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Estimation of Dislocation Density in Cold-Rolled Commercially Pure Titanium by Using Synchrotron Diffraction

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An Erratum to this article was published on 04 June 2014

Abstract

Cold rolling (CR) leads to a heavy changes in the crystallographic texture and microstructure, especially crystal defects, such as dislocations, and stacking faults increase. The microstructure evolution in commercially pure titanium (cp-Ti) deformed by CR at the room temperature was determined by using the synchrotron peak profile analysis of full width at half maximum (FWHM). The computer program ANIZC has been used for the calculation of diffraction contrast factors of dislocations in elastically anisotropic hexagonal crystals. The dislocation density has a minimum value at 40 pct reduction. The increase of the dislocation density at higher deformation levels is caused by the nucleation of new generation of dislocations from the crystallite grain boundaries. The high-cycle fatigue strength (HCF) has a maximum value at 80 pct reduction and it has a minimum value at 40 pct reduction in the commercially pure titanium.

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Notes

  1. ANIZC program was developed by Dr. A. Borbely from the University of Budapest, Hungary.

Abbreviations

RT:

Room temperature

FWHM:

Full width at half maximum

HCF:

High-cycle fatigue strength

CR:

Cold rolling

A 0 :

Original area of the cross section

A d :

Cross-sectional area after deformation

SM:

Starting material

kt:

Notch factor

AL:

Bragg reflection

ALS:

Size coefficient

ADS:

Distortion coefficient

L :

Line vector

g :

Diffraction vector

ε :

Strain

ρ :

Density

b :

Burgers vectors

\( {\bar{C}} \) :

Average contrast factor

F(η):

Wilkens function

Re:

Effective outer cut-off radius of dislocations

λ :

X-ray wavelength

θ :

Diffraction angle

D :

Column length of the crystallites

M :

A constant depending on the effective outer cut-off radius of dislocations

References

  1. M. Burlat, D. Julien, M. Lévesque, T. Bui-Quoc, and M. Bernard: Eng. Fract. Mech., 2008, vol. 75, no. 8, pp. 2042-61.

    Article  Google Scholar 

  2. D.L. Rich and L.F. Impellizzeri: Cyclic Stress–Strain and Plastic Deformation Aspects of Fatigue Crack Growth, American Society for Testing and Materials, Philadelphia, PA, 1997, pp. 153–75.

  3. R.W. Hertzberg: Deformation and Fracture Mechanics of Engineering Materials, Wiley, New York, NY, 1996.

    Google Scholar 

  4. V.B. John: Engineering Materials, Macmillan Education Ltd., London, U.K., 1990.

    Google Scholar 

  5. R.C. Picu and A. Majorell: Mater. Sci. Eng. A, 2002, vol. 326, pp. 306-16.

    Article  Google Scholar 

  6. L. Wcislak, H. Klein, H.J. Bunge, U. Garbe, T. Tschentscher, and J.R. Schneider: J. Appl. Crystallogr., 2002, vol. 35, p. 82.

    Article  Google Scholar 

  7. R.W.K. Honeycombe: The Plastic Deformation of Metals, Edward Arnold, London, U.K., 1984, pp. 12-118.

    Google Scholar 

  8. A. Borbely, J. Dragomir-Cernatescu, G. Ribarik, and T. Ungar: J. Appl. Crystallogr., 2003, vol. 36, pp. 160-62.

    Article  Google Scholar 

  9. T. Ungar and G. Tichy: Phys. Status Solidi, 1999, vol. 171, pp. 425-34.

    Article  Google Scholar 

  10. M. Wilkens: Phys. Status Solidi A Appl. Res., 1970, vol. 2, pp. 359–70.

  11. J.A. Simmons, R. de wit, and R. Bullough: Fundamental Aspects of Dislocation Theory, vol. 2 (317), Nat. Bur. Stand. (U.S.) Spec. Publ., 1970, pp. 1195–221.

  12. M.A. Krivoglaz: X-ray and Neutron Diffraction in Nonideal Crystals, Springer, Berlin, 1996, p. 358.

    Book  Google Scholar 

  13. P. Klimanek and R. Kuzel, Jr.: J. Appl. Crystallogr., 1988, vol. 21, pp. 59-66.

    Article  Google Scholar 

  14. R. Kuzel, Jr. and P. Klimanek: J. Appl. Crystallogr., 1988, vol. 21, p. 363.

    Article  Google Scholar 

  15. R. Kuzel, Jr. and P. Klimanek: J. Appl. Crystallogr., 1989, vol. 22, pp. 299-307.

    Article  Google Scholar 

  16. I.C. Dragomir and T. Ungar: J. Appl. Crystallogr., 2002, vol. 35, pp. 556-64.

    Article  Google Scholar 

  17. G.K. Williamson and W.H. Hall: Acta Metall., 1953, vol. 1, pp. 22-31.

    Article  Google Scholar 

  18. M. Wilkens: Phys. Status Solidi, 1970, vol. 2, p. 359.

    Article  Google Scholar 

  19. C. Dragomir, D.S. Li, G.A. Castello-Branco, H. Garmestani, R.L. Snyder, G. Ribarik, and T. Ungar: Mater. Charact., 2005, vol. 55, pp. 66-74.

