ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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(Eq 18)
Thus, it is only necessary to measure the incident projectile velocity, the skew angle, and the particle velocity at
the rear surface of the anvil to construct a shear stress versus shear strain curve at high strain rates and high
hydrostatic pressures.
Reference cited in this section
89. C.H. Li, A Pressure-Shear Experiment for Studying the Dynamic Plastic Response of Metals and Shear
Strain Rates of 10
5
s
-1
, Ph.D. thesis, Brown University, Providence, RI, 1982
High Strain Rate Shear Testing
Acknowledgments
Portions of this article were adapted from the following articles published in Mechanical Testing, Volume 8,
ASM Handbook, 1985:
• R.J. Clifton and R.W. Klopp, Pressure-Shear Plate Impact Testing, p 230–238
• Harding, Double-Notch Shear Testing and Punch Loading, p 228–230
• K.A. Hartley and J. Duffy, High Strain Rate Shear Testing: Introduction, p 215
• K.A. Hartley, J. Duffy, and R.H. Hawley, The Torsional Kolsky (Split-Hopkinson) Bar, p 218–228
• U.S. Lindholm, High-Speed Hydraulic Torsional Machines, p 215–216
• U.S. Lindholm, Torsional Impact Testing, p 216–218
High Strain Rate Shear Testing
References
1. U.S. Lindholm, A. Nagy, G.R. Johnson, and J.M. Hoegfeldt, Large Strain, High Strain Rate Testing of
Copper, J. Eng. Mater. Technol. (Trans. ASME), Vol 102, 1980, p 376–381
2. K. Stiebler, Beitragzum Flieβverhalten der Stähle Ck35 und X2CoNiMnMoNNb211653 unter
zweiachsiger dynamisher Belastung, Ph.D. thesis, RWTH Aachen, Germany, 1989
3. K. Stiebler, H.-D. Kunze, and E. El-Magd, Description of the Flow Behaviour of a High Strength
Austenitic Steel under Biaxial Loading by a Constitutive Equation, Nuclear Engineering and Design,
Vol 127, 1991
4. R.S. Culver, Torsional-Impact Apparatus, Exp. Mech., Vol 12, 1972, p 398–405
5. C.E. Work and T.J. Dolan, The Influence of Strain Rate and Temperature on the Strength and Ductility
of Mild Steel in Torsion, Proc. ASTM, Vol 53, 1953, p 611–626
6. N.G. Calvert, Impact Torsion Experiments, Inst. Mech. Eng., Vol 169 (No. 44), 1955, p 897
7. R.S. Culver, Thermal Instability Strain in Dynamic Plastic Deformation, Metallurgical Effects at High
Strain Rates, R.W. Rohde, B.M. Butcher, J.R. Holland, and C.H. Karnes, Ed., Plenum Press, 1973, p
519–530
8. U.S. Lindholm and G.R. Johnson, Strain-Rate Effects in Metals at Large Shear Strains, Material
Behavior under High Stress and Ultrahigh Loading Rates, J. Mescall and V. Weiss, Ed., Plenum Press,
1983, p 61–79
9. K.A. Hartley, J. Duffy, and R.H. Hawley, The Torsional Kolsky (Split-Hopkinson) Bar, Mechanical
Testing, Vol 8, Metals Handbook, 9th ed., American Society for Metals, 1985, p 218–230
10. R.A. Frantz and J. Duffy, The Dynamic Stress-Strain Behavior in Torsion of 1100-O Aluminum
Subjected to a Sharp Increase in Strain Rate, J. Appl. Mech., Vol 39, 1972, p 939–945
11. J. Duffy, J.D. Campbell, and R.H. Hawley, On the Use of a Torsional Split Hopkinson Bar to Study
Rate Effects in 1100-O Aluminum, J. Appl. Mech., Vol 38, 1971, p 83–91
12. U.S. Lindholm, Deformation Maps in the Region of High Dislocation Velocity, High Velocity
Deformation of Solids, K. Kawata and J. Shioiri, Ed., International Union of Theoretical and Applied
Mechanics Symposium, Springer-Verlag, Berlin, 1978
13. G.L. Wulf, Dynamic Stress-Strain Measurements at Large Strains, Mechanical Properties at High Rates
of Strain, J. Harding, Ed., Institute of Physics Conf. Series (No. 21), 1974, p 48–52
14. D.A. Gorham, Measurement of Stress-Strain Properties of Strong Metals at Very High Rates of Strain,
Mechanical Properties at High Rates of Strain, J. Harding, Ed., Institute of Physics Conf. Series (No.
