High Strain rate Testing; Tension and Compression.pdf

8/13/2019 High Strain rate Testing; Tension and Compression.pdf

http://slidepdf.com/reader/full/high-strain-rate-testing-tension-and-compressionpdf 1/9

High S t ra in ra te Test ing: Ten s ion and Co m press ion

I n t h i s pa pe r t he a u t hor s p r e s e n t a s p l i t- p r e s s ur e - ba r

m e t hod f o r ob t a i n i ng c om pl e t e s t r e s s - s t r a i n c ur v e s a t s t r a i n r a t e s

i n t he o r d e r o f 1 0 0 0 s e c - ~ in e i t he r t e n s i on o r c om pr e s s i on

b y U . S . L i n d h o l m a n d L . M . Y e a k l e y

A B S T R A C T -- D e ta i ls o f t h e s p l i t H o p k i n s o n p r e s s u r e - b a rm e t h o d f o r o b t a i n i n g c o m p l e t e s t r e s s - s t r a i n c u r v e s t

s t r a i n r a t e s o n t h e o r d e r o f 1 0 0 0 se c - ~ i n e i t h e r t e n s i o n o rc o m p r e s s i o n ar e p r es e n t e d . I n c o m p r e s s i o n , a g a g e f o rm e a s u r i n g r a d i a l s t r a i n a n d , t h e r e fo r e , P o i s s o n s r a t i o i sa l s o d e s c r i b e d . S o m e t y p i c a l r e s u l t s a r e p r e s e n t e d f o r

a l u m i n u m , a n d v a r i o u s f a c t o r s p e r t a i n i n g t o t h e a c c u r a c yo f t h e r e s u l t s a r e d i s c u s s e d .

I n t r o d u c t i o n

T h e s p l i t H o p k i n s o n p r e s s u r e - b a r m e t h o d f o r ob -

t a i n i n g s t r e s s - s t r a i n c u r v e s a t v e r y h i g h s t r a i n r a t e s

w a s fi r st i n t r o d u c e d b y K o l s k y ~ i n 19 49 . S u b s e -

q u e n t l y , m o d i f i c a t i o n s o f K o l s k y s o r i g i n a l t e c h -

n i q u e h a v e b e e n d e s c r i b e d b y D a v i e s a n d H u n t e r , ~-

L i n d h o l m ~ a n d H a u s e r . 4 A t p r e s en t , m a n y l a b -

o r a t o r i e s a r e u s i n g t h e b a s i c m e t h o d w i t h o n l y s l i g h t

v a r i a t i o n s i n t h e m a n n e r o f l o a d i n g a n d i n s t r u m e n -

t a t io n . H o w e v e r , a p p l i c a t i o n o f t h e m e t h o d t o

d a t e h a s b e e n p r i m a r i l y i n t h e c o m p r e s s i o n o f s h o r tc y l i n d r i c a l s p e c i m e n s . S i n c e t h i s g e o m e t r y of f er s

o n l y a p l a n a r d i s c o n t i n u i t y b e t w e e n t h e p r e s s u r e

b a r s a n d t h e s p e c im e n , t h e a s s o c i a t e d o n e - d i m e n -

s i o na l w a v e m e c h a n i c s o f t h e c o m p r e s s i o n t e s t a r e

c o m p a r a t i v e l y s i m p le . W h i l e s e v e r a l s u g g e s t io n s

h a v e b e e n m a d e o n w a y s t o us e t h e m e t h o d i n t e n -

s i on , t h e y h a v e r e q u i r e d t h e u s e o f t h r e a d e d c o n n e c -

t i o n s b e t w e e n t h e s p e c i m e n a n d t h e p r e s s u r e b a r s ,

a s w e l l a s c o m p l e x b a r c o n f i g u r a t i o n s i n o r d e r t o o b -

t a i n t h e te n s i l e l o a d i n g . T h e s e f a c t o r s a d d u n c e r -

t a i n t y t o t h e w a v e m e c h a n i c s o f t h e p r o b l e m a n d ,

t h u s , r e c o n s t r u c t i o n o f t h e t r u e b o u n d a r y c o n d i t i o n s

o n t h e s p e c i m e n . T h e r e f o r e , f e w r e a l r e s u l t s h a v e

y e t b e e n p u b l i s h e d f o r t h e t e n s i l e t e s t .I n t h i s p a p e r , t h e a u t h o r s w o u l d l i k e t o p r e s e n t a

s p l i t - p r e s s u r e - b a r m e t h o d o f t e n s i l e te s t i n g w h i c h ,

w e f ee l, a v o i d s t h e d i f fi c u lt i es m e n t i o n e d a b o v e a n d

U . S . L in d h o l m a n d L . M . Y e a k l e y a r e M a n a g e r , E n g i n e e r i n g M e c h a n i c sS e c t i on a n d R e s e a r c h E n g i n e e r , r e s p e c t iv e l y , D e p a r t m e n t o f M e c h a n i c a lS c i e n c es , S o u t h w e s t R e s e a r c h I n s t i t u t e , S a n A n t o n i o , T e x .

