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M. Gonzales and N. N. Thadhani
tion, adiabatic shear localization, and other deformation modes becoming activated
such as deformation twinning [54, 57–59]. Even if the quasi-static behavior of
the material lends itself to a bulk isotropic formulation of its constitutive law, the
meso-scale response at dynamic loading rates may be drastically different due to
percolation effects [60]. The meso-scale response has implications on the measured
bulk behavior in an experiment and cannot be ignored. The fascinating aspects
of heterogeneous materials lie in the length scales, microstructural features, and
property contrasts that impart the physical and mechanochemical properties that
themselves make the materials suitable candidates for use in extreme dynamic
environments.
1.1 The Challenge of Dynamic Property Measurements
Experimental methods to evaluate material response at dynamic loading rates
involve generating stress waves in the material and evaluating the wave propagation
response either via indirect or direct measurement or by inferring the response from
computer simulation. The stress waves are generated by mechanical insult on a
material to be tested, usually by striking the material with a projectile, via contact
detonation with an explosive, or by the confined expansion of a plasma generated
by a pulsed-power laser. Experimental methods in dynamic behavior can range in
the strain rate regime of applicability, from quasi-static and slow-strain-rate testing
using load frames to drop weight testing, split Hopkinson pressure bar (SHPB)
testing, flyer plate testing, and contact detonation with explosives. The accessible
strain rates depend on the materials tested as well as the size and shape of the
testing articles. Figure 1 demonstrates the relative strain rate regimes achievable by
common testing methods applied to metallic materials. The shock impedance and
constitutive properties will determine the strain rates achievable. It should be noted
that these strain rates are typical at meso-scales and that macro-scale strain rates
may be up to an order of magnitude lower than those represented in this plot. The
local strain rates at smaller scales may be much higher, as strain rate scales with the
deformation length scale. Strain rates achievable in powder and particulate mixtures
are a strong function of the packing density and local microstructure, as well as the
topology of the void space and connectivity of phases. Furthermore, crush strength
also affects the strain rate achievable and can disperse the insulting waves as they
expend energy to compact the powder.
There are extensive descriptions in the monographs by Meyers [54], Field et al.
[21], Ramesh [62], and Horie and Sawaoka [42] on dynamic testing, especially
under shock compression conditions. Indirect measurements include the strain gage
output from split Hopkinson pressure bars (SHPBs), postmortem measurements of
the final bulk strain/deformation of recovered impacted specimens, or postmortem
microstructural characterization. Direct measurement techniques include directcontact stress gages, magnetic particle velocity gages, digital image correlation
(DIC) measurements of speckle patterns, high-speed photography/videography, and
M. Gonzales and N. N. Thadhani
tion, adiabatic shear localization, and other deformation modes becoming activated
such as deformation twinning [54, 57–59]. Even if the quasi-static behavior of
the material lends itself to a bulk isotropic formulation of its constitutive law, the
meso-scale response at dynamic loading rates may be drastically different due to
percolation effects [60]. The meso-scale response has implications on the measured
bulk behavior in an experiment and cannot be ignored. The fascinating aspects
of heterogeneous materials lie in the length scales, microstructural features, and
property contrasts that impart the physical and mechanochemical properties that
themselves make the materials suitable candidates for use in extreme dynamic
environments.
1.1 The Challenge of Dynamic Property Measurements
Experimental methods to evaluate material response at dynamic loading rates
involve generating stress waves in the material and evaluating the wave propagation
response either via indirect or direct measurement or by inferring the response from
computer simulation. The stress waves are generated by mechanical insult on a
material to be tested, usually by striking the material with a projectile, via contact
detonation with an explosive, or by the confined expansion of a plasma generated
by a pulsed-power laser. Experimental methods in dynamic behavior can range in
the strain rate regime of applicability, from quasi-static and slow-strain-rate testing
using load frames to drop weight testing, split Hopkinson pressure bar (SHPB)
testing, flyer plate testing, and contact detonation with explosives. The accessible
strain rates depend on the materials tested as well as the size and shape of the
testing articles. Figure 1 demonstrates the relative strain rate regimes achievable by
common testing methods applied to metallic materials. The shock impedance and
constitutive properties will determine the strain rates achievable. It should be noted
that these strain rates are typical at meso-scales and that macro-scale strain rates
may be up to an order of magnitude lower than those represented in this plot. The
local strain rates at smaller scales may be much higher, as strain rate scales with the
deformation length scale. Strain rates achievable in powder and particulate mixtures
are a strong function of the packing density and local microstructure, as well as the
topology of the void space and connectivity of phases. Furthermore, crush strength
also affects the strain rate achievable and can disperse the insulting waves as they
expend energy to compact the powder.
There are extensive descriptions in the monographs by Meyers [54], Field et al.
[21], Ramesh [62], and Horie and Sawaoka [42] on dynamic testing, especially
under shock compression conditions. Indirect measurements include the strain gage
output from split Hopkinson pressure bars (SHPBs), postmortem measurements of
the final bulk strain/deformation of recovered impacted specimens, or postmortem
microstructural characterization. Direct measurement techniques include directcontact stress gages, magnetic particle velocity gages, digital image correlation
(DIC) measurements of speckle patterns, high-speed photography/videography, and