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Computer simulation of solidification processes—The evolution of a technology

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Abstract

The historical development of solidification modeling is traced, as applied to solidification processing. Clearly, the growth of this technology followed the computer explosion, particularly with regard to hardware. However, universities and government laboratories made substantial contributions in the software area, particularly in removing roadblocks to the further development of the technology and by creative examples. The commercial software houses have utilized these leading-edge developments, a practice continued and expanding today. Heat-transfer analyses by computer were initiated by utilizing the analog computer, which appeared to be a competing technology, but by the early 1960s, the digital computer had become the winner in larger-scale computation. A number of benchmark achievements followed over the next several decades. The evolution of this technology is documented, including predictions of solidification microstructure and resulting material properties. Future developments are projected.

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References

  1. David P. Kanicki: Modern Casting, 2000, Dec., pp. 24–28.

  2. D.L. Katz and E.I. Organick: J. Eng. Education, 1960, vol. 51 (3), pp. 183–205.

    Google Scholar 

  3. D.L. Katz et al.: “Electronic Computers in Engineering Education,” First Annual Report, College of Engineering, University of Michigan, Ann Arbor, MI, Aug. 26, 1960.

    Google Scholar 

  4. Transactions of American Foundrymen’s Society, 1941–1961, Publications of V. Paschkis (for a complete list of the papers of Paschkis and co-workers, see pp. 10–11 of Ref. 11).

  5. G.M. Dusinberre: Heat-Transfer Calculations by Finite Differences, International Textbook Company, Scranton, PA, 1961.

    Google Scholar 

  6. T.X. Hou, J.O. Wilkes, and R.D. Pehlke: Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes V, Davos, Switzerland, M. Rappaz, M.R. Ozgu, and K.W. Mahin, eds., TMS-AIME, Warrendale, PA, 1990, pp. 15–22.

    Google Scholar 

  7. T.X. Hou, J.O. Wilkes, and R.D. Pehlke: Trans. Am. Foundrymen’s Soc., 1991, vol. 99, pp. 325–32.

    CAS  Google Scholar 

  8. Computer Applications in Metallurgical Engineering, 1963 Metal Congress, Cleveland, OH, 1963, ASM Seminar Volume, Robert D. Pehlke and Maurice J. Sinnott, eds., ASM, Metals Park, OH, 1964.

    Google Scholar 

  9. K. Forsund, Giesserei, 1962, vol. 14, p. 51.

    Google Scholar 

  10. J.G. Henzel and J. Keverian: AFS Cast Met. Res. J., 1965, vol. 1 (1), pp. 19–36.

    CAS  Google Scholar 

  11. R.D. Pehlke, R.E. Marrone, and J.O. Wilkes: Computer Simulation of Solidification, American Foundrymen’s Society, Des Plaines, IL, 1976.

    Google Scholar 

  12. F.A. Brandt, H.F. Bishop, and W.S. Pellini: Trans. Am. Foundrymen’s Soc., 1953, vol. 62, pp. 451–56.

    Google Scholar 

  13. H.F. Bishop, F.A. Brandt, and W.S. Pellini: Trans. Am. Foundrymen’s Soc., 1951, vol. 59, pp. 435–50.

    Google Scholar 

  14. H.F. Bishop and W.S. Pellini: The Foundry, 1952, Feb.

  15. P.K. Trojan, M.J. Weins, and R.A. Flinn: Trans. Am. Foundrymen’s Soc., 1963, vol. 71, p. 656.

    Google Scholar 

  16. R.D. Pehlke, M.J. Kirt, R.E. Marrone, and D.J. Cook: AFS Cast Met. Res. J., 1973, vol. 9 (2), pp. 49–55.

    CAS  Google Scholar 

  17. A. Jeyarajan and R.D. Pehlke: Trans. Am. Foundrymen’s Soc., 1975, vol. 83, pp. 405–12.

    Google Scholar 

  18. A. Jeyarajan and R.D. Pehlke: Trans. Am. Foundrymen’s Soc., 1978, vol. 86, pp. 457–64.

    Google Scholar 

  19. R.D. Pehlke, J.T. Berry, W.C. Erickson, and C.H. Jacobs: Proc. Int. Conf. on Solidification, The Metals Society, University of Sheffield, Sheffield, United Kingdom, July 18–21, 1977, pp. 371–79.

    Google Scholar 

  20. J.T. Berry and R.D. Pehlke: USA Official Exchange Paper, 50th Int. Foundry Congr., Cairo, Nov. 1983. Proceedings, No. 5; AFS Trans., 1984, vol. 92, pp. 101–108.

