Carbon Diffusion In Austenite Research Articles

Application of explainable artificial intelligence for prediction and feature analysis of carbon diffusivity in austenite

Application of explainable artificial intelligence for prediction and feature analysis of carbon diffusivity in austenite

Modelling and simulation of isothermal and continuous-heating surface decarburization behaviour of Fe-0.6C-1.8Si-0.8Mn spring steel

Steel surface decarburization leads to insufficient hardness in the surface area due to carbon depletion, reducing its fatigue life significantly. Various models have been proposed to simulate the decarburization behaviour. However, the influence of steel oxidation is either completely ignored or calculated separately, and the concentration-dependent carbon diffusivity in austenite is seldom considered. In this research, a numerical decarburization-oxidation integrated model based on the control volume method considering concentration-dependent carbon diffusivity was proposed. Isothermal and continuous-heating decarburization tests were conducted for a Fe-0.6C-1.8Si-0.8Mn spring steel in the air. Under isothermal holding between 700–1000 °C for 30–60min, the decarburization ferrite thickness rises with the increase of temperature, levelling off around 800–825 °C, and then starts to decrease. During continuous heating, the decarburization ferrite thickness increases at first to 76.1 μm at 840 °C and then starts to decrease to 61.6 μm after holding at 900 °C for 300s, finally rising to 65.8 μm after holding at 900 °C for 900s. Predictions of the proposed decarburization model were compared with experimental results, and a good match can be found between them. The significance of considering oxidation and concentration-dependent carbon diffusivity during modelling was emphasised as well.

Dynamic strain aging mechanisms in a metastable austenitic stainless steel

Discontinuous plastic flow due to dynamic strain aging (DSA) in a Fe–13Cr–3.4Mn–0.47C metastable stainless steel was studied by uniaxial tensile tests in the temperature range from 20 °C to 500 °C. A complex picture of the discontinuous flow and its disappearance in an intermediate temperature interval was interpreted in terms of an existing model, which had to be modified. Different mechanisms of DSA were proposed for different temperature intervals. DSA at temperatures up to 200 °C was attributed to deformation-induced martensitic transformation within glide bands. Immobilization of dislocations at martensite/austenite boundaries and emission of fresh dislocations into the adjacent austenite was considered as a major process in this temperature regime. Rapid diffusion of carbon from martensite to the martensite/austenite boundaries was considered as an additional pinning mechanism contributing to discontinuous plastic flow. Serrations on the deformation curves at temperatures between 200 °C and 300 °C were associated with dislocation pinning due to carbon diffusion in austenite. This regime of DSA did not involve high diffusivity martensite. In spite of an increase in the diffusivity of carbon in the temperature range of 350-450 °C, a serration-free regime was observed there. The absence of intermittent dislocation pinning/unpinning events responsible for serrations implied continuous solute drag by carbon atoms according to the Cottrell mechanism. Serrations reappeared at 500 °C and were attributed to dislocation pinning by substitutional chromium and manganese atoms.

Cellular automaton modeling of austenite formation from ferrite plus pearlite microstructures during intercritical annealing of a C-Mn steel

A mesoscopic cellular automaton model was developed to study the microstructure evolution and solute redistribution of austenization during intercritical annealing of a C-Mn steel. This model enables a depiction of three-stage kinetics of the transformation combined with the thermodynamic analysis: (1) the rapid austenite growth accompanied with pearlite degeneration until the pearlite dissolves completely; (2) the slower austenite growth into ferrite with a rate limiting factor of carbon diffusion in austenite; and (3) the slow austenite growth in control of the manganese diffusion until the final equilibrium reached for ferrite and austenite. The effect of the annealing temperature on the transformation kinetics and solute partition is also quantitatively rationalized using this model.

