Numerical Determination of Secondary Dendrite Arm Spacing for IN738LC Investment Castings

A numerical model was developed to estimate the solidification conditions and the secondary dendrite arm spacing of equiaxed solidified IN738LC investment castings. The model, composed of geometric data, thermophysical properties, and boundary conditions, was verified by a comparison of calculated and measured process temperatures obtained from casting experiments. The computation of the secondary dendrite arm spacing was carried out from temperature gradient G, solidification rate v, and an alloy-specific parameter M, determined by means of an inverse approach. The calculated secondary dendrite arm spacing was found to be in very good agreement with metallographic measurements.     

Refinement of dendrite arm spacings in aluminum ingots through heat flow control

A model for heat flow during solidification of alloys is presented which treats the heat of fusion released during solidification separately for three distinct regions of a casting: portions released isothermally at the liquidus temperature, between the liquidus and solidus in a specified manner and the remainder released at the solidus. The model is solved numerically by a finite difference technique for unidirectional and two-dimensional heat flow in end-chilled thin plates. Effects of heat transfer coefficient at the chill, superheat, heat input, liquid convection and amount of sidewise heat loss are considered. Results are presented in terms of position of liquidus and solidus isotherms as a function of time, width of the mushy zone and local solidification time and secondary dendrite arm spacingvs distance from the chill. Results from experimental castings made under controlled heat flow conditions are compared with computer calculations. The local solidification time and resultant dendrite arm spacing are shown to decrease at a given location as a) the chill heat transfer coefficient increases, b) superheat increases, c) the gradient of temperature at the solidification front increases, and d) the multidimensionality of the heat flow path increases. Formerly Graduate Students in the Department of Materials Science and Engineering, M.I.T., Cambridge, MA, Department of Metallurgy and Mining Engineering.     

Solidification structure and micro-segregation of unidirectionally solidified steels

Two linepipe steels with carbon mass contents of 0.09 and 0.15% were subjected to steady state unidirectional solidification in a special apparatus. The specimens were positioned in alumina tubes of 15 mm internal diameter, and were pulled downwards at a constant rate, R, from the high temperature furnace. The temperature gradient, G, at the solidification boundary was varied between 5 and 136 K/cm. The dendrite arm spacings measured were quantitatively assessed using the relationship Λ = cR^mGⁿ. The exponents m and n for the primary arm spacing, Λ₁, are in agreement with theoretical predictions, at m = ?1/4 and n = ?1/2. Comparison with other steels containing 0.59 % C and 1.48 % C showed that Λ₁ increases with increasing carbon content. The exponents m and n for secondary arm spacing are nearly the same, at ?0.4 to ?0.5. Correlations with local solidification time, θ_f, show that Λ₂ decreases as the carbon content increases. In the δ-phase regime, coarsening of the secondary arms is possible through remelting. Interdendritic segregation peaks are more quickly reduced in the δ-phase regime. This is confirmed by the results of electron beam microprobe analyses for segregation. Reduction of the carbon content of linepipe steels reduces the susceptibility to centreline segregation in the continuously cast slabs.     

Modeling on Dendrite Growth of Medium Carbon Steel during Continuous Casting

Dendrite growth is an important phenomenon during steel solidification. In the current paper, a numerical method was used to analyse and calculate the dendrite tip radius, dendrite growth velocity, liquid concentration, temperature gradient, cooling rate, secondary dendrite arm spacing, and the dendrite tip temperature in front of the solid/liquid (S/L) interface for the solidification process of medium carbon steels during continuous casting. The current model was well validated by published models and measurement data. The results show that in the continuous casting process, the dendrite growth rate is dominated by the casting speed. Dendrite growth rate, liquid concentration at the S/L interface, temperature gradient and cooling rate decrease with proceeding solidification and solid shell thickness growth, while other parameters such as dendrite tip radius, secondary dendrite arm spacing, and dendrite tip temperature in front of the S/L interface become larger with solidification progress and solid shell thickness growth. Parametric investigations were carried out. The effects of the stability coefficient, temperature gradient and casting speed on the micro‐structural parameters were discussed. Under the same conditions, higher casting speed promotes coarser secondary dendrite arm spacing and enlarges the dendrite tip radius, while decreasing temperature gradient, reducing the dendrite growth rate and making the solute distribute more uniform.     

