Techniques for Measuring Stress-Strain Relations

at High Strain Rates

Paper reviews briefly some of the experimental techniques

for measuring the stress, strain and strain-rate relationship,
and points out some of the difficulties and shortcomings.
Also, experimental techniques used by author are explained
and typical results presented

by Frank E. Hauser

ABSTRACT---Thequalitative dependence of the mechanical suits have been valuable to check proposed rate-
behavior of some materials on strain rate is now well determining plastic-deformation mechanisms. T h e
known. But the quantitative relation between stress,
strain and strain rate has been established for only a few necessity of knowing the effect of rate on the be-
materials and for only a limited range. This relation, havior of materials is not only necessary to scientific
the so-called constitutive equation, must be known before endeavors, b u t also to practical engineering con-
plasticity or plastic-wave-propagation theory can be used siderations when designing members which are sub-
to predict the stress or strain distribution in parts sub- jected to impacts. Thus, under the combined
jected to impact stresses above the yield strength.
In this paper, a brief review of some of the experi- pressure of scientific as well as practical investiga-
mental techniques for measuring the stress, strain, tions of the rate effect, m a n y schemes have been
strain-rate relationship is given, and some of the difficul- devised to measure the stress, strain and strain
ties and shortcomings pointed out. Ordinary creep or rate over wide ranges of strain rate.
tensile tests can be used at plastic-strain rates from 10 -8
to about 10-1/sec. Special quasi-static tests, in which J. NI. Krafft I and H. Kolsky ~have given excellent
the stress- and strain-measuring devices as well as the reviews of some of the earlier schemes of measuring
specimen geometry and support have been optimized, high strain rates. I n prior publications on strain-
are capable of giving accm'ate results to strain rates of rate effects by the author, 3-5 the emphasis has been
about i02/sec. At higher strain rates, it is shown that
on the material properties, and the experimental
wave-propagation effects must be included in the design
and analysis of the experiments. Special testing machines techniques for measuring these properties were not
for measuring stress, strain and strain-rate relation- included. I n this paper, after a brief section on the
ships in compression~ tension and shear at strain rates up derivation of pertinent equations, the experimental
to 105/sec are described, and some of the results pre- techniques used b y the author will be explained and
sented. With this type of testing machine, the analysis
of the data requires certain assumptions whose validity typical results presented.
depends upon proper design of the equipment. A I n a simple tension test, such as Fig. l(a), the
critical evaluation of the accuracy of these types of load and the initial specimen area are k n o w n and,
tests is presented. thus, the engineering stress readily defined. Also,
the initial gage length and change in length as a
Introduction function of time can be measured, and the engineer-
The mechanical behavior of most materials is known ing strain and strain rate calculated. Then, if one
to be influenced greatly by the testing temperature assumes uniform strain distribution t h r o u g h o u t the
and, to a somewhat lesser degree, b y the rate of de- gage section, the true stress and strain can be cal-
formation. The m a n y studies of the temperature culated. B u t if localized deformation such as a
effect have helped not only the engineer in design- Lfiders' band or necking occurs, the local stress and
ing structures at temperature extremes, but also the strain can only be obtained b y measuring the
scientist in the understanding of the basic plastic- elongation in the small region where these strains
deformation mechanisms. Only more recently can again be assumed to be uniform. Similarly, if
have accurate studies of the rate effect over wide the rate of loading is increased greatly, at a n y in-
ranges of strain rate become possible, and these re- stant of time the load reading at the load cell m a y be
different from the load carried b y the specimen.
Frank E. Hauser is Associate Pzwfessor of Mechanical Engineering and The strain distribution within the gage length m a y
Research Engineer for the Inorganic Materials Research Division of the also v a r y considerably due to the finite rate of
Lawrence Radiation Laboratory, University of California, Berkeley, Calif.
stress and strain propagation. T o obtain useful
Paper was presented at 1965 S E S A Spring Meeting held in Denver, Colo.,
on M a y 5-7. data at high strain rates, the load cell must be small

