Growth kinetics and morphology of grain boundary ferrite allotriomorphs in an Fe-C-V alloy

Grain boundary ferrite allotriomorphs in an Fe-0.12 pct C-0.11 pct V alloy reacted in the temperature range 800‡ to 870 ‡C develop in two morphologies: conventional allotriomorphs, with an aspect ratio of about one-half, and “snakes≓, whose aspect ratio approaches zero. Interphase boundary vanadium carbides (VC) precipitate densely in association with conventional allotriomorphs but not with “snakes≓. Thickening kinetics of “snakes≓ are about an order of magnitude slower than predicted by the paraequilibrium model. Conventional allotriomorphs, on the other hand, thicken with the kinetics predicted by paraequilibrium. These observations are considered in terms of the solute drag-like effect and of “wetting≓ of austenite grain boundaries by ferrite in the presence of V. Absence of a distinct change in the thickening kinetics of conventional allotriomorphs in the vicinity of 845 ‡C, the approximate upper temperature limit of interphase boundary carbide precipitation, strongly supports the view that such carbides can precipitate only on immobile,i.e., partially coherent areas of austenite : ferrite boundaries. Formerly Visiting Research Associate, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 Formerly Republic Steel Corporation Fellow, Michigan Technological University, Houghton, MI 49931 Formerly Professor, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931     

Growth kinetics of grain boundary ferrite allotriomorphs in Fe-C-X alloys

Parabolic rate constants for the thickening (α) and lengthening (β) kinetics of grain boundary allotriomorphs of proeutectoid ferrite have been measured as a function of isothermal transformation temperature in several Fe-C-X’ alloys whereX = Si, Ni, Mn, and Cr. These constants have been corrected approximately for the growth inhibition produced by facets on the allotriomorphs. The corrected α values are compared with those calculated on the basis of three models: equilibrium at α:γ boundaries with partition ofX, local equilibrium with “pile-up” ofX rather than bulk partition, and paraequilibrium. Values calculated from both the paraequilibrium and the “pile-up” models were in order of magnitude or better agreement with the corrected experimental α’s. Similar levels of agreement were obtained for the equilibrium model in the Si and Cr alloys and also in one Ni alloy at lower reaction temperatures. However, an estimate of the maximum possible diffusion distance of alloying element into austenite during growth supported only the paraequilibrium model under nearly all conditions investigated. Even for this model, however, measured rate constants are significantly less than those calculated for Fe-C-Mn and Fe-C-Cr and greater for Fe-C-Si and the higher Ni, Fe-C-Ni alloy. The Mn and Cr discrepancies seem best explained at present by a solute drag-like effect; an accompanying paper indicates that interphase boundary precipitation of carbides is involved in the Si and Ni alloys, though an inverse solute drag-like effect may also be operative. Formerly graduate student, Department of Metallurgical Engineering, Michigan Technological University. Formerly Professor at Michigan Technological University.     

Growth and overall transformation kinetics above the bay temperature in Fe-C-Mo alloys

The kinetics and morphology of isothermal transformation in the vicinity of the time-temperaturetransformation (TTT) diagram bay have been investigated with optical and transmission electron microscopy (TEM) in 19 Fe-C-Mo alloys at three levels of carbon concentration (approximately 0.15, 0.20, and 0.25 wt pct) and at Mo concentrations from 2.3 to 4.3 wt pct, essentially always at temperatures above or at that of the bay,T _b . Quantitative metallography yielded no evidence for incomplete transformation (stasis) in any of these alloys atT > T _b . Measurements of the thickening kinetics of grain boundary ferrite allotriomorphs (invariably containing either interphase boundary or fibrous Mo₂C) demonstrated four different patterns of behavior. The customary parabolic time law for allotriomorph thickening in Fe-C and in many Fe-C-X systems was obtained only at higher temperatures and in the more dilute Fe-C-Mo alloys studied. With decreasing temperature and increasing solute concentrations, a two-stage and then two successive variants of a three-stage thickening process are found. In the most concentrated alloys and at temperatures nearest the bay, the second stage of the three-stage thickening process corresponds to “growth stasis”—the cessation of allotriomorph thickening. Sufficient prolongation of growth stasis presumably leads to “transformation stasis.” A number of models for growth of the carbide-containing allotriomorphs were investigated during attempts to explain the observed kinetics. It was concluded that their growth is controlled by carbon diffusion in austenite but with a driving force drastically reduced by a very strong solute drag-like effect (SDLE) induced by Mo segregation at disordered-type austenite: ferrite boundaries. Carbide growth in the fibrous structure appears to be fed by diffusion of Mo along austenite: ferrite boundaries, whereas carbides in the interphase boundary structure grow primarily by volume diffusion of Mo through austenite. Formerly Republic Steel Corporation Fellow, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI, and Visiting Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA. Formerly Professor, Michigan Technological University. This paper is based on a presentation made in the symposium “International Conference on Bainite” presented at the 1988 World Materials Congress in Chicago, IL, on September 26 and 27, 1988, under the auspices of the ASM INTERNATIONAL Phase Transformations Committee and the TMS Ferrous Metallurgy Committee.     

