C-Curves for Lengthening of Widmanstätten and Bainitic Ferrite

Widmanstätten ferrite and bainitic ferrite are both acicular and their lengthening rate in binary Fe-C alloys and low-alloyed steels under isothermal conditions is studied by searching the literature and through new measurements. As a function of temperature, the lengthening rate can be represented by a common curve for both kinds of acicular ferrite in contrast to the separate C-curves often presented in time-temperature-transformation (TTT) diagrams. The curves for Fe-C alloys with low carbon content show no obvious decrease in rate at low temperatures down to 623 K (350 °C). For alloys with higher carbon content, the expected decrease of rate as a function of temperature below a nose was observed. An attempt to explain the absence of a nose for low carbon contents by an increasing deviation from local equilibrium at high growth rates is presented. This explanation is based on a simple kinetic model, which predicts that the growth rates for Fe-C alloys with less than 0.3 mass pct carbon are high enough at low temperatures to make the carbon pileup, in front of the advancing tip of a ferrite plate, shrink below atomic dimensions, starting at about 600 K (323 °C).     

Non-Steady Equilibrium during Pro-Eutectoid Ferrite Formation in Fe-0.2C Alloy

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Simulation of Ferrite Formation in Fe-C Alloys Based on a Three-Dimensional Mixed-Mode Transformation Model

A three-dimensional mixed-mode (MM) transformation model accounting for both soft impingement and hard impingement was developed that calculates the growth kinetics of ferrite grains in an austenite matrix. The simulations are compared to the kinetics of ferrite formation in high-purity Fe-C alloys for which phase-transformation kinetics were measured isothermally by dilatometry at several temperatures in the range of 973 K to 1043 K (700 °C to 770 °C). The interface mobility is obtained from the best fit of the data at 1023 K (750 °C) for which the nucleus density N is estimated from the final microstructure. Subsequently, the experimental ferrite kinetics in Fe-0.36C at the other temperatures are simulated. The values of N extracted from the fits can be described with a nucleation model. The significance of the MM calculations is rationalized by comparing the results for Fe-0.17C with simulations assuming purely diffusion-controlled (DC) and purely interface-controlled (IC) growth. Comparison of simulated fraction curves for Fe-0.57C with the three models demonstrates that the transformation in high-carbon steels is essentially DC.     

Thermodynamic-kinetic simulation of constrained dendrite growth in steels

A model of constrained dendritic growth for steels, based on thermodynamic and kinetic theory, is presented. The model links thermodynamic chemical potential-equality equations to an existing, approximate treatment of constrained dendritic growth in multicomponent steels, taking into account the deviation from the local thermodynamic equilibrium of the phase interface caused by interface friction, capillarity, and solute trapping. Due to the thermodynamic approach, with a thermodynamic model and recently assessed data, the present treatment yields a more accurate determination of phase stabilities than the earlier methods. Depending on the steel composition and the growth conditions (growth rate and temperature gradient), the model determines the dendrite tip undercooling, the primary solid phase (ferrite or austenite), the stability of that phase, certain dimensions of the microstructure, and the solute accumulation ahead of the dendrite tip. A special optional calculation is that of the equally probable formation of ferrite and austenite in stainless steels. Calculations for testing the model and for validating it with experimental data are presented.     

Experimental and Thermokinetic Simulation Studies on the Formation of Deleterious Zones in Dissimilar Ferritic Steel Weldments

The methods to predict and prevent the formation of hard and soft zones in dissimilar weldments of 9Cr-1Mo and 2¼Cr-1Mo ferritic steels during high-temperature exposure are examined in this article. The computational studies have been carried out using multicomponent diffusion model incorporated in Dictra and validated by experimental methods using EPMA and TEM. Carbon concentration profiles across the interface of the weld joint between the two ferritic steels were simulated in the temperatures ranging from 823 K to 1023 K (from 550 °C to 750 °C) for various time durations using “diffusion in dispersed phase model” in Dictra. When precipitation and diffusion were incorporated into the calculations simultaneously, the agreement was better between the calculated and the experimentally measured values of carbon concentration profiles, type, and volume fractions of carbides in the hard zone and diffusion zone, width, and the activation energy. Calculation results of thermodynamic potentials of carbon in 2¼Cr-1Mo and 9Cr-1Mo steels suggested that the diffusion is driven by the activity gradient of carbon across the joint. The effectiveness of nickel-based diffusion barrier in suppressing the formation of hard and soft zones is demonstrated using calculations based on the cell model incorporated in Dictra.     

