Numerical simulation of solidification for aluminum-base multicomponent alloy

Solidification simulation of an aluminum-base multicomponent alloy was carried out by a method combining thermodynamic analysis using Thermo-Calc and heat-transfer calculation. An Al-9.5% Si-3% Cu-1% Mg-0.8% Fe (all mass%) aluminum-base multicomponent alloy was used for the simulation. The effect of latent heat on the heat-transfer calculation was considered by using an enthalpy method. The temperature-enthalpy curves for both an equilibrium state and nonequilibrium state with assumptions of no diffusion in the solid were calculated by using Thermo-Calc. A small casting with a cylindrical shape was used for the heat-transfer simulation. The vertical cross section of the casting was divided into rectangular grids, and the enthalpy change of each grid was numerically calculated. The calculated enthalpies in the grids were converted for each time-step into temperatures by using the temperature-enthalpy curve. A casting experiment was carried out under the same conditions as those of the simulation, and the calculated cooling curves obtained under the nonequilibrium condition agreed with the experimental ones.     

Calculation of thermophysical properties of iron casting alloys

Abstract

A simple and easy calculation tool to determine thermophysical properties, such as density, heat capacity, liquidus and solidus temperature, thermal conductivity, latent heat, and volume contraction, of iron casting alloys based on equilibrium phase diagrams is introduced. It is well known that accurate thermophysical properties of iron casting alloys are necessary for a valid simulation of the casting process. While there are a number of thermophysical calculation programs, a specific knowledge of thermodynamics is required to operate them. The calculation method proposed in the present study does not require any special knowledge of thermodynamics, only information regarding the composition of the alloy. The proposed calculation tool is based on the CALPHAD approach for the modelling of multicomponent alloys using experimental published data. Comparison of calculated thermophysical properties for several conventional iron casting alloys with experimental results showed good agreement.     

铸造充型与凝固过程的变网格数值模拟研究

鉴于充型过程的模拟计算极为复杂，是铸造模拟过程中耗时最多的部分，为缩短充型过程计算时间，提高计算效率，提出了一种利用变网格进行模拟计算的新思路，即采用不同的空间步长分别模拟计算充型和凝固过程，在充型过程的模拟计算中采用比较大的网格，而在凝固过程的模拟计算中采用比较细的网格，并设计程序模块实现两种网格之间的转换和对应，使得充型过程结束时刻的大网格系统温度场能够精确完整地转换为凝固过程开始时刻的细网格系统的温度场。对这种变网格方法进行了验证，并对实际零件进行了模拟分析。结果表明，变网格方法是一种提高模拟计算效率的有效方法，这种方法能够克服充型和凝固过程采用统一的细网格进行模拟计算而产生的计算时间过长，效率低的缺点，使得铸造过程数值模拟的计算速度大大提高，而计算结果仍能满足工程实用的要求。     

Interfacial heat-transfer between A356-aluminium alloy and metal mould

The interracial heat-transfer coefficient at casting/mould interface is a key factor that impacts the simulation accuracy of solidification progress. At present, the simulation result of using available data is comparatively different from the practice. In the current study, the methods of radial heating and electricity measurement under steady-state condition were employed to study the nature of interfacial heat-transfer between A356 Aluminum alloy and metal mould. The experimental results show that the interracial heat-transfer between A356 Aluminum alloy and the outer mould drops linearly with time while that of A356 aluminum alloy and the inner mould increases with time during cooling. The interracial heat-transfer coefficient between A356 aluminum alloy and mould is inversely proportional to the electrical resistance.     

用Cellular Automaton方法模拟压铸镁合金AM50的微观组织

基于Cellular Automaton(CA)方法的基本原理,建立了压铸镁合金AM50形核和等轴晶粒生长的二维数学物理模型,能够对任意晶向的等轴晶晶粒生长进行模拟。模型耦合了宏观传热与微观组织模拟计算,镁合金AM50阶梯块压铸件的温度场通过热传导反算法计算求得。对阶梯块压铸件不同阶梯表面的微观组织进行了模拟,并与金相试验结果进行了对比,它们在晶粒尺寸上吻合较好。     

基于Thermo-Calc及T-f_S-C_L耦合方法预测Biot≤0.1的合金凝固路径(英文)

