Binary Fe-C Alloys Research Articles

Modelling of the Density Changes of Nodular Cast Iron During Solidification by CA-FD Method

Formation of the shrinkage defects in ductile iron castings is far more complicated phenomenon than in other casting alloys. In the presented paper changes the ductile iron density during solidification is analyzed. During the solidification path the influence of the temperature, phase fractions and phase composition is taking into account. Computer model, using cellular automata method, for estimation of changes in density of ductile iron during its solidification is applied. Results of the solidification modeling for Fe-C binary alloys with different composition in the castings with a different wall thickness are presented. As a result of calculations it was stated that after undercooling ductile iron below liquidus temperature volumetric changes proceed in three stages: pre-eutectic shrinkage (minimal in eutectic cast iron), eutectic expansion and the last shrinkage.

A Mathematical Model of Interdendritic Thermometallurgical Strain for Dendritic Solidification Processes

A mathematical model of interdendritic thermometallurgical strain (ITM) generated during dendritic solidification of steel alloys has been developed. The model consists of two main parts in which the first part represents the derivation of ITM strain based on the concept of thermal storage energy. Consequently, the second one represents the volume changes associated with dendritic solidification phenomena during the interdendritic coherent region in the mushy zone. Calculations for Fe-C binary alloys show that the straining criteria such as strain rate and accumulated strain are sensitive to the solidification behavior of different steel alloys. The results also point out that good predications of different phases, accurate alloy properties (especially thermal expansion coefficient), and precise enthalpy functions during dendritic solidification are extremely necessary. Also, the predications show that the dendrite coherency criterion is considered an essential parameter to define ITM strain of particularly long solidification interval alloys. Model predications of ITM strain are compared and discussed with other established theoretical approaches and previous modeling work.

Precipitation behavior of M2N in a high-nitrogen austenitic stainless steel during isothermal aging

The precipitation behavior of M 2 N and the microstructural evolution in a Cr-Mn austenitic stainless steel with a high nitrogen content of 0.43mass% during isothermal aging has been investigated using optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The aging treatments have led to the decomposition of nitrogen supersaturated austenitic matrix through discontinuous cellular precipitation. The precipitated cells comprise alternate lamellae of M 2 N precipitate and austenitic matrix. This kind of precipitate morphology is similar to that of pearlite. However, owing to the non-eutectoidic mechanism of the reaction, the growth characteristic of the cellular precipitates is different from that of pearlite in Fe-C binary alloys. M 2 N precipitate in the cell possesses a hexagonal crystal structure with the parameters a = 0.4752nnm and c = 0.4429nm, and the orientation relationship between the M 2 N precipitates and austenite determined from the SADP is [0110] M2N //[101]γ, [2110] M2N //[010]γ,

Substructure and Crystallography of Degenerate Pearlite in an Fe-C Binary Alloy

Microstructures formed by degenerate pearlite transformation in an Fe-0.38mass%C alloy were studied by means of scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Degenerate pearlite which contains fine cementite particles even at the growth front was observed with other structures such as proeutectoid ferrite, lamellar pearlite and bainite in a temperature range between 773K and 923K. As the isothermal transformation temperature is lowered, a fraction of the degenerate pearlite increases. The degenerate pearlite consists of ‘block’ (a region in which ferrite orientations are nearly the same) and ‘colony’ (a region containing cementite particles of nearly the same orientation), both of which are similar to those in lamellar pearlite. Block boundaries within an austenite grain are generally of high-angle type and their misorientations deviate largely from intervariant relationships for the K-S orientation relationship. In contrast, colony boundaries are of low-angle type. Cementite films are formed along those ferrite boundaries in the degenerate pearlite, presumably formed by encounter of the blocks or colonies.

Numerical simulation of dendrite growth and microsegregation formation of binary alloys during solidification process

The dendrite growth and solute microsegregation of Fe-C binary alloy are simulated during solidification process by using cellular automaton method. In the model the solid fraction is deduced from the relationship among the temperature, solute concentration and curvature of the solid/liquid interface unit, which can be expressed as a quadric equation, instead of assuming the interface position and calculating the solid fraction from the interface velocity. Then by using this model a dendrite with 0 and 45 degree of preferential growth direction are simulated respectively. Furthermore, a solidification microstructure and solute microsegregation are simulated by this method. Finally, different Gibbs-Thomson coefficient and liquid solute diffusing coefficient are adopted to investigate their influences on the morphology of dendrite.