A numerical and experimental study of the solidification rate in a twin-belt caster

A numerical and experimental study was carried out to investigate the solidification process in a twin-belt (Hazelett) caster. The numerical model considers a generalized energy equation that is valid for the solid, liquid, and mushy zones in the cast. Ak-ε turbulence model is used to calculate the turbulent viscosity in the melt pool. The process variables considered are the belt speed, strip thickness, nozzle width, and heat removal rates at the belt-cast interface. From the computed flow and temperature fields, the local cooling rates in the cast and trajectories of inclusions were computed. The cooling rate calculations were used to predict the dendrite arm spacing in the cast. The inclusion trajectories agree with earlier findings on the distribution of inclusion particles for near horizontally cast surfaces. This article also reports the results of an experimental study of the measurement of heat flux values at the belt-cast interface during the solidification of steel and aluminum on a water-cooled surface. High heat fluxes encountered during the solidification process warranted the use of a custom-made heat flux gage. The heat flux data for the belt surface were used as a boundary condition for the numerical model. Objectives of the measurements also included obtaining an estimate of the heat-transfer coefficient distribution at the water-cooled side of the caster belt. Y.G. KIM, formerly Graduate Student, Materials Engineering Department, Drexel University.     

<Emphasis Type="Italic">In-Situ</Emphasis> Analysis of Coarsening during Directional Solidification Experiments in High-Solute Aluminum Alloys

Coarsening within the mushy zone during continuous directional solidification experiments was studied on an Al-30 wt pct Cu alloy. High brilliance synchrotron X-radiation microscopy allowed images to be taken in-situ during solidification. Transient conditions were present during directional solidification. Under these conditions, solute-rich settling liquid flow affects the dendritic array and thus coarsening. Coarsening was studied by following the secondary dendrite arm spacing (SDAS) of a developing dendrite at different local solidification times according to the mush depth and instant interface velocity. Solute enrichment and liquid flow cause deceleration and acceleration of the solidification front, which in turn influences both the mush depth and local growth and coarsening due to variations in solutal gradients and thus local undercooling. In addition, spacing between neighboring dendrites (i.e., primary dendrite arm spacing), which determines permeability within the mushy zone, affects the development of high-order branches. This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France.     

The microstructures of strip-cast low-carbon steels and their response to thermal processing

The as-cast microstructure and its modification when subjected to heat treatment is examined for strip-cast low carbon steels. The local solidification rate in the twin-roll strip casting process is estimated to. be 590 to 850 °C/s, and the primary and secondary dendrite arm spacings are approximately 17 to 25 and 10 μm, respectively. The as-cast structure is predominantly Widmanstätten ferrite and, thereby, differs from the conventional hot-rolled sheet. It is suggested that the as-cast morphology is a result of the large initial austenite grain size and the cooling rate and is not a unique characteristic of rapid solidification of strip casting. By restricting the austenite grain size and cooling rate, polygonal ferrite morphology probably can be produced during strip casting. The response to heat treatment depends on the presence of aluminum; with a moderate amount of aluminum, the A1N precipitates in the as-cast structure inhibit the subsequent grain boundary movement and may affect the subsequent recrystallization behavior.     

Dynamic Coarsening of 3.3C–1.9Si Gray Cast Iron

The dynamic coarsening of primary austenite has been investigated by means of interrupted solidification in a hypoeutectic gray cast iron at three different cooling rates. The fundamental characteristic of the coarsening phenomenon, which is the reduction of the total interfacial area (i.e., the primary austenite surface) over time, has been investigated along the solidification interval for the first time in gray cast iron. The primary austenite surface is confirmed to decrease with increasing solidification time. The relation between primary austenite surface reduction and the secondary dendrite arm spacing is reported as well as the time dependence of the inverse surface area of the primary phase per unit volume. The primary austenite surface has been determined via a stereological approach. The secondary dendrite arm spacing is observed to increase throughout the whole solidification range. A novel stereological relation, the modulus of primary dendrite, has been implemented on the calculation of the primary austenite surface. The size scale of the interdendritic phase has been determined by the hydraulic diameter of the interdendritic phase. The linear relations between secondary arm spacing and eutectic cells size and between secondary arm spacing and solidification time have been found to exist during solidification independently of cooling rate. The cooling rate dependence of the secondary dendrite arm spacing and the eutectic cells size is confirmed.     

连铸坯枝晶臂间距检测方法的优化与应用实践

介绍了连铸坯凝固组织中树枝晶臂间距检测方法的优化试验及其应用效果。通过对连铸坯凝固冷却过程的分析及批量数据的采集,确定了测定连铸坯树枝晶臂间距的代表性区域,建立了一种科学测量枝晶臂间距的方法。将该方法应用于连铸圆坯生产检验中,能快速准确地找出铸坯枝晶臂间距随连铸二冷强度变化的规律,采取调整连铸二冷强度的措施,来控制一、二次枝晶臂间距大小,达到了减轻或消除铸坯开裂缺陷、提高连铸质量的目的。     