P a p e r w a s p r e s e n t e d a t 1 9 6 7 S E S A S p r i n g M e e t i n g h e l d i n O t t a w a , O n t .C a n . o n M a y 1 6 - 1 9 .

W o r k w a s s u p p o r t e d p a r t i a l ly b y th e A r m y R e s e a r c h O l ~ ce , D u r h a m , a n d t h eU . S . A i r F o r c e M t tt e r i a ls L a b o r a t o r y , W r i g h t - P a t l e r s o n A i r F o r c e B a s e ,O h i o .

i s o f t h e s a m e a c c u r a c y a s t h e c o m p r e s s i o n t e s t .

S i n ce b o t h m o d e s o f o p e r a t io n , t e n s i o n a n d c o m p r e s -

s i on , a r e b a s e d u p o n t h e s a m e p r i n c i p l e s , a u n i f i e d

p r e s e n t a t i o n w i l l b e m a d e h e r e f or t h e s a k e o f c o m -

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

t a i n e d f r o m t h i s a n d s i m i l a r m e t h o d s s t i l l a p p e a r t o

b e t h e s u b j e c t o f s o m e d i s c u s s io n , w e w i l l t r y t o

o u t l in e s e v e r a l r e l a t i v e l y i n d e p e n d e n t c h e c k s c o n -

c e r n in g t h e a c c u r a c y o f t h e m e a s u r e m e n t s a n d a s -

s u m p t i o n s m a d e .

B a s ic E x p e r i m e n t a l P r o c e d u r e

B e f o r e d e s c r i b i n g t h e d e t a i l s o f t h e m e t h o d , w e

m i g h t c o m m e n t b r i e f l y o n t h e g e n er a l a p p r o a c h t o

t h e d y n a m i c t e s t . I t is d e s i r e d t o f i n d a f u n c t i o n a l

r e l a t i o n s h i p b e t w e e n t h e i n d e p e n d e n t v a r i a b l e s o f

s t r e s s , a , s t r a i n , ~, s t r a i n r a t e , ~ a n d t e m p e r a t u r e , T .

E x p e r i m e n t a l l y , w e w o u l d l ik e t o o b t a i n i n d e p e n -

d e n t m e a s u r e m e n t s o f e a c h o f t h e s e q u a n t i t i e s d u r -i n g t h e d e f o r m a t i o n p r o c e s s . A l s o , t h e m e a s u r e -

m e n t s s h o u l d b e m a d e a t a p o i n t o r o v e r a v o l u m e

e l e m e n t t h r o u g h w h i c h t h e i n d e p e n d e n t v a r i a b l e s

d o n o t v a r y s i g n i f i c a n t l y .

G e n e r a l l y , t e m p e r a t u r e i s t a k e n a s th e i n i t i a l

e q u i l i b r i u m t e m p e r a t u r e o f t h e s p e c im e n * a n d

t h e r e f o r e po s e s n o e x p e r i m e n t a l p ro b l e m s . S t r e s s

c a n o n l y b e m e a s u r e d b y m e a n s o f a n e l a s t ic e l e m e n t

i n s e ri e s w i t h t h e s p e c i m e n . F o r t h e d y n a m i c t e s t s

u n d e r c o n s i d e r a t i o n , w h e r e s t r e s s w a v e s a r e ge n -

e r a t e d , t h e e l a s t i c e l e m e n t t a k e s t h e f o r m o f a l o n g

b a r s o t h a t t h e d u r a t i o n o f t h e l o a d i n g i s l e s s t h a n

t h e w a v e t r a n s i t t i m e in t h e b a r . T h i s a v o i d s t h e

o c c u r r e n c e o f c o m p l i c a t i n g r e f l e c t e d w a v e s i n t h er e c o r d e d s i g n al s . S i n c e t h e p r e s s u r e b a r r e m a i n s

