A more curious feature is the obvious multiwave structure seen in the simulation performed with The origin of this multiwave structure is provided in Figure 17 , where release paths have been included from shocked states above the threshold for reaction. The isentrope from retains the structure built into the cold curve, as shown in Figure 15 right. Because the products are treated as an entirely separate material—with a different EOS—no such feature is present in Similar results hold for , where the structure due to reaction was not included as part of the cold curve.
The way shock-driven transitions are incorporated into EOS representations can thus have hydrodynamic consequences, depending on how hard the material is shocked and how long it is simulated. Please note that the structure built into the cold curve of see Figure 15 , right is retained also in the isentrope.
The reaction is accompanied by an increase in density, the extent of which varies widely and correlates at least qualitatively with initial chain structure and degree of crystallinity. We believe the products of this reaction to be those of full chemical decomposition i. The transition manifests itself as a cusp in the principal Hugoniot Figure 1 A and as multiwave structure in particle velocity profiles obtained in situ Figure 1 B or at interfaces Figure Introduction of porosity complicates the picture largely through the significantly higher temperatures generated in the process of pore collapse.
Thermal expansion due to shock heating can be so considerable that the Hugoniot becomes anomalous in the sense that final volumes actually increase with increasing input stress Figure 3 C , an effect observed also in metal foams.
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Detonating high explosives also expand as they react, but with exothermic heat release sufficient to drive a self-sustaining wave [ 54 ]. While preliminary indications are that some solid polymers do decompose exothermically Figure 11 , the degree of heat release is insufficient to compensate for the effects of volume collapse and the criterion for detonation is not satisfied. There are several outstanding questions regarding shock-driven compression and dissociation of polymers and foams. As in the case of high explosives, in situ measurement of the product composition remains challenging experimentally, and even the best post-mortem studies are now decades old [ 18 , 19 ].
X-ray-based methods are promising in their ability to penetrate the optically dense, high-pressure—temperature product mixture, and we have recently reported the evolution of carbon particle size and morphology in a detonating explosive in situ [ , ]. New in situ measurements of reactive wave profiles in polysulfone [ ] demonstrate strong temperature-dependence of chemical reaction rates and complex two-wave structures such as those observed in CP and CE. These wave profiles are being used to calibrate reactive flow models for polymers, the first of their kind.
However, EOS temperatures are unconstrained by experiment and most reaction rate forms depend exponentially on temperature, so a great deal of uncertainty regarding the details remains. Many interesting facets of the chemistry—mechanisms, intermediates, even the number of basic steps—are almost completely unknown.
High-Pressure Shock Compression of Solids VII
In the absence of such knowledge, there is little justification for use of anything beyond a single, global Arrhenius reaction rate. Precise measurement of shock response in foams is also hindered by several sources of ill-quantified uncertainty. Sample heterogeneity often of an extreme degree, see Figure 4 and high shock temperatures Figure 11 can reduce the quality of velocimetric and embedded gauge data, as well as that of other diagnostics. Impedance matching to a high impedance impactor or drive plate can result in errors in particle velocity with measured shock velocities.
In addition, it remains the case that only the initial first shock breakout is measured in many experiments, and wave profiles that might otherwise display temporal evolution are incapable of doing so. Advances in in situ and spatially resolved diagnostics, such as direct density measurements using proton or X-ray radiography and multiple point or line imaging velocimetry, offer the potential for reducing these errors.
We also thank Stephen Sheffield, E. Mark Byers and Steve DiMarino fired the high-performance powder gun. Department of Energy Contract No. National Center for Biotechnology Information , U. Journal List Polymers Basel v. Polymers Basel. Published online Mar Dana M. Joshua D. Author information Article notes Copyright and License information Disclaimer. Received Jan 18; Accepted Mar 3. This article has been cited by other articles in PMC. Abstract Polymers and foams are pervasive in everyday life, as well as in specialized contexts such as space exploration, industry, and defense.
Keywords: polymers, foams, shock compression, equation of state. Introduction Polymers, polymeric composites, and polymeric foams are used extensively as cushioning, insulation, structural support, and for shock mitigation. Shock Physics Background 1. Basic Concepts Shock waves produce discontinuous changes in material properties while remaining subject to conservation of mass, momentum, and energy across the discontinuity [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ].
Wave Splitting Shock-driven transitions often are accompanied by abrupt changes in volume. Open in a separate window. Figure 1. Shockwave Compression of Porous Foams At the same mass velocity, porous materials typically have lower wave velocities relative to their fully dense counterparts. Figure 2. Figure 3. Materials and Methods 2. Materials The concepts discussed above will be used to interpret results obtained for the following materials: solid and porous foamed polyurethane [ 6 , 13 , 47 , 48 , 57 , 58 ], Epon- and Jeffamine-based epoxies [ 59 , 60 ], carbon fiber-filled phenolic CP and cyanate ester CE composites [ 5 , 60 , 61 ], and filled polydimethylsiloxane foam SX [ 62 , 63 ].
Table 1 Polymers and foams discussed in the Results section. Figure 4. Figure 5.
High-Pressure Shock Compression of Solids VIII: The Science and Technology - Google книги
Figure 6. Gas Gun-Driven Plate Impact Experiments Most modern shockwave compression experiments are based on projectile impact driven by light gas guns or direct laser drive not discussed here. Figure 7. Figure 8. Figure 9. Equations of State 2. Global The EOS of polymers can be described with a variety of models, differing widely in their quality and level of detail. Thermochemical The EOS of shock-driven reaction products discussed below were based on thermochemical modeling [ 87 ], where full thermodynamic equilibrium of chemically distinct atomic, molecular, or solid components is assumed.
Results and Discussion 3. Table 2 Representative polymers, their threshold pressure for decomposition on their principal Hugoniot, and the percentage volume change upon decomposition. Figure Product Temperatures and Compositions One of the most difficult quantities to measure in a dynamic experiment is temperature, making theoretical estimates particularly valuable.
Wave Profiles One of the great advantages of modern velocimetric diagnostics is their ability to measure wave profiles. Future Directions There are several outstanding questions regarding shock-driven compression and dissociation of polymers and foams. Author Contributions D. Conflicts of Interest The authors declare no conflict of interest.
Ferry J. Viscoelastic Properties of Polymers.
Clements B. A continuum glassy polymer model applicable to dynamic loading. Zarzycki J.
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Glasses and the Vitreous State. Coe J. Dattelbaum D. Shockwave response of two carbon fiber-polymer composites to 50 GPa. Reactive, anomalous compression in shocked polyurethane foams. Wunderlich B. Heat capacities of linear high polymers. Menikoff R. Empirical Equations of State for Solids. In: Horie Y. Chapter 4. Fredenburg D. High-fidelity Hugoniot analysis of porous materials. Systematics of compaction for porous metal and metal-oxide systems. AIP Conf. Gourdin W. Dynamic consolidation of metal powders. Grady D.