Columnar-to-equiaxed Transition Position Research Articles

Influence of hot top geometry on columnar-to-equiaxed transition in a 12 MT steel ingot

In the present work, the impact of hot top geometry and thermal history on the Columnar-to-Equiaxed Transition (CET) point, of a 12 MT steel ingot was determined using finite element modeling. Experimental validation of the model was conducted on an industrial-size ingot, focusing on temperature, macrosegregation, and shrinkage microporosity. The anticipated Columnar-to-Equiaxed Transition point, influenced by the interaction of solid front rate, thermal gradient, and solid fraction was considered in the analysis. The findings revealed a shift in the CET position in new configurations, up to 56 mm, 63 mm, and 60 mm from the ingot wall in the bottom, middle, and top of the ingot, respectively. The changes are attributed to variations in the kinetics of solidification, particularly the solidification time. Thermo-mechanical phenomena, encompassing mold filling, cooling, solutal convection, and flow driven by shrinkage, were incorporated into the model to predict macrosegregation and the risk of porosity and shrinkage cavity formation for different hot top geometries. A criterion is proposed that allows mitigating macrosegregation and minimizing the risk of porosity and shrinkage cavity.

Effect of Pressure on Second Dendrite Arm Spacing and Columnar to Equiaxed Transition of 30Cr15Mo1N Ingot

In order to clarify the effects of pressure on the second dendrite arm spacing (SDAS) and columnar to equiaxed transition (CET) of 30Cr15Mo1N ingot, changes in solidification parameters, cooling rate and columnar dendrite tip growth rate with pressure have been investigated. A formula is proposed to obtain the quantitative correlation between pressure (≤ 2 MPa) and interfacial heat transfer coefficient: . And then, A formula is proposed to calculate SDAS with cooling rate: , which is applicable for low pressure (≤2 MPa) and low cooling rate (0.4–1.4 K · s−1). There are tiny changes in solidification mode and equilibrium partition coefficient with increasing pressure from 0.5 to 2 MPa. Therefore, increasing pressure refines SDAS mainly by enlarging cooling rate. Pressurization can increase columnar dendrite tip growth rate by enhancing undercooling, and inhibit nucleation and growth of equiaxed dendrite by decreasing constitutional undercooling. It results that the distance between the center of ingot and CET position decreased with increasing pressure from 0.5 to 2 MPa. And a formula is proposed to calculate columnar dendrite tip growth rate with undercooling: , which is suitable for low pressure (≤2 MPa).

Mechanism and Control of Sulfide Inclusion Accumulation in CET Zone of 37Mn5 Round Billet

In the current study, the R/2 accumulation was found from the results of sulfide inclusion distribution across the diameter of 37Mn5 round billet using ASPEX. In order to reveal the mechanism and furthermore control this phenomenon, the distribution of sulfur content and the macrostructure of billet after etching were analyzed. The results showed that there was obvious segregation in the same position as sulfide inclusion accumulation, where the columnar-to-equiaxed transition (CET) took place. Therefore, the mechanism of sulfide inclusion accumulation in the CET zone was discussed on the basis of the mechanism of R/2 sulfur segregation. The interlaced and coarse dendrites in the CET zone blocked solute concentrated from select crystallization, thus caused sulfur segregation near R/2. Higher sulfur content and larger secondary dendrite arm spacing (SDAS) in the CET zone benefited the precipitation and growth of sulfide inclusions. The effect factors of CET position were discussed on the purpose that by proper cooling conditions, the morphology of solidification structure can be controlled, by which the element segregation can be modified; thereafter, the control of sulfide inclusion distribution in the billet can be realized.

Conditions for CET in a gamma TiAl alloy

The solidification of gamma TiAl alloys is of interest to the aerospace and automotive industries. A gamma TiAl multicomponent alloy: Ti-45.5Al-4.7Nb-0.2C-0.2B (at. %) has been the focus of a study to investigate the solidification conditions that led to a Columnar to Equiaxed Transition (CET) in a directional solidification experiment where traditional Bridgman solidification was combined in series with the power down method. In this paper, a numerical modelling result (a locus plot of columnar growth rate and temperature gradient) from this experiment is superimposed onto CET maps generated using an established analytical model for CET from the literature. A parametric study is carried out over suitable ranges of nucleation undercooling and nuclei density values. The predicted CET positions are compared with the experimentally measured CET position. Reasonable agreement is found at low levels of nuclei density. The paper concludes with estimates for the solidification conditions (nuclei density and nucleation undercooling) that led to the CET.

