EXPERIMENTAL METHODS IN BIAXIAL LOADING AT HIGH STRAIN RATES

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EXPERIMENTAL METHODS IN BIAXIAL LOADING AT HIGH STRAIN RATES

N. Ohlson

To cite this version:

N. Ohlson. EXPERIMENTAL METHODS IN BIAXIAL LOADING AT HIGH STRAIN RATES.

Journal de Physique Colloques, 1985, 46 (C5), pp.C5-599-C5-605. �10.1051/jphyscol:1985577�. �jpa- 00224811�

JOURNAL DE PHYSIQUE

Colloque C5, supplCment au n08, Tome 46, aoQt 1985 page C5-599

EXPERIMENTAL METHODS I N BIAXIAL LOADING A T HIGH STRAIN RATES

N . G . Ohlson

Materials Research Center, The Royal I n s t i t u t e of Technology, 100 44 StockhoZm, Sweden

Rksumk - Le comportement mkcanique de la majoritk des matQriaux de construc- tion dkpend de la vitesse de dgformation. Cette investigation concerne l'in- fluence de la vitesse de dkformation sur les propriktks de rupture et de dk- formation plastique. Quatre appareils spkciaux ont kt6 construits pour ces expkriences. Les allongements ont Qtk determines en utilisant des mkthodes optiques. On donne des exemples de rksuitats obtenus : des courbes de seuil dlQcoulement, la te'nacitg de rupture, la valeur critique de l'intkgral de J, prksentks en fonction de la vitesse de d6formation.

Abstract - The mechanical behaviour of most structural materials depends on strain rate. This investigation is concerned with the influence of the strain rate on fracture properties and on plas- tic deformation properties. Four special testing machines were designed and built for these experiments. The strains were de- termined through use of optical methods. Examples are given of results achieved: yield loci, fracture toughness and critical J integral values are presented as functions of strain rate.

I - INTRODUCTION

Transient phenomena in the mechanical behaviour of solids and structu- res are attributed partly to dynamical effects caused by wave propaga- tion and reflection, partly also to the dependence of material proper- ties on strain rate. In the interpretation of such phenomena it is so- metimes difficult to determine whether and to what extent they origi- nate from material effects. Experimental data concerning the material behaviour at high strain rates are to a large extent still lacking.

Even those data which have been published should be applied with some caution because of the difficulty in interpreting certain experimental observations.

Biaxial loading in practice is usually connected with a high degree of complexity regardless of the purpose of the experiments. This is even more obvious if the strain rate is increased. Nevertheless, such expe- riments are required for the purpose of proving or disproving the va- lidity of proposed hypotheses in the mechanics of materials.

I1 - SCOPE OF INVESTIGATION

The present paper is concerned with biaxial experiments in two fields of mechanics, namely, plasticity and fracture. Special testing machi- nes were developed in the Royal Institute of Technology for high-speed experiments. These can be utilized for studying plastic deformation as well as fracture. The measuring equipment, however, is selected to

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985577

JOURNAL DE _PHYSIQUE

meet the requirements of each purpose and will be described separately.

I11 - HOPKINSON BAR WITH ELECTROMAGNETIC APPLICATION OF THE LOAD Following the ideas of Harding /I/, the main features of this testing machine are shown in fig. 1. The well-known split Hopkinson bar con-

sists of two rods whose relative lengths were chosen in such a way that the traveling time for a tensile wave from the left end to the specimen equals the traveling time for a torsional wave from the right end. Therefore, simultaneous initiation of the loads in tension and torsion at the two ends will cause the elastic waves to arrive simul- taneously in the specimen. The loads are produced by discharging large capacitors through coils consisting of a few turns of coarse copper wire. By electromagnetic induction between these coils and solid metal blocs, acting as secondary coils, forces are created between the blocs and the primary coils. These forces are then transmitted to the rods of the Hopkinson bar.

o a a 2

!iP3

Fig. 1 . Electromagnetically loaded Hopkinson bar for biaxial tests.

