Abstract. Governing equations for two-phase compressible flow with different phase pressures and temperatures are presented, the derivation of which is based on the formalism of thermodynamically compatible hyperbolic systems and extended irreversible thermodynamics principles. These equations form a hyperbolic system in conservationlaw form. A two-phase isentropic flow model proposed earlier and the hyperbolic model for heat transfer underlie the developed theory of this paper. A set of interfacial exchange processes such as pressure relaxation, interfacial friction, temperature relaxation and phase transition is taken into account by source terms in the balance equations. It is shown that the heat flux relaxation limit of the governing equations can be written in the Baer-Nunziato form, in which the Fourier thermal conductivity diffusion terms for each phase are included.
A fracture wave (FW) in a brittle material is a narrow transition region (border) of a continuous fracture zone, which may be associated with the damage accumulation process initiated by propagation of shock waves. In multidimensional structures the fracture wave may behave in an unusual way. The high-speed photography of penetration of a borosilicate (Pyrex) glass block [N. K. Bourne, L. Forde, and J. E. Field, Proc. SPIE 2869, 626 (1997)] shows a visible fracture zone with an apparent flat front although the projectile is a hemispherically nosed rod. A strain-rate-sensitive model is being developed and employed for analysis of the role of the complex stress state and kinetic description of the damage accumulation to describe the process of the impact. Numerical analysis is conducted with a one-dimensional wave propagation code employing the model and with the LS-DYNA2D hydrocode in which the model has been implemented. The analysis demonstrates that (i) the second (plastic) shock wave is superseded by quicker FW relaxing stress behind the elastic precursor, and (ii) the FW front flattening is apparently caused by the change in the acoustic directional properties. This change is associated with the phase-like transition due to the damage accumulation within the FW. In particular, the FW transition separates a highly anisotropic zone of material characterized acoustically by longitudinal and shear waves in front of the FW from a nearly isotropic region of the material characterized only by bulk waves behind the FW.
Porous materials may exhibit highly nonstationary behavior under shock-wave loading. The majority of existing experiments have measured the dependence between shock-wave velocity and particle velocity to define the Hugoniot for subsequent derivation of an equation of state. Such equations of state are nonconvex, which leads to significant thermodynamic and numerical problems. The present article suggests an experimental configuration and mathematical model, to overcome these difficulties. The experiment is based on a setup resulting in a continuous record of the stress profile with time using embedded manganin gauges. The model employs a homogenization approach enabling us to obtain a hyperbolic system of equations, which is completed with a convex equation of state so as to be suitable for implementation in commercial hydrocodes. Using available data for porous aluminum, an approach is elaborated for construction of constitutive equations. The model is tested with the present stress profiles in sand and demonstrates good agreement.
The complex pressure and temperature dependent phase behavior of the semicrystalline polymer polytetrafluoroethylene (PTFE) has been investigated experimentally. One manifestation of this behavior has been observed as an anomalous abrupt ductile-to-brittle transition in the failure mode of PTFE rods in Taylor cylinder impact tests when impact velocity exceeds a narrow critical threshold. Earlier, hydrocode calculations and Hugoniot estimates have indicated that this critical velocity corresponds to the pressure in PTFE associated with the transition from a crystalline phase of helical structure to the high pressure crystalline phase (phase III) of a planar form. The present work represents PTFE as a material in a simplified phase structure with the transition between the modeled phases regulated by a kinetic description. The constitutive modeling describes the evolution of mechanical characteristics corresponding to the change of mechanical properties due to either an increase of crystallinity or the phase transition of a crystalline low-pressure component into phase III. The modeling results demonstrate that a change in the kinetics of the transition mechanism in PTFE when traversing the critical impact velocity can be used to explain the failure of the polymer in the Taylor cylinder impact tests.
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