Bainite viewed three different ways

Bainite Viewed Three Different Ways

H.I. AARONSON, W.T. REYNOLDS, Jr., G.J. SHIFLET, and G. SPANOS

The present status of the three principal definitions of bainite currently in use is reviewed. On the surface relief definition, bainite consists of precipitate plates, producing an invariant plane strain (IPS) surface relief effect, which form by shear, i.e., martensitically, at temperatures usually above Ms and Md. The generalized microstructural definition describes bainite as the product of the diffusional, noncooperative, competitive ledgewise growth of two precipitate phases formed during eutectoid decomposition, with the minority phase appearing in nonlamellar form. This alternative mode of eutectoid decomposition is thus fundamentally different from the diffusional, cooperative, shared growth ledges mechanism for the formation of pearlite developed by Hackney and Shiflet. The overall reaction kinetics definition of bainite views this transformation as being confined to a temperature range well below that of the eutectoid temperature and being increasingly incomplete as its upper limiting temperature, the kinetic Bs, is approached. Recent research has shown, however, that even in steels (the only alloys in which this set of phenomena has been reported), incomplete transformation is not generally operative. Revisions in and additions to the phenomenology of bainite defined in this manner have been recently made. Extensive conflicts among the three definitions are readily demonstrated. Ar- guments are developed in favor of preference for the generalized microstructural definition, reassessment of the overall reaction kinetics definition, and discarding of the surface relief definition.

I. INTRODUCTION

ABOUT 20 years ago, the proposal was made that much of the confusion then enveloping the bainite reaction (which has since become considerably worse!) had its origin in the curious circumstance that at least three major definitions of bainite were currently in use, each of which encompassed a different group of incompletely over- lapping phase transformations phenomena. ~zl Thus, a transformation product which one definition would de- scribe as bainite might not be so classified by either or both of the other two. In their current form, these definitions are the following. The generalized microstructural definition states that bainite is the product of the diffusional nucleation and the competitive ledgewise diffusional growth of the two phases comprising the products of a eutectoid reaction.~2] The unit atomic process is the thermally activated diffusion of single atoms. The surface relief definition I3,4,51 terms bainite the plate- shaped product of a shear mode of phase transformation, usually taking place above the Ms or even the Md temperature, as evidenced by an invariant plane strain (IPS) relief effect when the plate forms at a free surface. On this definition, simultaneous or highly coordinated, non-

H.I. AARONSON, R.F. Mehl Professor, is with the Department of Metallurgical Engineering and Materials Science, Carnegie Mellon University, Pittsburgh, PA 15213-3890. W.T. REYNOLDS, Jr., Assistant Professor, is with the Department of Materials Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0237. G.J. SHIFLET, Professor, is with the Department of Materials Science, University of Virginia, Charlottesville, VA 22903. G. SPANOS is with the Physical Metallurgy Branch, Naval Research Laboratory, Code 6324, Washington, DC 20375-5000.

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 Transfor- mations Committee and the TMS Ferrous Metallurgy Committee.

thermally activated glide of atoms across the advancing interphase boundary is the unit atomic process. On some views, the kinetics of shear are controlled by interstitial solute diffusion in the matrix phase, while on others, growth takes place more rapidly than volume diffusion in the matrix phase would allow in either a substitutionally or an interstitially alloyed matrix. The overall reaction kinetics definition t4,61 views bainite as having its own C-curve on a time-temperature-transformation (TTT) diagram whose upper limiting temperature, termed the "kinetic Bs," is well below that of the eutectoid temperature. Between the kinetic Bs and some lower temperature, inappropriately known as the "bainite finish" or "kinetic B/" temperature, the bainite reaction ceases entirely before all of the austenite has decomposed. The proportion of the austenite transformed to bainite decreases monotonically from 100 pct at the kinetic By to zero at the kinetic Bs. This has become known as the "incomplete transformation phenomenon." After an interval of "transformation stasis," which may last from seconds to months or longer, austenite decomposition re- sumes and goes to completion, presumably by the pearlite reaction. Bainite also forms, though without incomplete transformation, at temperatures below the kinetic BI, in principle, at temperatures down to that of the M I (martensite finish) temperature.

The original form of the microstructural definition (in which the morphology of the ferritic component of bainite was restricted to that of plates and its atomic mechanism was not specified) is due to Robertson I71 and Davenport and Bain. t8j The surface relief definition, in nearly its principal present form, originated with Ko and Cottrell, c31 though it remained to later workers to quan- tify the surface upheaval as being of the IPS type.tgl The phenomena comprising the incomplete transformation definition were largely identified by Wever and co- workers, i10-141

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Although two opportunities to consider these three definitions further recently arose, D5,16] enough additional experimental and interpretive information has become available since that time and sufficient discussion of various fundamental aspects of the bainite reaction has appeared in the literature to justify yet another effort in this direction. In particular, two of the succeeding papers in these proceedings provide improved information on the temperature-composition regions in which the various morphologies of bainite predominate tlTj and a new, purely diffusional mechanism for lower bainite formation in steel. I~81 Both are important in the context of the generalized microstructural definition of bainite. The other following papers provide new data on growth and overall reaction kinetics above the kinetic Bs temperature tlg~ and below this temperature, c2~ respectively, in Fe-C-Mo alloys, while a sixth paper furnishes overall reaction kinetics data relevant to the incomplete transformation phenomenon in several other Fe-C-X systems, t2q and a seventh paper provides microstructural and overall reaction kinetics data on an Fe-C-Cr alloy, t2~~ In a current critical review, fundamental aspects of the surface relief definition are examined in some detail. I221 Recent reviews of the bainite reaction (or closely related topics) by other authors t23-291 and extensive discussions of these reviews I3~ have added further material of interest to the present critique.

While much of the foregoing research activity has dealt with bainite defined in various ways in steel, many papers have also been published on bainite in nonferrous alloys, as defined by the generalized microstructural and/ or by the surface relief definitions. The numerous papers presented in this conference on bainite formation in both ferrous and nonferrous alloys further attest to the recent marked increase in interest in this most controversial area of phase transformations research.

In Sections II through IV, the status of each of the three definitions will be successively assessed. Section V will then be devoted to emphasizing the depth and generality of the conflicts among them and, thus, the importance of arriving at a generally acceptable single definition of the bainite reaction. The main contents of each section will be outlined at its beginning. Table I provides a list of frequently used acronyms for the con- venience of the reader.

II. THE SURF ACE RELIEF DEFINITION OF BAINITE

After noting the requirements of the phenomenological theory of martensite crystallography (PTMC) which must be fulfilled in order that a phase transformation qualify as having taken place by shear, the mechanism for the formation of an IPS surface relief effect by ledgewise diffusional growth is considered. Much emphasis is then placed upon the fulfillment of derivative requirements of the PTMC. Finally, an assessment is made of the surface relief definition of bainite as a whole.

A. Fulfillment of the Requirements of the PTMC

In order that a transformation product qualify as one produced by a shear or martensitic transformation, the

Table I. List of Acronyms Used

at. pct FCB FIM/AP IL IPS kinetic Bs

kinetic B I

LRO PTMC

SDLE SEM STEM To

TEM THEEM TTT

curve WLR wt pct

atomic percent ferritic component of bainite field ion microscopy/atom probe invariant line invariant plane strain highest temperature at which bainite forms,

on the overall reaction kinetics definition of bainite

highest temperature at which 100 pct of the microstructure can be transformed to bainite, similarly defined

long-range order phenomenological theory of martensite

crystallography solute drag-like effect scanning electron microscopy scanning transmission electron microscopy temperature at which stress-free austenite and

ferrite (or counterpart phases in a nonferrous system) with the same composition have the same free energy

transmission electron microscopy thermionic electron emission microscopy isothermal time temperature transformation

curve Wechsler, Lieberman, and Read PTMC weight percent

current view is that it must not only exhibit (1) an IPS relief effect when formed in contact with a free surface but must also fulfill, in an entirely self-consistent manner, 15J all of the other requirements of the PTMC. 14~ These requirements include: (2) a plate morphology (when formed in the interior of a specimen); (3) a lattice correspondence between the matrix and product phases; (4) an irrational lattice orientation relationship between the matrix and product [except during fcc/hcp and fcc/dhcp (double hcp) transformations]; (5) an irrational habit plane [with the same exception as in (4)]; and (6) the presence of an internal inhomogeneity such as twinning or slip through which the lattice invariant deformation is conducted [same exceptions as in (4)]. Fulfillment of only some of these requirements does not support the postu- late that a given transformation has taken place by means of a shear mechanism.L51

Studies sufficiently thorough to ascertain whether or not all of these requirements are indeed self-consistently fulfilled have been conducted on a few representative transformations which are also legitimately suspected of having formed through the operation of a diffusional mechanism. Among substitutional alloys, a I Cu-Zn t42~ and a~ Ag-Cd I43j plates both not only properly fulfill all of the foregoing conditions but also closely resemble the martensite formed in the same alloys at much lower temperatures. AuCu II plates formed in a disordered Au-50 at. pct Cu alloy r441 have been shown to meet these requirements with particularly high accuracy. Inasmuch as all appear to grow slowly, at least upon the length scales investigated so far, t45-481 all are candidates for description as bainite on the most frequently used version of the surface relief definition. Additionally, y A1Ag2 plates initially yield an IPS surface relief and have the same

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habit plane and crystallography as characterize martensitic fcc/hcp transformations. 149] Hence, this reaction can serve as an example of bainite described by the surface relief definition in which no lattice invariant deformation is required. ]5] These four transformations will thus serve as our "models" for surface relief bainite in substitutional alloys. On historical as well as current usage grounds, proeutectoid ferrite plates, singly and variously grouped, both in the absence of carbides and with a dispersion of nonlamellar carbides among them (i.e., microstructural bainite), will serve in the same role for interstitial alloys. The well-studied precipitation of /3 VH045 plates from bcc V-H solutions I5~ will serve as a second model transformation between interstitial phases.

