ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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selection of the optimal tip material and thickness for a given test sample is not readily calculated and remains a

matter of experience via trial and error. The use of tip materials to shape the incident pulse is particularly

effective in attaining constant strain rates and stress-state equilibrium in modest-and high-strength materials

exhibiting steep strain-hardening rates.

A recent proposed alternative to the use of tip material to increase the incident pulse rise time is to use a three-

bar Hopkinson configuration (Ref 44, 45). In the three-bar configuration, an additional pressure bar and a

dummy sample are positioned between the striker bar and the traditional incident bar. The pulse transmitted by

the dummy specimen becomes the new incident pulse applied to the incident bar. With this method, the

transmitted pulse sent into the incident pressure bar is ramp shaped, with only a minor amount of oscillations

(Ref 45). The disadvantages of this method are the need for an additional pressure bar and an additional sample

for each test. Alternately, a lower-strength preloading bar can be substituted, which damps many of the high-

frequency oscillations and removes the need for a second sample (Ref 45).

Hopkinson Bar Test Setup. Once the Hopkinson bar system has been calibrated and the optimal specimen

length, l

, has been selected, preparations for testing can proceed (Ref 3). At a constant strain rate, the

maximum strain that can be achieved in the specimen is directly proportional to the length of the striker bar

utilized, L:

(Eq 18)

The nominal strain rate in the specimen may be conservatively approximated by considering momentum

conservation between the striker bar and incident bar. It can similarly be shown that (Ref 3):

(Eq 19)

where V is the striker bar velocity, and l

is the length of the specimen. This equation overestimates the strain

rate but can provide a useful value for test design. At higher striker-bar velocities, this relationship has been

found to be a good first approximation for soft metals, such as annealed copper or aluminum. Equations 18 and

19 can be used to approximate the striker-bar length and striker-bar velocity required to achieve a desired strain

and strain rate for a given sample size. These formulas provide a good starting point for selecting test

parameters to achieve a valid SHPB test. However, samples possessing high initial yield strengths, yield drops

such as those often seen in low-carbon steels or other refractory metals, and/or very high strain-hardening

responses, will require increased striker-bar lengths and impact velocities to achieve the desired strain value.

Stress-State Equilibrium during Split-Hopkinson Pressure Bar Testing. The classic split-Hopkinson pressure bar

equations relating strain-gage measurement to stress-strain behavior in the deforming specimen require that the

specimen deform uniformly. This behavior is opposed by both radial and longitudinal inertia and by frictional

constraint at the specimen-pressure bar interfaces. To understand the procedure to validate attainment of a

uniform stress state in the sample in an SHPB test, it is instructive to review the different analyses discussed,

which are used to calculate sample stress from the pressure bar strains and what they indicate. In the 1-wave

analysis, the sample stress is directly proportional to the bar strain measured in the output bar as calculated

using Eq 13. This waveform characteristically exhibits low oscillation amplitude because the deforming sample

effectively damps much of the high-frequency oscillations inherent in the incident pulse as it propagates

through the sample. More importantly, the 1-wave stress analysis reflects the conditions at the sample-

transmitted bar interface and is often referred to as the sample back stress.

Alternatively, in a 2-wave analysis, the sum of the synchronized incident and reflected bar waveforms (which

are opposite in sign) is proportional to the sample front stress and represents the conditions at the incident bar-

sample interface. Unfortunately, both the incident and reflected waveforms contain substantial inherent

oscillations which, compared to the transmitted waveform, cause uncertainty in the interpretation of stress,

especially near the yield point. In addition, these harmonic oscillations are subject to dispersion due to the

wavespeed dependence of different frequencies that causes asynchronization of the raw overlapped waveforms

and, therefore, inaccuracy in the calculation of the front stress (Ref 18, 32).

A dispersion-correction analysis has been developed (Ref 3, 40, 43) to account for these changes in phase angle

of the primary mode harmonic oscillation of all three strain signals. This analysis results in more accurate and

smoother stress-strain curves, especially near the yield point. Finally, a third stress-calculation variation that

considers the complete set of three measured bar waveforms, the 3-wave analysis, is simply the average of the

front and the back stress. The 3-wave average is calculated as described by Eq 15.