    Google Scholar 

  21. Process Modeling—Fundamentals and Applications to Metals, Proc. American Society for Metals Process Modeling Sessions, Materials and Processing Congresses, 1978–1979, Materials/Metalworking Technology Series, American Society for Metals, Metals Park, OH.

  22. W.C. Erickson and A.V. Houghton: Trans. Am. Foundrymen’s Soc., 1977, vol. 85, p. 59.

    Google Scholar 

  23. P.V. Desai et al.: “A Computer-Aided Design System for Castings,” Progress Report No. 2, Grant No. DAR78-214301, Dec. 1981.

  24. P.V. Desai et al.: “A Computer-Aided Design System for Castings,” Progress Report No. 3, Grant No. DAR78-214301, Dec. 1982.

  25. R.D. Pehlke, P.K. Trojan, R.A. Flinn, B.P. Winter, and M.C. Sutton: Paper presented at 49th Int. Foundry Congr., Chicago, IL, Apr. 1982.

  26. R.D. Pehlke, B.P. Winter, and P.K. Trojan: Trans. Am. Foundrymen’s Soc., 1983, vol. 91, pp. 81–88.

    Google Scholar 

  27. R.D. Pehlke, B.P. Winter, T.R. Ostrom, K.J. Hartman, and P.K. Trojan: Trans. Foundrymen’s Soc., 1984, vol. 92, pp. 551–60.

    Google Scholar 

  28. R.D. Pehlke: USA Official Exchange Paper for 60th Int. Foundry Congress, The Hague, Netherlands, 1993; Foundry Management Technol., 1994, June, pp. 26–28; and 1994, July, p. 18.

  29. R.D. Pehlke, A. Jeyarajan, and H. Wada: Summary of Thermal Properties for Casting Alloys and Mold Materials, University of Michigan, Ann Arbor, MI, 1982; NTIS, 5285 Port Royal Road, Springfield, VA 22161.

    Google Scholar 

  30. Proc. Engineering Foundation Conf. on Modeling of Castings and Welding Processes, Rindge, NH, Aug. 1980, Harold D. Brody and Diran Apelian, eds., TMS-AIME, Warrendale, PA, 1980.

    Google Scholar 

  31. Proc. Engineering Foundation Conf. on Modeling of Castings and Welding Processes, Henniker, NH, July 31–Aug. 5, 1983, J.A. Dantzig and J.T. Berry, eds., TMS-AIME, Warrendale, PA, 1984.

    Google Scholar 

  32. Proc. Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes IX, Aachen, Germany, Aug. 2001, P. Sahm, P. Hansen, and J. Conley, eds., Springer-Verlag, New York, 2001.

    Google Scholar 

  33. D.J.P. Adenis, Keith Coates, and David V. Ragone: J. Inst. Met., 1963, vol. 91, pp. 395–403.

    Google Scholar 

  34. R.D. Pehlke: Met. Eng. Q., 1964, vol. 4 (2), pp. 266–80.

    Google Scholar 

  35. R.D. Pehlke: “Computer Simulation of Heat Transfer During Continuous Casting—A Summary of the Development and Application of a Computer Model for Heat Transfer During Continuous Casting of Steel Using Finite Differences Approximations,” Prepared for McLouth Steel Corporation, Trenton, MI, June 15, 1967.

    Google Scholar 

  36. R.D. Pehlke: “Heat Transfer During Continuous Casting—Calculation of Slab Surface Temperatures and Heat Transfer Rates in the Spray Zone of a Continuous Casting Machine,” Prepared for McLouth Steel Corporation, Trenton, MI, Sept. 26, 1967.

    Google Scholar 

  37. R.D. Pehlke: “Heat Transfer During Continuous Casting—A Study of Mold Heat Transfer and the Effect of Water Cooling Passage Configurations,” Prepared for McLouth Steel Corporation, Trenton, MI, Mar. 1968.

    Google Scholar 

  38. R.D. Pehlke: “Computer Simulation of Heat Transfer During Continuous Casting—A Modification of the Spray Zone Heat Transfer Calculation and Evaluation of Heat Transfer During a Stopped Cast,” Prepared for McLouth Steel Corporation, Trenton, MI, Aug. 19, 1968.

    Google Scholar 

  39. D.R. Glass, P.O. Hays, and R.D. Pehlke: “Experimental Study of Heat Transfer During Water Spraying of Hot Steel Surfaces,” Prepared for McLouth Steel Corporation, Trenton, MI, June 1968.