Bainite formation in low carbon Cr-Ni steels

A low carbon Cr-Ni steel has been used to investigate the formation of upper bainite. Experimental results indicate that the start temperatures of the three morphologies of upper bainite in this steel,i.e., carbide-free bainite, bainite with carbide between and within ferrite laths, are about 600°, 500δ, and 425 °C, respectively; the habit plane of bainitic ferrite in this steel is close to (1 7 11)_α, which is 13.3 deg away from (0 ll)_α; and the orientation relationship between cementite and ferrite is consistent with Bagaryatskii’s. By means of the superelement approach, a thermodynamic treatment which applies to Fe-C alloys is extended into that suitable for low alloy steels, and calculation shows that the driving force for bainite formation at B_S temperatures is insufficient to compensate for shear strain energy. Formerly Graduate Student, Department of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, People’s Republic of China.     

共析钢中铌对珠光体相变行为的影响

 通过金相、扫描电镜,相变临界点和过冷奥氏体等温转变的分析,研究了Nb对共析钢（质量分数：C 075%,C 0.78%）珠光体相变微观组织和等温转变动力学的影响。结果表明：微量Nb（质量分数为0.04%、0064%）的加入使钢中先共析铁素体的量较未含铌钢有所增加,这很可能是Nb的加入使得共析碳含量明显升高的结果,同时使珠光体相变产物的形貌发生明显变化,珠光体中渗碳体的展弦比显著降低。此外Nb提高了先共析铁素体和珠光体的开始转变温度,即Nb的加入在一定程度上降低了过冷奥氏体的热力学稳定性;相变动力学表明加入Nb 0.04%可使珠光体相变的鼻子点温度升高约50℃,且最快开始相变时间比不含铌钢推迟一个数量级以上,即Nb的加入推迟了鼻子点和较低温度下的珠光体相变,提高了钢的淬透性。     

Critical Driving Forces for Formation of Bainite

An empirical equation for predicting bainite start temperatures of steels was recently derived by starting from binary Fe-C alloys and continuing with ternary Fe-C-M alloys. This result is now illustrated with a family of B_S lines in a T,C diagram for a series of constant Mn contents. The critical driving force for the formation of ferrite is calculated for diffusionless or diffusional processes, and these quantities are used as dependent variables with carbon content or temperature as independent variables. Negative critical driving forces are predicted for a diffusionless process in binary Fe-C alloys, showing that this process cannot apply to the formation of bainite. The critical driving force for a diffusional process increases strongly with decreasing temperature and increasing carbon content. Mn and Ni, contrary to Cr, Mo and Si, have remarkably small effects on this critical driving force. The results are discussed by imagining that the magnitude of the critical driving force is governed by the height of an energy barrier that must be surmounted during growth. It is modeled as completely determined by the alloy composition. It is represented with an equation evaluated by fitting to the recent empirical equation and describing the carbon dependence of the barrier.     