Thickening kinetics of proeutectoid ferrite plates in Fe-C alloys

Thermionic electron emission microscopy was used to measure directly the thickening kinetics of proeutectoid ferrite sideplates in Fe-C alloys. These kinetics were found to be exceedingly irregular. During the first few seconds of growth, the thickening rate is 5 xl0^-5±1 cm/s; afterwards it usually diminishes to 1 - 30 × 10^-6 cm/s. As predicted by a general theory of precipitate morphology, thickening was shown to occur only by the ledge mechanism, despite the relatively poor matching of the austenite and the ferrite lattices. Ledges were observed to lengthen at rates controlled by the diffusion of carbon in austenite. Tent-shaped and other more complex surface relief effects, rather than the invariant plane strain relief, were found to predominate. These features are shown to be the expected result of a diffusional transformation occurring by means of a ledge mechanism. Formerly with the Scientific Research Staff Formerly with the Scientific Research Staff, Ford Motor Company     

Effects of austenitizing temperature on the kinetics of the proeutectoid ferrite reaction at constant austenite grain size in an Fe-C alloy

Austenitizing an Fe-0.23 pct C alloy at 1300°C and further at 900°C prior to isothermal transformation was found to increase the growth kinetics of grain boundary ferrite allotriomorphs while decreasing their rate of nucleation. A scanning Auger microprobe was used to establish that sulfur segregates to the austenite grain boundaries and does so increasingly with decreasing austenitizing temperature. A binding free energy of sulfur to these boundaries of approximately 13 kcal/mole (54.4 kj/mole) was calculated from theMcLean adsorption isotherm. The kinetic results were explained in terms of preferential reduction of the austenite grain boundary energy decreasig nucleation kinetics, and adsorption of sulfur at α:γ boundaries increasing the carbon concentration gradient in austenite driving growth.     

Influence of al,co, and si upon the kinetics of the proeutectoid ferrite reaction

The effects ofca. 3 at. pct of Al, Si, or Co upon the kinetics of grain boundary ferrite allotriomorph formation (and thus upon hardenability) relative to those in Fe-C alloys of comparable carbon content were evaluated. All three alloying elements displace the TTT curve for the initiation of transformation to shorter times at the higher reaction temperatures. Both aluminum and silicon increase the parabolic rate constant for allotriomorph thickening,α, relative to that in their counterpart Fe-C alloys; the influence of cobalt uponα, if any, is appreciably less. In the Fe-C-Al and Fe-C-Si alloys, thickening proceeds noticeably less rapidly than volume diffusion control (as assessed by Atkinson’s analysis of the growth of an oblate ellipsoid) allows. In the Fe-C-Co and Fe-C alloys, the average calculated and experimental α’s are in better agreement but, evidently as a result of the presence of dislocation facets at a broad face of allotriomorphs, some allotriomorphs actually thickened more rapidly than calculated. The substantial scatter inα in all alloys was also attributed to these facets. Indirect determinations indicated that all three elements increased the rate of nucleation of ferrite allotriomorphs. Formerly with Ford Motor Co., Dearborn Mich.     