Heat transfer and microstructure during the early stages of metal solidification

Transient heat transfer in the early stages of solidification of an alloy on a water-cooled chill and the consequent evolution of microstructure, quantified in terms of secondary dendrite arm spacing (SDAS), have been studied. Based on dip tests of the chill, instrumented with thermocouples, into Al-Si alloys, the influence of process variables such as mold surface roughness, mold material, metal superheat, alloy composition, and lubricant on heat transfer and cast structure has been determined. The heat flux between the solidifying metal and substrate, computed from measurements of transient temperature in the chill by the inverse heat-transfer technique, ranged from low values of 0.3 to 0.4 MW/m² to peak values of 0.95 to 2.0 MW/m². A onedimensional, implicit, finite-difference model was applied to compute heat-transfer coefficients, which ranged from 0.45 to 4.0 kW/m² °C, and local cooling rates of 10 °C/s to 100 °C/s near the chill surface, as well as growth of the solidifying shell. Near the chill surface, the SDAS varied from 12 to 22 (μm while at 20 mm from the chill, values of up to 80/smm were measured. Although the SDAS depended on the cooling rate and local solidification time, it was also found to be a direct function of the heat-transfer coefficient at distances very near to the casting/chill interface. A three-stage empirical heat-flux model based on the thermophysical properties of the mold and casting has been proposed for the simulation of the mold/casting boundary condition during solidification. The applicability of the various models proposed in the literature relating the SDAS to heat-transfer parameters has been evaluated and the extension of these models to continuous casting processes pursued.     

Reanalysis of solidification behaviour from the microstructure in near-net-shape casting of steels

Numerical calculations revealing the relationship between the as-cast structure and cooling conditions in near-net-shape casting of steels are presented. The solidification behaviour of steels of different composition was investigated for different process conditions with a one-dimensional heat-flow model. The dependence of the secondary dendrite arm spacing (SDAS) on the distance from the chill surface was determined on the basis of the empirical relationship between local solidification time and SDAS. The numerical results were compared with experimental values of SDAS for a stainless steel, a carbon tool steel and a high-speed steel, resp. Reasonable agreement of model calculations with the experimentally determined SDAS was obtained utilizing time-dependent effective heat-transfer coefficients of the order of 2.5 to 4.5 · 10³ W/m²K for typical thin-slab dimensions and 6.0 · 10³ W/m²K for thin-strip casting.     

Dendritic solidification of alloys in low gravity

Gravity-driven convective flow influences dendrite morphology, interdendritic fluid flow, dendrite interface morphology, casting macrosegregation, formation of channel type casting defects, and casting grain structure. Dendritic solidification experiments during multiple parabolic aircraft maneuvers for iron-carbon type alloys and superalloys show increased dendritic spacing in low-gravity periods. Larger dendrite spacings for low-gravity solidification have also been reported for sounding rocket and space laboratory experiments for metal-model and binary alloys. Convection decreases local solidification time and increases the rate of interdendritic solute removal. The elimination of convection in low gravity is thus expected to increase dendritic spacing. Convection's effect on dendritic arm coarsening is expected to be dependent on the coarsening mechanism. Decreased coarsening in low gravity found for Al-Cu is indicative of coarsening predominately by arm coalescence. This paper is based on a presentation made in the symposium “Experimental Methods for Microgravity Materials Science Research” presented at the 1988 TMS-AIME Annual Meeting in Phoenix, Arizona, January 25–29, 1988, under the auspices of the ASM/MSD Thermodynamic Data Committee and the Material Processing Committee.     

Modelling of Heat Transfer,Dendrite Microstructure and Grain Size in Continuous Casting of Steels

The dendrite arm spacing and grain size in continuous casting has been studied by mathematical modelling and experimental measurements. Two in‐house tools have been used in the study. The heat transfer is calculated by the model called TEMPSIMU and the solidification as well as the microstructural phenomena by the thermodynamic‐kinetic software called IDS. The models are validated by comparison the calculated results with experiments from steel plants. In continuous casting, the solidification structure is also influenced by process parameters. In this study the effect casting speed, superheat and secondary cooling on arm spacings and grain size is also studied. The in‐house models and the obtained results are presented in this paper. Using the developed models, the heat transfer and microstructure can be controlled more accurately.     

Simple model of microsegregation during solidification of steels

A simple analytical model of microsegregation for the solidification of multicomponent steel alloys is presented. This model is based on the Clyne-Kurz model and is extended to take into account the effects of multiple components, a columnar dendrite microstructure, coarsening, and the δ/γ transformation. A new empirical equation to predict secondary dendrite arm spacing as a function of cooling rate and carbon content is presented, based on experimental data measured by several different researchers. The simple microsegregation model is applied to predict phase fractions during solidification, microsegregation of solute elements, and the solidus temperature. The predictions agree well with a range of measured data and the results of a complete finite-difference model. The solidus temperature decreases with either increasing cooling rate or increasing secondary dendrite arm spacing. However, the secondary dendrite arm spacing during solidification decreases with increasing cooling rate. These two opposite effects partly cancel each other, so the solidus temperature does not change much during solidification of a real casting.     

