Abstract

Deterministic microgrinding of precision optical components with rigid, computer-controlled machining centers and high-speed tool spindles is now possible on a commercial scale. Platforms such as the Opticam systems at the Center for Optics Manufacturing produce convex and concave spherical surfaces with radii from 5 mm to ∞, i.e., planar, and work diameters from 10 to 150 mm. Aspherical surfaces are also being manufactured. The resulting specular surfaces have a typical rms microroughness of 20 nm, 1 μm of subsurface damage, and a figure error of less than 1 wave peak to valley. Surface roughness under deterministic microgrinding conditions (fixed infeed rate) with bound abrasive diamond ring tools with various degrees of bond hardness is correlated to a material length scale, identified as a ductility index, involving the hardness and fracture toughness of glasses. This result is in contrast to loose abrasive grinding (fixed nominal pressure), in which surface microroughness is determined by the elastic stiffness and the hardness of the glass. We summarize measurements of fracture toughness and microhardness by microindentation for crown and flint optical glasses, and fused silica. The microindentation fracture toughness in nondensifying optical glasses is in good agreement with bulk fracture toughness measurement methods.

© 1996 Optical Society of America

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    [CrossRef]

1994 (2)

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News15–19 (June1994).
[CrossRef]

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

1993 (2)

M. Sakai, R. C. Bradt, “Fracture toughness testing of brittle materials,” Int. Mater. Rev. 38, 53–78 (1993).
[CrossRef]

Y. Namba, M. Abe, “Ultraprecision grinding of optical glasses to produce super-smooth surfaces,” Ann. CIRP 42, 417–420 (1993).
[CrossRef]

1992 (2)

D. Golini, W. Czajkowski, “Microgrinding makes ultrasmooth optics fast,” Laser Focus World 28 (7), 146–150 (1992).

H. Li, R. C. Bradt, “The indentation load/size effect and the measurement of the hardness of vitreous silica,” J. Non-Cryst. Solids 146, 197–212 (1992).
[CrossRef]

1991 (4)

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113, 184–189 (1991).
[CrossRef]

D. Golini, S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt. 30, 2761–2777 (1991).
[CrossRef] [PubMed]

H. H. Pollicove, D. T. Moore, “Optics manufacturing technology moves toward automation,” Laser Focus World 27 (3), 145–148 (1991).

M. G. Schinker, “Subsurface damage mechanisms at highspeed ductile machining of optical glasses,” Precis. Eng. 13, 208–218 (1991).
[CrossRef]

1990 (2)

S. Yoshida, H. Ito, “The present and future of ductileregime grinding of optical parts,” Bull. Jpn. Soc. Precis. Eng. 24, 239–243 (1990).

R. F. Cook, G. M. Pharr, “Direct observation and analysis of indentation cracking in glasses and ceramics,” J. Am. Ceram. Soc. 73, 787–817 (1990).
[CrossRef]

1989 (1)

I. M. Androsov, S. N. Dub, V. P. Maslov, “Unique features associated with using the indentation method for determining the crack resistance of brittle materials,” Sov. J. Opt. Technol. 56, 691–693 (1989).

1987 (3)

1986 (1)

O. Podzimek, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

1985 (1)

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

1983 (1)

R. F. Cook, B. R. Lawn, “A modified indentation toughness technique,” J. Am. Ceram. Soc. 66, C200–C201 (1983).
[CrossRef]

1982 (4)

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, I. stresses and residual stresses,” J. Appl. Phys. 53, 298–311 (1982).
[CrossRef]

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, II. fracture initiation,” J. Appl. Phys. 53, 312–317 (1982).
[CrossRef]

J. Lankford, “Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method,” J. Mater. Sci. Lett. 1, 493–495 (1982).
[CrossRef]

K. Niihara, R. Morena, D. P. H. Hasselman, “Evaluation of KIc of brittle solids by the indentation method with low crack-to-indent ratios,” J. Mater. Sci. Lett. 1, 13–16 (1982).
[CrossRef]

1981 (2)

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

G. S. Khodakov, Y. A. Glukhov, “Fine grinding of optical components with a diamond tool,” Sov. J. Opt. Technol. 48, 428–435 (1981).

1980 (3)

A. L. Ardamatskii, “Principles of diamond tool operation,” Sov. J. Opt. Technol. 47, 613–622 (1980).

G. S. Khodakov, V. P. Korovkin, V. M. Altshuler, “Physical principles of the fine grinding of optical glass with a diamond tool,” Sov. J. Opt. Technol. 47, 552–560 (1980).

