基于MPI并行的PF-LBM三维枝晶生长模型模拟计算

材料微观组织数值模型模拟是一个密集型计算问题,其模拟时间太长且模拟规模太小.特别是在反映现实模拟的三维多场耦合材料枝晶成型过程中,由于模拟规模太小和计算时间太长,从而导致不能清楚地、及时地反映出枝晶的生长过程.为解决这两个问题,提出使用MPI对等模式对耦合流场的相场法进行三维晶枝生长模型模拟计算,并沿x轴等值面切割整个模型,把分割后的小模型分到不同MPI节点中实现并行运算.结果表明:在相同模拟规模下,10个MPI并行计算节点的加速比可达串行的19.9倍;同时其模拟规模也从串行的211×211×211个网格数增加到388×388×388个网格数.证明使用MPI并行计算对PF-LBM进行模拟解决了单CPU上模拟规模太小和计算时间太长的问题.

Phase field model for strong interfacial energy anisotropy of HCP materials

Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value（1/35）, the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.

Phase-field simulations of forced flow effect on dendritic growth perpendicular to flow

The effect of supercooled melt forced laminar flow at low Reynolds Number on dendritic growth perpendicular to melt flow direction was investigated with the phase-field method by incorporating melt convection and thermal noise under non-isothermal condition. By taking the dendritic growth of high pure succinonitrile （SCN） supercooled melt as an example, side-branching shape difference of melts with flow and without flow was analyzed. Relationships among supercooled melt inflow velocity, deflexion angle of dendritic arm and dendritic tip growth velocity were studied. Results show that the melt inflow velocity has few effects on the dendritic tip growth velocity. A formula of relationship between the velocity of the melt in front of primary dendritic tip and the dendritic growth time was deduced, and the calculated result was in quantitative agreement with the simulation result.

Modeling of equiaxed and columnar dendritic growth of magnesium alloy

Based on the cellular automaton （CA） method, a numerical model was developed to simulate the dendritic growth of magnesium alloy with HCP crystal structure. The growth kinetics was calculated from the complete solution of the transport equations. By defining a special neighborhood configuration with the square CA cell, and using a set of capturing rules which were proposed by BELTRAN-SANCHEZ and STEFANESCU for the dendritic growth of cubic crystal metals during solidification, modeling of dendritic growth of magnesium alloy with different growth orientations was achieved. Simulation of equiaxed dendritic growth and columnar dendritic growth under directional solidification was carried out, and validation was performed by comparing the simulated results with the experimental results and those in the previously published works.

Phase-field modeling of dendritic growth under forced flow based on adaptive finite element method

A mathematical model combined projection algorithm with phase-field method was applied. The adaptive finite element method was adopted to solve the model based on the non-uniform grid, and the behavior of dendritic growth was simulated from undercooled nickel melt under the forced flow. The simulation results show that the asymmetry behavior of the dendritic growth is caused by the forced flow. When the flow velocity is less than the critical value, the asymmetry of dendrite is little influenced by the forced flow. Once the flow velocity reaches or exceeds the critical value, the controlling factor of dendrite growth gradually changes from thermal diffusion to convection. With the increase of the flow velocity, the deflection angle towards upstream direction of the primary dendrite stem becomes larger. The effect of the dendrite growth on the flow field of the melt is apparent. With the increase of the dendrite size, the vortex is present in the downstream regions, and the vortex region is gradually enlarged. Dendrite tips appear to remelt. In addition, the adaptive finite element method can reduce CPU running time by one order of magnitude compared with uniform grid method, and the speed-up ratio is proportional to the size of computational domain.

Simulation and experimental validation of three-dimensional dendrite growth

A three-dimensional （3-D） modified cellular automaton （MCA） method was developed for simulating the dendrite morphology of cubic system alloys. Two-dimensional （2-D） equations of growth velocities of the dendrite tip, interface curvature and anisotropy of the surface energy were extended to 3-D system in the model. Therefore, the model was able to describe the morphology evolution of 3-D dendrites. Then, the model was applied to simulate the mechanism of spacing adjustment for 3-D columnar dendrite growth, and the competitive growth of columnar dendrites with different preferred growth orientations under constant temperature gradient and pulling velocity. Directional solidification experiments of NH4Cl-H2O transparent alloy were performed. It was found that the simulated results compared well with the experimental results. Therefore, the model was reliable for simulating the 3-D dendrite growth of cubic system alloys.