Experimental Mechanics I 395

 Fig. 1--Three
possble imaterial-test
arrangements , ,mpoct ,ore

//JJ
JH~"Jz.~
/,'Fz.z
/,"I///L'//////
,.z.z,-p,,..~,.J-- I~"~
/ ' ,, Input bar

Specime

Specimen~ Oscilloscope _J-Strain goges B

~1/11/I/111/I//I
Lood
cell " ~ I
'//////I/////////
OutputbarL

o. STATIC b. QUASI-STATIC c. DYNAMIC

and be in i n t i m a t e contact with the specimen, and Elastic-wave Propagation at Discontinuities

the specimen itself m u s t be v e r y small in order to
Figure 2 derives the pertinent equations describ-
a p p r o a c h uniform strain distribution in a short
ing the reflected stress zr and the t r a n s m i t t e d stress
time. T h i s is the quasi-static testing a p p r o a c h
at in t e r m s of the incoming stress w a v e ~ and the
shown in Fig. l(b). I t assumes t h a t the u p p e r
areas A1, As and mass densities pl, p2. T h i s deriva-
a n d lower loading m e m b e r s a p p r o a c h each other at
tion assumes uniaxial stress and, thus, holds only
a known velocity and are essentially infinite in size.
for slender bars. Figure 3 shows the repeated ap-
I f these loading m e m b e r s h a v e changes in cross
plications of eqs (4) and (5) to an example where a
section, elastic stress waves within the m e m b e r s will
l-in.-long reduced section of one-half the area of the
be reflected f r o m these discontinuities and cause a
i n p u t and o u t p u t rod is inserted. T h e incoming
peculiar stepwise loading rate. T o avoid this
stress wave z~ has a rise t i m e of 2 #sec. N o t e t h a t
difficulty, one can use long slender elastic input and
the stress in B a r 1 first rises to zt, t h e n drops due to
o u t p u t bars, s u c h as in Fig. l(c), in which the
the reflection f r o m the discontinuity, and t h e n
theoretical solutions to w a v e - p r o p a g a t i o n equations
rises again stepwise at 10-#sec intervals a s y m p t o -
are relatively simple and, so, the stress variation can
tically toward z~. I n the center of the reduced
be predicted and controlled. I n Fig. 1(c), on im-
section, the stress rises a t 5-#sec intervals to the
p a c t of the r a m with the input bar, a stress wave
equilibrium value of 2 ~ , and, in Section 3, the stress
p r o p a g a t e s down the bar, p a s t strain gage A, where
rises a t 10-#sec intervals toward the equilibrium
the m a g n i t u d e can be measured. On reaching the
value of r T h e duration of each step is governed
specimen, p a r t of the wave is t r a n s m i t t e d through
b y the transit time of the wave t h r o u g h the reduced
the specimen and p a r t is reflected b a c k toward the
section, and the sloping p a r t of each step is of the
ram. T h e m a g n i t u d e of the reflected wave can be
same duration, n a m e l y t h a t of the rise time. While
measured again at gage A, and the stress trans-
the example in Fig. 3 pertained to an area discon-
mitted t h r o u g h the specimen can be measured in
tinuity, a change in material in Section 2 would
the o u t p u t bar with gage B. Eventually, the com-
produce similar results because of the change in
pressive stress wave is reflected from the free end
modulus E and density p. Chiddister and Mal-
as a tension wave and arrives b a c k at the specimen. v e r n 6 h a v e shown t h a t the effect of a t e m p e r a t u r e
This unloading wave t e r m i n a t e s the test. I f prop- gradient in a uniform bar causes similar stress
erly analyzed, enough d a t a are available from the transients. I n all cases, the t o t a l t i m e required to
strain gages to determine the stress, strain and reach the equilibrium value of stress depends on
strain r a t e of the material in the specimen. T h e b o t h the impedance (pcA) m i s m a t c h and on the
analysis of the d a t a and the optimization of the length of the discontinuity. I n a complex struc-
experiment require some background in simple ture subjected to impact, the transient-stress condi-
w a v e - p r o p a g a t i o n theory. A review of the per- tion persists for a long t i m e in the long elements;
tinent p a r t of the theory follows. while in the short elements, the stress reaches

396 I August 1966

 Specimen
Ram ('P2 C2A2)
-( [% D 2I Input bar ~77J
~ Output bar

Pz j o = moss density Input gage ~'1 e [4-- Output gage

I n
Ai Az

a~ff\[
COMPRESSION

At the i n t e r f a c e , Ram

~BF = O~

Continuity v, = v 2 ~ V'i - V r = V t (2} SHEAR

o- = P c v , - .......... (3)
Ram ,./j/Transmitter bars
for elastic wove propagating with v e l o c i t y c =E ~ - 7