B. R. Lawn, A. G. Evans, D. B. Marshall, “Elastic/plastic indentation damage in ceramics: the median/radial crack system,” J. Am. Ceram. Soc. 63, 574–581 (1980).
[CrossRef]

1979 (1)

A. Arora, D. B. Marshall, B. R. Lawn, “Indentation deformation/fracture of normal and anomalous glasses,” J. Non-Cryst. Solids 31, 415–428 (1979).
[CrossRef]

1976 (1)

A. G. Evans, E. A. Charles, “Fracture toughness determination by indentation,” J. Am. Ceram. Soc. 59, 371–372 (1976).
[CrossRef]

1975 (1)

B. R. Lawn, T. Jensen, A. Arora, “Brittleness as an indentation size effect,” J. Mater. Sci. 11, 573–575 (1975).
[CrossRef]

1974 (1)

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

1973 (1)

T. S. Izumitani, I. Suzuki, “Indentation hardness and lapping hardness of optical glass,” Glass Technol. 14, 35–41 (1973).

1969 (1)

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Ceram. Soc. 52, 99–105 (1969).
[CrossRef]

1963 (1)

J. D. Mackenzie, “High-pressure effects on oxide glasses: I. densification in rigid state,” J. Am. Ceram. Soc. 46, 461–470 (1963).
[CrossRef]

1957 (1)

F. K. Aleinikov, “The effect of certain physical and mechanical properties on the grinding of brittle materials,” Sov. Phys. Tech. Phys. 27, 2529–2538 (1957).

Abe, M.

Y. Namba, M. Abe, “Ultraprecision grinding of optical glasses to produce super-smooth surfaces,” Ann. CIRP 42, 417–420 (1993).
[CrossRef]

Aleinikov, F. K.

F. K. Aleinikov, “The effect of certain physical and mechanical properties on the grinding of brittle materials,” Sov. Phys. Tech. Phys. 27, 2529–2538 (1957).

Altshuler, V. M.

G. S. Khodakov, V. P. Korovkin, V. M. Altshuler, “Physical principles of the fine grinding of optical glass with a diamond tool,” Sov. J. Opt. Technol. 47, 552–560 (1980).

Anderson, T. L.

T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 2nd ed. (CRC Press, Cleveland, Ohio, 1995).

Androsov, I. M.

I. M. Androsov, S. N. Dub, V. P. Maslov, “Unique features associated with using the indentation method for determining the crack resistance of brittle materials,” Sov. J. Opt. Technol. 56, 691–693 (1989).

Anstis, G. R.

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

Ardamatskii, A. L.

A. L. Ardamatskii, “Principles of diamond tool operation,” Sov. J. Opt. Technol. 47, 613–622 (1980).

Arora, A.

A. Arora, D. B. Marshall, B. R. Lawn, “Indentation deformation/fracture of normal and anomalous glasses,” J. Non-Cryst. Solids 31, 415–428 (1979).
[CrossRef]

B. R. Lawn, T. Jensen, A. Arora, “Brittleness as an indentation size effect,” J. Mater. Sci. 11, 573–575 (1975).
[CrossRef]

Atwood, M.

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 28–31.

Barker, L. M.

L. M. Barker, “Short bar specimens for KIc measurements,” in Fracture Mechanics Applied to Brittle Materials, S. W. Freiman, ed. (American Society for Testing and Materials, Philadelphia, Pa., 1979), pp. 73–82.
[CrossRef]

Bifano, T. G.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113, 184–189 (1991).
[CrossRef]

Bradt, R. C.

M. Sakai, R. C. Bradt, “Fracture toughness testing of brittle materials,” Int. Mater. Rev. 38, 53–78 (1993).
[CrossRef]

H. Li, R. C. Bradt, “The indentation load/size effect and the measurement of the hardness of vitreous silica,” J. Non-Cryst. Solids 146, 197–212 (1992).
[CrossRef]

Brown, N. J.

N. J. Brown, B. A. Fuchs, “Brittle to shear grinding mode transition for loose abrasive grinding,” Report UCRL-100043 (Lawrence Livermore National Laboratory, Livermore, Calif, 1988).

N. J. Brown, B. A. Fuchs, “Shear mode grinding,” in 43rd Annual Symposium on Frequency Control (IEEE, New York, 1989), pp. 606–610.
[CrossRef]

N. J. Brown, B. A. Fuchs, P. P. Hed, I. F. Stowers, “The response of isotropic brittle materials to abrasive processes,” in 43rd Annual Symposium on Frequency Control (IEEE, New York, 1989), pp. 611–616.
[CrossRef]

Buijs, M.

M. Buijs, K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci.28, 3014–3020 (1993).
[CrossRef]

Chanticul, P.

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

Charles, E. A.

A. G. Evans, E. A. Charles, “Fracture toughness determination by indentation,” J. Am. Ceram. Soc. 59, 371–372 (1976).
[CrossRef]

Chiang, S. S.