47), 1979, p 16
15. W.G. Ferguson, J.E. Hauser, and J.E. Dorn, The Dynamic Punching of Metals, Dislocation Damping in
Zinc Single Crystals, Brit. J. Appl. Phys., Vol 18, 1967, p 411–417
16. J.D. Campbell and W.G. Ferguson, The Temperature and Strain Rate Dependence of Shear Strength of
Mild Steel, Philos. Mag., Vol 21, 1970, p 63–82
17. J. Harding and J. Huddart, The Use of the Double-Notch Shear Test in Determining the Mechanical
Properties of Uranium at Very High Rates of Strain, Proc. 2nd International Conf. Mechanical
Properties at High Rates of Strain, J. Harding, Ed., The Institute of Physics, London, 1979, p 49–61
18. A.R. Dowling, J. Harding, and J.D. Campbell, The Dynamic Punching of Metals, J. Inst. Metals, Vol
98, 1970, p 215–224
19. K.-H. Hartmann, H.D. Kunze, and L.W. Meyer, Metallurgical Effects on Impact Loaded Materials,
Shock Wave and High-Strain-Rate Phenomena in Metals, M.A. Meyers and L.E. Murr, Ed., Plenum
Press, 1981, p 325–337
20. L.W. Meyer and S. Manwaring, Critical Adiabatic Shear Strength of Low Alloyed Steel under
Compressive Loading, Metallurgical Applications of Shock Wave and High-Strain-Rate Phenomena,
L.E. Murr, K.P. Staudhammer, and M.A. Meyers, Ed., Marcell Dekker, 1986, p 657–674
21. J.A. Hines and K.S. Veccio, Dynamic Recrystallization in Adiabatic Shear Bands in Shock-Loaded
Copper, Metallurgical and Materials Application of Shock Wave and High-Strain-Rate Phenomena,
L.E. Murr, K.P. Staudhammer, and M.A. Meyers, Ed., Elsevier Science B.V., 1995, p 421–428
22. F.D.S. Marquis, M.A. Meyers, Y.J. Chen, and D.S. Kim, High-Strain, High-Strain-Rate Of Tantalum,
Metall. Mater. Trans. A, Physical Metallurgy and Materials Science, Vol 26 (No. 10), 1995, p 2493–
2501
23. S. Nemat-Nasser, Y.-F. Li, and J.B. Isaacs, Experimental/Computational Evaluation of Flow Stress at
High Strain Rates with Application to Adiabatic Shear Banding, Mech. Mater., Vol 17 (No. 2–3), 1994,
p 111–134
24. R.W. Chen and K.S. Vecchio, Microstructural Characterization of Shear Band Formation in Al-Li
Alloys, J. Physique IV (France), tome 4, Coll. C8, 1994, p 459–463
25. U. Andrade, “High-Strain, High-Strain-Rate Deformation of Copper,” Ph.D. thesis, University of
California, San Diego, 1993
26. M.A. Meyers, L.W. Meyer, J. Beatty, U. Andrade, K.S. Vecchio, and A.H. Chokshi, High Strain, High-
Strain Rate Deformation of Copper, Shock Wave and High-Strain-Rate Phenomena in Materials, M.A.
