Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985580

JOURNAL DE PHYSIQUE

Colloque C5, supplkrnent au n08, Tome 46, aoClt 1985 page C5-623

NEW A P P L I C A T I O N S OF S P L I T HOPKINSON BAR TO M A T E R I A L S T E S T I N G

T. Nojirna and K. Ogawa

Department o f AeronuuticaZ Engineering, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto, 606 Japan

R6sum6

-

La methode de l a barre dlHopkinson e s t appliquee 2 de nouveaux e s s a i s de t r a c t i o n ,

a

des e s s a i s mettant en oeuvre des increments ou des dEcr6ments de v i t e s s e de d&formation, 2 des e s s a i s de recompression e t 5 des e s s a i s de cycle e t de relaxation.

Abstract -Conventional s p l i t Hopkinson pressure bar method (SHPB) i s applied t o new types of t e n s i l e t e s t s , s t r a i n r a t e incremental o r decremental t e s t s , reloading t e s t s , sequenced reverse t e s t s and relaxation t e s t s .

I

-

INTRODUCTION

Extensive works f o r mechanical behaviours of many materials a t high r a t e s of s t r a i n have been done by using compressive /1%3/, t e n s i l e /4%6/ o r torsional version /7%9/

SHPB. Punching and double shear version t e s t s were a l s o performed t o achieve higher r a t e s of s t r a i n

/ l o ,

11/. By these works a l o t of mechanical behaviours under dynamic load have been characterised.

In order t o i n t e r p r e t t h e r a t e e f f e c t onthe mechanical behaviours more i n d e t a i l s , it i s necessary t h a t various kinds of t e s t i n g techninues such as a t conventional low s t r a i n r a t e s a r e developed i n material t e s t i n g under dynamic load. The S!PB i s so compact t o be modified t h a t there seems t o be a l o t of p o s s i b i l i t i e s t o develope some r e l i a b l e new t e s t i n g techniques.

In t h i s paper, some applications of SHPB are intr0duced;newtensile t e s t i n g method i n compressive apparatus, interruption t e s t s (reloading t e s t s ) techniques, f u l l y s e - quenced reverse t e s t techniques and relaxation t e s t s method. These techniques a r e explained with some experimental and calculation r e s u l t s .

I 1 - EXPERIMENTAL TECHNIQUES AND RESULTS 11-A Tensile Tests

Tensile type SHPBisusually more complicated i n i t s designandlahorious than compre- s s i v e version SHPB/4%6/. Therefore, it w i l l be relevant f o r v e r s a t i l i t y of the SHPB method t o develop a simpler arrangement of loading bars f o r a tension t e s t which can be performed i n a compressive SHPB apparatus. Nicholas /12/ modifiedthecompressive apparatus f o r the t e n s i l e t e s t where a s p l i t c o l l a r surrounds t h e t e n s i l e specimen t o carry an i n i t i a l compressive pulse. I t i s always necessary t o t a k e care not only t h a t the s p l i t c o l l a r i s suitably adjusted not t o produce any damage p r i o r t o the t e s t but t h a t the i n i t i a l compressive pulse i s e n t i r e l y c a r r i e d by the s p l i t col- l a r s o t h a t no s i g n i f i c a n t compressive loading i s applied t o the specimen. To avoid these d i f f i c u l t i e s and uncertainties, it i s prefered t o apply t h e t e n s i l e p u l s e d i - r e c t l y t o t h e specimen without any preceding compressive pulse.

Two arrangements are proposed and a r e schematically shown i n Figs. 1 and 2 . An input bar with a flange and an anvil with a flange-cover a r e i n contact with each other.

When the s t r i k e r bar h i t s the end of the anvil, t h e t e n s i l e o r the compressive s t r e s s wavepropagates toward t h e d i s t a l end o f t h e a n v i l i n t h e case of Figs. l a n d 2, respectively. The r e f l e c t e d stresswavefromthedistalendis r e f l e c t e d again a t the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985580

C5-624 J O U R N A L DE PHYSIQUE

f r e e end of t h e a n v i l , and the t e n s i l e s t r e s s wave is t r a n s - Flange-cover Flange mitted t o the input bar. The d u r a t i o n , T, of the t e n s i l e

wave i n the input bar depends upon t h e condition when the re-impingement occurs between the s t r i k e r and the a n v i l . I t should be noted t h a t i n the case of Fig. 1, the maximum value of T i s limited t o T,/2 (To; the duration of the incident wave i n the a n v i l ) , while i n the case of Fig. 2, it can be i d e n t i c a l t o the duration To.