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, I. stresses and residual stresses,” J. Appl. Phys. 53, 298–311 (1982).
[CrossRef]

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, II. fracture initiation,” J. Appl. Phys. 53, 312–317 (1982).
[CrossRef]

Clauer, A. H.

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

Cook, R. F.

R. F. Cook, G. M. Pharr, “Direct observation and analysis of indentation cracking in glasses and ceramics,” J. Am. Ceram. Soc. 73, 787–817 (1990).
[CrossRef]

R. F. Cook, B. R. Lawn, “A modified indentation toughness technique,” J. Am. Ceram. Soc. 66, C200–C201 (1983).
[CrossRef]

Cumbo, M.

M. Cumbo, The Institute of Optics, University of Rochester, Rochester, New York 14627 (personal communication), 1992.

M. Cumbo, “Chemo-mechanical interactions in optical polishing,” Ph.D. dissertation (University of Rochester, Rochester, New York, 1993).

Czajkowski, W.

D. Golini, W. Czajkowski, “Microgrinding makes ultrasmooth optics fast,” Laser Focus World 28 (7), 146–150 (1992).

Diness, A. M.

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

Dow, T. A.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113, 184–189 (1991).
[CrossRef]

Dub, S. N.

I. M. Androsov, S. N. Dub, V. P. Maslov, “Unique features associated with using the indentation method for determining the crack resistance of brittle materials,” Sov. J. Opt. Technol. 56, 691–693 (1989).

Edwards, D. F.

Evans, A. G.

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, I. stresses and residual stresses,” J. Appl. Phys. 53, 298–311 (1982).
[CrossRef]

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, II. fracture initiation,” J. Appl. Phys. 53, 312–317 (1982).
[CrossRef]

B. R. Lawn, A. G. Evans, D. B. Marshall, “Elastic/plastic indentation damage in ceramics: the median/radial crack system,” J. Am. Ceram. Soc. 63, 574–581 (1980).
[CrossRef]

A. G. Evans, E. A. Charles, “Fracture toughness determination by indentation,” J. Am. Ceram. Soc. 59, 371–372 (1976).
[CrossRef]

A. G. Evans, “Fracture toughness: the role of indentation techniques,” in Fracture Mechanics Applied to Brittle Materials, S. W. Freiman, ed. (American Society for Testing and Materials, Philadelphia, Pa., 1979), pp. 112–135.
[CrossRef]

A. G. Evans, D. B. Marshall, “Wear mechanisms in ceramics,” in Fundamentals of Friction and Wear of Materials, D. A. Rigney, ed. (American Society for Metals, Metals Park, Ohio, 1981), pp. 441–452.

Fang, T.

J. C. Lambropoulos, T. Fang, A. Lindquist, D. Golini, “Mechanics aspects of the Twyman effect under loose abrasive grinding, loose abrasive microgrinding, and deterministic microgrinding conditions,” Ceram. Trans. (to be published).

J. C. Lambropoulos, T. Fang, S. Xu, S. M. Gracewski, “Constitutive law for the densification of fused silica, with applications in polishing and microgrinding,” in Optical Manufacturing and Testing, V. J. Doherty, ed., Proc. SPIE2536, 275–286 (1995).

Feltz, A.

A. Lindquist, S. D. Jacobs, A. Feltz, “Surface preparation technique for rapid measurement of subsurface damage depth,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper SMC3-1/57.

Ferreira, C.

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 28–31.

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N. J. Brown, B. A. Fuchs, “Brittle to shear grinding mode transition for loose abrasive grinding,” Report UCRL-100043 (Lawrence Livermore National Laboratory, Livermore, Calif, 1988).

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Funkenbusch, P. D.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

J. C. Lambropoulos, P. D. Funkenbusch, D. J. Quesnel, S. M. Gracewski, R. F. Gans, “Mechanics and materials issues in optics manufacturing,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering, (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 370–373.

P. D. Funkenbusch, S. M. Gracewski, “Tool property characterization,” presented at the Optifab 1994 Conference, Rochester, N.Y., 17–18 October 1994.

P. D. Funkenbusch, Y. Y. Zhou, T. Takahashi, D. J. Quesnel, J. C. Lambropoulos, “Characterization of fine abrasive particles for optical fabrication,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 46–52 (1995).

Gans, R. F.

J. C. Lambropoulos, P. D. Funkenbusch, D. J. Quesnel, S. M. Gracewski, R. F. Gans, “Mechanics and materials issues in optics manufacturing,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering, (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 370–373.

Glukhov, Y. A.

G. S. Khodakov, Y. A. Glukhov, “Fine grinding of optical components with a diamond tool,” Sov. J. Opt. Technol. 48, 428–435 (1981).

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H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News15–19 (June1994).
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Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
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D. Golini, W. Czajkowski, “Microgrinding makes ultrasmooth optics fast,” Laser Focus World 28 (7), 146–150 (1992).