Sample equilibrium can be checked by comparing the 1-wave and 2-wave (or 3-wave) stress-strain response

(Ref 18, 40, 46, 47, 48). Recent studies have demonstrated that both inertia and wave propagation effects can

significantly affect the stress differences across the length of a specimen deformed in a compression SHPB (Ref

18, 32, 47, 49).

The validity of an SHPB test may be verified by examining the incident and transmitted pressure-bar data for

stress-state equilibrium as well as a constant strain rate. When the stress state is uniform throughout the sample,

the 2-wave stress oscillates equally above and below the 1-wave stress. Figure 5 shows the 1-wave, 2-wave, and

strain-rate data as a function of strain for an SHPB test conducted on a 304L stainless steel sample. In this

illustration, the front and back stress data reductions exhibit very similar response beyond ~0.02 strain,

verifying that the sample attained a uniform stress state. Verification of attaining an essentially constant strain

rate throughout an SHPB test will serve as validation of a careful balance of striker-bar length, striker-bar

velocity, and the use of tip material. In addition to a check of the stress equilibrium in the specimen, a constant

strain rate demonstrates a high-precision, valid material characterization measurement.

Fig. 5 Stress-strain response of a 304 stainless steel specimen showing the 1- and 2-wave stress curves

and the strain rate

Contrarily, when the stress state is not uniform throughout the SHPB sample, the 2-wave stress diverges and

exceeds the 1-wave stress values. Previous Hopkinson bar studies of ceramic materials using this 1-wave versus

2-wave comparison have shown quite dramatically that a sample is not in stress equilibrium when divergence is

observed (Ref 50). In ceramic and cermet materials, this divergence correlates very well with the onset of

nonuniform plastic flow and/or premature fracture events. Split-Hopkinson bar analysis for attenuating

materials, such as in the case of testing soils, has shown that the time required to achieve stress uniformity can

be considerable (Ref 51). Valid analysis of the dynamic stress-strain behavior of the soil samples during the

course of testing required the use of a Lagrangian analysis coupled with a standard analysis.

Results have revealed that the slow longitudinal sound speeds typical for some polymeric materials make stress

equilibrium during SHPB testing difficult to achieve (Ref 32, 34, 52, 53). The pronounced difference in the

initial 1-wave and 2-wave signals for a 6.35 mm (0.25 in.) long, 1 to 1 aspect ratio, high-purity lead sample is

shown in Fig. 6. This behavior can be viewed as an indication of a sluggish sample ringup to stress-state

equilibrium, compared with the incident wave rise time and a marginally valid Hopkinson bar test at strains

>6%, even though a reasonably stable strain rate is indicated throughout the entire test. The data in Fig. 6 and

recent studies on polymeric materials, therefore, assert the need to examine the technique of using thinner

sample aspect ratios when studying the high strain rate constitutive response of low sound speed, dispersive

materials (Ref 47, 49) and low-strength, high-density solids. Based on the data in Fig. 6, all subsequent testing

for this sample material used 3.2 mm (0.12 in.) long samples with a length-to-diameter aspect ratio of 0.5 and

lower striker-bar velocities to reduce the strain rate, thereby helping sample ringup. The combination of these

measures proved successful in attaining stress equilibrium at lower strain levels in metallic lead samples.

Fig. 6 Room-temperature stress-strain response of a high-purity lead (6.35 mm long by 6.35 mm diam)

sample showing the 1- and 2-wave stress curves in addition to strain rate

The finite time to achieve stress-state equilibrium demonstrates that the high-rate elastic modulus of a sample

cannot be measured by any Hopkinson bar. Because the stress equilibrium does not occur until well over 1%

plastic strain, it is impossible to accurately measure the compressive Young's modulus of materials at high

strain rates using the SHPB. The compressive Young's modulus of a material is best measured using ultrasonic

techniques.

Increased resolution of the ringup during SHPB testing of materials possessing high sound speeds and/or low

fracture toughness values can be achieved by measuring the strain in the sample via strain gages bonded

directly on the sample (Ref 54). Testing of ceramics, cermets, thermoset epoxies, and geological materials

requires accurate measurement of the local strains. The difficulties with this technique are that reproducible

gage application on small samples is challenging and labor intensive, and the specimens often deform to strains

greater than the gages can survive (nominally, 5% strain) so they can only be used once.

