Constitutive algorithm, constitutive modeling and simulation of high-strain, high-strain-rate finite-deformation of heavy metals

In computational mechanics, for large-scale computer simulation of finite-deformation problems, accurate and stable constitutive algorithms play a vital role. An explicit, always stable, and always accurate algorithm is developed for stiff phenomenological rate-independent elastoplastic and rate-dependent elastoviscoplasticity models, including isotropic, kinematic, and combined isotropic and kinematic workhardening, as well as thermal softening, and noncoaxiality of the plastic strain rate and the deviatoric stress (or stress-difference, when back stress exists). The algorithm is based on a plastic predictor, followed by elastic corrector. The results are illustrated by means of several examples which show that the technique is accurate (for both the stress magnitude and the stress orientation) and always stable, essentially independent of the magnitude of the time or strain, but not rotation increment. The algorithm is then extended to accommodate large rotations produced by large spins. The extended algorithm provides accurate results for relatively large strain increments, e.g., 5% or greater, accompanied by up to 45-degree-rotation increments.; Parallel with the above efforts, experimental techniques are described and illustrated for direct measurements of temperature, strain-rate, and strain effects on the flow stress of metals over a broad range of strains and strain rates. The approach utilizes: (1) the dynamic recovery Hopkinson bar technique recently developed at UCSD (Nemat-Nasser et al., 1991); (2) direct measurement of sample temperature by high-speed infra-red detectors; and (3) ability to change the strain rate during the course of experiment at high strain rates. In this manner, constitutive parameters of elasto-viscoplastic flow stress of metals and metallic alloys are established and used in constitutive models for large-scale computational simulation of high strain-rate phenomena such as adiabatic shear banding. Taylor anvil tests are performed, accompanied by high-speed photographic recording of the deformation, and the results are compared with those obtained by finite-element simulations, leading to fine tuning of parameters in the material's flow stress. This procedure is illustrated for tantalum and tantalum/tungsten alloys, as well as for VAR 4340 steel. The simulations are performed using PRONTO-2D finite-element code with the constitutive algorithm mentioned in the preceding paragraph. The constitutive model and the constitutive algorithm are used to simulate adiabatic shear bands produced in a hat-shaped specimen under controlled conditions, arriving at excellent correlation with the experimental data of Beatty et al. (1991).