Glass Tutorial Series: prepared for and produced by the International Material Institute for New Functionality in Glass An NSF sponsored program material herein not for sale Available at www.lehigh.edu/imi DENSIFICATION OF FUSED SILICA BY STRESS OR LASER IRRADIATION John C. Lambropoulos Dept. Mechanical Eng ng, Materials Science Program, & Laboratory for Laser Energetics University of Rochester, Rochester, NY Contributions: Kang-Hua Chen, Lianjqing Zheng, Joe Randi, Kai Xin, Ed Fess, Steve Jacobs & Ansgar Schmid rd Int l Workshop on Flow/Fracture of Advanced Glasses Penn State, October 00
OUTLINE REVIEW Densification expts via pressure Surface response: Grinding & Polishing Indentation (microscopy, SEM, Raman) MD simulations CONSTITUTIVE LAW: Yield function, flow potential, hardening FEM RESULTS: Axisymmetric, Berkovich, Vickers, Knoop MD SIMULATIONS: laser-induced densification Fluence, pulse duration, elastic moduli
POLISHING OF FUSED SILICA & IMPLICATIONS (Yokota et al., 99; Malin & Vedam, 9) Ellipsometric measurement of index of refraction n/n %; Layer thickness 0-0 nm L n 0 densified layer with n > n 0 Reflectance (%) Polishing data, layer n/n0=.0 n 0.0.0 Phase δ = 0 n L/λ (degrees)
DETERMINISTIC MICROGRINDING(Rochester, 99-98) - µm bound diamond abrasive tool Infeed rate ~ µm/min FS produces superior finish, minimal subsurface damage 0 KzFSN rms microroughness, nm 0 0 0 SF BK FS 0 subsurface damage SSD, µm
PERMANENT DENSIFICATION Effects of pressure (and shear) Permanent densification of fused silica @ C C 0 permanent densification ρ/ρ, % 0 Roy & Cohen (9) Christiansen et al. (9) Bridgman & Simon (9) 0 0 0 0 pressure, GPa Pressure transmitting medium in high pressure cell: AlO (high shear) vs AgCl (low shear)
EFFECT OF DENSIFICATION ON n: n/ ρ ~ 0.0 /(g/cc). n vs. ρ in densified glasses (Arndt, 98) 00% TiO glass. Refractive index n... % TiO. % TiO silica glass.........8.9 density, g/cm
Different glasses densify: n vs pressure. n vs densification pressure (Cohen & Roy, 9) Refractive index n D.... n, GeO (-00 C) n, phosphate n, SiO (00 C) n, BO ( C) n, SiO ( C). 0 0 0 pressure p, GPa
Densification of SiO shows saturation and thermal activation (Cohen & Roy, 9) Effect of pressure & temperature on densification Index of refraction n....8 00 C C n, SiO @ C n, SiO @ 00 C. 0 0 0 pressure, GPa
Volume strain vs pressure in fused SiO (Meade & Jeanloz, 98) In situ measurements; diamond cell; scribed grid on sample : mixture of MeOH-EtOH; pressure is hydrostatic up to (at least) 0 GPa V/V0, loading or unloading 0.9 0.8 Loading to more than 0 GPa, then unloading Loading/unloading up to ~ 0 GPa 0. 0 8 0 pressure, GPa
Vickers indentation in quartz, soda-lime glass, FS at RT or at K (Kurkjian et al., 99) QUARTZ: plastic flow by shear @ RT and @ K SODA-LIME GLASS: plastic flow by shear @ RT, densifies @ K FUSED SILICA: densifies both @ RT and @ K Topography of indentation in densified glass: Absence of shear flow lines, Absence of pile up around indent edge
Raman micro-spectroscopy (Perriot et al., 00) Iso-densification lines for ρ/ρ0 (%) under indent : Densification from - %
MD simulation in amorphous SiO @ RT (Tse, 99) Si coordination number increases from to ~ as permanent volume V decreases from V0 to ~0. V0 permanent volume V / V 0. 0.9 0.8 0. 0. 0 8 0 pressure, GPa
MD of uniaxial compression (Vogel et al., 99) Plastic (i.e. permanent) strain vs. total strain (i.e. max load) Permanent strain -[ ε(σ max )- ε(0)] 0. 0. 0.0 RT, 0 Š σ max Š 0 GPa 0 0 0.0 0. 0. ε(σ=σ ) max max load
CONSTITUTIVE LAW: Stress-strain curve Effective stress completion of densification onset of densification permanent strain elastic strain Effective strain