    Google Scholar 

  40. E.A. Mizikar: Trans. TMS-AIME, 1967, vol. 239, pp. 1747–53.

    CAS  Google Scholar 

  41. J.K. Brimacombe and F. Weinberg: J. Iron Steel Inst., 1973, vol. 211, pp. 24–33.

    CAS  Google Scholar 

  42. J.E. Lait, J.K. Brimacombe, and F. Weinberg: Ironmaking and Steelmaking, 1974, vol. 1, pp. 35–42.

    CAS  Google Scholar 

  43. R.D. Pehlke: Continuous Casting of Steel, Section I, Introduction to Continuous Casting, Engineering Summer Conf., Center for Professional Development, College of Engineering, University of Michigan, Ann Arbor, MI, 1996.

    Google Scholar 

  44. L.J. Heaslip, A. McLean, and I.D. Sommerville: Continuous Casting Volume One, ISS-AIME, Warrendale, PA, 1983.

    Google Scholar 

  45. N.A. McPherson and A. McLean: Continuous Casting Volume Six, ISS-AIME, Warrendale, PA, 1992.

    Google Scholar 

  46. L.J. Heaslip and A. McLean: ISS-AIME 39th Electric Furnace Conf., ISS-AIME, Warrendale, PA, 1981, pp. 108–20.

    Google Scholar 

  47. L.J. Heaslip and J.D. Dorricott: Continuous Casting of Steel, Engineering Summer Conf., The University of Michigan, Ann Arbor, MI, private communication, 1993.

    Google Scholar 

  48. J. Szekely and O.J.L. Legbusi: The Physical and Mathematical Modeling of Tundish Operation, Springer-Verlag, New York, NY, 1989, pp. 13–107.

    Google Scholar 

  49. Huiqing Chen: Ph.D. Thesis, The University of Michigan, Ann Arbor, MI, 1994.

    Google Scholar 

  50. H. Chen and R.D. Pehlke: ISS-AIME Steelmaking Conf. Proc., ISS-AIME, Warrendale, PA, 1994, pp. 695–702.

    Google Scholar 

  51. H. Chen and R.D. Pehlke: 13th Process Technology Conf., Theme: Continuous Casting, Nashville, TN, Apr. 1995, ISS-AIME, Warrendale, PA.

    Google Scholar 

  52. H. Chen and R.D. Pehlke: Metall. Mater. Trans. B, 1996, vol. 27B, pp. 745–56.

    Article  CAS  Google Scholar 

  53. R.A. Stoehr: in Modeling of Casting and Welding Processes, H.D. Brody and D. Apelian, eds., TMS-AIME, Warrendale, PA, 1981, pp. 3–18.

    Google Scholar 

  54. T.C. Midea and David Schmidt: Modern Casting, 1999, vol. 89, pp. 47–51.

    Google Scholar 

  55. P. Krishna, K.T. Bilkey, and R.D. Pehlke: Proc. Int. Symp. on Light Metals, 40th Annual Conf. of Metallurgists of CIM, Toronto, Aug. 2001, Mahi Sahoo and Trevor Lewis, eds., Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, Canada, pp. 417–30.

    Google Scholar 

  56. P. Krishna, K.T. Bilkey and R.D. Pehlke: Proc. Int. Symp. on Light Metals. 40th Annual Conf. of Metallurgists of CIM, Toronto, Aug. 2001, eds., Mahi Sahoo and Trevor Lewis, Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, Canada, pp. 377–90.

    Google Scholar 

  57. J.H. Weiner and B.A. Boley: J. Mech. Phys. Solids, 1963, vol. 11, pp. 145–54.

    Article  Google Scholar 

  58. R.W. Lewis and P.M. Roberts: Appl. Scientific Res., 1987, vol. 44, pp. 61–92.

    Article  CAS  Google Scholar 

  59. J.O. Krisstiansson: J. Thermal Stresses, 1982, vol. 5 (3–4) 1982, pp. 315–30.

    Google Scholar 

  60. I. Cormeau: Int. J. Num. Methods Eng., 1975, vol. 9, pp. 109–27.

    Article  Google Scholar 

  61. M.D. Snyder and K.J. Bathe: Nucl. Eng Design, 1981, vol. 64, pp. 49–80.

    Article  Google Scholar 

  62. A.L. Purvis, E. Kannatey-Asibu, and R.D. Pehlke: Engineering Foundation Conf. on Modeling of Casting and Welding and Advanced Solidification Processes VI, Palm Coast, FL, 1993, T.S. Piwonka, V. Voller, and L. Katgerman, eds., TMS-AIME, Warrendale, PA, 601–08.