1 - loading bloc, 2 - coil, 3 - capacitor, 4 - incident bar for ten- sile pulse, 5 - specimen, 6 - torsional bar, 7,8 - loading device for torsion, 9 - capacitor for torsional load.

The advantage about this testing machine is that it allows for good versatility in specimen design. For facilitating the evaluation of re- sults, however, the thin-walled tube seems superior to other types, particularly for the determination of the yield stress.

The long rods allow for attenuation of the current oscillation before the load pulses reach the specimen. Measurements can be made by means of strain gages of incident, reflected and transmitted load pulses in the way which has become common practice for the split Hopkinson bar.

111: 1 - LOADING RATE

As seen from fig. 2, the load pulse differs quite considerably in sha- pe from what is expected in a drop-weight loaded bar, whose pulse form is almost rectangular. The present load is sinusoYda1 in shape, hence the rise time is long in comparison with the rectangular pulse. Its precise value can be selected within rather wide limits by altering the inductance of the primary coil, the mutual inductance between coil and loading bloc, and the size of the capacitor. Therefore, the elec-

Fig. 2. Shape of loading pulse in the machine of fig. 1 (left) and in the machine described in sec-

tion VI (right). ^L time

tromagnetic loading device may become a means for bridging the gap in loading rate between conventional testing machines and machines operat-

i n g w i t h i m p a c t l o a d i n g .

A c o m p l e t e d e s c r i p t i o n o f $ h i s t e s t i n g m a c h i n e i s g i v e n i n / 2 / . The l o a d i n g r a t e may a t t a i n 1 0 o r s l i g h t l y m o r e , d e p e n d i n g on t h e l e n g t h of t h e s p e c i m e n .

I V - COMPACT TENSILE AND TORSIONAL TESTING MACHINE

I n a t t a i n i n g v e r y h i g h r a t e s of s t r a i n t h e t e s t i n g e q u i p m e n t p r e v i o u s - l y d e s c r i b e d h a s r o v e d i n a d e q u a t e , a s t h e t i m e c o n s t a n t of t h e e l e c t -

P-

r i c c i r c u i t ^T = LC c a n n o t b e r e d u c e d t o o much, l e s t t h e peak c u r r e n t becomes t o o low. A l s o , t h e l o a d i n g r a t e i s n o t c o n s t a n t i n t i m e and t h e l e n g t h of t h e l o a d i n g p u l s e c a n n o t b e s e l e c t e d a r b i t r a r i l y . I n - s t e a d , t h e t e n s i l e s t r e s s p u l s e i s f o l l o w e d b y a c o m p r e s s i o n p u l s e , sometimes w i t h unknown c o n s e q u e n c e s f o r m a t e r i a l t e s t i n g .

I n o r d e r t o overcome some o f t h e s e d i f f i c u l t i e s , a compact machine w a s b u i l t , a c c o r d i n g t o f i g . 3 . F o r

o b t a i n i n g a t o r q u e , t h e p r i n c i p l e o f t h e u n i p o l a r machine was a d o p t - e d : t h e c u r r e n t i s g u i d e d r a d i a l - l y i n t h e p r i m a r y c o i l , t h r o u g h t h e l o a d i n g b l o c , where t h e mag- n e t i c f i e l d i s i n t h e a x i a l d i - r e c t i o n . Due t o t h e s m a l l d i s t a n - c e between l o a d i n g b l o c and s p e c i m e n , m u l t i p l e r e f l e c t i o n s of s t r e s s waves

o c c u r w i t h i n a s h o r t t i m e . When F i g . 3. Compact t e s t i n g machine.

t h e s e s u p e r i m p o s e , a n a p p r o x i m a t e l y 1 - l o a d i n g b l o c s , 2 - c o i l , s t a t i o n a r y s t a t e o f s t r e s s i s a c h i e - 3 - dynamometer t e n s i o n , 4 - s p e -

ved. c i m e n , 5 - dynamometer t o r s i o n .