Meyers, L.E. Murr, and K.P. Staudhammer, Ed., Marcel Dekker, 1992, p 529–542
27. M.A. Meyers, G. Subhash, B.K. Kad, and L. Prasad, Evolution of Microstructure and Shear-Band
Formation in α-hcp Titanium, Mech. Mater., Vol 17 (No. 2–3), 1994, p 175–193
28. M.A. Meyers, Y.-J. Chen, F.D.S. Marquis, and D.S. Kim, High-Strain, High-Strain-Rate Behavior of
Tantalum, Metall. Mater. Trans. A, Vol 26, Oct 1995, p 2493–2501
29. L.W. Meyer and A. Schrödter, Mechanical Reduction of Oscillations on a Split Hopkinson Bar—A
Simple, but Efficient Method for High Strain Rate Material Testing, ACAM, Canberra, ISBN 0-7334-
0558-4, 1999
30. J.H. Beatty, L.W. Meyer, M.A. Meyers, and S. Nemat-Nasser, Formation of Controlled Adiabatic Shear
Bands in AISI 4340 High Strength Steel, Shock Wave and High-Strain-Rate Phenomena in Materials,
M.A. Meyers, L.E. Murr, and K.P. Staudhammer, Ed., Marcel Dekker, 1992, p 645–656
31. S. Nemat-Nasser, J.B. Isaacs, and J. Starrett, Hopkinson Techniques for Dynamic Recovery
Experiments, Proc. R. Soc. (London) A, Vol 435, 1991, p 371–391
32. T. Pintat, Ph.D. thesis, University Bremen, Germany, 1993
33. M.A. Meyers, U.R. Andrade, and A.H. Chokshi, The Effect of Grain Size on the High-Strain, High-
Strain-Rate Behavior of Copper, Metall. Mater. Trans. A, Vol 26, Nov 1995, p 2881–2893
34. T. Pintat, L.W. Meyer, and H. Schrader, Properties of Inhomogeneous Shear Zones in Different
Materials, J. Phys., Coll. C5, 1985
35. T. Pintat, B. Scholz, H.D. Kunze, and O. Vöhringer, The Influence of Carbon Content and Grain Size on
Energy Consumption during Adiabatic Shearing, J. Phys., Coll. C3, 1988, p 237–244
36. M.A. Meyers, L.W. Meyer, K.S. Vecchio, and U. Andrade, High Strain, High-Strain Rate Deformation
of Copper, J. Phys. (France) IV, Coll. C3, 1991, p 11–17
37. K. Minnaar and M. Zhou, An Analysis of the Dynamic Shear Failure Resistance of Structural Metals, J.
Mech. Phys. Solids, Vol 46 (No. 10), 1998, p 2155–2170
38. L.W. Myer, F.-J. Behler, K. Frank, and L.S. Magness, Interdependencies between the Dynamic
Mechanical Properties and the Ballistic Behaviour of Materials, Proc. of the 12th International
Symposium on Ballistics, Vol 1, p 419–428
39. L.S. Costin, E.E. Crisman, R.H. Hawley, and J. Duffy, On the Localization of Plastic Flow in Mild Steel
Tubes under Dynamic Torsional Loading, Mechanical Properties at High Rate of Strain, Institute of
Physics Conf. Series (No. 47), J. Harding, Ed., 1979, p 90–100
40. J.H. Giovanola, Observation of Adiabatic Shear Banding in Simple Torsion, Impact Loading and
Dynamic Behaviour of Materials, C.Y. Chiem, H.-D. Kunze, and L.W. Meyer, Ed., DGM Informations-
gesellschaft, Oberursel, 1988, p 705–710
41. J. Duffy, Experimental Studies of Shear Band Formation Through Temperature Measurements and High
Speed Photography, Proc. 3rd International Conf. on Mechanical and Physical Behaviour of Materials
under Dynamic Loading, DYMAT Association, Paris, 1991, p 645–652
42. K.T. Ramesh, On the Localization of Shearing Deformations in Tungsten Heavy Alloys, Mech. Mater.,
Vol 17 (No. 2–3), Elsevier, 1994, p 165–173
43. K.-H. Hartmann, H.D. Kunze, and L.W. Meyer, Metallurgical Effects on Impact Loaded Materials,
Shock Wave and High-Strain-Rate Phenomena in Metals, M.A. Meyers and L.E. Murr, Ed., Plenum
Press, 1981, p 325–337
44. L.W. Meyer and S. Manwaring, Critical Adiabatic Shear Strength of Low Alloyed Steel under
Compressive Loading, Metallurgical Applications of Shock Wave and High-Strain-Rate Phenomena,
L.E. Murr, K.P. Staudhammer, and M.A. Meyers, Ed., Marcell Dekker, 1986, p 657–674
45. S. Nemat-Nasser, Y.-F. Li, and J.B. Isaacs, Experimental/Computational Evaluation of Flow Stress at
High Strain Rates with Application to Adiabatic Shear Banding, Mech. Mater., Vol 17 (No. 2–3), 1994,
p 111–134
46. L.W. Myer, Dynamic Behavior of Thermomechanically Treated Ultra High Strength Steel under Tensile
and Compressive Loading, I. Berman and J.W. Schroeder, Ed., High Energy Rate Fabrication, ASME,
1984, p 245–252
47. C.H. Nguyen, Evaluation of the Elastic Response to Impact for High-Strength Steels, Metallurgical and
Materials Applications of Shock-Wave and High-Strain-Rate Phenomena, L.E. Murr, K.P.
