The Morphological Dynamics And Evolution Of Rod Eutectic Growth Using The Analytic Method

Eutectic growth is that the closely adjacent two-phases or multi-phases are separated from the same parent phase at the same time during the solidification.Low melting temperature and small freezing range contribute to excellent casting fluidity and fine composite structures give rise to favorable properties.Both of these features contribute to the wide application of eutectic alloys in the casting,welding,and soldering of engineered components.Despite the broad-based technological importance,many fundamental questions regarding eutectic solidification remain unanswered,which severely limits the microstructure prediction of new materials and new process design.Hence,the research of eutectic growth theory is very important to practical application.At the core of the most persistent questions,eutectic growth problems involving multicomponent thermodynamics,solid-liquid and solid-solid interfacial phenomena,morphological stability,chemical and thermal diffusion of physical phenomena.The current theory does not predict the solid-liquid interface and the critical spacing.So based on the directional solidification of rod eutectic growth system as the research object,considering the solid-solid-liquid phase junction caused by contact Angle and the mathematical model of singularity.The analytic solution of the mathematical model is obtained by using multiple scale,asymptotic expansion and matching method.Hence,the whole liquid will be divide into the region into three subregions according to the different length scales:the outer subregion,which is far away from liquid-solid interface,the triple phase junction subregion,and interface subregion far from the triple junction,while the interface slope is normal order,respectively.When the order of interface slope is small,according to different length scales,we divide the whole liquid region into two subregions:the outer subregion,which is far away from liquid-solid interface and interface subregion,respectively.Solutions in every subregion have been derived by asymptotic expansion method.Finally,the uniformly valid asymptotic solutions have been obtained by the matching method.The influences of the pulling speed and temperature gradient on the eutectic growth of solid-liquid interface have been obtained in this paper.Especially,when the order of solid-liquid interface slope of triple phase junction is the normal,the relationship of the undercooling of eutectic growth interface and the eutectic spacing is obtained.In addition,the critical eutectic spacing is determined.Results show that the liquid-solid interface shapes are mainly determined by coupling effects of curvature undercooling and solute undercooling.The average undercoolings in front of both solid-liquid interface are not equal.The average undercooling of solid-liquid interface decreases firstly then increases with increase of the eutectic spacing.Moerover,the minimum average undercooling of the solid-liquid interface is corresponding to the critical spacing in the growth of the eutectic.The critical spacing of SCN-DC is predicted in this paper which is 0.65 times of the critical spacing Jackson and Hunt's result,and it is in agreement with the result of S.Akamatsu's experiment.