Phase equilibria in the Fe–Si binary system were investigated experimentally and thermodynamic assessment was carried out. The αFe (A2) + α"Fe₃Si (D0₃) two-phase microstructures at 600°C and 650°C were obtained, whose grain sizes were sufficiently coarsened to be analyzed by FE-EPMA with a spatial resolution below 0.5 μm under the condition of 6 kV accelerating voltage. α'FeSi (B2) + α"Fe₃Si (D0₃) two-phase equilibria above 700°C were detected for the first time and equilibrium compositions were determined by the diffusion couple method. The horn-shaped two-phase miscibility gap extends from the low temperature αFe + α"Fe₃Si equilibrium along the B2/D0₃ second-order transition boundary and closes below 1000°C. Four-sublattice split compound energy formalism was applied to calculate the Gibbs energy of the bcc phases, A2(αFe), B2(α'FeSi) and D0₃(α"Fe₃Si), and the thermodynamic parameters in the Fe–Si binary system were evaluated. Equilibrium relations in the binary system were well reproduced, especially the effect of the B2 and D0₃ ordering on the liquidus and solidus curves and the miscibility gap between bcc phases. Optimized thermodynamic parameters as well as the experimental results are expected to be helpful for developing higher multi-component systems for practical steels.

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The objective of this paper is to describe a method of calculating the decarburized ferrite depth and scale thickness during heating and cooling for hypoeutectoid steel in ambient atmosphere. The decarburization behavior in hypoeutectoid steel is divided into three regions. In temperature region above A₃ ferrite is not formed during decarburization from austenite with a carbon concentration C = 0.0 wt%. In temperature region below A₃ (C = 0.0 wt.%) and above A₃ (C = C₀) the decarburized ferrite forms from austenite during decarburization, but its carbon concentration ranges from 0.0 to the nominal carbon concentration C₀. Finally, in the temperature region below A₃ (C = C₀) austenite transforms to ferrite + austenite or ferrite + cementite and the decarburized ferrite forms from ferrite + austenite or ferrite + cementite by surface decarburization with the appropriate equilibrium concentration. Separate decarburization models were developed for the three temperature regions due to the difference in decarburization behavior. The proposed model also handles simultaneous oxidation. The quantitative information obtained on the oxidation and decarburization characteristics is in good agreement with the experiments.

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The objective of the paper is an application of the model of the microstructure evolution based on three-dimensional cellular automata (CA) for hot shape rolling simulation. A short description of frontal cellular automata (FCA) is presented. The model contains two parts: the deformation and the microstructure evolution. The CA cells do not remain as undistorted cubes, but they are deformed according to the strain tensor. The independence of the grain growing from the shape and the sizes of the cell is ensured by the so-called “virtual front tracking”. The microstructural part of the model simulates two phenomena: the nucleation and the growth of nuclei. There are three issues considered in the paper: the creation of the initial microstructure, the recrystallization and the phase transformation. When recrystallization is simulated, the nucleation and the grain boundary migration depend on the deformation parameters such as: the temperature, the strain, the strain rate, the dislocation density and the crystallographic orientation. The nucleation during the phase transformation is a function of the cooling rate and the final microstructure. These phenomena along with the deformation can be modeled over a wide range of multi-stage deformation processes. The process of shape rolling is chosen as an example. The data needed for the FCA calculations is received from the modeling by the finite element method. The results of the simulation of the microstructure evolution, during the last three passes of the round bars rolling with the consequent phase transformation, are presented in the paper.

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In this study a modified model, using a non linear estimation of strain hardening rate vs. strain up to the critical stress, has been developed to predict single peak dynamic recrystallization (DRX) flow stress curves. The critical stress and strain for initiation of dynamic recrystallization were determined using: (1) the strain hardening rate versus stress curve, (2) the constitutive equation. In order to evaluate the accuracy of the compound model, the mean error was calculated. The results indicate that the proposed model give a good estimate of the flow stress curves.

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A method of predicting the microstructure evolution and shape in the hot forming process is important for optimizing the process conditions. To develop a new analytical model that can be used to predict microstructure behavior in the actual process, a high-speed with multistage compression testing machine is required for physical simulation of the production process and to obtain material data for the prediction model. A high-speed uniform true strain rate (~300 s^–1) was achieved by a servo-hydraulic computer-driven machine with a deviation control feedforward program. The effects of processing parameter and chemical composition of plane carbon and Nb alloyed steels on ferrite grain size were investigated. A grain size of about 1 μm was accomplished in this simulator by severe hot plastic deformation.