Staudhammer, and M.A. Meyers, Ed., Elsevier, 1995, p 699–706
48. M. Stelly and R. Dormeval, Adiabatic Shearing, Metallurgical Applications of Shock-Wave and High-
Strain-Rate Phenomena, L.E. Murr, K. Staudhammer, and M.A. Meyers, Ed., Marcel Dekker, 1986, p
607–632
49. L.W. Meyer, E. Staskewitsch, and A. Burblies, Adiabatic Shear Failure under Biaxial Dynamic
Compression/Shear Loading, Mech. Mater., Vol 17 (No. 2–3), 1994, p 203–214
50. L.W. Meyer, L. Krueger, W. Gooch, and M. Burkins, Analysis of Shear Band Effects in Titanium
Relative to High Strain-Rate Laboratory/Ballistic Impact Tests, J. Phys. (France) IV, Vol 7, 1997, p
415–422
51. L.W. Meyer, L. Krüger, and S. Abdel-Malek, Adiabatic Shearing Banding: Strength and Deformation
Behaviour as well as Damage Process, Materialprüfung, Vol 41, Hanserverlag, 1999, p 31–34 (in
German)
52. V.F. Nesterenko, A.N. Lazaridi, and S.A. Pershin, Localization of Deformation in Copper by Explosive
Compression of Hollow Cylinders, Fiz. Goren. Vzryva, Vol 25 (No. 4), 1989, p 154–155 (in Russian)
53. M.P. Bondar and V.F. Nesterenko, Strain Correlation at Different Structural Levels for Dynamically
Loaded Hollow Copper Cylinders, J. Phys. (France) IV Coll. C3, Vol 1, supplement to J. Phys.
(France) III, p 163–170
54. V.F. Nesterenko, M.P. Bondar, and I.V. Ershov, Instability of Plastic Flow at Dynamic Pore Collapse,
High-Pressure Science and Technology 1993 (Joint International Association for Research and
Advancement of High Pressure Science and Technology and American Physical Society Topical Group
on Shock Compression of Condensed Matter Conf.), (Colorado Springs), 28 June to 2 July 1993, AIP
Conf. Proceedings, Part 2 (No. 309), p 1173–1176
55. V.F. Nesterenko and M.P. Bondar, Localization of Deformation in Collapse of a Thick Walled Cylinder,
Fiz. Goren. Vzryva, Vol 30 (No. 4), 1994, p 99–111 (in Russian)
56. V.F. Nesterenko and M.P. Bondar, Investigation of Deformation Localization by the “Thick-Walled
Cylinder” Method, DYMAT J., Vol 1 (No. 3), 1994, p 245–251
57. V.F. Nesterenko, M.A. Myers, C.H. Chen, and J.C. LaSalvia, Controlled High-Rate Localized Shear in
Porous Reactive Media, Appl. Phys. Lett., Vol 65 (No. 24), 1994, p 3069–3071
58. V.F. Nesterenko, M.A. Myers, C.H. Chen, and J. LaSalvia, The Structure of Controlled Shear Bands in
Dynamically Deformed Reactive Mixtures, Metall. Mater. Trans. A, Vol 26, 1995, p 2511–2519
59. R.W. Klopp, D.A. Shockey, L. Seaman, D.R. Curran, J.T. McGinn, and T. Resseguier, A Spherical
Cavity Expansion Experiment for Characterizing Penetration Resistance of Armor Ceramics, Mech.
Test. Ceram. Ceram. Comp., AMD, Vol 197, ASME, 1996, p 41–55
60. D.E. Grady and M.E. Kipp, The Growth of Unstable Thermoplastic Shear with Application to Steady-
Wave Shock Compression in Solids, J. Mech. Phys. Solids, Vol 35, 1987, p 95–119
61. T.W. Wright and H. Ockendon, Research Note: a Scaling Law for the Effect of Inertia on the Formation
of Adiabatic Shear Bands, Int. J. Plast., Vol 12 (No. 7), 1996, p 927–934
62. A. Molinari, Collective Behavior and Spacing of Adiabatic Shear Bands, J. Mech. Phys. Solids, Vol 45
(No. 9), 1997, p 1551–1575
63. Y.-J. Chen, M.A. Myers, and V.F. Nesterenko, Spontaneous and Forced Shear Localization in High-
Strain-Rate Deformation of Tantalum, Mater. Sci. Eng., A, Vol 268, 1999, p 70–82
64. S. Nemat-Nasser, T. Okinaka, and V.F. Nesterenko, Experimental Observation and Computational
Simulation of Dynamic Void Collapse in Single Crystal Copper, Mater. Sci. Eng. A, Vol 249 (No. 1–2),
1998, p 22–29