Free dendritic growth model incorporating interfacial nonisosolutal nature due to normal velocity variation

Considering both the effects of the interfacial normal velocity dependence of solute segregation and the local nonequilibrium solute diffusion,an extended free dendritic growth model was analyzed.Compared with the predictions from the dendritic model with isosolutal interface assumption,the transition from solutal dendrite to thermal dendrite moves to higher undercoolings,i.e.,the region of undercoolings with solute controlled growth is extended.At high undercoolings,the transition from the mainly thermal-controlled growth to the purely thermal-controlled growth is not sharp as predicted by the isosolute model,but occurs in a range of undercooling,due to both the effects of the interfacial normal velocity dependence of solute segregation and the local nonequilibrium solute diffusion.Model test indicates that the present model can give a satisfactory agreement with the available experimental data for the Ni-0.7% B（mole fraction） alloy.

Simulation of faceted dendrite growth of non-isothermal alloy in forced flow by phase field method

Numerical simulation based on a new regularized phase field model was presented to simulate the dendritic shape of a non-isothermal alloy with strong anisotropy in a forced flow. The simulation results show that a crystal nucleus grows into a symmetric dendrite in a free flow and into an asymmetry dendrite in a forced flow. As the forced flow velocity is increased, both of the promoting effect on the upstream arm and the inhibiting effects on the downstream and perpendicular arms are intensified, and the perpendicular arm tilts to the upstream direction. With increasing the anisotropy value to 0.14, all of the dendrite arms tip velocities are gradually stabilized and finally reach their relative saturation values. In addition, the effects of an undercooling parameter and a forced compound flow on the faceted dendrite growth were also investigated.

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton-finite difference(CA-FD) method was used to investigate the dendrite growth during directional solidification(DS)process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail.Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.

Formation of twinned dendrites during unidirectional solidification of Al-32%Zn alloy

The present study focused on the formation and crystallographic orientation of twinned dendrites coexisting with equiaxed grains in unidirectional solidification of Al-32%Zn(mass fraction)alloy.The morphology was investigated by optical metallograph and electron back-scattered diffraction technique.Results showed that the macrostructure of the alloy exhibited a typical feathery and fan-like structure while the microstructures were elongated lamellas,which were separated by coherent and incoherent twin boundaries.Both the primary trunk and all lateral arms of twinned dendrites grew along〈110〉directions,unlike regular〈100〉α(Al)dendrites.The facet growth of crystals at solid/liquid interface was responsible for the origin of twinned dendrites during the weak local convection,and high thermal gradient and medium solidification velocity had significant contribution to the formation of twinned dendrites.The formation mechanism of twinned dendrites which consisted of three multiplication ways of new twin boundaries formation and one way of dendrite evolution in twin plane was shown schematically.

Liquid phase separation and subsequent dendritic solidification of ternary Fe_(35)Cu_(35)Si_(30) alloy

Liquid Fe35Cu35Si30alloy has achievedthemaximum undercooling of 328 K （0.24TL） with glass fluxing method, and it displayed triple solidification mechanisms. A critical undercooling of 24 K was determined for metastable liquid phase separation. At lower undercoolings,α-Fe phase was the primary phase and the solidification microstructure appeared as homogeneous well-defined dendrites. When the undercooling exceeded 24 K, the sample segregated into Fe-rich and Cu-rich zones. In the Fe-rich zone, FeSi intermetallic compound was the primary phase within the undercooling regime below 230 K, while Fe5Si3intermetallic compound replaced FeSi phase as the primary phase at larger undercoolings. The growth velocity of FeSi phase increased whereas that ofFe5Si3 phase decreased with increasing undercooling. For the Cu-rich zone, FeSi intermetallic compound was always the primary phase. Energy-dispersive spectrometry analyses showed that the average compositions of separated zones have deviated substantially from the original alloycomposition.