Split-Hopkinson Bar Testing as a Function of Temperature. The development of robust constitutive material

model descriptions of a material's mechanical behavior often requires quantitative knowledge of the coincident

influence of temperature and strain rate variations. Accurate measurement of the high strain-rate mechanical

response of a material using an SHPB at temperatures other than ambient, however, presents several technical

and scientific challenges. Because the stress and strain as a function of time within the deforming specimen are

determined by strain-gage measurements made using the elastic pressure bars, the longitudinal sound speed and

elastic modulus of the pressure bars, both of which vary with temperature, are important parameters. The

pronounced effect of temperature on the elastic properties of viscoelastic materials, which have been proposed

as alternate bar materials to achieve increased stress resolution, has been a chief barrier to their adoption to

measuring the high-rate response of polymers over a range of temperatures (Ref 32, 35). In this case, both a rate

and temperature-dependent constitutive model for elastomer pressure bars themselves would be required to

reduce SHPB data for a sample of interest because an assumption of linear elasticity cannot be invoked for

polymeric pressure bars over a range of strain rates and temperatures.

Various techniques have been developed to heat samples in an SHPB depending on whether it is a compression

or tensile Hopkinson bar. The combined length of both pressure bars (which can easily exceed 2 m, or 6.5 ft)

while simultaneously maintaining alignment within the supporting stanchions makes it operationally impossible

to heat or cool the entire bar assembly, either tensile or compressive, with any uniformity of temperature. Even

if heating or cooling were feasible, it would require a bar material capable of withstanding the high/low

temperatures desired as well as the development of new temperature-calibrated strain gages and robust

adhesives/epoxies to rigidly attach them to the bars. Operationally, therefore, the most common techniques for

elevated-temperature testing include the following (Ref 3, 5):

• Heating only the sample and perhaps a short section of the pressure bars and then correcting for the

temperature gradient effects on the properties of the pressure bars if they are significant (Ref 55)

• Correcting the temperature-dependent sound velocity and elastic modulus of the bars based on an

assessment of the temperature gradient, either estimated or measured with a thermocouple. The strain-

gage signals are then corrected for the temperature-dependent sound velocity and elastic modulus of the

bars (Ref 14).

• Tapering the bars to maintain the mechanical impedance constant along the length of the bars (Ref 56).

A disadvantage of this method is that a bar of a particular profile can only compensate for one particular

temperature gradient and is, therefore, of minimal use.

• Using mechanical devices that bring the ambient temperature pressure bars into contact with the heated

sample a fraction of a second before the stress pulse arrives at the end of the incident bar (Ref 57)

In the first method, heat input into the pressure bars can be minimized in the case of tensile Hopkinson bar

testing by rapid heating of the sample gage section using either high-speed radiant (Ref 58) or induction heating

(Ref 59, 60). This technique of sample heating will not avoid the altering of the elastic properties of the

pressure bars in the case of compressive Hopkinson bar testing unless heating of the bars can be avoided. The

second method has been used at temperatures up to 613 °C (Ref 14). Alternately, the selection of a bar material,

such as Inconel, which exhibits only a small variability in its elastic properties up to ~600 °C, can alternately be

used without the need for corrections up to modest temperatures. Heating/cooling to modest temperatures (-55

to +55 °C) of interest for polymer testing over which the elastic properties of Ti-6Al-4V or Mg bars are

unaffected can also be achieved using heated/cooled helium (He) gas as a heat transfer medium (Ref 32, 49).

The last heating technique provides a solution that eliminates the need for corrections to the strain-gage data

because heat is applied only to the specimen and not to any part of the bars. This method, however, is only

practical in the case of a compression SHPB because in a tensile or a torsion bar the sample is mechanically

coupled to the pressure bars. In the case of a compression SHPB, this heating method is accomplished by

starting with the bars separated from the sample. The sample is heated independently in a specially designed

resistance furnace (a vacuum furnace minimizes radiant heating), by direct radiant heating, or by an induction-

heating coil. Just prior to firing the striker bar, the pressure bars are mechanically positioned into contact with

the heated sample using bar movers (Ref 43). If the contact time between the sample and the bars is minimized

to less than 200 milliseconds, the specimen temperature and the temperature at the ends of the bars remain

approximately constant. This approach, while requiring careful attention to the timing between the movement

of the pressure bars and the firing of the striker bar, has been used successfully at temperatures up to 1200 °C

(Ref 61).