When the flange and the flange-cover a r e of l i g h t metal (e.g., Duralumin) not t o d i s t u r b the s t r e s s wave. the r e l a t i v e l y

short r i s e time of a b o u t ' 4 0 ~ s i s usually

&

obtained.

11-B S t r a i n Rate Incremental and De- cremental Tests

Strain r a t e incrementalordecremental t e s t s a r e performed by using a bar which consists of two d i f f e r e n t cross sectional areas

(step-shaped bar) /13/. Stress-time diagram of the t e s t is schematically depicted i n Fig. 3. An example of the t e s t on pure A1 i s shown i n Fig. 4.

The Au/Alog~ ( ~ = 0 . 0 5 ) through the in-

-

cremental t e s t s i s depicted i n Fig. 5 4--- w i t h the r a t e s e n s i t i v i t y of the

s t r e s s , (acr/alogE), evaluated from the

slopes of a-log; curves through a s e r i e s , :

of constant s t r a i n r a t e t e s t s . The d i f

-

ference between (Ao/AlogB) and (aa/

log:) shows the h i s t o r y e f f e c t of the s t r a i n r a t e up .to E=O .05. The values of (Ao/Aloge) and (aa/alogi) have been obtained a l s o i n s t e e l s and Ti alloys /14, 15/. By analysing the r a t e dependence of (Aa/~log:)

,

^{the ef}

-

f e c t i v e s t r e s s (the thermal componentof the s t r e s s ) , crX,has been evaluated.

c-:_

t

Recently Leroy e t a2 performed decre-

mental t e s t s on A 1 and evaluated the Figs. 1 and 2 Two 'kinds of t e n s i l e t e s t s t r a i n r a t e dependence of a* /16/. arrangements and the x - t diagrams o f e l a s t i c When s t r a i n r a t e incremental o r decre- waves f o r t h e u s e inacompressive apparatus.

mental t e s t s a r e performed i n the SHPB

o r any impact t e s t i n g machine, the Striker Bar Input Output Bar

r i s e time from a s t r a i n r a t e

(cl)

t o a ^{D? I)+}

higher (or a lower) s t r a i n r a t e

( E n )

*=--.-.-.

t;--

&

-

-+. --

w i l l considerably a f f e c t the t r a n -

-

s i e n t behaviour i n s t r e s s - s t r a i n r e - ^x

l a t i o n . A simple numerical example based on the experimental data of pure A l /17/ i s shown i n Fig. 6 . The r i s e times t*=O, 10, 20 and 3 0 ~ s a r e chosen.

The s t r a i n r a t e ,

E t ,

during the i n - t e r v a l (t=O%tx) i s assumed .to $ha?ge

l i n e a r l y from

E l

t o

e2

as E ~ = ( E ~ - E ~ ) mental

x(t/t*)+El. The s t r e s s , u, i s assumed D?<D$

t o consist of the thermal component k c r e -

of the s t r e s s , a*, and the athermal ^'

component of the s t r e s s , o and u* Fig. 3 Experimental set-up f o r s t r a i n r a t e and oU a r e given by the "following incremental o r decremental t e s t .

equations; a=a*+o,,

,

^{~ * = a} ( ~ / E * ) ~ E ~ and u =

{b+c (?/;*)q}En (n=0.5, ~ 4 . 2 , qr0.8 a=y5 MN/m2

,

b = 1 6 5 ~ ~ / m ~

,

c=0 .11blIV/m2 and E*=

1

-

In t h i s section, the E and C are the p l a s t i c s t r a i n and the p l a s t i c s t r a i n r a t e , respectively. Two cases a r e c a l - culated.

(a) Transient s t r e s s - s t r a i n behaviour due t o only t h e r i s e time e f f e c t ; f o r ~ ~ 0 . 0 5 , t h e a is g i v e n b y E q . l . For ~ > 0 . 0 5 , the a

,

o i s given by Eq. 2 f o r t=O%t* and by Eq. 3 b f o r t > t * .

o=a (E l / E * ) P ~ ~ + { b + c ( h l/E*)q (1)

Fig. 4 Input (a) and output (b) waves a=a (t,/E*)P~~+{b+c (it/E*)q}~n (2) i n incremental t e s t , t*%lOl~s (A1,450a o = a ( & 2 / e * ) P ~ ~ + { b + c ( 6 2 / t * ) q } ~ ~ ( 3 ) ^C, compression t e s t , 100us/div.).

