developed i n t h i s l a b o r a t o r y / l o / . I n t h e s e experiments a s o l i d c y l i n d e r of polymer 2mm i n diameter and 1mm i n l e n g t h is mounted on t h e end of a 3mm diameter tungsten a l l o y p r e s s u r e bar. I t is then impacted by a 70mm l o n g , 3mm diameter Ti a l l o y rod mounted i n a nylon sabot. This is a c c e l e r a t e d t o ca. 20 m s-' using a l a b o r a t o r y gas-gun, t h e speed being a c c u r a t e l y measured with t h r e e photodiodes near t h e end of t h e b a r r e l . The l e n g t h and a c o u s t i c impedance of t h e T i p r o j e c t i l e a r e such t h a t t h e time f o r a double wave t r a n s i t is 30 ps ( f i g . 1 ) .

The s t r e s s pulse i n t h e pressure bar is detected by a p a i r of miniature semiconductor s t r a i n gauges (0.15mm x O.1Omm) mounted d i a m e t r i c a l l y opposite each o t h e r t o minimise t h e e f f e c t s of f l e x u r a l waves. They a r e p o s i t i o n e d 10 bar diameters (3Omm) from t h e specimen, t h e minimum d i s t a n c e recommended i n /11/ t o

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985578

C5-608 JOURNAL DE PHYSIQUE

ensure t h a t t h e s p a t i a l d e t a i l s of t h e l o a d i n g do not s i g n i f i c a n t l y a f f e c t t h e s t r a i n i n t h e b a r ' s s u r f a c e . The voltage changes a c r o s s a r e s i s t o r i n s e r i e s a r e recorded using a Datalab Transient. Recorder sampling every 5C ns.

This information is analysed on a microcomputer. F i r s t t h e e l e c t r i c a l s i g n a l i s converted t o f o r c e using a dynamically determined c a l i b r a t i o n f a c t o r . This i s s l i g h t l y amplitude dependent a s t h e gauges a r e non-linear. ^A moving average technique is used t o smooth away o s c i l l a t i o n s a r i s i n g from d i s p e r s i o n . Several r e c e n t attempts have been made using Fourier methods t o c o r r e c t f o r t h i s / 1 2 / , / 1 3 / , /14/, but they a l l used t h e o r e t i c a l d i s p e r s i o n r e l a t i o n s . We a r e working on an empirical d i s p e r s i o n c o r r e c t i o n /15/. Preliminary r e s u l t s show t h a t smoothing i s s a t i s f a c t o r y f o r giving flow s t r e s s e s .

Fig.1 Voltage-time t r a c e obtained from t h e s t r a i n gauges when t h e p r e s s u r e bar is impacted d i r e c t l y by t h e 70 mm long T i a l l o y bar. Note t h a t d i s p e r s i o n r e s u l t s i n a f i n i t e r i s e time of ca. 1 u s and Pochhammer-Chree, o s c i l l a t i o n s on t h e f l a t - t o p . V e r t i c a l s c a l e a r b i t r a r y , h o r i z o n t a l s c a l e 10 u s per l a r g e d i v i s i o n .

The c o r r e c t e d force-time d a t a can be used t o compute both s t r e s s and s t r a i n i n t h e specimen /16/ provided: ( i ) t h e s t r e s s g r a d i e n t is zero; ( i i ) s t r e s s e s due t o f r i c t i o n a t t h e i n t e r f a c e s and i n e r t i a a r e n e g l i g i b l e ; ( i i i ) t h e volume remains c o n s t a n t . A one-dimensional wave c a l c u l a t i o n /9/ i n d i c a t e s t h a t s t r e s s e q u i l i - brium should be achieved by t h e time 4-5 u s have passed. Gorham found by recor- ding t h e r a d i a l expansion of d i s c s ( i n c l u d i n g polycarbonate) using high speed photography t h a t with t h e r i g h t l u b r i c a t i o n no non-uniformity i n cross-section along t h e l e n g t h was produced / I T / . The b e s t l u b r i c a t i o n c o n d i t i o n s (determined e m p i r i c a l l y ) have been published i n / I T / , and we f i n d they meet t h e c r i t e r i a i n /9/. There is no specimen geometry i n d i r e c t impact f o r i n e r t i a l s t r e s s e s t o be zero. However, f o r our specimens, t h e measured flow s t r e s s should exceed t h e i n t r i n s i c value by only 1-28.