e l a s t i c t h r o u g h o u t t h e t e s t , i t c a n a ls o g i v e t h e d i s -

p l a c e m e n t a n d v e l o c i t y o f t h e i n t e r fa c e b e t w e e n t h e

s p e c i m e n a n d th e b a r . T h e u s e o f t w o p r e s s u r e

b a r s o n e i t h e r s i d e o f t h e s p e c i m e n a l l o w s r e c o r d i n g

o f t h e d i s p l a c e m e n t , v e l o c i t y a n d s t r e s s b o u n d a r y

c o n d i t i o n s o n e a c h e n d o f t h e s p e c i m e n . I f t h e

H e a t g e n e ra t e d d u r i n g t h e d e f o r m a t i o n p r o c e s s i s u s u a l l y n e g l e ct e d ,

a l t h o u g h a c h a n g e f r o m i s o t h e r m a l t o a d i a b a t i c c o n d i t i o n s o c c u r s w i t h i n -c re a sD T g r a t e o f d e f o r m a t i o n .

E x p e r i m e n t a l M e c h a n i c s J



TRANSMITTER PRESSURE BAR INCIDENT PRESSURE BAR

5 VAC

SO p s

STRESS STRAIN STRAIN RATE

Fig. 1--Schematic of pressure bars and associated recording circuitry

TRIGGER

STRIKER BAR

~ AGNETIC ~ICKUP

l l - - I I - - - ; \ A M P / - L = ~ - -- g o v

,11

VELOCITY RADIAL STRAIN

specimen is sufficiently lower in strength than the

pressure bars, relatively large plastic deformations

can be produced.

The dynamic test then becomes quite analogous

to the standard quasi-static test, i.e., strain and

strain rate are recorded from relative cross head

displacements and velocities, while stresses are ob-

tained from series connected dyna momet er bars

(load cells). Also, ave ragi ng occurs over a gage

length, in this case the length o f the specimen.

The main concern relating to the technique is the

adeq uacy of these a verage values in representing

true material response. This adequacy is depen-

dent: upon how close stress equilibrium in the

specimen is appro ached during the loading. This

will be comment ed upon during subsequent develop-

men t of the test technique and presentati on of re-

sults.

The a rrangement of the pressure bars and the

associated electronic circuitry is shown in Fig. 1.

The specimen is sandwiched between the two long

incident and transmitter pressure bars which remain

elastic thr ough out the impact. The loading is ini-

t iated by impacting the incident pressure bar with

the striker bar, producing a constant-amplitude

stress pulse whose duration is determined by the

length of the striker bar.

The applied loading and deforma tion of the speci-

men are determined from the displacements and

forces at the t wo faces of the pressure bars in con-

tinuous contact with the specimen. These may be

determined from the strain-time histories in the

two elastic pressure bars by means of resistance-

strain-gage measurements . Three separate strain

pulses are recorded: the incid ent loadin g pulse, e~,

the reflected pulse, eR, from incident pressure bar-

specimen interface, and the transmitted pulse, eT,

propagated into the transmitter pressure bar.

Oscilloscope records of these three pulses are shown

in Fig. 2 (the gain on the transmitted pulse is 2.5

times that of the incident pulse).

From these three strain-time histories and the

application of one-dimensional elastic-wave-propa-

gation theory, one can determine the displacement,

velocity and pressure at both faces of the specimen

as functions of time. Since both mode s of opera-

tion, tension and compression, are based on the

same principles, a single derivation will be made

here. If we denote by subscripts 1 and 2 the inci-

dent and trans mitte r side of the specimen, respec-

tively, we can derive the following relations from

simple one-dimensional elastic-wave-propagation

theory.

Displacements:

Velocities:

f o Tl = C o 4 1 - e R ) d t (1)

f o ~u s = C o e r d t

v l = c o e z - - e R ) (2)

V = C o E T

2 I J a n u a r y 1 9 6 8



Forces:

P 1 = E A e ~ + eR) (3)

P ~ = E A e r

where

E = Young s modulu s

co = wave veloci ty

A = cross-sectional area of the pressure bars .