Combine to get-

= ~c2Az-P, c,A, ~ (4) Output bar ~'~'~I onnection

1~ CZ A 2 +.~1ClA [
I
2& czA, ~i (5) TENSION
.Pzcz Az+~ cj A,
Fig. 4--Examples of compression, shear
Fig. 2--Elastic-wave propagation and tension-test arrangements

@ |
I | J
- Effect of Plastic:Deformation
on Wave Propagation
~=ld~ c I = c2 = Cs = 2 0 0 , 0 0 0 in/sec.
Hence transit time = 5/.zsecs. T h e use of eq (3) in the previous section implied
Let A,= A3= 2A2; ~='P2 = & the assumption t h a t d z / d e = E and t h a t E is a
Then (I)'-'-'~) ~tt = 4'/5 o~ and ~rr = - I/3 ~r~ constant for a given material. This a s s u m p t i o n is
so a~ : z/3 o~, a-c: 4/3 ai valid for crystalline solids where the stretching of
|174 ~t'= z/3 % and ~ ' = I/3 % the atomic bonds is nearly linear and r a t e inde-
so o~ = 8/9 o-1 , a-| I % o~ pendent. T h e a s s u m p t i o n of constant E for poly-
mers would certainly not be a good one because the
complex molecular bonding causes a nonlinear a n d
,% rate-sensitive stress-strain relation. Similarly, if
i r the stress at a n y point in a m e t a l exceeds the yield
l---2,u secs. rise time 20 30 40 t # secs. strength, plastic d e f o r m a t i o n occurs, and d z / d e is no

+l 0 I0

5g.
longer constant. T o m a k e use of a unique static
stress-strain relation in order to determine ( d z /

-[ de)plastic would a priori assume t h a t no strain-rate

effects exists and, thus, void a n y experimental
strain-rate-effect d e t e r m i n a t i o n which requires this
a s s u m p t i o n in the analysis. B u t one can a p p r o a c h
O
i
IO 12.5 IZ520 22.5 27.550 32.5 4[0 t/~ s e & the p r o b l e m indirectly: use long elastic i n p u t a n d
o u t p u t m e m b e r s in which the transient-stress condi-
tions c a n be calculated for loading and measuring,
and use v e r y short test specimens in which equilib-
r i u m can be established v e r y rapidly to provide t h e
0 1~3 20 25 30 35 40 45 t F s~'cs._ plastic-property information.
Fig. ?,--Example of elastic-wave propagation
Experimental Technique
equilibrium after a short t i m e interval. B o t h of Figure 4 shows three a r r a n g e m e n t s of a modified
these effects m u s t be considered in the design of a split H o p k i n s o n b a r for performing compression,
dynamic-stress-testing machine. One wishes to double shear and tension tests on a n y a r b i t r a r y
h a v e a constant stress of long duration applied to material at high strain rates. I n each case, long
the specimen b u t also wants to reach the equilib- elastic i n p u t and o u t p u t rods are used for stress-
rium-stress distribution in the specimen as quickly pulse shaping and measuring. On i m p a c t of the r a m
as possible. with the i n p u t bar, a step in stress is p r o p a g a t e d