将二元合金枝晶凝固传输模型及相应的T-fS-CL耦合求解方法扩展到描述多元合金在Biot≤0.1条件下的凝固。基于提出的扩展模型及算法,提出一种考虑传热影响的预测Biot≤0.1合金凝固路径及微观偏析的方法。该算法与Thermo-Calc热力学计算软件接口程序TQ6相耦合,用于实时计算每次迭代需要的热力学数据。Al-2Si-3Mg三元合金实例计算证实提出的模型及算法和凝固路径与微观偏析预测方法的实用性与可靠性,Al-5.17Cu-2.63Si三元合金凝固实验结果与预测结果的取得较好的一致性。     

A Theoretical and Experimental Study of Heat Line Formation in a Roll Caster

The authors show that a steady state two-dimensional finite difference model has been developed to describe the roll casting process, incorporating a variable heat transfer coefficient through the roll bite. The model explains the formation of the speed limiting defects called ‘heat lines’ in terms of this variable strip/roll heat transfer coefficient. The results of subsequent casting speed trials are compared with the predictions made by the numerical model. Approximate values of the heat-transfer coefficients through the roll bite in the various regions proposed for the roll caster model have been determined by matching predicted strip exit temperatures to experimental measurements for various casting speeds. Further evidence for the values of the alloy/mould heat transfer coefficients were obtained from cooling curves. The model has been used to investigate the effect of varying various casting parameters on the strip exit temperature and the critical casting speed above which heat lines form.     

基于扫描线种子填充算法的铸件孤立域搜索算法

搜索铸件孤立域热节的方法——即缩即补法,存在对铸件网格重复扫描而致其计算效率低的问题.文中提出了扫描线种子填充算法,该方法每次扫描时把已经确定为固态网格的单元排除出扫描序列,避免重复扫描,这使搜索的网格数量随着时间步长的循环逐次降低,即每经过一个时间步长,随着温度降低,固态网格单元增多,液态网格单元减少,则每次循环的扫描时间越少.针对大链轮铸件的两种方法的计算结果表明,计算效率提高了21.4％.     

Development of thermophysical calculator for stainless steel casting alloys by using CALPHAD approach

The calculation of thermophysical properties of stainless steel castings and its application to casting simulation is discussed. It is considered that accurate thermophysical properties of the casting alloys are necessary for the valid simulation of the casting processes. Although previous thermophysical calculation software requires a specific knowledge of thermodynamics, the calculation method proposed in the present study does not require any special knowledge of thermodynamics, but only the information of compositions of the alloy. The proposed calculator is based on the CALPHAD approach for modeling of multi-component alloys, especial y in stainless steels. The calculator proposed in the present study can calculate thermophysical properties of eight-component systems on an iron base alloy (Fe-C-Si-Cr-Mn-Ni-Cu-Mo), and several Korean standard stainless steel alloys were calculated and discussed. The calculator can evaluate the thermophysical properties of the alloys such as density, heat capacity, enthalpy, latent heat, etc, based on full Gibbs energy for each phase. It is expected the proposed method can help casting experts to devise the casting design and its process easily in the field of not only stainless steels but also other alloy systems such as aluminum, copper, zinc, etc.     

利用短程序改进Al-Cu熔体的热力学模型

将Al-Cu熔体中的缔合物AlCu3以短程序的形式引入置换溶液模型中，提出了一个Redlich—Kister多项式表示的缔合溶液模型，可以直接用于Thermo—Calc相图计算软件，并用这个模型改进了Al一Cu合金体系中液相的热力学描述，计算了Al-Cu熔体混合焓、固相线和平衡分凝因数结果表明，本模型比目前广泛应用的Saunders模型能给出更好的结果，而且适用于Mg-Sn和In—Sb等二元合金体系液相的热力学描述．     

Microstructure and Tensile Behavior of Al8Co17Cr17Cu8Fe17Ni33 (at.%) High-Entropy Alloy

Microstructure evolution and tensile behavior of the high-entropy alloy Al₈Co₁₇Cr₁₇Cu₈Fe₁₇Ni₃₃ (at.%) are investigated at room temperature and at 500°C in the as-cast state and under different heat-treatment conditions. Detailed microstructural characterizations are carried out using optical microscopy, scanning electron microscopy, and transmission electron microscopy. The equilibrium phase evolution as a function of temperature was calculated using the Thermo-Calc software (Thermo-Calc Software, Stockholm, Sweden) integrated with TTNi-7 database. The observed majority phase is a face-centered cubic solid solution for all tested specimens. Tensile ductility at room temperature and at elevated temperature is enhanced by heat treatment at 1150°C. An embrittlement phenomenon has been observed after a heat treatment at 700°C resulting in significant degradation in tensile properties.     