65. W. Chen and G. Ravichandran, Static and Dynamic Compressive Behavior of Aluminum Nitride under
Moderate Confinement, J. Am. Ceram. Soc., Vol 79, 1996, p 579–584
66. W. Chen and G. Ravichandran, Dynamic Compressive Failure of a Glass Ceramic under Lateral
Confinement, J. Mech. Phys. Solids, Vol 45 (No. 8), 1997, p 1303–1328
67. D.R. Curran, L. Seaman, T. Cooper and D.A. Shockey, Micromechanical Model for Comminution and
Granular Flow of Brittle Material under High Strain Rate Application to Penetration of Ceramic
Targets, Int. J. Impact Eng., Vol 13, 1993, p 53–83
68. R.W. Klopp, D.A. Shockey, D.R. Curran, and T. Copper, “A Granular Flow Model for Developing
Smart Armor Ceramics,” Final Technical Report on Contract DAAH04-94-K-0001, Jan 1998, p 85
69. V.F. Nesterenko, M.A. Myers, and H.C. Chen, Shear Localization in High-Strain-Rate Deformation of
Granular Alumina, Acta Mater., Vol 44 (No. 5), 1996, p 2017–2026
70. C.J. Shih, V.F. Nesterenko, and M.A. Myers, High-Strain-Rate Deformation and Comminution of
Silicon Carbide, J. Appl. Phys., Vol 83 (No. 9), 1998, p 4660–4671
71. C.J. Shih, M.A. Meyers, and V.F. Nesterenko, High-Strain-Rate Deformation of Granular Silicon
Carbide, Acta Mater., Vol 46 (No. 11), 1998, p 4037–4065
72. J. Stokes, D. Oro, R.D. Fulton, D. Morgan, A. Obst, H. Oona, W. Anderson, E. Chandler, and P. Egan,
Material Failure and Pattern Growth in Shock-Driven Aluminium Cylinders at the Pegasus Facility,
Bull. Amer. Phys. Soc., Vol 44 (No. 2), 1999, p 33
73. J.L. Stokes, V.F. Nesterenko, J.S. Shlachter, and R.D. Fulton, Comparative Behavior of Ti and 304
Stainless Steel in Magnetically-Driven Implosion at the Pegasus-II Facility, personal communication
74. S.V. Serikov, Stability of a Viscoplastic Ring, Zh. Prik. Mekh. Tekh. Fiz., Vol 25 (No. 1), 1984, p 157–
168 or Appl. Mech. Tech. Phys., July 1984, Vol 25, p 142–153
75. H.E. Lindberg, Buckling of a Very Think Cylindrical Shell due to an Impulsive Pressure, Trans. ASME
E, J. Appl. Mech., Vol 31, 1964, p 267–273
76. A.L. Florence and G. R. Abrahamson, Critical Velocity for Collapse of Viscoplastic Cylindrical Shells
without Buckling, J. Appl. Mech. (Trans. ASME), March 1977, p 89–94
77. A.G. Ivanov, V.A. Ogorodnikov, and E.S. Tyun'kin, The Behavior of Shells under Impulsive Loading:
Small Perturbations, Zh. Prikl. Mekh. Tekh. Fiz., Vol 33 (No. 6),1992, p. 112–115 or J. Appl. Mech.
Tech. Phys. (USSR), May 1993, p 871–874
78. V.F. Nesterenko, M.A. Meyers, and T.W. Wright, Self-Organization in the Initiation of Adiabatic Shear
Bands, Acta Mater., Vol 46 (No. 1), 1998, p 327–340
79. S. Nemat-Nasser, T. Okinaka, V.F. Nesterenko, and M. Liu, Dynamic Void Collapse in Crystals:
Computational Modeling and Experiments, Philos. Mag., Vol 78 (No. 5), 1998, p 1151–1174
80. R.J. Clifton and R.W. Klopp, Pressure-Shear Plate Impact Testing, Mechanical Testing, Vol 8, Metals
Handbook, 9th ed., American Society for Metals, 1985, p 231–237
81. A.S. Abou-Sayed, R.J. Clifton, and L. Hermann, The Oblique Plate Impact Experiment, Exp. Mech.,
Vol 16, 1976, p 127–132
82. Y.M. Gupta, Shear Measurements in Shock Loaded Solids, Appl. Phys. Lett., Vol 29, 1976, p 694–697
83. K.S. Kim, R.J. Clifton, and P. Kumar, A Combined Normal and Transverse Displacement
Interferometer with an Application to Impact of Y-Cut Quartz, J. Appl. Phys., Vol 48, 1977, p 4132–
4139
84. L.C. Chhabildas, H.J. Sutherland, and J.R. Asay, Velocity Interferometer Technique to Determine
Shear-Wave Particle Velocity in Shock-Loaded Solids, J. Appl. Phys., Vol 50, 1979, p 5196–5201
