John C. Lambropoulos, Tong Fang, Paul D. Funkenbusch, Stephen D. Jacobs, Michael J. Cumbo, and Donald Golini, "Surface microroughness of optical glasses under deterministic microgrinding," Appl. Opt. 35, 4448-4462 (1996)
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.
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All data were reduced by using the Ref. 38 model. Ref. 47 used a load of 500 gf in air; Ref. 48 used indenting loads of 50, 100, and 200 gf in anhydrous methanol; Ref. 34 used 200 gf in air. The bulk measurements of SF6 used the Ref. 49 short-rod technique. The bulk measurements of BK7 and fused silica were done with the double cantilever method of Ref. 50, the single edge-notch three-point bending of Ref. 51, or the strength method, using the Knoop indent of Ref. 31.
The data for the Young’s moduli and Knoop hardness Hk (at 200 gf) are from the Schott Optical Glass (Ref. 46). Parentheses in the E or Hk value show that the property was estimated from those of neighboring glasses.
The Vickers hardness is extracted from the measurements of Ref. 34 with a load of 200 gf. Parentheses in the Hυ value indicate that the Vickers hardness was estimated from the correlation of Hυ and Hk, similar to the one shown in Fig. 3, using the data from Ref. 34.
Parentheses in the Kc value denote that the estimated Hυ for that glass was used. The bulk measurements of Kc for SF1 and UBK7 are from Ref. 51, for F2 are from Ref. 31, and for SF6 are from Refs. 31 and 49.
Uniaxial yield stress σY was estimated by using the model of Ref. 58 (see Appendix A).
Tables (5)
Table 1
Chemical Composition of the Tested Glasses (mol. %)
All data were reduced by using the Ref. 38 model. Ref. 47 used a load of 500 gf in air; Ref. 48 used indenting loads of 50, 100, and 200 gf in anhydrous methanol; Ref. 34 used 200 gf in air. The bulk measurements of SF6 used the Ref. 49 short-rod technique. The bulk measurements of BK7 and fused silica were done with the double cantilever method of Ref. 50, the single edge-notch three-point bending of Ref. 51, or the strength method, using the Knoop indent of Ref. 31.
The data for the Young’s moduli and Knoop hardness Hk (at 200 gf) are from the Schott Optical Glass (Ref. 46). Parentheses in the E or Hk value show that the property was estimated from those of neighboring glasses.
The Vickers hardness is extracted from the measurements of Ref. 34 with a load of 200 gf. Parentheses in the Hυ value indicate that the Vickers hardness was estimated from the correlation of Hυ and Hk, similar to the one shown in Fig. 3, using the data from Ref. 34.
Parentheses in the Kc value denote that the estimated Hυ for that glass was used. The bulk measurements of Kc for SF1 and UBK7 are from Ref. 51, for F2 are from Ref. 31, and for SF6 are from Refs. 31 and 49.
Uniaxial yield stress σY was estimated by using the model of Ref. 58 (see Appendix A).