H. I. Aaronson

A debate on the bainite reaction

The authors debate three topics central to the controversies which have enveloped the bainite reaction ever since it was first recognized as a distinctive mode of austenite decomposition. These include: “what is bainite?”, “the growth mechanism of the ferritic component of bainite”, and “the sources of bainitic carbide precipitation.” RFH concludes that bainite is the product of a shear transformation. Individual bainite plates are suggested to grow substantially more rapidly than volume diffusion-control allows, but a constraint such as the build-up of volume strain energy limits the extent of their growth. This mechanism of growth ensures extensive supersaturation of bainitic ferrite with respect to carbon. Whether or not carbides precipitate in association with bainite plates and whether the carbide is cementite orε, however, is a complex question in competitive reaction kinetics. New experimental evidence is presented to demonstrate thatε carbide precipitated in lower bainite dissolves upon heating above the kinetic-Bstemperature in an alloy steel containing 1.5 pct Si. This result is taken to support the existence of the metastable eutectoid reactionγ ⇌ α + ε atca 350°C. HIA and KRK define bainite as the product of a nonlamellar eutectoid reaction. On this view, carbide precipitation thus plays an essential, rather than an ancillary role. Development of the Widmanstatten morphology by the ferritic component of bainite is shown to be inessential to the classification of a eutectoid structure as bainite. When this morphology is present, however, it is concluded to grow by the ledge mechanism, without the participation of shear, at rates of the order of or less than those allowed by volume diffusion-control. New experimental evidence is presented to show that the lengthening and thickening kinetics of individual plates within sheaves of upper bainite are consistent with this description. The results of a new calculation indicate that the initial carbon content of bainite plates lies between theα/α + Fe3C) and the extrapolatedα/(α+ γ) phase boundaries, in agreement with expectation from the ledge mechanism of growth.

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.

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.

Anisotropy of coherent interphase boundary energy

Abstract A nearest neighbor, broken bond model is employed to develop general relationships for the concentration profile associated with a coherent interphase boundary and for the interfacial energy of such a boundary, σc. This development incorporates a simple crystallographic method for describing the distribution of nearest neighboring atoms about a given atom in an interface of arbitrary orientation between two cubic-type crystals. Contours of constant σc are constructed on the unit steriographic triangle at several temperatures and illustrate the manner in which the anisotropy of σc evolves with decreasing temperature. Mathematical equivalency of the discrete lattice model and the continuum method of Cahn and Hilliard is demonstrated at high temperatures when the regular solution model is applicable. A comparison between the two approaches is used to demonstrate that σc is relatively insensitive to the concentration profile.

Precipitation at interphase boundaries

Three problems in precipitation at interphase boundaries are examined. 1) The classu argument as to the particular phase in which such a precipitate nucleates is shown to be irrelevant; except in a special situation, the critical nucleus must normally penetrate both phases forming the interphase boundary. 2) The relative penetrations into the two phases achieved during growth can be very different than those expected during nucleation; hence, deductions about the nucleation process based upon observations on growth morphologies can be quite misleading. 3) The observations of Honeycombe and others that the nucleation of carbides at austenite: ferrite boundaries occurs predominantly at the low energy, immobile broad faces of ledges rather than at the higher energy, mobile risers of ledges are accounted for theoretically on the basis of the high velocities of the risers preventing nucleation. Example calculations on a Ti-Ni alloy indicate that precipitation at the risers of ledges may become possible in substitutional systems, but only at lower homologous temperatures, and if the migration of these boundaries is still controlled by volume diffusion while nucleation is controlled by interfacial diffusion.

Lengthening kinetics of ferrite and bainite sideplates

The rate of lengthening of ferrite and bainite sideplates and the radius of curvature of the plate edges were measured as a function of reaction temperature in three Fe-C alloys. These data were analyzed on the basis of an equation due to Trivedi. The analysis proved that the mobility of the sideplate edges is limited. The interfacial energy of these edges is of the order of 200 erg/cm2. Most of the supersaturation is used to drive the diffusion of carbon in austenite; comparatively little is accounted for by capillarity and by the finite mobility of the interface. On the basis of both the present results and of published micro-structural observations, it was concluded that ferrite and bainite sideplates lengthen by a ledge mechanism.

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.

A re-examination of the thermodynamics of the proeutectoid ferrite transformation in Fe-C alloys

Three models of the statistical thermodynamics of interstitial solid solutions have been used to reevaluate the thermodynamics of the proeutectoid ferrite reaction. The models of Kaufman, Radcliffe and Cohen and of Lacher, Fowler and Guggenheim, which were em-ployed in a previous study of this type, together with the model recently developed by McLellan and Dunn are used in conjunction with the extensive experimental data of Ban-ya, Elliott and Chipman, of Lobo and Geiger and of Dunn and McLellan on the activities of carbon in austenite and ferrite. Application of the McLellan and Dunn model and that of Lacher, Fowler and Guggenheim to carbon in austenite yields activities of carbon which are numerically indistinguishable and activities of iron which are mathematically identi-cal. However, the new activity data have revealed important differences between the pres-ent calculations and those of Aaronson, Domian and Pound. An average carbon-carbon repulsion energy in austenite of 1925 cal/mole (8054 J/mole) was determined from the CO/CO2 data of Ban-yaet al. However, the C-C interaction energy in ferrite was found to be opposite in sign but exhibited erratic variations with temperature despite the large amount of activity data available. The γ/(α + γ) phase boundary calculated from the new data differs significantly, at lower temperatures, from the best curves reported by Aaron-sonet al. The calculateda/(α +γ) phase boundary also differs appreciably from the pre-vious results and exhibits only limited agreement with the experimentally determined phase boundary. Calculation of the free energy change associated with the proeutectoid ferrite reaction andT0- composition curves differs little from previous results; internal agreement among the new sets of curves, however, is much improved.

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.

On the existence of the β→αm transformation in the alloy systems Ti-Ag, Ti-Au, and Ti-Si

The existence of the β (bcc) to αim (hcp) massive transformation is demonstrated in three titanium-base eutectoid systems: Ti-Ag, Ti-Au, and Ti-Si. Confirmation is accomplished through optical microscopy and phase composition analysis by EDAX microprobe, supplemented by transmission electron microscopy. In these three alloy systems, the characteristics of the massive transformation were found to be quite similar, with very irregularly shaped αm grains consuming most or all the parent grains during moderate to rapid quenching from the β region. The transformation occurs at compositions well into the hypereutectoid region in the Ti-Ag system but is confined mainly to hypoeutectoid alloys in Ti-Au and Ti-Si.