References cited in this section

3. P.S. Follansbee, The Hopkinson Bar, Mechanical Testing, Vol 8, ASM Handbook, American Society for

Metals, 1985, p 198–203

5. J.E. Field, S.M. Walley, N.K. Bourne, and J.M. Huntley, Review of Experimental Techniques for High

Rate Deformation Studies, Proc. Acoustics and Vibration Asia '98 (Singapore), 1998, p 9–38

14. U.S. Lindholm and L.M. Yeakley, High Strain Rate Testing: Tension and Compression, Exp. Mech.,

Vol 8, 1968, p 1–9

18. G.T. Gray III, High-Strain-Rate Testing of Materials: The Split-Hopkinson Pressure Bar, Methods in

Materials Research, E. Kaufmann, Ed., John Wiley Press, 1999, in press

32. G.T. Gray III, D.J. Idar, W.R. Blumenthal, C.M. Cady, and P.D. Peterson, High- and Low-Strain Rate

Compression Properties of Several Energetic Material Composites as a Function of Strain Rate and

Temperature, 11th Detonation Symposium, 1998 (Snow Mass, CO), J. Short, Ed., in press

34. G. Gary, L. Rota, and H. Zhao, Testing Viscous Soft Materials at Medium and High Strain Rates,

Constitutive Relation in High/Very High Strain Rates, K. Kawata and J. Shioiri, Ed., Springer-Verlag,

Tokyo, 1996, p 25–32

35. G.T. Gray III, W.R. Blumenthal, C.P. Trujillo, and R.W. Carpenter II, Influence of Temperature and

Strain Rate on the Mechanical Behavior of Adiprene-L100, J. Phys. (France), C3 (DYMAT 97), Vol 7,

1997, p 523–528

40. P.S. Follansbee and C. Frantz, Wave Propagation in the SHPB, J. Eng. Mater. Technol. (Trans. ASME),

Vol 105, 1983, p 61–66

42. E.D.H. Davies and S.C. Hunter, The Dynamic Compression Testing of Solids by the Method of the Split

Hopkinson Pressure Bar (SHPB), J. Mech. Phys. Solids, Vol 11, 1963, p 155–179

43. C.E. Frantz, P.S. Follansbee, and W.T. Wright, Experimental Techniques with the SHPB, High Energy

Rate Fabrication—1984, I. Berman and J.W. Schroeder, Ed., American Society of Mechanical

Engineers, 1984, p 229–236

44. S. Ellwood, L.J. Griffiths, and D.J. Parry, Materials Testing at High Constant Strain Rates, J. Phys. E,

Sci. Instrum., Vol 15, 1982, p 280–282

45. D.J. Parry, A.G. Walker, and P.R. Dixon, Hopkinson Bar Pulse Smoothing, Meas. Sci. Technol., Vol 6,

1995, p 443–446

46. P.S. Follansbee, High Strain Rate Deformation of FCC Metals and Alloys, Metallurgical Applications

of Shock Wave and High Strain Rate Phenomena, L.E. Murr, K.P. Staudhammer, and M.A. Meyers,

Ed., Marcel Dekker, 1986, p 451–480

47. X.J. Wu and D.A. Gorham, Stress Equilibrium in the Split Hopkinson Pressure Bar Test, J. Phys.

(France) IV Colloq., C3 (EURODYMAT 97), Vol 7, 1997, p 91–96

48. G.T. Gray III, W.R. Blumenthal, C.P. Trujillo, and R.W. Carpenter, Influence of Temperature and

Strain Rate on the Mechanical Behavior of Adiprene L-100, J. Phys. IV Colloq., C3 (DYMAT 97),

1997, p 523–528

49. G.T. Gray III, W.R. Blumenthal, C.P. Trujillo, and R.W. Carpenter II, Influence of Temperature and

Strain Rate on the Mechanical Behavior of Adiprene L-100, J. Phys. (France) IV Colloq., C3

(EURODYMAT 97), Vol 7, 1997, p 523–528

50. W.R. Blumenthal and G.T. Gray III, Structure-Property Characterization of Shock-Loaded B

C-Al, Inst.