The d i f f i c u l t y i n u s i n g t h e compact m a c h i n e i s due t o t h e f a c t t h a t a n a l t e r n a t i n g c u r r e n t o f t h e o r d e r o f t e n s t o h u n d r e d s o f k i l o a m p e r e s e f f e c t i v e l y drowns s i g n a l s f r o m e l e c t r i c a l l y o p e r a t e d m e a s u r i n g g a g e s , s i n c e t h e r e i s no d e l a y between t h e d i s c h a r g e m e n t o f t h e c a p a c i t o r s and t h e l o a d i n g of t h e s p e c i m e n . O p t i c a l measurements h a v e p r o v e d most u s e f u l u n d e r t h e s e c i r c u m s t a n c e s and w i l l b e d e s c r i b e d l a t e r . F o r more d e t , a i l s of t h e compact t e s t i n g m a c h i n e t h e r e a d e r i s r e f e r r e d t o / 3 / .

V - RING-SHAPED SPECIMENS

F o r t h e p u r p o s e of r e d u c i n g t h e e f f e c t s of i n e r t i a of t h e m e c h a n i c a l p a r t s o f t h e compact t e s t i n g m a c h i n e and h e n c e i n c r e a s i n g t h e l o a d i n g r a t e , t h e specimen may b e s h a p e d as an a n n u l u s , h a v i n g t h e same a x i s a s t h e c o i l ; . f i g . 4 , and a c t i n g as i t s own s e c o n d a r y c o i l . The c u r r e n t i n d u c e d i n it w i l l c a u s e t h e a n n u l u s t o expand u n d e r i n t e r i o r p r e s s u r e . No d i r e c t measurement of t h e l o a d was

a t t e m p t e d i n t h i s c a s e , n o r e v e n n e c e s - s a r y , a s it i s p o s s i b l e t o c a l c u l a t e t h e l o a d u s i n g e l e m e n t a r y l a w s of e l e c t r i - c i t y , l i k e M a x w e l l ' s e q u a t i o n s . The main draw-back o f t h e t e s t i n g method l i e s i n t h e f a c t t h a t t h e r i n g - s h a p e d s p e c i m e n i s h e a t e d u p c o n s i d e r a b l y by t h e c u r r e n t c i r c u l a t i n g i n i t . The t e m p e r a t u r e r i s e may a l s o b e c a l c u l a t e d w i t h p r e c i s i o n ,

however, as t h e p r o c e s s i s t y p i c a l l y a d i a b a t i c . A n o t h e r d i f f i c u l t y o c c u r s when t h e s e s ~ e c i -

mens a r e u s e d f o r c r a c k i n i t i a t i o n s t u d i e s . ~ i4 . A~~~~~~~~~~ ~ . with An e l e c t r i c a r c i s formed a c r o s s t h e c r a c k , specimen as

e f f e c t i v e l y s m o o t h i n g o u t a l l t h e d e t a i l s c o i l .

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of t h e i n i t i a t i o n p r o c e s s . On t h e o t h e r h a n d , t h e moment of i n i t i a t i o n and h e n c e t h e c r i t i c a l l o a d r e q u i r e d f o r i t c a n b e d e t e r m i n e d d i r e c t l y on t h e r e c o r d i n g of t h e p r i m a r y c o i l c u r r e n t , which u n d e r g o e s an ab- r u p t i n c r e a s e , i n a n a t t e m p t by n a t u r e t o m a i n t a i n t h e c u r r e n t o f t h e s e c o n d a r y c o i l , d e s p i t e t h e g r o w i n g r e s i s t a n c e d u e t o c r a c k f o r m a t i o n , f i g . 5 ( L e n z ' l a w ) .

F i g . 5 . P r i m a r y c o i l c u r r e n t d i s p l a y s a jump when s p e c i - men f r a c t u r e s .