85. L.M. Barker and R.E. Hollenbach, Laser Interferometer for Measuring High Velocities of Any
Reflecting Surface, J. Appl. Phys., Vol 43, 1972, p 4669–4675
86. K.S. Kim and R. J. Clifton, Pressure-Shear Impact of 6061-T6 Aluminum and Alpha-Titanium, J. Appl.
Mech., Vol 47, 1980, p 11–16
87. L.C. Chhabildas and J.W. Swegle, Dynamic Pressure-Shear Loading of Materials Using Anisotropic
Crystals, J. Appl. Phys., Vol 51, 1980, p 4799–4807
88. A. Gilat and R.J. Clifton, Pressure-Shear Waves in 6061-T6 Aluminum and Alpha-Titanium, J. Mech.
Phys. Solids, Vol 33, 1985, p 263–284
89. C.H. Li, A Pressure-Shear Experiment for Studying the Dynamic Plastic Response of Metals and Shear
Strain Rates of 10
5
s
-1
, Ph.D. thesis, Brown University, Providence, RI, 1982
Classic Split-Hopkinson Pressure Bar Testing
George T. (Rusty) Gray III, Los Alamos National Laboratory
Introduction
EXPERIMENTAL TECHNIQUES in characterizing the behavior of materials at high rates of strain are
concerned with measuring the change in mechanical properties, such as yield strength, work hardening, and
ductility, which can vary with strain rate. Strain rate, , is defined as the rate of change of strain (defined as the
ratio of change in the length of a mechanical test sample) with respect to time, t. Minimal scientific or
engineering attention was historically paid to the effects of high strain rates on material behavior until increased
manufacturing production techniques (Ref 1, 2, 3, 4, 5), such as high-speed wire drawing and cold rolling, as
well as studies supporting military technologies concerned with ballistics (Ref 6, 7), armor, and detonation
physics, required further knowledge. Interest in the high-rate mechanical behavior of materials has continued to
expand during the last 40 years, driven by demands for increased understanding of material response subjected
to high-rate loading and impact events. High-rate-loading experiments provide the critically needed data
required for the development of predictive constitutive model descriptions of materials.
Constitutive models strive to capture the fundamental relationships between how independent variables, such as
stress, strain rate, strain, stress state, and temperature, independently affect the constitutive behavior of
materials (Ref 8, 9, 10). Robust material models capturing the controlling physics of high-rate materials
response are required for large-scale finite-element simulations of many complex engineering systems and
processes, including the following:
• Automotive crashworthiness
• Aerospace impacts, including foreign-object damage, such as during bird ingestion in jet engines, blade
containment in engines, and meteorite impact on satellites
• Dynamic structural loadings, such as those occurring during an earthquake
• High-rate manufacturing processes, including high-rate forging, machining, shot peening, shock
welding, and laser surface processing
• Cavitation and particulate erosion in turbines and marine propulsion
• Defense applications, including projectile/armor and explosive or propellant/material interactions
Measurement of the mechanical properties of materials is normally conducted via loading test samples in
compression, tension, or torsion. Conventional mechanical testing frames can be used to achieve nominally
constant loading rates for limited plastic strains and thereby a constant engineering strain rate. Typical screw-
driven or servohydraulic testing machines are routinely used to measure the stress-strain response of materials
up to strain rates as high as 1 s
-1
. Specially designed testing machines, typically equipped with high-capacity
servohydraulic valves and high-speed control and data acquisition instrumentation, can be used during
compression and tensile testing to achieve strain rates as high as 200 s
-1
. Above this strain rate regime, > 200 s
-
1
, alternate techniques employing projectile driven impacts have been developed to directly or indirectly induce
stress-wave propagation in a sample material.
Chief among these techniques is the split-Hopkinson pressure bar, which is capable of achieving the highest
uniform uniaxial stress loading of a specimen in compression at nominally constant strain rates of the order of
10
3
s
-1
. Hopkinson bar techniques have also been developed to probe the high-rate response of materials in
tensile- and torsion-loading stress states. In each instance, stress is directly measured using elastic elements in
series with the specimen of interest. Stress waves are generated via an impact event, and the elastic elements
used are long bars such that the duration of the loading pulse is less than the wave transit time in the bar. In
each of the Hopkinson bar techniques, the dynamic stress-strain response of materials at strain rates up to 2 ×
10
4
s
-1
in compression, and somewhat lower in tension or torsion, and true strains of 0.3 can be readily achieved
in a single test.
