| With the development of materials science, it was found that the solidificationprocess has an important influence on the properties of the materials. Recently thenumerical simulation of microstructure has attracted more and more people to study it.The phase field method is one of the most important methods in microstructuresimulation. It avoids tracking the solid-liquid interface, and accurately describes themicrostructure of the solidification process by coupling the phase-field and otherfields. The studies found that factors which affect material properties depend not onlyon the grain size, but also on the grain morphology. Dendritic is a commonmicroscopic morphology in the solidification process. Therefore simulate thedendritic growth and its morphology is conducive to research and explore thesolidification microstructure, and improve properties of the material. Therefore, thedendritic growth in the temperature was simulated by the phase-field method in thisthesis, and its morphology and evolution was discussed.In this thesis, a model of dendritic growth was established based on the principle ofentropy increase. And equation of the phase-field and temperature field equationswere derived. In addition, we introduce the anisotropy, and set up a phase-field modelof dendritic growth under temperature field. The finite differential approach was usedto discrete the equations for the phase-field and the temperature field.The mentioned above the phase-field model and numerical method were used tosimulate the solidification process of dendritic growth. And the effects of the phasefield parameter change on the dendrite growth process was also studied and discussed.The parameters include the space step, supercooling degree and anisotropy intensity.The conclusions are as follows:Firstly, the space step size (grid resolution) affects not only the speed of simulation,but also the morphology of dendritic. The greater the space step, the smaller theamount of computation, the faster the speed of simulation of the dendritic growth.Meantime the morphologies are sharp and rough. Although smaller step spends morecomputation time and affects the simulation speed of dendrite growth, it made itsmorphology more smooth and mellow.Secondly, the supercooling is the driving force for solidification, its value play a key role for dendritic growth. The greater the supercooling is, the faster the speed ofdendritic growth is. But the too greater supercooling will make the solid-liquidinterface lose stability.Thirdly, anisotropy intensity has an impact on the morphology of dendritic. Thegrowth rates of the dendritic in all directions are the same when the anisotropyintensity is small. When the anisotropy increases, the dendritic tip rapid grows alongdifferent crystal axis and change the morphology of dendritic. In addition, if theanisotropy intensity is over large, secondary crystal arms will appear in the dendritic. |