We cannot t a k e volume conservation f o r granted i n polymers /19/. The calcula- t i o n method t o be described assumes i t is conserved, and d i r e c t observation shows t h a t f o r metals i t is t o much b e t t e r than 1 % /16/. Two e f f e c t s could l e a d t o volume changes. The f i r s t is a d i a b a t i c h e a t i n g due t o p l a s t i c work /20/. We e s t i m a t e a volume i n c r e a s e of c a . 2% a t a s t r a i n of 0.8 i f t h e polymer were unconstrained. The second is compression due t o t h e h y d r o s t a t i c pressure a/3 of a u n i a x i a l s t r e s s f i e l d of magnitude ^{o .} Previous work on t h e q u a s i s t a t i c u n i a x i a l compression of g l a s s y polymers /21/ showed t h a t a t y i e l d t h e volume c o n t r a c t i o n was ca. 3%. After y i e l d , t h e r e was no f u r t h e r change i n volume, s o t h a t t h e f r a c t i o n a l e r r o r becomes smaller a s deformation proceeds /22/. Adiabatic heating w i l l counteract t h e e f f e c t of e l a s t i c c o n t r a c t i o n .

It is shown i n /16/ t h a t t h e specimen l e n g t h l ( t ) during t h e double t r a n s i t

t i m e f o r a n e l a s t i c wave i n t h e p r o j e c t i l e is g i v e n by:- l ( t )

ls - ~t + (zl + ^{Z 2 )} + b t f ( t f ) d t '

Z l

-

where ls is t h e o r i g i n a l l e n g t h , v t h e impact s p e e d , Z 1 and Z 2 t h e a c o u s t i c impe- d a n c e s of t h e p r o j e c t i l e and p r e s s u r e b a r m a t e r i a l s , A t h e i r c r o s s s e c t i o n a l a r e a

( e q u a l h e r e ) and f ( t ) t h e c o r r e c t e d f o r c e p u l s e . The n a t u r a l s t r a i n ~ ( t ) and t r u e s t r e s s o ( t ) a r e t h e n g i v e n by:-

AS 1s \

where As is t h e o r i g i n a l c r o s s s e c t i o n a l a r e a of t h e specimen. Using t h e s e , s t r e s s - s t r a i n c u r v e s ( f i g . 2 ) may be computed from t h e raw d a t a . Most of t h e poly- mers flowed a t c o n s t a n t s t r e s s , though PTFE and PC showed some s t r a i n h a r d e n i n g . PTFE, PC and Noryl a l l s h a t t e r e d i f impacted a t 20 m s-'. T a b l e 1 g i v e s t h e f l o w s t r e s s e s measured w i t h t h i s a p p a r a t u s . Values f o r t h e dynamic Young's modulus c a n n o t b e o b t a i n e d because o f u n c e r t a i n t y a b o u t t h e f i r s t few microseconds due t o d i s p e r s i o n and t h e need t o e s t a b l i s h s t r e s s e q u i l i b r i u m . Also g i v e n a r e low s t r a i n r a t e v a l u e s . We i n t e n d t o c o n t i n u e o u r own q u a s i - s t a t i c measurements, and a l s o check volume c o n s e r v a t i o n .

Strain

F i g . 2 S t r e s s - s t r a i n c u r v e s f o r Nylon 66 a t a s t r a i n r a t e of 2.5 f 0.3 X l o * s-'.

The v a r i a t i o n i n f l o w s t r e s s s e e n h e r e g i v e s t h e e r r o r quoted i n T a b l e 1 . The

i n i t i a l r i s e does not g i v e t h e dynamic Young's modulus.

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TABLE 1

Compressive u n i a x i a l flow stresses/MPa f o r c e r t a i n polymers a t two d i f f e r e n t s t r a i n r a t e s

Note: t h e f i g u r e s i n b r a c k e t s a r e taken from " P r o p e r t i e s of P l a s t i c s " published by S h e l l Chemicals. The range of values f o r a given polymer is due t o v a r i a t i o n of mechanical p r o p e r t i e s between samples of d i f f e r i n g o r i g i n s and h i s t o r i e s .

I11 - APPARATUS FOR H I G H SPEED PHOTOGRAPHY Polymer

Nylon 6

Nylon 66

Polycar- bonate (PC)

Noryl (PPO + PS)

HDPE PTFE

I n t h i s study we use a r o t a t i n g mirror camera of a continuous access type. For t h e s e experiments we use an interframe time of 7 ps. Polymer d i s c s a r e deformed between toughened g l a s s a n v i l s i n a modified drop-weight machine /23/. This has a l i g h t path through t h e a x i s of t h e d i s c ( f i g . 3 ) . Uniaxial loading can be achieved by a d j u s t i n g t h e lower a n v i l i n t h e absence of a specimen u n t i l Newton's r i n g a r e seen i n t h e middle. I f t h i s is done, t h e d i s c deforms about i t s c e n t r e ( f i g . 4 ) ; i f n o t , t h e "no-flow!' p o i n t is o f f t o one s i d e ( f i g . 5 ) .