Now consider first whether or not these model transformations are accompanied by an IPS relief effect when formed at a free surface. The answer to this question is apparently in the affirmative for the four transformations serving as models for substitutional alloys, i42-44,49] How- ever, plate- or lath-shaped precipitates in other substitutional alloys do not necessarily exhibit the same behavior. For example, proeutectoid a plates in a Ti- 6.62 at. pct Cr alloy have been found to yield tent-shaped reliefs 4 times as frequently as those of the IPS type, though transmission electron microscopy (TEM) experiments demonstrated that all plates examined were single crystals. 152]

In the case of proeutectoid ferrite and bainite, on the other hand, a quite different pattern of results is obtained. The three-dimensional (3-D) morphology of the Widmanst~itten structure tends to be lathlike at higher reaction temperatures but to be better described as plates at lower temperatures. ]53] Although some proeutectoid ferrite plates can indeed yield IPS reliefs, t54J tent-shaped and more complicated relief morphologies are much more general, tSa'55j even though all are evidently produced by monocrystals, t55,56] Watson and McDougall t54~ observed tents and assumed that they were pairs of plates formed back-to-back but did not investigate this point experimentally.r571 In only one investigation of those with which the present authors are familiar were back-to-back proeutectoid ferrite plates actually formed. Bhadeshia ]58j isothermally reacted specimens of an Fe-0.4 pct C alloy and then deliberately slowly cooled them. Particularly given the very rapid transformation kinetics in high-purity Fe-C alloys, this procedure markedly increased the prob- ability that face-to-face sympathetic nucleation tsgj of another ferrite plate would take place, at some lower temperature, at a broad face of most plates isothermally formed at a higher temperature. Hence, the relief effects of proeutectoid ferrite plates are usually not of the IPS type, as required by the PTMC. Similarly, lower bainite plates, suggested to be monocrystals, t6~ even though this now seems less likely, t181 can also form tent-shaped reliefs, ]6~ though IPS reliefs have been observed in thin plates of lower bainite and both plastic accommodation and carbide precipitation have been suggested to perturb the reliefs associated with thicker plates.tSl The situation with respect to/3 VH0.45 surface relief morphology is less clear. Although no photographs of these reliefs appear to have been published, an IPS tilt is implied, I511 with "rounding" of many tilts evidently having occurred as a result of accommodation slip. tr~]

All four of the "model" transformations in substitutional alloys have habit planes and orientation relationships well explained by the P T M C . [42-44'49] On the other hand, the example transformations in steel again display significant discrepancies with respect to the behaviors thereby forecast. Watson and McDougall t541 thus reported important scatter in the habit plane of ferrite plates, as determined with optical microscopy, and their orientation relationship and shape strain data on these plates are inconsistent with one another. [621 The crystallography of upper bainite cannot be rationalized by the PTMC. [631 Unlikely irrational modes of lattice invariant deformation are too often required to explain habit plane and orientation relationship data on bainite.[64.651 On the view that lower bainite closely resembles martensite of similar composition, t661 both the absence of twinning within the ferritic component t64,651 and different habit planes and orientation relationships than those associated with martensite formed in the same alloy [65,67] are anomalous. In view of this plethora of serious disagreements, the in- sistence in the current literature tz3.z6j that Widmanst~itten ferrite and bainite formation agrees with the PTMC can only be regarded as puzzling. On the other hand, agreement between the PTMC and experiment for fl VH0.45 is generally good. tS~ Such disagreements as did appear are likely due to uncertainties in the exact crystal structure of this hydride and also to the presence of slightly misoriented microdomains within the hydride plates, tS~J

The disagreements between PTMC and experiment in steel suggest the desirability of briefly surveying parallel results on transformations, particularly in steel, which are undeniably martensitic. Wayman TM has shown con- vincingly in a variety of alloy systems that single martensite plates produce an IPS surface relief. Tent-shaped reliefs are here due to the formation of back-to-back pairs of martensite plates. In Au-47.5 at. pct Cd 1681 and Fe- 0.8 wt pct C-22 wt pct Ni, t4~ habit plane, orientation relationship, shear direction, and shear angle are all accurately predicted by the Wechsler, Lieberman, and Read (WLR) t4~ version of the PTMC. t5,7~ In steels, however, near {1 1 1}v, {225}v, and {259} v habit planes have proved difficult to understand in a self-consistent manner, t71] However, volume changes in the range of 2.5 to 4 pct tend to characterize transformations in steels which the PTMC cannot fully explain, whereas volume changes of less than 1 pct yield habit planes such as {3, 10, 15}v and other crystallographic characteristics which can be properly rationalized, t71j indicating that deformation processes not included in the PTMC are taking place when the transformation volume change is large, t71~ Hence, it now appears that particularly in steel, but perhaps in substitutional alloys as well, in which an appreciable volume change attends the transformation, neither agreement nor disagreement with the predictions of the PTMC provides good evidence as to the operative transformation mechanism at the atomic level.

B. Formation of an IPS Surface Relief Effect by Ledgewise Diffusional Growth

Among some adherents of the view that bainite forms by shear, it now seems de rigueur to state that no mechanism has been proposed to explain the evolution of IPS

METALLURGICAL TRANSACTIONS A VOLUME 21A, JUNE 1990-- 1345

reliefs through ledgewise diffusional growth.[23.26] However, in a recent publication on the subject, I52] six earlier references involving one of the present authors, [1,49,55,72-74] as well as another to a paper by Dahmen, [281 were cited in which just this was done. In brief, when all ledges through which a plate thickens have the same "shear," the surface relief effect produced will be the same IPS as would have developed had the plate formed by a shear mechanism. This conclusion has, in fact, been implicitly recognized by Christian and Edmonds. [231 Presumably, one "shear" or Burgers vector of a given system of growth ledges permits a larger reduction in shear strain energy than other crystallographically equivalent systems when a precipitate plate is in contact with a free surface (though not when the plate is wholly enclosed within a monocrystalline matrix grain), hence leading to a preference for a particular set of ledges. I491 However, when this is not the case, more complex relief effects are generated, tSs] Such non-IPS reliefs cannot develop during a martensitic transformation. Hence, failure of monocrystalline plates to produce IPS reliefs consistently indicates that a shear mechanism of growth is not operative. However, the presence of an IPS relief cannot be regarded as definitive evidence in favor of the operation of a shear growth mechanism.

C. Fulfillment of Other Requirements of a Shear Mechanism of Growth

Although the PTMC does not directly introduce the following additional requirements for transformation by a shear mechanism, each is inescapable if a phase transformation in a substitutional alloy is to take place by shear: [5,7~ (1) absence of a difference in composition between product and matrix phases; (2) absence of a difference in long-range order (LRO) between product and matrix phases; and (3) an interphase boundary structure capable of sustaining a shear mechanism of phase transformation. [s,7~ When the matrix and product phases are interstitial solid solutions, the first requirement, [661 and by implication the second as well, may be r e l axed- - though discussion of these exceptions is required. The third, on the other hand, is as indispensable for interstitial alloys as it is for those which are substitutional in character.

1. Absence of a composition change during growth In substitutional alloys, a significant difference in

composition between the transformation product and surrounding matrix from the earliest validly examinable stage of growth has now been established for a~ C u - Z n , ]76'771

at Ag-Cd, [78] and 3/A1Ag2 [491 plates, though the position with respect to the first transformation remained obscure for some time because of extensive conflicts among various sets of experimental results.[76,79-83] Inasmuch as AuCu II plates form in a single-phase region, the question of a composition change has not been raised with respect to this transformation. Recently, Enomoto and Fujita I84] have obtained the same type of result for proeutectoid a plates in Ti-Fe and Ti-V alloys. Particularly for a~ Cu- Zn and a~ Ag-Cd plates, wherein full agreement with the purely phenomenological requirements of the PTMC has been well established, ~4~,431 these results furnish critical support for the view that obedience to the PTMC is

a necessary, but not a sufficient, condition for identifi- cation of the transformation mechanism as shear. [1,721 Justifying these results in terms of the PTMC as indicative of shear in the sense of a "lattice site correspondence "[78'85] rather than an "atomic correspondence" not only destroys the mechanistic significance of composition differences during the early stages of growth but also eliminates the distinction between diffusional and shear mechanisms of growth. In view of the growing likelihood that all nucleated first-order phase transformations enjoy at least lattice site correspondences because of the prevalence of partially coherent interphase boundaries, this viewpoint ignores the fundamental differences in the atomic mechanisms through which these two growth processes take place.

In interstitial alloys, the situation is considerably more complicated. The possibility has been suggested that the substitutional atoms in such an alloy can rearrange by shear at rates controlled by the long-range diffusion of the interstitial solute toward or away from the advancing interphase boundary. TM Alternatively, transformation of both species may occur by shear, i.e., in the usual martensitic manner. However, subsequent diffusion of the excess solute out of the product phase and/or its precipitation as a component of the "second" eutectoid phase, such as a carbide, can quickly produce a radical change in the composition of a bainite plate, as Zener [86] clearly explained more than 40 years ago. Two fundamental is- sues must thus be considered: (1) are substitutional shear and interstitial diffusion compatible processes, and (2) what is the evidence for inheritance of excess solute during the growth of "surface relief bainite" plates? "Ex- cess" solute is defined here, in the context of Fe-C-base alloys, as carbon in ferrite in concentrations in excess of those allowed by the metastable equilibrium c~/(a + 30 phase boundary extrapolated to the transformation temperature.

The central problem with respect to compatibility is that of combining the biased random walk character of interstitial solute diffusion with the precisely organized and sequenced motion of substitutional atom transport by shear. Unless areas of the advancing interface being displaced by shear are limited to such small dimensions that only one interstitial atom is expected to be in contact with them, the compatibility problem seems unmanage- able. Maintenance of a driving force for the growth of ferrite requires extensive partitioning of carbon to austenite. Failure of some carbon atoms to jump synchronously with the coordinated displacement by shear of an a : ? boundary would introduce sharp local diminutions in driving force, which should hinder motion over large areas of a glissile boundary by introducing curvature capable of adding a sessile component to the interfacial dislocation structure. Particularly in transformations such as the formation of ferrite from austenite, in which a high concentration of carbon atoms in austenite is in equilibrium with ferrite at a : y boundaries (especially at low reaction temperatures[87]), this requirement would appear to restrict the mobile areas of such boundaries essentially to monatomic kinks. This may indeed be the situation at transformation dislocations, migrating by a double kink mechanism across the closely packed terraces of ledged interfaces, [88,89[ but not at the planar areas

1346--VOLUME 21A, JUNE 1990 METALLURGICAL TRANSACTIONS A

of the terraces, when these are being displaced en bloc by simultaneous glide of the array of glissilely oriented edge dislocations or of screw dislocations t751 (performing the lattice invariant deformation) in each terrace comprising a given boundary orientation.

As to the experimental evidence for excess solute in the ferritic component of bainite (FCB), nearly all of it cited in the unending published arguments on the subject is highly indirect and of the most limited v a l u e . 14'a3'74]

Similarity of orientation relationships between bainitic ferrite and carbides to those between tempered martensite and its precipitated carbides is of especially questionable importance for reasons derived from elementary nucleation theory. [9~ Dilatometric [9~1 and electrical resistivity t921 data are difficult to interpret unambiguously because of carbon concentration gradients in austenite, dislocation generation by plastic deformation attending transformation, and some uncertainty as to whether cementite, e carbide, or both are being precipitated. More direct methods have tended to show that the proportion of carbon remaining in the FCB is less than the detection limit of X-ray lattice parameter measurements, i .e. , approximately 0.1 wt pct C, [93'94'95] o r of electron probe X-ray microanalysis, approximately 0.03 wt pct C. [96] Field ion microscopy/atom probe (FIM/AP) studies have shown much higher carbon concentrations in the F E B . (97'98'991 However, the extreme localization of measurement which this technique allows and the nonuni- form distribution of the carbon atoms thereby revealed strongly suggests that Cottrell atmospheres about dislocations may be responsible for this result, I23,1~176 and thus that it cannot be taken as supporting a high initial supersaturation. 11001

On the other hand, X-ray measurements indicating that the FCB is sometimes tetragonal tl~176 have suggested carbon concentrations in the range of 0.1 to 0.1 5 wt pct. Zener I861 has shown that below a composition-dependent critical temperature, ferrite is made tetragonal by a high- velocity shear transformation which places carbon atoms in sites causing a distortion of the ferrite lattice parallel to a common tetragonal direction. Subsequent "leakage" of carbon into austenite through a: 3, boundaries or precipitation of carbides within ferrite or in both phases at a : T boundaries would cause such tetragonality to provide an underestimate of the carbon concentration in the ferrite. I221 On the other hand, c /a ratios greater than unity may have arisen from the formation of martensite above M~ (though, of course, below Ma) as a consequence of straining of the austenite by bainite formation, l~~ even though followed by partial autotempering.[741 Hence, this evidence for substantial supersaturation with respect to carbon of the FCB is presently indecisive. Attempts to demonstrate such supersaturation by means of the incomplete transformation phenomenon t~~ will be shown in Section I V - H - 2 to be invalidated by an incorrect analysis of this phenomenon.

