A Model for Rate-dependent Plasticity

The purpose of this note is to propose an improvement to the widely-used Steinberg-Lund model for rate-dependent plasticity. The improved model is rate-dependent above, as well as below, the Peierls stress. As a result of this change, one material constant in the Steinberg-Lund model acquires a new value, and we thereby obtain a revised estimate for the dislocation density in tantalum. 1. Introduction In this note we discuss the widely-used Steinberg-Lund model 8] of rate-dependent plasticity and propose an improvement that overcomes a limitation of this model. Models of plastic behavior at high strain rates are validated by comparison to data from longitudinal impact experiments. In such an experiment, an elastic-plastic wave is generated when two thin metal plates collide. The velocity of the free surface at the outer edge of the target plate is measured, allowing a reconstruction of proole of the wave. These experimental data are used to determine unknown, or otherwise unmeasurable, parameters in the plasticity model. Validating the model means choosing parameters so as to obtain a good match between the observed free-surface velocity and that obtained by numerical simulation of the model. Our modiied model allows a satisfactory t to experimental data | comparable to that of Steinberg-Lund | although with a diierent value for one of the model parameters. From this fact, we observe that validation, as deened above, does not uniquely determine the plasticity constitutive law. In addition to experimental data, a constitutive law is constrained by consistency with general principles of physics. In this regard, we believe the model we propose to be an improvement. Dislocation theory predicts that there is a characteristic level of shear stress, the Peierls stress 3], required to move a straight dislocation over the energy barrier between adjacent close-packed rows of atoms on its glide plane. In the model of Ref. 8], the plastic response