Pergamon Int. J. Impact Engnq Vol. 16, No. 2, pp. 321 330, 1995

Elsevier Science Ltd Printed in Great Britain

0734-743X(94)00042-3 0734-743x/95 $9.50+0.00

METHODOLOGICAL ASPECTS OF STUDYING DYNAMIC MATERIAL PROPERTIES USING THE

KOLSKY METHOD

A. M. BRAGOV and A. K. LOMUNOV Research Institute of Mechanics, Nizhny Novgorod State University, 23 Gagarin Ave., 603600

Nizhny Novgorod, GSP-1000, Russia

(Received 26 July 1993; in rerised form 19 July 1994)

Summary--An experimental configuration designed for studying properties of structural materials within the strain-rate range of 5 x 102-5 × 103 s-1 is described. The configuration is based on the conventional versions of the dynamic testing methodologies using the split Hopkinson bar (SHB) method and modifications of these methods originally proposed by the authors. Special emphasis is given to discussing the modifications of the Kolsky method that render new possibilities for studying history effects (including those for alternating dynamic loading) and dynamic hardness. Examples are given illustrating the capabilities of the experimental configuration in studying the dynamic properties of some materials.

INTRODUCTION

Numerous structures in modern machine-building are known to function under extreme conditions characterized by high stress amplitudes and short-term loads. Besides, some technological processes (forging, forming, rolling) are characterized by high strain rates of the metal worked. For optimal design of such structures and technological processes, an extensive data base on the physical-mechanical material properties and their dependence on the loading conditions is required. The issue of the strain rate and its history effects on the mechanical properties of structural materials is among the topical problems of today. Despite a great number of publications on this problem, the question remains open. It can be attributed primarily to an insufficiently developed expermental base for dynamic tests on the one hand, and to a growing number of novel materials used in dynamically loaded structures, on the other hand.

The split Hopkinson bar (SHB) method originally proposed by Kolsky [1] is today one of the most thoroughly developed and verified methods for obtaining the dynamic strain curves for materials within the strain rate range of ~ 103 s-1. In what follows we shall describe an experimental complex of software and hardware means for dynamically testing materials within the strain rate range of 5 x 102-5 x 103 s- 1 for different types of the stressed and strained states, based on the Kolsky method.

EXPERIMENTAL APPARATUS FOR DYNAMIC TESTS

The main components of the experimental apparatus (Fig. 1) are loading devices with a control system, changeable SHB units for various types of tests, and registering devices with a PC for data processing. Pulsed loads in a SHB are generated using compact, 10- and 20-mm gas guns. The projectiles are accelerated by compressed air. The gas guns make it possible, in laboratory conditions, to accelerate projectiles 50-500 mm long up to the impact velocities of 10-100 m s- 1. Such parameters of the loading systems allow one to study the strain-rate dependence of the mechanical properties of maerials in the velocity range of 5X 1 0 2 - 5 × 103S -1.

In testing high-strength materials, sets of 10- and 20-mm-dia. bars, 1 m long, made of a high-strength steel with the yield strength of about 1800 M Pa were used. Polymeric materials

321

322 A.M. Bragov and A. K. Lomunov

Incident bar Transmitter bar D G a ? n / ~ I ~ Striker ,I r - l"~=. Specime~ r-n rn =x~"N~ [~.

ii V~-- I Power? I Triggers I supply ~'-Strain' gauge

II o c 50v I C°unter ] I "~- I Pulse - -

I .~ generator

Digital oscilloscope I AO-- I ~C°mputer

~ o . I: . l ~ l J l l f ( IF.I:F, 488

Fig. 1. Diagram of the SHB apparatus and instrumentation.

(a)

] -

(b)

(c) (d)

. . . . . . . . . .

Fig. 2. Original specimen SHB configurations: (a),(b) tension; (c) crack resistance; (d) hardness.

were tested using the bars of a high-stength aluminium alloy. To minimize friction during testing, the ends of the bars are thoroughly polished and covered with a thin layer of grease before testing.

