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Anisotropy of yielding in a Zr-2.5Nb pressure tube material

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Abstract

The anisotropy of yielding, as measured by the ratio of yield stress in the axial and transverse directions of Zr-2.5Nb pressure tubes used in Canada Deuterium Uranium (CANDU) nuclear reactors, was determined experimentally by testing samples in uniaxial tension. The yield anisotropy was measured in uniaxial tension in samples obtained from the three directions of a Zr-2.5Nb plate and in shear, by testing in torsion “mini” pressure tubes from the same material. From these experiments, the temperature and strain-rate dependence of the yield stress and the dependence of the anisotropy of yielding on temperature were also determined. It is shown that the yield anisotropy of pressure tube material is constant for temperatures up to about 800 K and that the strain-rate sensitivity is also constant up to about 700 K and is equal to ∼0.02. In addition, the activation energy (Q) of this material was estimated by using the temperature dependence and rate sensitivity of the yield stress. It was found to be of the same order of magnitude as that determined earlier by other investigators. A polycrystalline, nonlinear self-consistent model that takes into account the crystallographic texture of the material was used to derive the values of the critical resolved shear stress (CRSS) which are consistent with prismatic, basal, and pyramidal glide and the values of the Hill’s plastic anisotropy coefficients which are consistent with the observed anisotropy of yielding. The model provided an estimate of the complete stress tensor, describing yielding of a Zr-2.5Nb pressure tube material.

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Abbreviations

n :

stress exponent

m = 1/n :

strain-rate sensitivity

f i :

resolved fraction of basal plane normals in direction i, i = R, T, L

φ, ϑ, θ :

Euler angles

α, β :

polar and azimuthal angle, respecively

T c :

texture coefficient

V f :

volume fraction

σ i y :

scalar 0.2 pct yield stress (MPa) in specimen direction i, where i = R, T, L

ε :

viscoplastic strain-rate tensor in the crystal (s−1)

σ′:

deviatoric stress tensor in the crystal (MPa)

\(\bar \varepsilon \) :

overall strain-rate tensor (s−1)

\(\bar \sigma '\) :

applied overall deviatoric stress tensor (MPa)

M c(sec), M (sec) :

secant and tangent compliance tensors, respectively, in the crystal (MPa−1s−1)

M (sec), M (tan) :

secant and tangent compliance tensors of the polycrystal (MPa−1s−1)

s :

type of slip system, s = prismatic (pr), basal (bas), and/or pyramidal (pyr)

m s :

Schmid tensor of slip system s

τ s, γ s0 :

CRSS (MPa) and reference shear strain rate (s−1), respectively

Θ:

domain defining the inclusion

Γ∼ V :

boundary of the HEM defined by domain V

M (tg) :

interaction tensor (MPa−1s−1)

S :

Eshelby tensor

I :

identity tensor

T :

absolute temperature (K)

R:

gas constant (8.3143 × 10−3 kJ/[mole·K])

Q a , Q b :

parameter describing temperature dependence of yield stress (K)

K :

material parameter dependent on temperature (MPa·s)

ε 0 :

pre-exponential factor (s−1)

F, G, H :

Hill’s anisotropy coefficients for diagonal stress components σ A , σ T , σ R

L, M, N :

Hill’s anisotropy coefficients for shear stress components σ AT , σ TR , σ RA

k :

material constant describing dependence of yield stress on grain size (MPa·√m)

d :

grain size (m)

References

  1. D.D. Himbeault, C.K. Chow, and M.P. Puls: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 135–45.

    CAS  Google Scholar 

  2. C.K. Chow, C.E. Coleman, M.H. Koike, A.R. Causey, C.E. Ells, R.R. Hosbons, S. Sagat, V.F. Urbanic, and D.K. Rodgers: in Zirconium in the Nuclear Industry: 11th Int. Symp., ASTM STP 1295, E.R. Bradley and G.P. Sabol, eds., ASTM, Philadelphia, PA, 1996, pp. 469–91.

    Google Scholar 

  3. A.R. Causey, V. Fidleris, S.R. MacEwen, and C.W. Schulte: in Influence of Radiation on Material Properties: 13th Int. Symp.(Part II), ASTM STP 956, F.A. Garner, C.H. Henager, Jr., and N. Igata, eds., ASTM, Philadelphia, PA, 1988, pp. 54–68.

    Google Scholar 

  4. R.A. Holt: J. Nucl. Mater., 1976, vol. 59, pp. 234–42.

    Article  CAS  Google Scholar 

  5. N. Christodoulou, A.R. Causey, R.A. Holt, C.N. Tome, N. Badie, R.J. Klassen, R. Sauve, and C.H. Woo: in Zirconium in the Nuclear Industry: 11th Int. Symp., ASTM STP 1295, E.R. Bradley and G.P. Sabol, eds., ASTM, Philadelphia, PA, 1996, pp. 518–37.

    Google Scholar 

  6. M. Griffiths, C.K. Chow, C.E. Coleman, R.A. Holt, S. Sagat, and V.F. Urbanic: Effects of Radiation on Materials, 16th Int. Symp., ASTM STP 1175, ASTM, Philadelphia, PA, 1994, pp. 1077–1110.

    Google Scholar 

  7. H.-J. Bunge: Texture Analysis in Materials Science, Mathematical Methods, Butterworth and Co., London, 1982 (English translation).

