77
charge. When there is a gap, increasing the tube thickness reduces the peak velocity for small charges. This appears to be the
result of energy absorbed by the tube as it deforms. For the max charge size, the presence of a gap does not diminish the peak
velocity much. The amount of energy being supplied by the charge must be much in excess of what the tube is dissipating.
A number of these cases proved to have a much longer deceleration phase than those tested when exploring sample ring
cross-section geometry, but still not as long as the original experimental configuration by Warnes et al. [9].
14.4 Conclusion
The explosively driven variant of the expanding ring tension test was introduced by Johnson et al. [4] in 1963. While it is not
without limitations, this test has some utility in testing materials in tension, particularly high strain rates where Split
Hopkinson Pressure bars typically have difficulty reaching and where uniaxial strain spall strength may not provide the
desired information. In this work, I studied some of the many geometric variables in the explosively driven expanding ring
test: charge size, tube thickness, ring geometry, and the presence of a gap between the copper tube containing the explosive
and the driver. Each of these can influence the ring velocity.
This study found that the sample ring thickness should be minimized to minimize stress equilibration time. Tube thickness
did not consistently prove to have a strong effect on velocity by itself, but it interacted with the presence of a gap between
the driver and the copper tube. The presence of a gap reduced velocity for small charges but had little impact on larger
charges. It appears that great control over radial velocity is possible by fine-tuning the charge size in combination with other
factors, though further work is required to develop an optimal experimental configuration.
Acknowledgments I would like to acknowledge a grant of time on the INL HPC systems Lemhi and Sawtooth and the assistance of the ALEGRA
development team at Sandia National Laboratory. My views and opinions expressed herein do not necessarily state or reflect those of the
U.S. Government or any agency thereof.
References
1. Gama, B.A., Lopatnikov, S.L., Gillespie Jr., J.W.: Hopkinson bar experimental technique: a critical review. Appl. Mech. Rev. 57(4), 223–250
(2004). https://doi.org/10.1115/1.1704626
2. Marsh, S.P. (ed.): LASL Shock Hugoniot Data. University of California Press, Berkeley and Los Angeles, CA (1980)
3. Antoun, T., Seaman, L., Curran, D.R., Kanel, G.I., Razorenov, S.V., Utkin, A.V.: Spall Fracture, 1st edn. Springer, Cham (2003)
4. Johnson, P., Stein, B., Davis, R.: Measurement of dynamic plastic flow properties under uniform stress. Presented at the symposium on
dynamic behavior of materials, 1963
5. Perrone, N.: On the use of the ring test for determining rate- sensitive material constants. Exp. Mech. 8(5), 232–236 (1968). https://doi.
org/10.1007/BF02326281.
6. Hoggatt, C.R., Recht, R.F.: Stress-strain data obtained at high rates using an expanding ring. Exp. Mech. 9(10), 441–448 (1969). https://doi.
org/10.1007/BF02410405.
7. Warnes, R.H., Duffey, T.A., Karpp, R.R., Carden, A.E.: An improved technique for determining dynamic material properties using the expanding ring. In: Meyers, M.A., Murr, L.E. (eds.) Shock Waves and High-Strain-Rate Phenomena in Metals: Concepts and Applications, pp. 23–36.
Springer US, Boston, MA (1981)
8. Barker, L.M.: Laser interferometer for measuring high velocities of any reflecting surface. J. Appl. Phys. 43(11), 4669 (1972). https://doi.
org/10.1063/1.1660986.
9. Warnes, R.H., Karpp, R.R., Follansbee, P.S.: The freely expanding ring test—a test to determine material strength at high strain rates. J. Phys.
Colloq. 46(C5), C5-583–C5-590 (1985). https://doi.org/10.1051/jphyscol:1985575
10. Bova, S.W., et al.: ALEGRA user manual. Sandia National Laboratory, Albuquerque, NM, SAND2020-DRAFT (2020)
14 Analysis of the Explosively Driven Expanding Ring Tension Test
charge. When there is a gap, increasing the tube thickness reduces the peak velocity for small charges. This appears to be the
result of energy absorbed by the tube as it deforms. For the max charge size, the presence of a gap does not diminish the peak
velocity much. The amount of energy being supplied by the charge must be much in excess of what the tube is dissipating.