(b) Transient s t r e s s - s t r a i n behav- 3 16 iour due t o both the r i s e time and the h i s t o r y e f f e c t s ; the a i s giv- en by Eqs. 4 and 5 f o r t=O%t* and t>

..;.

t * , respectively. In t h e equations

5

only a* = a (i / ? * ) P ~ n i s assumed t o 8

respond immediately t o the instan-

5

taneous s t r a i n r a t e ( f t i n Eq. 4 and

&

i n Eq. 5) and the athermal

.';'

component of the s t r e s s ( l a s t two terms i n Eqs. 4and 5) changesgrad-

<

u a l l y t o t h a t a t the corresponding

8

s t r a i n r a t e . The AE i n Eq.6 i s the O ²⁰⁰ 400 600 800

TEMPERATURE (*K)

s t r a i n increment a f t e r t = O , and r Fig.

strain

rate sensitivities of pure Al is an arbitrary 'Onstant (r=50 is through incremental (hollow circles) and con- used i n t h i s calculation). ventional c o n s t a n t r a t e ( s o l i d c i r c l e s ) t e s t s .

crrmental Test

."

4 5 6 7 4 5 6 7 4 5 6 7 8 4 5 6 7 8

Plastic Strain f % I

Fig. 6 Calculated transient stress-straincurves throughincremental and decremental t e s t s (0: only s t r a i n r a t e change e f f e c t

,m:

both s t r a i n r a t e change andhistory e f f e c t s )

.

C5-626 JOURNAL DE PHYSIQllE

The r i s the parameter which governs how the av changes t o the one a t newstrainrate.

. .

a=a ( ~ , / C * ) P E ~ + { ~ + C ( c l / g * ) q l ~ n + { [ b + e ( ~ ~ / ~

*

⁾ q ] ~ n - [b+c(:l/E*)q]~n) t1-exp (-FA€) 1 (4)

O = U ( ~ ~ / E * ) P E ~ + { ~ + C ( ~ ~ / ~ * ) ~ } E ~ + { [ b + c ( z 2 / E * ) q ] ~ ~ - [ b + C ( i l / A * ) q ] ~ ~ } { l - e x p [ - p ( ~ - ~ .05)])

A E = ( ~ ;tdt=[(i2-;1)/(2t*)]t2+;It. (6) (5)

The fi&e reveals t h a t the t * seriously affects the transient s t r e s s - s t r a i n r e l a t i o n ; as the t * gets larger, material's true response i s veiled b y t h e d u l l change of the s t r a i n r a t e . In order t o clear the true response of materials characteristics, a short r i s e time is recommended; t*%lOps, a minimum r i s e time experimentally achieved, i s an allowable one.

Lipkineta2 performed s t r a i n r a t e decrementaltestsof t*=50%80vs /18/. They showed that flow s t r e s s does not decrease immediately following the reduction i n s t r a i n r a t e and has i t s maximum 30%40vs a f t e r the s t r a i n r a t e begins to change. Leroy e t a2 also pointed out the delay of the s t r e s s response (%lops) /16/. The delay of t h e s t r e s s r e - duction can be seen i n Fig. 6 (g) and (h), even when the history e f f e c t is not taken into account. The reason of the delay is t h a t thestrainhardening due t o A ~ i s l a r g e r than the reduction of the s t r e s s due to s t r a i n r a t e decrease.

11-C Sequenced Reverse Tests

As well as the monotonic deformation a t high rates of s t r a i n , it i s greatly concerned to investigate a reverse deformation which may be frequently associated with the re- flection of s t r e s s waves i n the component materials ofstructures subjected to the i m - pact loading.

Sequenced reverse loading from low (10"/s) t o high (10*%10~/s) s t r a i n r a t e s was f i r s t carried out by Eleiche and Campbell modifing the torsional version SHPB /19/. Eleiche e t a2 have done extensive researches on the reversed s t r e s s - s t r a i n relations by ap- plying repeated impacts where the dwell-time i n successive loadings was approximately 5 minutes/20/ which may seriously affect the deformation characteristics a t high tem- peratures. There has not yet been reported on the f u l l y sequenced reverse deformation a t high rates of s t r a i n with short dwell-time of the order of microseconds.