V

V I - IMPACT LOADED HOPKINSON BAR WITH TUBULAR SPECIMENS SUBJECTED TO INTERIOR PRESSURE

F o r v e r y h i g h s t r a i n r a t e s , t h e Hopkinson b a r l o a d e d by a d r o p - w e i g h t i s s t i l l a u s e f u l t o o l . I n b i a x i a l e x p e r i m e n t s , it h a s t o b e m o d i f i e d / 4 / . T h i s may b e d o n e a c c o r d i n g t o f i g . 6 . A t h i n - w a l l e d t u b e i s sub- j e c t e d t o i n t e r i o r p r e s s u r e by l e t t i n g t h e c o m p r e s s i o n p u l s e of t h e i n c i d e n t b a r a c t on t h e g r e a s e o r o i l i n s i d e t h e t u b e , which t h u s be- h a v e s a s i f i t were l o a d e d by a p i s t o n . I f t h e r e i s no c o n s t r a i n t i n i t s a x i a l d i r e c t i o n , o n l y a c i r c u m f e r e n t i a l s t r e s s i s p r o d u c e d . By c l a m p i n g t h e t u b e a x i a l l y , t h e a x i a l s t r a i n i s z e r o and a b i a x i a l s t r e s s s t a t e i s r e a c h e d , w i t h o u t any p o s s i b i l i t y of a l t e r i n g t h e p r i n - c i p a l s t r e s s r a t i o , f i g . 6 a . A t y p i c a l stress p a t h t h e n c o n s i s t s o f an a x i a l s t a t i o n a r y p r e s t r e s s , f o l l o w e d by a r a p i d l y applied c i r c u m - f e r e n t i a l s t r e s s . As p r o p o s e d i n f i g . 6 b , a n a x i a l l o a d may b e a p p l i - ed w i t h h i g h s p e e d a s w e l l , b u t o n l y i n c o m p r e s s i o n , t h u s hampering t h e c o m p l e t i o n o f t h e y i e l d l o c u s , a s c e r t a i n c o m b i n a t i o n s o f p r i n c i - p a l s t r e s s e s c a n n o t

b e r e a c h e d .

. - . ^-.

T h i s e q u i p m e n t h a s

p r o v e d e x t r e m e l y u s e - ^--C -I ^{a 6} f u l and e a s y t o h a n d l e w e i g h t

f o r a l a r g e number of t e s t s i n y i e l d i n g and i n c r a c k i n i t i a t i o n . S t r a i n r a t e s of t h e

o r d e r of 1 o 4 s - I may i n c i d e n t specimen t r a n s m .

b e o b t a i n e d . b a r b a r

F i g . 6 . Two t y p e s of d r o p - w e i g h t s . V I I

-

The r a p i d d e v e l o p m e n t o f e l e c t r o n i c a l and o p t i c a l d e v i c e s f o r measure- ment i n r e c e n t y e a r s h a s b e e n b e n e f i c i a l f o r s t u d y i n g h i g h - s p e e d p h e -

nomena. R i s e -times a r e r e d u c e d and s e n s i t i v i t y i s i n c r e a s e d . Modern s y s t e m s a r e a l s o more r e l i a b l e t h a n p r e v i o u s s y s t e m s which were o f t e n m e c h a n i c a l .

V I I : 1 - OPTICAL INTERFEROMETRIC REGISTRATION

I n t h e e l e c t r o m a g n e t i c t e s t i n g m a c h i n e s , e x c l u s i v e l y o p t i c a l r e g i s t r a - t i o n w a s u s e d . E l o n g a t i o n a s w e l l as t o r s i o n w e r e r e c o r d e d by means of an o p t i c a l i n t e r f e r e n c e t e c h n i q u e , shown i n f i g . 7 a f o r d i s p l a c e m e n t measurement. B a s i c l y , t h i s i s a M i c h e l s o n i n t e r f e r o m e t e r and by c o u n t - i n g t h e number o f i n t e r f e r e n c e f r i n g e s t h a t p a s s e d t h e d e t e c t o r as a f u n c t i o n of t i m e , t h e d i s p l a c e m e n t c a n b e m e a s u r e d a c c u r a t e l y .