Experimental investigation on solidification of GCr15 bearing steel by the simulated continuous casting

ABSTRACT

An experimental apparatus for simulation of continuous casting process of GCr15 bearing steel billet is established. With the apparatus, the billets of diameter 140?mm are casted in various superheats and cooling conditions. The solidification macrostructure, dendrite morphology, segregation and carbide are investigated. It is shown that melting superheats and cooling conditions remarkably influence the microstructure and solute segregation. It is found that the secondary dendrite arm spacing of the steel increases with the increase of the superheat temperature, and with decrease of the cooling rate. Lower superheat with higher cooling rate promotes the refining of the microstructure. Refining equiaxed grains structure in the centre of the billet leads to lower segregation of carbon. Furthermore, with increasing cooling rates, the spacing of the pearlite laminar is refined and the precipitation of proeutectic carbides is suppressed.     

Structure Refinement by a Liquid Metal Cooling Solidification Process for Single-Crystal Nickel-Base Superalloys

Single crystals of a nickel-base superalloy were directionally solidified (DS) over a range of cooling rates to evaluate the benefits of a new high thermal gradient solidification process. Solidification experiments were conducted on cylindrical bars with a liquid-metal-enhanced cooling process. This higher gradient casting process was evaluated for the degree of structure refinement, microstructural variability, and porosity distributions. Cylindrical bars of 1.6-cm diameter were solidified at rates between 8.4 and 21.2 mm/min using a tin-based, liquid metal cooling (LMC) technique and at a rate of 3.4 mm/min with a conventional Bridgman process. The LMC process produced a refined microstructure with average primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS) values as low as 164 and 25 μm, respectively, for the bar geometry evaluated. An optimum intermediate withdrawal velocity of 12.7 mm/min produced up to a 50 and 60 pct refinement in PDAS and SDAS, respectively. Further increases in withdrawal velocity produced smaller SDAS and pore sizes, but undesirable grain boundaries and excessive secondary dendrite arm growth. Voronoi tessellation methods were used to examine the extremes of the dendrite arm spacings in comparison to the average measurements, the packing of dendrites, and the correlation of porosity size and location with the dendrite structure. A simple expression for prediction of the maximum pore size is developed.     

Microstructure and precipitation in as cast low carbon Nb–V–Ti microalloyed medium thin slab

Abstract

The solidification structure, austenite and precipitates in a quenched compact strip processing (CSP) medium thin slab (170 mm thick) of Nb–V–Ti microalloyed steel have been studied. It was found that secondary dendrite arm spacing and austenite grain size are slightly larger than that of similar steel produced by CSP thin slab. This is partially attributed to the slower cooling rate caused by the increased slab thickness. On the other hand, the formation of carbonitride during solidification reduces the width of secondary dendrite arm spacing, while TiN particles and alloying elements in solution may inhibit the growth of austenite grain during solidification and subsequent cooling. In addition to the semidendritic, larger cubic and fine cubic precipitates, which can be observed in CSP thin slab, dendritic precipitates were also found in CSP medium thin slab.     

The effect of grain refining on macrosegregation and dendrite arm spacing of direct chill cast AA5182

The effect of titanium and titanium diboride inoculation on the spatial variation of local solidification time for direct chill (DC) cast ingots of aluminum alloy 5182 (AA5182) was studied. The results have been compared to those of an ingot cast without grain refining. To accomplish this, the effect of grain refining on a number of ingot characteristics such as grain size, macrosegregation, spatial variation of dendrite arm spacing, and thermal conductivity was investigated. Furthermore, the effect of grain refining on the well-known relationship between dendrite arm spacing and local solidification time had to be established for AA5182. The results indicated that the spatial variation of dendrite arm spacing in the industrial ingots was independent of grain refining, although the nonrefined ingot produced significantly finer dendrite arm spacings in its center. This was attributed to the influence of showering crystals in the nonrefined ingot. The relationship between dendrite arm spacing and local solidification time was also found to be independent of grain refining.     

高品质车轮钢二冷区冷却方式

为了探索高品质低成本车轮钢生产工艺,比较了两种二冷区冷却方式(气雾冷却和全水冷却)对车轮钢铸坯表面温度、凝固组织与宏观偏析的影响.结果表明:两种冷却方式下的二冷区矫直段铸坯表面温度均高于950℃,处于高温塑性区,可避免产生矫直裂纹;两种冷却方式均得到了均匀对称的凝固组织;虽然气雾冷却可略微增加等轴晶比例和降低铸坯中心偏析,但是使铸坯枝晶间距变得较为粗大,并且加重了1/2半径附近处的偏析,对随后的加工和成品的质量更为不利.综合考虑实验结果和生产成本,认为全水冷却方式更适合高品质车轮钢的生产.