A Report on the Validation of Beryllium Strength Models

Abstract

This report discusses work on validating beryllium strength models with flyer plate and Taylor rod experimental data. Strength models are calibrated with Hopkinson bar and quasi-static data. The Hopkinson bar data for beryllium provides strain rates up to about 4000 per second. A limitation of the Hopkinson bar data for beryllium is that it only provides information on strain up to about 0.15. The lack of high strain data at high strain rates makes it difficult to distinguish between various strength model settings. The PTW model has been calibrated many different times over the last 12 years. The lack of high strain data for high strain rates has resulted in these calibrated PTW models for beryllium exhibiting significantly different behavior when extrapolated to high strain. For beryllium, the α parameter of PTW has recently been calibrated to high precision shear modulus data. In the past the α value for beryllium was set based on expert judgment. The new α value for beryllium was used in a calibration of the beryllium PTW model by Sky Sjue. The calibration by Sjue used EOS table information to model the temperature dependence of the heat capacity. Also, the calibration by Sjue used EOS table information to model the density changes of the beryllium sample during the Hopkinson bar and quasi-static experiments. In this paper, the calibrated PTW model by Sjue is compared against experimental data and other strength models. The other strength models being considered are a PTW model calibrated by Shuh-Rong Chen and a Steinberg-Guinan type model by John Pedicini. The three strength models are used in a comparison against flyer plate and Taylor rod data. The results show that the Chen PTW model provides better agreement to this data. The Chen PTW model settings have been previously adjusted to provide a better fit to flyer plate data, whereas the Sjue PTW model has not been changed based on flyer plate data. However, the Sjue model provides a reasonable fit to flyer plate and Taylor rod data, and also gives a better match to recently analyzed Z-machine data which has a strain of about 0.35 and a strain rate of 3e5 s −1 .