In the following, the newly developed techniques for the sequenced reverse testing i s described / 2 1 / . One dimensional propagation of s t r e s s waves i n a step-shaped anvil and a connected impact bar i s i l l u s t r a t e d i n Fig. 7 . Whenastriker h i t s the connecting end of the anvil and the input bar, the s t r e s s waves are generated both i n the anvil and the input bar. The s t r e s s wave i n the anvil i s reflected a t discontinuities as shown i n the figure, and a series of s t r e s s pulses, q

,

^ca

,

am

,

e t c . propagates down the input bar. Assuming that an anvil wjth large and small cross-sectional areas, each of equal length, and an input b a ~ are of the same material, anplitudes of the s t r e s s waves on and a, are written i n terms of 01 as

an = A U ~ , am =pa

.

(7)

The uarameter A and u are emressed as follows; ^Anvil S t r i k e r ,Input bar I I

where a =Al/A2 and B =A2/A3.

I t w i l l be relevant t o show some examples of the incident s t r e s s wave.

(a) Tension-Tension (or Compression-Comp- ression) Wave; i n the .case of A3=0 and a=1.0, the parameters are A =1 and p=0.0, i . e . , the second wave, q

,

which i s r e - flected from the d i s t a l e n d of the anvil i s of the same sign and amplitude of the f i r s t wave q . The time interval,T,depicted i n Fig. 8 (a) is expressed as T= 2(Z1-Zo)/Co where l o and Z1 are thelength o f t h e s t r i k -

e r and the right part of the anvil, re- Fig. 7 The x-t diagram of the e l a s t i c spectively, and C o i s the e l a s t i c wave ve- waveina step-shaped anvil and an input locity of the rods. This kind of incident bar.

wave i s available t o reloadaspecimen a f t e r short time cease of deformation.

(b) Tens ion-Compress ion (or Compress ion- Tens ion) Wave ; a i n t h e case of A3- and a=1.0, theparametersare X=-1.0 and p=0.0. Then the second wave onwhich i s of the op- posite sign but t h e same amplitude of t h e f i r s t wave 07 i s generated as i l l u s t r a t e d i n Fig. 8 (b)

.

This kind of incident s t r e s s wave is e s s e n t i a l f o r the sequenced r e - b verse deformation.

(c) Tension-Compression-Tension(orCompression-Tension- Compression) Wave; i n t h e c a s e t h a t A, is a c e r t a i n non

+-

zero value and i s l a r g e r than A z , an incident wave p a t - t e r n shown i n Fig. 8 (c) i s obtained. This kind of

'

wave i s available t o investigate a dynamic hysteresis

loop of materials a t high r a t e s of s t r a i n .

v-

Fig. 8 Three kinds of

An example of input a i ~ d output wave records incident wave patterns f o r the tension-compressionitensi3n t e s t is described i n the t e x t . given i n Fig. 9. I t i s v e r i f i e d t h a t the

incident wave agrees f a i r l y well with the t h e o r e t i c a l prediction based on the one-di- mensional s t r e s s wave analysis a s shown by broken l i n e . I t i s a l s o confirmed t h a t the

s t r e s s on the both ends of a specimen are

C

loo,,

4

nearly i d e n t i c a l during deformation, and the s t r e s s , the s t r a i n and the s t r a i n r a t e of the specimen can be evaluated by the usual way. Experimental set-ups f o r the

examples (b) and (c) a r e schematically shown Output i n Fig. 10. The set-up f o r the example (a)

i s obtained by removing the blocker i n the e x q l e (b)

.

^{Fig. 11} shows an example of dy-

namc and s t a t i c hysteresis loops f o r 0.45% Fig. 9 Input and outputwaverecords carbon s t e e l obtained by t h i s method. More i n the case of tension-compression- detailed r e s u l t s havebeenreported i n /22/. tension t e s t .

Blocker Anvil Striker

,

Input bar Specimen Output bar

0.45%C Steel

I # I 11 I

Fig. 10 Experimental set-ups f o r the example 5.0

(b) (above), and the example (c) (below) de- scribed i n the t e x t .

11-D Interruption Tests (Reloading Tests) The reloading t e s t has been performed t o measure the temperature and the s t r a i n r a t e e f f e c t s on the flow s t r e s s o r simply t o extend t h e s t r e s s - s t r a i n r e l a t i o n s f o r large s t r a i n s , but it should be a l - ways noted t h a t a change of i n t e r n a l s t r u c t u r e s

would be involved f o r t h e dwell-time a t zero s t r e s s . -1000-

Lindholm was the f i r s t t o investigate the e f f e c t Fig. 11 Dynamic a n d s t a t i c hys- of the dwell-time on t h e reloaded flow curves a t t e r e s i s loops of 0.45%C s t e e l high s t r a i n r a t e s f o r A l , and c l a r i f i e d t h a t - t h e a t room temperature.