Phys. Conf. Ser., Vol 102, 1989, p 363–370

51. C.W. Felice, E.S. Gaffney, and J.A. Brown, Extended Split-Hopkinson Bar Analysis for Attenuating

Materials, J. Eng. Mech., Vol 117, 1991, p 1119–1135

52. S.M. Walley and J.E. Field, Strain Rate Sensitivity of Polymers in Compression from Low to High

Strain Rates, DYMAT J., Vol 1, 1994, p 211–228

53. S.M. Walley, J.E. Field, and N.A. Safford, A Comparison of the High Strain Rate Behaviour in

Compression of Polymers at 300K and 100K, J. Phys. (France) IV Colloq., C3 (DYMAT 91), Vol 1,

1991, p 185–190

54. W.R. Blumenthal and G.T. Gray III, Structure-Property Characterization of Shock-Loaded B

C-Al,

Oxford, 1989, p 363–370

55. C. Bacon, Numerical Prediction of the Propagation of Elastic Waves in Longitudinally Impacted Rods:

Applications to Hopkinson Testing, Int. J. Impact Eng., Vol 13, 1993, p 527–539

56. A.M. Eleiche, Impedance Matching in Non-Homogeneous Elastic Bars, J. Phys. D, Appl. Phys., Vol 8,

1975, p 505–511

57. C.E. Frantz, P.S. Follansbee, and W.J. Wright, New Experimental Techniques with the Kolsky Bar, I.

Berman and J.W. Schroeder, Ed., American Society of Mechanical Engineers, 1984, p 229–236

58. D. Macdougall, A Radiant Heating Method for Performing High-Temperature High-Strain-Rate Tests,

Meas. Sci. Technol., Vol 9, 1998, p 1657–1662

59. Z. Rosenberg, D. Dawicke, E. Strader, and S.J. Bless, A New Technique for Heating Specimens in

Split-Hopkinson-Bar Experiments Using Induction Coil Heaters, Exp. Mech., Vol 26, 1986, p 275–278

60. Z. Rosenberg, D. Dawicke, and S.J. Bless, A New Technique for Heating Specimens in Split Hopkinson

Bar Experiments Using Induction Coil Heaters, Metallurgical Applications of Shock Wave and High

Strain Rate Phenomena, L.E. Murr, K.P. Staudhammer, and M.A. Meyers, Ed., Marcel Dekker, 1986, p

543–552

61. H.W. Sizek and G.T. Gray III, Deformation of Polycrystalline Ni

Al at High Strain Rates and Elevated

Temperatures, Acta Metall. Mater., Vol 41, 1993, p 1855–1860

Classic Split-Hopkinson Pressure Bar Testing

George T. (Rusty) Gray III, Los Alamos National Laboratory

Split-Hopkinson Pressure Bar in Tension

Tensile-Loading Techniques. The principles and the data analysis for the tensile split-Hopkinson pressure bar

are similar to those discussed for the compression SHPB (Ref 62, 63, 64). The primary differences are the

methods of generating a tensile-loading pulse, specimen geometry, and the method of attaching the specimen to

the two bars (incident and transmitted). Three separate general types of tension split-Hopkinson pressure bar

design have been developed (Ref 63). All three loading techniques use measures of the tensile pulses in the

input and transmitter bars, as in the compressive SHPB, to study the dynamic tensile response of a material.

Method 1. In the first method, developed by Lindholm and Yeakley (Ref 14), the incident bar is solid, while the

transmitted bar is a hollow tube of the same cross-sectional area as the input bar. A complex “top-hat” type of

sample geometry, as shown in Fig. 7, is machined from the material of interest. The specimen essentially

comprises four parallel tensile bars of equal cross-sectional area. Although specimen machining is somewhat

complex in this method, the actual SHPB test is conducted in the identical manner because compressive testing

and the data analysis is identical to that outlined previously. The advantage of this tensile loading method is

that, given a suitable hollow transmitted bar matched to the incident bar, tensile Hopkinson bar tests can be

conducted using a standard compressive SHPB loading setup as shown in Fig. 1 and 2.