    Article  Google Scholar 

  20. T. Ungar and A. Borbely: Appl. Phys. Lett., 1996, vol. 69, p. 3173.

    Article  Google Scholar 

  21. A.J.C. Wilson: Il Nuovo Cimento, 1955, vol. 1, no. 2, pp. 277-83.

    Article  Google Scholar 

  22. I. Groma: Phys. Rev. B, 1998, vol. 57, pp. 7535-42.

    Article  Google Scholar 

  23. R.F. Hearmon: Landolt-Börnstein Tables, Group III, K.-H. Hellwege and A.M. Hellwege, Eds., Springer-Verlag, Berlin, Germany, 1979, vol. 11, pp. 1-154.

  24. D. Tromans: IJRRAS, 2011, vol. 6, no. 4, pp. 4-14.

    Google Scholar 

  25. N. Hansen: Mater. Sci. Technol., 1990, vol. 6, no. 11, pp. 1039-47.

    Article  Google Scholar 

  26. T. Ungar, A. Revesz, and A. Borbely: J. Appl. Crystallogr., 1998, vol. 31, pp. 554-58.

    Article  Google Scholar 

  27. Y.B. Chun, S.H. Yu, S.L. Semiatin, and S.K. Hwang: Mater. Sci. Eng. A, 2005, vol. 398, pp. 209-19.

    Article  Google Scholar 

  28. E.P. DeGarmo, J.T. Black, and R.A. Kohser: Materials and Processes in Manufacturing, 9th ed., Wiley, New York, NY, 2003.

    Google Scholar 

  29. G. Ribarik, T. Ungar, and J. Gubicza: J. Appl. Crystallogr., 2001, vol. 34, pp. 669-76.

    Article  Google Scholar 

  30. K. Mathis, K. Nyilas, A. Axt, I.D. Cernatescu, T. Ungar, and P. Lukac:. Acta Mater., 2004, vol. 52, pp. 2889-94.

    Article  Google Scholar 

  31. Z.B. Sajuri, Y. Miyashita, Y. Hosokai, and Y.J. Mutoh: Int. J. Mech. Sci., 2006, vol. 48, pp. 198-209.

    Article  Google Scholar 

  32. L. Wu, A. Jain, D.W. Brown, G.M. Stoica, S.R. Agnew, B. Clausen, D.E. Fielden, and P.K. Liaw: Acta Mater., 2008, vol. 56, pp. 688-95.

    Article  Google Scholar 

  33. S. Suresh: Fatigue of Materials, Cambridge University Press, Cambridge, U.K., 1998.

    Book  Google Scholar 

  34. Z. Deng, L.L. Wang, D. Zhang, J. Liu, C. Liu, and J. Ma: Med. Sci. Monit., 2014, vol. 20, pp. 163-66.

    Article  Google Scholar 

  35. H.W. Höppel, M. Korn, R. Lapovok, and H. Mughrabi: J. Phys. Conf. Ser., 2010, vol. 240, p. 012147.

    Article  Google Scholar 

Download references

Acknowledgments

One author (Mr. Alkhazraji) would like to thank the Ministry of Higher Education & Scientific Research, Iraq (MoHESR) and the German Academic Exchange Service (DAAD) for supporting his stay at TU Clausthal.

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Authors and Affiliations

  1. Institute of Materials Science and Engineering, Clausthal University of Technology, 38678, Clausthal-Zellerfeld, Germany

    Hasan ALkhazraji (Ph.D. Student), Mohammed Z. Salih (Ph.D. Student), Zhengye Zhong (Ph.D. Student), Mansour Mhaede (Dr.-Ing) & Lothar Wagner (Director)

  2. Institute of Materials Research, Helmholtz Zentrum Geesthacht (HZG), Max-Planckstr.1, 21502, Geesthacht, Germany

    Hans-Günter Brokmeier (Professor) & N. Schell (Scientist)

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  1. Hasan ALkhazraji
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  2. Mohammed Z. Salih
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Correspondence to Hasan ALkhazraji.

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Manuscript submitted November 26, 2013.

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ALkhazraji, H., Salih, M.Z., Zhong, Z. et al. Estimation of Dislocation Density in Cold-Rolled Commercially Pure Titanium by Using Synchrotron Diffraction. Metall Mater Trans B 45, 1557–1564 (2014). https://doi.org/10.1007/s11663-014-0066-3

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