A useful indirect approach to the problem is provided by measurements of the lengthening kinetics of ferrite and bainite plates. These are easily made quite accurately. Because the diffusivity of carbon in ferrite is roughly two orders of magnitude higher than that in austenite at the temperatures of interest here, ferrite cannot sustain significant supersaturation with respect to carbon

unless the kinetics of lengthening are much faster than those permitted by the diffusivity of carbon in austenite. Simonen et al. [~~ have made the most complete comparison between the measured lengthening rates of these plates and those calculated from the sophisticated Trivedi [~~ analysis by using Fe-C alloys and measuring not only lengthening kinetics but also the radii of curvature of the leading edges of ferrite and bainite plates over a wide reaction temperature range. They demonstrated that calculating instead of measuring these radii can introduce significant errors. Use of frequency histo- grams permitted conversion of measured apparent to true radii of curvature. They found that these plates invariably lengthen more slowly than permitted by carbon diffusion kinetics in austenite.

Bhadeshia[110] and Ali and Bhadeshia In 1] have recently reanalyzed published data on the lengthening of ferrite and bainite plates and reached the reverse conclusion. However, their manipulations of the Trivedi analysis and the necessary ancillary data are inappropriate, and even their plotted findings are inaccurately described. This conclusion was mainly reached by introducing the effects of arbitrary amounts of stored energy arising from the shear, supposedly accomplishing transformation of austenite to ferrite. ~Ssl However, no consideration was given to relaxation of this stored energy by glide and diffusional processes at the often quite high temperatures at which the growth kinetics measurements were made or by the growth processes producing tent-shaped and more complex surface reliefs. The possibility that some of these plates were actually needles was usefully introduced, but no calculations were reported for lengthening kinetics of needles in the absence of stored energy (though such results were reported for plates). When Bhadeshia's [11~ plots are reconsidered with these points in mind, it is clear that his calculated lengthening rates are either essentially the same as or slower than those permitted by the diffusion of carbon in austenite. Hence, growth kinetics evidence supports the view that there is no supersaturation of the FCB with respect to carbon.*

*It also seems worth noting that Bhadeshia tl12j has reported ferrite/ bainite plate lengthening measurements made in s i tu with photo- emission electron microscopy, in which kinetics three orders of magnitude faster than those permitted by carbon diffusion in austenite were recorded. The suggestion has been made 114] that these measurements may have been taken on plates of martensite formed above Ms in the manner described by Smith e t al . t~~ and more recently by Okamoto and Oka. Ij~s-~4j These studies should be repeated, but this time followed by TEM examination of some of the plates studied in order to ascertain (mainly from their internal structure) whether or not they were actually martensite.

One more effort to evaluate the carbon concentration in the FCB during growth should be noted. Published data on the average carbon concentration in retained austenite associated with partial transformation to bainite, evaluated by means of X-ray diffraction, were coupled with knowledge of the proportion of austenite retained as a function of carbon concentration in alloy steels. I741 The X-ray diffraction data of Pevzner et al. InSj used were obtained on Si and AI steels, wherein replacement of carbon rejection into austenite by carbide precipitation at a: 3, boundaries should be minimized. The average


carbon concentration of the retained austenite was first calculated on the assumption that there is no interfacial structure barrier to the thickening of ferrite or bainite plates. Comparison 'with the measured average carbon concentrations showed deviations which increased with decreasing reaction temperature (Figure 1). Ledged interphase boundaries were then simulated by introducing a uniform barrier to growth sufficient to reduce the carbon concentration in austenite in contact with a : y boundaries to the level where agreement was achieved between calculated and measured average carbon concentrations. Assuming no substitutional alloying element partition between austenite and ferrite and equating partial molar free energies of carbon in austenite and in ferrite in contact with the boundary, the carbon concentration in ferrite at the boundary was evaluated. As shown in Figure 2, this carbon concentration lies between the extrapolated a/(a + y) and the a/(a + Fe3C) phase boundaries. Hence, as might have been qualitatively anticipated, the barrier to growth at the broad faces of ferrite plates (Section Il l-A) reduces the carbon concentration in ferrite below the metastable equilibrium level it would have achieved in the absence of the growth barrier. While some carbide precipitation can still occur from ferrite, an even larger proportion of it than would be obtained at metastable equilibrium must have occurred from austenite. Of course, this result further supports a diffusional mechanism for the growth of the FCB.

Despite the conclusion so far reached about the lack of significant supersaturation of the FCB with respect to carbon, this important issue still cannot be regarded as entirely closed. Oblak and Hehemann tl~6] proposed that individual ferrite plates in bainite sheaves grow by shear for short distances at high velocities; prolonged "rest pe- riods" between shears yield the carbon diffusion-controlled

.14

o It.

0 :E

{:n o

.12 - t 1 1 t ' ' - " ~:~ i I " ~ i t

"~ . I 0 - - i . . - I " 1 1 t~ / / / 0.40 %C, 108%AI

8 ,08 ':' o.3c*,'. ~

0 4 - -

.02 - -

I I I q ,00 4 0 0 300 200

Reaction Temperature, ~

Fig. 1 - Average mole fraction of carbon in retained austenite as a function of reaction temperature as calculated (dashed curves) and as determined experimentally by Pevzner et al. tHS~ (solid curves) in two alloy steels. 1741

c

3 g 16 4

m

N

id~ / I I I 500 400 300 2 O0

Reoction Temperature, ~

Fig. 2 - - C o m p a r i s o n of the calculated initial carbon concentration of the ferritic component "in bainite" for an Fe-C-Si alloy with the a/(c~ + Fe3C) and the extrapolated a / ( a + y) phase boundaries, t741

growth kinetics reported in the literature. Thermionic electron emission microscopy (THEEM) measurements of the growth kinetics of individual plates within bainite sheaves do not support this mechanism, t741 However, the argument can still be made that the length of the individual shears is less than the approximately 0.1 btm resolution limit of this technique. The question thus arises as to the length of time a ferrite plate will remain supersaturated upon the cessation of shear. Assuming full inheritance of the carbon concentration of the parent austenite, Fe-2 at. pct C (0.44 wt pct C), and a temperature-independent plate thickness of 0 .6 /xm (measured from Oblak-Hehemann micrographs ill6]), decarburization time was found to increase from milli- seconds above 500 ~ to 50 seconds at 200 ~ by means of a published [~ 17] analysis.f z2]* These results suggest that

*Bhadeshia p6j has recently incorrectly rederived this analysis. However, the two equations for decarburization time yield nearly the same numerical results.

a definitive experiment on the initial carbon concentration in the FCB might be performed in a higher carbon alloy whose Ms (and preferably also Md) lies below 200 ~ and to which a sufficient Si concentration has been added to delay adequately the onset of carbide precipitation in association with ferrite.

2. Absence of a change in LRO during growth This criterion is usually meaningful only in substitu-

tional alloys. Three of the four model substitutional transformations permit application of this criterion. Whereas AuCu II plates form in a disordered matrix, the


AuCu II structure is actually a super-superlattice, re- quiting 10 fcc unit cells to complete the basic "building block. "1urn Hence, this is a clear violation of this cri- teflon for the operation of a martensitic transformation mechanism.15,47,48,7~ Bowles and Wayman[119] have counterproposed that growth of these plates takes place by the glide of transformation dislocations at rates controlled "by the rate of ordering at the dislocation steps." However, this mechanism yields only "lattice site correspondence" rather than "atomic correspondence" across the order: disorder boundaries. Hence, this transformation cannot proceed by shear at the atomic level. Con- versely, disordered a l Ag-Cd plates form in an ordered f12 matrix.179] oq Cu-Zn-A1 plates appear to inherit both first and second nearest-neighbor ordering from their/32 Cu-Zn-A1 matrix. B2~ However, the finding that al Cu- Zn (and doubtless also Cu-Zn-A1 uEH) plates differ continuously in composition from their/32 matrix means that a I plate growth is paced by long-range volume interdiffusion of Cu, Zn, and Al atoms. This process necessarily subsumes the short-range volume interdiffusion required to accomplish long-range ordering. Hence, the claim that LRO is inherited from the/32 matr ixu2~ appears physically unacceptable. Instead, the preexisting ordered domains in the/32 matrix must be presumed to serve as "templates" upon which a~ plates develop their ordered structure. Ordering of epitaxial layers of semi- conducting phases controlled in this manner by their sub- strates has been recently recognized. I122,123J241

3. Interphase boundary structure capable of supporting growth by shear Of the six model transformations being considered,

TEM studies of the interphase boundary structure of plate broad faces have been conducted on only two of the reactions in substitutional systems, a~ Cu-Zn B25~ and 31 A1Ag2, I731 but on both of the transformations in the two interstitial systems, a Fe-C-X~ B26-129~ and /3 VH045. tSu Considering first the results reported on Cu-Zn alloys, the initial transformation product was found to be fully coherent plates, up to 500-nm long, and containing none of the closely spaced (approximately 2 nm) stacking faults which trace the path of the lattice invariant deformation in at[ martensite in the same alloys. B3~ The absence of both interfacial dislocations and internal inhomogene- ities in these plates demonstrates that a mechanism was not available for their formation by shear. Therefore, growth ledges which could not be resolved with the TEM instrument employed must have been responsible for the diffusional growth of these plates.

Except at the present resolution limit of TEM, the appearance, after quenching to room temperature, of hcp 31 AIAg2 plates growing into fcc a A1-Ag I731 is indistinguishable from the fcc ---> hcp martensitic transformation in Co-Ni a l l o y s . U32,1331 Ledges bounded by Shockley partials sweep across alternate {111} planes in the matrix phase to accomplish this transformation. When 3' A1Ag2 formation is observed in situ, on the other hand, significant differences are readily apparent: (1) the upper limiting lateral migration rate of ledges is determined by the long-range volume interdiffusion of AI and Ag atoms; B341 and (2) the migration rate of an individual ledge at a given temperature and alloy composition varies with its

orientation, suggesting that the atomic mechanism of migration is the formation and lateral movement of kinks along the risers of the Shockley partial ledges. I72A341 Howe I1351 and Prabhu and H o w e [136,1371 have observed superkinks with hot-stage TEM and have evaluated various mechanisms for kink formation. During the martensitic version of the fcc --~ hcp transformation, glide (at the atomic level) of Shockley partials accomplishes the transformation. While kink formation and lateral propagation may again be required, both processes can be accomplished in this context with little or no thermal activation and must take place in a much more strictly organized and "military "I751 manner than during diffusional growth.