Fe-C间隙固溶体热力学模型

详细考察了目前文献中常用的几种Fe-C间隙固熔体热力学模型,并讨论了它们在钢中马氏体及贝氏体相变中的应用情况。首次表明KRC、LFG/MD以及X-K模型均不能用来建立奥氏体与马氏体中是否发生Spinodal分解的热力学判据。     

基于原子-分子理论的二元合金熔体热力学计算

分别使用Miedema、MIVM、NRTL、Wilson二元合金系热力学模型及FactSage热力学软件计算Bi-Pb、Bi-Sn、Cd-Pb、Pb-Sn 4个二元合金系的活度值,并与实验值进行比较.结果表明:Miedema、MIVM、NRTL、Wilson模型计算不同体系活度的效果不同,每种模型都有其适用的体系.而FactSage热力学软件计算的活度均与实验值吻合较好,文中使用FactSage分别计算Bi-Pb、Bi-Sn、Cd-Pb、Pb-Sn 4个二元系不同温度下的活度值.同时利用原子-分子理论计算Bi-Pb二元系质量作用浓度,给出生成金属间化合物BiPb反应的标准吉布斯自由能的表达式.      

Model for Microstructure Prediction in Hot Strip Rolled Steels

Phase transformations from work‐hardened austenite after hot rolling of steel are of paramount importance for achieving the required mechanical properties. Moreover, it influences the control of cooling process in the cooling table. This paper proposes semi‐empirical mathematical models for predicting such transformations in carbon‐manganese and microalloyed steels, subjected to transformations conditions leading to a microstructure constituted by ferrite and pearlite. To develop the models, dilatometric tests were carried out in a Gleeble 3500 machine, simulating the industrial processing conditions as close as possible, including the effect of coiling. Emphasis was placed on the application of a criterion for determining the start of pearlite formation, which was based on carbon enrichment of austenite during the ferrite formation. Based on comparisons between measured and calculated ferrite fractions in tested specimens, it was proposed to consider a transition of the thermodynamic conditions prevailing during ferrite formation, which depend on steel chemistry and transformation conditions. As a preliminary assessment of its predictability the model was applied to a typical industrial process condition for microalloyed steels in hot strip rolling. It was shown that the model was capable of predicting reasonably well the evolution of ferrite and pearlite during the cooling in and also during the subsequent coiling process.     

Equilibrium Model of Precipitation in Microalloyed Steels

The formation of precipitates during thermal processing of microalloyed steels greatly influences their mechanical properties. Precipitation behavior varies with steel composition and temperature history and can lead to beneficial grain refinement or detrimental transverse surface cracks. This work presents an efficient computational model of equilibrium precipitation of oxides, sulfides, nitrides, and carbides in steels, based on satisfying solubility limits including Wagner interaction between elements, mutual solubility between precipitates, and mass conservation of alloying elements. The model predicts the compositions and amounts of stable precipitates for multicomponent microalloyed steels in liquid, ferrite, and austenite phases at any temperature. The model is first validated by comparing with analytical solutions of simple cases, predictions using the commercial package JMat-PRO, and previous experimental observations. Then it is applied to track the evolution of precipitate amounts during continuous casting of two commercial steels (1004 LCAK and 1006Nb HSLA) at two different casting speeds. This model is easy to modify to incorporate other precipitates, or new thermodynamic data, and is a useful tool for equilibrium precipitation analysis.     

合金钢γ→α转变温度的计算

采用Wagner的热力学模型,设计了计算程序。计算含Mn、Si、Ni、Cr、Mo、Cu、V、Nb、w、Co等10种合金元素(合金含量<7%)的多元系低合金钢的奥氏体-铁素体平衡及仲平衡温度,用该程序计算了多元系统合金钢的奥氏体-铁素体平衡温度,计算结果和实际测量值符合得很好。     

High-Temperature Phase Equilibria of Duplex Stainless Steels Assessed with a Novel <Emphasis Type="Italic">In-Situ</Emphasis> Neutron Scattering Approach

Duplex stainless steels are designed to solidify with ferrite as the parent phase, with subsequent austenite formation occurring in the solid state, implying that, thermodynamically, a fully ferritic range should exist at high temperatures. However, computational thermodynamic tools appear currently to overestimate the austenite stability of these systems, and contradictory data exist in the literature. In the present work, the high-temperature phase equilibria of four commercial duplex stainless steel grades, denoted 2304, 2101, 2507, and 3207, with varying alloying levels were assessed by measurements of the austenite-to-ferrite transformation at temperatures approaching 1673 K (1400 °C) using a novel in-situ neutron scattering approach. All grades became fully ferritic at some point during progressive heating. Higher austenite dissolution temperatures were measured for the higher alloyed grades, and for 3207, the temperature range for a single-phase ferritic structure approached zero. The influence of temperatures in the region of austenite dissolution was further evaluated by microstructural characterization using electron backscattered diffraction of isothermally heat-treated and quenched samples. The new experimental data are compared to thermodynamic calculations, and the precision of databases is discussed.     

