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Computer Models of Micrometeoroid Impact on Fused Silica Glass - - PowerPoint PPT Presentation
Computer Models of Micrometeoroid Impact on Fused Silica Glass - - PowerPoint PPT Presentation
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
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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.
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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.
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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
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Validation of Computer Model for Fused Silica
1 2 3 4 5 6 7 8 Time (µs) 0.0 0.8 1.6 2.4 3.2 Velocity (mm/µs) Inflection First Wave: Uf = 1.78 mm/µs Up = 0.89 mm/µs Second Wave: Uf = 3.04 mm/µs Up = 1.90 mm/µs 4I Up Uf
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).
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Matching of Crater and Spall, Low-Energy Impact
YS = 56 µ DS = 614 µ 6F Experiment Spall Crater DC = 109 µ YC = 96 µ
The calculation (shaded) matched the crater depth (YC) and diameter (DC) and the spall depth (YS) and diameter (DS).
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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: YC = 103 µ, DC = 63x90 µ, YS = 51 µ, and DS = 740x780 µ.
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Crater and Spall, High-Energy Impact
Crater Spall 7J DS2 = 2768 µ DS1 = 1382 µ DC = 318 µ YC = 291 µ YS = 158 µ Fractures
The impact analysis showed a large region of incipient front-surface
- spall. Not shown is aft surface spall also predicted by the analysis.
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Crater and Spall Dimensions
Energy Type YC (µ) DC (µ) YS (µ) DS (µ) 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
Energy DP (µ) VP (km/s) KE (erg) Low 62 6.2 5.38⋅104 High 124 9.9 1.098⋅106
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Glasses and Their Constituents
Constituents Type ρ (gm/cm³) SiO2 TiO2 B2O3 Na2O Al2O3 Quartz 2.65 ~100
- Fused Silica
(Corning 7940) 2.20 99.9
- Ultra-Low Expansion
(ULE, Corning 7971) 2.21 92.5 7.5
- Borosilicate
(Pyrex, Corning 7740) 2.23 81
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4 2 Vycor 2.2 94
- 5
1
- Soda-Lime (Float)*
2.53 74
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2 *Other constituents: 9% CaO, 3% MgO, & 1% K2O
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Penetration (Crater Depth)
0.7 0.8 0.9 1.0 1.1 1.2 Log(Vp) for Vp in km/s 0.0 0.2 0.4 0.6
- 0.2
Y = Log[(P/dp
1.2)/ρ0.5]
From Fit Pyrex Fused Silica Vycor AU/HIF #1 AU/HIF Data Y-Values #1 #2 AU/HIF 0.465 -0.014 From Fit
- 0.487
AUTODYN 0.460 0.581 AUTODYN AUTODYN AU/HIF #2 P = YC = K⋅dp
1.2⋅ρ0.5⋅VP 0.67,
where P & dP are in cm Historical Data Vycor Pyrex
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Penetration Data for Glass from AU/HIF
0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 log(Vp) 0.0 0.2 0.4 0.6 0.8 1.0 1.2
- 0.2
- 0.4
log[(P/dp
1.2)/ρp 0.5]
FS ULE Selected FS Fit ULE Fit
The FS data lies higher than the ULE data. The scatter is large.
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Surface Displacements Low Energy Impact/One-Inch Disk
0.0 0.1 0.2 0.3
- 0.1
Negative Displacement (µ) Front Surface Y (mm) 2 4 6 8 10 12 14
- 2
- 4
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6F t = 40 µs Aft Surface
The impact affected the glass to a diameter of 20 mm.
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Surface Displacements High Energy Impact/Three-Inch Disk
0.0 0.4 0.8 1.2 Negative Displacement (µ) t = 140 µs Y (mm) 10 20 30 40
- 10
- 20
- 30
- 40
Front Surface 8J (-0.2 µ < D < 1.2 µ Cutoffs) Aft Surface
The impact affected the entire disk (note scales).
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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