The broad faces of proeutectoid ferrite plates in an Fe- C-Si alloy (which were converted into upper bainite after slightly longer reaction times by carbide precipitation at their broad faces) have been shown to have an interracial structure of the type schematically illustrated in Figure 3(a): (immobile) structural ledges and one set of parallel misfit dislocations in the terraces of these ledges whose orientation ranged from pure edge to mixed edge and screw (but never pure screw). I126,x381 Hence, this

M~SFIT D SLOCATLON ~ / DIRECTION b O T ] ~

_2 0 DIRECTION [01T]'~, [(30]]0 a: STRUCTURAL LEDGE HEIGHT ~

b: STRUCTURAL LEDGE SPACING ~ TAN-' (a/b)

(a)

(b)

Fig. 3 - - (a) Isometric sketch of an fcc : bcc interface in the presence of a Nishiyama-Wassermann orientation relationship, showing structural ledges, the most coherent areas on the terraces of these ledges, and misfit dislocations, u~sl (b) Schematic of the shared growth ledge mechanism of Hackney and Shiflet t~66j for the edgewise growth of pearlite, u661


interfacial structure cannot be displaced by either shear or diffusional mechanisms. High and widely spaced growth superledges account for the observed growth kinetics of these interfaces, c551 Some objections raised to the interpretation of these structures [23,35,37,391 have been answered in detail. 134,36,381 The principal source of these concerns was the failure to recognize that structural ledges replace one set of misfit dislocations. I1391 Such replacement has also been observed during a current study of partially coherent bcc:hcp interfaces in a hypoeutectoid Ti-Cr alloy, tl4~

Purdy and co-workers [127A28A291 have extended these studies to lower temperatures in other alloys. They, too, observed misfit dislocations on the broad faces of ferrite plates, now formed well within the upper bainite region of their alloys (and perhaps even in the lower bainite range). These dislocations were found to have a predominantly edge character and were concluded to prevent interface displacement by shear. They also observed a fine set of ledges with approximately the same height and interledge spacing as the structural ledges previously reported.t~ 26]

A quite different interfacial structure was found on the broad faces of/3 VH0.45 plates, rSu A single array of parallel dislocations was shown to lie in glissile orientation, agreeing in all respects with expectation from the PTMC. Inasmuch as all other aspects of these plates fulfill the requirements of the PTMC, it appears that these plates must thicken by diffusion-limited shear. Bourret et al. [14~] have recently made in situ high-resolution TEM observations on the thickening of 3, Til l plates by means of the ledge mechanism. It is not yet known, however, whether the interfacial structure and crystallography of these plates conform to the specifications of the PTMC. However, this important observation lends weight to an earlier suggestion [~42] that the growth of/3 VH045 plates be similarly examined.

D. Evaluation of the Surface Relief Definition of Bainite

As emphasized in the Introduction, surface relief bainite is a transformation product formed by the glidelike movement of individual atoms in a highly cooperative manner. The only readily apparent fundamental difference between martensite and surface relief bainite is that the latter may be paced by diffusional processes in the matrix being consumed. Inasmuch as microscopy is not yet sufficiently developed to permit these atomic mo- tions to be observed directly, however, indirect evidence must be utilized in order to identify surface relief bainite. Because of the essentially martensitic character of surface relief bainite, the evidence used has inevitably been largely the same as that employed to identify martensite.

In an influential article on "The Martensite Transformation" published in the 1948 ASM Handbook, Greninger and Troiano t~a3j emphasized the kinetic aspects of martensite formation as its most prominent feature. Very fast growth rates of individual plates, the anisothermal nature of the transformation, and its insup- pressibility during quenching were particularly noted. However, publication of the PTMC five and six years later, f4~ coupled with the extension of experimental

studies to a much wider range of alloys than carbon- containing steels, soon led to replacement of this char- acterization by one emphasizing the IPS relief effects formed when a martensite plate develops in contact with a free surface. U44A451 This view, in turn, soon expanded into one requiring obedience to the habit plane, orientation relationship, and other features of the PTMC. That agreement with the theory was often unsatisfactory, as recounted in Section I I -A from a review of martensitic transformations in Fe-base alloys by Wayman, r711 has not discouraged general adoption of this viewpoint. Unfor- tunately, reports that at least some portions of the PTMC are applicable to phase transformations evidently involving diffusion, which began to appear soon after the PTMC was published I146A47A481 and continue to flow to the present day, t12~ did not immediately prompt deeper inquiry into the factors which might underlie such commonality between these two very different modes of transformation. Instead, a growing effort has been devoted to prov- ing that diffusional transformations to which the PTMC appears applicable actually do take place by a shear process! We hope that the evidence marshaled in the present and in a related [2zl review has demonstrated the failure of such efforts.

It now seems clear that the development of an IPS surface relief and agreement with the formal crystallographic dicta of the PTMC should no longer be accepted as complete proof that a phase transformation actually does take place by shear. Instead, we would urge that requirements which might have been previously regarded as derivative should now be put forward as the primary criteria for the operation of a shear mechanism at the atomic level. Quite definitely in substitutional alloys, but still somewhat tentatively in interstitial alloys, these include the absence of a composition change and, where applicable, the inheritance of the state of LRO characterizing the matrix phase. But more importantly, now that TEM is able to resolve columns of a t o m s - - and hopefully, some day soon, even individual atoms in these co lumns- - the most essential criterion for shear, short of actually watching how atoms jump across an advancing interphase boundary, is that the interphase boundary structure (and the internal inhomogeneity within the product phase) be capable of supporting a shear mechanism of growth.

As we have attempted to demonstrate up to this point, when these criteria are applied, successful distinction between shear and diffusional mechanisms of growth readily follows. Hence, it now appears much more strongly than it did 20 years ago [lj that the surface relief definition of bainite should be discarded as a non sequitur.

III. THE GENERALIZED M I C R O S T R U C T U R A L

DEFINITION OF BAINITE

This section will begin with a summary of atomic mechanisms of diffusional growth and how they may be connected to the PTMC without involving shear. The bainite reaction will then be considered as a competitive (rather than as a cooperative) mechanism of eutectoid decomposition, and on this basis, the wide variations


possible in the internal morphology of bainite will be deduced. The many variations found in the external morphology of microstructurally defined bainite are described and discussed in the following section. Then the growth kinetics of both the fundamental and the derivative external morphologies of bainite will be examined.

A. Atomic Mechanism of Ledgewise Diffusional Growth and Its Connection to the PTMC

The material of this section is intended to review the basic diffusional transformation mechanism underlying the greater complexities of the generalized microstructural definition of bainite. This mechanism is an alternative to the shear mechanisms of the preceding section. At the same time, this mechanism provides a framework through which the previously recounted successes of the PTMC in rationalizing important aspects of diffusional transformations can be explained. Inasmuch as this topic is currently discussed in considerable detail by some of us, t221 this section is presented in condensed form, with the reader being referred to our more extensive review for further details and discussion.

Particularly at relatively small undercoolings, minimization of interfacial energy is the dominant factor determining the work required to form a critical nucleus, AF*, and, thus, the rate of diffusional nucleation. Hence, critical nuclei of one crystalline phase forming within another will be as coherent as possible with their matrix phase. I1491 On both thermodynamic 172,~5~ and kinetic grounds, acquisition of even a single misfit dislocation loop by critical nuclei now appears to be quite unlikely. II491 As critical nuclei pass into the growth stage, however, interracial energy per se rapidly becomes less important. Whereas the shape of the critical nucleus is largely determined by interracial energy minimization, growth kinetics are soon determined by the orientation dependence of interphase boundary mobility. I721 It is be- coming increasingly clear that full or partial coherency can be established at a sufficient number of boundary orientations, at least for the pairs of crystal structure most common among metallic alloys, to enclose precipitate crystals completely, t~5~l As long as the stacking sequence of the planes in the two phases parallel to such boundaries is different, these boundaries are wholly immobile during diffusional growth in the direction normal to themselves, even at very high driving forces, because such mobility would require emplacement of substitutional atoms in sites which are (initially) interstitial in character. I721 Displacement of such boundaries can only be accomplished by means of the ledge mechanism. I72'~521 ff the risers of ledges are not disordered, kinks must be established upon them in order to provide at least local areas with sufficient atomic disorder to make transfer of atoms across the interphase boundary energetically feasible, f721 Thus, the boundary orientation dependence of growth kinetics is translated mechanistically into a dependence upon boundary orientation of the interledge spacing and probably of the interkink spacing as well. Because there are many different mechanisms for the formation of ledges, I72'1531 and evidently also of k i n k s , 172'134-1371 and little progress has been made so far in placing these mechanisms on a realistically quantita-

tive basis, well-grounded prediction of the boundary orientation dependencies of diffusional growth kinetics is not yet feasible. However, the following proposal t221 should provide a basis for predicting the boundary orientation dependence of interledge spacing when ledges are formed solely by sympathetic nucleation.

This approach is based upon the invariant line (IL) concept, taken from the PTMC by Dahmen and co- workers t154-1571 and used by them and by Luo and Weatherly I~58,159j with much success in predicting the habit direction of precipitate needles, the habit plane of precipitate plates, and the orientation relationship of these crystals with their matrix phase. The IL is the direction of zero misfit between the two lattices forming an interphase boundary, tg4,251 Usually, this direction is irrational. Hence, the interface through which the IL passes is com- posed, at the atomic level, of a terrace and riser structure, with the terraces being fully coherent3 24,25j Now, for reasons of simplicity and tractability, assume that the critical nuclei of sympathetically nucleated ledges are circular discs, I~6~ one of whose broad faces is coplanar with a terrace at an IL interface. That the interfacial energy of the broad faces of the discs is low is of no direct consequence, since the energy of the newly formed broad face of each disc is, in effect, supplied by elimination of the same area of interphase boundary by the coplanar broad face. However, it has long been recognized that the energy of the interphase boundaries orthogonal to a minimum energy boundary tends to be high; Ij621 here, these boundaries are taken to have the same energy, o iv , and to form the edge or rim of the disc-shaped nuclei. Particularly at relatively low undercoolings, nucleation kinetics are predominantly determined by AF*, the work required to form critical nuclei. For the present geometry of sympathetic nucleation,

AF* = 4"tr(trev)Zor~a

(AFv + W ) 2

where AFv = volume free energy change driving nucleation; W = volume strain energy associated with nucleation; o-~ = interfacial energy of the small-angle boundary, usually present during sympathetic nucleation, f~6~ between a terrace and a broad face of a disc- shaped nucleus; and the precipitate and matrix phases are designated a and 7, respectively. Since the rate of nucleation is proportional to exp ( - A F * / k T ) , where k = Boltzman~'s constant and T = absolute temperature, and AF* is itself seen to be proportional to the second power of o'iv, it is clear that the rate of sympathetic nucleation of ledges on IL terraces should be very low. Assuming that the same critical nucleus geometry is obtained at the tip of a needle- or rod-shaped precipitate or at the edges of a plate, the much smaller average value of ~rev then expected should cause a high nucleation rate of ledges.

