Critical Wavelengths for Gap Nucleation in Solidification— Part I: Theoretical Methodology

[+] Author and Article Information
F. Yigit

Department of Mechanical Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

L. G. Hector

Surface Science Division, Alcoa Technical Center, Alcoa Center, PA 15069

J. Appl. Mech 67(1), 66-76 (Sep 30, 1999) (11 pages) doi:10.1115/1.321166 History: Received March 09, 1999; Revised September 30, 1999
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.


Singh, S., and Blazek, K., 1974, “Heat Transfer and Skin Formation in a Continuous Casting Mold as a Function of Steel Carbon Content,” J. Metals, pp. 17–27.
Cisse,  J., Cole,  G., and Bolling,  G., 1971, “Freezing Front Asymmetry During Ingot Solidification of Aluminum and Its Alloys,” AFS Cast Metals. Res. J., 7, pp. 158–161.
Wray, P. J., 1977, “Nonuniform Growth of a Plate Solidifying on a Chilled Surface,” Presentation Notes, Proceedings of the AIME Conference, Atlanta, GA.
Wray,  P. J., 1981, “Geometric Features of Chill-Cast Surfaces,” Metall. Trans. B, 12B, pp. 167–176.
Sugitani,  Y., Nakamura,  M., Okuda,  M., Kawasaki,  M., and Miyahara,  S., 1992, “Control of Uneven Solidified Shell Formation of Hypo-peritectic Carbon Steels in Continuous Casting Mold,” Trans. Iron Steel Inst. Jpn., 25, pp. B–91.
Collins,  D. W. L., 1967, “A New Explanation of the Surface Structure of DC Ingots,” Metallurgica, 76, pp. 137–144.
Halliday, J. M. D., 1965, discussion one, Iron and Steel Institute Special Report, No. 89, p. 98.
Richmond, O., and Huang, N. C., 1979, “Interface Instability During Unidirectional Solidification of a Pure Metal,” Proc. Sixth Canadian Congress of Applied Mechanics, National Research Council of Canada, Vancouver, pp. 453–454.
Richmond,  O., Hector,  L. G., and Fridy,  J. M., 1990, “Growth Instability During Nonuniform Directional Solidification of Pure Metals” ASME J. Appl. Mech., 57, pp. 529–536.
Li,  N.-Y., and Barber,  J. R., 1991, “Thermoelastic Instability in Planar Solidification,” Int. J. Mech. Sci., 33, pp. 945–959.
Hector,  L. G., Li,  N.-Y., and Barber,  J. R., 1994, “Strain Rate Relaxation Effect on Freezing Front Growth Instability During Planar Solidification of Pure Metals, Part 1: Uncoupled Theory,” J. Thermal Stresses, 17, pp. 619–646.
Yigit, F., and Barber, J. R., 1992, “Effect of Thermal Capacity on the Development of Sinusoidal Perturbation During the Unidirectional Solidification of Pure Metals,” Micro/Macro Scale Phenomena in Solidification, ASME, New York, pp. 141–150.
Mizikar, E. A., Wojcik, W. M., and Li, K., 1967, “Method of Producing Steel Strip of Uniform Thickness by Direct Casting,” U.S. letters patent #3,345,738.
Morales, A., Glicksman, M. E., and Biloni, H., 1977, “Influence of Mould Wall Microgeometry on Casting Structure,” Proc. Int. Conf. on Solidification, Sheffield Metallurgical Eng. Assn., Univ. Sheffield, and The Metals Society, Sheffield, U.K. pp. 184–192.
Buxmann, K., Boliger, M., and Gyongyos, I., 1981, “Mould With Roughened Surface for Casting Metals,” U.S. letters patent #4,250,950.
Laki,  R. S., Beech,  J., and Davies,  G. J., 1985, “Surface Structures of Chill and Continuously Cast Stainless Steels,” Ironmaking Steelmaking, 12, pp. 233–241.
Gaspar, T. A., 1987, “Textured Substrate and Method for the Direct, Continuous Casting of Metal Sheet Exhibiting Improved Uniformity,” U.S. letters patent #4,705,095.
Ostlund,  A., and West,  R., 1988, “Influence of Wheel Surface Roughness on Microstructure and Heat Transfer in Meltspun Fe0.79Si0.03C0.04B0.14,” Int. J. Rapid Solidif., 3, pp. 177–188.
Bartlett, E., Maringer, R., and Rayment, J., 1989, “Direct Strip Casting on Grooved Wheels,” U.S. letters patent #4,865,117.
Murakami,  H., Suzuki,  M., Kitagawa,  T., and Miyahara,  S., 1992, “Control of Uneven Solidified Shell Formation of Hypo-peritectic Carbon Steels in Continuous Casting Mold,” Trans. Iron Steel Inst. Jpn., 78, pp. 105–112.
Haga,  T., and Motomura,  M., 1994, “Effect of Polishing Condition on the Roll of the Surface of Foils of Pure Aluminum and Al-Si Alloy Manufactured by Single Roll Rapid Solidification,” J. Jpn. Inst. Light Metals, 44, pp. 22–27.
Hector,  L. G., Howarth,  J. A., Richmond,  O., and Kim,  W.-S., 2000, “Mold Surface Wavelength Effect on Gap Nucleation in Solidification,” ASME J. Appl. Mech., 67, pp. 155–164.
Comninou,  M., and Dundurs,  J., 1980, “On the Lack of Uniqueness in Heat Conduction Through a Solid to Solid Contact,” ASME J. Heat Transfer, 102, pp. 319–323.
Zhang,  R. G., and Barber,  J. R., 1990, “Effect of Material Properties on the Stability of Static Thermoelastic Contact,” ASME J. Appl. Mech., 57, pp. 365–369.
Weirauch, Jr., D. A., and Giron, A., 1998, “The Early Stages of Aluminum Solidification in the Presence of a Moving Meniscus,” Proceedings on the Integration of Material, Process and Product Design—A Conference dedicated to the 70th birthday of Owen Richmond, A. A. Balkema, Rotterdam, Netherlands, pp. 183–191.
Yigit,  F., 1998, “Effect of Mold Properties on Thermoelastic Instability in Unidirectional Planar Solidification,” J. Thermal Stresses, 21, pp. 55–81.
Westegraard, H. M., 1964, Theory of Elasticity and Plasticity, Dover, New York.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd Ed., McGraw-Hill, New York.
Byrne,  G. D., and Hindmarsh,  A. C., 1975, “A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations,” ACM Trans. Math. Softw., 1, pp. 71–96.


Grahic Jump Location
Pure metal shell solidifying on a deformable mold with nominal thickness h0 and sinusoidal surface topographies with wavelength λ




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In