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[CrossRef] [PubMed]

J. C. Lambropoulos, T. Fang, A. Lindquist, D. Golini, “Mechanics aspects of the Twyman effect under loose abrasive grinding, loose abrasive microgrinding, and deterministic microgrinding conditions,” Ceram. Trans. (to be published).

D. Golini, S. D. Jacobs, “Transition between brittle and ductile mode in loose abrasive grinding,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 80–91 (1990).

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 28–31.

Gracewski, S. M.

P. D. Funkenbusch, S. M. Gracewski, “Tool property characterization,” presented at the Optifab 1994 Conference, Rochester, N.Y., 17–18 October 1994.

J. C. Lambropoulos, P. D. Funkenbusch, D. J. Quesnel, S. M. Gracewski, R. F. Gans, “Mechanics and materials issues in optics manufacturing,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering, (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 370–373.

J. C. Lambropoulos, T. Fang, S. Xu, S. M. Gracewski, “Constitutive law for the densification of fused silica, with applications in polishing and microgrinding,” in Optical Manufacturing and Testing, V. J. Doherty, ed., Proc. SPIE2536, 275–286 (1995).

Hasselman, D. P. H.

K. Niihara, R. Morena, D. P. H. Hasselman, “Evaluation of KIc of brittle solids by the indentation method with low crack-to-indent ratios,” J. Mater. Sci. Lett. 1, 13–16 (1982).
[CrossRef]

Hed, P. P.

Heuer, A. H.

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

Hill, R.

R. Hill, The Mathematical Theory of Plasticity (Oxford U. Press, New York, 1950).

Ito, H.

S. Yoshida, H. Ito, “The present and future of ductileregime grinding of optical parts,” Bull. Jpn. Soc. Precis. Eng. 24, 239–243 (1990).

Izumitani, T. S.

T. S. Izumitani, I. Suzuki, “Indentation hardness and lapping hardness of optical glass,” Glass Technol. 14, 35–41 (1973).

T. S. Izumitani, “Lapping hardness of optical glass,” Hoya Tech. Rep. HGW-O-7E (Hoya Glass Works, Tokyo, Japan, 1971).

T. S. Izumitani, Optical Glass (American Institute of Physics, New York, N.Y., 1986).

Jacobs, S. D.

D. Golini, S. D. Jacobs, “Physics of loose abrasive microgrinding,” Appl. Opt. 30, 2761–2777 (1991).
[CrossRef] [PubMed]

D. Golini, S. D. Jacobs, “Transition between brittle and ductile mode in loose abrasive grinding,” in Advanced Optical Manufacturing and Testing, L. R. Baker, P. B. Reid, G. M. Sanger, eds., Proc. SPIE1333, 80–91 (1990).

A. Lindquist, S. D. Jacobs, A. Feltz, “Surface preparation technique for rapid measurement of subsurface damage depth,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper SMC3-1/57.

Jensen, T.

B. R. Lawn, T. Jensen, A. Arora, “Brittleness as an indentation size effect,” J. Mater. Sci. 11, 573–575 (1975).
[CrossRef]

Johnson, H.

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

Karow, H. H.

H. H. Karow, Fabrication Methods for Precision Optics (Wiley, New York, 1993).

Khodakov, G. S.

G. S. Khodakov, Y. A. Glukhov, “Fine grinding of optical components with a diamond tool,” Sov. J. Opt. Technol. 48, 428–435 (1981).

G. S. Khodakov, V. P. Korovkin, V. M. Altshuler, “Physical principles of the fine grinding of optical glass with a diamond tool,” Sov. J. Opt. Technol. 47, 552–560 (1980).

Korovkin, V. P.

G. S. Khodakov, V. P. Korovkin, V. M. Altshuler, “Physical principles of the fine grinding of optical glass with a diamond tool,” Sov. J. Opt. Technol. 47, 552–560 (1980).

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M. Buijs, K. Korpel-Van Houten, “A model for lapping of glass,” J. Mater. Sci.28, 3014–3020 (1993).
[CrossRef]

Lambropoulos, J. C.

J. C. Lambropoulos, T. Fang, S. Xu, S. M. Gracewski, “Constitutive law for the densification of fused silica, with applications in polishing and microgrinding,” in Optical Manufacturing and Testing, V. J. Doherty, ed., Proc. SPIE2536, 275–286 (1995).

J. C. Lambropoulos, T. Fang, A. Lindquist, D. Golini, “Mechanics aspects of the Twyman effect under loose abrasive grinding, loose abrasive microgrinding, and deterministic microgrinding conditions,” Ceram. Trans. (to be published).

J. C. Lambropoulos, “Mechanical, thermal, diffusional, and geometrical length scales in polishing and grinding,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 97–100.