Experimental Mechanics ] 397

 down each member. I f b o t h the r a m and input bar tapered sections in the input bar m a y be used if a
are free of discontinuities, a constant value of stress nonconstant input stress is desired. But, even
is obtained whose magnitude depends on the impact with uniform sections, the stress level will fluctuate
velocity and the respective impedances (pcA) of the somewhat because of the transverse stress oscilla-
members. I f the r a m should contain a discon- tions in the bars due to the Poisson's expansion.
tinuity, such as an attached anvil head, the effect The magnitude of these oscillations can be mini-
would be similar to the one described in Fig. 3, mized by using small-diameter bars or tubes.
and a series of steps would result in the stress wave The input gages m u s t provide a measurement of
propagated down each bar. These steps would the stress level of the incoming stress wave and the
make the plastic analysis of the specimen more magnitude of the reflected waves from the specimen.
difficult. I f an anvil is required because of in- The o u t p u t gage provides a measurement of the
sufficient hardness of the ram, the length of the transmitted stress. The measurements can be
discontinuity should either be very short so equilib- accomplished b y either strain gages or velocity
rium is reached quickly, or it should be very long gages. Since the behavior in the input and o u t p u t
so the duration of a single step in stress level is bars is purely elastic, E is constant, and if p and c
equal to the test duration. The rise time of the are known for the material, eq (3) relates the stress
stress wave depends on the perfection of alignment and particle velocity. Velocity transducers which
between the impact faces of the r a m and the input do not require a discontinuity in the bar have been
bar. W i t h reasonable constraints, a rise time of used b y Ripperger and Yeakley 7 and Malvern and
2-3 ~sec is possible on 1/4-in.-diam input bars. For Efron, 8 b u t these gages are difficult to construct
the tension test in Fig. 4, the rise time of the ten- and calibrate. I t is easier to use symmetrically
sion stress in the input bar is determined both by the mounted strain gages, wired in such a way as to
impact of the r a m with the transmitter bars and the cancel stresses due to a n y bending m o m e n t present.
dimensions of the transfer connection. T h e stress I f subjected to impact, electric strain gages require
level in the input bar corresponds to z3 and t h a t in the use of nonmagnetic gage-and-rod material to
the transmitter bar to ~ in Fig. 3. Again, one has avoid the signal induced by magnetostriction, which
the choice of making the connection v e r y short to would appear as an apparent strain. T h e gages
achieve rapid equilibrium, or to make the connection must be mounted with a thin layer of nonbrittle
very long and use the first step in stress level for cement to give a true reading and not break off due
the entire test. Ideally, then, one wishes to have to the high shock load. The electrical connections
an elastic-stress wave of constant amplitude and must be made with a minimum of solder and with
rapid rise time to propagate past the input gage fine wire or ribbon to reduce the over-all mass.
and reach the specimen. Discontinuities or even This minimizes the load on the cement when the

DUMMY
LAND
CAMERAS
I--"-]
U
IUMMY
I GAGES I ___

WATER BRIDGE AND

~ALIBRATIOI~
TANK SOLENOID
~ - ~ OPERATED CIRCUITS
~..VALVE
;UPPORTS HYGE
RAM
PUT BAR

(
SR-4 STRAIN LSR-4 STRAIN
OUT-PUT BAR~ (TRANSMI
WAVE)TTED(IN-POTWAVE)
GAGE GAGE

ADJUSTABLE -SPLIT LUCITE HOLDER

SUPPORTS SAMPLE
Fig. 5--Experimental arrangement and instrumentation

398 ] August 1966

 I n /Specimen

i r
ou,pu,

AREA =~ c la gove. at t[

9 -o7 at I

+~atO
O~t ~ O~t" ~c,o gove. at t, Level of O~i
/
/
/

/ \ /1" \
/
\
/ //(T t' at B
/ Fig. 6--Graphical solution
/ i to eqs (7) and (8)
I~ 2 d L / c l -~ ~zz " tl d~ -c
_L 2/ct (,~output_do)~