C5-628 JOURNAL DE PHYSIQUE

contineous flow curveswereobtainedonlyin t h e case ofreloading w i t h a s h o r t dwell-time ofhun- dreds microseconds /22/.

In the present experiment, the incident wave of the example (c)wasused. Fig. 12 shows the e f f e c t of reloading on the compressive s t r e s s - s t r a i n r e l a t i o n s o f zinc which i s remarkably influenced by the thermal recovery even a t room temperature. I t i s c l e a r l y observed t h a t the contineous s t r e s s - s t r a i n r e l a t i o n s a r e ob- tained f o r the dwell-time of 1 0 ~ ~ s e c , while the reduction of the flow s t r e s s i s detected with the reloading f o r t h e dwell-time of 50sec.

The flow s t r e s s i s seriously reduced i n the case of the dwell-time of five minutes. Char-

R.T. i= 7x102/s

0 10 20

a c t e r i s t i c nature of these reloaded s t r e s s - ^E ($1

s t r a i n curves was well u n d e r s t o o d i n c o ~ e c t i o n lzig. 12 ~ ~ lstress-strain ~ ~ d ~ d with the thermal recovery during unloading /23/. cu,es of ,inC w i t h different A s well as the thermal recoveryonthe reloaded h e l l - t i i l l e s at zero stress.

flow curves, it i s a l s o necessary t o take ac-

count of a temperature change during the dwell-time, since many authors pointed out the p o s s i b i l i t y of temperature r i s e which would occur under adiabatic conditions a t h i g h r a t e s o f s t r a i n /24,25/. Eleicheetalperformedatorsional reloadingonAl-alloy a t high s t r a i n r a t e s where the specimens were f i r s t deformed uptoabout 200% s t r a i n s and were reloaded within a maximum of five minutes /26/. Even though t h e temperature r i s e i n the course o f f i r s t deformation was estimatedaswell above 100°C, it was only found t h a t the reloading curve is a c t u a l l y a continuation of the o r i g i n a l curve. I f the temperature a c t u a l l y r i s e s up t o above 100°C, the o r i g i n a l flow curve i s conse- quently influenced by such a temperature r i s e , and then, a higher f l o w s t r e s s i s rea- sonably expected i n reloading with longer dwell-time, such as f i v e minutes, s u f f i - cient f o r a specimen t o cool down. As f a r as t h e authors aware, there has not been reported such an experimental r e s u l t as t o c l a r i f y the temperature r i s e associated with high s t r a i n r a t e s and i t s e f f e c t on t h e reloaded s t r e s s - s t r a i n r e l a t i o n s .

11-E Abrupt Stop Tests (Relaxation Tests)

Relaxation t e s t s of a 0.02%C s t e e l a f t e r an abrupt stop of high r a t e of deformation were performed by i n s t a l l i n g a s t e e l chock between input andoutput bars /14/. I t s alignment and stress-time curves i n the bars and the load c e l l are depicted i n Fig.

12. The a i n the specimen begins t o get smaller when the input bar h i t s the chock.

Because the e l a s t i c deformation of the chock i s q u i t e important during t h e t e s t , i t s behaviour is carefully analyzed by experiments andalso by numerical calculations, which show t h a t the chock ceases i t s deformation a f t e r tX'L60us and keeps an almost constant length.

When t h e chock i s r i g i d enough t o keep almost constant length, the sumofthe defor- mation amounts f o r the load c e l l and the specimen is expressed as

where XZ i s thercompliance of the load c e l l , and A , L , EE (=a/E), E and E are the cross sectional area, the length, the e l a s t i c s t r a i n , the p l a s t i c s g a i n and Youngs modulus of t h e specimen, respectively. Eq. 9 becomes

From Eq. 9 , Aa =-aAcp is obtained. In the mild s t e e l a t R.Ts200°K, the Aa is about 150~N/m' during 4 0 0 ~ s . Putting a=5x104a1. 5x105 M N which seems t o be an available s t i f f n e s s i n the t e s t s , Aspbecomes 0.001s0.003 (E g e t s l a r g e r d u r i n g relaxation).