The s t r a i n r a t e f o r t h e s e experiments may be found by p l o t t i n g t h e s t r a i n , defined as:-

Impact bar (1 o r 2 x l o ' s - ' )

150 + ¹⁰

165

5

100 i 5

120 k 5

30 i 5 25 i 5 I n s t r o n

s - ' ) 86 i 2 (48 - ⁹⁷⁾

86 + 6 (48 - 110)

70 i 1 ( 7 6 )

76 t 5 (102 - 104)

(16.5) (5 - 12)

€ = I n - A ( 3 )

A s

a g a i n s t time (A is t h e present and As t h e o r i g i n a l c r o s s s e c t i o n a l a r e a ) , eg.

f i g s . 4 i i , 5 i i .

Two types of behaviour have been observed, e.g. f i g s . 4 i , 5 i . Nylon 66 deforms homogeneously t o l a r g e compressive s t r a i n s , and then c o n t r a c t s . Flow l i n e s can be seen a s t h e a n v i l l i f t s o f f . Polycarbonate (PC) deforms t o a s t r a i n of about 1 before f a i l i n g c a t a s t r o p h i c a l l y . The behaviour of t h e s e and o t h e r polymers is given i n Table 2.

S p e c i a l notes

2 x lo' s-'

2 x l o 4 s-I

1 & 2 x l o 4 s-'.

Specimens s h a t t e r e d a t t h e higher s t r a i n r a t e .

2 x lo' s-'

2 l o r s-' 1 x l o 4

Specimens s h a t t e r e d

a t t h e higher

s t r a i n r a t e .

F i g . 3 M o d i f i e d drop-weight f o r high-speed photography.

W w e i g h t (mass 5 k g ) , M m i r r o r s ,

G I and G 2 g l a s s a n v i l s , X specimen.

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Fig.4 ( i ) 5 mm diameter, 1 mm t h i c k unlubricated PC d i s c deforming a t a s t r a i n r a t e of 4.7 x 10"-'. The s t r a i n i n frame ( d ) is 1.1. The mean speed of t h e fragments between frames ( e ) and ( f ) is 350 m s-'. Times from impact: ( a ) 0; ( b ) 217 !.IS; ( c ) 224 ps; ( d ) 308 us; ( e l 315 us; ( f ) 322 us; (g) 329 us; ( h ) 336 p s ; ( i ) 350 u s .

Fig.4 ( i i ) P l o t of t h e s t r a i n a g a i n s t time measured from t h e f i l m t h e sequence of

f i g . b ( i ) was taken from. The arrows i n d i c a t e t h e times when f a i l u r e occurred.

I s ,

I

L

_i ^{\-/ :\} 1 J

Fig.5 ( i ) 5 mm d i a m e t e r , I mm t h i c k unlubricated d e s s i c a t e d nylon 66 d i s c deforming a t a s t r a i n r a t e of 5.4 x l o 3 s-' a c c e l e r a t i n g t o I . Z x 10' s-' ( s e e f i g . 5 ( i i i ) . L a s t f o u r frames show unloading ~hen0mena;and o v e r w r i t i n g i n frame

( i ) compares t h e i n i t i a l and f i n a l s t a t e s d i r e c t l y . Times from impact: ( a ) 0;

( b ) 134 u s ; ( c ) 201 us; ( d ) 228 us; ( e ) 255 us; ( f ) 503 us; ( g ) 563 u s ; ( h ) 637 us;

( i ) 771 u s ;

... . ^{' '} .*..

^..-".

' . _'.

CI

VI .

0.8

'

0.4 . . . _' .

Fig.5 ( i i ) P l o t of t h e s t r a i n a g a i n s t time measured from t h e f i l m t h e sequence of

f i g . s ( i ) was t a k e n from. Note t h e change i n s t r a i n r a t e during l o a d i n g .

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TABLE 2

Behaviour of c e r t a i n polymers i n a drop-weight machine a t a s t r a i n r a t e of ca. 5 x l o 3 s-'

Note: t h e l a t e n t h e a t of a polymeric m a t e r i a l depends on t h e c r y s t a l l i n i t y of t h e sample, which f o r a given chemical depends on t h e method of p r e p a r a t i o n and t h e subsequent h i s t o r y of t h e sample.