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In this study, we have performed phase-field simulations of grain growth in two-dimensional systems containing finely dispersed coarsening particles. In particular, the effects of the Ostwald ripening of particles on the grain growth kinetics and the morphology of the matrix grains have been investigated. After reaching a steady state, not only does the growth of the particles obey power-law kinetics, but also the growth of the matrix grains, with an exponent of 3. In the case of systems having a small fraction of immobile particles, the grain size distributions (GSDs) of the matrix grains become broader with a small fraction of particles. For systems containing particles that coarsen with simulation time, the GSDs become narrower with an increase in the area fraction of the particles, f_p(0). We have applied both active parameter tracking (APT) algorithms and parallel coding techniques to the multi-phase-field (MPF) model to accelerate the computations and to embody large-scale calculations.

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T.M.C.P. (Thermo Mechanical Control Process) has been widely used in the steel industry. We have produced ultra low-carbon steel strip and ferritic stainless-steel strip through T.M.C.P. rolling method. Next, we analyze rolling texture and recrystallization texture of the ultra low-carbon strip and the ferritic stainless- steel strip using our developed texture prediction model. We can predict rolling texture accurately using the conventional Taylor model. Moreover, we precisely predict recrystallization texture classifying the total number of microscopic slips which are calculated using the Taylor model. We consider that these calculated results prove nucleation-oriented model and two types of recrystallization and grain growth mechanisms exit in our studies. One mechanism is that grains which had the lowest total number of microscopic slips are preferred orientation for the hot rolled and annealed ferritic stainless-steel strip. The other mechanism is that grains which had the highest total number of microscopic slips are preferred orientation for the cold rolled and annealed ultra low-carbon strip.

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Crystallographic textures of ferrite, bainite and martensite in hot-rolled steel sheets are thought to be inherited from developed textures of austenite due to the orientation relationship between austenite and the product phases. However, despite numerous investigations, there is still much difficulty in predicting such transformation textures. In this article, the present state of the prediction of transformation texture in hot-rolled steel as well as a recently proposed method that enables the quantitative prediction of the transformation texture are described. As the orientation relationship is assumed to be fulfilled not only between a nucleating ferrite particle and an adjoining austenite grain but also between the same ferrite and another adjoining austenite grain, the derived variant selection rule can provide us with a remarkable reproduction of the ferritic texture in hot-rolled steel sheets from the texture of prior austenite, and vice versa.

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The strength of quenched Co-free martensitic PH 13–8 Mo steel increases significantly during isothermal ageing at 575°C due to precipitation of nanometer-sized particles. The evolution of these ordered B2 type precipitates is simulated by thermo-kinetic calculations and compared with experimental results. The composition of the B2-nuclei is determined from minimization of the critical nucleation free energy. The results of the simulations are utilized for the assessment of contributions of different strengthening mechanisms to the total lower yield strength evolution. We observe good qualitative agreement between the simulations and the experimental data.

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The interphase boundary precipitation behavior of vanadium carbide during isothermal ferrite transformation, which is the important phenomena for the hot forged medium carbon steels, was investigated and modeled. It was found that the intersheet spacing of interphase boundary precipitation of VC decreased with a decrease of ferrite growth rate during isothermal transformation. As a major factor affecting such an interphase boundary precipitation behavior, it was deduced that the vanadium segregation on migrating austenite/ferrite interphse boundary is quite important to understand the repeated precipitation of VC. In numerical simulation of VC precipitation, the influence of the vanadium concentration on the precipitation behavior at austenite/ferrite interface during isothermal transformation was examined based on a time-dependent solute drag model incorporated with parabolic growth rate. It was found that the change of the intersheet spacing during ferrite growth can be simulated by the newly proposed model for interphase boundary precipitation of alloy carbide.

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A computer model was developed to simulate pearlite transformation in Fe–C base near-eutectoid alloys during isothermal holding, continuous cooling and patenting in view of its application to high carbon super-high strength wire rods. The model is based upon Johnson-Mehl-Avrami theory; it consists of calculation of nucleation and growth rates and conversion of the extended to real volume as well as calculation of lamellar spacing from the well-known correlation with undercooling. Calculated pearlite start and finish temperatures, number and size of nodules and lamellar spacing were in good agreement with those obtained from Gleeble thermomechanical simulation.