Effects of Start and Finish Cooling Temperatures on Microstructure and Mechanical Properties of Low-Carbon High-Strength and Low-Yield Ratio Bainitic Steels

The effects of start and finish cooling temperatures on microstructure and mechanical properties of low-carbon high-strength and low-yield ratio bainitic steels were investigated in this study. Four kinds of low-carbon high-strength and low-yield ratio bainitic steels were fabricated by varying the start and finish cooling temperatures and cooling rates, and their microstructure and mechanical properties such as tensile and Charpy impact properties were measured. In the steels cooled down from the high start cooling temperature above Ar₁ [978 K (705 °C)], the volume fraction of acicular ferrite is lower than in the steels cooled down from the low start cooling temperature below Ar₁ [978 K (705 °C)]. The finish cooling temperatures and cooling rates affect the formation of bainitic ferrite, granular bainite, and martensite–austenite (MA) constituents. According to the correlation between microstructure and mechanical properties, the tensile strength increases with increasing the volume fractions of bainitic ferrite and MA constituents, whereas the elongation decreases. The yield ratio decreases as the volume fraction of MA constituents increases. Charpy impact absorbed energy is proportional to the volume fraction of acicular ferrite, and is inversely proportional to the volume fraction of granular bainite.     

Carbon Clustering in Low-Temperature Bainite

The bainitic ferrite phase formed at temperatures below 573 K (300 °C) in high-carbon high-silicon steels holds an amount of carbon well above that expected from the thermodynamic paraequilibrium with austenite. Diffraction experiments have shown that the ferrite lattice is sufficiently Zener-ordered to possess a tetragonal symmetry, which allows the structures to be supersaturated in carbon. It could be expected that carbon undergoes ordering beyond that indicated by the Zener-ordering temperature as in the early stages of tempering of Fe-based martensites. This study examines the formation of cluster arrangements of carbon within bainitic ferrite and their relationship to the tetragonal distortion.     

Thermodynamics and phase relationships of transition metal-sulfur systems: Part V. A reevaluation of the Fe-S system using an associated solution model for the liquid phase

The relevant thermodynamic and phase equilibrium data for the Fe-S binary system have been reevaluated in light of more recent data. An associated solution model is used to describe the thermodynamic properties of the liquid phase as a function of composition and temperature. For the pyrrhotite phase, a statistical thermodynamic model based on the formation of Frenkel defects in the lattice is used. For the austenite and ferrite phases, the solute is assumed to follow Henry’s law, and pyrite is taken to be a stoichiometric compound. The model parameters for the various phases are obtained by evaluating all relevant experimental data reported in the literature. The calculated phase diagram is in good agreement with the experimental data. The calculated sulfur activity values for the liquid phase agree well with experimental values including those at higher sulfur concentrations. This is an improvement of an earlier evaluation by Sharma and Chang using the same model with the same number of parameters.     

A theoretical analysis of the spinodal decomposition in Fe- C martensite during aging stage of tempering

A thermodynamic model of Fe-C martensite is proposed, which has a distinct physical meaning and is easily treated mathematically (high order derivation). When applying this model to the spinodal decomposition in Fe-C martensite during aging, the theoretical values (critical compositions, sizes of products) are in good agreement with experimental data. The miscibility gap of Fe-C martensite is set up. From this diagram, it is clear that spinodal decomposition may affect the later stages of tempering of medium and high carbon steels. Finally, the discussion shows that A1, A2 stages of aging are both spinodal decomposition, but to different extents.