Tensile tests are conducted following the Lindholm scheme [2] and a modified Nicholas scheme [3] with the preference for the latter, as it uses specimens of a simpler manufacturing technology. The first pressure bar is 1.5 m long, and the second bar, 0.75 m long, has a free rear end. The bars are also made either of a high-strength steel or of an aluminium alloy. The specimens may be either solid or tubular, connected to the bars by the threaded connection (Fig. 2a,b). Traditionally, a tensile pulse in the Nicholas scheme is formed due to the presence of a split ring surrounding the specimen. The same purpose can also be achieved by precisely adjusting the sizes of the threaded portions of the specimen and the bars to provide, after turning the former into the latter, a close fit at the bar ends. In this case, the split ring is no longer necessary. Therefore, the pulses will be less subject to additional high-frequency vibrations as the waves travel through the butt joints of the bars and the split ring. The dimensions (in mm) of the bars and specimens used are given in Table 1.

Dynamic material properties

Table 1

323

Pressure bars Deformed part o f the specimen

Diameter Cross-section area Diameter Cross- Specimen section .form external internal bars contact external internal area

Solid 20.0 10.0 314.2 235.6 5.0 19.6 specimen Tubular 12.0 9.8 113.1 75.4 11.5 10.0 25.3 specimen

For the solid specimens, the ratio of the pressure bar end contact area to the full bar cross-section area is 3:4. The ratio of the contact area to the specimen cross-section area is 12:1. This is a guarantee that no compressive force high enough to deform it plastically is transmitted to the specimen. For the tubular specimens, the corresponding ratios are 2:3 and 3:1. The latter configuration is less preferable and could be recommended for the tensile experiments when studying the dynamic properties of the materials furnished in tubular blanks. The advantage of this scheme is that it is more tolerant to the precision of the threaded parts of the specimen than the scheme with the solid specimen, as after the threaded portions of the bars are turned into the specimen and are in close contact, the backlash in the threaded connections can be taken up using check-nuts. Besides, the radial inertia effects are minimal in the case of a deforming tubular specimen.

In addition to obtaining the dynamic deformation diagrams, the apparatus allows the dynamic fracture toughness to be determined for the compact specimens, using the Klepaczko method [4]. Moreover, to measure the crack propagation velocity, a special strain gauge is to be cemented to a compact specimen in the direction of wave propagation, which is a set of separate 1-mm base grids mounted on a common substrate 1.7 mm apart from each other. When propagating through the specimen, the crack breaks the grids one by one, causing changes in the total resistance of the gauge and the related jumps on the oscilloscope display, thus making it possible to determine the crack propagation velocity along with measuring the dynamic stress intensity factor.

In [5], the dynamic fracture toughness data were determined using a solid cylindrical specimen with a circular slot and a pregrown fatigue crack. A tensile load in the SHB was generated by an explosion. The proposed configuration also uses solid cylindrical specimens with a circular slot and a fatigue crack, but using a tensile version of the SHB (Fig. 2c) to generate a tensile load in the specimen. Such a scheme for determining the dynamic fracture toughness may become popular due to the simplicity of specimen production and the ease of generating a tensile load in the specimen.

AUTOMATION OF THE EXPERIMENTAL DATA PROCESSING

Conventional processing of experimental data in the SHB method is usually time-consuming. The present authors worked out an automated system for collecting and processing the experimental data that includes a two-channel digital oscilloscope (with 2 × 1 kb of memory) and an IBM computer. The processing program makes it possible to synchronize the registered pulses and to generate the dynamic deformation diagrams for different test types, to characterize the dynamic fracture toughness, to perform the statistical processing of the test results, to construct the regression models, to carry out the factor analysis, etc.

The experimental information from the gauges cemented to the pressure bars equidistantly from the specimen is registered by a two-channel digital oscilloscope with a memory. After the experiment, the entire oscilloscope memory area containing the strain pulses in the pressure bars is transmitted to the PC via an IEEE-488 interface, to be processed there.

324 A.M. Bragov and A. K. Lomunov

The data on the specimen and the pressure bars, as well as the accompanying information required to process and identify the tests, are input manually from the keyboad. When processing the data, the pulses can be corrected both automatically and manually, allowing one to remove the short-time signal peaks that sometimes appear in the oscilloscope's ADC system and to approximate individual portions of the oscillogram to smooth down high-frequency oscillations.