Effect of growth rate on microstructure and solute distribution of Al-Zn-Mg alloy

An Al-5.3%Zn-5.3%Mg alloy was unidirectionally solidified to determine morphological transition and solute distribution by a modification of the Bridgman technique for crystal growth with growth rates ranging from 4-500 μm/s and a temperature gradient of 25 K/cm. It was determined that growth rates from 6.5-9.5 μm/s generated a cell morphology, where the lower limit corresponds to the plane front to cellular transition and the upper limit indicates the cellular to columnar dendrite transition. The microstructures of the alloys solidified from 30 μm/s to growth rates less than 500 μm/s were mainly composed of columnar dendrites, while the microstructures solidified at growth rates greater than 500 μm/s were equiaxed. Regarding experimental results on solute distribution, a prediction of the model developed by Rappaz and Boettinger for dendrite solidification of multicomponent alloys was applied with excellent agreement. Results of solute distribution were employed to derive the precipitation fraction of τ-phase needed to increase the electrochemical properties of the alloy to be used as an Al-sacrificial anode.

Effects of RE and Sr additions on dendrite growth and phase precipitation in AZ91D magnesium alloy

To develop AZ91D alloys with fine microstructure, effects of the addition of rare earth (RE), Sr and RE + Sr on the dendrite growth and phase precipitation in AZ91D magnesium alloy were studied, respectively. The results show that the microstructure is refined and the morphology of β-Mg17A112 phase is modified with RE or Sr addition, especially with the RE+Sr composite addition which can reduce the average grain size of AZ91D alloy obviously to 141 μm. The needle-like or block-like new phases adhering to β-Mg17A112 phase form at interdendrites during solidification. The enrichment of RE or/and Sr elements in front of the solidification interface, especially at the tips of α-Mg dendrite, which restricts the growth of α-Mg dendrite, changes the preferential growth of α-Mg and finally results in the grain refinement and the blunting of α-Mg dendrite.

Effect of nonlinear liquidus and solidus on dendrite growth in bulk undercooled melts

On the base of nonlinear liquidus and solidus,an extended model for dendrite growth in bulk undercooled melts was developed under local non-equilibrium conditions both at the interface and in the bulk liquid.In terms of thermodynamic calculations of the phase diagram,the model predictions are relatively realistic physically,since few fitting parameters are used in the model predictions.Adopting three characteristic velocities,i.e.the critical velocity of absolute solute stability(VC*),the velocity of maximal tip radius(VRm),and the velocity of bulk liquid diffusion(VD),a quantitative agreement is obtained between the model predictions and the experimental results in undercooled Ni-0.7%B and Ni-1%Zr(molar fraction) alloys,and the overall solidification process can be categorized.

Simulation of facet dendrite growth with strong interfacial energy anisotropy by phase field method

Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites,displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the<100> direction, which is eliminated by setting the b/a(a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.

Low-temperature fusion fabrication of Li-Cu alloy anode with in situ formed 3D framework of inert LiCu_x nanowires for excellent Li storage performance

The commercialization of rechargeable Li metal batteries is hindered by dendrite growth and volumetric variation. Herein, we report a Li-rich dual-phase Li-Cu alloy with built-in 3 D conductive skeleton to replace conventional planar Li anode. The Li-Cu alloy is simply prepared by fusion of Li and Cu metals at a relatively low-temperature of 500 °C, followed by a cooling process where phase-segregation leads to metallic Li phase distributed in the network of LiCu_x solid solution phase. Different from the common Li alloy, the electrochemical alloying reaction between Li and Cu metals is not observed. Therefore, the lithiophilic LiCu_x nanowires guides conformal plating of Li and the porous framework provides superior dimensional stability for the anode. This unique ferroconcrete-like structure of Li-Cu alloy enables dendrite-free Li plating for an expanded cycling lifetime. Constructing a new type of Li alloy with in situ formed electrochemically inactive framework is a promising and easily scaled-up strategy toward practical application of Li metal anodes.

Phase-field simulation of dendritic growth in a forced liquid metal flow coupling with boundary heat flux

A phase-field model with forced liquid metal flow was employed to study the effect of boundary heat flux on the dendritic structure forming of a Ni-40.8%Cu alloy with liquid flow during solidification.The effect of the flow field coupling with boundary heat extractions on the morphology change and distributions of concentration and temperature fields was analyzed and discussed.The forced liquid flow could significantly affect the dendrite morphology,concentration and temperature distributions in the solidifying microstructure.And coupling with boundary heat extraction,the solute segregation and concentration diffusion were changed with different heat flux.The morphology,concentration and temperature distributions were significantly influenced by increasing the heat extraction,which could relatively make the effect of liquid flow constrained.With increasing the initial velocity of liquid flow,the lopsided rate of the primary dendrite arm was enlarged and the transition of developing manner of the secondary arms moved to the large heat extraction direction.It was the competition between heat flux and forced liquid flow that finally determined microstructure forming during solidification.

