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TECHNICAL PAPERS

Anisotropic Yield Locus Evolution During Cold Pilgering of Titanium Alloy Tubing

[+] Author and Article Information
Richard W. Davies, Mohammad A. Khaleel

Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352

William C. Kinsel

Washington State University, 100 Sprout Road, Richland, WA 99352

Hussein M. Zbib

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920

J. Eng. Mater. Technol 124(2), 125-134 (Mar 26, 2002) (10 pages) doi:10.1115/1.1446472 History: Received October 12, 1999; Revised July 20, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Schemel, United States Patent #4,655,068, 1987.
Dressler,  G., Matucha,  K. H., and Wincierz,  P., 1972, “Yield Loci of Zircaloy Tubing with Different Textures,” Can. Metall. Q., 11, No. 1, pp. 177–184.
Kallstrom,  K., 1972, “Texture and Anisotropy of Zirconium in Relation to Plastic Deformation,” Can. Metall. Q., 11, No. 1, pp. 185–198.
Larson, F., and Zarkades, A., 1974, “Properties of Textured Titanium Alloys,” Metals and Ceramics Information Center, Battelle Columbus Laboratories, 505 King Ave., Columbus OH.
Hill,  R. A., 1948, “Theory of Yielding and Plastic Flow in Anisotropic Metals,” Proc. R. Soc. London, Ser. B, 193, p. 281.
Dieter, G. E., 1972 Mechanical Metallurgy, McGraw Hill, New York, pp. 82–86.
Tenckhoff, E., 1988, “Deformation Mechanisms, Texture, and Anisotropy in Zirconium and Zircaloy,” ASTM STP 966.
Kearns, J. J., 1965, “Thermal Expansion and Preferred Orientation in Zircaloy,” WAPD-TM-472, Westinghouse Electric Corp., Pittsburgh, PA.
Wilson,  S. A., 1989, “Determination of Texture in Zircaloy Using Complete Pole Figures,” Scand. J. Metall., 18, pp. 67–72.
Eisenberg,  M. A., and Yen,  C-F., 1981, “A Thoery of Multiaxial Anisotropic Viscoplasticity,” ASME J. Appl. Mech., 48, pp. 276–284.
Eisenberg,  M. A., and Yen,  C-F., 1984, “The Anisotropic Deformation of Yield Surfaces,” ASME J. Eng. Mater. Technol., 106, pp. 355–360.
Mulot,  S., Hacquin,  A., Montmitonnet,  P., and Aubin,  J. L., 1996, “A fully 3-D finite element simulation of cold pilgering.” J. Mater. Process. Technol., 60, pp. 505–515.

Figures

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Schematic section through cold pilgering rolling area
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Schematic of biaxial test apparatus
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Typical strain versus time curve from the biaxial tensile testing apparatus. Illustrated test represents specimen loaded in a condition of low axial stress.
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Experimental results of biaxial loading showing axial stress versus axial strain, and tangential stress versus tangential strain. Also shown in the 0.2 percent plastic offset linear regression to determine yield stress.
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Experimental yield data for the HFMOD population with associated yield locus. Also shown is a Von Mises (isotropic) yield locus for reference.
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Experimental biaxial yield data for HFMOD, LFMOD, and ARMOD populations with associated yield loci
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Experimental biaxial yield data for the HFMOD, HF, and SRHF populations with the associated yield loci
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(a) Pole figures illustrating the initial and final textures from the pilgering pass using the ARMOD initial size tube and the resulting HFMOD final tube. The pole figure axes labels RD and TD designate the rolling and tangential directions, respectively. (b) Pole figures illustrating the initial and final textures from the pilgering pass using the AR initial size tube and the resulting HF final tube. The pole figure axes labels RD and TD designate the rolling and tangential directions, respectively.
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(a) Schematic illustration of the 2-D finite element model of cold pilgering. (b) Schematic illustration showing the four positions along the pilger reduction where two-dimensional finite element models were constructed (one roll die not shown on bottom-left for clarity).
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Finite element analysis results for the two-dimensional pilgering analysis performed at a point where the total pass was 50% complete. The results shown are the equivalent plastic strains of deformation at a single point of analysis.
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Equivalent plastic strain on the inside diameter surface as a function of model angular position. Each curve represents FEA results at a different axial position in the pass.
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Equivalent plastic strain direction on the inside diameter surface as a function of model angular position. Each curve represents FEA results at a different axial position in the pass.
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Magnitudes of deviatoric stress on the inside diameter surface as a function of model angular position. The curves represent FEA results for one solution at an axial position where the pass is 100% complete.
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Directions of deviatoric stress on the inside and outside diameter surfaces as a function of model angular position. The curves represent FEA results for one solution at an axial position where the pass is 100% complete.
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A π-plane plot illustrating the primary and redundant strain vector resolved to scale and achieve an overall prescribed strain path of the subject pilgering pass
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A π-plane (deviatoric stress space) plot illustrating the proposed hardening vectors produced by plastic strains predicted by the finite element model. The data points shown are from the ARMOD and HFMOD sample populations.

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