I f lo and A o are the ini tial length and cross-sectional area of the specimen, respectivel y, the

average s t ress , s t ra in and s t ra in ra te in the specimen

are given by:

ul - u~ • Co fres = lo lo ~ -- eR -- e~ )d t

2co e~dt (4)lo

is - v~ - v~ _ ~_ co 2Co

6)

Th e =E s igns designate compression or tension

compress ion be ing taken as pos i t ive . The approx i -

mations on the r ight- hand s ide of the above equa-

t ions are based on the approximate equivalence of

the forces on both faces, so that

PI -~ P2 or el q- e~ er (7)

This approx imat i on can be checked exper iment al ly

by d irect ly summing the indicated s ignals. For the

specimen mater ia l s and d imens ions used, the ap-

proximat ion is val id to wi th in exper imental accu-

racy .Us ing the appro ximat e express ions on the r ight of

eqs (4) and (5), the s tre ss- str ain curves ma y be re-

corded d irect ly on an x - y oscilloscope. The re-

flected pulse, e~, is integrated with an operational

amplifier to yiel d a s ignal propor tion al to es while

eT is direct ly propo rtio nal to as. Since the two

s tra in-gage s ta t ions are equ id is tant f rom the speci-

men, these two signals are t ime coincident. Rec-

ords f rom the outp ut of the ope rat ional ampli fier

and a typ ical s t ress -s t r a in curve in tens ion (not to

failure) are given in Fig. 2.

Cal ibrat ion of the ent i re sys tem is obta ined in one

s tep by compar ing the cons tant ampli tude of the

incident pulse wi th the impact velocity . These arel inear ly re la ted by the express ion

V~ = - - (8)

2co

i f the impac t and pressure bars are the same mate-

rial and have the same cross-sectional area. The

Transmitter Bar

Speci men Str iker Bar

Incident Bar

. tl

-. -Stress

-. -Stra in--

X - Y O scilloscope

ER t)

Time

Interva l

Counter

Fig. 2--Typical oscilloscope records from pressure-bar system

E x p e r i m e n t a l M e c h a n i c s ] 3



GuardRings Brass ~ . [--Epoxy

..... Teflon~./~,Z,~,.~/Z,~ /--Suppot Ring

I I ' / l i @ / I i i , I / / ) ' / I

Incident ~ TransmitterPressureBar ~ PressureBar

SupportRing F//,//,~H/,Z/,/../ .~, Y.. fi~/X , ~]

Case Brass ~ ActiveCapacitance ingCompression

[-Specimen

~ \ \ \ \ \ \ \ \ \ \ \ \ \ ]

( . ~ Transmitter I(~ Inc'dent ressureBar ~ Pressure ar /

. . . . . . . . . . . . . . . . F ' /K ~ '4,~ ~ , ' < , ' \ \ \ ' - , - , \ \ \ \ ' - , \ \ t

Tension

Fig. 3--Compression- and tension-specimen configurations

32Rj_n0.5501 '~l-r~---~:.~3 132 - 00. 50

0 80-----~

Fig. 4--Details of tension specimen

/// ~

Initial Loading

a)

Reloading Of

Same Specimen

El -- 2

tRl

O

9 fE Rd t I ' -

= d t

b)

Fig. 5-- a) Typical stress-strain records for 1100-0 aluminumin compression; b) relationship between record and strainamplitudes in pressure bars

impact velocity, V, is measured from the induced-

voltage signal (see Fig. 2) of two fixed grooves on

the striker bar passing a magneti c pickup. The

time interval between the zero crossings of this

signal are recorded on an electronic counter.

The specimen and pressure-bar configurations for

compression and tension are shown in Fig. 3. The

compression specimen is a simple cylinder sand-

wiched between two identical pressure bars. The

diameter of the specimen is smaller than the bars

to allow for radial expansion during plastic defor-

mation. The interface between the specimen and

the bars is lubricated with MoS.2 in order to mini-

mize frictional boun dar y restraint. Concentric with

the compression specimen is shown a capacitance

ring used to measure radial displacement and which

will be described later.

The tensile specimen is hat-shaped, fitting between

a solid cylindrical incident bar and a tubular trans-

mitter bar. Detailed dimensions of this specimen

are given in Fig. 4. Thes e dimensi ons allow use of

incident and tr ansm itte r bars of equal cross-sec-

tiona l area so that eqs (4), (5) and (6) rema in ap-

plicable. Thus, the measuring system is unch anged

for either tension or compression testing. The

actual gage section of the tensile specimen has four

equal arms, each with a length-to-width ratio of

approxi mately 2 to 1. Because of the somewhat

unusua l geometry of the ha t specimen, its static

stress-strain behavior was compared with an ASTM

standard 0.250-in.-diam round tensile-test specimen

of the same material, 1100 = 0 aluminum. Stress-

strain curves for two specimens of each geometry

were found to be coincident up to 30-percent strain,

indicating no significant geometrical effects of the

ha t specimen. Failures in the ha t specimen

occur normally near the midsection. Specimens

which initiate failure at the fillets are discarded.