gages are subjected to high accelerations b y the uniformly within the specimen. T h e elastic rods at
passing stress waves. (The particle velocity in the the ends of the specimen constrain the lateral plastic
bar m a y go from zero to a b o u t 100 ft/sec in 3 ~sec.) deformation somewhat due to friction, but, with a
Because of the high harmonic content of a sharply good surface finish on the rods and a light film of
rising square wave, the electronic signal amplifiers lubricant, the final shape of the deformed compres-
must have a wide band pass, or the filtering action of sion specimens shows little barreling below 15-per-
t h e circuits will remove some of ~he information re- cent strain. This lateral constraint nevertheless
quired for analysis. For o p t i m u m results, a band limits the m i n i m u m thickness of the specimen.
pass of 10 mc or greater is desirable. T h e amplified The mathematical analysis for obtaining the
input and o u t p u t signals are displayed on single- stress, strain and strain-rate data has been pre-
sweep oscilloscopes and recorded by means of a sented previously 3 b u t is included here in a more
camera m o u n t e d on the scope. The over-all experi- complete form.
mental arrangement is shown in Fig. 5. I n Fig. 4 (a), on impact of the ram, a compressive
stress ~ propagates down the input bar and is
Analysis of the Measurements partially reflected on reaching the specimen. This
reflected stress ~, due to the impedance m i s m a t c h
As was shown in Fig. 3, reflections and transient
at the interface I, propagates back toward the r a m
stress waves arise even in a completely elastic
past the input gage. The input gage then records
specimen. These transients can be accounted for
( ~ - ~). At interface I, t h a t p a r t of the input
b y the use of eqs (4) and (5). B u t if plastic de-
stress which the specimen can support is trans-
formation takes place in the specimen, the transient
mitted as at. As the specimen strain-hardens, a
stress waves will differ from those predicted b y the
higher stress can be supported and at increases while
elastic analysis, and it is this difference t h a t con-
ar decreases as a function of time. T h e t r a n s m i t t e d
tains the information as to the plastic behavior of
stress at, in turn, is partially reflected at interface I I
the specimen. Since the input and o u t p u t rods re-
as ~1 and the stress ~t 1 is t r a n s m i t t e d into the out-
main in the elastic state at all times, the stress and
p u t bar and recorded at the o u t p u t gage. T h e
particle velocity can be determined for sections I
reflected part of at at interface I I is reflected back
and I I in Fig. 4 at all times. These sections are
and forth within the specimen and soon reaches the
c o m m o n to the bars and the specimen and, so, the
equilibrium distribution (see a2 in Fig. 3).
stress and particle velocity at each end of the gage
Considering the equilibrium of forces at I and I I ,
section is known. I f the specimen is small enough
we have
so t h a t the transit time for the elastic wave is short,
equilibrium t h r o u g h o u t the specimen is rapidly ~FI ~ (~i - ~r)A1 = ~tA2
established, and plastic deformation takes place ~FII --~ (~t -- ~rl)A~ = ~tIA1

Experimental Mechanics [ 399

 r
Material : A/
I I Ti lit, ! ! -i- PC : 50 Ib. sec./in.3

v, r 280 ft./see.

30, 0 0 0 Strain gage 0 output

/J ~ Predicted output

20,000
Fig. 7--Transient elastic-
stress distribution in a
Stress,
stepped bar o'-, psi I 0 , 0 0 0
I IfI \\ I

,oo /,,-.
TimeH secs. ', \
-I 0,000

~4
z
- 2

20

15
n
0
.J
IO
z
t~

Fig. 8--Experimental record

and analysis for 0.4-in.
0 tubular a l u m i n u m speci-
0 20 40 60 80 I00 120 140 160 180 200 men with an applied stress
TIME IN /1 SEC. of 20,OOOpsi

where all stresses are m e a s u r e d at t h e s a m e i n s t a n t o u t p u t ends of t h e s p e c i m e n can be c o m p u t e d using

of time. T h e a v e r a g e stress in t h e s p e c i m e n is eq (3) a n d setting the particle v e l o c i t y v in t h e bars
then equal to d X / d t .
Ca"g = 1/2 (~I -~ O'II)
d X = r dt
pc
~,,g _ ct + (r -- r (~i- r + r ,(AI/~I2 (6)

where all the stresses are m e a s u r e d a t I a n d I I . X I = pc (r - cr)dt

A c t u a l l y (r - CT) a n d r are m e a s u r e d at t h e gages,
and
b u t t h e y can be p h a s e d p r o p e r l y in t i m e to p e r m i t
calculations of t h e a v e r a g e stress in t h e specimen. XII= l l tl 1Lt
-- ctIdtl = ctldt
T h e d i s p l a c e m e n t s X~ a n d X n at t h e i n p u t a n d pc ~ /c

400 I A u g u s t 1 9 6 6
 thick section. F r o m t h a t time on, there is appre-
.././ :+ ~ ' - 1 5 9 ciable deviation of the observed record from the
I0,000 predicted wave shape. Therefore, the one-dimen-
7+ ~ 158 sional elastic analysis used is n o t very accurate
when one a t t e m p t s to predict stress waves in thick
141-~4~_~L_
7 7"-- I sections 9