    Google Scholar 

  63. R.A. Rosenberg, M.C. Flemings, and H.F. Taylor: AFS Trans., 1960, vol. 68, pp. 518–24.

    Google Scholar 

  64. Magma Times, Magma GmbH, Aachen, Germany, 2001, vol. 6 (21).

  65. J.A. Dantzig: J. Met., 2000, Dec. pp. 18–21.

  66. D.A. Tortorelli, M.M. Tiller, and J.A. Dantzig: Computer Methods Appl. Mech. Eng., 1994, vol. 113 (1–2), pp. 141–55.

    Article  Google Scholar 

  67. D.A. Tortorelli et al.: Computer Methods Appl. Mech. Eng., 1994, vol. 113 (1–2), pp. 157–72.

    Article  Google Scholar 

  68. T.E. Morthland et al.: Metall. Mater. Trans. B, 1995, vol. 26B, pp. 871–85.

    CAS  Google Scholar 

  69. M.M. Tiller and J.A. Dantzig: Appl. Math. Modeling, 1996, vol. 20 (11), pp. 792–99.

    Article  Google Scholar 

  70. R.M. McDavid and J.A. Dantzig: Metall. Mater. Trans. B, 1998, vol. 29B, pp. 679–90.

    CAS  Google Scholar 

  71. Neil E. Paton and Boyd A. Mueller: INCAST, 2000, vol. XIII (6), pp. 11–15.

    Google Scholar 

  72. W. Oldfield: Trans. ASM, 1996, vol. 59, pp. 945–60.

    Google Scholar 

  73. M. Rappaz: Int. Mater. Rev., 1989, vol. 34, pp. 93–123.

    CAS  Google Scholar 

  74. J.A. Warren and W.J. Boettinger: Acta Metall. Mater., 1995, vol. A43, pp. 689–703.

    Google Scholar 

  75. W.J. Boettinger and J.A. Warren: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 657–69.

    CAS  Google Scholar 

  76. J.A. Warren et al.: Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes IX, Aachen, Germany, Peter R. Sahm, Preben N. Hansen, and James G. Conley, eds., Shaker-Verlag, Aachen, Germany, 2000, pp. CII-CIX.

    Google Scholar 

  77. A. Karma and W.J. Rappel: Phys. Rev. E, 1998, vol. 57, pp. 4323–49.

    Article  CAS  Google Scholar 

  78. M. Plapp and A. Karma: Phys. Rev. Lett., 2000, vol. 84, pp. 1740–43.

    Article  CAS  Google Scholar 

  79. N. Provatas, N. Goldenfeld, and J. Dantzig: Solidification 1999, Symp. Proc. TMS Fall Meeting 1999, TMS, Warrendale, PA, pp. 151–60.

    Google Scholar 

  80. C. Beckermann, G. Fisher, D. Jensen, and S. Venkatasubramanian: “Final Report: Metalcasting Lead Time and Cost Reduction Project—1.1.1.2 Identify and Apply Software Tools,” American Metal Casting Consortium—1995, Steel Founders’ Society of America, Des Plaines, IL, Special Report No. 27, July 1996.

    Google Scholar 

  81. M. Blair and R. Monroe: Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes IX, Aachen, Peter R. Sahm, Preben N. Hansen, and James G. Conley, Shaker-Verlag, 2000, pp. XIX–XXIV.

  82. M. Cross, K. McManus, C. Bailey, K. Pericleous, T.N. Croft, and A. Williams: Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes IX, Aachen, Peter R. Sahm, Preben N. Hansen, and James G. Conley, eds., Shaker-Verlag, 2000, pp. XXV–XXXV.

  83. P.R. Sahm and P.N. Hansen: Engineering Foundation Conf. on Modeling of Casting, Welding and Advanced Solidification Processes IX, Aachen, Peter R. Sahm, Preben N. Hansen, and James G. Conley, eds., Shaker-Verlag, 2000, pp. LXXXI–XCII.

  84. E. Wyatt: AGARD Meeting on Virtual Manufacturing, Aalborg, Denmark, Oct. 1997, AGARD Report No. 821, 1998.

  85. Michael Evans: Gibbs Die Casting Corporation, Henderson, KY, personal communication, Aug. 2001.

  86. T.B. Harabuchi and R.D. Pehlke: Continuous Casting, vol. 4, Design and Operations, ISS-AIME, Warrendale, PA, 1988.

    Google Scholar 

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This lecture was presented to honor Edward DeMille Campbell (University of Michigan, Class of 1886), born in 1863, who was appointed Assistant Professor of Metallurgy in 1890. Dr. Campbell brought a strong interest in the study of the constitution of metals and alloys to the University of Michigan. In 1892, during a study of the composition of steel, he lost his eyesight in a laboratory explosion. Within five days, he returned to the University, and resumed his teaching and research. Over the next 30 years, he published 72 research papers, and developed a laboratory course in metallography. In 1924, working under the direction of Professor Campbell, William Fink discovered a new, tetragonal form of iron (martensite) in the first significant application of a new tool, X-ray diffraction, to physical metallurgy. It was these experiments that established the beginning of a strong tradition in physical metallurgy at the University of Michigan. In 1898, Campbell led the effort to establish Chemical Engineering at Michigan, becoming Professor of Chemical Engineering and Analytical Chemistry in 1902. In 1914, Campbell was appointed Director of the University’s Chemical Laboratory and Professor of Chemistry. Following his death in 1925, the American Society for Metals established this annual award in his name.