Nucleation kinetics of proeutectoid ferrite at austenite grain boundaries in Fe-C-X alloys

The nucleation kinetics of proeutectoid ferrite allotriomorphs at austenite grain boundaries in Fe-0.5 at. Pct C-3 at. Pct X alloys, where X is successively Mn, Ni, Co, and Si and in an Fe-0.8 at. Pct C-2.5 at. Pct Mo alloy have been measured using previously developed experimental techniques. The results were analyzed in terms of the influence of substitutional alloying elements upon the volume free energy change and upon the energies of austenite grain boundaries and nucleus: matrix boundaries. Classical nucleation theory was employed in conjunction with the pillbox model of the critical nucleus applied during the predecessor study of ferrite nucleation kinetics at grain boundaries in Fe-C alloys. The free energy change associated with nucleation was evaluated from both the Hillert-Staffanson and the Central Atoms Models of interstitial-substitutional solid solutions. The grain boundary concentrations of X determined with a Scanning Auger Microprobe were utilized to calculate the reduction in the austenite grain boundary energy produced by the segregation of alloying elements. Analysis of these data in terms of nucleation theory indicates that much of the influence of X upon ferrite nucleation rate derives from effects upon the volume-free energy change,i.e., upon alterations in the path of theγ/(α + γ) phase boundary. Additional effects arise from reductions in austenite grain boundary energy, with austenite-forming alloying elements being more effective in this regard than ferrite-formers. By difference, the remaining influence of the alloy elements studied evidently results from their ability to diminish the energies of the austenite: ferrite boundaries enclosing the critical nucleus. The role of nucleation kinetics in the formation of a bay in the TTT diagram of Fe-C-Mo alloys is also considered. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University     

Growth kinetics of grain boundary ferrite allotriomorphs in Fe−C alloys

The kinetics of lengthening and thickening of grain boundary allotriomorphs of proeutectoid ferrite were measured at several temperatures in high purity Fe−C alloys containing 0.11 pct, 0.23 pct and 0.42 pct C. These measurements were conducted by measuring the length of the longest and the width of the widest allotriomorph in each specimen. All specimens were austenitized so as to make the grain boundaries perpendicular to the plane of polish. This measurement technique appreciably reduced the scatter in the parabolic rate constant data previously encountered in thermionic emission microscopy measurements. Parabolic rate constants for lengthening and thickening were calculated, using the experimental aspect ratio, by means of the Atkinson analysis for oblate ellipsoids. The ratio of the measured to the calculated constants was in all cases less than unity. The previously made suggestion that these slow growth kinetics are due to faceting was supported through the observation of facets on allotriomorphs by means of scanning and transmission electron microscopy. The aspect ratio of ferrite allotriomorphs was shown to beca 1/3, independent of reaction time temperature and carbon content. The dihedral angle of the allotriomorphs was found to be 100±5 deg, as compared with a published angle for recrystallized and equilibrated specimens ofca 115 deg. Several possible explanations for the aspect ratio and dihedral angle findings are considered. M. RIGSBEE, formerly Postdoctoral Research Associate with Michigan Technological University     

The kinetics of ferrite nucleation at austenite grain boundaries in Fe-C alloys

The nucleation kinetics of grain boundary allotriomorphs of proeutectoid ferrite at austenite grain faces have been measured in three high purity Fe-C alloys as a function of isothermal reaction time and temperature. Several correction techniques, including discrimination between different nucleation sites and the effect of carbon diffusion fields on further nucleation of ferrite, were incorporated into a stereological procedure utilizing the SchwartzJSaltykov size distribution analysis. This analysis enabled the number of ferrite particles per unit unreacted grain boundary area to be obtained as a function of isothermal reaction time, and thus the time-dependent nucleation kinetics to be obtained as a function of temperature and carbon concentration. These rates were then compared with those predicted by classical heterogeneous nucleation theory using various models for the critical nucleus. It was concluded that viable critical nuclei must have predominately low energy interphase boundaries. Only a very small fraction of the austenite grain face area appears to be capable of supporting nucleation. Formerly Graduate Student, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 Formerly Professor at Michigan Technological University     