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A model of pearlite transformation developed in a companion paper was applied to the transformation in experimental multi-component super-high strength wire rods, which contained Si, Cr, Mn, V and Ti. It was assumed that the transformation occurred without partitioning of alloying elements below the nose temperature where patenting is usually performed. Calculated pearlite start and finish temperatures and lamellar spacing were in good agreement with experiment by Gleeble thermomechanical simulator. The importance of controlling recalescence was noted in order to make lamellar spacing as small as possible.

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Numerical simulations of phase separation in Fe–Cr–Ni ternary alloys and Fe–Cr–Mo–Ni quaternary alloys similar to ferrite phases in duplex stainless steels were performed with using of the Cahn-Hilliard equations. A new numerical model based on the Gauss-Seidel and Newton-Raphson methods were utilized to obtain efficient and accurate solution.
We obtained that small addition of Ni retard phase separation of Cr in Fe–Cr–Ni ternary alloys. The simulation results on behavior of Mo and Ni in Fe–Cr–Mo–Ni ternary alloys were quite similar to Mo in Fe–Cr–Mo and Ni in Fe–Cr–Ni ternary alloys. It is known that behavior of Mo or Ni along the trajectory of the peak tops of Cr concentration is determined by the sign of second derivative of Cr and Mo or which of Cr and Ni. The effect of Ni on the peak height of Cr in Fe–Cr–Mo–Ni quaternary alloys is similar to which in Fe–Cr–Ni alloys.
Numerical simulation results on the variation of peak height of Cr are qualitatively in good agreement with those obtained by the Atom-Probe-FIM.

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A unified model is proposed for the austenite-to-ferrite transformation kinetics in binary Fe–Mn alloys that accounts for solute drag of Mn. To aid the model development, continuous cooling transformation (CCT) tests were conducted for an interstitial-free steel that can be considered as Fe–0.1%Mn alloy. The experimental transformation data are supplemented with literature data for Fe–1%Mn and Fe–2%Mn alloys to establish a CCT database for Fe–Mn alloys. The austenite-to-ferrite transformation kinetics is described from a fundamental perspective by assuming an interface-controlled reaction and including solute drag of Mn. Using the solute drag model of Fazeli and Militzer, intrinsic interface mobility, trans-interface diffusivity of Mn and its binding energy have been determined from the CCT data. The interfacial parameters are critically analyzed and compared with independent measurements of diffusion and grain boundary segregation.

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The addition of 1.5–2 wt% Si is a commonly used alloying approach for TRIP steels. Si delays cementite precipitation during bainite transformation thereby enabling that an adequate amount of austenite can be retained at room temperature due to sufficient carbon enrichment. However, the degree of cementite prevention and thus the fraction of retained austenite depend on the employed processing parameters and steel chemistry. The present work proposes a modelling framework to quantify the delayed carbide precipitation during bainite formation. A nucleation-growth based model describes the simultaneous formation of bainitic ferrite and cementite precipitation for various continuous cooling scenarios. The retarding effect of Si on cementite precipitation is explicitly accounted for. The fraction of bainite and the carbon content of the remaining austenite, which determines the M_s temperature of remaining austenite, can be tracked along non-isothermal processing paths. The proposed model is evaluated using continuous cooling transformation data for a 0.19C–1.5Mn–1.6Si–0.2Mo (wt%) steel.

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A simulation model to describe the austenite-to-ferrite transformation in the deformed austenite phase is developed using the crystal plasticity finite element and multi-phase-field methods. Using the developed model, we simulate the plastic deformation behavior of the polycrystalline austenite phase during plane strain compression and the subsequent isothermal austenite-to-ferrite transformation. The ferrite nucleation behaviors on the elongated austenite grain boundary and the deformation bands formed in the austenite grain are estimated on the basis of the classical nucleation theory. In this study, the effects of plastic deformation of the austenite phase and the holding temperature on the transformation kinetics and the ferrite grain size are investigated. The simulation results show that transformation is accelerated with an increase in the strain in the austenite phase. Furthermore, it is confirmed that ferrite grain refinement occurs by the enhancement of ferrite nucleation within the deformed austenite grain interior and by the suppression of ferrite grain growth due to hard impingement.

