Features of Cerium Compressibility and Spall Strength in the ( ) Phase– Transformation Region under Explosive Loading V. I. Tarzhanov†, E. A. Kozlov†, Yu. N. Zuev†, D. G. Pankratov†, I. V. Telichko†, A. N. Grachev†, D. M. Gorbachev†, A. V. Vorobyev†, Yu. S. Moreva†, E. V. Kakshina†, N. A. Tsepilov†, E. A. Shmakov†, N. V. Ivanova†, M. A. Zocher ‡, G. T. Gray III ‡, F. Cherne ‡ † FSUE “RFNC-VNIITF”, 456770, Russia, Snezhinsk, Chelyabinsk region, P. O. Box 245; E-mail: V. I. Tarzhanov@vniitf. ru ‡Los Alamos National Laboratory , Los-Alamos , USA Joint Russian-American Conference on Advances in Materials Science, 1 August 31 -September 3, 2009, Prague, Czech
Introduction Cerium is the material with very complicated phase diagram. Particularly in cerium, the process of isostructural (with retention of crystal lattice type) – -electronic phase transformation with uniquely high ( 20%) specific volume jump was experimentally discovered more than 50 years ago. Cerium is the only element in Mendeleev's table, in which presence of a critical point is established in the solid phase range, and namely both in the range of positive (compressive), and negative (tensile) stresses. The objectives of this work are as follows: – refinement of data on compressibility of high-purity cerium under its explosive loading in the range of the - - and -liquid phase transformations ; – registration of wave profiles that demonstrate kinetics of high-rate deformation of cerium in the initial -phase and kinetics of the - - electron phase transformation; – determination of spall strength of cerium in the test range of longitudinal stress. 2
For investigation purposes, one used high-purity cerium (99. 99%) with initial density of 6. 75 g/cm 3. Eight wedge samples of size 30 40 6 mm 3 with 12 00 angle were made from special thermo-mechanically processed sheet blank with 6 -mm thickness. The material had a single-phase initial structure and 100 -μm size of equiaxed grains. The free surface of wedge samples was grinded, polished, and after the ionic cleaning, 10 -μm thin cooper layer was applied to it by the vacuumdeposition technique; then this layer was polished up to the required mirror state. Schematic diagrams of experiments on loading of wedge samples with (а) sliding or (b) normal detonation of HE layers a) b) 1–tested sample, 2–screen-cover, 3–slit aperture system (scan pattern) illuminated by explosive light source, 4–layer of plastic HE, which detonates in sliding mode, 5– PETN- or HMX-based HE layer, 3 which detonates in direction orthogonal to screen-cover surface.
Time profiles of free surface velocity for wedge samples and wave velocity in them were recorded by the photochronographic optical lever technique, which allows one to obtain in each experiment 5 -10 analogous optical tracks with spatial and time resolution of 0. 01 mm and 10 ns using SFR-2 M streak camera. High spatial resolution was achieved through the application of the developed computer program «OL Tracing» . The tracing algorithm is setting off the maximum on the photometric traverse profile of each track. Streak camera records of experiment #638 and screen line tracing 2 Time 2 a) 2 2 1 1 Time b) Loading – normal detonation of plastic HE layer, h. HE=5. 0 mm. Film scanning rate is 3. 75 mm/μs. Optical lever: а) – 30. 0 mm, b) – 130. 0 mm (displacement screen lines are not defined). 1 -1 – elastophase precursor, 2 -2 –principle plastic wave. 4
Data on cerium compressibility Cerium compression curves presented in D, u- and σхх, V/V 0 -coordinates are typical for materials with phase transformation and elastic behavior at low σхх. The velocity of elastic precursor (EP) in cerium was 2. 35± 0. 02 km/s. Maximum and minimum rates of phase precursor (PP) were equal to 2. 1 and 1. 7 km/s at ххmax =0. 6 and 0. 8 GPa with wedge thickness of х=2. 2 and 4. 6 mm. The achieved minimum velocity of plastic wave was D 3 min =1. 0 km/s (in laboratory coordinate system). In the coordinate system associated with PP its velocity will come to 0. 84 km/s. This velocity can be treated as an estimate of volume velocity of sound in heated and loose –phase formed on the width of plastic wave front. Dotted lines in figure present the boundaries of cerium regions, in which the single-wave, two-wave elastoplastic configurations, as well as three-wave configurations correspondent to the region of the mixture of - and -phases should exist. Wave velocities of propagation of axial stress amplitude values on fronts of the threewave and single-wave configurations in cerium vs. particle velocities u wave velocity D, km/s 1 2 3 particle velocity u, km/s 1, 2 – states on elastic and phase precursors, 3 – states on plastic wave. I, III – regions of single-wave, two-wave, and tree-wave configurations. 5
Amplitude values of axial stress хх vs. relative specific volume V/V 0 axial stress xx , GPa relative specific volume V/V 0 a) full measurement range, b) area A – enlarged. The curve of cerium compression in coordinates σхх, V/V 0 in the region σхх< 1 GPa is convex upwards. Just this convexity provides an increase in amplitudes of phase precursor as σхх is decreasing in the plastic wave. The best separation between PP and plastic wave having similar wave velocities is achieved with the minimum loading amplitude realized in wedge samples on the maximum wedge thickness. PP is capable of maximum forward running and demonstration of its profile maximum. The VNIITF data on high-purity cerium compressibility agree well with analogous laser-interferometric data obtained in Los-Alamos Laboratory for the metal of the same purity. Our data are characterized by a relatively small scatter of points. They agree well with the shock adiabat in the -region and with isentrope in the region of the mixed - and -phases from the multiphase equation of state for cerium, which was derived by V. M. Elkin, et al. using only static data. The absence of specifics on the cerium-compression curve, which could be indicative of (α-ε) transformation, confirms theoretic prediction that this curve has no intersection with the boundary of α- and ε-phases. Experimental points at ххmax =14 -16 GPa possibly lie near the boundary inside the cerium melting region on the shock adiabat and this is indirectly evidenced by sharp falloff in intensity of the light reflected from the sample free 6 surface.
