Simulation Methodology And Behavior Of Dendritic Growth During Solidification Process Of Steel

As the basis to reveal the intrinsic relationship between continuous casting processes and solidification defects,the dendritic growth of steel strands has drawn more and more attention of metallurgists.Because solidification processes of continuously cast steel strands are characterized by high temperature,opacity,and long mushy zone,the experimental investigation of the dendritic evolution of the continuously cast steel strand has not yet been realized,even though the in situ observation technique with synchrotron X-ray can successfully present the dendritic growth of small steel sample.With the springing up of numerical simulation methods such as phase field(PF),level set(LS)and cellular automaton(CA)and the rapid development of computers,the depiction of the dendritic solidification process of the continuously cast steel strand are gradually coming true.In consideration of the huge computational amount of the across scale modeling from the macroscopic strand to the microscopic dendrite,high efficient CA approach was used to deal with the growth kinetics of the solidification interface.In addition,the transport phenomena involved in the dendritic growth were solved with finite volume method(FVM).Therefore,a serial of CA-FVM models in two-dimenional(2D)and three-dimensioanl(3D)spaces were developed to simulate the dendritic growth of Fe-based alloys in the present work.Moreover,the limitation of the computational efficiency of 3D CA-FVM model was broken through,and the mesh anisotropy of CA approach was weakened.Under the premise that the preferential growth direction was ensured,the assumption of the sharp interface and the growth consistency of multi-oriented dendrites were met and kept as far as possible.Accordingly,the present work described equiaxed and columnar dendrites and colunmanr to equiaxed transition(CET)of Fe-0.82C(wt%)alloy in detail,emphatically analyzed the influences of the forced flow on the dendritic growth,and successfully simulated the dendritic evolution during the solidification of high carbon steel billet.Therefore,the present work contributes to exploring new ways to investigate and control the solidication structure of continuously cast steel strands.Main contents and conclusions are as follows:(1)Based on Neumann rule describing the conficells,CA-FVM models were developed to predict equiaxed and columnar dendritic growth of guration and the capture of neighboring Fe-C alloy.The results show that the parallel Jacobi code with once 2D iteration in 3D BCT can improve the computational efficiency of 3D CA-FVM model substantially.For the flow problem with the melt passing around orthogonally arranged blocks at the scale of 2013,it takes only 2.60 h,compared with 92.62 h with serial TDMA.CA-FVM models can well predict equiaxed dendritic growth in the undercooled melt and columanr dendritic growth during the unidirectional solidification process of Fe-C alloys,even with the forced flow,compared with their analytical and experimental results.(2)With CA-FVM models,the present work described dendritic growth behaviors of Fe-0.82C alloy in the undercooled melt and during the unidirectional solidification process and investigated similarities and differences between 2D and 3D results.The results show that influences of factors such as the melt undercooling,the flow type and the flow intensity on dendritic growth behaviors of alloy can be ascribed to the envelope with enriched solute aound the dendrite,that is,the distribution of the concentration gradient.With the increase of the melt undercooling,the solute envelope gets thinner,which promots the formation of secondary arms.With the forced flow,the enriched solute segregates more at the downstream side of the dendrite,so that the growth of the upstream arm of the equiaxed dendrite and the columnar dendrite(3D)near the inlet is promoted.Moreover,secondary arms prefer to forming and developing at upstream sides.Compared with 3D case,2D equiaxed dendrite is with much thicker solute envelope,which causes more significant upstream growth of primary arms and inhibits the formation of secondary arms.However,the difference between 2D and 3D columnar dendrites depends mainly on the dimensional space.For example,columnar dendrite near the inlet is the first to be inhibited in 2D space.Additionally,with the increase of the anisotropy parameter,3D equiaxed dendrite grows faster,while its secondary arms are first weakened,and then promoted,especially at low melt undercooling.During the unidirectional solidification process,small and fine columnar dendrites are easily blocked by secondary arms of adjacent strong ones,and are absorbed by them at last,which is the coarsening phenomenon of columnar dendrites and agrees with the experimental observation.Proper improvement of the cooling intensity can reduce primary and secondary dendrite arm spacings,enhance the compactness of columnar dendrites,accordingly improve the central quality of high carbon steel billet.(3)Based on the decentered square algorithm,the present work altered the determination of the half length of the square diagonal according to the preferential growth orientation,and then modified the interface evolution in the consideration of the contribution of neighboring solid cells,so as to reasonably match the growth of the interface cell and the evolution of decentered square.As a result,MCA-FVM models competent to describe multi-oriented dendritic growth of Fe-based alloys were established in 2D and 3D spaces.The results show that these models can reasonably keep preset preferential growth orientations of equiaxed dendrites,and ensure the growth consistence and the sharp interface.MCA-FVM-II model can even clearly depict the dendrites with preferential growth orientations close to CA meshes.Steady growth paramters of equiaxed dendritic tips predicted by present MCA-FVM models can agree with LGK analytical solutions to some extent.Meanwhile,through comparisons with results from in situ observations by synchrotron X-ray and dendritic etching of strands(ingots),MCA-FVM models can well depict the dendritic morphology of Fe-based alloys and quantitatively predict secondary and tertiary dendrite arm spacings.(4)Taking Fe-0.82C alloy as an example,MCA-FVM models were employed to investigate the solute segregation in the modeling domain,describe more complicated dendritic solidification phenomena such as the recalescence and CET,and eventually predict the dendritic structure of high carbon steel billet by continuous casting.The results show that both the recalescence temperature and the corresponding solid fraction ranges expand with the improvement of the cooling intensity during the solidification of multi-equiaxed dendrites.With the increase of the cooling rate,secondary arms of the equiaxed dendrite become more and more developed,the region with low concentration expands,however the solute segregation in the domain is severer.Under the condition with super cooling intensity,the low-concentration region tends to reduce the solute segregation in the domain a little.Additionally,the forced flow promotes the equiaxed dendritic solidification and deteriorates the solute segregation in the domain.Columnar dendrites with preferential growth directions consistent with the heat flow are the final solidification structure during the unidirectional solidification process.Meanwhile,the adjusting of primary dendritie arm spacing by tertiary arms is influenced by the cooling intensity and the competition of columnar dendrites.Generally,intensive cooling favours the survival of tertiary arms and is helpful to adjust primary dendrite arm spacing.As controlled by solute distributions around columnar dendritic tips,nuclei of equiaxed dendrites can form between columnar dendrites at first,or explode in front of dendritic tips.With the improvement of the cooling rate.and intial carbon content,or the decrease of the temperature gradient and the average nucleation undercooling,CET is promoted and changes from the mixed-dendrite model to explosive-equiaxed-dendrite one,moreover the number of equiaxed dendrites increases,while their average size declines.The dendrite arm spacings,the vertical height of columnar dendrites and the location of CET predicted by parallel MCA-FVM-II model agree with actual conditions in continuously cast high carbon steel billet.