Strain Rate Dependence in Steady, Plastic Shock Waves

Abstract

One-dimensional plane shock waves have been widely used to study the mechanical response of solids to high velocity deformation. For many materials, under a certain range of impact pressures, there exists a two-wave structure of which the first wave, the so-called elastic precursor, travels at the velocity of sound waves, while the second wave, the so-called plastic shock wave, travels at a slower speed which increases with the impact pressure. While the full two-wave structure is thus not steady (does not propagate without change of form), each component wave may be treated as steady after sufficient propagation distance. With regard to the steady plastic wave, Grady¹ noted that the wave profile data of Barker² for aluminum suggested the empirical relationship

$$ {\dot \in _{\text{M}}} = k\,p_{D,}^4 $$

(1)

where k is a material dependent constant, and where ${\dot \in _{\text{M}}}$ is the maximum of the absolute value of the strain rate in the plastic wave, while p _D is the driving or impact pressure required to create the wave. Within the class of materials meeting

$$ \sigma = f( \in ) + g(\dot \in ), $$

(2)

where σ is the axial stress and where f(∈) and $g\left( {\dot \in } \right)$ are certain functions of, respectively, the uniaxial strain ∈ and its material time rate ∈, Grady further observed that (1), along with a standard assumed form for f(·), implied that, to a first approximation,

$$g\left( {\dot \in } \right) = {\mu _0}{\mathop{\rm sgn}} \left( {\dot \in } \right){\left| {\dot \in } \right|^{\frac{1}{2}}}$$

(3)

where µ ₀ is a material dependent constant.

This work performed by Sandia National Laboratories supported by the U. S. Department of Energy under contract #DE-AC04-76-DP00789.