Abstract
Recent progress in the development of dynamic strength experimental platforms is allowing for unprecedented insight into the assumptions used to construct constitutive models operating in extreme conditions. In this work, we make a quantitative assessment of how tantalum strength scales with its shear modulus to pressures of hundreds of gigapascals through a cross-platform examination of three dynamic strength experiments. Specifically, we make use of Split–Hopkinson pressure bar and Richtmyer–Meshkov instability experiments to assess the low-pressure strain and strain rate dependence. Concurrent examination of magnetically driven ramp-release experiments up to pressures of 350GPa allows us to examine the pressure dependence. Using a modern description of the shear modulus, validated against both ab initio theory and experimental measurements, we then assess how the experimentally measured pressure dependence scales with shear modulus. We find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data.
Highlights
Understanding the constitutive response of metals compressed to high energy density (HED) conditions, typically defined as pressures . 100 GPa, is required for modeling a wide range of applications including high velocity impacts, planetary formation and interiors, and inertial confinement fusion implosions.[1]
We find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data
Significant effort has been put into performing a completely different type of dynamic high pressure strength experiment at the National Ignition Facility (NIF), which provides an opportunity for cross-platform validation of the pressure scaling
Summary
Understanding the constitutive response of metals compressed to high energy density (HED) conditions, typically defined as pressures . 100 GPa, is required for modeling a wide range of applications including high velocity impacts, planetary formation and interiors, and inertial confinement fusion implosions.[1]. 100 GPa, is required for modeling a wide range of applications including high velocity impacts, planetary formation and interiors, and inertial confinement fusion implosions.[1] A key component to predictive models under HED conditions is a description of how the material strength scales with pressure Modeling efforts such as those of Steinberg et al.[2] utilized first order expansions to describe the pressure scaling of the shear modulus, G, and strength, Y. While it was recognized the derivatives of G and Y with respect to pressure could be different, most low pressure experiments examining temperature dependence suggest the local forces or stresses that must be overcome to drive dislocations past obstacles are linearly proportional to the shear modulus[3] such that Y 1⁄4 Y0 G(P, T) G0 : (1). In dislocation-based plasticity models such as that of Barton et al.,[5] the the Thaarydloernienqguactoionntr,ibYu/tioGn ptoffiρffi t, hwehsetrreenρgtish is generally described by the dislocation density
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