Fig. 7 “Top-hat” tensile split-Hopkinson bar sample design. Source: Ref 14

Method 2. The second type of tensile split-Hopkinson bar test, and the most commonly implemented mode of

loading (Ref 5), involves direct tensile loading of the incident bar to subject a sample in a uniaxial tensile stress

state. This loading mode can be accomplished using a standard type of axisymmetric circular tension specimen

threaded directly into the ends of the incident and transmitted pressure bars, a dumbbell-shaped sample loaded

through flanges attached to the incident and transmitted bars, or a flat tensile sample loaded using a small

compression grip assembly designed into the ends of the incident and transmitted bars. A tensile pulse in each

instance is generated in the incident bar either by loading the end of the incident bar through direct impact of a

mass with a flange on the end of the incident bar (Ref 19) or by releasing a tensile pulse stored in the incident

bar using a clamping fixture (Ref 20). Figure 8 shows a schematic of a tensile split-Hopkinson bar setup using

the hollow-striker-bar loading method. In this loading method, a long tensile pulse, similarly stable as in a

compressive bar, can be imparted using a hollow striker tube accelerated along the incident bar from a

compressed gas breech or from a falling weight in a vertically configured tensile bar. In the second variation,

tensile wave loading in the incident bar is generated through the release of a tensile load that is initially stored

in a section of the incident bar.

Fig. 8 Schematic of a tensile split-Hopkinson pressure bar test setup

Method 3. The third type of Hopkinson bar loading in tension also uses a circular specimen threaded into the

ends of the two pressure bars but uses the reflection of the compression pulse at the free end of the transmitted

bar to load the sample in tension and a circular collar to protect the specimen from the initial compressive pulse

(Ref 62). After the specimen has been screwed into the incident and transmitted bars, a split shoulder or collar

is placed over the specimen, and it is screwed in until the pressure bars fit tightly against the shoulder. The

shoulder is made of the same material as the pressure bars, has the same outer diameter, and has an inner

diameter that just clears the specimen. The ratio of the cross-sectional area of the shoulder to that of the

pressure bars is typically 3 to 4, while the ratio of the area of the shoulder to the net cross-sectional area of the

specimen is typically 12 to 1 (Ref 62, 63). When the striker bar impacts the incident bar, a compressive pulse

travels down the incident bar until it reaches the specimen. The amplitude of the pulse, which is a function of

the striker velocity and length, is twice the elastic wave transit time in the striker bar.

In this loading method, the compression pulse travels through the composite cross section of the loading collar

and specimen in an essentially undisturbed manner. The relatively loose fit of the threaded joint of the specimen

into the bars and the large area ratio of the collar to the specimen ensure that no compression beyond the elastic

limit is transmitted through the specimen (Ref 63). Ideally, the entire compression pulse passes through the

supporting circular collar as if the specimen were not present, although in practice it is operationally difficult to

prevent prestraining of the specimen to some degree. The compression pulse continues to propagate until it

reaches the free end of the transmitted bar where it reflects and propagates back as a tensile pulse. Upon

reaching the specimen, the tensile pulse is partially transmitted through the specimen and partially reflected

back into the bar, which is now acting as the incident bar. Because the shoulder, which carried the entire

compressive pulse around the specimen, is not rigidly connected to the pressure bars, it will not support any

tensile load. Tight fitting of the collar against the two pressure bars is critical in transmitting the compression

pulse down the bars without significant wave dispersion or prestraining of the sample. Similarly, the fit of the

threaded tensile specimen against the bars is essential to achieve smooth and rapid loading of the specimen as

the tensile pulse arrives. Failure to remove all play from the threaded joint results in uneven loading of the

specimen and spurious wave reflections because of the open gaps in the loading thread area.

