Mathematical simulation of crystallization process in application to prognostication of structure of hard-tempered from the liquid state metals

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Category: Physical processes
Last Updated on Sunday, 14 July 2013 15:29
Published on Wednesday, 14 November 2012 11:21
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Ye.A. Yakunin, Cand. Sci. (Phys.-Math.), Associate Professor, State Higher Educational Institution “National Mining University”, Senior Lecturer of the Physics Department, Dnepropetrovsk, Ukraine


Purpose. To forecast the structure of metals and alloys hard-tempered from the liquid state and to determine the optimal modes of cooling of the melt for obtaining of the required structure of the material.

Methodology. The mathematical simulation of the process of solidification of melts was conducted. A model based on early obtained nonisothermic kinetic equalization of crystallization was offered. For forecasting of structure of metals an algorithm was complemented by the possibility of receiving of crystal distribution by size. By means of the new algorithm the modeling of influence of cooling speed on the structure of nickel was conducted. During modeling wide interval of cooling speeds including the critical speed providing the amorphization of the fusion was used.

Findings. Distribution of crystals of nickel by size was obtained. By data on distribution of crystals by size such structural characteristics of crystallized metal as average and most probable size of crystals were calculated. Those sizes of crystals which made the biggest part of volume of the crystallized metal were also determined. It is shown that in the narrow interval of cooling rates, close to the critical one, isothermal solidification of the melt during overcooling at the temperature of 800 degrees below the equilibrium temperature is possible. Size distribution of crystals, calculated for such an extreme mode of crystallization, proves the formation of the structure rather homogeneous in its grain size. The average and the most probable sizes of crystals do not exceed several dozens of nanometers. Thus the structural state, which is normally obtained by means of melt amorphization and the following annealing of the amorphous material was achieved.

Originality. The algorithm of determining of distribution of growing crystals by size in the process of modeling of ultra fast solidification of fusion was obtained.

Practical value. The offered algorithm allows calculating cooling modes in order to obtain metals with the homogeneous structure directly in the process of crystallization of fusion.


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Lysenko, A.B. and Yakunin, Ye.A. (2004), “Nonisothermic kinetic equalization of crystallization”, Sbornik nauchnykh trudov Natsionalnogo gornogo universiteta, no.20, pp. 143–147.

Date 2013-07-14 Filesize 348.16 KB Download 682

Tags: mathematical modelhardening from liquid statecrystallizationamorphousstructural statestrengtheningkinetic equation