Polymer

HD PE PP Nylon 6

PVC PS

PMMA

PTFE PC

I V - ^{A METHOD} FOR ESTIMATING TEMPERATURE RISES

I t is known t h a t r a p i d deformation, whether homogeneous /24/ o r inhomogeneous / 2 5 / , / 2 6 / , / 2 7 / , produces measurable temperature r i s e s . I t was suggested i n /28/ t h a t commercially a v a i l a b l e h e a t s e n s i t i v e f i l m (3M Type 570, composition given i n U.S.

P a t e n t 3031 329) c a l i b r a t e d f o r both temperature and time can r e c o r d t h e e n t i r e specimen s u r f a c e and a l s o r e v e a l l o c a l l y high temperatures. We have performed t h e c a l i b r a t i o n ( t o be p u b l i s h e d ) ( f i g . 6 ).

I f a p i e c e of t h e h e a t s e n s i t i v e f i l m is placed i n c o n t a c t w i t h a polymer d i s c and a drop weight experiment performed, t h e f i l m darkens ( f i g . 7 ) . Assuming t h a t t h e change is due p u r e l y t o p h y s i c a l causes ( h e a t generated w i t h i n t h e b u l k , a t c r a c k t i p s , s h e a r bands o r a t t h e polymer/film i n t e r f a c e ) a temperature may be a s s i g n e d by measuring t h e o p t i c a l d e n s i t y and a l s o t h e time of h e a t i n g ( w i t h h i g h speed photography);see Table 2. The v a l u e f o r PMMA a g r e e s with t h a t determined by o t h e r methods / 2 5 / . We b e l i e v e a high temperature w i l l occur i f : ( i ) t h e polymer h a s a l a r g e v a l u e f o r t h e product a s a t f a i l u r e ; ( i i ) t h e l a t e n t h e a t of f u s i o n is s m a l l . The f i r s t c o n d i t i o n means both t h a t t h e energy d i s s i p a t e d d u r i n g f l o w w i l l be l a r g e , and a l s o t h e s t o r e d energy d e n s i t y w i l l be h i g h . The second r e s u l t s i n more of t h e energy going i n t o r a i s i n g t h e temperature r a t h e r t h a n i n t o a phase change. More work w i l l be c a r r i e d o u t t o check t h i s h y p o t h e s i s .

Mode of deformation P l a s t i c flow P l a s t i c flow P l a s t i c flow P l a s t i c flow Shear c r a c k i n g

Shear c r a c k i n g

Shear c r a c k i n g Shear c r a c k i n g

F a i l u r e s t r a i n

-

-

- -

0.01

0.04

0.25 1.10

Bulk tem- p e r a t u r e /

<< 220 230 400 450

< 200

< 200

< 200

< 200

Crack tem- p e r a t u r e / ' C

- - - -

550

530

600 700

L a t e n t h e a t of f u s i o n / ~ g - '

115 95 80 85 Not y e t measured None

37

7

0

SO

.14o

contact v 330 t i m e s

A

440 onnn YS

Fig.6 Calibration curves for the heat sensitive film as a function of time and temperature.

Fig.7 Heat sensitive film darkened by the rapid deformation of PP in contact with

it. The original colour is yellowy-brown. The arrows indicate the final diameter

of the specimen,

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V - ACKNOWLEDGEMENTS

T h i s work was f u n d e d by t h e M i n i s t r y of Defence (Procurement E x e c u t i v e ) . We would l i k e t o t h a n k D r . J . R o b e r t s and Mr. R . T i c k n e r of RARDE f o r u s e f u l d i s c u s s i o n s and f o r p r o v i d i n g s p e c i m e n s ; a l s o Mr. N.A. S a f f o r d of PCS f o r much h e l p and i n s i g h t .

REFERENCES

/ 1 / Kolsky, H . , P r o c . Phys. S o c . Lond 62B ( 1 9 4 9 ) 676-700.

/ 2 / S e m i d o r - S i g n o r e t , C . , T h s s e de d o c t e u r - i n g g n i e u r , U n i v e r s i t e d e Bordeaux I ( 1 9 8 1 ) no. 1626.

/3/ L a t a i l l a d e , J . L., P o u y e t , J . M . , Hamdy, A . , S i g n o r e t , C . , J o u r n e e d e Mecanique P h y s i q u e , U n i v e r s i t 6 d e Bordeaux I ( 1 9 8 0 ) .