Data analysis for a tensile split-Hopkinson bar test is essentially identical to that of the compression Hopkinson

bar analysis detailed previously. The additional complications encountered in the tensile and torsional

Hopkinson techniques are related to the following:

• Modification of the pressure bar ends to accommodate gripping of complex samples, which alter wave

propagation in the sample and bars

• Potential need for additional diagnostics to calculate true stress

• Increased need to accurately incorporate inertial effects into data reduction to extract quantitative

material constitutive behavior

• More complicated stress pulse generation systems required for tensile and torsion bars

Alteration of the bar ends to accommodate threaded or clamped samples leads to complex boundary conditions

at the bar specimen interface and, therefore, introduces uncertainties in the wave mechanics description of the

test (Ref 14).

When complex sample geometries are used, signals measured in the pressure bars record the structural response

of the entire sample, not just the gage section, where plastic deformation is assumed to be occurring. When

plastic strain occurs in the sections adjacent to the sample's uniform gage area, accurate determination of the

stress-strain response of the material is more complicated. In these cases, additional diagnostics, such as high-

speed photography, are mandatory to quantify the loaded section of the deforming sample. In the tensile bar

case, an additional requirement is that exact quantification of the deforming sample cross-sectional area as a

function of strain is necessary to achieve true-stress data. Contrary to a compressive SHPB test, in which a

right-circular cylindrical sample is most often utilized, the tensile SHPB test uses a cylindrical specimen with

an attached shoulder and additional gripping, including threads. Because the split-Hopkinson bar data analysis

only provides data on the relative displacement between the ends of the incident and transmitter bars, an

effective gage length generally must be used. This is equivalent to determining strain in a tensile test through

cross-head displacement measurement. The use of strain gages on test samples to determine an effective gage

length is strongly recommended. This calibration is accomplished easily at low strain rates, preferably in a

conventional test machine in which the cross-head displacement is monitored separately.

As with any uniaxial tensile test, once localized necking occurs, it is no longer possible to simply convert load-

displacement data to stress-strain data. This lack of valid stress-state analysis is related to both the lack of

uniform plastic deformation in the sample and the attendant volumetric sample expansion, which damage-

evolution processes represent. The range of application of the Hopkinson bar test can be extended by high-

speed photography of necking specimens, although an accurate measure of the deforming volume of the sample

as necking proceeds is difficult at best, given a lack of knowledge of the damage processes evolving within the

sample. An analysis that allows estimation of effective stress and strain from the profile of the necking

specimen can be obtained. Using the apparatus described in method 3, photographs can be made with a suitable

high-speed camera system through windows provided in the collar (Ref 65, 66).

The final complexity inherent to the tension Hopkinson loading configurations has to do with the increased

sample dimensions required. Valid dynamic characterization of many material product forms, such as thin sheet

materials and small-section bar stock, may be significantly complicated or completely impractical using either

tensile or torsion Hopkinson bars because of an inability to fabricate test samples. Techniques have been

developed, however, to address these concerns in the case of testing sheet materials in the Hopkinson bar (Ref

66).

References cited in this section

5. J.E. Field, S.M. Walley, N.K. Bourne, and J.M. Huntley, Review of Experimental Techniques for High

Rate Deformation Studies, Proc. Acoustics and Vibration Asia '98 (Singapore), 1998, p 9–38

