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

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

E-mail: cheshire@front.ru

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.

(Part 3)
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