The Distribution of Carbon in Austenite Studied on a Water-Quenched Compacted Graphite Iron Using Electron Probe Microanalysis

Spheroidal graphite is the defining microstructural feature of ductile iron and also plays an important role in compacted graphite iron. It is widely accepted that graphite spheroids are engulfed by austenite at an early stage of solidification after which their growth is impeded by the slow diffusion of carbon through a layer of austenite. In this work, a compacted graphite iron-containing spheroidal graphite was studied after interruption of its solidification by water quenching. Selected areas of a cross section of the castings were investigated using quantitative electron probe microanalysis, with emphasis on the distribution of carbon in austenite. The measured carbon concentration near graphite was generally below the theoretical carbon concentration in austenite at equilibrium with graphite at 1140 °C. Numerical simulations of diffusion of carbon in austenite around spheroidal graphite suggest that a zone of austenite around graphite was likely depleted of carbon during quenching, possibly explaining the low measured concentrations. The measured carbon concentration near graphite varied by as much as 0.3 wt%, with the lowest concentrations consistently found in the central region of compacted graphite–austenite eutectic cells. Regardless of whether these differences were present prior to quenching or are consequences thereof, they seem to reflect either departures from, or displacements of, the carbon concentration in austenite at equilibrium with graphite. This indicates that there is something about growth of graphite embedded in austenite which is not well understood. Concentrations of Si, Mn and Cu are near equal in the compared regions and do not explain the observed differences in carbon content near graphite.

Decarburization of 60Si2MnA in Atmospheres Containing Different Levels of Oxygen, Water Vapour and Carbon Dioxide at 700–1000 °C

The decarburization behaviour of 60Si2MnA in atmospheres containing 0–21% O2, < 20 ppm–17%H2O, and with or without 8%CO2, at 700–1000 °C, was investigated. The new findings of the current study were: (a) severe decarburization was associated with the formation of wustite (FeO) scale on the steel surface, (b) the carbon activity at the steel–FeO interface was most likely determined by the reaction equilibrium between FeO and dissolved carbon in steel, (c) when a ferrite layer was able to form, the decarburization tendency was determined by the relative carbon permeability (defined as the product of carbon concentration difference at the two interfaces of the ferrite layer and carbon diffusivity) through the ferrite layer, and therefore, (d) the decarburization tendency at 800 °C was greater than those at 700 and 900 °C as the relative carbon permeability at 800 °C was the greatest. If FeO was absent when heating in dry O2-containing gases, however, possibly as a result of the formation of a SiO2 layer at the steel surface, decarburization was very much alleviated or avoided. At 1000 °C, the decarburization tendency was alleviated even when FeO was able to form because formation of a ferrite layer was not possible and carbon diffusivity in austenite was much lower than that in ferrite. A preformed oxide scale was effective in providing decarburization protection only when the steel was exposed to dry O2-containing atmospheres.

A cellular automaton-finite difference simulation of the ausferritic transformation in ductile iron

ABSTRACTThe development of the ausferritic transformation of a ductile iron was analysed using a novel cellular automaton-finite difference model, which considers geometrical details of the microstructure, nucleation of the new phase at graphite nodule surface, contact between growing phases, and carbon diffusion in austenite. The role of nucleation, austenite carbon enrichment, and contact between phases in the different stages of the growth kinetics was studied. Moreover, a parametric study was performed to investigate the influences of graphite nodule size, and austenitizing and austempering temperatures on the required time to end the transformation and final phase fractions. The obtained results are in agreement with experimental data reported in the literature.

Modeling the growth of austenite in association with cementite during continuous heating in low-carbon martensite

The growth of austenite during continuous heating in plain low-carbon martensite is simulated extending the analytical model by Judd and Paxton to include the carbon diffusion through the matrix. It is assumed that cementite is fully precipitated at an early stage of heating so that austenite is nucleated above the eutectoid temperature either on cementite or away from it, e.g., on prior austenite grain boundary. The austenite grows fast until all cementite particles vanish and thereafter continues to grow at a gradually increasing rate with temperature. Cementite particles remain up to a higher temperature with the increase in heating rate, initial particle size of cementite and the decrease in the number of austenite nuclei. Due to slow carbon diffusivity in austenite, the cementite free of austenite tends to dissolve faster than the cementite on which austenite was nucleated except when the particle size of cementite and/or the number of austenite nuclei is small.