The AE brings the increase of the s t r e s s which i8evaluatedby ( ~ ~ / ~ E ~ ) A E ~ = z o o o ~ / ~ ~ x (1.0%?1.0). 1 0 ' ~ =2'L6MN/m

.

The s t r e s s increment i s considered t o be enough

small being compared with A U = ~ S O M N / ~ ~ during the t e s t . I t i s a l s o reasonable t o consider t h a t the most of the s t r e s s increment i s t h a t of the athermal componentof the s t r e s s ow.

Only the thermal component of the s t r e s s (effective :tress), o * , i s assumedtochange during t h i s t e s t

(;=A*).

Eq. 10 can be solved when E ~ - G * r e l a t i o n is given. The

%

i s often expressed by a power r e l a t i o n striker ~a~ Input Bar Output Bar

as +,=~(a*)~ (Band m are constants). . ----,-----4 -p By introducing t h e r e l a t i o n i n t o Eq.

-

10 and solving,

I-

^zoo0

+

²⁰⁰⁰

Y

²⁰⁰⁰

i s obtained, where a t i s the s t r e s s q t o which the specimen is loaded and E O i s the corres~onding s t r a i n r a t e . A numerical example through Eq. l l i s i l l u s t r a t e d i n Fig. 13 with the constants used f o r the calcula- t i o n . The figure shows t h a t a* gets smaller a s the time elapses. The a*

- t curves depend considerably upon in-value. Especially m approaches t o

1, the o* rapidly reduces t o nearly zero. This showsthatwhen m i s small, ap i

.

^e

. ,

a* can be evaluated by the experiment. The a*-cp r e l a t i o n de- termined by incremental o r decremen- t a l t e s t s is a l s o rechecked by t h i s experiment.

From experimentally obtained a - t curve and Eq. 10, 4 - t r e l a t i o n can be determined and a - i p curve i s de- rived. The a-E, curve f o r the mild

Incident

[ T - p

J

S t r e s s i n Load C e l l s t e e l i s shown

i5

Fig. 14 with o-Ep

r e l a t i o n through conventional con- Fig. 12 Experimenzal set-up f o r stop s t a n t r a t e t e s t s . t e s t and stress-time curves i n input When the chock i s not r i g i d enough bar, output bar and load c e l l . compared with the r i g i d i t y of the

load c e l l , the e l a s t i c deformation

of the chock should be analyzed exactly. In t h i s case, Eq. 12 shouldbesolved nu- merically.

X~A;+(:~+$,) L=Z (%-aT) / P C ~ = X ( A ~ & ~ - A ~ ) , (12)

where As i s the compliance of the chock, and a I , o a n d o g a r e t h e incident and r e - f l e c t e d waves i n the input bar, and the transmittecfwave i n the output bar, respec- t i v e l y . The ^P and A O is the mass density and the cross-sectional area of the bars, respectively. aI+aR=aT i s assumed i n the equation /14/.

-

a=5x104m/m2 E,=zsO/S

----

a=1x105m/m2 ,o;=300~N/m~

0 200 400

time (PI

600 I I

0.02% C Constant S t r a i n Rate S t e e l Test (cp=0.05)

400

zoo I ^{I I I}

id'

^lo*z lo0 10' 10'

P l a s t i c S t r a i n Rate & W s l

Y - -

Fig. 13 Calculated (a*/cr:)-time Fig. 14 S t r e s s - p l a s t i c s t r a i n r a t e r e l a t i o n s r e l a t i o n i n stop t e s t (relaxa- through stop t e s t (solid c i r c l e s ) and conven- t i o n t e s t ) . t i o n a l compression t e s t s (hollow c i r c l e s ) .

C5-630 JOURNAL DE PHYSIQUE

111- CONCLUDING REMA?XS

In order t o i n t e r p r e t the r a t e e f f e c t on mechanical behaviours of materials, some applications of the SHPB methodaredeveloped. Two kinds of new t e n s i l e t e s t methods are proposed. S t r a i n r a t e incremental and decremental t e s t and its methods a r e d i s - cussed showing t h a t t r u e m a t e r i a l response i s o f t e n veiled by d u l l change o f t h e s t r a i n r a t e and a short r i s e time (%lops) i s e s s e n t i a l i n t h i s t e s t . Sequenced reverse t e s t methodispresented and the r a t e e f f e c t onthe hysteresis loop i s c l a r i f i e d . Reloading t e s t i s performed and the dwell-time e f f e c t i s shown. Relaxation t e s t s are c a r r i e d out and it is suggested t h a t the thermal component of t h e s t r e s s w i l l be evaluated s t r a i g h t forwards by this method.

