Computer Models of Micrometeoroid Impact on Fused Silica Glass Mirrors Hypervelocity Impact Symposium December 2003 Presented by David Davison Shock Transients, Inc., PO Box 5357, Hopkins, MN 55343-2357 USA (952) 944-3539, x101/944-8170 fax/dkd@shocktrans.com Co-Authors Burton Cour-Palais, Xiangyang Quan, T.J. Holmquist, Lester M. Cohen, Ron Ramsey, Ramona Cummings Sponsor NASA NGST/JWST Project HVIS03-1
Summary of Presentation � Objectives/Strategy/Outcome � Validation of computer model for glass � Results of cratering analysis � Analysis and Auburn University/Hypervelocity Impact Facility (AU/HIF) data in the context of historical data � Surface displacements � Conclusions/Recommendations HVIS03-2
Objectives � Review data on hypervelocity impact on glass. � Develop a computer model for glass suitable for analysis of impacts at high velocities. � Match the crater and spall parameters for impacts into glass from low-energy tests at AU/HIF. � Blindly predict the crater and spall parameters for impacts into glass (to be compared to results from high-energy tests at AU/HIF). � Damp the calculations to static solutions at late time for further analysis of the influence of impact on mirror optics. HVIS03-3
Strategy for Impact Analysis � Develop a context for the impact analysis and testing by examining data from terrestrial experiments. � For the fused silica model, include data from experiments at very high pressures, the first-order phase transformation to Stishovite, and a strength model that depends on pressure and strain rate. � Use coupled smooth particle hydrodynamics (SPH) and Lagrange representations of objects. � Vary the spall parameter to match the crater from the impact test at low-energy. � Use the same settings for the impact analysis at high energy. � Run to late time for both low and high energy impacts. HVIS03-4
Outcome � Obtained new fits to historical data on crater and spall in glass � Validated the computer model for the glass � Matched the low-energy impact calculation to historical trends and to the averaged result of tests at AU/HIF � Matched the high-energy impact calculation to historical trends but not to the averaged result of tests at AU/HIF � Predicted the effect of low-and high-energy impacts on the shape of the mirror HVIS03-5
Validation of Computer Model for Fused Silica Velocity (mm/µs) Uf 3.2 Second Wave: Uf = 3.04 mm/µs 2.4 Up = 1.90 mm/µs First Wave: 1.6 Uf = 1.78 mm/µs Up Inflection Up = 0.89 mm/µs 0.8 4I 0.0 0 1 2 3 4 5 6 7 8 Time (µs) The computer model for the fused silica reproduced the first and second waves observed in impact experiments by Wackerle ( J. Appl. Phys. , p.922, March 1962). HVIS03-6
Matching of Crater and Spall, Low-Energy Impact D S = 614 µ D C = 109 µ Spall Y S = 56 µ Y C = 96 µ Experiment 6F Crater The calculation (shaded) matched the crater depth (Y C ) and diameter (D C ) and the spall depth (Y S ) and diameter (D S ). HVIS03-7
AU/HIF Test of Low-Energy Impact in Fused Silica For this test the particle velocity was 5.6 km/s and its diameter, 57 µ . The crater and spall were nonsymmetric. The crater and spall dimen- sions were: Y C = 103 µ , D C = 63x90 µ , Y S = 51 µ , and D S = 740x780 µ . HVIS03-8
Crater and Spall, High-Energy Impact D S2 = 2768 µ D S1 = 1382 µ Spall D C = 318 µ Y S = 158 µ Y C = 291 µ 7J Crater Fractures The impact analysis showed a large region of incipient front-surface spall. Not shown is aft surface spall also predicted by the analysis. HVIS03-9
Crater and Spall Dimensions Y C ( µ ) D C ( µ ) Y S ( µ ) D S ( µ ) Energy Type Low AU/HIF* 97 91 51 681 Low AUTODYN 96 109 56 614 High AU/HIF* 74 68 34 516 High From Fit 234 243 - 3,356 High AUTODYN 291 318 158 2,768 *Average of three Definition of Low and High Energy D P ( µ ) Energy V P (km/s) KE (erg) 5.38 ⋅ 10 4 Low 62 6.2 1.098 ⋅ 10 6 High 124 9.9 HVIS03-10
Glasses and Their Constituents Constituents ρ Type SiO 2 TiO 2 B 2 O 3 Na 2 O Al 2 O 3 (gm/cm³) Quartz 2.65 ~100 - - - - Fused Silica 2.20 99.9 - - - - (Corning 7940) Ultra-Low Expansion 2.21 92.5 7.5 - - - (ULE, Corning 7971) Borosilicate 2.23 81 - 13 4 2 (Pyrex, Corning 7740) Vycor 2.2 94 - 5 1 - Soda-Lime (Float)* 2.53 74 - - 11 2 *Other constituents: 9% CaO, 3% MgO, & 1% K 2 O HVIS03-11
Penetration (Crater Depth) P = Y C = K ⋅ d p 1.2 ⋅ρ 0.5 ⋅ V P 1.2 )/ ρ 0.5 ] 0.67 , AUTODYN Y = Log[(P/d p where P & d P are in cm 0.6 AU/HIF #1 From Fit Vycor Pyrex Historical Data 0.4 Vycor Pyrex AUTODYN Fused Silica 0.2 AU/HIF #2 Y-Values #1 #2 AU/HIF 0.465 -0.014 0.0 From Fit - 0.487 AUTODYN 0.460 0.581 AU/HIF Data -0.2 0.7 0.8 0.9 1.0 1.1 1.2 Log(V p ) for V p in km/s HVIS03-12
Penetration Data for Glass from AU/HIF 1.2 )/ ρ p 0.5 ] log[(P/d p FS 1.2 ULE Selected 1.0 0.8 0.6 FS Fit 0.4 0.2 ULE Fit 0.0 -0.2 -0.4 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 log(V p ) The FS data lies higher than the ULE data. The scatter is large. HVIS03-13
Surface Displacements Low Energy Impact/One-Inch Disk Negative Displacement (µ) 0.3 t = 40 µs 6F 0.2 Front Surface 0.1 0.0 Aft Surface -0.1 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 Y (mm) The impact affected the glass to a diameter of 20 mm. HVIS03-14
Surface Displacements High Energy Impact/Three-Inch Disk Negative Displacement (µ) 1.2 (-0.2 µ < D < 1.2 µ Cutoffs) t = 140 µs 0.8 8J Front Surface 0.4 Aft Surface 0.0 -40 -30 -20 -10 0 10 20 30 40 Y (mm) The impact affected the entire disk (note scales). HVIS03-15
Conclusions � Historical glass impact data should guide interpretation of analysis and test results � AUTODYN matched cratering and spall data and predicted late-time surface shapes � The fused silica penetration data lay above the ULE data � The scatter in the AU/HIF data was large Recommendations � Obtain more data on glass impact at AU/HIF � For future work: - Consider an energy-dependent EOS (e.g., Sesame) - Examine the effect of temperature on cratering and spall HVIS03-16
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