On yield loci of HY80, HY100 steels and Ti-6AI-2Nb-1Ta-0.8Mo
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This research was supported by the National Science Foundation under grant DMR 79-24268 and by the National Aeronautics and Space Administration under grant NSG 7645. REFERENCES 1. J.P. Gabathuler and F. Weinberg: Metall. Trans. B, 1983, vol. 14B, pp. 733-41. 2. A.L. Maples and D. R. Poirier: Metall. Trans. B, 1984, vol. 15B, pp. 163-71. 3. D.N. Petrakis, M. C. Flemings, and D. R. Poirier: Modeling of Casting and Welding Processes, D. Apelian and H. D. Brody, eds., TMSAIME, Warrendale, PA, 1981, pp. 285-312. 4. R. Mehrabian, M. Keane, and M.C. Flemings: Metall. Trans. A, 1970, vol. 1, pp. 1209-20. 5. M.C. Flemings and G.E. Nereo: Trans. AIME, 1967, vol. 239, pp. 1449-61. 6. M.C. Flemings, R. Mehrabian, and G. E. Nereo: Trans. AIME, 1968, vol. 242, pp. 41-49. 7. M.C. Flemings and G.E. Nereo: Trans. AIME, 1968, vol. 242, pp. 50-55. 8. I. Ohnaka and T. Fukusako: Trans. ISIJ, 1981, vol. 21, pp. 485-94. 9. C.L. Jeanfils, J. H. Chen, and H. J. Klein: Modeling of Casting and Welding Processes, D. Apelian and H.D. Brody, eds., TMS-A1ME, Warrendale, PA, 1981, pp. 312-32. 10. T.S. Piwonka and M.C. Flemings: Trans. AIME, 1966, vol. 236, pp. 1157-65. 11. T. Takahashi, M. Kudoh, and K. Yodoshi: J. Japan Inst. Metals, 1979, vol. 43, pp. 1086-89. 12. T. Takahashi and M. Kudoh: Report of the 19th Comm., Japan Society for the Promotion of Science, Report No. 10227-271, 1980.
On Yield Loci of HY80, HY100 Steels and Ti-6AI-2Nb-ITa-0.8Mo K. S. CHAN, U.S. L I N D H O L M , and J. WISE It is well established that the plastic response of isotropic metals or alloys subjected to multiaxial states of stress can be characterized by the J2-based von Mises criterion (J2 is the second deviatoric stress invariant). For a yon Mises solid, the yield function and the plastic strain ratio p for plane stress (0"3 = 0) are as follows: ~ -
+
de~ deP~
2a -
P
=
2 -
2
--
1 a
-
[11
0"2 ;
a
=
- -
o'1
[2]
K. S. CHAN, Research Engineer, and U. S. LINDHOLM, Director, are with the Department of Materials Sciences, Southwest Research Institute, 6220 Culebra Road, P.O. Drawer 28510, San Antonio, TX 78284. J. WISE is Technical Assistant/Project Manager, Underwater Explosions Research Division, David Taylor Naval Ship R & D Center, Norfolk Naval Shipyard, Portsmouth, VA 23709. Manuscript submitted June 5, 1984. METALLURGICALTRANSACTIONS A
where o-t and 0"2 are the principal stresses, and 0"y is the yield stress of the material under uniaxial tension. It has long been recognized that metals such as copper, aluminum, and mild steel exhibit slight deviations to Eq. [1]. 2,3 The effective stress-strain curves of these materials have been found to vary with the stress state, and the apparent hardening behavior at or near the stress state of plane strain is lower when compared to that measured at either uniaxial or equibiaxial tension. In addition, the incremental plastic strain ratio at a given stress state has also been found to deviate from the von Mises predicted value. Considered as second order effects, 4 these small deviations are often neglect
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