Abstract
A mathematical model has been developed to predict the internal stresses generated in a steel ingot during thermal processing. The thermal history of the ingot has been predicted by a finite-element, heat-flow model, the subject of the first part of this two-part paper, which serves as input to the stress model. The stress model has been formulated for a two-dimensional transverse plane at mid-height of the ingot and is a transient, elasto-viscoplastic, finite-element analysis of the thermal stress field. Salient features of the model include the incorporation of time-temperature and temperature-dependent mechanical properties, and volume changes associated with nonequilibrium phase transformation. Model predictions demonstrate that the development of internal stresses in the ingot during thermal processing can be directly linked to the progress of the phase transformation front. Moreover, the low strain levels calculated indicate that metallurgical embrittlement must be very important to the formation of cracks in addition to the development of high tensile stresses.
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J. Mathew and H. Brody:Nuclear Metallurgy, 1976, vol. 20, Part 2, pp. 978–90.
F.G. Rammerstorfer, C. Jaquemar, D. Fischer, and H. Wiesinger:Numerical Methods in Thermal Problems, July 1979, pp. 712–22.
A. Grill and K. Schwerdtfeger:Ironmaking and Steelmaking, 1979, vol. 3, pp. 131–35.
A. Palmaers, A. Etienne, and J. Mignon:Stahl und Eisen, Sept. 1979, vol. 99, No. 19, pp. 1039–50.
J. R. Williams, R. W. Lewis, and K. Morgan:Int. J. Numer. Methods in Eng., 1979, vol. 14, No. 1, pp. 1–9.
J. O. Kristiansson:Journal of Thermal Stresses, 1982, vol. 5, pp. 315–30.
T. Hara:Tetsu-to-Hagané Overseas, 1964, vol. 4, No. 3, pp. 296–303.
R. H. Tien and V. Koump:J. Applied Mechanics (Trans. ASME), 1969, vol. 36, pp. 763–67.
K. Sakiu:Tetsu-to-Hagané, 1979, vol. 60, No. 12, pp. 1591–98.
B. G. Thomas, I. V. Samarasekera, and J. K. Brimacombe:Metall. Trans. B, 1987, vol. 18B, pp. 119–30.
B. Barber and A. Perkins:First International Conference on Numerical Methods in Thermal Problems, Swansea, England, 1979, pp. 691–701.
B. G. Thomas, I. V. Samarasekera, and J. K. Brimacombe:ISS Transactions, 1986, vol. 7, pp. 21–29.
A. Grill and K. Sorimachi:Int. J. Numer. Methods in Eng., 1979, vol. 14, pp. 499–505.
O. C. Zienkiewicz and I. C. Cormeau:Int. J. Numer. Methods in Eng., 1974, vol. 8, pp. 821–45.
A. Mendelson:Plasticity—Theory and Applications, R. E. Krieger Publishing, Malabar, FL, 1968 (reprinted 1983), pp. 213–15.
O. C. Zienkiewicz:The Finite Element Method, 3rd ed., McGraw-Hill, London, 1977.
Y. Yamada, N. Yoshimura, and T. Sakurai:Int. J. Mech. Sci., Pergamon Press, 1968, vol. 10, pp. 343–54.
O. C. Zienkiewicz, S. Valliappan, and I. P. King:Int. J. Numer. Methods in Eng., 1969, vol. 1, pp. 75–100.
B. G. Thomas: Ph.D. Thesis, University of British Columbia, Vancouver, BC, Canada, 1985.
P. J. Wray:Modeling of Casting and Welding Processes, AIME Conference Proceedings, 1980, pp. 245–57.
G. Forsythe and C. Moler:Computer Solution of Linear Algebraic Systems, Prentice Hall, Englewood Cliffs, NJ, 1967.
S. R. Bodner and Y. Partom:J. Applied Mechanics, 1975, vol. 42, pp. 385–89.
E. W. Hart:J. of Eng. Materials and Technology (Trans. ASME), 1976, vol. 98, pp. 193–201.
L. Anand:J. of Eng. Materials and Technology (Trans. ASME), 1982, vol. 104, pp. 12–17.
A. Palmaers:CRM, Oct. 1977.
T. Sakiu and M. Ohashi:Tetsu-to-Hagané, 1981, vol. 67, No. 11, pp. 134–43.
P. Feltham:Proc. Roy. Soc., 1953, vol. 66, No. 10-B, pp. 865–83.
P. J. Wray: E. C. Bain Laboratory for Fundamental Research, US Steel, Monroeville, PA, 1965, No. 1072, and 1968, No. 1113.
S. Sakui and T. Sakai:ISIJ Trans., 1977, vol. 63, No. 2, pp. 285–93.
B. Y. Pines and A. F. Sirenko:Soviet Physics—Solid State, January 1963, vol. 4, No. 7, pp. 1393–99.
O. D. Sherby:Acta Metall., 1962, vol. 10, pp. 135–47.
J. Robbins, O. C. Shepard, and O. D. Sherby:JISI, October 1961, vol. 199, pp. 175–80.
G. W. Greenwood and R. F. Johnson:Proceedings of the Royal Society, 1965, vol. A283, pp. 403–22.
D. M. Keane, C. M. Sellars, and W. J. Tegart: Univ. of Sheffield Dept. of Metallurgy, July 1966.
P. J. Wray:Metall. Trans. A, 1984, vol. 15A, pp. 2041–58.
E. B. Hawbolt, B. Chau, and J. K. Brimacombe:Metall. Trans. A, 1983, vol. 14A, pp. 1803–15.
O. M. Puhringer:Stahl und Eisen, 1976, vol. 96, No. 6, pp. 279–84.
W. Köster:Z. Metalkde., 1948, vol. 39, pp. 1–9.
C. Boulanger and C. Crussard:Revue de Metallurgie, 1956, No. 9, pp. 715–28.
D. R. Hub:Proc. IVth Intern. Cong. Acoustics, Copenhagen, 1962, No. 551.
P. J. Wray: E. C. Bain Laboratory for Fundamental Research, US Steel, Monroeville, PA, June 1965, No. 1054.
B. A. Boley and J. Weiner:Theory of Thermal Stresses, John Wiley and Sons, Inc., New York, NY, 1960, pp. 272–81, 311.
E. P. Popov:Introduction to Mechanics of Solids, Prentice-Hall Inc., Englewood Cliffs, NJ, 1968, pp. 316–26.
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B. G. THOMAS, formerly a Graduate Student at the University of British Columbia
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Thomas, B.G., Samarasekera, I.V. & Brimacombe, J.K. Mathematical model of the thermal processing of steel ingots: Part II. Stress model. Metall Trans B 18, 131–147 (1987). https://doi.org/10.1007/BF02658438
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DOI: https://doi.org/10.1007/BF02658438