Some typical oscilloscope records, this time in

compression , are show n in Fig. 5a for 1100 - 0

aluminum. An initial stress- strain curve and a

reloading of the same specimen are shown in order

to illustrate a soft and work-hardened specimen.

Note that the complete unloading curve is traced.

Oscillations, particularly evident in the reloading

curve, are due to Pochammer-Chree ringing in the

pressure bars. Figure 5b shows how all the required

information can be obtained from the stress-strain

4 I Janua ry 968



1 6 I [ I I I

1 . 4

1o2

o 1 o lO0 . 8 1 1

0 0 -

c a

0.~

.2

0 , ~ J , 0 2 ,

0.4 0.8 1.2 1.6 2.0 2.4

~], ( )

F ig . 6 - - Ra d i a l s t r a in an d l ong i t ud i na l s t res s v s . l ong i t ud i na ls t r a i n f r om a dy nam i c c om pr e s s i on t es t o f p r e s t r a i ned 1100 -0a l u m i n u m

trace, elimi~ating the time var iable completely.

R a d i a l S t r a i n M e a s u r e m e n t

Wit h the cylindrical compression specimen, radial

s t ra in may be measured d irect ly wi th the coaxial

capaci tance gage shown in Fig. 3. This measure-

ment serves as an independent check on the axial

s t ra in measurement obta ined f rom the pressure

bars . Also, a dynami c Poisson s ratio m ay be

determined f rom the two measurements . The ca-

pacitance gage consists of an active r ing mounted

coaxially inside a heavy brass case with guard rings

on either side. The rings are mou nte d and elec-

t r ical ly iso la ted with an epoxy cement .

An operational amplif ier was used to form a

charge amplif ier for measuring the small capacit ance

change during deforma tion of the specimen. This

circuit is shown in Fig. 1. The guard rings are

charged directly, and the active r ing through a 10-megohm resis tor by a 90-v batter y. A single

capaci tance feedback conver ts the operat i onal am-

plif ier into a charge amplif ier . I t can be shown that

the change in ou tpu t voltage, Ae0, is given by

A V A C ~ ~.~ V A C ~Aeo =

(1 + A ) C ~ + C g C ~

C i > > C f > > C ,, ( 9 )A

A > > I

where

V = vol tag e on gage

Cg = tot al capa citan ce of gage including leads

C ~ C IC x = series combin atio n of C~ and C d C i H - C I

C~ = d-c bloc king cap aci tor

Cf = feedback capac itor

A = gain of opera tion al amplif ier

Hence, the outp ut s ignal is only a funct ion of theappl ied vol tage, V, feedback capaci tance, CI , and

the capaci tance change in the gage. A cal ibrat ion

capaci tor cons is t ing of a push rod with a s teppe d

diameter and a coaxial capaci tance r ing was in-

corporated to make cal ibrat ion easier . The feed-

back network, R r C ~ , is a high-p ass f il ter to give d-c

s tabi l i ty .

The capaci tance between the specimen and the

activ e r ing of the gage can be easily calculated,

neglect ing any smal l amount of f r inging not t aken

care of by the guard rings, by the rela tion

C R = 2 7 re o IR [ l n ; ] - 1 = k ~ [ l n ; R ] - I (10)

where

CR = capaci tance from ring to specimen

e0 = per mit ivi ty of air

l R = length of active r ing

rR = radiu s of active r ing

r = radi us of specimen

Diff ere ntia tin g eq (10) gives

E r ; ~ ]2 d Rd r 1 I n d C R = k ~ -r k l CR ~

Int egr at in g this resu lt over the li mits ro -- r, C~0 -

CR, we get

e~ = ks CR - CRo _ l n r~ ( ACR ~ (11)

C R C ~o r o \ C R o + A C ~ ]

where

e~ = t rue rad ial strai n

ro, C~o = initia l specimen radius an d ini tial r ing

capaci tance

Thus, the ou tpu t of the charge amplif ier (a l inear

function of ACR) is a nonlinear function of s train.