CONSTITUTIVE LAW: FLOW RULE & HARDENING hardening modulus h = - GPa σ ~ "yield stress" 0 α ~ effect of pressure on yield stress α' ~ contribution of densification to total deformation equivalent shear stress τ e σ + dσ / α 0 0 D f = 0 Normality: densification & shear flow (α' = α) dγ p dεp σ / α 0 B f < 0 d p Lack of normality : Densification only (α' = ) p dε = d dγ p= 0 p A σ 0 /α C σ + dσ /α pressure p 0 0
Glass Tutorial Series: prepared for and produced by the International Material Institute for New Functionality in Glass An NSF sponsored program material herein not for sale Available at www.lehigh.edu/imi DENSIFICATION OF FUSED SILICA BY STRESS OR LASER IRRADIATION Part John C. Lambropoulos Dept. Mechanical Eng ng, Materials Science Program, & Laboratory for Laser Energetics University of Rochester, Rochester, NY Contributions: Kang-Hua Chen, Lianjqing Zheng, Joe Randi, Kai Xin, Ed Fess, Steve Jacobs & Ansgar Schmid rd Int l Workshop on Flow/Fracture of Advanced Glasses Penn State, October 00
FEM analysis: D, Berkovich tip Top View
FEM analysis: Effect of densification parameter α & comparison with nanoindentation (Berkovich)
Cavity model: Effect of densification on pressure required for yield
Cavity model: Densification effect on expansion
8 8 FEM analysis: Residual pressure under Berkovich α= 0 (no densification) α = 0. PRESS VALUE -.9E-0 +.E-0 +.E+00 +.E+00 +.9E+00 +.8E+00 +.E+00 8 +.0E+00 9 +.E+00 0 +.9E+00 (a) σ kk Unit: GPa µm 8 90 98 8 9 PRESS VALUE (c) -.8E+0 -.E+0 -.E+0 -.08E+0-9.E+00 -.8E+00 -.8E+00 8 -.E+00 9 -.0E+00 0-8.E-0 σ kk 0 Unit: GPa 9 8 09 µm 98 0 9 8 09 9 8 9 8 9 8 8 0 9 0 0 0
8 9 9 0 8 FEM analysis: Residual von-mises stress α = 0 (no densification) α= 0. (b) (d) MISES VALUE +.08E+00 +.E+00 +.E+00 +.E+00 +.E+00 +.0E+00 +.9E+00 8 +8.E+00 9 +9.E+00 0 +.08E+0 8 Unit: GPa µm 8 9 0 8 0 8 8 9 MISES VALUE +.8E+00 +.E+00 +.E+00 +.E+00 +9.0E+00 +.09E+0 +.E+0 8 +.E+0 9 +.E+0 0 +.8E+0 Unit: GPa µm 9 8 0 8 09 8 8
FEM analysis: permanent densification for α = 0. Berkovich tip, F = 0 mn SDV VALUE -.00E-0 -.E-0 -.E-0 -.E-0 -.E-0 -.8E-0 -.E-0 8 +.00E-0 µm ε kk p
FEM analysis: Indent surface topography
FEM analysis: Indent surface topography At P = Pmax (fully load) First Pmax, then fully unload QuickTime and a TIFF (LZW) decompressor are needed to see this picture. QuickTime and a TIFF (LZW) decompressor are needed to see this picture.
MD: EFFECTS OF LASE IRRADIATION NVE: Constant energy & constant V NVT: Constant volume and constant temp. Nth: Constant stress and constant enthalpy NtT: Constant stress and constant temp.
NUMERICAL MODEL FOR LASER INTERACTION Potential energy for silica (modified BKS potential: van Beest, 9; Saika et al., 000) U(r ij ) = k C q i q j r ij Coulomb + A ij e b ijrij c ij Buckingham r ij σ ij 0 + ε ij r σ ij ij r ij 0 Lennard Jones +
MD LASER IRRADIATION: Effect of pulse duration & absorbed fluence @ T = 00 K, p = 0 GPa
MD LASER IRRADIATION: Effect of pulse duration @ T = 00 K, p = 0 GPa Absorbed fluence = 0. J/cm^
MD LASER IRRADIATION: Effect of pressure @T = 00 K Higher pressure produces higher densification
MD simulations: Effect of radiation on Young s modulus
MD simulations: Effect of radiation on bulk modulus B
MD simulations: Effect of radiation on glass structure
CONCLUSIONS CONSTITUTIVE LAW: Yield function, flow potential, hardening INDENTATION: Load-displacement curves, residual stresses, topography, Effect of densification on hardening Grinding, Polishing MD SIMULATIONS: Laser-induced densification Effects of pulse duration, fluence, temperature, pressure on Densification, elastic moduli