Large-scale Quantitative Phase-field Simulation And In Situ Observation Of Alloy Solidification Microstructure

The microstructure of material determines its performance and is closely related to the solidification process.Dendrite is one of the most common solidification microstructures,and its morphology,size,and solute distribution directly affect the quality of the castings.Therefore,an in-depth understanding of the dendrite growth and the appropriate controlling are of significant importance in material science and metallurgical engineering.The quantitative phase-field(PF)method,which avoids explicit tracking of the complicated solid-liquid interface,has been developed as a widely used method to simulate dendrite growth during solidification.However,due to the low computational efficiency,the large-scale quantitative PF simulation is still a great challenge.In this dissertation,the fast calculation schemes for large-scale quantitative PF simulation of alloy polycrystalline solidification have been proposed.Combing with the in situ and real-time observation of solidification experiments by synchrotron X-ray radiography,the multi-dendrite growth in the experiments has been reproduced accurately and efficiently.The solute microsegregation and equiaxed dendrite growth kinetics are investigated comprehensively and deeply.The main contents and conclusions are as follows:(1)With the nonlinear preconditioning of the diffuse interface model,the original PF variable,whose value is constant in the solid and liquid phases while varies nonlinearly in the solid-liquid interface layer,has been transformed into a new linear variable.Then the grid size in the interface layer is allowed to be enlarged to 2?4 times of that for the original PF model.Consequently,the number of vertices of the computational mesh is significantly reduced to expedite computation.For polycrystalline solidification,an efficient front tracking method is developed to capture crystal orientations with consideration of the grain boundary energy,which avoids solving the complex governing equation of the orientation field in the traditional vector-valued PF model.Besides,a simple but efficient approach for adaptive mesh refinement/coarsening is proposed to furtherly improve the computing efficiency.On the basis of the above models and numerical methods,the spatial scale of the quantitative PF simulation can be enlarged to centimeter and millimeter scales,and the number of grains in simulations can also increase to 103 and 102 orders of magnitude,respectively in two dimension(2D)and three dimension(3D).These computations are realized just using an ordinary workstation,instead of clusters or supercomputers.(2)Equiaxed dendrite growth of binary alloys is simulated using the PF method,and the results of 2D and 3D simulations are compared quantitatively.Compring to the 2D simulation,it is demonstrated that owing to the extra freedom of the solute diffusion and liquid flow in 3D,the solute piled up ahead of the solid-liquid interface of the upstream dendritic arm tip is readily to diffuse and to be transported by the liquid flow,thus leading to a lower tip concentration,a higher concentration gradient,and a smaller thickness of the solute boundary layer.As a result,for the steady upstream dendritic arm tip in the 3D PF simulations,its growth velocity is larger while the radius is smaller than those in 2D.Furthermore,the ratios of the growth velocity or the radius between 3D and 2D simulations are not constant or confined in a certain range,but vary in a large range with the supersaturation and the liquid inflow velocity.These two ratios can also be expressed as power functions of the ratio of the growth Peclet number between 3D and 2D simulations.The differences between 2D and 3D simulations can be reduced by enlarging the supersaturation and liquid inflow velocity,but cannot be eliminated entirely.(3)Polycrystalline solidification of Al-Cu alloy under continuous cooling condition is simulated using the PF method,and effects of the grain refinement,cooling rate,and solid back diffusion on the solute microsegregation are investigated.It is indicated that for the slow solidification of alloys with substitutional solute,all of the grain refinement,cooling rate,and solid back diffusion are not the crucial factors affecting microsegregation behavior.The average and maximum solute concentration in liquid,as well as the solid fraction and the solute segregation index in PF simulations are between the predictions by the Lever rule and the Scheil equation.On the basis of the analysis of the PF simulations,a new microsegregation model has been developed,which provides a more accurate prediction of the solute concentration during polycrystalline solidfication than any current models,in particular at the late solidification stage when the solid fraction is close to 1.Furthermore,like the Lever rule and the Scheil equation,the new microsegregation model is simple and easy to use,so it is readily to be embed into CALPHAD softwares and macrosegregation models of castings,for calculation of phase equilibrium,prediction of precipitate,and modelling of macrosegregation.(4)The growth kinetics of the equiaxed crystal,from a critical nucleus to the final impinged growth,is studied using the PF simulation combing with the in situ and real-time observation by synchrotron X-ray radiography.Through quantiative 3D simulations,it is uneviled that a nucleation dominated growth(NDG)stage exists before the usual free steady-state growth and impinged growth which have been clarified in the classical crystal growth theory.During the NDG stage,the critical nucleus grows fast driven by the nucleation undercooling at first.And then its growth rate slows down to a minimum value,accompanied with the spherulite-dendrite transition.After the minimum value,the crystal growth rate increases again with undercooling increasing,and gradually approches to the steady-state free growth regime.The NDG stage is then validated by the in situ observation of the solidification experiments of Al-Cu alloys.Based on the growth kinetic characteristics during the NDG stage,a new method to precisely determine the nucleation undercooling is proposed for the alloy equiaxed dendrite growth.By means of this method,the nucleation undercoolings of all the grains in the solidification experiment are determined,and then a large-scale quantitative PF simulation in a computational domain comparable to the sample in the experiment is realized for polycrystalline solidification of Al-Cu alloy.The simulated grain morphology and growth kinetics are in good quantitative agreement with the experimental data,which not only recovers the three-stage grain growth kienetics in the experiment,but also validates the reliability of the NDG stage and the proposed method for determining the nucleation undercooling.