References cited in this section
1. U.S. Lindholm, High Strain Rate Testing, Part 1: Measurement of Mechanical Properties, Techniques of
Metals Research, Vol 5, R.F. Bunshah, Ed., Wiley Interscience, New York, 1971, p 199–271
2. U.S. Lindholm, Review of Dynamic Testing Techniques and Material Behaviour, Inst. Phys. Conf. Ser.,
Vol 21, 1974, p 3–21
3. P.S. Follansbee, The Hopkinson Bar, Mechanical Testing, Vol 8, ASM Handbook, American Society for
Metals, 1985, p 198–203
4. J.E. Field, S.M. Walley, N.K. Bourne, and J.M. Huntley, Experimental Methods at High Rates of Strain,
J. Phys. (France) IV Colloq., C8 (DYMAT 94), Vol 4, 1994, p 3–22
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
6. W.E. Carrington and M.L.V. Gayler, The Use of Flat Ended Projectiles for Determining Yield Stress,
Part III: Changes in Microstructure Caused by Deformation at High Striking Velocities, Proc. R. Soc.
(London) A, Vol 194, 1948, p 323–331
7. B. Hopkinson, A Method of Measuring the Pressure Produced in the Detonation of High Explosives or
by the Impact of Bullets, Philos. Trans. R. Soc. (London) A, Vol 213, 1914, p 437–456
8. P.S. Follansbee and U.F. Kocks, A Constitutive Description of Copper Based on the Use of the
Mechanical Threshold Stress as an Internal State Variable, Acta Metall., Vol 36, 1988, p 81–93
9. S.R. Chen and G.T. Gray III, Constitutive Behaviour of Tantalum and Tantalum-Tungsten Alloys,
Metall. Trans. A, Vol 27, 1996, p 2994–3006
10. J.R. Klepaczko, Constitutive Modeling in Dynamic Plasticity Based on Physical State Variables—A
Review, J. Phys. (France) Colloq., C3 (DYMAT 88), Vol 49, 1988, p 553–560
Classic Split-Hopkinson Pressure Bar Testing
George T. (Rusty) Gray III, Los Alamos National Laboratory
Historical Background of the Hopkinson Bar Technique
The split-Hopkinson pressure bar technique is named for Bertram Hopkinson (Ref 7) who, in 1914, used the
induced-wave propagation in a long elastic metallic bar to measure the pressures produced during dynamic
events. Through the use of momentum traps of differing lengths, Hopkinson studied the shape and evolution of
stress pulses as they propagated down long metallic rods as a function of time. Based on this pioneering work,
the experimental apparatus using elastic stress-wave propagation in long rods to study dynamic processes in
materials was named the Hopkinson pressure bar. Later work by Davies (Ref 11, 12) and Kolsky (Ref 13) used
two Hopkinson pressure bars in series, with the sample sandwiched in between, to measure the dynamic stress-
strain response of materials. This technique thereafter has been referred to as either the split-Hopkinson
pressure bar (Ref 3, 14), Davies bar (Ref 15), or Kolsky bar (Ref 3, 13, 16, 17, 18). The generalized split-
Hopkinson pressure bar technique in its current form owes a debt of gratitude to each of these innovative
scientists, as well as to the engineers and scientists responsible for the development of high-precision strain
gages, signal conditioners, and high-speed digital oscilloscopes, without which the sensitivity, accuracy, and
reproducibility of this technique would not be possible.
Following the original split-Hopkinson pressure bar apparatus developed to measure the compressive
mechanical behavior of a material, alternate Hopkinson bar schemes were designed for loading samples in
uniaxial tension (Ref 14, 19, 20), torsion (Ref 21), simultaneous torsion compression (Ref 22), and
simultaneous compression torsion (Ref 23). High-strain-rate testing in a Hopkinson bar under an imposed
lateral confinement has also been demonstrated using shrink-fit metallic containment sleeves on a sample (Ref
24). Split-Hopkinson bars have also been used to load notched samples to measure either the shear strength
(Ref 25, 26, 27, 28, 29) or the fracture toughness (Ref 30) of an impact-loaded material. The basic theory of
how to reduce the pressure bar data based upon one-dimensional stress wave analysis, as presented in the theory
of the split-Hopkinson pressure bar section, is common to all three loading stress states. Of the different
Hopkinson bar techniques (i.e., compression, tension, and torsion) the compression bar remains the most
readily analyzed and least complex method to achieve a uniform high-rate stress state. In addition, the
compression bar uses simple right-regular solid samples. Details of the dynamic loading of materials in tension
using either the tensile split-Hopkinson pressure bar or expanding ring test are compared and contrasted with
the compression Hopkinson bar technique discussed in the section “Stress-State Equilibrium during Split-
Hopkinson Pressure Bar Testing” in this article.