VII:2 - OPTICAL PROPORTIONAL REGISTRATION

T e n s i l e f o r c e a s w e l l a s t o r s i o n a l moment were measured t h r o u g h u s e of dynamometers whose d e f o r m a t i o n due t o l o a d was m o n i t o r e d by l i g h t beams. The i n t e n s i t y of e a c h beam was a f u n c t i o n of t h e l o a d .

I n c e r t a i n c a s e s , i n t e r f e r o m e t r i c and p r o p o r t i o n a l r e g i s t r a t i o n were u s e d t o g e t h e r . F i g . 7 b i l l u s t r a t e s d i r e c t s t r a i n measurement on t h e specimen s u r f a c e . An o p t i c a l g r a t i n g was engraved t h e r e and t h e r e - f l e c t e d , d i f f r a c t e d beam t h u s changes i t s d i f f r a c t i o n a n g l e w i t h t h e g r a t i n g p a r a m e t e r , depending on t h e s t r a i n , a c c o r d i n g t o Bragg's law.

A photo-diode w i t h a wedge-shaped opening s e r v e s a s a d e t e c t o r o f t h e a n g l e mentioned.

f i x e d

T

m l r r o r b e a m s p l i t t e r l a s e r

specimen

d e t e c t o r Fig. 7 . Displacement measurement

( 7 a , l e f t ) and s t r a i n measurement ( 7 b y r i g h t ) .

V I1 : 3 - HOLOGRAPHIC TECHNIQUE

Normally s p e a k i n g , h o l o g r a p h y i s n o t s u i t a b l e f o r s t u d y i n g high-speed d e f o r m a t i o n , u n l e s s e x p e n s i v e , p o w e r f u l l a s e r s a r e a v a i l a b l e . For spe- c i a l a p p l i c a t i o n s a s i m p l i f i e d t e c h n i q u e was d e v e l o p e d . The i n t e n t i o n was t o o b s e r v e i n - p l a n e d i s p l a c e m e n t s on t h e specimen s u r f a c e i n one p a r t i c u l a r moment d u r i n g t h e t e s t .

The p h o t o g r a p h i c p l a t e was p l a c e d i n c l o s e c o n t a c t w i t h t h e s u r f a c e . The l i g h t s o u r c e c o n s i s t e d of a l a s e r d i o d e whose o u t p u t power i n a p u l s e i s of t h e o r d e r of g i g a w a t t s . The c o h e r e n c e l e n g t h of such a d i - ode i s v e r y s h o r t y e t s u f f i c i e n t f o r t h i s p u r p o s e , a s t h e whole i n t e r - f e r e n c e p r o c e s s o c c u r s w i t h i n t h e e m u l s i o n , f i g . 8 .

A v a i l a b l e l a s e r d i o d e s e m i t i n f r a r e d l i g h t . Conver,tional e m u l s i o n s a r e n o t s e n s i t i v e i n t h i s r a n g e of w a v e - l e n g t h s . By u t i l i z a t i o n of t h e so- l a r i z a t i o n e f f e c t i n an emulsion one may o b t a i n c e r t a i n s e n s i t i v i t y .

F i g . 8 . H o l o g r a p h i c s e t - u p , l a s e r d i o d e i n t e r f e r e n c e w i t h i n emulsion

between r e f e r e n c e beam ( u p p e r ) o b j e c t

and o b j e c t beam ( l o w e r beam).

V I I I - EXAMPLES OF INVESTIGATIONS PERFORMED

1. Y i e l d s u r f a c e F i g . 9 shows p a r t of t h e y i e l d l o c u s i n p l a n e s t r e s s f o r a m i l d s t e e l a t t t h r e e s t r a i n r a t e s . The p r e c i s e meaning of t h e c o n c e p t may be s u b j e c t t o d i s c u s s i o n . Here, it i s t a k e n a s t h e r a t e of t h e von Mises e q u i v a l e n t s t r a i n , c a l c u l a t e d by means of known d i s - p l a c e m e n t s . I t c a n be shown t h a t it i s of t h e same o r d e r of magnitude a s t h e s t r a i n r a t e computed u n d e r t h e assumption t h a t t h e s t r a i n i n - crement i s p e r p e n d i c u l a r t o t h e y i e l d s u r f a c e ,

The y i e l d s u r f a c e and i t s s t r a i n r a t e dependence h a s been t r e a t e d by a l a r g e number o f a u t h o r s . One of t h e f i r s t t o produce c o n v i n c i n g expe- r i m e n t a l r e s u l t s was W R Campbell / 5 / . He was f o l l o w e d by many o t h e r s , e . g . U S Lindholm / 6 / .