Simulation of directional solidification of refined Al–7 wt.%Si alloys – Comparison with benchmark microgravity experiments

Formation of grain structure and segregation during solidification of refined Al–7wt.%Si alloys under microgravity is simulated using a two-dimensional axi-symmetrical Cellular Automaton-Finite Element (CAFE) solidification model. This fully integrated model resolves a complex interplay between heat transfer at the macroscale and grain structure evolution and microsegregation formation at the mesoscale. Direct comparison with benchmark experiments performed under microgravity conditions of the International Space Station is carried out. Boundary conditions used in the simulations are deduced from the experimental measurements of temperature. Qualitative agreement is achieved concerning CET (columnar-to-equiaxed transition) position, CET transition mode (sharp or progressive), distributions of grain elongation factor and equivalent diameter, and distribution of eutectic fraction. The influences of pulling velocity and thermal gradient on grain structure and intergranular segregation are correctly reflected and are discussed. Moreover, we take advantage of the simulation results to study the effect of otherwise inaccessible parameters such as the degree of constitutional undercooling and the amplitude of the undercooled region. Another originality of this paper is to conduct quantitative comparisons between experiments and simulations which allows discussion of the improvements needed in the simulation.

Macroscopic Model for Predicting Columnar to Equiaxed Transitions Using Columnar Front Tracking and Average Equiaxed Growth

A macroscopic model of Columnar-to-Equiaxed Transition (CET) formation is presented. The growth of a columnar zone and an equiaxed zone are treated separately and modeled on a fixed grid. The model uses a columnar Front Tracking (FT) formulation to compute the motion of the columnar front and the solidification of the dendritic columnar mushy zone. The model for the equiaxed zone calculates the average growth of equiaxed grains within the control volumes of undercooled liquid. The proposed model, which calculates the average equiaxed growth, is different from previous FT models which consider each equiaxed grain envelope separately. A lognormal size distribution model of seed particles is used for the equiaxed nucleation in the undercooled liquid zone. After nucleation, average equiaxed growth is computed by considering the equiaxed envelopes as spherical. The extended volume concept is used to deal with grain impingement. The Scheil equation is used to calculate the solid fraction and latent heat release. When the equiaxed fraction is great enough, advancement of the columnar front is halted and the CET position is determined. CET formation was simulated for directional solidification of an aluminium-silicon alloy. The results were compared with a previous FT-CET prediction model as well as with experimental data. Agreement was found in both cases.

A Comparison of Columnar-to-Equiaxed Transition Prediction Methods Using Simulation of the Growing Columnar Front

In this article, the columnar-to-equiaxed transition (CET) in directionally solidified castings is investigated. Three CET prediction methods from the literature that use a simulation of the growing columnar front are compared to the experimental results, for a range of Al-Si alloys: Al-3 wt pct Si, Al-7 wt pct Si, and Al-11 wt pct Si. The three CET prediction methods are the constrained-to-unconstrained criterion, the critical cooling rate criterion, and the equiaxed index criterion. These methods are termed indirect methods, because no information is required for modeling the equiaxed nucleation and growth; only the columnar solidification is modeled. A two-dimensional (2-D) front-tracking model of columnar growth is used to compare each criterion applied to each alloy. The constrained-to-unconstrained criterion and a peak equiaxed index criterion agree well with each other and some agreement is found with the experimental findings. For the critical cooling rate criterion, a minimum value for the cooling rate (between 0.07 and 0.11 K/s) is found to occur close to the CET position. However, this range of values differs from those cited in the literature (0.15 to 0.16 K/s), leading to a considerable difference in the prediction of the CET positions. A reason for this discrepancy is suggested, based on the fundamental differences in the modeling approaches.

Numerical Analysis on Columnar-to-equiaxed Transition of δ-Ferrite Dendrite in Carbon Steel Induced by Titanium Carbonitride Particles

Dendrite growth simulations have been performed to analyze Columnar-to-Equiaxed Transition (CET) of δ-ferrite dendrite structure triggered by fine particles of a primary Ti(C, N) crystal. The CET position estimated by Hunt's criterion and the present simulation indicated that the existence of a large number of the Ti(C, N) particles gives rise to the CET of the dendrite structure even in the vicinity of the mold wall under the present casting condition. Furthermore, the capability of the Ti(C, N) leading to the CET was discussed in the light of the different number of Ti(C, N) particles and the different thickness of cast ingot. It was shown that a sufficient number of Ti(C, N) leads to the formation of fully equiaxed dendrite structure irrespective of the ingot thickness.

Mechanical Blocking Mechanism for the Columnar to Equiaxed Transition

Mechanical blocking of the columnar front during the columnar to equiaxed transition (CET) is studied by quantitatively comparing the CET positions obtained with one stochastic model and two deterministic models for the unidirectional solidification of an Al-7 (wt pct) Si alloy. One of the deterministic models is based on the solutal blocking of the columnar front, whereas the other model is based on the mechanical blocking. The solutal-blocking model and the mechanical-blocking model with the traditional blocking fraction of 0.49 give columnar zones larger than those predicted with the stochastic model. When a blocking fraction of 0.2 is adopted, however, the agreement is very good for a range of nucleation undercoolings and number density of equiaxed grains. Therefore, changing the mechanical-blocking fraction in deterministic models from 0.49 to 0.2 seems to model more accurately the mechanical-blocking process that can lead to the CET.

