Phase-Field Study Of The Influence Of Interphase Boundary Anisotropy On Eutectic Lamellae Growth During Directional Solidification

Eutectic lamellar growth in directional solidification widely exists in materials fabrication process.It is of great significance to understand its growth for controlling the microstructure and properties of materials.The interphase boundary anisotropy has a significant influence on the eutectic lamellar growth in directional solidification which should be taken into consideration during research.So far,the study on eutectic lamellar growth in directional solidification has achieved fruitful results.However,in the aspect of eutectic lamellar growth with interphase boundary anisotropy in directional solidification,some fundamental problems are still need to be further investigated,such as the description of undercooling and tilted angle,morphology of solid-liquid interface,morphology of lamellar growth and lamellar spacing adjustment.Further understanding of these problems will give theoretical guidance for controlling the eutectic lamellae in directional solidification.Eutectic lamellar growth in directional solidification involves the interaction of solute diffusion,interface migration,process conditions and so on,which result in the limitations during experimental research.In view of the above problems,the theoretical analysis and phase-field simulation are used to study the eutectic lamellar growth of binary alloys with interphase boundary anisotropy in directional solidification.The main research contents and conclusions are as follows:(1)The lamellar tilted angle and undercooling in lamellar growth with interphase boundary anisotropy in directional solidification is studied.With interphase boundary anisotropy,the eutectic lamellae are tilted respected to the direction of heat-flow.The variation of tilted angle is studied by phase-field simulation and the simulation results are compared with the predicted results by theory.The results show that the theory based on describe the variation of tilted angle well and there is a difference of tilted angle between simulation results and theoretical results.The difference increases with the increase of lamellar spacing and contacted angle.Based on symmetric-pattern approximation,a modified Jackson-Hunt model is developed.The results show that there is a value of lamellar spacing where the undercooling have a minimum value.With the increase of orientation rotation angle,the contacted angle increase,which results in the increase of undercooling.(2)A theoretical model is developed to describe the asymmetric solid-liquid interface in lamellar growth with interphase boundary anisotropy in directional solidification.The results shows that the concentration field in liquid have an asymmetric part due to tilted growth of lamellae.As a result,the surface energy force of interphase boundary tilted respected to respected to the direction of heat-flow and the asymmetric solid-liquid interface exhibits.Because the tilted angle of surface energy force of interphase boundary is less than zero,the tilted angle of lamellae in simulation results is less than the value predicted by the theory based on symmetric-pattern approximation.Combined with phase-field simulation,the tilted angle of surface energy force of interphase boundary is influenced by growth condition.With the increase of lamellar spacing,contacted angle and tilted angle of lamellae,the absolute value of tilted angle of surface energy force of interphase boundary increase.The difference in tilted angle of eutectic lamellae also increase.(3)The influence of interphase boundary anisotropy on eutectic lamellar morphology in directional solidification is studied.The lamellar morphology is influence by anisotropy function,lamellar spacing and orientation rotation angle.As the lamellar spacing increases,eutectic lamellae transition from steady-state into oscillation.When the interphase boundary has weak four-fold anisotropy,eutectic lamellae exhibit steady floating patterns and floating oscillations.When the interphase boundary is nearly locked and highly locked,eutectic lamellae exhibit steady floating patterns,steady locked patterns,floating oscillations,locked oscillations and mixed oscillation.And with the lamellar spacing increasing,the range of orientation rotation angle where the mixed oscillation exhibit increases.(4)A theoretical model is developed to describe the process of lamellar spacing adjustment.Because of taking the asymmetric solid-liquid interface into consideration,it eliminated the mixed bias term.The disturbance analysis based on Fourier transform shows that when the diffusion coefficient of lamellar spacing is larger than zero,the lamellae can growth stably without the phenomenon of lamellar termination,and the lamellar spacing will be gradually homogenized with time.Combined with the phase-field simulation,the results show that the lamellar spacing diffusion coefficient of the locking type is much lower than that of the floating type,so the adjustment rate of lamellar spacing is slower than that of the floating type.When the lamellar spacing is larger than the minimum undercooling lamellar spacing,the lamellar spacing diffusion coefficient increases with the increase of the lamellar spacing and decreases with the increase of the temperature gradient.