14. U.S. Lindholm and L.M. Yeakley, High Strain Rate Testing: Tension and Compression, Exp. Mech.,

Vol 8, 1968, p 1–9

19. J. Harding, E.O. Wood, and J.D. Campbell, Tensile Testing of Materials at Impact Rates of Strain, J.

Mech. Eng. Sci., Vol 2, 1960, p 88–96

20. G.H. Staab and A. Gilat, A Direct-Tension Split Hopkinson Bar for High Strain-Rate Testing, Exp.

Mech., Vol 31, 1991, p 232–235

62. T. Nicholas, Tensile Testing of Materials at High Rates of Strain, Exp. Mech., Vol 21, 1981, p 177–185

63. T. Nicholas and S.J. Bless, High Strain-Rate Tension Testing, Mechanical Testing, Vol 8, ASM

Handbook, American Society for Metals, 1985, p 208–214

64. S. Ellwood, L.J. Griffiths, and D.J. Parry, A Tensile Technique for Materials Testing at High Strain

Rates, J. Phys. E, Sci. Instrum., Vol 15, 1982, p 1169–1172

65. L.A. Cross, S.J. Bless, A.M. Rajendran, E.A. Strader, and D.S. Dawicke, New Technique to Investigate

Necking in a Tensile Hopkinson Bar, Exp. Mech., Vol 24, 1984, p 184–186

66. M.M. LeBlanc and D.H. Lassila, Dynamic Tensile Testing of Sheet Materials Using the Split-

Hopkinson Bar Technique, Exp. Tech., Vol 17, 1993, p 37–42

Classic Split-Hopkinson Pressure Bar Testing

George T. (Rusty) Gray III, Los Alamos National Laboratory

Data Reduction Measurement and Analysis Automation

Acquisition of split-Hopkinson bar data requires a high degree of automation because of the high-speed nature

of the stress loading inherent to the Hopkinson bar and the need for signal measurement and storage equipment

capable of these acquisition speeds (Ref 18, 67, 68, 69). The measurement instrumentation required for a split-

Hopkinson pressure bar test includes two strain-gage signal conditioners and a means of recording these

signals. The strain-gage signal conditioners must have a frequency response of at least 1 MHz to achieve

adequate data resolution. Units with sampling frequencies as high as 1 GHz are now available. In addition,

modern signal conditioners possess variable gain amplification, up to 1000 times, while retaining high signal-

to-noise levels. Gain settings in excess of 500 are critical to the high-resolution measurement of the very low

flow stresses typical of many polymer and polymeric composites. Until recently, oscilloscopes were used

almost exclusively to capture and record the strain-gage signal pulses. When using one oscilloscope to capture

the strain-gage data, the transmitted wave and integrated reflected wave can be fed to an oscilloscope with x-y

capability to directly yield the dynamic stress-strain curve for the specimen. The reflected wave may be fed

through an operational amplifier to yield a signal directly proportional to the strain in the specimen but without

dispersion correction.

The three wave signals are now often captured using high-speed analog-to-digital (A/D) recorders or high-

speed A/D data-acquisition computer modules, which are directly interfaced with a personal computer. Using

either platform, it is now possible to digitize the raw data directly and perform the integration numerically.

With the improved availability of the digitized data, more robust Hopkinson bar data reduction software is now

regularly used by research labs conducting split-Hopkinson bar testing. This software can be used to calibrate

the bars and store the calibration information, adjust the timing between the transmitted and reflected waves to

account for the transit time through the specimen, and calculate the elastic wave dispersion in the measured

data.

References cited in this section

18. G.T. Gray III, High-Strain-Rate Testing of Materials: The Split-Hopkinson Pressure Bar, Methods in

Materials Research, E. Kaufmann, Ed., John Wiley Press, 1999, in press

67. J. Yuan, N. Takeda, and A.M. Waas, A Note on Data Processing in the Split Hopkinson Pressure Bar

Tests, Exp. Tech., Vol 1, 1998, p 21–24

68. J.M. Lifshitz and H. Leber, Data Processing in the Split Hopkinson Pressure Bar Tests, Int. J. Impact

Eng., Vol 15, 1994, p 723–733

69. T. Yokoyama and K. Kishida, A Microcomputer-Based System for the High-Speed Compression Test

by the Split Hopkinson Pressure Bar Technique, J. Test. Eval., Vol 14, 1986, p 236–242

Classic Split-Hopkinson Pressure Bar Testing

George T. (Rusty) Gray III, Los Alamos National Laboratory

Wave Dispersion in the Split-Hopkinson Pressure Bar

Applying the equations given in the theory of the Hopkinson bar section, the stress-strain behavior of the

specimen can be computed from the measured incident, reflected, and transmitted strain pulses made on the

elastic bars (Ref 3, 18, 67). Knowing the timing required for the elastic wave signals to traverse from the

specimen to the gages on the input and output bars based on the calibration procedure, the reflected and

transmitted pulses can be synchronized to coincide at the specimen interface. By integrating Eq 13, and

remembering that ε = ln (l

) in compression, ε(t) and l

(t) can be calculated in the specimen. Assuming

constancy of volume of the specimen during the course of deforming the specimen, A

(t) and, therefore, σ(t) can

now be calculated from Eq 13. The average true stress-true strain curve is then produced by removing time as a

variable between the stress and strain data.