    Google Scholar 

  8. R.A. Holt and E.F. Ibrahim: Acta Metall., 1979, vol. 27, pp. 1319–28.

    Article  CAS  Google Scholar 

  9. P.A. Turner, C.N. Tome, N. Christodoulou, and C.H. Woo: Phil. Mag. A, 1999, vol. 79 (10), pp. 2505–24.

    Article  CAS  Google Scholar 

  10. R.A. Lebensohn and C.N. Tome: Acta Metall. Mater., 1993, vol. 41, pp. 2611–24.

    Article  CAS  Google Scholar 

  11. A. Molinari, G.R. Canova, and S. Ahzi: Acta Metall., 1987, vol. 35, pp. 2983–94.

    Article  CAS  Google Scholar 

  12. J.W. Hutchinson: Proc. R. Soc. London A, 1976, vol. 348, pp. 101–27.

    Article  CAS  Google Scholar 

  13. R.A. Lebensohn, P.A. Turner, J.W. Signorelli, G.R. Canova, and C.N. Tome: Modelling Simulation Mater. Sci. Eng., 1998, vol. 6, pp. 447–65.

    Article  CAS  Google Scholar 

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

    Google Scholar 

  15. C.N. Tome, C.B. So, and C.H. Woo: Phil. Mag., 1993, vol. A67, pp. 917–30.

    Google Scholar 

  16. C.N. Tome: Modelling Simulation Mater. Sci. Eng., in press.

  17. H.J. McQueen and J.J. Jonas: in Treatise on Materials Science and Technology, vol. 6, Plastic Deformation of Materials, Academic Press, New York, NY, 1975, pp. 393–493.

    Google Scholar 

  18. R.S.W. Shewfelt, L.W. Lyall, and D.P. Godin: J. Nucl. Mater., 1984, vol. 125, pp. 228–35.

    Article  CAS  Google Scholar 

  19. E.F. Ibrahim, R. Choubey, and J.J. Jonas: J. Nucl. Mater., 1984, vol. 126, pp. 44–52.

    Article  CAS  Google Scholar 

  20. A. Akhtar: Acta Metall., 1973, vol. 21, pp. 1–11.

    Article  Google Scholar 

  21. A. Akhtar: Metall. Trans. A, 1975, vol. 6A, pp. 1217–22.

    CAS  Google Scholar 

  22. B. Heritier, M.J. Luton, and J.J. Jonas: Met. Sci., 1974, vol. 8, pp. 41–48.

    CAS  Google Scholar 

  23. U.F. Kocks: J. Eng. Mater. Technol., ASME(H), 1976, vol. 98, pp. 76–85.

    CAS  Google Scholar 

  24. H. Mecking and U.F. Kocks: Acta Metall., 1981, vol. 29, pp. 1865–75.

    Article  CAS  Google Scholar 

  25. S.G. Song and G.T. Gray III: Metall. Mater. Trans. A, 1995, vol. 26A, pp. 2665–76.

    CAS  Google Scholar 

  26. S.R. Chen and G.T. Gray III: J. Phys. IV France, 1997, vol. 7, pp. C3-741–C3-746.

    Google Scholar 

  27. J.W.L. Pang, T.M. Holden, P.A. Turner, and T.E. Mason: Acta Metall. Mater., 1999, vol. 47, pp. 373–83.

    CAS  Google Scholar 

  28. J.L. Martin and R.E. Reed-Hill: Trans. AIME, 1964, vol. 230, pp. 780–5.

    CAS  Google Scholar 

  29. J.E. Bailey: J. Nucl. Mater., 1962, vol. 7, pp. 300–10.

    Article  CAS  Google Scholar 

  30. R.E. Reed-Hill: in Deformation Twinning, R.E. Reed-Hill, J.P. Hirth, and H.C. Rogers, eds., Gordon and Breach Science Publishers, New York, NY, 1964, vol. 25, pp. 295–320.

    Google Scholar 

  31. B.A. Cheadle, C.E. Ells, and W. Evans: J. Nucl. Mater., 1967, vol. 23, pp. 199–208.

    Article  CAS  Google Scholar 

  32. P.A. Turner and C.N. Tome: Acta Metall. Mater., 1994, vol. 42, pp. 4143–53.

    Article  CAS  Google Scholar 

  33. A. Seeger: Z. Naturfosch., 1954, vol. 9a, pp. 758–856.

    CAS  Google Scholar 

  34. B.A. Cheadle: in Zirconium in the Nuclear Industry, ASTM STP 633, A.L. Lowe, Jr. and G.W. Parry, eds., ASTM, Philadelphia, PA, 1977, pp. 457–85.

    Google Scholar 

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Authors and Affiliations

  1. Deformation Technology Branch, the CRL, AECL, K0J 1J0, Chalk River, ON, Canada

    N. Christodoulou (Senior Research Scientist)

  2. Materials and Mechanics Branch, the CRL, AECL, K0J 1J0, Chalk River, ON, Canada

    M. Resta Levi (Research Scientist)

  3. IFIR, 2000, Rosario, Rosario, Argentina

    P. A. Turner (Professor)

  4. the Zirconium Metallurgy Department, Ontario Hydro Technologies, M8Z 5S4, Toronto, ON, Canada

    E. T. C. Ho (Principal Research Engineer)

  5. the Fuel Channel Engineering Branch, AECL, L5K 1B2, Mississauga, ON, Canada

    C. K. Chow (Research Scientist)

Authors
  1. N. Christodoulou
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  2. M. Resta Levi
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  3. P. A. Turner
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  4. E. T. C. Ho
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  5. C. K. Chow
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Christodoulou, N., Levi, M.R., Turner, P.A. et al. Anisotropy of yielding in a Zr-2.5Nb pressure tube material. Metall Mater Trans A 31, 409–420 (2000). https://doi.org/10.1007/s11661-000-0278-9

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