Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-18T05:15:18.887Z Has data issue: false hasContentIssue false
  • English
  • Français

Residual stress model for CaF2

Published online by Cambridge University Press:  31 January 2011

Q. Zhang  and
J.C. Lambropoulos
Q. Zhang*
Affiliation:
Department of Mechanical Engineering, Laboratory for Laser Energetics, and Center for Optics Manufacturing, University of Rochester, Rochester, New York 14627
J.C. Lambropoulos
Affiliation:
Department of Mechanical Engineering, Laboratory for Laser Energetics, and Center for Optics Manufacturing, University of Rochester, Rochester, New York 14627
*
a)Address all correspondence to this author. e-mail: qizhang@me.rochester.edu
Get access

Abstract

Nanoindentation tests and finite element analysis that considers elastic-mesoplastic deformation for single crystals were used to investigate the mechanical properties of CaF2 under spherical indentation. The goal was to gain a better understanding of microfractures and crystalline anisotropy and their effect on the surface quality of CaF2 during manufacturing. In this analysis, indentations of the three main crystallographic planes (100), (110), and (111) were studied and compared to examine the effects of crystalline anisotropy on the load–displacement curves, surface profiles, contact radius, spherical hardness, stress distributions, and cleavage at two stages, namely at the maximum indentation load and after the load had been removed. Our model results were compared with experimental observation of surface microroughness, subsurface damage, and material removal rate in grinding of CaF2.

Keywords

SimulationOpticalNanoscale
Type
Articles
Information
Journal of Materials Research , Volume 22 , Issue 10 , October 2007 , pp. 2796 - 2808
Copyright
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Stenzel, E., Gogoll, S., Sils, J., Huisinga, M., Johansen, H., Kastner, G., Reichling, M. and Matthias, E.: Laser damage of alkaline-earth fluorides at 248 nm and the influence of polishing grades. Appl. Surf. Sci. 109/110, 162 1997CrossRefGoogle Scholar
2Retherford, R.S., Sabia, R. and Sokira, V.P.: Effect of surface quality on transmission performance for (111) CaF2. Appl. Surf. Sci. 183, 264 2001CrossRefGoogle Scholar
3Kukleva, Z.A. and Lodygin, B.I.: Effect of the anisotropy of the physical and mechanical-properties of fluorite crystals on the shape accuracy of a polished surface. Sov. J. Opt. Technol. 49, 227 1982Google Scholar
4Arrasmith, S. and Jacobs, S.D.: Development of new magnetorheological fluids for polishing CaF2 and KDP. LLE Review. Laboratory for Laser Energetics, University of Rochester 80, 213 1999Google Scholar
5Yan, J.W., Tamaki, J., Syoji, K. and Kuriyagawa, T.: Single-point diamond turning of CaF2 for nanometric surface. Int. J. Adv. Manu. Technol. 24, 640 2004CrossRefGoogle Scholar
6Namba, Y., Ohnishi, N., Yoshida, S., Harada, K. and Yoshida, K.: Ultra-precision float polishing of calcium fluoride single crystals for deep ultra violet applications. CIRP ANNALS—Man. Technol. 53, 459 2004CrossRefGoogle Scholar
7Namba, Y., Yoshida, T., Yoshida, S. and Yoshida, K.: Surfaces of calcium fluoride single crystals ground with an ultra-precision surface grinder. CIRP ANNALS—Man. Technol. 54, 503 2005CrossRefGoogle Scholar
8Yan, J.W., Syoji, K. and Tamaki, J.: Crystallographic effects in micro/nanomachining of single-crystal calcium fluoride. J. Vac. Sci. Technol., B 22, 46 2004CrossRefGoogle Scholar
9Munoz, A., Rodriguez, A.D. and Castaing, J.: Slip systems and plastic anisotropy in CaF2. J. Mater. Sci. 29, 6207 1994CrossRefGoogle Scholar
10Hill, R.: Generalized constitutive relations for incremental deformation of metals crystals by multislip. J. Mech. Phys. Solids 14, 95 1966CrossRefGoogle Scholar
11Hill, R. and Rice, J.R.: Constitutive analysis of elastic–plastic crystals at arbitrary strain. J. Mech. Phys. Solids 20, 401 1972CrossRefGoogle Scholar
12Taylor, G.I. and Elam, C.F.: The distortion of an aluminum crystal during a tensile test. Proc. R. Soc. London A 102, 643 1923Google Scholar
13Peirce, D., Asaro, R.J. and Needleman, A.: An analysis of nonuniform and localized deformation in. ductile single crystals. Acta Metall. 30, 1087 1982CrossRefGoogle Scholar
14Yoshino, , Aoki, T., Chandrasekaran, N., Shirakashi, T. and Komanduri, R.: Finite element simulation of plane strain plastic– elastic indentation on single-crystal silicon. Int. J. Mech. Sci. 43, 313 2001CrossRefGoogle Scholar
15Liu, Y., Wang, B., Yoshino, M., Roy, S., Lu, H. and Komanduri, R.: Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J. Mech. Phys. Solids 53, 2718 2005CrossRefGoogle Scholar
16Wang, Y., Raabe, D., Kluber, C. and Roters, F.: Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals. Acta Mater. 52, 2229 2004CrossRefGoogle Scholar
17Hibbitt, , Karlson, , Sorensen, : Manual ABAQUS Standard User’s Inc. Version 6.3 (Pawtucket, RI, 2003)Google Scholar
18Asaro, R.J. and Rice, J.R.: Strain localization in ductile single crystals. J. Mech. Phys. Solids 25, 309 1977CrossRefGoogle Scholar
19Asaro, R.J.: Crystal plasticity. J. Appl. Mech. 50, 921 1983CrossRefGoogle Scholar
20Peirce, D., Asaro, R.J. and Needleman, A.: Material rate dependence and rate dependence and localization deformation in crystalline solids. Acta Metall. 31, 1951 1983CrossRefGoogle Scholar
21Needleman, A.: MRLE-134 Brown University 1981Google Scholar
22Willis, J.R.: Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids 14, 163 1966CrossRefGoogle Scholar
23Opto-Technological Laboratory http://www.optotl.ru/CaF2Eng.htm (2006).Google Scholar
24Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. London A 348, 101 1976Google Scholar
25Ladison, J.L., Price, J.J., Helfinstine, J.D. and Rosch, W.R.: Hardness, elastic modulus, and fracture toughness bulk properties in Corning calcium fluoride. Proc. SPIE, 5754, 1329 2004CrossRefGoogle Scholar
26Cook, R.F. and Pharr, G.M.: Direct observation and analysis of indentation cracking in glasses and ceramics. J. Am. Ceram. Soc. 73, 787 1990CrossRefGoogle Scholar
27Hed, P.P. and Edwards, D.F.: Optical-glass fabrication technology. 2. Relationship between surface-roughness and subsurface damage. Appl. Opt. 26, 4677 1987CrossRefGoogle ScholarPubMed
28Randi, J.A.: Near surface mechanical properties of optical single crystals and surface response to deterministic microgrinding, PhD Thesis, University of Rochester, Rochester, NY (2005)Google Scholar
29Franciosi, P., Berveiller, M. and Zaoui, A.: Latent hardening in copper and aluminum single crystals. Acta Metall. 28, 273 1980.CrossRefGoogle Scholar