It is thus suggested that the IL defines a direction or, when taken in conjunction with another minimization criterion, ~1581 assists in defining a plane at which the kinetics of ledge formation, and therefore the rate of growth in the normal direction, have minimum values, t221 The boundary orientations at which intermediate ledge nucleation kinetics are obtained also ought to be identified in this manner. Although complete analysis of the


boundary orientation dependence of interledge spacing obviously requires that all mechanisms of ledge formation operative during a given transformation be considered (not all of which may be hindered when the interface contains the IL), the present, sympathetic nucleation-based approach evidently does permit the kinetics of diffusional growth to be linked in a number of situations to the PTMC without postulating that growth takes place by shear.

The broad faces of precipitate plates, as well as of martensite plates, thus contain the IL of a transformation. For martensite plates, the IL lies at the intersection of the Burgers vector of the lattice invariant deformation dislocations and the plate broad faces. Except in fcc/hcp and fcc/dhcp transformations, where no lattice invariant deformation is required, this Burgers vector must form a nonzero angle with the broad faces if growth is to occur by the shear mechanism. Under this circumstance, these dislocations also inefficiently compensate misfit, t221 When this angle is zero, as at the broad faces of ferrite plates, t~261 shear is not possible. The dislocations which would otherwise have produced the lattice invariant deformation are then wholly devoted to the efficient compen- sation of misfit in the direction orthogonal to the IL. However, transformation dislocations, in the form of partials which do not disrupt lattice continuity, are also required at shear-capable interfaces. I88,89~ At interfaces displaced diffusionally, on the other hand, interruptions of lattice plane continuity sufficient to produce at least atomic-scale regions of disorder are needed at kinks on the risers of growth ledges (which are usually superledges) in order to make diffusional jumps across partially coherent boundaries kinetically feasible. The extent to which these crucial differences in interfacial structure influence the habit plane, orientation relationship, and shape deformation of martensite and of precipitate plates now requires careful theoretical and experimental investigation.

B. The Bainite Reaction Viewed as the Product of the Competitive Ledgewise Growth of Two Phases Formed by Eutectoid Decomposition and the "Internal Morphology" of Bainite

In microstructures developed during the decomposition of austenite at intermediate reaction temperatures, bainite was first described as a nonlamellar dispersion of carbides among Widmanst~itten ferrite plates3 7,8j Suffi- cient reduction of the austenite grain size, however, was later shown to result in replacement of the Widmans~tten morphology for the ferritic component of bainite by that of grain boundary allotriomorphs, t~ It was also recognized that in some nonferrous eutectoid systems, the counterpart phases to ferrite do not always appear in a plate or needle morphology, t~,163~ Hence, the microstructural definition of bainite implicit in the pioneering research in this field t7'81 was generalized so as to omit the specification that the predominant phase during the bainitic eutectoid decomposition process has a Widmanst~itten morphology, t~l Defining bainite as simply the product of a nonlamellar, noncooperative t~64~ mode of eutectoid de-

composition accomplishes this generalization and at the same time distinguishes between bainite and pearlite, rLl Pearlite, the morphologically more familiar product of eutectoid decomposition, is, conversely, the product of a lamellar, cooperative 1~64j mode of eutectoid decomposition.

Upon the basis of careful optical metallographic doc- umentation, Hillert t~651 explained pearlite formation as a gradual evolutionary process during which the two phases produced during eutectoid decomposition "learn" how to grow together in diffusionally cooperative fashion. This learning process was seen to be made possible by the predominantly disordered or incoherent boundaries of the participating crystals, particularly those of the proeutectoid phase initiating eutectoid decomposition, t1651 Con- versely, when the proeutectoid phase has mainly partially or fully coherent interfaces, development of cooperation was considered to be prevented; the noncooperative eutectoid structure of bainite evolves instead, r~651

Recent experimental discoveries, however, have dis- closed serious flaws and gaps in this most attractive picture. As both the resolution attainable with TEM and the techniques of employing electron microscopy have improved, interfaces which had previously been regarded as disordered are increasingly being found to have a ledged or a ledge-and-misfit dislocation structure, demonstrat- ing that they are actually partially coherent. Hackney and Shiflet In661 have demonstrated that pearlite formed in an Fe-0.81 pct C-12.3 pct Mn alloy grows edgewise by means of growth ledges shared between the ferrite and cementite phases, as sketched in Figure 3(b). Lee and Aaronson In671 subsequently found that while the a and the TiFe phases comprising the bainite formed during eutectoid decomposition of/3 Ti-Fe are partially coherent with respect to both their/3 matrix and each other, the ledge systems through which each of the eutectoid phases grows are physically (though not diffusionally) independent of one another. Although full resolution of the interfacial structure of pearlite may not yet have been achieved, the observation of growth ledges on the edges of pearlite colonies makes virtually certain the deduction that all interphase boundaries involved in pearlite formation are also at least partially coherent.

In response to these laboratory findings, the growth kinetics of both bainite and pearlite have been reconsidered. t1681 The basis for this reconsideration was provided by a linearized gradient analysis Hillert I1691 has written for the edgewise growth of pearlite. Two small but important changes were made in Hillert's analysis: (1) growth of both eutectoid phases (termed a and/3, with the matrix denoted as T, for purposes of generalization) was taken to occur by means of the ledge mechanism, and (2) growth rates of a and /3, G~ and G~, respectively, were first derived semi-independently and then matched against each other. In the simpler situation, obtained when proportions of a and/3 formed are immediately in their equilibrium ratio, the obvious condition for the development of pearlite, namely, that G~ = G~, can now be met only when

ha ht~

A~ At~

1 3 5 2 1 V O L U M E 21A, JUNE 1990 METALLURGICAL TRANSACTIONS A

where the A's represent the average interledge spacings and the h's denote the average ledge heights. Thus, when

ha h e # A~ A s

G, # Gt3; this situation describes the formation of bainite. The inequality of the two growth rates leads almost inevitably to crystals of the faster growing phase (arbi- trarily designated as c~) surrounding those of the slower growing phase, /3, and terminating their access to the 3, matrix. Hence, supersaturation of the y phase in contact with a: y boundaries develops with respect to the nucleation of /3 which, together with the availability of a : T interfacial energy and motionless terraces of ledges on the t~:3~ boundaries, provides encouragement for the (re-)nucleation of eutectoid/3 at these boundaries.

Whereas the G, = Gt3 condition ensures that pearlites formed in different eutectoid systems will closely resemble each other, as may be readily verified by examination of published photomicrographs of pearlite, [~63A7~ it now becomes clear that two essentially independent vari- ables, G,/G~ and , :~J~, the renucleation rate o f /3 at a: y boundaries, are involved in determining the "internal morphology" of bainite structures. Qualitatively varying G,/G~ from unity to a very high value and also letting ,:~J~ range from zero to a very large number, results in the wide range of bainitic microstructures, schematically illustrated in Figures 4(a) and (b), for the situation in which the maximum volume fraction of /3 permitted to form by the Lever Rule is low and ap- proaches one-half, respectively, t168~

The diversity of microstructures legitimately classifi- able as bainitic is now seen to be exceedingly large. This is almost certainly one of the more important reasons why "the bainite reaction . . . has been hard pressed, almost from the beginning, to establish and retain a definite identity. "t~l (Obviously, being "last born" among the major modes of austenite decomposition has also not helped in this regard.t~J) A second important result is that "intermediate" values of G,/G~ produce microstructures which, while resembling pearlite, are most certainly not pearlite. Although/3 crystals are able to keep up with the growth of their a neighbors for longer times in this situation, thus leading to shapes elongated in the growth direction of the "r:bainite interface, they are nonetheless inevitably cut off repeatedly from access to ~/and must be renucleated if eutectoid decomposition is to continue. Hence, these microstructures need no longer be termed "semi-pearlite" or "degenerate pearlite "[~651 but can be regarded as simply another variant in the internal morphology of bainite. Although it remains possible for pearlite to be formed by G~ = G~ through fulfilling the h~/h~ = h~/)t~ condition in the absence of shared growth ledges, such eutectoid microstructures should be quite rare. While finding other eutectoid systems in which examination of the interfacial structure at the edges of pearlite colonies is feasible has proved to be a difficult task. Shiflet et al. f~7~l have recently succeeded in doing so in a eutectoid Ti-Fe alloy. They found that shared growth ledges are again present. Through an ingenious application of interphase boundary carbide precipitation, Zhou and

(a)

(b)

Fig. 4 - - ( a ) Variation of the eutectoid microstructure with G~/G~ and ~:vJ~ when the volume fraction of the slower growing phase, /3, is small. (b) Variation of the eutectoid microstructure with G~/Go and , , : , J J when the volume fraction of the slower growing phase, /3, is relatively large. 06sj

Shiflet t~721 were also able to secure good indirect evidence for the operation of the shared growth ledge mechanism during the pearlite reaction in an Fe-0.5 pct C-0.5 pct V alloy. If such l edges - -whose origin is not yet under- s tood- - tu rn out to be a general feature of the edgewise growth of pearlite, then a nearly perfect distinction will have been made between pearlite and all other eutectoid microstructures, with the "all other" now being entirely encompassed by the term "bainite," except in the (hopefully) rare situation in which G~ = G~ in the absence of shared growth ledges.

A few additional comments on Figures 4(a) and (b) are now required. When the proportion of a is low (i.e., Figure 4(a)) and G,/G~ is "high" (i.e., the right-hand side of Figure 4(a)), as ,:~J~ increases, the schematics presented resemble the internal morphology of bainite formed at successively lower reaction temperatures in s t e e l 14'61 and in hypoeutectoid T i - X I173A741 alloys. When both GJG~ and the fraction of /3 formable are high


(Figure 4(b)), the bainitic structures sketched resemble those in eutectoid y Fe-N reacted just below the eutectoid temperature t~75j (high ~:yJ~) and the "divorced eutectoid structure" sometimes found at high temperatures in Si-containing hypereutectoid steels (low ~:yj~).[165]

As should now be reemphasized, the bainite start temperature on the generalized microstructural definition is, in principle, the eutectoid temperature.t~J Whether or not this is the microstructural Bs temperature actually operative in a given alloy depends especially upon the kinetic competition encountered from the pearlitic mode of eutectoid decomposition. Since the solute diffusion distance is both short and constant during the edgewise growth of pearlite and no renucleation of either euctec- toid phase is required, pearlite would always be expected to grow faster than bainite and thus markedly restrict the proportion of the microstructure which can be transformed to bainite. As has been repeatedly recognized, t17~ however, pearlite nucleation does not always occur readily. Perhaps this may one day be seen to be associated with kinetic problems involved in bringing the shared growth ledge mechanism into operation. Simi- larly, it is not at all obvious why pearlite in steel (say) should be replaced by (microstructurally defined) bainite at lower temperatures. Again, for the present, one can only speculate that for reasons as yet unknown, the shared growth ledge mechanism can no longer operate below a certain level of undercooling or reaction temperature.