镍基高温合金熔模铸件凝固过程宏/微观多尺度模拟

建立镍基高温合金熔模铸件凝固过程的宏/微观多尺度数理模型,基于射线追踪法处理热辐射,模拟铸件的温度分布,采用三维宏/微观网格嵌套和改进的CA方法模拟微观组织,并依据微观组织模拟结果处理结晶潜热,实现微观与宏观模拟的耦合.依据等效液面下降法、Niyama判据和Darcy定律预测铸件的宏观缩孔、宏观缩松和微观缩松缺陷分布位置,并浇注实际的高温合金叶轮铸件.结果表明:模拟获得的冷却曲线、微观组织及缺陷位置与实验结果吻合良好,模拟结果能够准确预测铸件中多种缺陷的分布.     

New Fe−Co−Ni−Cu−Al−Ti Alloy for Single-Crystal Permanent Magnets

A new alloy intended for single-crystal permanent magnets has been suggested. The new alloy has been designed based on the well-known Fe?Co?Ni?Cu?Al?Ti system and contains to 1 wt % Hf. The alloy demonstrates an enhanced potential ability for single-crystal forming in the course of unidirectional solidification of ingot. Single-crystal permanent magnets manufactured from this alloy are characterized by a high level of magnetic properties. When designing the new alloy, computer simulation of the phase composition and calculations of solidification parameters of complex metallic systems have been performed using the Thermo-Calc software and calculation and experimental procedures based on quantitative metallographic analysis of quenched structures. After the corresponding heat treatment, the content of high-magnetic phase in the alloy is 10% higher than that in available analogous alloys.     

Modelling of microsegregation in ternary alloys: Application to the solidification of Al–Mg–Si

A fast numerical model has been developed for the quantitative prediction of microsegregation during solidification of ternary alloys. Considering a small volume of uniform temperature, the back-diffusion equations in the primary solid phase are solved in a 1-dimensional configuration using an implicit finite difference formulation with a Landau transformation onto a fixed [0,1] interval. The other phases which may precipitate during solidification are supposed to be stoichiometric and at equilibrium while the liquid is in a state of complete mixing. These calculations are coupled with phase diagram data through the use of mapping files: the liquidus surface, the monovariant lines and all the pertaining information are mapped through calls to Thermo-Calc [B. Sundman, B. Jansson and J. O. Andersson, CALPHAD, 9, 153 (1985)], prior to starting the microsegregation calculation itself. This very efficient microsegregation model can thus be coupled directly to macrosegregation computations performed at the scale of a whole casting: from the average enthalpy and concentrations variations computed at each mesh point of a casting during one time step, this microsegregation model is capable of predicting the variations of temperature, of the volume fractions of the various phases, of the liquid concentrations and of the average density. The efficiency of this coupling between microsegregation calculation and thermodynamic mapping files is demonstrated in the particular case of the Al–Mg–Si system.     

Thermodynamic Evaluation of the Phase Stability and Microstructural Characterization of a Cast B1914 Superalloy

The boron-carbon superalloys (BC alloys) were developed to reduce the carbon content of the alloys to less than 0.02 wt.% and increase the boron content to 0.1 wt.% in some Ni-based superalloys. In this study, we have used characterization techniques, such as DTA, XRD, SEM coupling, and thermodynamic calculation using Thermo-Calc software, to obtain information about the phase transformation reaction temperatures and the elemental compositions of the microstructural constituents encountered in the B1914 superalloy. The microstructure of the B1914 superalloy was composed of a gamma (γ) phase with a dendritic structure and gamma prime (γ′) phase with a cuboidal shape. Precipitates of γ′ and a lamellar eutectic, composed of γ/(Mo,Cr,Ni)₃B₂, were identified in the interdendritic region. The thermodynamic calculation results have shown to be a valuable tool for predicting the transformation temperature, such as liquidus, γ’ solvus, and incipient melting point. These transformations are important parameters used in casting simulation software for determining the heat treatment and welding repair conditions for parts made from this alloy.     