Mathematical model for turbulent flow, heat transfer, and solidification

AbstractA steady‐state, two‐dimensional numerical model has been used to describe coupled liquid steel's turbulent flow and heat transfer with solidification for Fe‐C binary alloy in a crystallizer of inverse casting. The solid‐liquid phase change phenomena have been modeled by using continuum formulations and considering the mushy zone as porous media. The turbulence flow in the crystallizer has been accounted for using a modified version of the low‐Reynolds‐number κ−ε turbulence model. The flow pattern in the liquid zone and the temperature distribution in the solid, mushy, and liquid regions have been predicted. The numerical analysis indicates that the residence time of the mother sheet in the crystallizer is one of the key parameters. The effects of some other main parameters on the solidification behavior have also been studied, such as the thickness and the initial temperature of the mother sheet, and the superheat degree of liquid steel. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 582–592, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10112

The phase-field approach and solute drag modeling of the transition to massive γ → α transformation in binary Fe-C alloys

The transition between diffusion controlled and massive transformation γ →α in Fe–C alloys is investigated by means of phase-field simulations and thermodynamic functions assessed by the Calphad technique as well as diffusional mobilities available in the literature. A gradual variation in properties over an incoherent interface, having a thickness around 1 nm, is assumed. The phase-field simulations are compared with a newly developed technique to model solute drag during phase transformations. Both approaches show qualitatively the same behavior and predict a transition to a massive transformation at a critical temperature below the T 0 line and close to the α/ α + γ phase boundary. It is concluded that the quantitative difference between the two predictions stems from different assumptions on how the properties vary across the phase interface yielding a lower dissipation of Gibbs energy by diffusion in the phase-field simulations. The need for more detailed information about the actual variation in interfacial properties is emphasized.

Influence of Magnetic-Field Gradients on the Pearlitic Transformation in Steels

Carbon steels of 1 wt%C were subjected to the pearlitic transformation in a helium-free superconducting magnet in search for some influence of the magnetic field gradient on the transformation. It was found that steels containing Mn and/or Cr got hardened proportional to the field gradient present during the transformation at 560C. The hardness increase amounted to 8% at the field gradient of 50 T/m, the magnitude depending on the steel composition. It was confirmed that the hardening was irrelevant to the sign of the gradient and absent for homogeneous magnetic fields. This kind of hardening was not observed for a binary Fe-C alloy. The hardened specimens exhibited age hardening by annealing at 150 200C. TEM observations and internal friction measurements suggested that supersaturated carbon atoms were introduced into the ferrite layers of the pearlite phase under the field gradient. Such extra carbon atoms should have combined with Mn and/or Cr atoms during the quenching to impurity complexes responsible for the solution and age hardenings. Plausible arguments are made on the action of magnetic field gradients for the introduction of supersaturated carbon atoms in the pearlitic ferrite.

Detection, distribution, and quantification of carbon in steel microstructures by PEELS.

This work concerns the use of parallel electron energy loss spectroscopy (PEELS) to investigate the detection, distribution, and quantification of carbon in various steel microstructures generated by rapid cooling rates or by isothermal transformation. The feasibility of detecting C in steels containing very small amounts of carbon was first examined by calculating the minimum detectable mass fraction for a variety of binary Fe-C alloy specimen thicknesses and microscope conditions. These theoretical studies indicated that the detection of carbon in steel microconstituents containing about 0.01 wt.% (or even less) was easily possible with an analytical transmission electron microscope equipped with a LaB6 emitter and a PEEL spectrometer. These theoretical calculations seemed to be reasonable, as it proved possible to make a quantitative PEELS study of the partitioning between the microconstituents ferrite, retained austenite, and martensite found in an ultralow carbon (0.03 wt.%) steel weld metal provided care was taken to avoid hydrocarbon contamination. Studies of both carbon and molybdenum segregation to ferrite/martensite interfaces in an isothermally transformed Fe-C-Mo alloy were also carried out in order to investigate the nature of the "solute drag" effect in this alloy system.

Effects of Sulphur, Titanium and Zirconium on the Shape of Solid-Liquid Interface in Fe-C binary alloys

The effects of sulphur, titanium and zirconium on the shape of the eutectic solidification interface in Fe-C binary alloys were investigated by the quenching into ice water during unidirectional solidification.The oscillatory schematic model for graphite branching is proposed by considering the shape of the solidification interface and the protuberance length of the graphite flakes. The specimens contain 0.012, 0.108, 0.37 mass % S, 0.177 mass % Ti, and 0.078 mass % Zr, respectively. They are 80 g in weight, 18 mm in diameter, and 55 mm in length. The temperature gradient at the solid-liquid interface is about 2.5 K/mm.

