Nonlocal Regularization for Loss of Ellipticity in Inelastic Problems
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Journal of Physics: Conference Series
Density Functional Theory (DFT) based molecular dynamics has been established as a method capable of yielding high fidelity results for many materials at a wide range of pressures and temperatures and has recently been applied to complex polymers such as polyethylene, compounds such as ethane or CO2, and oxides such as MgO. We use this method to obtain a Grïneisen Γ and thereby build a Mie-Grüneisen equation of state (EOS) and a Rice-Walsh EOS for tantalum pentoxide (Ta2O5 or tantala) and compare to experimental data. The experimental data have initial densities (ρ00) of approximately 1.13, 3, and 7.4 g/cm 3 reduced from a crystalline of 8.36 g/cm3. We found that r becomes constant at higher temperatures and pressure, but is a function of both density and temperature at lower densities and temperatures. Finally, the Mie-Gruneisen EOS is adequate for modeling the slightly distended Hugoniot with an initial density of 7.4 g/cm3 however it is inadequate for the more porous Hugoniot, while the Rice-Walsh EOS combined with a P-λ crush model approximates the experimental data quite well. © Published under licence by IOP Publishing Ltd.
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Proposed for publication in Journal of Applied Physics.
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Pressure-shear experiments were performed on granular tungsten carbide and sand using a newly-refurbished slotted barrel gun. The sample is a thin layer of the granular material sandwiched between driver and anvil plates that remain elastic. Because of the obliquity, impact generates both a longitudinal wave, which compresses the sample, and a shear wave that probes the strength of the sample. Laser velocity interferometry is employed to measure the velocity history of the free surface of the anvil. Since the driver and anvil remain elastic, analysis of the results is, in principal, straightforward. Experiments were performed at pressures up to nearly 2 GPa using titanium plates and at higher pressure using zirconium plates. Those done with the titanium plates produced values of shear stress of 0.1-0.2 GPa, with the value increasing with pressure. On the other hand, those experiments conducted with zirconia anvils display results that may be related to slipping at an interface and shear stresses mostly at 0.1 GPa or less. Recovered samples display much greater particle fracture than is observed in planar loading, suggesting that shearing is a very effective mechanism for comminution of the grains.
Planar shock experiments were conducted on granular tungsten carbide (WC) and tantalum oxide (Ta{sub 2}O{sub 5}) using the Z machine and a 2-stage gas gun. Additional shock experiments were also conducted on a nearly fully dense form of Ta{sub 2}O{sub 5}. The experiments on WC yield some of the highest pressure results for granular materials obtained to date. Because of the high distention of Ta{sub 2}O{sub 5}, the pressures obtained were significantly lower, but the very high temperatures generated led to large contributions of thermal energy to the material response. These experiments demonstrate that the Z machine can be used to obtain accurate shock data on granular materials. The data on Ta{sub 2}O{sub 5} were utilized in making improvements to the P-{lambda} model for high pressures; the model is found to capture the results not only of the Z and gas gun experiments but also those from laser experiments on low density aerogels. The results are also used to illustrate an approach for generating an equation of state using only the limited data coming from nanoindentation. Although the EOS generated in this manner is rather simplistic, for this material it gives reasonably good results.
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