To determine the scale factors for converting the coordinates.of the points on the oscillogram into the strain and time values, electric calibration was used. It is effected by connecting some scale resistors of a known value to the circuits of the measuring strain gauges. The accuracy of calibration is controlled by comparing the loading pulse amplitude with the intensity of the generated wave computed using the one-dimensional theory, based on the known striker velocity. Besides, in every test, the observed residual deformation in the specimen is compared with the one computed based on the experimental data.

Accurate synchronization of the strain pulses is known to be of great importance for obtaining dynamic deformation diagrams of structural materials, including the expert choice of the origin for each pulse. In the tests with some materials that have low acoustic stiffness (polymers, composites, soils etc.) the rate of increase of the transmitted pulse may be considerably lower than that of the reflected one, leading to its apparent delay. Moreover, the registration of weak signals from the strain gauges is sometimes accompanied by the electromagnetic interferences superimposing the zero line. In tensile experiments using the Nicholas scheme, the reflected pulse appears somewhat earlier than the transmitted one. This is due to a pronounced difference between the cross-section areas of the pressure bars and the specimen and to taking up the backlash in the threaded connections. The above factors may lead to possible errors in choosing the origins for these pulses, even though the registering gauges are equidistant from the specimen.

The synchronization procedure is as follows. The point after which the first deviation of the registering beam from the zero line occurs is taken as the origin of the incident pulse. Then, based on the known wave propagation velocity in the pressure bars and the known distance between the strain gauges and the specimen, the position of the origins for the reflected and transmitted pulses is assigned (when the strain gauges are cemented at an equal distance from the specimen, the origins are chosen synchronously). For the chosen origins, it is checked that the main assumption of the Kolsky method is satisfied during the entire test, namely:

~:i(t) + ~:r(t) = et(t), (1)

where el(t), er(t) and g(t) are the incident, reflected and transmitted strain pulses, respectively. The three pulses are displayed on the screen simultaneously with the sum of the reflected and transmitted pulses. The program allows one to correct, automatically or manually, the relative positions of these pulses, though in the majority of the tests such a correction is not necessary. Special attention is paid to satisfying condition (1) as accurately as possible during the entire duration of the pulse, except for its beginning (several microseconds) when the stressed-strained state of the specimen cannot be considered uniform. Upon synchronization of the pulses, a dynamic deformation diagram and the related strain-rate history are constructed using the Kolsky formulae. The data processed are stored in a special data bank in the form of the dynamic deformation diagrams. Use of the automatic system saves time considerably and allows one to process the experimental data and to obtain the results in the form of diagrams and tables in a matter of minutes.

DETERMINING THE DYNAMIC HARDNESS

Based on the Kolsky method, a novel scheme for determining the dynamic plasticity of materials is also proposed (Fig. 2d). It differs from the conventional SHB scheme principally in that there is an accessory indentor in the form of a cone, a pyramid, or a hemisphere made of a high-strength hard material [6]. The SHB system loading and deformation

D y n a m i c mater ia l p roper t ies 325

scheme in this case is practically similar to the conventional compression test scheme in the Kolsky method.

It follows from the 1-D theory of propagation of elastic waves that displacement h(t) of the right-hand end of the incident bar and the indentor is described by the relation:

t

h(t) = C ~ [8 i ( t ) - - d(t)]dt. (2) 0

Knowing the indentor geometry, relation (2) allows one to compute the indentation surface area at any time of the loading history. For a cone-like indentor with the angle of the apex of 2~, the current area S(t) of the irreversible indentation will be:

S(t) = rch2(t)tg2~t/sinct. (3)

( a ) 2 4 8 - 0 7 . D A T P - l ' 9

> E

i.¢

<

1 0 - -

5 --

0 --

- 5 - -

-10 --

, j r -

I I I I t I I I I I I 0 1 2 3 4 5 6 7 8 9 10

t X 50 m k s

l0

5

0

-5

-10

>

, , ¢

(b) 2 4 8 - 0 4 . D A T ~ 1 ~

> lO E

o o

5 <

-5

-10

I I I I I I I I I I I 0 1 2 3 4 5 6 7 8 9 10

t x 50 m k s

- - l O

- - 5

- o

- - - 5

-10

> E

Fig. 3. Osc i l l og ram of the test for the A m g 6 alloy: (a) using the conven t iona l SHB scheme; (b) by load ing the SHB th rough an auxi l ia ry specimen.