Atomic Interaction and Distribution of Nitrogen and Carbon Atoms in Binary Fe-N and Fe-C Alloys

The Monte Carlo computer simulation of the fcc Fe-N and Fe-C alloys is performed using the data of abundances of different iron sites in the austenite lattice as obtained by means of transmission Mossbauer spectroscopy. The interaction energies between the interstitial atoms within two nearest coordination shells were estimated. A weak C-C repulsion in the first coordination sphere and a stronger one in the second sphere was found, which is consistent with the data of the carbon activity. N-N interaction is characterised by a strong repulsion in the first coordination sphere and by the soft one in the second sphere. It is also obtained that the available activity data are not consistent with the nitrogen distribution in the iron austenite as it follows from Mossbauer data The concentration dependence of nitrogen activity and an effect of the pressure of the N 2 gas on the nitrogen solubility in Fe-N austenite are calculated using the values of N-N interaction energies in two coordination spheres.

擬二元系化による低炭素鋼領域の一次デンドライトアーム間隔および組織形態の予測

擬二元系化による低炭素鋼領域の一次デンドライトアーム間隔および組織形態の予測

Ferrite formation in Fe-C alloys during austenite decomposition under non-equilibrium interface conditions

The growth of ferrite during the decomposition of supersaturated austenite in binary Fe-C alloys is studied using a numerical model that allows non-equilibrium conditions at the moving α-γ-interface. A numerical method is presented to account for non-equilibrium interface conditions during diffusional growth. In this model, the driving force for interface migration is given by the difference of the chemical potentials of the austenitic and the ferritic Fe-lattice at the interface. Carbon rearrangement, resulting from the movement of the interface, affects the driving force for interface migration during the transformation, thus establishing a mixed mode of growth control. The mode of control is predicted to vary from essentially a diffusion controlled mode at very low undercooling towards essentially an interface controlled mode at deep undercoolings. The results from this model are in good agreement with several sets of experimental growth rates and the carbon concentration profiles of partially transformed Fe-C alloys.

Formation of macrosegregation by multicomponent thermosolutal convection during the solidification of steel

The formation of macrosegregation by multicomponent thermosolutal convection during the solidification of steel is simulated by simultaneously solving macroscopic mass, momentum, energy, and species conservation equations with full coupling of the temperature and concentrations through thermodynamic equilibrium at the solid/liquid interface. The flow field, solid fraction evolution, and macrosegregation patterns for four cases are presented. The results show both the formation of channel segregates and the formation of islands of mush surrounded by bulk melt. In examining the solidification of a ten-element steel, the global extent of macrosegregation of an element is found to be linearly dependent on its partition coefficient (more severe segregation for small partition coefficient), although such scaling is not possible locally. Results for the solidification of a binary Fe-C alloy (with the same carbon content as the ten-element alloy) are similar to those for the ten-element alloy due solely to the large contribution of carbon to buoyancy driven flow in the ten-element steel chosen for study. While including only those elements that make significant contributions to buoyancy driven flow reproduces the global extent of macrosegregation seen in the ten-element alloy, local differences in the predictions are visible. Finally, comparison of results for the solidification of the same ten-element steel using two different sets of data to describe the partition coefficients and change in liquidus temperature with concentration of the elements shows completely opposite behavior,i.e., upward flow through the mushy zone for one case and downward flow for the other. Thus, the need to have accurate phase-equilibrium data when modeling multicomponent macrosegregation is illustrated. Together, the results give an indication of what areas require more careful examination if accurate modeling of multicomponent solidification is to be accomplished.

Tempering of Iron-Carbon-Nitrogen martensites

The tempering behavior of ternary FeCN martensitic specimens, with a total amount of interstitials of about 5.5 at. pct and carbon and nitrogen contents between about 1.5 and 3.9 at. pct, was investigated in the temperature range 110 to 830 K. Analysis of the corresponding changes in crystalline structure (X-ray diffraction), volume (dilatometry), and hardness and enthalpy (calorimetry) revealed that the following processes occurred: (a) martensitic transformation of retained austenite between 110 and 200 K; (b) redistribution of interstitials in martensite up to 370 K; (c) formation of nitrogen containing α′ precipitates and carbon containing e/η) precipitates between 370 and 450 K; (d) conversion of α′ nitride into γ′ nitride and coarsening of e/η carbide between 450 and 560 K; (e) decomposition of retained austenite above 540 K; and (f) conversion of e/η carbide into cementite above 570 K. Significant precipitation of carbon and nitrogen together, as nitrocarbides or carbonitrides, was not observed. From a comparison with the tempering behavior of binary FeC and FeN alloys of similar interstitial content, it was concluded for the ternary FeCN alloy that the transformation of the transition nitride (α′) into the “equilibrium” nitride (γ′) was advanced and that the precipitation of the transition carbide(e/η) and its conversion into the equilibrium carbide (cementite) and the decomposition of retained austenite were retarded.