n
,40,--~1
~/-~+/I'~J '+"~147
T h e experimental results of a plastically deform-
ing compression specimen are shown in Fig. 8.
(~ I 0 0 0 T h e 0.4-in.-long, a/4-in.-diam tubular a l u m i n u m
(D 150
DJ
(13
specimen was held between two hardened alu-
r~ m i n u m tubes of the same cross section. T h e experi-
Ld
D_ GAGE APPLIED mental arrangement and analysis are as shown in
TEST LENGTH STRESS
I,I NO. (1 {IN) 0"-A {PSI) Fig. 6. The resulting stresses, strains and strain
<
rr
140 0.2 19,500 rates at three points are indicated. Although the
14 I O. I 19,000
z I00 142 0.4 15,000 example shown in Fig. 8 shows poor alignment and
147 0.4 37, 000
148 0.1 36~000
large oscillations, the over-all strain measured on
t--
ffl 150 0.8 36,000 the specimen after the experiment was within
15 I 1.6 37,000
tJA 157 0.4 48,000 5 percent of the total strain predicted in the anal-
(.9
[58 0.2 49,000 ysis.
CK 159 0.1 48,000
> B y performing a series of experiments using dif-
I ferent gage length and impact velocities, the con-
g stitutive equation curves for the material at a par-
,UASI-STATIC o I% ticular temperature can be constructed, as shown in
T E STS [] 2%
A 4% Fig. 9. This particular stress, strain and strain-
~7 8% rate relation has been used b y R a j n a k and Hauser 4
+ 16 %
E=AVERAGE STRAIN to predict the final shape of a long t u b u l a r cylinder
AT T = 295r
impacted at one end and free at the other. T h e
I I I final " t r u m p e t " shape of the tube was calculated
10,000 15,000 2.0,000 25,000 50,000 35,000
~7~mE.-AVERAGE STRESS IN PSI
using the m e t h o d of characteristics to solve the
governing plastic-wave-propagation equations. Un-
Fig. 9--Effect of stress on strain rate in work-hardened fortunately, even with the simple b o u n d a r y con-
a l u m i n u m at c onstant strain, showing sampling of ditions in t h a t problem, the solution necessitated
experimental records
the lengthy use of a computer, b u t the final predicted
strain distribution agreed very closely to the meas-
where c2 is the wave velocity in the specimen and a ured distribution.
is the gage length. F o r very short specimens, the I n Fig. 9, it can be seen t h a t almost identical re-
lower time-limit correction for XH becomes negligi- sults are obtained for long specimens impacted at
ble. high velocities (such as No. 150) or short specimens
The average strain in the specimen of gage length at low velocities (No. 140). At the same strain and
a will then be strain rate, the measured flow stresses are equal,
XI - XII indicating the negligible effect t h a t the difference in
~avg
a ratio of end-constrained volume to total volume
produces.
lIs
pC~ (r -- ~ ) d t - f a ~tIdt1 (7) As an example of a more strain-rate-sensitive
/c2 material, the stress, strain and strain-rate relation
and the average strain rate for a t y p e 304 stainless steel are shown in Fig. 10.
Here, the static tests are also included showing the
9 d~ (~i - ~) - ~ (8)
~vg = ~It = pca effect of changing the strain rates by seven orders
Figure 6 shows the procedure for the graphical of magnitude. T h e m a x i m u m strain rate attained
solution of eqs (7) and (8). in these tests was limited b y the m a x i m u m velocity
of the impact r a m (1000 in./sec). T h e titanium
input and o u t p u t bars used in this test have a yield
Examples of Results strength of 150 ksi, and this strength would impose
Figure 7 illustrates the use of eqs (4) and (5) to a new upper stress limit if a higher-velocity-impact
predict the transient stress at station 1 in the source were available.
elastic bar with a single change in cross section. I n The final example shows the experimental records
the measured record, the rise time is a b o u t 10 #sec, obtained when testing a brittle material. Gabbro
and the oscillations on the first step are due to lat- rock, which normally crumbles at a compressive
eral vibrations excited b y the lateral Poisson's ex- stress of a b o u t 30 ksi, withstood over 65 ksi for
pansion. I n the fourth step on the stress curve, a b o u t 3 #sec when loaded rapidly, as shown in Fig.
the first reflection from the free end arrives with the 11. T h e dip in the input bar stress at 40 #sec
much larger amplitudes of oscillations from the corresponds to the elastic compression of the rock,

Experimental Mechanics i 401

 5000 I failure. Similar to the delay t i m e for crumbling
measured in Fig. 11, the delay t i m e for onset of
,ooo plastic d e f o r m a t i o n in steels can be measured b y the
" STS
~ LT E
same method.