The authors would l i k e t o express t h e i r appreciation t o Prof. K. Tanaka f o r h i s en- couragements throughout the work.

REFERENCES

/1/ Hauser, F. E., Simmons, J. A. and Dorn J. E., Responce of Materials t o High Ve- l o c i t y of Deformation (New York, Wiley) (1960) 93

/2/ Lindholm, U. S., J. Fkch. Phys. Solids 17 (1964) 317 /3/ Yoshida, S. and Nagata N, Trans. JIM. 971968) 110

/4/ Harding, J . , Wood,E.O.andCampbell,J~D., J.Mech.Eng. Sci. 2 (No.2) (1960)88 /5/ Tanaka, K., Noj ima, T and Kinosita, M., Proc. of 13th Japan C6ngr. Mat. Res

.

(1970) 97

/6/ Kawata, K, Hashimoto, S, Kurokawa, K and Kanayama,N, Proc. Conf. onMech. Proper.

a t High Rates of S t r a i n ed. Harding,' J. (London, The I n s t i t u t e of Physics) (1979) 71 /7/ Campbell, J . D. and Dowling. A. R., J. Mech. Phys. Solids 18 (1970) 43

/8/ Duffy, J., Proc. Conf. on Mech. Proper. a t High Rates of S c a i n , ed. Harding, J.

(London, The I n s t i t u t e of Physics) (1979) 1

/9/ Hayashi, T and Tanimoto, N, High Velocity Deformation of Solids, eds. Kawata, K and S h i o i r i (Berlin, Springer Verlag) (1978) 279

/lo/

Dowling, A. R., Harding, J and Campbell, J . D . , J. of 1nst. Metals

98

(1970) 215

Ill/

Campbell, J. D. and Ferguson W. G., Phil. Mag.

2

(1970) 63 /12/ Nicholas, T., Exp. Mech.

21

(1981) 177

/13/ Tanaka, K. and Nojima, T., Proc. I n t e r . Conf. on Mech. Behav. of Materials, ed.

Taira, S. (Kyoto, Japan Society of Materials Science) (1972) 176

/14/ Tanaka, K and Nojima, T, Proc. Conf. on Mech. Proper. a t High Rates of S t r a i n ed. Harding, J. (London, The I n s t i t u t e of Physics) (1979) 166

/15/ Tanaka, K., Ogawa, K. and Nojima, T., High Velocity Deformation of Solids, eds

.

Kawata, K. and S h i o i r i

,

J. (Berlin, Springer Verlag) (1978) 98

/16/ Leroy, M, Radd, M. K., Nkule, L. and Cheron, R . , R o c . Conf. on.%ch. Proper.

a t High Rates of S t r a i n , ed. Harding, J. (London, The I n s t i t u t e of Physics)(1984) 31 /17/ Nojima, T. and Tanaka, K., Proc. of 21st Japan Congr. Mat. Res. (1978) 6 /18/ Lipkin, J, Campbell, J. D. and Swearengen, J . , J. Mech. Phys.Solids - 26 (1978) 251 /19/ Eleiche, A. M. and Campbell, J., E%p. Mech. (1976) 281

/20/ Eleiche, A. M. and El-kady, M. M., Proc. ASM/TIM-AIME Sympo. on Novel. Tech.

Metal Deform Test (1983) 323

/21/ Ogawa, K., Exp. Mech. 24 (1984) 81

/22/ Ogawa, K., Proc. 1 s t I n t e r . Conf. on P l a s t i c i t y (Oklahoma) (1984) /23/ Tanaka, K and Ogawa, K, Bull. of JSME, 20-145 (1977) 769

/24/ Costin, L. S., Crisman, E. E., Hawley, R. H. and Duffy, J., Proc. Conf. onMech.

Proper. a t High Rates of Strain., ed. Harding., J. (London, The I n s t i t u t e of Phys- i c s ) (1979) 90

/25/ Bai, Y. and Dodd, B., Matals Tech., 8 (1981) 420

/26/ Eleiche, A. M., El-kady, M. M. and Ei-kabbany, H. H., Second Cairo Univ. Mech.

Design and Product Conf. (1982) 459