C. External Morphology of Bainite

1. Nodules, the fundamental external morphology of bainite Ever since bainite was first recognized, its micro-

structure has been strongly associated with that of Widmanst~itten ferrite or the plate morphology of the equivalent phase in other eutectoid systems. However, observation of roughly equiaxed bainite nodules, first in hypoeutectoid ~731 and later in hypereutectoid ~176'~771 (Figure 5) Ti-Cr alloys, has led to reconsideration of the problem, t1681 The proposal has been advanced that such nodules are the "true" or "fundamental" external morphology of bainite structures. I~68~ This concept derives

Fig. 5 - -Approx ima te ly spherical nodules of bainite nucleated at intragranular proeutectoid TiCr2 plates in a Ti-25 wt pct Cr alloy reacted 18,000 s at 685 ~

from the observation that all but one of the other bainite morphologies to be discussed in Section III-C, includ- ing upper bainite, lower bainite, inverse bainite, and allotriomorphic bainite, reflect primarily the morphology of their "substrate" crystal of the proeutectoid phase. The one exception, columnar bainite, will be seen to be a nonfundamental modification of the nodular morphology.

Nodular bainite has been observed in eutectoid and hypereutectoid steels during early stages of reaction in F e - C [178'179] and Fe-C-Mn t~Tj alloys and in the vicinity of the bay in the TTT diagram in other alloy steels, tls~ Nodular bainite was also found to decompose the last remaining volumes of untransformed austenite just above and just below the bay region in hypoeutectoid Fe-C-Mo alloys, where its ultimate morphology becomes that of these austenite regions, tl8~ The paper by Spanos et al. t~Tj on bainite morphology in Fe-C-2 pct Mn alloys in this issue contains a number of illustrations of nodular bainite. The similarity of the external morphologies of nodular bainite and of pearlite formed at low temperatures and the relatively fine scale on which carbides are dis- tributed in both microstructures explain why the two "internal morphologies" are sometimes confused, as appears to have happened during a recent study in a near-eutectoid Fe-C-Mn alloy. I181j

There appear to be at least three principal requirements for the development of bainite as nodules rather than with some other external morphology, t~68~ One is that large contiguous volumes of untransformed matrix be available. (Thus, thin sheets of untransformed matrix between closely spaced parallel sideplates are obviously unsuitable for this purpose.) Again taking a to be the faster growing eutectoid phase and now the proeutectoid phase as well, the second requirement is that the growth rate of eutectoid a must be higher than that of proeutectoid a. This situation is expected to be realized, because eutectoid a has a higher driving force propelling its growth, as may be seen from a free energy-composition diagram construction and as has been calculated in the case of Fe-C alloys, tlTj The third requirement is the more frequent nucleation of /3 crystals at eutectoid a: y than at proeutectoid a: y boundaries. Meeting this requirement is facilitated by the higher driving force for/3 nucleation at eutectoid a : y boundaries. Under this circumstance, growth of the composite eutectoid a + eutectoid /3 structure becomes approximately isotropic, thereby producing the nodular morphology. More rapid nucleation of the slower growing eutectoid phase (TiCr2) at eutectoid a interfaces has been observed with particular clarity in a hypoeutectoid Ti-Cr alloy t173~ (Figure 6(b)).

During optical metallographic studies of eutectoid a in hypoeutectoid Ti-Cr alloys, t~73J it was not possible to decide whether eutectoid a was formed merely by further growth of proeutectoid a (following Hultgren t~821) as the result of the local increase in supersaturation caused by precipitation of TiCr2 at eutectoid a:/3 boundaries (where/3 is the matrix phase) or by svmpathetic nucleation at proeutectoid a:/3 interfaces. A subsequent TEM study of eutectoid decomposition in several Ti-X systems led to the conclusion that sympathetic nucleation is a particularly important contributor to eutectoid a formation in upper bainite-like structures. It671 This conclusion was


(a)

(b)

Fig. 6 - -T i -10 .94 wt pct Cr, solution annealed 2400 s at 1000 ~ (a) Reacted 12 h at 650 ~ showing TiCr~ preferentially nucleated at grain boundary allotriomorphs; (b) reacted 2 days at 650 ~ illustrat- ing preferential nucleation of TiCr2 at eutectoid a:fl interfaces, t~731 Magnification 1000 times.

based upon repeated observations of a small-angle boundary between proeutectoid a and eutectoid a. As previously noted, such a boundary is now recognized [16~ as an important "signature" of sympathetic nucleation.

2. "Derivative" external morphologies of bainite a. Upper bainite When G~/G~ is high and the maximum volume frac-

tion of the slower growing (/3) phase is comparatively low, it is quite difficult, unless ~:vJ~ is high, for eutectoid/3 to play a significant role in determining the external morphology of the eutectoid a + eutectoid /3 aggregate structure. Further, since sympathetic nucleation occurs most readily when the orientations of the new and substrate crystals are nearly identical, [59,16~ even when the faster growing eutectoid a is formed sympathetically rather than by continued growth, it will nonetheless tend mainly to enlarge the preexisting proeutectoid a crystals without markedly changing their morphology. It is for this reason that the transition from Widmanstatten ferrite to microstructurally defined bainite occurs in essentially continuous fashion. IIs3,184~ Small carbides increasingly appear among sideplates and then among intragranular plates as the isothermal reaction temperature is decreased. Within a given colony of parallel sideplates, some may still be ferrite, while others, in association with which carbides have formed, have

now become microstructurally defined bainite. With further decreases in reaction temperature, ferrite plates tend to be grouped increasingly in "sheaves," whether formed intragranularly or as sideplates. [4,75,183,1851 The sheaf structure is the result of face-to-face sympathetic nucleation of ferrite plates, I1831 again the energetically least costly orientation for such nucleation. Both the individual ferrite plates and the sheaves of parallel ferrite plates are known as upper bainite when they contain a nonlamellar dispersion of carbides (usually, though not always, formed at a : y boundariestl,lS5-1871).

b. Lower bainite With further decreases in reaction temperature, an-

other grouping of ferrite plates appears in steel. In 1939, Mehl I~88J gave this structure the name "lower bainite" in order to distinguish it from the sheaves of parallel plates characterizing the microstructure formed at higher temperatures, which he termed "upper bainite." Lower bainite is now most frequently described as the product of a shear transformation occurring at sufficiently high velocities so that carbides precipitate within the ferrite rather than at a : y boundaries. This mechanism is at variance with all data on measured (though not calculated) growth kinetics of lower bainite, as will be discussed in Section I l l -D-1 . This mechanism is also inconsistent with strong evidence for the predominance of a single crystallographic variant of carbides in association with lower bainite.tt89j An isolated observation t19~ of multiple variants has been used to support the occurrence of carbide precipitation from within the supersaturated ferritic component of lower bainite, but this evidence now seems to have been abandoned, t241 In this issue of Metallurgical Transactions, Spanos et al. [181 propose a simple diffusional-nucleation-and-growth mechanism for the formation of lower bainite. When the driving force for ferrite nucleation is sufficiently high, ferrite plates can nucleate edge-to-face at the broad faces of those previously formed, even though the recovery of interfacial energy from this nucleation geometry is less than that during face-to-face sympathetic nucleation.t16~ How- ever, a single variant of a number of crystallographically equivalent habit planes should be nucleated edge-to-face at a given broad face of a substrate plate, again on simple geometric grounds.j16~ Hence, a colony of parallel sideplates develops against a broad face of a substrate plate. Carbide precipitation can then occur at the broad faces of these sideplates when their growth slows down as they approach impingement with their neighbors, now exactly as in the case of upper bainite. Further growth and/or face-to-face sympathetic nucleation of ferrite then completes decomposition of the austenite remaining trapped between adjacent sideplates. This sequence is illustrated in Figure 7 of Reference 1 8. Note that on this mechanism, carbide precipitation plays, at most, a minor role in establishing the external morphology of lower bainite microstrnctures.

c. Inverse bainite In hypereutectoid steels, another proeutectoid phase-

based derivative bainite morphology, first recognized by Hillert, ~164~ appears as a relatively minor, but nonetheless quite noticeable, feature of the microstructure. Hillert I164,1651 termed this eutectoid structure "inverse


bainite." An isolated plate (or perhaps even a sheaf of parallel plates) of proeutectoid cementite forms first. Ferrite then nucleates at the austenite:cementite interfaces and rapidly envelops the "substrate" cementite plate(s), occupying with especial rapidity the adjacent volume of austenite whose carbon concentration has been diminished by growth of the cementite structure. Fi- nally, a conventional upper bainite-like ferrite + carbide aggregate develops at the a : 7 boundaries, presumably through continued growth of the ferrite envelope and/or sympathetic nucleation of new ferrite crystals against the envelope alternating with nonlamellar, noncooperative carbide formation. Although a detailed TEM study is still needed in order to delineate the details of the mechanism through which inverse bainite develops, it is already clear that the external morphology is essentially an enlarge- ment of the substrate cementite plate(s).

d. Grain boundary allotriomorphic bainite Even in specimens austenitized for time/temperature

combinations sufficient to yield a coarse austenite grain size (the order of ASTM No. 1 or larger), grain boundary ferrite allotriomorphs provide a small but nonetheless detectable component of the microstructure in the proeutectoid ferrite region and also at higher temperatures in the (microstructurally defined) bainite region in lower carbon steels, t1831 However, when the carbon concentration exceeds 0.3 to 0.4 wt pct and elements, such as Mo and Cr, which preferentially hinder pearlite formation ~176 are largely or entirely absent, the pearlite reaction increasingly tends to obscure allotriomorph formation at lower temperatures in the proeutectoid ferrite region and at higher temperatures in the upper bainite region. At still lower temperatures, allotriomorphs seem to disappear and be replaced by sideplates growing directly from the austenite grain boundaries, though this subject has yet to be researched with sufficient thor- oughness in an alloy whose reaction kinetics are slow enough so that isothermality of transformation can be assured at all temperatures investigated. In the paper by Reynolds et al. t2~ on austenite decomposition on Fe-C- Mo alloys in this issue, the replacement of grain boundary ferrite allotriomorphs by highly degenerate Widmanst~itten ferrite growing directly from austenite grain boundaries just below the bay in the TTT curve for initiation of transformation is documented. Tsubakino and Aaronson t193J have previously shown a similar sequence in an Fe-C-Mo alloy.

