Modelling of shock waves in FCC and BCC metals using a dislocation based continuum approach

Abstract

Recent experimental data has revealed that, over short time scales (on the nanosecond time scale), during formation of a shock in metals the amplitude of the ‘elastic’ precursor greatly exceed the Hugoniot elastic limit (HEL), before decaying to the level of the HEL. Existing continuum scale material models are unable to reproduce this behaviour. To capture this aspect of material behaviour physical effects related to high rate dislocation mechanics have to be taken into consideration and included into the continuum scale material model. This is achieved with the use of a dislocation dynamics based model, where the state variable are calculated on the microscale, before being fed up to the continuum scale by use of the Orowan equation. Three state variable are used for the evolution of plasticity on the microscale; the density of mobile dislocation, the density of immobile dislocations and the velocity of dislocations. The model used in this work was previously available in literature in a 1D form only. Full 3D implementation of the model is made in a finite element hydrocode, including coupling with an appropriate equation of state Model validation was done by comparison of numerical results with experimental data for plate impact tests (1D strain state) for aluminium and copper, both fcc structured metals. The difference between the experimental and numerical values of the compared parameters (longitudinal stress, pulse length, elastic precursor relaxation time) was within 10%. Notably the plate impact tests show that over the first 50ns after impact the pre-cursor wave has an amplitude similar to the stress levels behind the shock wave, relaxing to HEL with time (wave propagation). Further developments are made to the model to allow for simulation of the more complexly yielding bcc single crystals, with a focus on the simulation of single crystal tantalum plate impact tests. It is observed that the model accurately predicts the shape of the rear surface velocity obtained experimentally for single crystal tantalum, with analysis of the generate simulation data allowing for explanation of the features observed. Further to the use of the model for simulations, method have been developed to allow for the determination of material parameter using the fitting of data.