Simulation of ferrite growth in continuously cooled low-carbon iron alloys

The growth of a planar ferrite (α): austenite (γ) boundary in low-carbon iron and Fe-Mn alloys continuously cooled from austenite through the (α+γ) two-phase field and the α single-phase field was simulated by incorporating carbon diffusion in austenite, intrinsic boundary mobility, and the drag of an alloying element. At a very high cooling rate (≥ 10³ °C/s), the width of the carbon diffusion spike in austenite approaches the limit at which spikes are viable, so that the growth of ferrite in which carbon is not partitioned can occur even above the α solvus. In this context, the upper limiting temperature of partitionless growth of ferrite is the T ₀ temperature. In the presence of drag of an alloying element, e.g., Mn, both carbon-partitioned and partitionless growth of ferrite begins to occur at finite undercoolings from the Ae ₃, T ₀, or α-solvus temperature, at which the driving force for transformation exceeds the drag force. The intrinsic mobility of the α:γ boundary may play a significant role at an extremely high cooling rate (≥10⁵ °C/s). This article is based on a presentation made at the symposium entitled “The Mechanisms of the Massive Transformation,” a part of the Fall 2000 TMS Meeting held October 16–19, 2000, in St. Louis, Missouri, under the auspices of the ASM Phase Transformations Committee.     

The influence of starting microstructure on the retention and mechanical stability of austenite in an intercritically annealed-low alloy dual-phase steel

Retention of austenite during the intercritical annealing of a low carbon, low-alloy, dual-phase steel and the mechanical stability of retained austenite(γ _R) have been studied as a function of starting microstructure and annealing conditions. A quenched and tempered(QT) starting microstructure has been found to result in higher γ_R volume fractions compared to fully martensitic(Q) and ferrite plus pearlitic(F + P) starting structures for all annealing conditions employed in this work. The austenite formed by annealing up to 792 °C (where the kinetics are dominated by higher nucleation rates) is more prone to retention compared to that formed by annealing beyond 792 °C (where the kinetics are mainly dominated by higher growth rates). A smaller size of γ_R particles has a better mechanical stability against deformation-induced martensite transformation. Formerly Master's Student at the University of Manitoba     

Modeling of kinetics of austenite-to-allotriomorphic ferrite transformation in 0.37C-1.45Mn-0.11V microalloyed steel

The present article is concerned with the theoretical and experimental study of the growth kinetics of allotriomorphic ferrite in medium carbon vanadium-titanium microalloyed steel. A theoretical model is presented in this work to calculate the evolution of austenite-to-allotriomorphic ferrite transformation with time at a very wide temperature range. At temperatures above eutectoid temperature, where allotriomorphic ferrite is the only austenite transformation product, the soft-impingement effect should be taken into account in the modeling. In that case, the Gilmour et al. analysis reliably predicts the progress of austenite-to-allotriomorphic ferrite transformation in this steel. By contrast, since pearlite acts as a carbon sink, the carbon enrichment of austenite due to the previous ferrite formation is avoided, and carbon concentration in austenite far from the α/γ interface remains the same as the overall carbon content of the steel. Hence, the soft-impingement effect should be neglected, and allotriomorphic ferrite is considered to grow under a parabolic law. Therefore, assumption of a semi-infinite extent austenite with constant boundary conditions is suitable for the kinetics of the isothermal decomposition of austenite. An excellent agreement (higher than 93 pct in R ²) has been obtained between the experimental and predicted values of the volume fraction of ferrite in all of the ranges of temperature studied.     