For very small s trains, however, the following ap-

proximat ion may be used:

In r~r

e~ ~ AC R ~12)1

CR O 2 A C R lIlaX)

where

ACR(m~x) = maxim um change in capaci tanc e dur-

ing test.

In the radia l s t ra in tes ts, a record of the out put

of the ca l ibra t ion but ton was a lways taken an d used

E x p e r i m e n t a l M e c h a n i c s t 5



as th e calibration for the ACR signal while the initial

capacita nce, CRo was dete rmined from the measure-

men t o f the initial specimen radius, the ring radius,

:and the value of kl. The max imu m strains in most

of the tests were small so tha t t he linear approxima-

tio n of eq (12) could be used. For example, in the

test of Fig. 6, the initial ca pacitanc e was 1.50 pf,

~he maximum change in capacitance was 0.04 pf

so that the maximum error in using eq (12) would

be less tha n 1.5 percent.Figure 6 shows the results of a compression test

on a prestrained 110 0- 0 aluminum specimen

(similar to Fig. 5a), including the radial strain

measurement. The experimental points are plotted

at uniform time increments of 6.5 ~sec below 0.5-

percent strain and 16.3 ~sec above 0.5-percent

strain. Several interesting features can be noted.

For the stress-strain curve, we can follow both the

loadi ng and unloading. Elastic moduli of 107 psi

for aluminum are drawn to indicate the relative ac-

curac y of the results. The experimental loading

modulu s is seen to be considerab ly in error. This is

expected because of the finite time it takes to come

to stress equilibrium across the length of the speci-men through the process of numerous internal wave

reflections. Durin g unloading, the elastic modulus

is in very close agreement, indicating th at the stress

relaxes fairly uniformly over the gage length of the

specimen.

The curve for radial strain, er, vs. longitudinal

strain, et, shows three d istinc t linear regions: the

initial slope during elastic loading which suffers from

the same inaccuracies as the loading modulus, a

slope of 0.50 during plastic defo rmation, a nd an un-

loadi ng elastic slope of 0.32 whic h is close to t he

elastic Poisson s ratio for aluminu m. If we assume

the plastic deformation to be incompressible, the

measured ratio of 0.50 indicates tha t both thecapacitance gage and the pressure bars are accu-

rately measur:ing the deformation.

E l e v a t e d - t e m p e r a t u r e T e s t s

Elevated-temperature tests pose a problem with

the pressure-bar methods in that, if temperature

gradients exist along the leng th of the pressure bars,

the propagation of elastic waves is affected through

the effect of temperatu re on the modulus and the

wave velocit y of the bar material. Since the entire

apparatus is very long, it is impractical to bring the

whole system to an equilibrium temperature. I t

was also found to be impractical to bring the speci-

men alone up to temperature, insert the cold pres-

sure bars, and then perform the impact rapidly.

With this procedure, i t was found from thermo-

couple measurements t hat the rate of heat loss from

the specimen was too rapid, especially in the case

of the tensile specimen, to yield reliable results.

Thus, it became necessary to correct elevated-

temperature data for the temperature gradients in

the pressure bars.

Elevated-temperature tests are performed in the

same manner as just described, with the exception

that a cylindrical, electric-resistance-type oven is

placed symmetrically around the specimen and a

short portion of the pressure bars adj acent to the

specimen. The temp erat ure is controlled from a

thermoc ouple on th e specimen to 5=2 ~ F.

The oven produces temperature gradients in the

incident and transmitter pressure bars which are

rough ly exponentially decreasing with distance from

the specimen and symmetric about the specimen.These gradients have two effects on the elastic

waves: a contin uous change in wave velocity and

a continuous change in amplitude. Since the strain-

gage stations are equidistant from the specimen and

the temperature profile is symmetric, the wave

transit time from the specimen to each gage station

will be the same, i.e., the changes in wave velocity

will not produce error in the recorded signals. The

change in signal amplit ude be tween the gage station

and the specimen, however, must be accounted for.