All three-wave configurations recorded in experiments contain the principle plastic wave and the merging elastic and phase precursors characterized by smoothly growing stress. Particle velocity profiles obtained from tracings of streak records for free surface velocity W(t) bear information on kinetics of elastic precursor, as well as on kinetics of the (γ – α) transformation and relaxation of stresses in cerium). Particle velocity profiles for cerium sample in elastoplastic precursor, exp. #638(a), #636(b) The above curve - is approximation of the maximum states on the phase precursor. Numbers above curves show sample thickness in mm, the upper line of figures – is amplitude хх in GPa. 7
It is obvious that elastic precursor profile smoothly grows up to its maximum parameters umax. EP = 6 m/s, σхх. EP = 0. 1 GPa. In this work, absence of the two-wave elastoplastic structure of compression in streak camera records is associated with low growth of stresses. In the predicted region II of this structure existence, the stress growth in the elastic precursor turns out to be lower than the optical lever method resolution even though the rate of the elastic precursor and plastic waves is almost the same and the run of the elastic wave is small. The merging of elastic and phase precursors is explained by kinetics slowness of stress growth in elastic precursor, as well as by the fact that their wave velocities are almost the same. But we succeeded in recording the separation of the elastic and phase precursors in the bottom range of stresses at σхх = 0. 6 – 1. 6 GPa and wedge thickness of 3. 5 -5 mm. This separation is accompanied by extraction on the phase precursor tip of the shock front with σххmax =0. 4 GPa. The neighborhood of this shock front is referred to as “X” wave. The reason for shock front extraction is the increase of the phase precursor amplitude and steepness. 8
Streak camera records of experiment #646 and tracing of screen lines 2 1 3 2 1 Time Loading – sliding detonation of plastic HE from sample “tip”, h. HE = 0. 99 mm. Scanning velocity on the film is 3. 75 mm/μs. 1 -1– elastoplastic precursor, 9 2 -2 – primary plastic wave, 3 – «Х» wave.
In the tested range of axial stresses, we determined the spall strength of cerium that turned out to be rather low and variable in the range хх* = 0. 2 -0. 4 GPa. The obtained values of spall strength agree with the data of VNIIEF. Thickness of spall layers calculated from the streak camera records was 0. 2 -0. 4 mm. The spall plates of the same thickness were found among the sample fragments recovered in the chamber. Figure illustrates existence of correlation between spall strength and the gradient of negative stress in the spall plane. The figure gives data of experiments with three types of loading devices and two types of HE. Spall strength vs. gradient of negative stresses in spall plane 10
Conclusions 1. The optical lever method was used to obtain new data on compressibility of high-purity cerium explosively loaded in the range σхх = 0. 6– 16 GPa with the high-rate deformation occurring in the initial -phase, as well as in the range of “ - ” and “ liquid” phase transformations. These data are in a good agreement with the published results and have smaller experimental scatter. Theoretical absence of intersection between the shock adiabat and the line of - –phase equilibrium was experimentally confirmed. At хх=14– 16 GPa, the optical lever method registered a sharp falloff in intensity of the light reflected from the free surface of the sample. This falloff can be conditioned by the shock-wave melting of cerium. 2. Registered profiles of stress waves in wedge samples of high-purity cerium demonstrate existence of one common plastoelastic precursor before the plastic wave front at хх≤ 7 GPA. Amplitude of this common complex increases up to 0. 9 -1 GPa with the decrease of loading level down to 3 -4 GPa. Separation of the - –phase and elastic precursors takes place at the bottom levels of loading ( хх=2– 3 ГПа) with the shock front extracted at the phase precursor tip. 3. Spall strength of cerium determined from wave profiles for the velocity of sample free surface is rather low, i. e. 0. 2– 0. 4 GPa. It depends on the gradient of the longitudinal stress in the tensile region. Thickness of the first spall is 0. 2 -0. 4 mm. 11
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