Journals →  CIS Iron and Steel Review →  2013 →  #1 →  Back

ArticleName Prediction of dendritic micro-heterogeneity of cast steel: review of models and computer-aided analysis of problems (Part 3. Local structural and chemical heterogeneity)
ArticleAuthor V. M. Golod, K. I. Emelyanov, I. G. Orlova
ArticleAuthorData

Saint-Petersburg State Polytechnic University (St. Petersburg, Russia):

V. M. Golod, K. I. Emelyanov, I. G. Orlova

E-mail: cheshire@front.ru

Abstract

In the third part of the review it is noted that the number of publications devoted to the problem of heterogeneity of dendritic structure on the microscale, is very little. They have no significant results and methods that can reveal the basic laws of the evolutionary transformation of secondary dendritic branches from the moment of their inception to the final state. The coalescence models of dendritic branches are traditionally used to calculate the average value of the secondary dendrite spacing. The experimental data evaluates considerable scatter of dendrite arm spacing relative to the average values with a coefficient of variation V = 0.20–0.25. Using a Monte Carlo simulation, it was implemented the solution of formation of an array of data, according to the final distribution of secondary dendrite arm spacing based on local system for the coalescence of neighboring secondary branches. Computer calculations of coalescence for the local systems were done repeatedly by varying their initial morphology randomly. This leads to the different character of evolution with the activation of various competing mechanisms for individual local systems. The multiple implementations of this procedure for a large number of local systems lead to the formation of data that describe the resulting dendritic structure with its statistical parameters — the mean, standard deviation and probability density distribution (frequency) in the form of a histogram. The simulation results are used to assess the contribution of different mechanisms of coalescence and are in good agreement with experimental data in predicting a broad spectrum of values dendrite arm spacing. The radical increase in the accuracy of forecasting and analysis of the conditions of formation of the dendritic structure can be achieved through the development and application of computer models of non-equilibrium solidification of ingots and castings that are based on the use of thermal-physical and physical-chemical characteristics of the alloys, determined by their thermodynamic simulation, taking into account the rate of convective heat transfer at the front formation of dendrites. At the analysis and synthesis of empirical information on the dendritic structure for the objective evaluation of the quality of initial information and to ensure the adequacy of the resulting models requires the use of modern statistical analysis of experimental data. It is advisable to unify the description of the experimental data on the basis of a polynomial form of the concentration factor of the regression equation.

keywords Dendritic structure, dendrite arm spacing, mechanisms of diffusion coalescence, Monte-Carlo method, computer simulations, non-equilibrium crystallization
References

(Part 3)
43. Chernov A. A. Kristallografiya — Crystallography Reports. 1956. Vol. 1, Iss. 5. pp. 589–593.
44. Kattamis T. Z., Coughlin J. C., Flemings M. C. Influence of coarsening on dendrite arm spacing of aluminium-copper alloys. Transactions of AIME. 1967. Vol. 239, No. 10. pp. 1504–1511.
45. Mortensen A. On the rate of dendrite arm coarsening. Metallurgical and Materials Transactions. 1991. Vol. 22A, No. 2. pp. 569–574.
46. Roosz A., Exner H. E. Numerical modeling of dendritic solidification in aluminium-rich Al-Cu-Mg alloys. Acta Metallurgica et Materialia. 1990. Vol. 38, No. 2. pp. 375–80.
47. Nastac L., Stefanescu D. M. Macrotransport — solidification kinetics modeling of equiaxed dendritic growth: Part. 1. Model development and discussion. Metallurgical and Materials Transactions. 1996. Vol. 27A, No. 12. pp. 4061–4074.
48. Rappaz M., Boettinger W. J. On solidification of multicomponent alloys with unequal liquid diffusion coefficient. Acta Materialia. 1999. Vol. 47, No. 11. pp. 3205–3219.
49. Emelyanov K. I., Golod V. M. Liteyshchik Rossii — Russian founder. 2013. No. 2. pp. 28–33.
50. Kolmogorov A. N. Doklady Akademii Nauk SSSR — Reports of USSR Academy of Sciences. 1949. Vol. 65, No. 5. pp. 681–684.
51. Feijoo D., Exner H. Surface curvature distribution of growing dendrite crystals. Journal of Crystal Growth. 1991. Vol. 113, No. 3–4. pp. 449–455
52. Tensi H. M., Fuchs H. Dendritenarmvegröberung bei binären und ternären Aluminium-Legierungen. Zeits crift für metallkunde. 1983. Bd. 74, H. 6. ss. 351–357.
53. Ronto V., Roosz A. Numerical simulation of dendrite arm coarsening in case of ternary Al alloys. Materials Science Forum. 2003. Vol. 414– 415. pp. 483–490.
54. Ilinskiy V. A., Kostyleva L. V., Goremykina S. S. Izvestiya vuzov. Chernaya metallurgiya – Proceedings of universities. Ferrous metallurgy. 2007. No. 1. pp. 16–19.
55. Ilinskiy V. A., Kostyleva L. V., Goremykina S. S. et al. Metally — Metals. 2005. No. 6. pp. 66–70.
56. Goremykina S. S., Kostyleva L. V., Ilinskiy V. A. Metallurgiya mashino stroeniya — Metallurgy of Machinery Building. 2005. No. 5. pp. 28–30.
57. Вoettinger W. J. et al. Phase-field simulation of solidification. Annual Review of Materials Research. 2002. Vol. 32. pp. 163–194.
58. Sobol I. M. Chislennye metody Monte-Karlo (Numerical methods of Monte-Carlo). Moscow : Nauka, 1973. 312 p.
59. Zade L. A. Ponyatie lingvisticheskoy peremennoy i ego primenenie k prinyatiyu priblizhennykh resheniy (Concept of linguistic variable and its application to approximate solutions making). Moscow : Mir, 1976. 163 p.
60. Ueshima Y. et al. Analysis of solute distribution in dendrites of carbon steel with / transformation during solidification. Metall. Trans., 1986, v. 17B, p. 845–859.
61. Thuinet L., Combeau H., Lesoult G. Microsegregation in steels during dendritic columnar growth and peritectic reaction. Part II: Modelling and numerical simulation. Comparison with experimental results. Mater. Sci. Forum, 2006, v. 508, p. 367–372.
62. Natsume Y., Shimamoto M., Ishida H. Numerical modeling of microsegregation for Fe-base multicomponent alloys with peritectic transformation coupled with thermodynamic calculations. ISIJ Int., 2010, v. 50, No. 12, 1867–1874.

Full content Prediction of dendritic micro-heterogeneity of cast steel: review of models and computer-aided analysis of problems (Part 3. Local structural and chemical heterogeneity)
Back