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An integrated model for predicting recrystallization, phase transformation and yield strength of vanadium-microalloyed carbon steel (V-steel) is developed. Two effects of vanadium addition on recrystallization are assumed: one is the solute-drag effect on mobility of grain boundary, the other is pinning-effect on austenite grain growth due to vanadium carbide (VC) precipitate in austenite. The austenite grain size is considered as the control variable for nucleation density in grain corner, grain boundary, and grain interior during phase transformation. Thermodynamic data for transformation including para-equilibrium of carbon concentration and driving force were calculated using ThermoCalc software. The vanadium addition leads to α/γ-interphase VC precipitation in ferrite, which accelerates the diffusion rate of carbon in austenite at α/γ interface and increases nucleation sites for intragranular ferrite transformation. In consequence, the ferrite fraction and grain size are increased. Brandt model²⁷⁾ is conducted to predict pearlite transformation. The lamellar spacing is considered as a function of carbon concentration and undercooling. The alloying elements, ferrite and pearlite fractions, ferrite grain size, and lamellar spacing were taken into account for predicting strength of V-free steels. Modified Ashby-Orowan equation is then used to calculate the VC precipitation strengthening of V-steels. Using this model the calculated results obtained are in good agreement with experimental results.

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Annealing treatment of cold-rolled steel sheets are mostly subjected to the continuous annealing line. In such process recovery, recrystallization, reverse transformation and dissolution or formation of precipitates occur during heating and homogenizing treatments, and the transformation and precipitation in the steel during the subsequent cooling and aging treatments. The required microstructure and mechanical properties are obtained by controlling these metallurgical phenomena appropriately. Because a simulation model that predicts the microstructure is a useful tool for the minute control of these phenomena, many models have been developed. In this review, the present status of these models is surveyed and their problems and future tasks are discussed.

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Hot stamping is a very promising method for producing ultrahigh-strength automotive components. The heating and cooling conditions in the conventional hot stamping process are quite limited. To improve the productivity of the process and/or the mechanical properties of the product, optimizing the heating and cooling conditions is an important and urgent research subject.
In this study, the influence of the heating rate, heating temperature, and cooling conditions on the microstructure and mechanical properties of 0.22%C–2.5%Mn steel was investigated. Samples were heated at two different heating rates (10°C/s and 200°C/s) to various temperatures and then either cooled in air or quenched using water sprays. The sample heated at 200°C/s to 800°C and then immediately quenched in water exhibited a very fine martensite microstructure having a grain size with an average diameter of 4 μm and a hardness value around 550 Hv. The sample heated above Ac3 and subsequently cooled in air exhibited a full martensite microstructure and a hardness of 450 Hv. A model that predicted the precipitation of cementite during cooling was developed to clarify the cause of the difference in hardness of the martensite in the samples that were quenched in water and cooled in air. The calculations showed that the hardness of samples cooled in air was lower mainly because of the decrease in the solid solution hardening of C owing to the precipitation of cementite below the Ms temperature. Drawing on the results obtained, hot stamping technology is discussed and favorable operational conditions proposed.

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Spheroidized pearlite microstructures in three-dimensions (3D) in a 0.8 mass% C–Fe steel under 700°C static annealing was examined focusing on topology and differential geometry. The topological or differential-geometric features of the microstructures were examined by evaluating the genus and the Gaussian/mean curvatures. 3D visualization demonstrated that the holes intrinsic in cementite lamellae are significant morphological features affecting the kinetics of the initial pearlite spheroidization, due to the mean curvature differences between the hole edge and the adjacent flat surface. The hole coalescence and expansion influence not only the morphological evolution, but also the topological characteristics. The genus per unit volume decreases at an earlier spheroidization time due to a decrease in the number of holes and an increase in independent bodies, but increases at longer coarsening time because of a decrease in independent bodies. The distribution area of nonzero probability of the mean and Gaussian curvature decreases with an increase in spheroidization time, which agrees with the increase in the length scale of the microstructures.

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Fundamental mechanism governing the fracture toughness of materials is reviewed in terms of a concept of the interaction between a crack and dislocations. The mechanism behind brittle-to-ductile transition (BDT) is demonstrated using a simple model based on dislocation dynamics and the theory of crack-tip shielding by dislocations. The effects of dislocation mobility as well as dislocation sources on the BDT behavior are discussed, which enables us to understand the various factors such as grain refinement influencing fracture toughness.

