New version page

Effect of Irreversible phase change

Upgrade to remove ads

This preview shows page 1-2-15-16-17-32-33 out of 33 pages.

Save
View Full Document
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 33 pages.
Access to all documents
Download any document
Ad free experience

Upgrade to remove ads
Unformatted text preview:

EFFECT OF IRREVERSIBLE PHASE CHANGE ONSHOCK-WAVE PROPAGATIONGeorge Q. Chen1, Thomas J. Ahrens2, Wenbo Yang3and James K. Knowles41Present address: Santa Cruz Operation, Santa Cruz, CA 950762Lindhurst Laboratory of Experimental Geophysics, California Institute of Technol-ogy, Pasadena, CA 911253Present address: Schlumberger, P. O. Box A, Rosharon, TX4Division of Engineering and Applied Science, California Institute of Technology,Pasadena, CA 91125ABSTRACTNew release adiabat data for vitreous GeO2are rep orted up to25 GPa using theVISAR technique. Numerical modeling of isentropic release waves induced dynamicstates achieved from one dimensional strain-stress waves is consistent with a phasechange that induce an increase in zero-pressure density from 3.7 to 6.3 Mg/m3start-ing at8GPa. The rst release adiabat data for SiO2(fused quartz) are presented(obtained with immersed foil technique). Above10GPa, the SiO2release isentrop es,in analogy with GeO2, are steeper than the Hugoniot in the volume-pressure space,indicating the presence of an irreversible phase transition (to a stishovite-like phase).We simulate propagation of a sho ck-waves in GeO2, in spherical and planar sym-metries, and predict enhanced attenuation for sho ck pressures (p)above the phasechange initiation pressure (8 GPa). The pressure from a spherical source decays withpropagation radiusr,prx, wherexis the decay co ecient. Mo deling hysteresisof the phase change givesx=;2:71, whereas without the phase change,x=;1:15.An analytical mo del is also given.1 INTRODUCTIONA single, planar sho ck-wave has the pro le of a sharp front, fol-lowed by a plateau of elevated pressure, then a trailing rarefaction1Journal of The Mechanics and Physics of Solids 47 (1999) 763-783wave, which always travels faster than the sho ck front. Whenthe plateau between the sho ck front and the rarefaction waveis present, the sho ck-wave is called \supported" when the rar-efaction wave overtakes the sho ck front, the sho ck-wave b ecomes\unsupp orted".In all materials, the duration of the high pressure plateau of sup-p orted, planar propagating sho ck-waves, or the amplitude of un-supp orted sho ck-waves, decays with time (and distance) b ecausepart of the sho ck-wave energy is converted into heat, determinedby the dierence in areas under the Rayleigh line (a straight linein theP-Vplane connecting the initial state and the Hugoniotstate) and the release isentrope (Figure 1). The thermo dynamicsasso ciated with the Rayleigh line is discussed in a monographby Zeldovich and Kompaneets (1960). However this treatment isnot well known by uidor solid dynamists. In the case of two-and three-dimensional wave propagation, the shock amplitudeis also reduced as the wave propagates into progressively largervolumes. In some materials, phase transitions to high-pressurephases (HPP) can take place up on sho ck compression. Up on un-loading the reverse transition usually occurs at lower pressures,giving rise to strongly irreversible stress-strain relations. This isseen graphically as a substantial area inside the Hugoniot-releaseisentrop e loop (Figure 2b a reversible mo del is shownin Fig-ure 2a for comparison). Notably this area in the pressure-volumeplane represents internal energy density dep osited in the media.In the absence of phase changes, this internal energy increase isirreversible heat With irreversible phase changes, this energy isabsorb ed, in part, by the structure change. Because of the higherdensity and change of interaction potential between atoms in thehigh pressure phase, the release isentrope is steep er for the high-pressure phase, thus the rarefaction wave velo city is higher andovertakes the sho ck front faster. This mechanism provides addi-tional attenuation to shock-wave propagation and has potentialapplications in situations where stress waveattenuation is impor-tant.2Journal of The Mechanics and Physics of Solids 47 (1999) 763-783Previously quartz and quartz-b earing ro cks have been mo deledby Swegle (1990) and Sekine et al. (1995). The present study iscentered on GeO2, a crystal-chemical analog of SiO2. Under shockconditions a phase change to a rutile structured regime begins at8 GPa versus15 GPa for quartz along the Hugoniot, andwith a larger density change (== 71:7%, v. 61.8% for the -quartz!stishovite transition (Table 1)). Therefore it is exp ectedto be a slightly better sho ckattenuator. In this pap er, we presentthe rst exp erimental results on release adiabats of SiO2(fusedquartz) and glassy GeO2, and a mo del of the eect of the GeO2'sphase change on wave attenuation. We then numerically simulatethe eect of its phase change on spherical sho ck-wave propaga-tion, and nally, we present an analytical model for qualitativecomparison with our simulations.2 HUGONIOT AND RELEASE ADIABAT DATA FOR FUSEDQUARTZHugoniot experiments on fused quartz have been conducted byWackerle (1962), Fowles (1967), Graham (1974) among others,and mo deled by Swegle (1990). Here we present unpublishedHugoniot and release adiabat data on fused quartz up to 37 GPa,from the earlier work of Ahrens and colleagues. The data areshown in Table 2 and Figure 3.2.1 EXPERIMENTAL METHODSThe sho ck waves were generated by explosively accelerated planeyer plates (e.g.Ahrens (1987)). To determine the sho ck statein a sample, the sho ck velo city in the sample and the velocityimparted tothe free-surface of the driver plate were measured.These velo cities and the measured initial sample densities areused in an imp edance match solution to obtain the Hugoniotstate. Sho ck waves in fused quartz display a Hugoniot elastic3Journal of The Mechanics and Physics of Solids 47 (1999) 763-783limit precursor (Wackerle, 1962). The intermediate particle ve-lo cities due to the elastic sho ck are approximately one-half ofthe asso ciated free-surface velocities, which were measured. Thetimes at which the shock fronts arrived at the sample free sur-face were measured and used to calculate the resp ective sho ckvelo cities. The nal sho ck states in fused quartz were obtainedby using the imp edance match metho d, taking into account theintermediate sho ck states. Sho ck and free-surfacevelo city datawere recorded with a high-sp eed streak camera.The release isentrop e is de ned by the lo cus of states throughwhichshocked material passes up on b eing isentropically returnedto atmospheric pressure. Thus for any Hugoniot a family of


Download Effect of Irreversible phase change
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Effect of Irreversible phase change and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Effect of Irreversible phase change 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?