326 A. M. Bragov and A. K. Lomunov

The pulse gt(t) in the transmitter bar allows one to determine the time history of the force F(t) arising when the indentor penetrates into the sample:

F ( t ) = EAd(t), (4)

where E and A are the elastic modulus and the cross-section area of the transmitter bar. Based on relations (3) and (4), one can determine the dynamic hardness, HD(t), as the ratio of the effective resistance to indentation and the current indentation area:

HD(t) = EAst(t)sin~

t

x {tgccC J" [ei(t) - f f ( t ) ]d t } 2 0

A great merit of this method is that it allows the dynamic hardness value to be computed at any stage of the indentation process.

ENSURING CONSTANT STRAIN RATE

It is known that the compression tests using the SHB are not always constant strain-rate tests. Generally, a SHB is loaded by a trapezoidal compression pulse of a practically constant amplitude. During the deformation the specimen hardens and its cross-section increases. As a result, the strain rate, proportional to the pulse reflected by the specimen and determined by the difference between the incident and the transmitted pulses, tends to decrease during the experiment. To ensure a constant strain rate during the experiment, it is desirable to have the loading pulse similar to the transmitted one but of a larger amplitude. To this end, it was proposed to add another pressure bar and an additional specimen [7] to the SHB configuration or to load the SHB by a projectile of a variable cross-section in the form of a tapered cone [8]. Practically the same results can be achieved in a simpler way by loading the SHB through an auxiliary specimen placed at the end of the incident bar on which the projectile impacts [9]. The auxiliary specimen can be made of a material with the hardening characteristic similar to the tested one. The incident compressive pulse with an increasing amplitude formed in the SHB under such loading scheme is similar to the transmitted pulse. As an example, Fig. 3 shows oscillograms of tests for the AMg6 alloy using the conventional (a) and the proposed (b) schemes. It is evident that the proposed scheme ensures a practically constant strain rate during the process of plastic deformation.

EXPERIMENTAL DEVICES FOR STUDYING THE STRAIN RATE HISTORY EFFECTS

Recently, great attention has been paid in dynamic plasticity to the problem of dependence of mechanical properties on the strain-rate history effects [10-13]. Special attention was paid to the experiments with the incremental strain rate. To create a complex strain-rate history including partial or full loading with the subsequent after-loading of the specimen in the process of dynamic tests, it was proposed to load SHBs by specially designed projectiles [14]. The projectiles are made of two or more parts, of materials with different acoustic impedances. The component bars may be arranged both with or without the gap between them (cemented together). In the former case, the projectile's bars have specially processed ends and are connected by low-strength flexible brackets (Fig. 4). On accelerating such a projectile in the bore of a gas gun, when it is subject to inertial forces, the brackets in the bore cannot bend, preventing the projectile components from approaching each other; thus, the preset gap does not change. Upon leaving the bore, the first projectile component strikes the SHB and generates in it a compressive pulse, its amplitude and duration being determined by its acoustic impedance and length, and by the projectile velocity. Meanwhile, the second projectile component continues its way due to the inertia

Dynamic material properties 327

(a)

Gas gun bore Brackets Striker

(b)

Gas gun bore Brackets Striker SHB

Fig. 4. A projectile with a gap.

forces and, with a certain time delay, hits the first bar, generating in it a compressive wave, its amplitude being determined by the ratio of the acoustic impedances of the projectile components. This wave passes along the first component to the incident pressure bar. Upon leaving the bore, the connecting brackets practically do not affect the pulse generation process in the SHB due to their flexibility.