The Edward DeMille Campbell Memorial Lecture was established in 1926 as an annual lecture in memory of and in recognition of the outstanding scientific contributions to the metallurgical profession by a distinguished educator who was blind for all but two years of his professional life. It recognizes demonstrated ability in metallurgical science and engineering.

Robert D. Pehlke studied at the University of Michigan, B.S.E. (Met. Eng.) 1955, Massachusetts Institute of Technology, S.M. (Met.) 1958, and Sc.D. (Met.) 1960, and at the Technical Institute, Aachen, as a Fulbright Fellow, 1956–57. He joined the faculty of the University of Michigan as Assistant Professor in February 1960, and was appointed Associate Professor in June 1963 and full Professor in June 1968. In May 1973, he was named Chairman of the Department of Materials and Metallurgical Engineering. In June 1978 and 1983, he was reappointed Department Chairman and served until June 1984. In 1994, he was Visiting Professor at Tohoku University (Sendai, Japan).

He is a member of AIME and ASM, and has served on numerous divisional and award committees within these societies. He has served on the Technical Divisions Board (1982–84), as Secretary of the ASM Academy for Metals and Materials Committee, and in 1976 was named a Fellow of the Society. In 1964, he co-edited the ASM seminar volume on Computers in Metallurgy. He has served as Chairman of the Process Technology Division and as a Director of the ISS-AIME. In 1980, he was named a Distinguished Life Member of the ISS. In 1976, he received the Science Award Gold Medal of the Extractive Metallurgy Division of TMS-AIME. In 1983, he was named a Fellow of TMS. He was chairman of the former AIME-ISS Division Publications Committee. He served as chairman of the Editorial Board for the AIME Monograph Series on Oxygen Steelmaking. In 1980, he presented the Howe Memorial Lecture on “Steelmaking—The Jet Age.”

In 1991–92, he was the Krumb Lecturer of the Metallurgical Society. In 1980, he was named a Case Institute Centennial Scholar and the Van Horn Distinguished Lecturer at Case Western Reserve University. He has lectured widely internationally, and at technical conferences, universities, corporations, and technical society chapters, including presenting a number of keynote, invited, and honorary lectures.

He was National President of Alpha Sigma Mu and a member of Tau Beta Pi, Sigma Xi, and the New York Academy of Sciences. He is also a member of the American Society for Engineering Education and the American Foundry Society. He has held memberships in the Iron and Steel Institute of London, the Iron and Steel Institute of Japan, and the Verein Deutscher Eisenhuttenleute. He is a registered professional engineer in the State of Michigan. Dr. Pehlke has served as Foundry Educational Foundation Professor at The University of Michigan for 17 years.

Professor Pehlke has authored or co-authored over 300 publications, including editing, authoring, or co-authoring 11 books. His text Unit Processes of Extractive Metallurgy has been widely used throughout the world. He co-authored Continuous Casting—Design and Operations, which is Volume 4 of the ISS-AIME series. He has won seven American Foundry Society Best Paper awards.

In 1963, Dr. Pehlke published an ASM pioneering paper first describing computer modeling of continuous casting of steel. In 1964, he continued this work in conjunction with McLouth Steel Corporation, which had just installed the first slab casting machine for steel in the United States. In 1968, he, with the support of the Heat Transfer Committee of the American Foundry Society, initiated the first university research program in North America on computer modeling of the solidification of shaped castings.

His early professional employment included three summers each with General Motors Research Laboratories and the Ford Scientific Laboratory. He has consulted extensively on a wide range of metallurgical subjects, principally with ferrous and nonferrous metal producers and their suppliers.

His research has covered a broad range of metallurgical topics with an emphasis on high-temperature physical chemistry of metallurgical systems, modeling of solidification of metals, and computer applications in metallurgy.

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Pehlke, R.D. Computer simulation of solidification processes—The evolution of a technology. Metall Mater Trans A 33, 2251–2273 (2002). https://doi.org/10.1007/s11661-002-0349-1

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