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Numerical simulation of the X-ray stress analysis technique in polycrystalline materials under elastic loading

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Abstract

In this article, the correlation between the local stress distributions and the average stresses obtained by X-ray measurement is studied through numerical modeling. The finite element method (FEM) is used to simulate the local stress distributions within a three-dimensional random aggregate of anisotropic and isotropic single crystals under uniaxial elastic tension. The local stresses are calculated for polycrystalline W, Al, or Cu slabs with the same geometry and crystallite distribution. The stress/strain values in the crystallites that satisfy the diffraction condition are then used to simulate the X-ray data that would be obtained if the diffraction peaks from such aggregates were actually measured. In particular, the 200, 222, and 420 reflections are analyzed. The correlations between the far-field stress, the local stresses, and the average stresses determined through X-ray analysis are presented.

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References

  1. Measurement of Residual and Applied Stress Using Neutron Diffraction, Michael T. Hutchings and Aaron D. Krawitz, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.

    Google Scholar 

  2. Proc. 4th Int. Conf. on Residual Stresses, Michael R. James, ed., Society of Experimental Mechanics, Bethel, CN, 1994.

    Google Scholar 

  3. J. Stickforth: Techn. Mitt. Krupp, 1966, vol. 24, pp. 89–102.

    Google Scholar 

  4. H. Dölle: J. Appl. Cryst., 1979, vol. 12, pp. 489–501.

    Article  Google Scholar 

  5. I.C. Noyan and J.B. Cohen: Residual Stress: Measurement by Diffraction and Interpretation, Springer-Verlag, Inc., New York, NY, 1987.

    Google Scholar 

  6. R. Hill: Proc. Phys. Soc., 1952, vol. A65, pp. 349–54.

    Google Scholar 

  7. R. Hill: Proc. R. Soc. London A, 1972, vol. 326, pp. 131–47.

    Article  Google Scholar 

  8. C.M. Sayers: Phil. Mag. A, 1984, vol. 49, pp. 243–62.

    CAS  Google Scholar 

  9. T. Mura: Micromechanics of Defects in Solids, 2nd ed., Kluwer Publishers, The Netherlands, 1987.

    Google Scholar 

  10. Y. Song and I.C. Noyan: Phil. Mag. A, 1996, vol. 73, pp. 1105–12.

    CAS  Google Scholar 

  11. F. Bollenrath, V. Hauk, and E.H. Müller: Z. Metallkd., 1967, vol. 58, pp. 76–82.

    CAS  Google Scholar 

  12. C.E. Murray and I.C. Noyan: IBM Research Division, Yorktown Heights, NY, unpublished research, 1996.

  13. W. Reimers: Measurement of Residual and Applied Stress Using Neutron Diffraction, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992, pp. 159–70.

    Google Scholar 

  14. W. Voigt: Lehrbuch del Kristallphysik, B.G. Teubner, Leipzig/Berlin, 1910.

    Google Scholar 

  15. A. Reuss: Z. Angew. Math. Mech., 1929, vol. 9, pp. 49–58.

    CAS  Google Scholar 

  16. J.D. Eshelby: Proc. R. Soc., 1957, vol. A241, pp. 376–96.

    Google Scholar 

  17. E. Kroner: J. Mech. Phys. Solids, 1977, vol. 25, pp. 137–55.

    Article  Google Scholar 

  18. Micromechanics and Inhomogeneity, The Toshio Mura Anniversary Volume, G.J. Weng, M. Taya, and H. Abe, eds., Springer, New York, NY, 1990.

    Google Scholar 

  19. W.L. Kreher and A. Molinari: J. Mech. Phys. Solids, 1993, vol. 41, pp. 1955–77.

    Article  CAS  Google Scholar 

  20. Joël Krier: Doctoral Thesis, Universite de Metz, Metz, Cedex France, Jan. 1993.

    Google Scholar 

  21. P. Van Houtte and L. De Buyser: Acta Metall., 1993, vol. 41, pp. 323–36.

    Article  Google Scholar 

  22. A. Baczmanski, K. Wierzbanowski, P. Lipinski, R.B. Helmholdt, G. Ekambaranathan, and B. Pathiraj: Phil. Mag. A, 1994, vol. 69, pp. 437–49.

    CAS  Google Scholar 

  23. Karel Van Acker: Doctoral Thesis, Katholieke Universiteit Leuven, Leuven, Belgium, Sept. 1996.

    Google Scholar 

  24. C.M. Brakman: Phil. Mag. A, 1987, vol. 55, pp. 39–58.

    Google Scholar 

  25. I.C. Noyan and L.T. Nguyen: Adv. X-Ray Analysis, 1988, vol. 31, pp. 191–204.

    Google Scholar 

  26. I.C. Noyan and L.T. Nguyen: Adv. X-Ray Analysis, 1989, vol. 32, pp. 355–64.

    Google Scholar 

  27. I.C. Noyan and L.S. Schadler: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 341–47.

    CAS  Google Scholar 

  28. John P. Hirth and Jens Lothe: Theory of Dislocations, 2nd ed., Wiley Interscience, New York, NY, 1982, pp. 836–37.

    Google Scholar 

  29. Richard W. Hertzberg: Deformation and Fracture Mechanics of Engineering Materials, 4th ed., John Wiley & Sons, Inc., New York, NY, 1996, pp. 13–15.

    Google Scholar 

  30. Abaqus User’s Manual, Version 5.5, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI, 1996.

  31. T.D. Riney: J. Appl. Phys., 19961, vol. 32, pp. 454–61.

    Article  Google Scholar 

  32. W.A. Brantley: J. Appl. Phys., 1973, vol. 44, pp. 534–35.

    Article  CAS  Google Scholar 

  33. V. Hauk: Adv. X-Ray Analysis, 1992, vol. 35A, pp. 449–60.

    Google Scholar 

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Authors and Affiliations

  1. the IBM Semiconductor Research and Development Center, 12533, Hopewell Junction, NY

    D. Chidambarrao (Advisory Engineer)

  2. the Henry Krumb School of Mines, Department of Chemical Engineering, Materials Science and Mining Engineering, Columbia University, 10027, New York, NY

    Y. C. Song (Graduate Student)

  3. the IBM Research Division, 10598, Yorktown Heights, NY

    I. C. Noyan (Research Staff Member)

Authors
  1. D. Chidambarrao
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  2. Y. C. Song
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  3. I. C. Noyan
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Chidambarrao, D., Song, Y.C. & Noyan, I.C. Numerical simulation of the X-ray stress analysis technique in polycrystalline materials under elastic loading. Metall Mater Trans A 28, 2515–2525 (1997). https://doi.org/10.1007/s11661-997-0009-6

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  • DOI: https://doi.org/10.1007/s11661-997-0009-6

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