Reducing the austenite grain size below ASTM No. 8 markedly increases the proportion of the ferritic component of the microstructure which is of the allotriomorphic morphology. ~ Allotriomorphs can actually replace plates entirely if the grain size is sufficiently small. [IA941 Replacement of hcp Widmanst~itten a plates by grain boundary a allotriomorphs in a Ti-6 wt pct A1- 4 wt pct V alloy through drastic reduction in the grain size of the bcc/3 matrix by residual porosity has recently been demonstrated as an analogous effect, t1951 When an alloy steel contains a deep bay in the TTT diagram, Widmanst/itten plate formation is increasingly sup- pressed in coarse-grained specimens by another mechanism (Section IV-H-3 ) in the temperature region between the upper nose and the bay in the TTT dia-

gram. t~961 Allotriomorphs can then become virtually the only ferrite morphology present. 119,1961

The allotriomorphs in hypoeutectoid steels are, of course, purely ferritic above the eutectoid temperature (or range) and, for diminishing intervals of reaction time, at somewhat lower temperatures. At the latter temperatures, carbides precipitate in association with the allotriomorphs, converting them to microstructurally defined bainite when the carbide morphology is such that they are soon overtaken, surrounded, and "buried" by the advancing a: 7 interface.* This composite micro-

*When the carbides develop as needles growing synchronously with the ferrite surrounding them, a pearlite-like aggregate known as "fibrous carbides" develops) 198j Thus, this ferrite + carbide structure is explicitly not regarded as microstructurally defined bainite. "68~

structure has been termed "interphase boundary carbides" when the carbide nucleation rate at a : 7 boundaries is high enough so that the carbides can be regarded as having been formed as successive sheets on the terraces of growth ledges at these boundaries. ~97A981 How- ever, this special terminology has been implicitly recognized as unnecessary by understanding that carbide precipitation at the broad faces of sideplates is an equivalent process. ~I991 For immediate purposes, though, it is mainly necessary to note that this process largely serves to reproduce the allotriomorphic morphology on a larger scale, thus making bainitic grain boundary allotriomorphs yet another derivative morphology of bainite. The generality of this morphology is emphasized by noting that bainitic allotriomorphs almost indistinguishable from those appearing in steel are formed in many Ti-X a l l o y s [173'1741 (Figure 6(a)).

e. Columnar bainite The final morphology to be noted in this section, that

of columnar bainite, is derivative in another sense than those preceding. This microstructure, illustrated in Figure 14 in the paper by Spanos et al. tt71 in this issue, has been observed in Fe-C alloys containing 1.4 wt pct C o r m o r e 078,1791 and in high-carbon steels alloyed with Mn and Cr. t2~176176 Nilan t2~ has reported columnar bainite in hypoeutectoid steels reacted under hydrostatic pressure. He suggested that columnar bainite forms by nucleation and growth, whereas lower bainite is the result of "isothermal growth of martensite embryos, which can occur over a temperature range above the Ms." Spanos et a l . I171

have provided a simpler explanation: columnar bainite is merely nodular bainite channeled along certain paths by the formation of inverse bainite in hypereutectoid alloys or upper bainite in hypoeutectoid steels. Figure 14 in Reference 20 provides some direct support for this mechanism. Hence, columnar bainite is a modification or derivative of the nodular bainite morphology, rather than of a proeutectoid phase morphology.

D. Growth Kinetics of Fundamental and Derivative External Bainite Morphologies

On the considerations of Section I l l -C, the growth kinetics of the fundamental external bainite morphology ought to reflect the combined influence of the a and/3 phases during the eutectoid reaction 7 ~ a + /3. On the

1356-- VOLUME 21 A, JUNE 1990 METALLURGICAL TRANSACTIONS A

other hand, growth kinetics of derivative bainite morphologies should be dominated by those of the proeutectoid morphology whose development primarily controls their evolution. Columnar bainite, being a modification of the nodular morphology rather than a derivative of a proeutectoid morphology, however, should exhibit essentially the same growth kinetics, even in its preferred growth direction, as those of nodular bainite.

1. Growth kinetics of derivative morphologies of bainite Only in steels have measurements been made of the

growth kinetics of the derivative morphologies of bainite. Speich and Cohen [z~ and Speich [6~ have shown that the leading edges of lower bainite plates or sheaves of plates are free of carbide. Hence, one should expect that the lengthening rate of these structures will be that of their substrate crystal(s) of ferrite. On the new lower bainite model illustrated in Figure 7 of Reference 18, the largely carbide-free ferrite plate, against which ferrite plates are sympathetically nucleated parallel to another habit plane, is the one whose lengthening rate is determined by measurements of this rate of lower bainite structures. Since in the case of upper bainite it has long been accepted that ferrite plates are the leading phase and morphology, I186.2~ the lengthening rate of proeutectoid ferrite and upper and lower bainite plates in a given alloy should vary smoothly with decreasing reaction temperature and show no discontinuity as the identity of the transformation product changes. This is in fact just what the plate lengthening data of Hillert [2~ on ferrite and (presumably) upper bainite sideplates demonstrated in four plain carbon steels. Simonen et al. tl~ obtained equivalent results on three high-purity Fe-C alloys. Growth rates of both upper and lower bainite have been measured at a given composition only in alloy steels. Goodenow et al. ~2~ have shown reasonably clear evidence for a discontinuity in the temperature dependence of the lengthening rate at the upper to lower bainite transition, approximately 350 ~ in two complexly alloyed steels: 0.50 pet C, 0.68 pet Mn, 0.36 pet Si, and 8.7 pet Ni and 0.69 pet C, 0.85 pet Mn, 0.70 pet Si, 0.85 pct Cr, 0.81 pet Mo, and 1.80 pet Ni. It is possible that these alloying element groups are involved in the change in kinetic behavior. Hence, it would be of value to acquire such data on Fe-C alloys. However, a more likely source of this kinetic difference is the probable differences in the detailed morphology and interfacial structure of the leading edge of upper and lower bainite sheaves. Figure 10 in the paper by Spanos et al. ~8) on lower bainite thus shows severe faceting at each of two different ferrite crystals at the leading edge of a lower bainite sheaf. Al- though comparable TEM micrographs of the leading edges of upper bainite sheaves were not located in the literature, Figures 2(b) and (c) in Reference 1 8 suggest, albeit at up to 20 times lower magnification and with replication instead of TEM, that the leading edges of upper bainite plates may be more simply shaped. Hence, the change in the temperature dependence of the lengthening kinetics at the upper/lower bainite transition may arise from another aspect of the change in ferrite morphology attending this transition. Clearly, more attention to these fine-scale morphological differences is now needed.

Purdy and Hillert, [271 Hillert, t2~176 and Olson et al. [z~ have predicted a continuum of growth kinetics between bainite and martensite. Purdy and Hillert view lath martensite formation as the result of a kinetic instability in the bainite reaction, leading to nearly complete trapping of solute, t271 Martensite growth kinetics are then determined by the mobility of the martensite: austenite boundaries. Olson et al. [2~ developed a more detailed model in which both bainite and martensite were viewed in the context of shear. The interfaces of both transformation products were taken to be glissile; capillarity effects upon the carbon concentration in austenite in contact with

: y boundaries were ignored; the radius of curvature of the advancing plates was taken to be that needed to min- imize strain energy; and the stored energy claimed to be associated with the formation of ferrite, bainite, and martensite plates was incorporated. The ratio of the carbon concentration in the ferritic component of bainite to that in the bulk alloy during growth was predicted to rise smoothly with decreasing reaction temperature, reaching unity somewhat above the Ms. Likewise, the growth kinetics of bainite were forecast to increase continually toward those of martensite. The sessile interfacial structure of ferrite tlzr) and upper bainite l127,1zS,lz9j plates noted in Section I I - C - 3 was not considered in this treatment nor were the frequent absence of IPS surface reliefs, the existence of disagreements between the PTMC and the crystallography of lower bainite, Ir~ the effects of plastic deformation and recovery during growth and tent- shaped reliefs upon stored energy, etc. As recounted in Section I I - C - 1 , there is as yet no evidence for the predicted high carbon supersaturations of the ferritic component of bainite, and the observations of Smith et al. [~~ on bainite growing very slowly below Ma are hardly consistent with essentially complete inheritance of the carbon concentration in the parent austenite. It appears considerably more likely to the present authors that there are large discontinuities in most important aspects of transformation behavior as lower bainite is increasingly replaced by martensite.

2. Growth kinetics of the fundamental morphology of bainite The only growth kinetics measurements on nodular

bainite so far reported have been made on a hypereutectoid Ti-25 pct Cr alloy, in which the/3 matrix de- composes to a + TiCr2 .0771 Since proeutectoid TiCr2 nucleates and grows slowly and large volume fractions of it cannot form in this alloy, the bainite nodules formed at the grain boundaries quickly "bury" the grain boundary allotriomorphs of proeutectoid TiCr2 and are able to grow into the interiors of the/3 matrix grains with comparatively little interference from either intragranular TiCr2 crystals or from bainite nodules which later nucleate on them. The growth rate of the grain boundary-nucleated nodules was found to be constant. Measurements were made at four temperatures of the growth rate, the spacing between adjacent eutectoid TiCr2 crystals in the nodules which were in contact with the/3 matrix, and also the height and the spacing of growth ledges on eutectoid a:/3 and eutectoid TiCr2:/3 interfaces. Hillert-type analyses were written for the growth rate of eutectoid a, clearly the faster growing eutectoid phase, on four different

METALLURGICAL TRANSACTIONS A VOLUME 21 A, JUNE 1 9 9 0 - - 1357

growth models: uniform atomic attachment with volume diffusion through the/3 matrix, diffusion along the advancing fl:eutectoid a and /3:eutectoid TiCr2 boundaries, and ledgewise growth with the same alternate transport paths. Additionally, the ledgewise growth rate was calculated for eutectoid a from the Jones-Trivedi t2~ version of the equation for ledgewise growth of a single- phase precipitate in a single-phase matrix controlled by volume diffusion. This relationship can be periodically more nearly applicable than any of the previous four when eutectoid a has just surrounded a eutectoid TiCr2 crystal, and thus, the local distance between adjacent eutectoid TiCr2 crystals in contact with the/3 matrix is markedly increased. Figure 7 compares the experimental growth rates (denoted by filled squares) with those calculated from all five models. This comparison suggests that modeling the growth of eutectoid o~ as if it were a proeutectoid phase precipitating alone gives a surprisingly good accounting for the measured growth kinetics, even though the volume fraction of TiCr2 present in the nodules was 0.46. However, the shallower slope of the line correlating the measured growth rates with reaction temperature than that of the various calculated correlating lines suggests that boundary diffusion plays an increasing role in mass transport with decreasing reaction temperature.