A correction factor of the form

eo = (1 -k C a 3 / ~) ; C a - - a 2 T - - T o ) (13}

~ al

was derived from previous work 5 on elastic-wave

propagation in a bar with a temperature gradient of

the form

T - T o = T s e - g x ; T > T o

and a l inearly temperature-dependent modulus

E = a l A - a 2 T - T o )

1.30

1.20

i . I 0

oTT 1.00

0.90

0.80

- o

~ Theory

o Exper imental

0 I I I I0 200 400 600 800

Temperature ~

F ig . 7 - - R a t i o o f pa r t i c l e v e l oc i t y a t s t r a i n -gage s t a t i on t o pa r-t i c l e v e l oc i t y a t hea t ed en d ; c om p a r i s on o f t heo r y w i the x p e r i m e n t

1000

6 I J a n u a r y 1 9 6 8



F i g 8 S t r e s s s t r a i n c u r v e s

f o r 1 10 0 0 a l u m i n u m i n t e n

s i o n a n d c o m p r e s s i o n

l I I l I

I I 0 0 0 A l u m i n u m

25 20 5 I0

e n s i o n

4

O

12

8

4

5

a: 3.0 x lO-3(sec- )~

I I I I I

I I I I 1

E-- 1 . 8 x l O~ /

F C o m p r e s s i o n

4

8

12

15

20

24

I t I I I

5 I0 15 20 25

S t r a i n ( )

I I I I I 1 2 4

w h e r e

a ~, a 2 a n d K = c o n s t a n t s

To a m b i e n t t e m p e r a t u r e

T ~ . = ( T - T , ) . ~ = o

T h e r a t i o e o / e T i s t h e r a t i o o f t h e s t r a i n r e c o r d e d a tt h e g a g e s ta t i o n , w h i c h i s a t a m b i e n t t e m p e r a t u r e

T o, t o t h e a c t u a l s t r a i n a t t h e s p e c i m e n w h i c h i s a t

t e m p e r a t u r e T .

I n o r d e r t o c h e c k t h e r e l a t i v e a c c u r a c y o f t h i s

c o r r e c t i o n f a c t o r , a s i m p l e e x p e r i m e n t w a s r u n .

T h e e l a s t i c a n d s t r e n g t h p r o p e r t i e s o f t h e b a r m a t e -

r i a l w e r e d e t e r m i n e d . T h e y i e l d s t r e n g t h d e t e r -

m i n e s t h e u p p e r l i m i t o f i m p a c t v e l o c i t y t h a t c a n b e

u s e d a n d a ls o l i m i t s t h e t e m p e r a t u r e r a n g e . T h e

e l a s t ic - w a v e v e l o c i ty w a s m e a s u r e d f r o m w a v e

t r a n s i t t i m e s i n b a r s o f f ix e d l e n g t h a n d u n i f o r m

t e m p e r a t u r e . I n o r d e r t o c h e c k e q 1 3 ), a c o m p a r i -

s o n o f v e l o c i t y ra t h e r t h a n s t r a i n w a s m a d e b e t w e e n

t h e g a g e s t a t i o n o n t h e i n c i d e n t b a r a t r o o m t e m p e r -a t u r e a n d t h e f r e e e n d o f th e i n c i d e n t b a r w h i c h

w a s h e a t e d b y t h e s p e c i m e n ov e n . V e l o c i t y o f t h i s

f re e e n d w a s m e a s u r e d w i t h a c a p a c i t a n c e - t y p e

v e l o c i ty p ic k u p . T h e v e l o c i t y a t th e s t r a i n - g a g e

s t a t i o n i s g i v e n b y th e s t r a i n a m p l i t u d e m u l t i p l i e d

b y t h e e l a s t i c -w a v e s p e ed . T h u s , t h e v e l o c i t y - r a t i o

c o r r e c t i o n i s g i v e n b y

Vo co- 1 + Ca ) ~I4

UT T

A c o m p a r i s o n o f t h i s e x p r e s s i o n w i t h t h e e x p e r i -

m e n t a l r e s u l t s i s g i v e n i n F i g . 7 . T h e c o r r e c t i o n

f a c t o r i s s e e n to b e s m a l l o v e r t h e t e m p e r a t u r e r a n g e

c o n s i d e r e d a n d a g r e e s r e a s o n a b l y w i t h t h e e x p e r i -

m e n t a l d a t a a c t u a l l y i s w i t h i n t h e a c c u r a c y o f t h e

e x p e r i m e n t ) . T h e r e l a t i v e m a g n i t u d e o f t h e co r -r e c t i o n i s i n a g r e e m e n t w i t h C h i d d e s t e r a n d M a l -

v e r n ~ w h o u s e d a m o r e l a b o r i o u s n u m e r i c a l p r o c e-

d u r e . T h i s c o r r e c t i o n f a c t o r h a s b e e n u s e d f o r

e l e v a t e d t e m p e r a t u r e t e s t s t o 7 5 0 ~ F .