Influence of bainite reaction on the kinetics of carbon redistribution during the Quenching and Partitioning process

In the present study the microstructural evolution and kinetics of carbon redistribution during the partitioning step of the Quenching and Partitioning process are investigated by means of a modeling approach that simultaneously considers the martensite-austenite carbon partitioning and the decomposition of austenite into bainitic ferrite. The development of the phase fractions, interface position, and carbon compositions are analyzed for two different binary Fe-C alloys with distinct initial carbon compositions and simulation geometries. The composition dependence of carbon diffusivity in austenite is taken into account for solving the diffusion field equations. Simulations indicate that kinetics of carbon partitioning from martensite to austenite is controlled by carbon diffusion in martensite and it is little affected by simultaneous occurrence of bainite reaction. On the other hand martensite-austenite carbon partitioning strongly influences the bainite reaction by inhibiting the growth of bainitic ferrite.

High-Temperature Oxidation and Decarburization of 14.55 wt pct Cr-Cast Iron in Dry Air Atmosphere

The oxidation and decarburization behavior of 14.55 wt pct Cr-cast iron at 1273 K to 1423 K (1000 °C to 1150 °C) in a dry air atmosphere was studied. A gravimetric investigation showed that intensive oxidation of cast iron takes place at temperatures above 1273 K (1000 °C). It is found that oxidizing heating is accompanied by decarburization, which manifests itself in secondary and eutectic carbide dissolution. The volume fraction of carbides decreases with temperature and holding duration increasing. Decarburization results in the formation of a decarburized layer up to 4 mm in depth. A carbide-free layer in depth up to 100 μm appears in the free surface after 6 to 8 hours holding at 1373 K to 1423 K (1100 °C to 1150 °C). Preliminary activation energy calculations suggested that the eutectic carbide dissolution at the depths of 50 to 400 μm is controlled by carbon diffusion in austenite. The dissolution of eutectic carbides involves a capillarity-induced mechanism, which consists of formation and growth of capillary cavities inside carbides.

Modeling C-Curves for the Growth Rate of Widmanstätten and Bainitic Ferrite in Fe-C Alloys

When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstatten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstatten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.

Analysis of the mobility of migrating austenite–ferrite interfaces

Dilatometric studies assisted by high-temperature laser scanning confocal microscopy provide a comprehensive experimental picture with regard to cyclic austenite-to-ferrite transformations in Fe–C alloys. The validity range for the sharp interface and effective mobility approach is identified by comparing modelling results with calculations based on experiments. The interface velocity for the austenite-to-ferrite transformation in pure iron is exclusively controlled by the intrinsic interface mobility conforming to the upper boundary of mobilities. The austenite-to-ferrite transformation in Fe–C alloys under conventional cooling and heating conditions is primarily controlled by carbon diffusion in austenite. The lower boundary of the temperature-dependent interface mobility has been established for an Fe–C alloy over a wide range of temperatures during cycling transformation. Austenite-to-ferrite transformations in Fe–C–X alloys are characterized by still lower effective mobilities depending on both temperature and composition, because substitutional elements X give rise to a solute drag effect. An estimate for the effective mobility valid for the austenite-to-ferrite transformation in lean Fe–C–Mn alloys is provided.