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In this paper, the strengthening mechanism of martensite was investigated by using an ultra low carbon Fe–18%Ni alloy to eliminate the confusion caused by carbon. In addition, Fe–18%Ni–C alloys were used to compare with the data of Fe–C alloys already reported and the effect of solute Ni was discussed in terms of solid solution strengthening in martensitic steels. The results obtained are as follows: 1) Microstructure of lath martensite is markedly refined by lowering the solution treatment temperature, nevertheless no large difference is found on the nominal stress-strain curves, especially on the yielding behavior. 2) Low elastic limit of ultra low carbon martensite is due to the existence of high density of mobile dislocation which has been introduced during martensitic transformation. Extra mobile dislocations can be eliminated by charging small amount of pre-strain more than 0.6% and this leads to an increase of 0.2% proof stress. 3) Substantial yield strength of carbon free martensite is determined by only the mechanism of dislocation strengthening without the contribution by grain refinement strengthening depending on microstructural parameters such as prior austenite grain size, packet size and block size. 4) Solid solution strengthening by Ni does not appear in martensitic steels which contains high density of dislocation, even though it is significant in ferritic steels.

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Though as-quenched martensite exhibits a low uniform elongation in tension, it is highlighted that this phase has a very high strain-hardening which increases with carbon content and a large Bauschinger effect. Because usual dislocation storage can not explain reasonably this particular behaviour, an approach based on a continuum composite view of martensite (CCA) is developed suitable to capture all the experimental features.

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The secant method proposed by Weng is a practical calculation method to evaluate the stress-strain curve of the two-phase materials, but the shape of the inclusion phase has been often assumed to be a sphere or an ellipsoid in the calculation. In this study, we proposed the modified secant method which is able to calculate the stress-strain curves of the two-phase composite materials including the microstructure with arbitrary morphology, and applied this method to the conventional microstructures in steels, i.e., the ferrite-pearlite and the ferrite-bainite two-phase microstructures.

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Effects of temperature and strain rate on stress-strain curves for two types of dual-phase (DP) steel with different carbon contents were investigated from the viewpoints of tensile tests and the Kocks-Mecking (KM) model based on thermal activation theory. In the tensile tests, flow stress increased but elongation decreased with decreasing temperature or increasing strain rate. Uniform elongation for each DP steel was almost independent of deformation temperature between 123 and 373 K. In the comparison of strain rate sensitivity exponent (m), the m-value increased with decreasing the volume fraction of martensite. The calculated true stress-true strain curves by using the KM model agreed with the measured ones at various temperatures and strain rates for the DP steels. In terms of the parameters for the KM model, the athermal stress and mechanical threshold stresses were different between the two types of DP steel. This seems to be associated with the difference of volume fractions of ferrite and martensite.

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Elasto-plasticity behavior of an IF steel sheet was investigated by performing uniaxial tension tests in three directions (0°, 45° and 90° to the rolling direction of the sheet), in-plane cyclic tension compression test and bi-axial tension test. The sheet has strong planar anisotropy (r₀ = 2.15, r₄₅ = 2.12 and r₉₀ = 2.89) but very weak flow stress directionality. Equi-biaxial flow stress is as large as 1.23 times of the uniaxial flow stress. These elasto-plasticity deformation characteristics, as well as the Bauschinger effect and cyclic hardening behavior, are well described by a macro-plasticity model (Yoshida-Uemori model incorporating with the 4th-order anisotropic yield function). Further, the simulation of elasto-plasticity stress strain responses of the sheet were conducted by two types of crystal plasticity models, i.e., Taylor hypothesis based model and CPFEM, using the crystallographic orientation distribution data measured by neutron diffraction method. The models capture most of the above-mentioned deformation characteristics qualitatively, but the predicted anisotropy and the Bauschinger effect are weaker than those of the real material. The CPFEM gives more realistic results than the Taylor model.

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Dual-phase steels show complex damage mechanisms that complicate the prediction of sheet formability. The ductile crack initiation locus (DCIL) has been developed as a failure criterion to better describe the characteristic forming behaviour in dual-phase steels. It displays the equivalent plastic strain at a critical combination of stress triaxiality and Lode angle with four damage parameters. Due to the high experimental complexity of the determination of these parameters and the missing link to the microstructure, an alternative numerical approach is of great interest. In this study, the micromechanical Gurson-Tvergaard-Needleman (GTN) model was employed to predict the damage parameters of a dual-phase steel. An adequate calibration procedure of the GTN parameters was defined with the consideration of the link between microstructural features and mechanical behaviours. After the determination of the GTN parameters, tensile tests of different specimens expressing different stress states were simulated using the GTN model. An overall good agreement was obtained for the force–displacement response. However, due to the exclusion of the Lode angle effect of the GTN model, the limitation of the capability of predicting the damage parameters in the whole stress state was also indicated and discussed.

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