J. C. Lambropoulos, P. D. Funkenbusch, D. J. Quesnel, S. M. Gracewski, R. F. Gans, “Mechanics and materials issues in optics manufacturing,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering, (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 370–373.

P. D. Funkenbusch, Y. Y. Zhou, T. Takahashi, D. J. Quesnel, J. C. Lambropoulos, “Characterization of fine abrasive particles for optical fabrication,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 46–52 (1995).

Lankford, J.

J. Lankford, “Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method,” J. Mater. Sci. Lett. 1, 493–495 (1982).
[CrossRef]

Lawn, B. R.

R. F. Cook, B. R. Lawn, “A modified indentation toughness technique,” J. Am. Ceram. Soc. 66, C200–C201 (1983).
[CrossRef]

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

B. R. Lawn, A. G. Evans, D. B. Marshall, “Elastic/plastic indentation damage in ceramics: the median/radial crack system,” J. Am. Ceram. Soc. 63, 574–581 (1980).
[CrossRef]

A. Arora, D. B. Marshall, B. R. Lawn, “Indentation deformation/fracture of normal and anomalous glasses,” J. Non-Cryst. Solids 31, 415–428 (1979).
[CrossRef]

B. R. Lawn, T. Jensen, A. Arora, “Brittleness as an indentation size effect,” J. Mater. Sci. 11, 573–575 (1975).
[CrossRef]

Li, H.

H. Li, R. C. Bradt, “The indentation load/size effect and the measurement of the hardness of vitreous silica,” J. Non-Cryst. Solids 146, 197–212 (1992).
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Liedes, J.

J. Liedes, “Opticam SM update,” in Current Developments in Optical Design and Optical Engineering II, R. E. Fischer, W. J. Smith, eds., Proc. SPIE1752, 153–157 (1992).

Lindquist, A.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

A. Lindquist, S. D. Jacobs, A. Feltz, “Surface preparation technique for rapid measurement of subsurface damage depth,” in Optical Computing, Vol. 9 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), paper SMC3-1/57.

D. Golini, A. Lindquist, M. Atwood, C. Ferreira, “Influence of process parameters in deterministic microgrinding,” in Optical Fabrication and Testing, Vol. 13 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 28–31.

J. C. Lambropoulos, T. Fang, A. Lindquist, D. Golini, “Mechanics aspects of the Twyman effect under loose abrasive grinding, loose abrasive microgrinding, and deterministic microgrinding conditions,” Ceram. Trans. (to be published).

Mackenzie, J. D.

J. D. Mackenzie, “High-pressure effects on oxide glasses: I. densification in rigid state,” J. Am. Ceram. Soc. 46, 461–470 (1963).
[CrossRef]

Marshall, D. B.

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, I. stresses and residual stresses,” J. Appl. Phys. 53, 298–311 (1982).
[CrossRef]

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, II. fracture initiation,” J. Appl. Phys. 53, 312–317 (1982).
[CrossRef]

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

B. R. Lawn, A. G. Evans, D. B. Marshall, “Elastic/plastic indentation damage in ceramics: the median/radial crack system,” J. Am. Ceram. Soc. 63, 574–581 (1980).
[CrossRef]

A. Arora, D. B. Marshall, B. R. Lawn, “Indentation deformation/fracture of normal and anomalous glasses,” J. Non-Cryst. Solids 31, 415–428 (1979).
[CrossRef]

A. G. Evans, D. B. Marshall, “Wear mechanisms in ceramics,” in Fundamentals of Friction and Wear of Materials, D. A. Rigney, ed. (American Society for Metals, Metals Park, Ohio, 1981), pp. 441–452.

Maslov, V. P.

I. M. Androsov, S. N. Dub, V. P. Maslov, “Unique features associated with using the indentation method for determining the crack resistance of brittle materials,” Sov. J. Opt. Technol. 56, 691–693 (1989).

Matsumoto, R. L. K.

R. L. K. Matsumoto, “Evaluation of fracture toughness determination methods as applied to ceria-stabilized tetragonal zirconia polycrystal,” J. Am. Ceram. Soc. 70, C366–C368 (1987).
[CrossRef]

McColm, I. J.

I. J. McColm, Ceramic Hardness (Plenum, New York, 1990).

Mincer, P. N.

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

Moore, D. T.

H. H. Pollicove, D. T. Moore, “Optics manufacturing technology moves toward automation,” Laser Focus World 27 (3), 145–148 (1991).

H. H. Pollicove, D. T. Moore, “Center for Optics Manufacturing overview,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 44–47.

Morena, R.

K. Niihara, R. Morena, D. P. H. Hasselman, “Evaluation of KIc of brittle solids by the indentation method with low crack-to-indent ratios,” J. Mater. Sci. Lett. 1, 13–16 (1982).
[CrossRef]

Namba, Y.