Influence of Carbide Morphology and Microstructure on the Kinetics of Superficial Decarburization of C-Mn Steels

Decarburization is an important process during the heat treatment of steels. It can be divided into three separated events: dissolution of carbides, diffusion of carbon through the iron matrix, and surface reactions. The process is very sensitive to temperature. During intercritical annealing, austenite nucleates in the cementite-ferrite interface and grows at the rate determined by the diffusion of carbon in austenite. The presence of a decarburizing atmosphere during annealing guides the carbon diffusion in ferrite toward the surface, generating a flux of carbon from austenite toward ferrite, disturbing the austenite growth. In the presence of pearlite, the ferrite-austenite interface can be assumed to remain static until pearlite is completely dissolved, reducing then the carbon flux in austenite, consequently diminishing the austenite formation rate. At intercritical temperatures, the cementite-free ferrite layer at the surface reaches a greater width due to the combination of the thermodynamic fraction of austenite, dissolution rate of cementite, and the diffusivity of carbon in austenite and ferrite. In this study, an experimental investigation of the effects of the carbide morphology and distribution and the $$\alpha -\gamma $$ phase transformation in the decarburization kinetics on hypo-eutectoid steels is presented. It is suggested that the change of the dissolution kinetics of the carbides due to its morphology will affect the austenitization kinetics. Thus, the distribution of the carbon in the microstructure may determine the rate of decarburization in combination with the carbon diffusion through the phases or the gas-metal reactions.

Thermal stability and growth kinetics of the interfacial TiC layer in the Ti alloy/carbon steel system

The thermal stability and growth kinetics of the titanium carbide interfacial layer, formed in the course of the diffusion bonding of low-alloy carbon steel (0.3wt.% C) and Ti alloy, were investigated. Thermal stability of the titanium carbide interfacial layer was evaluated based on the thermodynamic analysis of the Fe–Ti–C ternary system. Thermodynamic analysis of the Fe–Ti–C system confirmed that the titanium carbide layer is stable in contact with the steel part of the diffusion couple. An experiment with inert markers at the interface confirms that growth kinetics of the TiC layer is governed by carbon diffusion from steel to titanium alloy through the titanium carbide phase. In the 800–950°C temperature range, carbon diffusion in austenite was found to be a rate-determining step of the titanium carbide layer growth during the initial stage of the interaction (<40min). For advanced stages, the thickness of the layer depends on two simultaneously occurring processes, namely flow of carbon atoms through the titanium carbide layer and that from the titanium carbide layer into the titanium alloy. The estimated values of the carbon diffusion coefficient and the activation energy of the process reflect the grain boundary mechanism of carbon diffusion through the interfacial layer.

Microstructure Evolution of Cold‐Rolled Dual Phase Steel Simulated by Cellular Automata

The microstructure evolution simulation of the whole process, i.e., the cooling after hot rolling, cold rolling, recrystallization, austenitizing, slow cooling, and quenching, for dual phase steel is conducted based on the cellular automata model. The state values of fraction, morphology, grain size, and carbon concentration distribution etc. of austenite, ferrite, and pearlite were obtained. The calculated kinetics curves and microstructure morphology with different chemical composition and heating or cooling rates agree well with the experiment. The growth of new phase is controlled by both interface mobility and carbon diffusivity due to the carbon diffusion in austenite and the driving force for phase interface migration are interacted with each other.

Growth of austenite from as-quenched martensite during intercritical annealing in an Fe–0.1C–3Mn–1.5Si alloy

The growth of austenite from as-quenched martensite during intercritical annealing was studied in a quaternary Fe–0.1C–3Mn–1.5Si alloy. Fine austenite grains either grew from interlath-retained austenite films or were newly nucleated at lath and martensite packet boundaries. Both types grew to a size comparable to the width of the martensite lath. It was found both metallographically and by dilatometry that the austenite grew to an amount in excess of the volume fraction at final equilibrium. Simulation by DICTRA, which assumed local equilibrium at the α/γ boundary, confirmed that the development of austenite is composed of three stages: initial negligible-partitioning growth controlled by rapid carbon diffusion in ferrite, which is gradually replaced by carbon diffusion in austenite; intermediate slow growth, controlled by diffusion of Mn and/or Si in ferrite; and a final stage controlled by diffusion of substitutional elements in austenite for final equilibration, which may result in the shrinkage of austenite. The formation of austenite in excess of the equilibrium amount is considered to occur due to very slow substitutional diffusion in the growing austenite compared to the boundary migration.