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20

-

10

-200 MPa 0 1

-

1 0 30 5 0 ? M N / m 3 / 2 . s l

F i g . 9 . Y i e l d l o c u s f o r m i l d F i g . 10. P l a n e s t r a i n f r a c t u r e s t e e l Sw. c o d e 1550 a t t h r e e t o u g h n e s s f o r aluminium a l l o y

r a t e s of s t r a i n . Sw. code 4332.

2 . P l a n e s t r a i n f r a c t u r e t o u g h n e s s The impact l o a d e d s p l i t Hopkinson b a r i s s u i t a b l e f o r s t u d y i n g c r a c k i n i t i a t i o n i n combined modes o f l o a d i n g by c h a n g i n g t h e i n c l i n a t i o n o f t h e c r a c k w i t h r e s p e c t - t o t h e a x i s o f t h e t u b e . F i g . 10 shows i n p u r e mode I t h e e f f e c t o f KI on t h e f r a c t u r e t o u g h n e s s K I c . A more comprehensive d e s c r i p t i o n o f t h e e q u i p - ment and of dynamic K v a l u e s i s g i v e n i n / 7 / . For a r e v i e w o f problems c o n n e c t e d w i t h d9namic f r a c t u r e t o u g h n e s s t h e r e a d e r i s r e f - e r r e d t o / % / .

T h i s t y p e of e x p e r i m e n t s h a s r e c e i v e d much a t t e n t i o n . I n s m a l l - s c a l e y i e l d i n g t h e c r a c k t i p r e g i o n g e t s i t s i n f o r m a t i o n a b o u t t h e s u r r o u n d - i n g m a t e r i a l o n l y t h r o u g h KI. S i n c e d i f f e r e n t s t r e s s - i n t e n s i t y h i s t o - r i e s may p r o d u c e d i f f e r e n t s t a t e s a v e r y c o m p l i c a t e d h i s t o r y dependen- c e i s a n t i c i p a t e d . F o r example, e x p e r i m e n t s i n d i c a t e t h a t KI s h o u l d e x c e e d a c r i t i c a l v a l u e f o r some t i m e f o r i m p l y i n g i n i t i a t i o n .

3 . EPFM i n i t i a t i o n c r i t e r i a Using t h e J i n t e g r a l c o n c e p t a c c o r d i n g t o e l a s t i c - p l a s t i c f r a c t u r e m e c h a n i c s , J v a l u e s may b e o b t a i n e d a s a f u n c t i o n of l o a d i n g r a t e . F i g . 11 sho& examples o f t h e s e d e t e r m i n a - t i o n s . Among s e v e r a l methods f o r o b t a i n i n g s t a t i o n a r y J v a l u e s , o n l y t h e one b a s e d on a s i n g l e specimen may b e u s e d i n h i g h - s p e e d t e s t i n g .

A J~ M J / ~ '

A G l .. ¹

aluminium s t e e l

-

. 3 3 30 300 v m m / s

-

F i g . 1 1 . C r i t i c a l J v a l u e f o r F i g . 1 2 . S t r e s s - s t r a i n c u r v e w i t h Sw. s t e e l 1550 a s a f u n c t i o n o f a change o f s t r a i n r a t e f o r a l u m i - c r o s s - h e a d s p e e d v i n a conven- nium 4212. A o l i s a m e a s u r e o f t h e t i o n a l t e s t i n g machine. h i s t o r y d e p e n d e n c e , A u 2 e s t i m a t e s