Columnar front tracking algorithm for prediction of the columnar-to-equiaxed transition in two-dimensional solidification

A novel algorithm to track the columnar front in one- (1D) and two-dimensional (2D) solidification problems has been developed and coupled with the governing equations of a deterministic model to predict the columnar-to-equiaxed transition (CET). The new algorithm, inspired by the cellular automaton (CA) technique, requires a CA mesh as coarse as that for the numerical solution of the governing equations. Front positions predicted with the new algorithm during transient and steady-state growth under given 1D and 2D temperature fields matched the results from analytical solutions. The time evolution of the columnar front agreed well with the published results for the 1D and 2D solidification of an Al–3(wt%) Cu alloy. Some discrepancy observed in the CET position was attributed to the different implementation of the columnar front blocking criterion and to the nonisothermal character of the front line.

Stochastic modeling of columnar-to-equiaxed transition in Ti–(45–48 at%) Al alloy ingots

A two-dimensional (2-D) stochastic model of macro–micro type for predicting the columnar-to-equiaxed transition (CET) during solidification processes of the large size Ti–(45–48 at%) Al alloy ingots is developed in this paper. The macroscopic part is based on a finite differential method (FDM) for modeling of heat transfer. The microscopic part consists of a cellular automaton method (CA) for modeling of nucleation and growth. The formation of a shrinkage cavity at the top of ingot is taken into account. The effects of casting variables on CET are presented and discussed. A quantitative relation between CET position and casting variables is obtained. The columnar zone is found to expand with decreasing alloy composition, mold-preheated temperature and convection, and increasing the thermal conductivity of mold, superheat and heat transfer coefficient.

Simulation of columnar-to-equiaxed transition in solidified Al–Cu alloy ingots by stochastic model

A two-dimensional stochastic model for the prediction of the columnar-to-equiaxed transition (CET) during solidification processes of Al–Cu alloy ingots is developed, based on a finite differential method (FDM) for macroscopic modelling of heat transfer and a cellular automaton method (CA) for microscopic modelling of nucleation and growth. The formation of a shrinkage cavity at the top of the ingot is taken into account. The effects of the casting variables on the CET are presented and discussed. A quantitative relation between CET position and casting variables is obtained. The columnar zone is found to expand with decreasing alloy composition and mould preheated temperature, and with increasing superheat and initial heat transfer coefficient. However, increasing the mould preheated temperature in a particular range has a negligible influence on the CET. With a low rate of heat extraction, the CET is found to be independent of melt superheat.

A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification

A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during solidification of binary alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar front—as opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity (VT) vs temperature gradient (G) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional solidification experiments involving Al-Si alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites.

Numerical modeling of columnar to equiaxed transition with consideration of molten steel flow

The numerical model of columnar to equiaxed transition (CET) was constructed with consideration of molten steel flow. Solid shell growth was analyzed by using macroscopic heat flow model in addition to heat transfer due to the fluid flow at the solidification front, which was calculated by fluid flow model. At the same time, the dendrite tip temperature and the growth of equiaxed crystal in the undercooled liquid region was estimated and the CET position was diagnosed. By the application of electromagnetic stirrer (EMS), the superheat in the pool diminished and undercooled region was enlarged by heat transfer due to fluid flow at the solidification front. In addition, the ratio of equiaxed zone increased with the increase of grain density by EMS. Therefore, it has been estimated that solidification structure change by application of EMS was caused by superimposition of these two effects. Moreover the size of equiaxed crystal estimated by this model could show good agreements with experimental ones.

The columnar to equiaxed transition during solidification of Sn–Pb alloys

In the present article, some important trends are shown regarding the influence of solidification thermal parameters on the columnar to equiaxed transition (CET) during the unsteady state solidification of Sn–Pb alloys. A comparison of the results obtained in the present work with results from the literature concerning similar experiments, but undertaken under conditions of lower heat transfer efficiency at the metal–mold interface, has shown that a realistic CET criterion should be based on a critical cooling rate at the dendrite tips of about 0.014 K/s, which depends only on the alloy system. The effects of melt superheat, solute concentration and metal–mold heat transfer coefficient on the CET position are also investigated.

Prediction of Columnar to Equiaxed Transition during Diffusion-Controlled Dendritic Alloy Solidification

A model is presented to predict the columnar to equiaxed transition (CET) in alloy castings. The model is based on a multiphase approach and accounts for heat and solute diffusion, as well as for grain nucleation, growth, and morphology. The model equations are applicable to both columnar and equiaxed dendritic solidification, thus offering an efficient single-domain formulation. A fixed grid, fully implicit finite-difference procedure is employed in the numerical solution, and a novel front tracking technique is incorporated that is also implicit in nature and readily applies to multidimensional situations. Calculations are performed for one-dimensional (1-D) and two-dimensional (2-D) castings of Al-Cu and Sn-Pb alloys. The calculated CET positions are compared with previous measurements in a (1-D) ingot cast under well-controlled conditions, and good agreement is found. The effects of various casting parameters on the CET are numerically explored.