Growth kinetics of grain boundary allotriomorphs of proeutectoid ferrite in Fe-C-Mn-X2 alloys

The parabolic rate constant for the thickening of grain boundary ferrite allotriomorphs at the faces of austenite grain boundaries was measured as a function of isothermal transformation temperature in three Fe-C-X₁-X₂ alloys where X₁ is Mn and X₂ is successively Si, Ni, and Co. The results were compared with the predictions of the local equilibrium model for multi-component systems and with those derived from the theory of growth under paraequilibrium conditions. The distribution of Mn and Si in ferrite and austenite in the Fe-C-Mn-Si alloy was also measured as a function of reaction temperature with transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDX). The observed temperature below which alloying element partition ceased was in good agreement with the local equilibrium model. Whereas the parabolic rate constant for thickening was considerably larger than the amount predicted by this theory in the alloying element diffusion-controlled regime, the opposite was true in the carbon diffusion-controlled regime. Similarly, the calculated paraequilibrium constant was usually considerably larger than that measured experimentally. Synergistic enhancements of the effects of Mn and X₂ in diminishing thickening kinetics were observed for each X₂. The time-temperature-transformation (TTT) curves for the beginning of transformation were calculated from a modified Cahn analysis for the overall kinetics of grain-boundary-nucleated reactions using values of the nucleation rate and the parabolic growth rate constant computed from various models and compared with experimentally determined TTT curves. Substantial discrepancies between the calculated and measured curves were ascribed to synergistic effects of Mn and X₂ upon nucleation and growth kinetics. Formerly Graduate Student, Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA Formerly Mehl Professor Emeritus at Carnegie Mellon University.     

On the influence of carbide formation upon the growth kinetics of proeutectoid ferrite in Fe-C-X alloys

In the preceeding paper, the growth kinetics of grain boundary ferrite allotriomorphs in Fe-C-Si, Fe-C-Mn, Fe-C-Ni, and Fe-C-Cr alloys are reported to be best described by the paraequilibrium model. Significant differences are still observed, however, between the experimentally measured kinetics and those calculated from this model. A TEM study was conducted on these alloys to ascertain whether any of these differences could be attributed to carbide precipitation. In the Fe-C-Mn and Fe-C-Cr alloys, where the measured growth kinetics are low, carbides precipitate on dislocations within the ferrite and are effectively absent, respectively; hence carbide precipitation cannot be responsible for the deviations in these alloys. In the low Ni, Fe-C-Ni alloy, where calculated and measured kinetics agree, carbide precipitation was again found on dislocations in the ferrite. Faster than calculated growth kinetics in the Fe-C-Si and the high Ni, Fe-C-Ni alloys, on the other hand, are attributed in part to carbide precipitation at austenite:ferrite boundaries. Formerly Republic Steel Fellow, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 and Visiting Graduate Student, Carnegie-Mellon University, Pittsburgh, PA 15213 Formerly Professor, Department of Metallurgical Engineering, Michigan Technological University Formerly Graduate Student, Department of Metallurgical Engineering, Michigan Technological University     

The stereology of grain boundary allotriomorphs

Grain boundary allotriomorphs have been modeled as two abutting spherical caps of equal radius. The effects of the distance from the center of the allotriomorph, х, and the angle with respect to the plane normal to the grain boundary, ψ, at which a plane of polish sections the allotriomorph have been investigated. Expressions were derived relating the apparent to the true thickness, length, aspect ratio and dihedral angle. The effects of х and ϕ upon measurements of the lengthening and thickening kinetics of allotriomorphs were found to be significant, particularly at larger values of ψ. Analysis of published high-temperature measurements of allotriomorph growth kinetics indicated that an appreciable portion of the scatter in this data may have been due to nonzero values of х and ψ. A room temperature technique for making these measurements which minimizes such effects is concluded to be stereologically more reliable.     

Nucleation,growth, and overall transformation kinetics of grain boundary allotriomorphs of proeutectoid alpha in Ti-3.2 At. Pct Co and Ti-6.6 At. Pct Cr alloys

The nucleation, growth, and overall transformation kinetics of grain boundary α allotriomorphs were measured in Ti-3.2 at. pct Co and Ti-6.6 at. pct Cr alloys with optical microscopy. Nucleation kinetics were interpreted with classical heterogeneous nucleation theory, using the pillbox model of the critical nucleus. Growth kinetics of allotriomorphs were significantly accelerated by the rejector plate mechanism, but much less so than allotriomorphs formed in fcc substitutional matrices at comparable homologous temperatures. Overall transformation kinetics were accounted for with a modified version of Cahn’s theory of grain boundary nucleated reactions. Formerly Graduate Student, Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213     