Limitations of the Tester

o I00 ~ o\o / T h e test e q u i p m e n t described permits the deter-
mination of the stress, strain and strain-rate rela-

///
I0 QUASI-STATIC
TESTS " tion of m a n y materials in the range f r o m 100/sec
to a b o u t 100,000/sec. However, there are certain
limitations inherent in the method. As the anal-
ysis assumes equilibrium conditions in the sample
z being deformed, and this condition does not exist
~- 0.1 during the first few microseconds of the test, the
w d a t a obtained at v e r y low strain values are not
reliable. Proper design of the e q u i p m e n t helps,
b u t the problem can only be minimized and not
eliminated. T h e u p p e r limit of strain r a t e and
stress are determined b y the yield strength of the
0.001 i n p u t bar. I f plastic deformation takes place in
this bar, the analysis as described no longer applies,
as the position of the interface between specimen
0.0001 and bar can no longer be determined b y the elastic
40 50 60 70 80 eq (3). Finally, the operation of the tester and the
O~AV.-E AVERAGESTRESS IN (lO3-PSI)
interpretation of the records require a thorough
Fig. 10--Effect of stress on strain rate at constant strain understanding of the mechanical and electrical
for stainless steel, showing sampling of experimental systems involved. This, unfortunately, prevents
record
the procedure f r o m becoming a simple routine test.
B u t as a research tool, the tester operated b y m a n y
different students at the University of California
80 has yielded heretofore unavailable high-strain-rate
information. These d a t a h a v e been of great help
in research on basic deformation and fracture
mechanisms.

6o Acknowledgments
T h e a u t h o r wishes to express his appreciation to
the C o n v a i r Division of General D y n a m i c s Corp.
a. 50
o and to the Inorganic Materials Research Division of
o
_o the Lawrence R a d i a t i o n L a b o r a t o r y for s u p p o r t and
z_ 4c L sponsorship of the research. H e also wishes to
t h a n k C. A. Winter for help in the design of the
hJ tester and to J. E. D o r n for his continued interest
(nt- 3 0
cr
f//INPUT BAR k~, and suggestions.

2O
.,,\ References
1. Krafft, 17. M . , "'Instrumentation for High-Speed Strain Measure-
(~t') BAR
OUTPUT I
~1~ ments," Response of Metals to High Velocity Deformation, 9, Interscience,
N e w York (1961).
jc "~ I 2. Kolsky, H., Stress Waves in Solids, Oxford University Pressl London
(1953).
3. Hauser, F. E., Simmons, g. A., and Dorn, J . E., "Strain Rate
0 I d/ ~-, Effects in Plastic Wave Propagation," Response of Metals to High Velocity
0 I0 20 50 40 50 60 70 Deformation, 93, lnterseience, N e w York (1961).
TIME IN p SEC. 4. Rajnak, S. L., and Hauser, F . E., "Plastic Wave Propagath~n in
Rods," Syrup. Dynamic Behavior of Marls., A S T M Special Publ. No. 336,
167 (1962).
Fig. 11--Experimental record for ~/4-in.-Ionggabro rock 5. Larsen, T. L., Rajnak, S. L., Haaser, F . E., and Dorn, J. E., "Plastic
(static yield strength = 30,000 psi) Stress~Strain Rate~Temperature Relations in H.C.P. Ag-Al Under
Impact Loading," Jnl. Mech. Phys. Solids, 12, 361 (1964).
6. Chiddister, J. L., and Malvern, L. E., "'Compression-impact Testing
while the dip at a b o u t 47/~sec in b o t h records corre- of A1 at Elevated Temperatures," EXPERIMENTAL MECHANICS, 3 (4), 81
(1963).
sponds to the stepwise crumbling of the material. 7. Ripperger, E. A., and Yeakley, L. M., "'Measurement of Particle
Velocities Associated with Waves Propagating in Bars," 1bid. (2), 47
Other tests on single crystals of MgO show steps (1963).
on t h e rising p a r t o f the output~ba-r -stress, indicating 8. Malvern, L. E., and Efron, L., "'Longitudinal Plastic Wave Propaga-
tion in Annealed Aluminum Bars," Tech. Rpt. No. 1, N S F Grant G-24898,
some possible local yielding or cracking before final Michigan State Univ. (1964).

402 I August 1966