Numerical simulation of rapid solidification in 2D

The columnar and equiaxed types of microstructure are observed in many solidification processes. Equiaxed dendrites usually grow in the central zone of casting ingots characterized by a small value of the temperature gradient. Columnar dendrites form under conditions of directional solidification at the significant temperature gradient near walls of the casting mold. Both types of microstructure are very common in steel and have been explored intensively for applied and fundamental purposes in numerous experiments. Although the LNS model is developed for study of rapid solidification, it can be successfully used in description of "slow" solidification like in casting processes.

The shape of dendritic tips in 2D and 3D

Equiaxed growth of a single dendrite in a Fe-C alloy

A small spherical seed of the solid phase forms in the undercooled melt. Due to nonequilibrium conditions, the seed grows in time reducing a deviation from equilibrium. The phase transformation is accompanied by release of the latent heat of solidification and rejection of the impurity. The diffusion-limited heat and mass transfer leads to development of multiple instabilities at the interface and transition to the dendritic morphology. Different microstructural characteristics like the grain size and microsegregation can be processed by the analysis of the temperature and concentration distributions shown below.

Concentration distribution

Temperature distribution

Equiaxed growth, concentration distribution Equiaxed growth, temperature distribution

Growth of a dendritic ensemble into undercooled melt in a Fe-C alloy

During growth of a dendritic ensemble, an additional mechanism related to the interdendritic length selection is predicted from modelling and experiments on transparent liquids. Interaction of the thermal and concentration fields of neighboring dendrites results in declining of some dendrites and evolution of other dendrites. The length between the faster growing dendrites is increasing in time and finally approaching to a constant value that characterizes the space distribution of dendrites in a whole dendritic ensemble.

Concentration distribution

Temperature distribution

Growth of a dendritic ensemble, concentration distribution Growth of a dendritic ensemble, temperature distribution

Animation of microstructure evolution in a Fe-C alloy

An animated GIF movie, 6 Mb Click on this link to watch the movie   An animated GIF movie, 6 Mb

Microstructure formation in a thin Ni-B ribbon quenched by spinning

Microstructure formation during rapid solidification of a binary Ni-B alloy by spinning has been studied using the LNS model [25]. In spinning process, the melt is injected on a cold rotating disk. This technique results in fast undercooling of the melt followed by rapid solidification and production of a thin ribbon with the amorphous or crystal structure. Due to a large positive temperature gradient inside a ribbon, the internal (contact) side of the ribbon has a different structure in comparison with the external side. The figures below show the results of the full-scale spinning experiment in comparison with the modelling results. The lower (contact) side of a ribbon does not demonstrate any grain structure. Approximately at half of the ribbon width a transition from the structureless morphology to the dendritic structure occurred clearly observed in both experimental and theoretical data. Such transition is a result of decay of the solidification velocity below the velocity of absolute stability. The spinning speed is 120 m/s. The ribbon width is 35 micron.

Experimental data

Modeling results

Experimental data Modeling results

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