Y. Namba, M. Abe, “Ultraprecision grinding of optical glasses to produce super-smooth surfaces,” Ann. CIRP 42, 417–420 (1993).
[CrossRef]

Niihara, K.

K. Niihara, R. Morena, D. P. H. Hasselman, “Evaluation of KIc of brittle solids by the indentation method with low crack-to-indent ratios,” J. Mater. Sci. Lett. 1, 13–16 (1982).
[CrossRef]

Pharr, G. M.

R. F. Cook, G. M. Pharr, “Direct observation and analysis of indentation cracking in glasses and ceramics,” J. Am. Ceram. Soc. 73, 787–817 (1990).
[CrossRef]

Podzimek, O.

O. Podzimek, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

O. Podzimek, “Residual stress and deformation energy under ground surfaces of brittle solids,” Tech. Rep. WB-85-16 (Twente University of Technology, Enschede, The Netherlands, 1986).

O. Podzimek, “Deformation energy under optical surfaces,” in High Power Lasers: Sources, Laser-Material Interactions, High Excitations, and Fast Dynamics, E. W. Kreutz, A. Quenzer, D. Schuoecker, eds., Proc. SPIE801, 221–225 (1987).

Pollicove, H. H.

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News15–19 (June1994).
[CrossRef]

H. H. Pollicove, D. T. Moore, “Optics manufacturing technology moves toward automation,” Laser Focus World 27 (3), 145–148 (1991).

H. H. Pollicove, D. T. Moore, “Center for Optics Manufacturing overview,” in Optical Fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 44–47.

Quesnel, D. J.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

J. C. Lambropoulos, P. D. Funkenbusch, D. J. Quesnel, S. M. Gracewski, R. F. Gans, “Mechanics and materials issues in optics manufacturing,” in Proceedings of the Ninth Annual Meeting of the American Society for Precision Engineering, (American Society for Precision Engineering, Raleigh, N.C., 1994), pp. 370–373.

P. D. Funkenbusch, Y. Y. Zhou, T. Takahashi, D. J. Quesnel, J. C. Lambropoulos, “Characterization of fine abrasive particles for optical fabrication,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 46–52 (1995).

Roberts, D. E.

S. Wiederhorn, D. E. Roberts, “Fracture mechanics study of skylab windows,” Rep. 10892, prepared for NASA Manned Spacecraft Center, Structures and Mechanics Division, PR1-168-022, T-5330A (National Bureau of Standards, Washington, D.C., 1972).

Ruckman, J.

H. H. Pollicove, D. Golini, J. Ruckman, “Computer aided optics manufacturing,” Opt. Photon. News15–19 (June1994).
[CrossRef]

Sakai, M.

M. Sakai, R. C. Bradt, “Fracture toughness testing of brittle materials,” Int. Mater. Rev. 38, 53–78 (1993).
[CrossRef]

Scattergood, R. O.

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113, 184–189 (1991).
[CrossRef]

Schinker, M. G.

M. G. Schinker, “Subsurface damage mechanisms at highspeed ductile machining of optical glasses,” Precis. Eng. 13, 208–218 (1991).
[CrossRef]

Shetty, D. K.

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

Stowers, I. F.

N. J. Brown, B. A. Fuchs, P. P. Hed, I. F. Stowers, “The response of isotropic brittle materials to abrasive processes,” in 43rd Annual Symposium on Frequency Control (IEEE, New York, 1989), pp. 611–616.
[CrossRef]

Suzuki, I.

T. S. Izumitani, I. Suzuki, “Indentation hardness and lapping hardness of optical glass,” Glass Technol. 14, 35–41 (1973).

Takahashi, T.

P. D. Funkenbusch, Y. Y. Zhou, T. Takahashi, D. J. Quesnel, J. C. Lambropoulos, “Characterization of fine abrasive particles for optical fabrication,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 46–52 (1995).

Wiederhorn, S.

S. Wiederhorn, D. E. Roberts, “Fracture mechanics study of skylab windows,” Rep. 10892, prepared for NASA Manned Spacecraft Center, Structures and Mechanics Division, PR1-168-022, T-5330A (National Bureau of Standards, Washington, D.C., 1972).

Wiederhorn, S. M.

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Ceram. Soc. 52, 99–105 (1969).
[CrossRef]

Wright, I. G.

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

Xu, S.

J. C. Lambropoulos, T. Fang, S. Xu, S. M. Gracewski, “Constitutive law for the densification of fused silica, with applications in polishing and microgrinding,” in Optical Manufacturing and Testing, V. J. Doherty, ed., Proc. SPIE2536, 275–286 (1995).

Yoshida, S.