Using the projectiles of the second type allows one to generate in the SHB a loading pulse with a sharp increase or decrease of the amplitude, thus making it possible to carry out the tests with both the positive and negative stress-strain increments. Projectiles of the first type form in the SHB system a loading compressive pulse of a complex form consisting of two or more parts (with the same or different amplitudes), with the time intervals of several tens of microseconds between them. Such a loading mode makes it possible to perform full unloading of the specimen after it has reached some plastic deformation, with a subsequent reloading (after a controlled time interval) using a higher, a lower, or the same strain rate. Examples of using such projectiles in testing aluminium and copper are shown in Figs 5 and 6. The deformation curves for the AD1 aluminium obtained when loading the SHB by a projectile made up of three parts cemented together (the middle part was made of aluminium alloy, and the first and the last ones of steel) are shown in Fig. 5. Sharp jumps from the lower strain rates to the higher ones and vice versa were accomplished in the experiments. The results are compared with the constant strain-rate curves (dotted lines in the figure). It is evident that aluminium responds quickly enough to the changes in strain rate, while being fairly sensitive to the deformation history (the curves for strain-rate jumps do not reach the ones for constant strain rates), this sensitivity increasing with the decrease of the strain rate. Figure 6 shows the deformation curves for copper obtained using the striker with the first component made of an aluminium alloy and the second one of steel. In one of the tests, the striker components were cemented together (the dotted curve), and in the other they were positioned with a gap (the solid curve). Analysis of the results testifies to a weak sensitivity of this material to the strain rate for its twofold variation.

Ogawa [15] was the first to study the Bauschinger dynamic effect by impacting a stepped anvil with a cylindrical striker, thus creating an alternating pulse in a pressure bar and achieving an alternating loading mode in a specimen. The present authors analyse the dynamic Bauschinger effect using a modified tensile SBH scheme [14]. The SHB configuration versions proposed to this end are shown in Figs 7a and b and differ from each other in the specimen-type used. A tubular or a solid specimen is connected to the bars by a threaded connection, so that there is a small gap between the bar ends allowing

328 A . M . Bragov and A. K. L o m u n o v

200 -

160

~ r n

? - : !

120

80

40

o-.- t I I t I 0 4 8 12 16 2() 24

S t r a in (%)

6000 F

o 4 o o o

2000

o_~ J I ~o i J 0 4 8 12 16 20 24

S t r a in (%)

Fig. 5. Behav iour of a l u m i n i u m (cemented projectiles).

400 --

300

200

100

f -t

Copper o I I I I

0 2 4 6 8 10

S t r a in (%)

2500 -

1500 ¢D

.=-- 500

- 5 0 0 I 0 10 2 4 6 8

S t r a in (%)

Fig. 6. Behav iour of copper (a sol id curve for the project i le wi th a gap; a do t ted curve for the cemented projectile).

Dynamic material properties 329

I

(b)

L I ' '

Fig. 7. Specimen at tachment patterns for alternating tests: (a) a tubular specimen; (b) a solid specimen.

4O0

300

200

I 100 -200

-300 2000 1/c AMg6M (annealed)

-400 I I I I I 0 1 2 3 4 5

Strain (%)

Fig. 8. Alternating loading of the a luminium alloy.

lO0 e~

o

for an additional compressive cycle of the specimen before the tensile cycle. Until the entire gap is taken up during the first compressive loading cycle, the amplitude of the wave passing to the transmitter bar will be equal to a part of the original wave amplitude depending on the specimen material properties and the ratio of cross-section areas of the sample and the pressure bars. After deformation in the specimen has reached a certain value, the bar ends will come into contact and the remaining part of the original pulse will pass entirely to the transmitter bar without any changes in the amplitude. The compressive strain of the specimen reached will remain unchanged during the effective period of the original pulse, after which relaxation of the specimen will take place. The stresses will drop to zero, the total strain will be reduced by the value of its elastic component, thus eliminating the acoustic contact between the ends of the bars. Upon reaching the free end, the compression pulse in the transmitter bar is reflected by a tensile wave. The bar

330 A.M. Bragov and A. K. Lomunov

ends do not prevent the specimen from free tension, the tensile pulse ampl i tude being adequa te for p las t ica l ly deforming the specimen.

The results ob ta ined with this conf igura t ion are i l lus t ra ted in Fig. 8 showing the s t ra in d i ag rams for the A M g 6 a lumin ium al loy ob ta ined with the help of the a l t e rna t ing load scheme developed. Also shown for c o m p a r i s o n is a stat ic d i a g r a m for this mater ia l .

