Modeling of the elastic precursor behavior and dynamic inelasticity of tantalum under ramp wave loading to 17 GPa

Abstract

In a previous study by Asay et al. [J. Appl. Phys. 106, 073515 (2009)], the inelastic response of annealed and cold-rolled pure polycrystalline tantalum at intermediate strain rates was characterized with ramp wave loading to peak longitudinal stresses of 17 GPa. It was found that the annealed Ta at strain rates of about 106/s exhibited pronounced elastic overshoot, followed by rapid stress relaxation and the amplitude of the elastic precursor depicted essentially no dependence on sample thickness for samples with controlled initial properties, in contrast to the precursor attenuation typically observed in shock wave experiments. The precursor for the cold-rolled sample was more dispersive and did not exhibit the characteristics depicted by the annealed samples. A principal objective of the present study was to gain some insights into this behavior and its implication on the deformation mechanisms for tantalum. Another objective was to gain a fundamental understanding of the dynamic inelasticity of polycrystalline tantalum, its evolution with the processing history, and the resultant thermomechanical behavior. The approach used to achieve these objectives was to first develop a material model that captured the observed material characteristics and then to use numerical simulations of dynamic experiments to gain additional insights into the observed material behavior. The constitutive model developed is based on the concept of dislocation generation and motion. Despite its simplicity, the model works quite well for both sets of data and serves a valuable tool to achieve the research objectives. The tantalum studied here essentially exhibits a strong rate sensitivity and this behavior is modeled through the low dislocation density and the strong stress dependence of the dislocation velocity. For the annealed material, the mobile dislocation density is assumed to be essentially zero in the model. This low dislocation density combined with strong stress dependence of dislocation velocity results in a metastable elastic response and a precursor that shows little attenuation. The increase of mobile dislocations through the cold-rolling process leads to a less rate-sensitive behavior for the cold-rolled tantalum and also the disappearance of the precursor behavior observed for the annealed samples. Both the low dislocation density and the strong rate dependence of the dislocation velocity may be related to the low mobility of the screw dislocations in bcc metals. This low mobility results from its extended, three-dimensional core structure.