S. Yoshida, H. Ito, “The present and future of ductileregime grinding of optical parts,” Bull. Jpn. Soc. Precis. Eng. 24, 239–243 (1990).

Zhou, Y.

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

Zhou, Y. Y.

P. D. Funkenbusch, Y. Y. Zhou, T. Takahashi, D. J. Quesnel, J. C. Lambropoulos, “Characterization of fine abrasive particles for optical fabrication,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 46–52 (1995).

Ann. CIRP (2)

Y. Namba, M. Abe, “Ultraprecision grinding of optical glasses to produce super-smooth surfaces,” Ann. CIRP 42, 417–420 (1993).
[CrossRef]

O. Podzimek, “Residual stress and deformation energy under ground surfaces of brittle solids,” Ann. CIRP 35, 397–400 (1986).
[CrossRef]

Appl. Opt. (3)

Bull. Jpn. Soc. Precis. Eng. (1)

S. Yoshida, H. Ito, “The present and future of ductileregime grinding of optical parts,” Bull. Jpn. Soc. Precis. Eng. 24, 239–243 (1990).

Glass Technol. (1)

T. S. Izumitani, I. Suzuki, “Indentation hardness and lapping hardness of optical glass,” Glass Technol. 14, 35–41 (1973).

Int. Mater. Rev. (1)

M. Sakai, R. C. Bradt, “Fracture toughness testing of brittle materials,” Int. Mater. Rev. 38, 53–78 (1993).
[CrossRef]

J. Am. Ceram. Soc. (9)

A. G. Evans, E. A. Charles, “Fracture toughness determination by indentation,” J. Am. Ceram. Soc. 59, 371–372 (1976).
[CrossRef]

S. M. Wiederhorn, “Fracture surface energy of glass,” J. Am. Ceram. Soc. 52, 99–105 (1969).
[CrossRef]

J. D. Mackenzie, “High-pressure effects on oxide glasses: I. densification in rigid state,” J. Am. Ceram. Soc. 46, 461–470 (1963).
[CrossRef]

Y. Zhou, P. D. Funkenbusch, D. J. Quesnel, D. Golini, A. Lindquist, “Effect of etching and imaging mode on the measurement of subsurface damage in microground optical glasses,” J. Am. Ceram. Soc. 77, 3277–3280 (1994).
[CrossRef]

B. R. Lawn, A. G. Evans, D. B. Marshall, “Elastic/plastic indentation damage in ceramics: the median/radial crack system,” J. Am. Ceram. Soc. 63, 574–581 (1980).
[CrossRef]

G. R. Anstis, P. Chanticul, B. R. Lawn, D. B. Marshall, “A critical evaluation of indentation techniques for measuring fracture toughness: I. direct crack measurements,” J. Am. Ceram. Soc. 64, 533–543 (1981).
[CrossRef]

R. L. K. Matsumoto, “Evaluation of fracture toughness determination methods as applied to ceria-stabilized tetragonal zirconia polycrystal,” J. Am. Ceram. Soc. 70, C366–C368 (1987).
[CrossRef]

R. F. Cook, G. M. Pharr, “Direct observation and analysis of indentation cracking in glasses and ceramics,” J. Am. Ceram. Soc. 73, 787–817 (1990).
[CrossRef]

R. F. Cook, B. R. Lawn, “A modified indentation toughness technique,” J. Am. Ceram. Soc. 66, C200–C201 (1983).
[CrossRef]

J. Amer. Ceram. Soc. (1)

S. M. Wiederhorn, H. Johnson, A. M. Diness, A. H. Heuer, “Fracture of glass in vacuum,” J. Amer. Ceram. Soc. 57, 337– 341 (1974).
[CrossRef]

J. Appl. Phys. (2)

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, I. stresses and residual stresses,” J. Appl. Phys. 53, 298–311 (1982).
[CrossRef]

S. S. Chiang, D. B. Marshall, A. G. Evans, “The response of solids to elastic/plastic indentation, II. fracture initiation,” J. Appl. Phys. 53, 312–317 (1982).
[CrossRef]

J. Eng. Ind. (1)

T. G. Bifano, T. A. Dow, R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113, 184–189 (1991).
[CrossRef]

J. Mater. Sci. (2)

B. R. Lawn, T. Jensen, A. Arora, “Brittleness as an indentation size effect,” J. Mater. Sci. 11, 573–575 (1975).
[CrossRef]

D. K. Shetty, I. G. Wright, P. N. Mincer, A. H. Clauer, “Indentation fracture of WC-Co cermets,” J. Mater. Sci. 20, 1873–1882 (1985).
[CrossRef]

J. Mater. Sci. Lett. (2)

J. Lankford, “Indentation microfracture in the Palmqvist crack regime: implications for fracture toughness evaluation by the indentation method,” J. Mater. Sci. Lett. 1, 493–495 (1982).
[CrossRef]

K. Niihara, R. Morena, D. P. H. Hasselman, “Evaluation of KIc of brittle solids by the indentation method with low crack-to-indent ratios,” J. Mater. Sci. Lett. 1, 13–16 (1982).
[CrossRef]

J. Non-Cryst. Solids (2)

A. Arora, D. B. Marshall, B. R. Lawn, “Indentation deformation/fracture of normal and anomalous glasses,” J. Non-Cryst. Solids 31, 415–428 (1979).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Load dependence of the Vickers microhardness for some optical glasses. The hardness was measured at loads of 2, 5, 10, 25, 50, 100, 200, 500, and 1000 gf.