Solidification researches using transparent model materials——A review

A review is given in the paper for solidification researches with transparent model materials. The effective experimental me- thod was first proposed by Jackson and Hunt in 1965. The transparent model materials for solidification researches are a kind of non-faceted crystals known as ＂plastic crystals＂ or ＂globular molecules＂, which have very low entropy of melting as that of metals. According to Jackson＇s theory proposed in 1958, entropy of phase transformation will determine whether the phase interface morphology is smooth or rough in atomic scale, which will lead to faceted or nonfacted phase interface in mi- croscopic and macroscopic scales. Succinonitrile （SCN） and its alloys with water, ethanol, acetone, and NH4C1-H：O solution are most commonly used as transparent model materials for solidification researches of dendritic growth, anisotropy of solid-liquid interfacial energy, crystal nucleation, crystal grain formation, directional solidification, eutectic and peritectic so- lidification, solidification defects formation such as bubble, hot tearing, etc. Among these researches, the most impressive work was the critical test of dendritic growth theories with high purity succinonitrile by Glicksman et al., which gave positive answer to the Ivantsov＇s analysis and negative answer to the ad hoc condition of the maximum velocity hypothesis. The future researches with transparent model materials could be suggested in three aspects： 1） accurate measurement of material proper- ties and alloy phase diagrams in more plastic crystals, especially to find more transparent eutectic and peritectic alloys; 2） accurate measurement of the grain boundary groove shape to obtain precise data of the anisotropy parameters of the interfacial free energy in transparent model materials; 3） to get clear pictures of solidification processes with morphology details in a rela- tively large area, with continuous movement of liquid and particles, in order to give experimental support to numerical simula- tions aimming at accurate description of microstructure formation during solidification of multicomponent alloys under complex conditions of real casting and welding processes.

Dendritic growth and solute trapping in rapidly solidified Cu-based alloys

Rapid solidification of binary Cu-22%Sn peritectic alloys and Cu-5%Sn-5%Ni-5%Ag quaternary alloys was accomplished by glass fluxing, drop tube and melt spinning methods. The undercooled, by glass fluxing method, Cu-22%Sn peritectic alloy was composed of a（Cu） and δ（Cu41Snll） phases. If rapidly solidified in a drop tube, the alloy phase constitution changed from α（Cu） and δ（Cu41Sn11） phases into a single supersaturated （Cu） phase with the reducing of droplet diameter, and the maximum solubility of Sn in （Cu） phase extended to 22%. The Cu-5%Sn-5%Ni-5%Ag quaternary alloy was composed of （Cu） and （Ag） phases under the containerless processing condition in a drop tube, and the solute microsegregation of （Cu） phase was obvious. When the Cu-5%Sn-5%Ni-5%Ag quaternary alloy was solidified by melt spinning method, microsegregation was suppressed and solute trapping occurred. The experimental results show that the microstructures of primary （Cu） phase in the two alloys transfer from coarse dendrites into equiaxed grains with the increase of cooling rate and undercooling, which is accompanied by the grain refinement effect.

Effect of solidification temperature range on the dendritic growth mode

Electromagnetic levitation technique was used to undercool bulk samples of Co-20% Cu and Co-60% Cu alloys and high undercoolings up to 303 and 110 K were achieved,respectively.The dendritic growth velocities were measured as a function of undercooling.The dendrite growth velocity of the Co-20% Cu alloy was much higher than that of the Co-60% Cu alloy.The experimental data were analyzed on the basis of the LKT/BCT dendritic growth model by taking into account non-equilibrium interface kinetics.It has been revealed that a transition from solute diffusion controlled dendritic growth to thermal diffusion controlled dendritic growth occurs at an undercooling of about 66 K for the Co-20% Cu alloy,whereas the dendrite growth in Co-60% Cu alloy proceeds in a solute diffusion controlled mode within a large solidification temperature range,and the solutal undercooling plays a dominant role.It is thus deduced that certain distinct solidification temperature ranges may be responsible for the different solidification modes for the two alloys.