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A constitutive model which considers both plastic deformation and solid–solid phase transformations has been developed for zirconium under high-rate loading. Within the multiphase mixture regime, a lower-bound (Ruess) or uniform-stress assumption is used. It also is assumed that coexisting phases are in thermal equilibrium. The plastic deformation of the mixture is given by the contributions of individual phases. Each phase has a separate plastic yield surface, which evolves (strain-hardening) according to the plastic strain accumulated in the phase. A novel, fully implicit numerical algorithm for the plastic response of multiphase materials with separate yield surfaces is developed. The model is validated using data for plate impact experiments on a zirconium target. Simulations also are provided to demonstrate the ability of the model to capture the relevant aspects of the high-strain-rate deformation of a zirconium plate loaded with explosives. The numerical results indicate that the phase histories of the material under a general, three-dimensional (3D) stress state can be very complicated and cannot be anticipated without a detailed 3D calculation including the effects of phase transformations. The results presented here may have an important implication in designing systems involving zirconium for high-rate applications.

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An improved model of the mechanical properties of the explosive contained in conventional munitions is needed to accurately simulate performance and accident scenarios in weapons storage facilities. A specific class of explosives can be idealized as a mixture of two components: energetic crystals randomly suspended in a polymeric matrix (binder). Strength characteristics of each component material are important in the macroscopic behavior of the composite (explosive). Of interest here is the determination of an appropriate constitutive law for a polyurethane binder material. This paper is a continuation of previous work in modeling polyurethane at moderately high strain rates and for large deformations. Simulation of a large deformation (strains in excess of 100%) Taylor Anvil experiment revealed numerical difficulties which have been addressed. Additional experimental data have been obtained including improved resolution Taylor Anvil data, and stress relaxation data at various strain rates. A thorough evaluation of the candidate viscoelastic constitutive model is made and possible improvements discussed.