Fig. 2
Fig. 2

Comparison of measured H υ with published values of the Knoop hardness from the Hoya and Schott glass catalogs. The open squares are the Vickers data from Ref. 34.

Fig. 3
Fig. 3

Dependence of crack length c on load P for typical optical glasses.

Fig. 4
Fig. 4

Correlation with Knoop hardness (from Ref. 46) of the measured K c , extracted from c(P) with the model Ref. 38.

Fig. 5
Fig. 5

Measured ultrasonic wave speeds for different bond hardness designations.

Fig. 6
Fig. 6

Measured Vickers microhardness for different bond hardness designations.

Fig. 7
Fig. 7

Comparison of the measured SSD and the SR (measured with the Zygo MX interferometer). For each glass, ~12 different samples were used for the roughness and two samples for the SSD measurements.

Fig. 8
Fig. 8

Correlation of measured SR (with Zygo MX interferometer) with the Knoop hardness published in the Ref. 46. For flint silicate glasses the SR increases with H k ; it decreases for the crown silicate optical glasses.

Fig. 9
Fig. 9

Correlation of measured SR (with Zygo MX interferometer) with ductility index Ξ = (K c /H k )2 of various optical glasses. The correlation holds for both flint and crown glasses, as well as fused silica. The straight line, with slope 4.2 ± 0.5 A/nm, has correlation R = 0.95.

Fig. 10
Fig. 10

Correlation of measured Vickers hardness (open squares are from Ref. 34) with σ Y as calculated from Ref. 58.

Fig. 11
Fig. 11

Correlation of measured SR (with Zygo MX interferometer) with total height R p of the plastic zone in a crack tip growing under mode-I (opening) conditions. The straight-line fit has correlation R = 0.95.

Fig. 12
Fig. 12

Correlation of measured SR (with Zygo MX interferometer) with critical depth of cut d c , from Ref. 15. The straight line, with slope 2.1 ± 0.3 A/nm, has correlation R = 0.94.

Fig. 13
Fig. 13

Correlation of measured SR (with Zygo NV interferometer) with the Knoop hardness of optical glasses for (a) softer L tools, (b) medium N tools, (c) harder T tools.

Fig. 14
Fig. 14

Correlation of measured SR (with Zygo NV interferometer) with ductility index Ξ = (K c /H k )2 for various optical glasses for (a) softer L tools, (b) medium N tools, (c) harder T tools. Power-law fitting gives an exponent of 1.5 ± 0.1 for the dependence of SR on Ξ, with correlation R = 0.92–0.99.

Tables (5)

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Table 1 Chemical Composition of the Tested Glasses (mol. %)

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Table 2 Range of Measured Indentation Diagonals and Vickers Hardnesses, and Parameters H and D 0 Describing the ISE for the Used Optical Glasses a

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Table 3 Coefficients in Correlating Measured Crack Size c to Applied Load P a

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Table 4 Mechanical Properties of Representative Optical Glasses a

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Table 5 Extracted Fracture Toughness

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

H υ = H ( 1 + D 0 D ) ,
c = α P 2 / 3 + β P .
K c = H D / 2 ( E H ) 0 . 4 10 f ( x ) , x = log 10 ( c D / 2 ) , f ( x ) = 1 . 59 0 . 34 x 2 . 02 x 2 + 11 . 23 x 3 24 . 97 x 4 + 16 . 32 x 5 ,
υ = M ρ .
Ξ = ( K c H k ) 2 .
R p 2 0 . 35 π ( K c σ Y ) 2 .
SR R p 2 0 . 35 π ( K c σ Y ) 2 ,
rms SR ( NV ) Ξ m .
rms SR ( MX ) [ rms SR ( NV ) ] n ,
rms SR ( MX ) Ξ m n .
p = 2 3 [ 1 + 3 ln ( b a ) ] σ Y .
( b a ) 3 = E 3 ( 1 ν ) σ Y .
p H υ .
( E / H υ ) 3 ( 1 ν ) 1 ( σ Y / H υ ) = exp [ 1 + 3 / 2 ( σ Y / H υ ) ]

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