R e s u l t s

T e s t s a r e c u r r e n t l y b e i n g p e r f o r m e d o n a l a r g e

n u m b e r o f m e t a l s o f t e c h n i c a l i n t e r e s t . O n l y a f e w

i l l u s t r a t i v e r e s u l t s w il l b e p r e s e n t e d h e r e. F i g u r e 8

s h o w s s t r e s s - s t r a i n c u r v es f o r 1 1 0 0 - 0 a l u m i n u m

i n b o t h t e n s i o n a n d c o m p r e s s i o n a t v a r i o u s s t r a i n

r a t es . T h e l o w e r s t r a i n - r a t e te s t s w e r e p e r f o r m e d

o n a s t a n d a r d I n s t r o n t e s t i n g m a c h i n e w i t h t h e s a m e

s p e c i m e n g e o m e t r i e s a s t h e d y n a m i c t e s t s . F i g u r e 9

s h o w s t h e s a m e t y p e o f d a t a p l o t t e d a s c o m p r e s s i v e

a n d t e n s i l e s t r e s s a t c o n s t a n t s t r a i n v s . s t r a i n r a t e .

F o r t h e c o m p a r i s o n b e t w e e n t h e t e n s i o n a n d c o m -

p r e s s i o n d a t a , a l l v a l u e s o f s tr e s s , s t r a i n a n d s t r a i n

r a t e a r e t r u e v a l u e s .

F o r v e r y l o w s t r a i n r a t e s , t h e s t r e s s le v e l s i n

t e n s i o n a n d c o m p r e s s i o n a g r e e , a l th o u g h t h e i n -

c r e a s e i n f l ow s t r e s s w i t h i n c r e a s i n g s t r a i n r a t e d i f-

f e r s i n d e t a i l . T h e q u e s t i o n i m m e d i a t e l y a r i s e s

E x p e r i m e n t a l M e c h a n i c s I 7



A

", I

V')

(I.)~>

em

EO~.)

nV'}v

w..-*(j')

5(--

<D

I---

i 0 - 3 I 0 - 2 i 0 - ' I 0 ~ I 0 ' I 0 z

A v e ra ge S t ra i n R a t e ( s e c - ' )

Fig. 9--Ef fect of strain rate on the fl ow stress of 1100-0 alumi num in tension and compression

1 3

i24

1 4

whether this difference in rate dependence is real or

a funct ion of the tes t and specimen geometry . At

present we must conclude tha t i t is real s ince for

o ther nonrate-sens i t ive metals we obtain the same

s tress -s t ra in curve dynamica l ly or s ta t ical ly . The

difference could result from previous nonisotropic

work hardening of the mater ia l . The specimens

were annea led to 650 o F before testing.

Figure 10 shows compression stress-strain curves

for 6061-T6 a lumi num alloy for which the wide vari-

a t ion in s t ra in ra te appears to have neglig ib le ef fect

on the s tress levels. This is found to be true for

o ther h igh-s t rength a luminum al loys as wel l. In

this case the equivalence of the d ata obta ined from

the sp l i t Hopkinson pressure bar wi th that obta ined

at low s t ra in ra tes on an Ins t ron machine can be

taken as one indicat ion that wave propagat ion

effects in the dy namic tes t are not c ontr ibut ing any

significant error to the measurem ents .

D i s c u s s i o n

The spl i t Hopkinson method has the advant ages

of s impl ic i ty of exper imental equipment d i rect dy-

namic cal ibra t i on of the ent i re sys tem f rom mea-

surement of the impact veloci ty and cont inuous

measurement of forces and d isp lacements on both

faces of a short specimen. The mai n question con-

80

60

5O

o ~40

[]

30

20

~o0 0 c]

O O

<>

O

[]

O- E=2 X I0 ~ sec l

[3 - ~= 2 x 10 z sec-'

9 ,~ =2 x 10 5 sec ~

0 E=780 see-'

A- t=960sec ~

i o

o I ]0 0.02 0.04 0.06 0.08 0.10 0.12

Strain

F ig . 1 0 S t r e s s s t r a i n c u r v e s f o r 60 6 1 T 6 a l u m i n u m i n c o m

p r e s s i o n a t s e v e r a l s t r a i n r a t e s

4 ~

O 14

8 I J a n u a r y 9 6 8

High Strain rate Testing; Tension and Compression.pdf

Documents

Transcript of High Strain rate Testing; Tension and Compression.pdf