On the morphology of the modulated precipitation of extended multiplets and Fe9C4 epsilon or eta carbide obtained by aging and tempering in Fe- C martensite

The clustering of carbon atoms into isolated multiplets followed by their ordering into (100)α’ mono-layers leads to the B2 monoclinic multilayer structure called the extended multiplet, during the low temperature aging of Fe-C martensite. The ultimate step of the process is obtained by a lC,2Fe, lC,5Fe, lC,5Fe sequence along the [001]α′. direction giving rise to a 12 lattice parameter periodicity associated with antiphase domains, for matching the lattices of the precipitate and of the matrix. It explains the satellites observed by electron diffraction as well as the (023)α′. habit plane revealed by the diffuse scattering streaks and TEM observations. The carbon free regions between the antiphase domains correspond to the ‘C ’ or ‘к’ phase as determined from the (200)/(020) and (002) martensite peak profile X-ray analysis. The laterin situ transformation to the ordered Fe9C4 e- or η-carbide, corresponds to an orthorhombic structure with parametersαη =3αe,bη≈ 3αe√3, andcη =ce, ifαe andce are the initial parameters of the Fe hcp stacking,i.e., αη= 8.46 to 8.49 A,bη = 14.04 to 14.07 A, andcη = 4.31 to 4.32 A for the binary Fe-C alloys. The transformation induces plate-like carbide precipitates with a (035)(gα′). predicted habit plane, which is 4.40 deg away from the approximate (012)ga′. plane observed by TEM.

Improvement of hot ductility of continuously cast carbon steels.

To improve the quality of continuously cast carbon steels, the characteristics of the hot ductility were studied via in-situ melted and solidified tensile testing method. Special emphases were placed on the effect of C and P on the hot ductility in the temperature range between melting temperature and 700°C.It was found that zero strength temperature (ZSTc) and zero ductility temperature (ZDTc) have a linear relationship with the equilibrium solidus temperature in Fe-C binary alloys ranging from 0.003 to 1.6% C and does not have the singularity between 0.1 to 0.2% C content. The embrittlement due to P exists only in the carbon steels having C content higher than 0.25%, which are subjected to the melting thermal history. This embrittlement is caused by the segregation of P along the austenite grain boundary.Mild cooling in the secondary cooling stage is very effective to diminish the embrittlement resulting in producing defect free cast slabs.

Thermodynamics of solute distributions between solid and liquid phases in iron-base ternary alloys.

The equilibrium distribution coefficients ko for some solutes in iron-base ternary alloys have been experimentally investigated. The mechanisms of these solute distributions between solid and liquid phases were also discussed on the basis of thermodynamics.The experimental results show that ko of Ni increases and ko of V decreases with the increasing carbon content, and the distributions of C in Fe-C-Ni and Fe-C-V alloys differ little from those in Fe-C binary alloys. This effect of carbon on kos of Ni and V could be thermodynamically explained by using the interaction parameter, the activity coefficient and so on.And also, the effects of various alloying elements on the equilibrium distributions of nitrogen and hydrogen were discussed thermodynamically.

Elastic constants of binary iron-base alloys

The Young’s modulus (E) and shear modulus (G) of isotropic Fe and binary Fe-C, Fe-Co, Fe-Cr, Fe-Ir, Fe-Mn, Fe-Ni, Fe-Pt, Fe-Re, Fe-Rh, and Fe-Ru alloys have been determined as functions of composition (0 to 10 at. pet) and temperature (77 to 473 K) by a pulse-echo technique (100 kHz elastic waves). Poisson’s ratio (v) and the bulk modulus (K) have been derived from the values of E and G. The rates of change of E and G with composition (ΔE/Δc and ΔG/Δc) depend on the change of lattice parameter with composition and upon the position of the solute in the periodic table. Both negative and positive values of ΔE/Δc and ΔG/Δc are observed. The values of ΔE/Δc and ΔG/Δc are generally different so that Poisson’s ratio may increase or decrease with composition. Comparable changes in the value ofK/G also occur. These changes cannot be used to predict the effects of alloying additions on the toughness of iron. The temperature dependence of E andG of the alloys is similar to that of iron, decreasing in a nonlinear manner from 77 to 473 K.

Activity of carbon in liquid iron alloys at 1550°C

The effect of chromium, cobalt, molybdenum, nickel, and vanadium on the activity of carbon in liquid iron alloys at 1550°C was investigated by equilibrating Fe-C binary alloys with Fe-C-i ternary alloys in an isothermal closed chamber through transport in the gas phase. From the equilibrium distribution of carbon among the charges, free energy interaction coefficients have been deduced. The first order coefficients ∈i C fori = Cr, Co, Mo, Ni, and V were found to be equal to -5.4, 1.8, -4.0, 2.4, and -6.2, respectively. Extrapolation of the data through the “Central Atoms” statistical model shows good agreement with data reported in the literature on the effect of the solutesi on the solubility of graphite.