Influence of Interfacial Structure upon Carbide Precipitation at Austenite : Ferrite Boundaries in an Fe-C-Mo Alloy

During conventional isothermal transformation of an Fe-0.11 pct C-1.95 pct Mo alloy, eutectoid decomposition occurs by the interphase boundary carbide precipitation and the fibrous carbide mechanisms at 770° to 825 °C. When proeutectoid ferrite is formed and then recrystallized within the α + γ region, and subsequently further transformed at 770° to 825 °C, however, both of these eutectoid decomposition mechanisms are rendered inoperative. Carbide precipitation occurs instead entirely as isolated particles. This result supports the deduction that carbide precipitation at austenite : ferrite boundaries can occur only when these boundaries are locally immobilized by a partially coherent interfacial structure. A general approach to explaining the development of planar and curved interphase boundary precipitation, fibrous structure, and pearlite is developed in terms of two crystallographic factors. Formerly Research Associate in the Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931 and the Department of Metallurgical Engineering and Materials Science, Carnegie-Mellon University, Pittsburgh, PA 15213 Formerly Graduate Student, Michigan Technological University, and Visiting Graduate Student, Camegie-Mellon University Formerly Professor at Michigan Technological University     

Partition of Mn during the growth of proeutectoid ferrite allotriomorphs in an Fe-1.6 at. pct C-2.8 at. pct Mn alloy

A STEM analysis is made of the Mn distribution around grain boundary allotriomorphs of proeutectoid ferrite in an Fe-1.6 at. Pct C-2.8 at. Pct Mn alloy. Whereas the Mn enriched region is readily observed to extend along the austenite grain boundary, no substantial build-up or depletion of Mn near the ferrite : austenite interface is detected, consistent with the electron probe microanalysis previously reported. In the temperature range where the partition-local equilibrium (P-LE) mode has been proposed to prevail, measured parabolic growth rate constantsfall 1 to 2 orders of magnitude above that predicted from this model, but also below that calculated from the paraequilibrium (PE) model by roughly the same amount. A modification of the theory of grain boundary diffusion-aided growth of precipitates,i.e., the collector/rejector plate mechanism, on the other hand, accounts fairly well for the observed growth kinetics of ferrite allotriomorphs. However, only a slightly better accounting than the P-LE model is provided by this mechanism for the temperature dependence of Mn partition. Data on Ni partition, obtained in an Fe-0.5 at. Pct C-3.1 at. Pct Ni alloy, are also analyzed with the rejector plate model.     

Modeling of kinetics of austenite-to-allotriomorphic ferrite transformation in 0.37C-1.45Mn-0.11V microalloyed steel

The present article is concerened with the theoretical and experimental study of the growth kinetics of allotriomorphic ferrite in medium carbon vanadium-titanium microalloyed steel. A theoretical model is presented in this work to calculate the evolution of austente-to-allotriomorphic ferrite transformation with time at a very wide temperature range. At temperatures above eutectoid temperature, where allotriomorphic ferrite is the only austenite transormation product, thesoft-impingement effect should be taken into account in the modeling. In that case, the Gilmouret al., analysis reliably predicts the progress of austenite-to-allotriomorphic ferrite transformation in this steel. By contrast, since pearlite acts as a carbon sink, the carbon enrichment of austenite due to the previous ferrite formation is avoided, and carbon concentration in austenite far from the α/λ interface remains the same as the overal carbon content of the steel. Hence, the soft-impingement effect should be neglected, and allotriomorphic ferrite is considered to grow under a parabolic law. Therefore, assumption of a semi-infinite extent austenite with constant boundary conditions is suitable for the kinetics of the isothermal decomposition of austenite. An excellent agreement (higher than 93 pct inR ²) has been obtained between the experimental and predicted values of the volume fraction of ferrite in all of the ranges of temperature studied. C. CAPDEVILA, Research Associate, formerly with the Department of Physical Metallurgy, Centro Nacional de Investigaciones Metalurgicas (CENIM), Consejo Superior de Investigaciones Cientificas (CSIC), 28040 Madrid, Spain