C O N C L U S I O N S

An exper imenta l conf igura t ion is descr ibed based on the c o m m o n me thodo log i ca l basis (Kolsky me thod) tha t al lows us to per form complex studies of the dyna mic p roper t i e s of structural materials loaded in pressure or tension in the strain-rate range of 5 x 102-5 x 103 s - 1. A simple p rocedure is descr ibed for ensur ing a cons tan t s t ra in ra te dur ing the tests. New modi f ica t ions of the K o l s k y m e t h o d are discussed tha t make it poss ib le to per form incrementa l and a l t e rna t ing load ing tests which could be a basis for s tudying the s t ra in

rate effect on the Bauschinger effect. These modi f ica t ions may be successfully used in verifying the adequacy of dynamic plas t ic i ty const i tu t ive equat ions . A m e t h o d for de t e rmin ing the dynamic hardness of mate r ia l s is descr ibed that may be useful in pene t ra t ion mechanics for ana lys ing the forces resist ing pene t r a t ion for m o d e r a t e impac t velocities. To subs tan t i a te the me thod , fur ther studies are requi red to assess the iner t ia effects on the values of the dynamic hardness ob ta ined .

R E F E R E N C E S

1. H. Kolsky, An investigation of the mechanical properties of materials at very high rates of loading. Proc. Phys. Soc. B 62, 676-699 (1949).

2. U. S, Lindholm and L. M. Yeakley, High strain-rate testing: tension and compression. Exp. Mech. 8, 1-9 (1968). 3. T. Nicholas, Tensile testing of materials at high rates of strain. Exp. Mech. 21, 17~186 (1981). 4. J. Klepaczko, Application of the split Hopkinson pressure bar to fracture dynamics. In Mechanical Properties

at High Rates of Strain (Edited by J. Harding), pp. 201-214. Institute of Physics, London (t980). 5. L. S. Costin, J. Duffy and L. B. Freund, Fracture initiation in metals under stress wave loading conditions.

In Fast Fracture and Crack Arrest (Edited by G. T. Hahn and M. F. Kanninen), pp. 301-318. ASTM STP 627 (1977).

6. Pat. No. 1486878 (Russia). A method for determining materials hardness; A. M. Bragov, A. K. Lomunov and A. I. Sadyrin, Bul. i-obr. 22 (1989) (in Russian).

7. S. Ellwood, L, J. Griffiths and D. J. Parry, Material testing at high constant strain rates. J. Phys. E." Scientific Instruments 15, 280-282 (192).

8. Y. Sato and H. Takeyama, The use of the split Hopkinson pressure bar to obtain dynamic stress-strain data at constant strain-rates. Technol. Rep. Tohoku Univ. 43, 303-315 (1978).

9. A.M. Bragov and A. K. Lomunov, Specific features in deformation diagrams construction by Kolsky method. In Prikladnye problemy prochnosti i plastichnosti. Vsesoyuz. mezhvuz, sb. 28, 125-137. Gorky University (1984) (in Russian).

10. L. E. Malvern, Experimental and theoretical approaches to characterization of material behaviour at high rates of deformation. In Mechanical Properties at High Rates of Strain (Edited by J. Harding), pp. 1-20. Institute of Physics, London (1984).

11. R. J. Clifton, Dynamic plasticity. J. Appl. Mech., Trans. A S M E E 50, 941-952 (1983). 12. J. Duffy, The J. D. Campbell memorial lecture: Testing techniques and material behaviour at high rates of'

strain. In Mechanical Properties at High Rates o f Strain (Edited by J. Harding) pp. 1 15. Institute of Physics, London (1980).

13. J. Klepaczko and J. Duffy, History effects in polycrystalline b.c.c, metals and steel subjected to rapid changes in strain rate and temperature. Arch. Mech. 34, 419-436 (1982).

14. A. M. Bragov, A. K. Lomunov and A. A. Medvedev, A modified Kolsky method for the investigation of the strain-rate history dependence of mechanical properties of materials. J. Phys. IV, 1, C3-471 (1991).

15. K. Ogawa, Impact tension-compression test by using a split Hopkinson pressure bar. Exp. Mech. 24, 81-86 (1984).