Residual stress model for CaF2

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.

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References

  1. 1

    E. Stenzel, S. Gogoll, J. Sils, M. Huisinga, H. Johansen, G. Kastner, M. Reichling and E. Matthias: Laser damage of alkaline-earth fluorides at 248 nm and the influence of polishing grades. Appl. Surf. Sci. 109/110, 162 1997

    CAS  Article  Google Scholar 

  2. 2

    R.S. Retherford, R. Sabia and V.P. Sokira: Effect of surface quality on transmission performance for (111) CaF2. Appl. Surf. Sci. 183, 264 2001

    CAS  Article  Google Scholar 

  3. 3

    Z.A. Kukleva and B.I. Lodygin: 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 1982

    Google Scholar 

  4. 4

    S. Arrasmith and S.D. Jacobs: Development of new magnetorheological fluids for polishing CaF2 and KDP. LLE Review. Laboratory for Laser Energetics, University of Rochester 80, 213 1999

    Google Scholar 

  5. 5

    J.W. Yan, J. Tamaki, K. Syoji and T. Kuriyagawa: Single-point diamond turning of CaF2 for nanometric surface. Int. J. Adv. Manu. Technol. 24, 640 2004

    Article  Google Scholar 

  6. 6

    Y. Namba, N. Ohnishi, S. Yoshida, K. Harada and K. Yoshida: Ultra-precision float polishing of calcium fluoride single crystals for deep ultra violet applications. CIRP ANNALS—Man. Technol. 53, 459 2004

    Article  Google Scholar 

  7. 7

    Y. Namba, T. Yoshida, S. Yoshida and K. Yoshida: Surfaces of calcium fluoride single crystals ground with an ultra-precision surface grinder. CIRP ANNALS—Man. Technol. 54, 503 2005

    Article  Google Scholar 

  8. 8

    J.W. Yan, K. Syoji and J. Tamaki: Crystallographic effects in micro/nanomachining of single-crystal calcium fluoride. J. Vac. Sci. Technol., B 22, 46 2004

    CAS  Article  Google Scholar 

  9. 9

    A. Munoz, A.D. Rodriguez and J. Castaing: Slip systems and plastic anisotropy in CaF2. J. Mater. Sci. 29, 6207 1994

    CAS  Article  Google Scholar 

  10. 10

    R. Hill: Generalized constitutive relations for incremental deformation of metals crystals by multislip. J. Mech. Phys. Solids 14, 95 1966

    CAS  Article  Google Scholar 

  11. 11

    R. Hill and J.R. Rice: Constitutive analysis of elastic–plastic crystals at arbitrary strain. J. Mech. Phys. Solids 20, 401 1972

    Article  Google Scholar 

  12. 12

    G.I. Taylor and C.F. Elam: The distortion of an aluminum crystal during a tensile test. Proc. R. Soc. London A 102, 643 1923

    Article  Google Scholar 

  13. 13

    D. Peirce, R.J. Asaro and A. Needleman: An analysis of nonuniform and localized deformation in. ductile single crystals. Acta Metall. 30, 1087 1982

    CAS  Article  Google Scholar 

  14. 14

    Yoshino, T. Aoki, N. Chandrasekaran, T. Shirakashi and R. Komanduri: Finite element simulation of plane strain plastic–elastic indentation on single-crystal silicon. Int. J. Mech. Sci. 43, 313 2001

    Article  Google Scholar 

  15. 15

    Y. Liu, B. Wang, M. Yoshino, S. Roy, H. Lu and R. Komanduri: Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J. Mech. Phys. Solids 53, 2718 2005

    CAS  Article  Google Scholar 

  16. 16

    Y. Wang, D. Raabe, C. Kluber and F. Roters: Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals. Acta Mater. 52, 2229 2004

    CAS  Article  Google Scholar 

  17. 17

    Hibbitt, Karlson, Sorensen: Manual ABAQUS Standard User’s Inc. Version 6.3 (Pawtucket, RI, 2003)

    Google Scholar 

  18. 18

    R.J. Asaro and J.R. Rice: Strain localization in ductile single crystals. J. Mech. Phys. Solids 25, 309 1977

    Article  Google Scholar 

  19. 19

    R.J. Asaro: Crystal plasticity. J. Appl. Mech. 50, 921 1983

    Article  Google Scholar 

  20. 20

    D. Peirce, R.J. Asaro and A. Needleman: Material rate dependence and rate dependence and localization deformation in crystalline solids. Acta Metall. 31, 1951 1983

    CAS  Article  Google Scholar 

  21. 21

    A. Needleman: MRLE-134 Brown University 1981

    Google Scholar 

  22. 22

    J.R. Willis: Hertzian contact of anisotropic bodies. J. Mech. Phys. Solids 14, 163 1966

    Article  Google Scholar 

  23. 23

    Opto-Technological Laboratory http://www.optotl.ru/CaF2Eng.htm (2006).

  24. 24

    J.W. Hutchinson: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. London A 348, 101 1976

    CAS  Article  Google Scholar 

  25. 25

    J.L. Ladison, J.J. Price, J.D. Helfinstine and W.R. Rosch: Hardness, elastic modulus, and fracture toughness bulk properties in Corning calcium fluoride. Proc. SPIE, 5754, 1329 2004

    Google Scholar 

  26. 26

    R.F. Cook and G.M. Pharr: Direct observation and analysis of indentation cracking in glasses and ceramics. J. Am. Ceram. Soc. 73, 787 1990

    CAS  Article  Google Scholar 

  27. 27

    P.P. Hed and D.F. Edwards: Optical-glass fabrication technology. 2. Relationship between surface-roughness and subsurface damage. Appl. Opt. 26, 4677 1987

    CAS  Article  Google Scholar 

  28. 28

    J.A. Randi: Near surface mechanical properties of optical single crystals and surface response to deterministic microgrinding, PhD Thesis, University of Rochester, Rochester, NY (2005)

    Google Scholar 

  29. 29

    P. Franciosi, M. Berveiller and A. Zaoui: Latent hardening in copper and aluminum single crystals. Acta Metall. 28, 273 1980.

    CAS  Article  Google Scholar 

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Acknowledgment

We gratefully appreciate the financial support from the F.J. Horton Fellowship, Laboratory for Laser Energetics, University of Rochester, Rochester, NY.

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Correspondence to Q. Zhang.

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Zhang, Q., Lambropoulos, J.C. Residual stress model for CaF2. Journal of Materials Research 22, 2796–2808 (2007). https://doi.org/10.1557/JMR.2007.0348

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