Phase Field Simulation Of Dendrite Growth In Microstructure Of Fe-Cr-C Ternary Alloy

Cold work abrasive steel is widely used in steel manufacturing industry because of its high compressive strength and high wear resistance.Because of its composition characteristics of high carbon and high alloy,it is easy to cause solute segregation and instability of microstructure growth morphology,which further affects carbide precipitation in the microstructure.Fe,Cr and C are the most important elements in high strength steel and wear-resistant steel.The primary phase composition of Fe-CrC ternary alloy formed in the initial solidification stage is the basis of microstructure research during solidification.As the primary phase,dendrite precipitates from the liquid phase,which not only determines the properties of steel,but also is the base phase for further precipitation of carbides.Therefore,it is of great significance to study the morphology of dendrite.Traditional experimental methods have high cost and difficulty in studying microstructure.With the continuous development of computational science,phase field method is used to simulate the evolution of dendritic morphology of microstructure,and strict mathematical modeling is used to predict the evolution process of morphology and microstructure of crystal or amorphous materials.The purpose of this study is to establish the phase field model of Fe-Cr-C ternary alloy solidification.Based on Ginzburg landau theory,the binary phase field model is deduced according to Karma model and KKS model.Considering the introduction of new solute element terms,the free energy equations of different solutes in the ternary alloy system are obtained,and a new ternary phase field model is proposed.The thin interface model based on the phase field theory is applied to the micro segregation analysis of Fe-Cr-C alloy under the condition of approximate dilute solution.Considering that the chemical formula of the interface is equal,the phase field dynamics equation is derived,and the dendrite growth of the primary phase in Fe-CrC alloy is obtained.By introducing anisotropic dynamic function,the influence of anisotropic strength coefficient on phase field model is analyzed.The temperature field distribution and dendrite growth temperature curve were obtained by coupling the temperature field equation.The relationship between the phase field parameters and the material properties is derived by using the thin interface limit theory.The isothermal dendrite growth of Fe-C and Fe-Cr-C alloys is calculated and simulated by using the two-dimensional discretization method.The results show that:(1)The high anisotropy strength makes the growth of dendrite arms more active,the number of dendrite arms increases,and the radius of main dendrite arms becomes smaller.The weak anisotropy strength results in fewer dendrite arms and coarser radius of main dendrite arms.(2)When noise is introduced,the number of dendrite arms will become more random.The introduction of noise does not affect the number of primary dendrite arms and secondary dendrite arms,and the noise does not change the steady-state behavior of the dendrite tip.(3)Fe-Cr-C ternary dendrite system and Fe-C binary dendrite system have similar dendritic morphology distribution.The interface of binary and ternary systems is convex and concave,and the area near the crystal nucleus but without solute enrichment is shrunk,which then evolves into dendritic morphology.(4)Introduction of new element Cr,and Cr and C compounds are enriched in the shrinkage zone during solidification.With the increase of Cr concentration,the dendrite growth speed is accelerated,the secondary dendrite spacing is shortened,and the dendrite morphology becomes more ambiguous.(5)In the melt near the crystal nucleus,the temperature gradient decreases slowly;At the solidification interface,the temperature gradient rapidly reaches the same temperature gradient as the external solute.With the increase of the initial undercooling temperature,the dendrite evolution rate,and the growth rate of the secondary dendrite arm increase,while the main dendrite arm remains unchanged.