The mechanical properties of polymers are becoming increasingly important as they are used in structural applications, both on their own and as matrix materials for composites. It has long been known that these mechanical properties are dependent on strain rate, temperature, and pressure. In this paper, the methods for dynamic loading of polymers will be briefly reviewed. The high strain rate mechanical properties of several classes of polymers, i.e. glassy and rubbery amorphous polymers and semi-crystalline polymers will be reviewed. Additionally, time–temperature superposition for rate dependent large strain properties and pressure dependence in polymers will be discussed. Constitutive modeling and shock properties of polymers will not be discussed in this review.

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High Strain Rate Mechanics of Polymers: A Review

Stress-strain behavior of sand at high strain rates

A review on split Hopkinson bar experiments on the dynamic characterisation of concrete

Examples of multiphase mixtures for which velocity and pressure relaxation are a stiff phenomenon are involved in many practical applications dealing with condensed phase mixtures, solid alloys, propellants and solid explosives, specific composite materials, micro- and nano-structured mixtures, etc. Shock relations for the mixture necessitate the determination of the volume fraction jump or any other thermodynamic variable jump. Examination of the shock dispersion mechanism suggests such jump relations. These relations are the phase Hugoniots which are compatible with the mixture energy equation. The corresponding model is conservative and symmetric. It fulfils the single-phase limit and guarantees volume fraction positivity. The shock relations are validated over a large set of experimental data and provide a remarkable agreement.

Shock jump relations for multiphase mixtures with stiff mechanical relaxation

Static and dynamic compaction of ceramic powders

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 ...

Shock-wave compression of a porous material

Polytetrafluoroethylene (PTFE) is a polymer with a simple atomic structure that shows complex behavior under pressure and demonstrates a highly variable metastable phase structure in shock waves with amorphous and crystalline components In turn, the crystalline component has four known phases with the high-pressure transition of the crystalline domain from crystalline phase IV at ambient through phase II to III At the same time, as has been recently studied using spectrometry, the crystalline region nucleates from the amorphous one with load Stress and velocity shock-wave profiles acquired recently with embedded gauges demonstrate features that may be related to the impedance mismatch between the phase domains subjected to such transitions resulting in variations of mechanical and thermophysical characteristics We consider the inter-phase non-equilibrium and the amorphous-to-crystalline and inter-crystalline transitions that are associated with the high pressure and temperature transformations under shock wave loading as possible candidates for the analysis The present work utilizes a multi-phase constitutive model that considers strength effects to describe the observed response under shock loading of the PTFE material Experimental plate impact shock-wave histories are compared with calculated profiles using kinetics describing the transitions The study demonstrates that the inter-phase pressure non-equilibrium of the state parameters plays the key role in the delay of the shock wave attenuation At the same time, the forward transition associated with the crystallization might be responsible for the velocity spike in the experimental velocity profiles at high impact velocity and the modulus variation at low impact velocity On the other hand, an accelerated attenuation of the velocity in the rarefaction wave is associated with another transition resulting in the residual crystallinity change during unloading

Constitutive modeling of shock response of polytetrafluoroethylene

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.

Constitutive modeling of fracture waves

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.

Phase transition modeling of polytetrafluoroethylene during Taylor impact

The use of stress gauges for characterization of the shock behaviour of porous materials is an important tool for the description of non‐equilibrium response in shock compression. The present paper demonstrates that gauge measurements can be employed for both dry and hydrated sand. In a previous publication [Resnyansky, A. D., et al. J. Appl. Phys. 2003], a single‐phase rate sensitive model was employed to describe tests for dry sand. In the present paper a two‐phase model has been developed, which allows us to describe the dry and hydrated sand with a uniform approach. Specification of the material is achieved by involving air or water as a matrix material in a two‐phase representation of the sand. The effect of the gauge embedding on the stress profiles is analysed numerically to understand features of the test records. Comparison of experimental and numerical results demonstrates a good agreement.

A. D. Resnyansky

Papers

Shock-wave compression of a porous material

Constitutive modeling of shock response of polytetrafluoroethylene

Constitutive modeling of fracture waves

Phase transition modeling of polytetrafluoroethylene during Taylor impact

Shock Compression of Dry and Hydrated Sand