73
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society
for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_14
Chapter 14
Analysis of the Explosively Driven Expanding Ring Tension Test
Brady Aydelotte
Abstract The expanding ring tension test has been available in some form for decades, but it remains little utilized compared
with shock-induced spallation or the tension Split Hopkinson Pressure Bar test. The explosively driven ring tension test was
introduced first, followed by an electromagnetically driven version. The electromagnetically driven ring tension test appears to
have overshadowed the explosively driven version; however, the explosively driven expanding ring tension test remains useful
in cases where the joule heating of the sample material is undesirable or the use of high voltage power supplies is not practical.
In this work, the explosively driven expanding ring tension test was reexamined. Numerical simulations were used to explore
the results of different explosive and material geometries. This study found that the sample ring cross-section size 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.
Keywords Tension · Dynamic · Ring · Explosive · Strength
14.1 Introduction
Dynamic materials property characterization is important for crashworthiness models, designing shock mitigation, and other
areas. Many dynamic materials characterization techniques, such as the Split Hopkinson Pressure Bar (SHPB) [1] or shock
compression [2], measure properties in compression or the initial load is applied in compression, such as shock-induced
spallation [3]. A number of tension based techniques have also been developed based on the SHPB [1]. These techniques are
popular and well established but suffer from difficulties due to the dispersive nature of elastic- plastic waves and their low
velocity in uniaxial stress loading conditions.
σ
ρ
ring = 0 r r
(14.1)
ring =
r
r 0
(14.2)
An alternative to these SHPB tension tests is the explosively driven expanding ring tension test, where symmetric expansion can avoid wave propagation issues. The explosively driven expanding ring tension test is also advantageous because it
allows large plastic strains. This method was first proposed by Johnson et al. [4] who published a method of using explosives
to place a sample ring into tension. They demonstrated that for thin, decelerating rings the stress in the ring is proportional
to the product of the ring radius and the ring acceleration as shown in Eq. (14.1). The strain in the ring is proportional to its
current radius as shown in Eq. (14.2). They suffered from difficulties in reducing the data because their image data yielded
displacement which required differentiation to obtain the acceleration data required to determine the stress state in the ring.
Their approach was studied and improved upon by Perrone [5] and Hoggatt and Recht [6] though the fundamental issues
B. Aydelotte (*)
Idaho National Laboratory, Idaho Falls, USA
e-mail: brady.aydelotte@inl.gov
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society
for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_14
Chapter 14
Analysis of the Explosively Driven Expanding Ring Tension Test
Brady Aydelotte
Abstract The expanding ring tension test has been available in some form for decades, but it remains little utilized compared
with shock-induced spallation or the tension Split Hopkinson Pressure Bar test. The explosively driven ring tension test was
introduced first, followed by an electromagnetically driven version. The electromagnetically driven ring tension test appears to
have overshadowed the explosively driven version; however, the explosively driven expanding ring tension test remains useful
in cases where the joule heating of the sample material is undesirable or the use of high voltage power supplies is not practical.
In this work, the explosively driven expanding ring tension test was reexamined. Numerical simulations were used to explore
the results of different explosive and material geometries. This study found that the sample ring cross-section size 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.
Keywords Tension · Dynamic · Ring · Explosive · Strength
14.1 Introduction
Dynamic materials property characterization is important for crashworthiness models, designing shock mitigation, and other
areas. Many dynamic materials characterization techniques, such as the Split Hopkinson Pressure Bar (SHPB) [1] or shock
compression [2], measure properties in compression or the initial load is applied in compression, such as shock-induced
spallation [3]. A number of tension based techniques have also been developed based on the SHPB [1]. These techniques are
popular and well established but suffer from difficulties due to the dispersive nature of elastic- plastic waves and their low
velocity in uniaxial stress loading conditions.
σ
ρ
ring = 0 r r
(14.1)
ring =
r
r 0
(14.2)
An alternative to these SHPB tension tests is the explosively driven expanding ring tension test, where symmetric expansion can avoid wave propagation issues. The explosively driven expanding ring tension test is also advantageous because it
allows large plastic strains. This method was first proposed by Johnson et al. [4] who published a method of using explosives
to place a sample ring into tension. They demonstrated that for thin, decelerating rings the stress in the ring is proportional
to the product of the ring radius and the ring acceleration as shown in Eq. (14.1). The strain in the ring is proportional to its
current radius as shown in Eq. (14.2). They suffered from difficulties in reducing the data because their image data yielded
displacement which required differentiation to obtain the acceleration data required to determine the stress state in the ring.
Their approach was studied and improved upon by Perrone [5] and Hoggatt and Recht [6] though the fundamental issues
B. Aydelotte (*)
Idaho National Laboratory, Idaho Falls, USA
e-mail: brady.aydelotte@inl.gov