t h e t r u e s t r a i n r a t e s e n s i t i v i t y of t h e m a t e r i a l . I n s e r t e d : f i g . 1 2 b y showing t h e t y p e o f d r o p - w e i g h t u s e d . 4. T h e r m o - p l a s t i c i t y A r e q u i r e m e n t o f t h e t e s t i n g equipment f o r s t u - d y i n g s p e c i a l m a t e r i a l e f f e c t s i s t h e p o s s i b i l i t y o f c h a n g i n g t h e s t r a i n r a t e i n t h e c o u r s e o f a t e n s i l e t e s t . F o r example, t h e a b i l i t y

of t h e m a t e r i a l of memorizing p r e v i o u s l o a d i n g i s o f i n t e r e s t i n s t u - d y i n g t h e r m o - p l a s t i c i t y . A m e c h a n i c a l e q u a t i o n o f s t a t e , o = f ( ~ , ; ) , do- e s n o t e x i s t f o r t h e s e m a t e r i a l s . The b e h a v i o u r o f a n aluminium a l l o y i s i l l u s t r a t e d i n f i g . 12 a . T h i s change of s t r a i n r a t e i n a n i m p a c t t e s t c a n be a c h i e v e d i n t h e Hopkinson b a r by u s i n g a "composite" d r o p - w e i g h t , f i g . 12 b .

I X - CONCLUSIONS

E x p e r i m e n t s a t h i g h l o a d i n g r a t e s performed a t t h e R o y a l I n s t i t u t e f o r more t h a n 1 5 y e a r s h a v e d e m o n s t r a t e d t h a t it i s a d v a n t a g e o u s t o u s e s e v e r a l t y p e s o f t e s t i n g m a c h i n e s which supplement e a c h o t h e r . Owing t o r e c e n t improvement o f measuring e q u i p m e n t , enhanced p r e c i s i o n c a n be e x p e c t e d . A l s o , more e l a b o r a t e e x p e r i m e n t s , l i k e b i a x i a l t e s t s , c a n b e c a r r i e d o u t . S i m u l t a n e o u s r e c o r d i n g of s e v e r a l v a r i a b l e s i s now p o s s i b l e , t h r o u g h u s e of broad-band t a p e r e c o r d e r s and d i g i t i z e d me- m o r i e s which h a v e r e p l a c e d memory o s c i l l o s c o p e s w i t h t h e i r l i m i t e d r e -

s o l u t i o n . X - REFERENCES

/ I / J. H a r d i n g , J. Mech. Engn. S c i . 7 1 6 3 , 1965.

/ 2 / N.G. Ohlson, "A h i g h - s p e e d t e s t i f i g machine f o r b i a x i a l s t a t e s o f stress". R e p r t no. 1 9 2 , Royal I n s t . Techn., D e p t . S t r e n g t h o f Ma- t e r i a l s , Stockholm 1973.

/ 3 / N . G . Ohlson, Rev. S c i . I n s t r u m . 45 827, 1974.

/ 4 / J . H . P e r c y , S t r e s s a n d S t r a i n i n T n g n . , N a t . Conf. P u b l . no. 7 3 / 5 I n s t . E n g r s , A u s t r a l i a , 1973.

/ 5 / W . R . Campbell, P r o c . Soc. Exp. S t r e s s A n a l y s i s

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/ 6 / U.S. Lindholm, "Dynamic D e f o r m a t i o n o f M e t a l s " . B e h a v i o r o f M e t a l s u n d e r Dynamic L o a d i n g , p. 42, e d . H u f f i n g t o n , ASME, Chicago 1 9 6 5 . / 7 / N . G . Ohlson, " D e t e r m i n a t i o n o f c r a c k i n i t i a t i o n a t h i g h s t r a i n

r a t e s " , p . 215, I n s t . Phys. C o n f . S e r . no. 47,ed. J . Harding 1 9 7 9 . / 8 / L.S. C o s t i n , J . D u f f y & L.B. F r e u n d , ASTM STP 627, 301,1977.