An alternate method of probing the mechanical behavior of materials at high strain rates, of the order of 10
3
s
-1
,
is the Taylor rod impact test. This technique, named after G.I. Taylor (Ref 31), who developed the test, entails
firing a solid cylinder of the material of interest against a rigid target. The deformation induced in the rod due to
the impact in the Taylor test shortens the rod as radial flow occurs at the impact surface. The fractional change
in the rod length can then, by assuming one-dimensional rigid-plastic analysis, be related to the dynamic yield
strength. By measuring the overall length of the impacted cylinder and the length of the undeformed (rear)
section of the projectile, the dynamic yield stress of the material can be calculated (Ref 31). The Taylor test
technique offers an apparently simplistic method to ascertain information concerning the dynamic strength
properties of a material. However, this test represents an integrated test rather than a unique experiment with a
uniform stress state or strain rate, as does the split-Hopkinson pressure bar. Accordingly, the Taylor test has
been used most prevalently as a validation experiment in concert with two-dimensional finite- element
calculations.
This article describes the techniques involved in measuring the high-strain-rate stress-strain response of
materials using a split-Hopkinson pressure bar, hereafter abbreviated as SHPB (Ref 18). The focus of this
article is on the generalized techniques applicable to all SHPBs, whether compressive, tensile, or torsion.
Emphasis is given to the methods of collecting and analyzing compressive high-rate mechanical property data
and a discussion of the critical experimental variables that must be controlled to yield valid and reproducible
high-strain-rate stress-strain data. Comparisons and contrasts to the differences invoked when using a tensile
Hopkinson bar in terms of loading technique, sample design, and stress-state stability also are discussed.
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
7. B. Hopkinson, A Method of Measuring the Pressure Produced in the Detonation of High Explosives or
by the Impact of Bullets, Philos. Trans. R. Soc. (London) A, Vol 213, 1914, p 437–456
11. R.M. Davies, A Simple Modification of the Hopkinson Pressure Bar, Proc. 7th Int. Cong. on Applied
Mechanics, Vol 1, 1948, p 404
12. R.M. Davies, A Critical Study of the Hopkinson Pressure Bar, Philos. Trans. R. Soc. (London) A, Vol
240, 1948, p 375–457
13. H. Kolsky, An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading,
Proc. Phys. Soc. (London), Vol 62B, 1949, p 676–700
14. U.S. Lindholm and L.M. Yeakley, High Strain Rate Testing: Tension and Compression, Exp. Mech.,
Vol 8, 1968, p 1–9
15. H. Kolsky, Stress Waves in Solids, J. Sound Vib., Vol 1, 1964, p 88–110
16. V.P. Muzychenko, S.I. Kashchenko, and V.A. Guskov, Use of the Split Hopkinson Pressure Bar
Method for Examining the Dynamic Properties of Materials: Review, Ind. Lab. (USSR), Vol 52, 1986, p
72–83
17. H. Zhao and G. Gary, On the Use of SHPB Techniques to Determine the Dynamic Behavior of
Materials in the Range of Small Strains, Int. J. Solids Struct., Vol 33, 1996, p 3363–3375
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
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
21. J. Duffy, J.D. Campbell, and R.H. Hawley, On the Use of a Torsional Split Hopkinson Bar to Study
Rate Effects in 1100-O Aluminum, J. Appl. Mech. (Trans. ASME), Vol 38, 1971, p 83–91
22. J.L. Lewis and W. Goldsmith, A Biaxial Split Hopkinson Bar for Simultaneous Torsion and
Compression, Rev. Sci. Instrum., Vol 44, 1973, p 811–813
23. D.R. Chichili and K.T. Ramesh, Recovery Experiments for Adiabatic Shear Localization: A Novel
Experimental Technique, Trans. ASME, Vol 66, 1999, p 10–20
24. W. Chen and G. Ravichandran, Static and Dynamic Compressive Behavior of Aluminum Nitride under
Moderate Confinement, J. Amer. Ceram. Soc., Vol 79, 1996, p 579–584