Statistical derivation of basic equations of diffusional kinetics in alloys with application to the description of diffusion of carbon in austenite

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the “quasi-equilibrium” kinetic equation that generalizes its earlier versions by taking possible “interaction renormalization” effects into account. For the interstitial alloys Me-X, we derive an explicit expression for the diffusivity D of an interstitial atom X. This expression notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite based on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions and about the scale of the “transition state entropy” for diffusion of carbon in austenite.

Lengthening Kinetics of Pro-Eutectoid Ferrite Ledge in Fe-C Alloy under Interface-Diffusion Mixed Control Mode

A mixed control mode is developed to model the ledge growth of pro-eutectoid ferrite, considering coupled effects of migration of austenite/ferrite interface and carbon diffusion in austenite. Carbon concentration of austenite at the austenite/ferrite interface increases from the bulk carbon concentration to a steady level, which is lower than that in local equilibrium, during the ferrite growth process. Correspondingly, ferrite grows rapidly at the beginning since all the driving force of ferrite transformation is dissipated on the interface migration. In the later stage of isothermal transformation, the growth rate of ferrite decreases towards a steady level since a part of driving force is dissipated on carbon diffusion in austenite. The effect of interface migration on ferrite growth rate by changing the interface mobility is emphatically discussed. In the case of the low interface mobility, the growth rate of ferrite is very small while the growth is dominated by the carbon diffusion ability in the case of large interface mobility. When a medium interface mobility is obtained, the growth rate of ferrite may reach a maximum value, which exceed the limitation of diffusion control and interface control modes. After comparing the modeled growth rate of ferrite with the experimental data of 0.11-0.49 wt% C alloy at 973-1113 K, the pre-expontential factor (M0) of interface mobility is estimated within the range of 0.1-1 mol m J-1 s-1, around the value 0.5 mol m J-1 s-1 theoretically estimated.

Alloying Element Partition and Growth Kinetics of Proeutectoid Ferrite in Hot-Deformed Fe-0.1C-3Mn-1.5Si Austenite

Alloying element partition and growth kinetics of proeutectoid ferrite in deformed austenite were studied in an Fe-0.1C-3Mn-1.5Si alloy. Very small ferrite particles, less than several microns in size, were formed within the austenite matrix, presumably at twin boundaries as well as at austenite grain boundaries. Scanning transmission electron microscopy–energy-dispersive X-ray (STEM-EDX) analysis revealed that Mn was depleted and Si was enriched in the particles formed at temperatures higher than 943 K (670 °C). These were compared with the calculation of local equilibrium in quaternary alloys, in which the difference in diffusivity between two substitutional alloying elements was assumed to be small compared to the difference from the carbon diffusivity in austenite. Although the growth kinetics were considerably faster than calculated under volume diffusion control, a fine dispersion of ferrite particles was readily obtained in the partition regime due to sluggish growth engendered by diffusion of Mn and Si.

An Empirical Model for Carbon Diffusion in Austenite Incorporating Alloying Element Effects

The diffusion of carbon in austenite is important to the design and implementation of many steel heat-treating processes. The present study proposes a simple and computationally efficient equation for the diffusion of carbon in austenite for iron-carbon alloys, as well as for steels alloyed with a variety of elements. The proposed empirical model provides a pragmatic engineering approach to this important diffusion process. The model is shown to better match the carbon diffusion profiles of several carburized steel alloys, as compared to other equations that have been reported in the literature. These other equations were primarily obtained from experiments on iron-carbon alloys, and it is not surprising that they are less accurate when compared to the proposed equation that takes the full range of alloy compositions into account.