新型FeMB系纳米晶软磁材料的成分设计

运用Miedema理论,系统计算Fe,B与Cu,Mo,Ni,Cr,V,Ga,Nb,Hf和Zr等元素形成合金系时的热力学性质。运用理想溶液理论,计算1 600 K时该二元合金系的过剩Gibbs自由能、过剩熵和活度。结果表明,在FeMB体系中,Fe-Zr-B的混合焓最小;1 600 K时Fe-M-B体系的过剩Gibbs自由能与其混合焓相似,其过剩熵趋近于零,活度相对于理想溶液偏差极小,在实际应用中可忽略不计。     

Thermodynamic calculation for precipitation hardening steels and titanium aluminides

Thermodynamic calculation using Thermo-Calc was carried out to quantify the phase fraction and element partition in precipitation hardening steels and γ-TiAl based alloys. Calculations show that the precipitates formed in Fe–Ni–Al–Mo systems and PH13-8 stainless steel are NiAl phases, in accordance with atom probe microanalysis. Calculations of the phase constitution and element distribution in several titanium aluminides show again a good agreement with the experimental measurement from atom probe. In addition, Thermo-Calc calculation can help identify the existence of some phases which were not readily observed experimentally. It can be used as a guide in alloy design, especially the design of the γ-TiAl based alloys.     

用数值计算技术和试错法确定金属材料表面对激光的吸收率

提出了一种激光重熔条件下确定金属材料激光吸收率的方法,通过改变输出功率,控制试样表面状态,利用计算机数据采集系统对激光表面重溶的试样进行定点温度采集,按不同表面状态假定材料对激光的吸收率,采用经营验证的激光表面重熔数值模拟程序计算温度场并与实测结果对比,以试错法修正所假定的吸收率,确定了DL31合金表面对激光的吸收率,与文献中实验得到的吸收率值较为接近,用所吸收率值计算不同功率条件下试样定点温度的变化,与实测温度变化规律基本吻合。     

Precipitation of paraequilibrium cementite: Experiments,and thermodynamic and kinetic modeling

The precipitation of cementite prior to the precipitation of the strengthening M₂C phase is investigated using two model ultra-high strength (UHS) steels. The structure, microstructure and chemical composition of cementite are studied by analytical electron microscopy techniques. The structure of cementite precipitated during early stages of tempering at 755 and 783 K was confirmed by convergent beam electron diffraction. In an alloy containing 0.16 mass% C, the cementite particles were primarily plate shaped and interlath type, whereas in an alloy containing 0.247 mass% C both inter- and intralath particles were observed. Consistent with the earlier studies on tempering of Fe-C martensite, lattice imaging of cementite suggests microsyntactic intergrowth of M₅C₂ (Hägg carbide). Quantification of the substitutional elements in cementite confirms its paraequilibrium state with ferrite at the very early stage of tempering. Computational thermodynamic and kinetic tools, Thermo-Calc and dictra (diffusion controlled transformation) software, respectively, are used to model the precipitaton of paraequilibrium cementite in several multicomponent alloys. A thermodynamic model parameter describing the effect of Si on the stability of cementite is proposed. The model parameter is consistent with the following results: (a) that Si does not partition to cementite in Fe–Si–C and Co–Si–C alloys under orthoequilibrium conditions, and (b) there is a large driving force for the precipitation of paraequilibrum cementite in an Fe–0.41C–3Mn–2Si alloy where it has been experimentally verified. The nucleation driving forces for the precipitation of paraequilibrium cementite, and the two-phase (ferrite and cementite) paraequilibrium boundaries for multicomponent alloys are calculated using the Thero–Calc software systems. The results of growth simulations of cementite under paraequilibrium condition in multicomponent systems using the dictra software are also presented.     

Numerical modeling of the transient liquid phase bonding process of Ni using Ni-B-Cr ternary filler metal

A model of dissolution and isothermal solidification during the transient liquid phase (TLP) bonding process of nickel using Ni-15.2wt.%Cr-4.0wt.%B ternary filler metal is presented. The model combined thermodynamic calculation with Thermo-Calc software and diffusion analysis by a finite difference method. The model assumed diffusion-controlled transformation, and the equilibrium compositions at the solid-liquid interface were calculated using Thermo-Calc software. The interface velocity was determined from the mass balance of solutes diffusing into or out from the interface. When a Ni specimen with a 30 μm thick filler metal was kept at 1473 K for 3.6 ks, isothermal solidification was almost complete. On the other hand, when the specimen was kept at 1373 K for 3.6 ks, residual liquid remained in the bonding region. The solidification sequence of the residual liquid during the cooling stage was calculated by the Scheil simulation. The simulation showed that solidification of the residual liquid is completed with a ternary eutectic reaction, L→fcc+Ni₃B+CrB. The calculated width of the eutectic region concurred with the experimental result.