4 Hamdy, A . , These de d o c t e u r - i n g g n i e u r , U n i v e r s i t 6 d e Bordeaux I (1981) no.

305.

/5/ PSakkZ~nen, E. J . , Kuokkala, V.-T., Tormala, P., Acta P o l y t e c h n i c a S c a n d i n a v i c a , Ph. 130 ( 1981 ) .

/ 6 / L a t a i l l a d e , J . L., P o u y e t , J . , Rheol. A c t a 21 (1982) 431-434.

/ 7 / Marchand, A . , Th'ese d e docteur-ing'enieur,, ~ X v e r s i t 6 d e Bordeaux I (19841, n o . 1928.

/8/ Kukureka, S. N . , H u t c h l n g s , I . M . , Proo. 7 t h I n t . Conf. on High Energy R a t e F a b r i c a t i o n , U n i v e r s i t y of Leeds (1981) ( e d . T. Z . B l a z y n s k i ) pp 29-38.

/ 9 / B r i s c o e . B. J . , Nosker, R . W . , Wear 95 ( 1 9 8 4 ) 241-262.

/ l o / Gorham, D . A . , Mechanical P r o p e r t i e s a t High R a t e s of S t r a i n ( 1 9 7 9 ) ( I n s t . Phys. Conf. S e r . 47) pp 16-24.

/11/ Kennedy, L. W . , J o n e s , 0 . E., T r a n s . ASME, J . Appl . ^{Mech. 36} (1969) 470-478.

/12/ Gorham. D . A . , J . Phys. E., S c i . I n s t r u m . 3 ( 1 9 8 3 ) 477-479.

/13/ F o l l a n s b e e , P. S . , F r a n t z , C . , T r a n s . ASME, J . Eng. Mat. and Tech. 105 (1983) 61-66.

/14/ F r a n t z , C. E., F o l l a n s b e e , P. S . , W r i g h t , W:T., P r o c . 8 t h I n t . Conf. on High Energy R a t e F a b r i c a t i o n , San A n t o n i o , Texas (1984) pp 229-236 p u b l . ASME.

/15/ Gorham, D . A . , Mentha, S . N , , Cox, 0 . P . , Proc. 8 t h I n t . Conf. on High Energy Rate F a b r i c a t i o n , S a n Antonio, T e x a s (1984) pp 207-212 publ. ASME.

/ 1 6 / Pope, P. H . , F i e l d , J . E., J. Phys. E., S c i . I n s t r u m . M (1984) 817-820.

/17/ Gorham, D . A . , P r o c . 1 3 t h I n t . Cong. on High Speed Photography and P h o t o n i c s , Tokyo (1978) pp 313-316.

/ 1 8 / Gorham, D . A . , Pope, P. H . , Cox. 0 . . Mechanical P r o p e r t i e s a t High R a t e s of S t r a i n (1984) ( I n s t . Phys. Conf. S e r . 7 0 ) pp 151-158.

/19/ P u t t i c k , K . E., S m i t h , L. S. A . , M i l l e r , L . E., J . Phys. D . , Appl. Phys. 10

(1 977) 617-631 .

/20/ T a y l o r , G . I . , Q u i n n e y , H . , P r o c . Roy. Soc. Lond. (1934) 307-326.

/21/ Whitney, W . , Andrews, R . D . , J . Polym. S c i . C . no. 16 (1967) 2981-2990.

/22/ G t S e l l , C . , J o n a s , J . J . , J . Mater. S c i . 14 (1979) 583-591.

/23/ Heavens, S. N . , F i e l d , J . E., P r o c . Roy. Soc. Lond. A338 (1974) 77-93.

/24/ Chou, S. C . , R o b e r t s o n , K . D., R a i n e y , J . H., Exp. Mech. 1 3 (1973) 422-432.

/25/ F u l l e r , K . N . G . , Fox, P. G . , F i e l d , 3. E., Proc. Roy. SOT Lond. (1975) 537-557.

/26/ W i l l i a m s , J . G . , Hodgkinaon, J . M . , Proc. Roy. Soc. Lond. A375 (1981 ^J 231-248.

1 2 7 1 C l u t t o n , E. Q . , W i l l i a m s , J . G., J . M a t e r . S c i . 16 (1981) 2583-2589.

/28/ C o f f e y , C. S., J a c o b s , S. J . , J. Appl. Phys. ,2 (1981) 6991-5993.