F. L. Addessio

Equations of state for the α and γ polymorphs of cyclotrimethylene trinitramine

Equations of state for the α and γpolymorphs of the energetic molecular crystal cyclotrimethylene trinitramine (RDX) have been developed from their Helmholtz free energies. The ion motion contribution to the Helmholtz free energy is represented by Debye models with density-dependent Debye temperatures that are parameterized to vibrational densities of states computed from dispersion-corrected density functional theory. By separating the vibrational density of states into low frequency modes of mainly lattice phonon character and high frequency modes of intramolecular character we were able to significantly improve the description of the heat capacity at low temperatures and the thermal contribution to the pressure. The ion motion contribution to the Helmholtz free energy of the high pressureγpolymorph was constructed from that of the αpolymorph to reproduce the temperature-independent transformation pressure seen experimentally. The static lattice energies for both polymorphs were constructed to reproduce published isothermal compression data. The equations of state have been applied to the prediction of the path of the principal Hugoniot in the equilibrium phase diagram.

The influence of peak shock stress on the high pressure phase transformation in Zr

At high pressures zirconium is known to undergo a phase transformation from the hexagonal close packed (HCP) alpha phase to the simple hexagonal omega phase. Under conditions of shock loading, a significant volume fraction of high-pressure omega phase is retained upon release. However, the hysteresis in this transformation is not well represented by equilibrium phase diagrams and the multi-phase plasticity under shock conditions is not well understood. For these reasons, the influence of peak shock stress and temperature on the retention of omega phase in Zr has been explored. VISAR and PDV measurements along with post-mortem metallographic and neutron diffraction characterization of soft recovered specimens have been utilized to quantify the volume fraction of retained omega phase and qualitatively understand the kinetics of this transformation. In turn, soft recovered specimens with varying volume fractions of retained omega phase have been utilized to understand the contribution of omega and alpha phases to strength in shock loaded Zr.

A constitutive model for a uranium-niobium alloy

A constitutive model that includes the effects of elasticity, crystal reorientation (twinning or detwinning), phase transformations, and plasticity is presented. The model is applied to a uranium-6wt% niobium (U-6Nb) alloy, which is known to exhibit the shape memory effect. The inelastic strains for phase transformation and reorientation are based on the material’s phase diagrams. The model captures the effects of martensitic transformation and reorientation; both of the phenomena are coupled with the alloy’s phase diagrams, which are defined in terms of temperature, hydrostatic pressure, and shear stress. Computational simulations are presented that demonstrate the ability of the model to capture the relevant physical response of the material. Also, we include experimental results that demonstrate the phenomena of phase transformation, reorientation, and plasticity for low- and high-strain rates and for variations in temperature. The model replicates the experimental data for the broad range of strain ra...

The effects of shockwave profile shape and shock obliquity on spallation: Kinetic and stress-state effects on damage evolution

Shock‐loading of a material in contact with a high explosive (HE) experiences a “Taylor wave” (triangular wave) loading profile in contrast to the square‐wave loading profile imparted via the impact of a flyer plate. Detailed metallographic and microtextural analysis of the damage evolution in spalled Cu samples as a function of square/triangle and sweeping detonation‐wave loading is presented.

Dynamically driven phase transformations in heterogeneous materials. I. Theory and microstructure considerations

A theoretical model recently developed for heterogeneous materials undergoing dynamically driven thermodynamic phase transitions [F. L. Addessio et al. J. Appl. Phys. 97, 083509 (2005)] has been extended to allow for complex material microstructures. The model is applied to silicon carbide—titanium (SiC–Ti) unidirectional metal matrix composites where the aligned SiC fibers are filler and Ti is the matrix. Ti is known to undergo a low pressure and temperature solid-solid first-order phase transition. The microstructural analysis uses the generalized method of cells, which partitions a representative volume element into subcells containing the SiC fibers and the Ti matrix. The thermomechanical analysis has been reformulated from the previous work. In the reformulation it is found that thermodynamic quantities are naturally expressed as mass fraction averages over the two coexisting phases while the mechanical quantities are expressed naturally as volume averages. Consequently, the thermomechanical reformul...

Dynamic Response of PBX‐9501 through the β‐δ Phase Transition

The Gibbs free energies of the β and δ phases of HMX are constructed from zero pressure heat capacity data, specific volume measurements, numerical simulations, and diamond anvil experiments. The free energies provide input into a dynamic phase transition model developed for heterogeneous materials that undergo dynamically driven phase transitions. This model, which uses the method of cells analysis to treat the HMX‐polymer binder composite, is used to study dynamically loaded PBX‐9501 as it transforms from the beta to the delta phase.

Dynamically driven phase transformations in heterogeneous materials. II. Applications including damage

A model, developed for heterogeneous materials undergoing dynamically driven phase transformations in its constituents, has been extended to include the evolution of damage. Damage is described by two mechanisms: interfacial debonding between the constituents and brittle failure micro-crack growth within the constituents. The analysis is applied to silicon carbide-titanium (SiC-Ti) unidirectional metal matrix composites that undergo the following phenomena: Ti has a yield stress of approximately 0.5 GPa and above a pressure of about 2 GPa undergoes a solid-solid phase transformation. The inelastic work from plastic dissipation contributes to the temperature and pressure rise in the Ti. SiC behaves elastically below a critical stress, above which it is damaged by microcrack growth. Finally, under tensile loading, the interface between Ti and SiC debonds according to an interfacial decohesion law. Each process is first examined independently in order to understand how its characteristic behavior is manifest...

A model for plastic deformation and phase transformations of zirconium under high-rate loading

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.

Dynamically driven phase transformations in damaged composite materials

A model developed for composite materials undergoing dynamicaly driven phase transitions in its constituents has been extended to allow for complex material micro‐structure and evolution of damage. In this work, damage is described by interfacial debonding and micro‐crack growth. We have applied the analysis to silicon carbide‐titanium (SiC‐Ti) unidirectional metal matrix composites. In these composites, Ti can undergo a low pressure and temperature solid‐solid phase transition. With these extensions we have carried out simulations to study the complex interplay between loading rates, micro‐structure, damage, and the thermo‐mechanical response of the system as it undergoes a solid‐solid phase transitions.

A Strength Model For Materials With Phase Change

A material strength model has been developed for the deviatoric stress of zirconium. The model takes into account different material properties for each phase and evolves separate yield surfaces for each phase. The strength model is coupled with a free energy approach for the equation of state that is applicable to high‐pressure applications. The material model has been implemented into a three‐dimensional Lagrangian finite‐element code. Results from a simulation of an explosively‐loaded plate demonstrate the importance of including phase change in the constitutive model.