A number of these cases proved to have a much longer deceleration phase than those tested when exploring sample ring
cross-section geometry, but still not as long as the original experimental configuration by Warnes et al. [9].
14.4 Conclusion
The explosively driven variant of the expanding ring tension test was introduced by Johnson et al. [4] in 1963. While it is not
without limitations, this test has some utility in testing materials in tension, particularly high strain rates where Split
Hopkinson Pressure bars typically have difficulty reaching and where uniaxial strain spall strength may not provide the
desired information. In this work, I studied some of the many geometric variables in the explosively driven expanding ring
test: charge size, tube thickness, ring geometry, and the presence of a gap between the copper tube containing the explosive
and the driver. Each of these can influence the ring velocity.
This study found that the sample ring thickness should be minimized to minimize stress equilibration time. Tube thickness
did not consistently prove to have a strong effect on velocity by itself, but it interacted with the presence of a gap between
the driver and the copper tube. The presence of a gap reduced velocity for small charges but had little impact on larger
charges. It appears that great control over radial velocity is possible by fine-tuning the charge size in combination with other
factors, though further work is required to develop an optimal experimental configuration.
Acknowledgments I would like to acknowledge a grant of time on the INL HPC systems Lemhi and Sawtooth and the assistance of the ALEGRA
development team at Sandia National Laboratory. My views and opinions expressed herein do not necessarily state or reflect those of the
U.S. Government or any agency thereof.
References
1. Gama, B.A., Lopatnikov, S.L., Gillespie Jr., J.W.: Hopkinson bar experimental technique: a critical review. Appl. Mech. Rev. 57(4), 223–250
(2004). https://doi.org/10.1115/1.1704626
2. Marsh, S.P. (ed.): LASL Shock Hugoniot Data. University of California Press, Berkeley and Los Angeles, CA (1980)
3. Antoun, T., Seaman, L., Curran, D.R., Kanel, G.I., Razorenov, S.V., Utkin, A.V.: Spall Fracture, 1st edn. Springer, Cham (2003)
4. Johnson, P., Stein, B., Davis, R.: Measurement of dynamic plastic flow properties under uniform stress. Presented at the symposium on
dynamic behavior of materials, 1963
5. Perrone, N.: On the use of the ring test for determining rate- sensitive material constants. Exp. Mech. 8(5), 232–236 (1968). https://doi.
org/10.1007/BF02326281.
6. Hoggatt, C.R., Recht, R.F.: Stress-strain data obtained at high rates using an expanding ring. Exp. Mech. 9(10), 441–448 (1969). https://doi.
org/10.1007/BF02410405.
7. Warnes, R.H., Duffey, T.A., Karpp, R.R., Carden, A.E.: An improved technique for determining dynamic material properties using the expanding ring. In: Meyers, M.A., Murr, L.E. (eds.) Shock Waves and High-Strain-Rate Phenomena in Metals: Concepts and Applications, pp. 23–36.
Springer US, Boston, MA (1981)
8. Barker, L.M.: Laser interferometer for measuring high velocities of any reflecting surface. J. Appl. Phys. 43(11), 4669 (1972). https://doi.
org/10.1063/1.1660986.
9. Warnes, R.H., Karpp, R.R., Follansbee, P.S.: The freely expanding ring test—a test to determine material strength at high strain rates. J. Phys.
Colloq. 46(C5), C5-583–C5-590 (1985). https://doi.org/10.1051/jphyscol:1985575
10. Bova, S.W., et al.: ALEGRA user manual. Sandia National Laboratory, Albuquerque, NM, SAND2020-DRAFT (2020)
14 Analysis of the Explosively Driven Expanding Ring Tension Test