Speich and Cohen [2~ have compared the indirectly measured thickening rates of lower bainite sheaves in Fe-C alloys with those calculated on the assumptions that

10- 6

I0- 7

I o - e

E

P 10- 9

o

10-1o

10-11

�9 Measured growth rote o Uniform vo tume-d i f fus ion

�9 Uniform boundary--di f fusion v Ledged voLume--diffusion

zx Ledged boundary--di f fusion x J - T Anotysis

- _......~ ~_. . . . X . ~

I I I I I 665 65,5 60,5 57'5 54.5

Temperature (*C)

Fig. 7 - - C o m p a r i s o n of the measured growth kinetics of bainite nodules with those calculated from five different models in a Ti-25 wt pct Cr alloy, tl77j

mass transport between ferrite and carbide phases occurs by volume diffusion through the ferrite and by diffusion along the advancing interphase boundaries.* Although

*Although lower bainite is a derivative bainite morphology, the Speich-Cohen work is discussed in this section because the diffusion geometry applicable during thickening of lower bainite sheaves closely resembles that of nodular bainite.

the former appeared to give the better accounting for the experimental thickening kinetics, this mechanism is surely the least likely of those considered. Unfortunately, no attempt was made to analyze these experimental data on the assumption that carbon diffusion through austenite controls the mass transfer process. Inasmuch as both precipitate phases presumably grow by means of the ledge mechanism, data on the height and spacings of ledges on both would be desirable but would also be very difficult to obtain because of destruction of the austenite matrix by martensite formation during quenching to room temperature.

IV. T H E O V E R A L L REA CTIO N KINETICS DEFINITION OF BAINITE

The overall reaction kinetics definition has received less attention in the recent literature but more in this conference, and hence, a larger number of topics must be treated. A separate introductory section follows in the hope of reducing "interference" from increasingly obvious conflicts with the surface relief and the microstructural definitions of bainite. Absence of overall reaction kinetics bainite above the kinetic B~ is first af- firmed. The crucial question of the generality of the incomplete transformation phenomenon, which is central to the overall reaction kinetics definition, is then investigated. In the following two sections, first the morphology of ferrite, and then of carbides formed in association with ferrite, both above and below the kinetic Bs is examined. Growth kinetics in the same temperature range are then analyzed upon the basis of the morphological observations. A section on the influence which nonequilibrium segregation of substitutional alloying elements to ~ : y boundaries can exert upon growth kinetics follows, as an attempt to explain not only these kinetics but also the preceding experimental observations. This section is concluded with a critical review of present theories of incomplete transformation.

A. Introduction

As noted in Section I, on this definition the bainite reaction is confined to temperatures well below that of the eutectoid. When the upper limiting temperature of this range, the kinetic Bs, is approached, transformation to bainite becomes increasingly incomplete, ceasing entirely at this temperature. The kinetic B, is often associated with the temperature of the bay in the T T T diagram, t61 Incomplete transformation in steel occurs when transformation to ferrite/bainite ceases after less than the Lever Rule-allowed proportion of ferrite has formed lT4]- and this termination has not occurred prematurely as a result of intervention by the pearlite reaction. Four of


the succeeding papers in this issue of Metallurgical Transactions provide much new information about bainite defined in this manner, f19-2~'zl~ This information will be combined with other recently published findings on this subject and summarized in succeeding sections; its implications concerning the nature of the fundamental transformation phenomena involved will then be further explored. A substantial fraction of the current (and past) description of the empirical aspects of overall reaction kinetics bainite will be seen to be either incorrect or incomplete. Restriction of these phenomena to steel (at least insofar as is presently known) and, further, to only certain steel composition ranges will be particularly emphasized. The association of highly degenerate Widmanstatten ferrite with incomplete transformation t2~ and the equally important absence of carbide precipitation until the interval of incomplete transformation ends t2~ will also be stressed.

During the presentation of this material, the perceptive reader will soon realize that the bainite being discussed from the standpoint of the overall reaction kinetics definition is often not so classified on the basis of the generalized microstructural and/or the surface relief definitions. Within this section, however, the overall reaction kinetics definition will be accepted (and, where necessary, corrected) on its own terms. Consideration of conflicts among the three definitions is deliberately de- layed until Section V, where they are grouped together so as to make clear the severity and seriousness of these conflicts.

This introduction is usefully concluded by calling attention to two older reviews which emphasized phenomena centered about the overall reaction kinetics definition of bainite. These reviews were provided by Paranjpe and Kaushal t2111 in 1951 and by Hehemann and Troiano f61 in 1956. They reference the wealth of experimental data on this topic reported in the 1930's and 1940's. A review published by Hehemann c41 in 1970 references and directly provides additional data but is oriented primarily toward applying such information to the interpretation of various aspects of this topic.

B. Absence of Overall Reaction Kinetics Bainite above the Kinetic Bs

Nearly all of the earlier data on the incomplete transformation phenomenon were obtained through measurements of physical properties such as dilatometry, magnetometry, calorimetry, colorimetry, and resistivity (see References 3 through 37 in Shiflet and Aaronsontlgl). Very little data relevant to this problem have been obtained, particularly during earlier studies, by means of the much more tedious but also more reliable technique of quantitative optical metallography. As early as 1935, Smith 12121 compared numerous experimental techniques for measuring the fraction of the austenite matrix transformed to bainite vs isothermal reaction time, using data obtained through quantitative optical metallography as a standard. Remarkably large discrepancies were thereby revealed. Since reports that bainite does not form above the kinetic Bs were usually based upon nonmetallo- graphic techniques, it was thus considered important to recheck this conclusion with quantitative optical metal-

lography.* This has been done mainly by utilizing high-

*Use of TEM for this purpose would be prohibitively costly in time and effort, because microstructures of steel are both highly diverse, since so many are nucleated at or influenced by grain boundaries of diverse crystallography, and are also spread out on a large scale as a consequence of the high diffusivity of carbon in austenite. Scanning electron microscopy (SEM) would appear to be a useful compromise technique, but the present authors' experience with it when attempting to reveal microstructural details of ferrite and bainite has not been particularly favorable. Replication TEM does better at detailing these microstructures but is still tedious and also difficult to control for purposes of quantitative analysis. Further work in developing a higher resolution technique than optical microscopy for quantitative microstructural analysis would thus be highly desirable for studies on steel and other alloys, such as those of Ti, in which high diffusivities lead to large-scale morphologies but which also contain important microstructural features, such as precipitates within precipitates and substructure, on a much finer scale.

purity Fe-C-Mo alloys as a model system. Molybdenum additions readily produce a deep bay in the TTT diagram, and the pearlite reaction, if present at all, does not appear until temperatures high above the kinetic Bs .119'2131 In Shiflet and Aaronson, 1191 the absence of incomplete transformation above the kinetic Bs is demonstrated in numerous Fe-C-Mo alloys. These results are supported by additional data on some of these alloys secured at much longer times in Reynolds et al. 12~ While this point should probably be examined in equivalent detail in at least one other Fe-C-X system which exhibits incomplete transformation, these results provide detailed metallographic substantiation for previous findings, secured with less direct measurement techniques, that the incomplete transformation phenomenon is indeed confined to temperatures below that of the kinetic Bs.

C. Evolution and Generality of Incomplete Transformation from the Standpoint of Overall Reaction Kinetics

For many decades, this phenomenon has been considered to occur universally in steel.[6] Failure to detect incomplete transformation has been taken to result from overlap of the pearlite and bainite C-curves to a sufficient extent so that the incompleteness of the bainite reaction at high temperatures is obscured. The schematic TTT diagram in Figure 8(a) illustrates this situation, 161 whereas that in Figure 8(b) shows that when a steel is sufficiently and appropriately alloyed (particularly by carbide-forming alloying elements), the pearlite and bainite C-curves are well separated, and incomplete transformation can be readily observed.

In Fe-C-Mo alloys, the situation is more nearly akin to that in Figure 8(b). However, as just indicated, the transformation phenomena encompassed by the upper C-curve are different from and more complex than Figure 8(b) suggests. The upper C-curve in such alloys does not refer to the pearlite reaction either at the bay or over an appreciable temperature region above the bay. Instead, pearlite is present, if at all, only at the highest temperatures. I19,213j Hence, pearlite formation cannot prevent observation of the incomplete transformation phenomenon in Fe-C-Mo alloys. As demonstrated by Reynolds et al., t2~ incomplete transformation does develop in the region of the lower C-curve in these alloys,

METALLURGICAL TRANSACTIONS A VOLUME 21A, JUNE 1990--1359

A I Austenite

1 Pearl i te St o r t s ~ _.._....---

~ s {.-" ( Z ~ ~. k Fe.ite PI~, "5 ~ k N N Carb ide \ " . . \

�9 % I M a r t e n s i t e Starts ~ t - r

A I . . . . . . . . - - =

[ A + F + C / " . . . . . . k ' - ' " - { Ferrite Plus Austemte

Bainite Starts

Region o f Incomplete I Reactidn

\ A+F+C \ q - F+c

Time ~ Time

(a) (b)

Fig. 8 - - ( a ) TTT diagram in which the pearlite and bainite regions extensively overlap. (b) TTT diagram wherein the pearlite and bainite regions are well separated in the temperature ranges within which they occurJ 6I

but only when characteristic pairs of carbon and Mo concentrations are exceeded, as shown in their Figure 17. Note that as the carbon concentration is increased, the Mo concentration needed to produce incomplete transformation is reduced.

The manner in which incomplete transformation evolves in Fe-C-Mo alloys also turns out to be more complex than was previously realized, t2~ At alloy compositions and reaction temperatures where incomplete transformation appears, the fraction of the austenite matrix transformed to overall reaction kinetics bainite, f , varies with reaction time, as shown in the curve marked IV in Figure 9. Type IV kinetics involve three distinct stages, of which the middle one has a zero slope. The time interval in which d f / d (log t) (where t is the reaction time) is zero has been termed "transformation stasis." It is during an interval of such stasis that transformation of austenite to bainite may be termed "incomplete," as long as f is less than that allowed by the Lever Rule. When an Fe- C-Mo alloy in which stasis can develop is reacted at a temperature just below that at which stasis no longer appears or when the alloy composition falls just inside the "no stasis" composition region of Reynolds et a l . ' s [2~

?: g

o

"5

"5

I

Log (reaction time)

Fig. 9--Schematic of the four types of overall reaction kinetics behavior observed below the kinetic Bs in Fe-C-Mo alloys by Reynolds el al.[2~

Figure 17, Type III behavior, illustrated in Figure 9, can be observed. This is again a three-stage sequence, but now the middle stage has a relatively small but nonetheless finite slope. Hence, there is no stasis, and therefore, transformation cannot at any stage in its development be regarded as incomplete. At still lower temperatures in alloys that exhibit stasis or at alloy compositions further away from the boundary between "stasis" and "no stasis" C and Mo concentrations, Type II behavior appears. This includes only two stages of kinetics; the middle stage characteristic of Types III and IV has now been eliminated. Finally, in more dilute alloys or at a still lower reaction temperature below the kinetic Bs in a stasis- producing alloy, Type I behavior develops, in which Johnson-Mehl-type kinetics are present at all stages of transformation. Type I behavior is also obtained at temperatures above the kinetic Bs in both stasis- and non- stasis-producing alloys. The final (second or third) stage of transformation during Types II through IV kinetics yields bainite in every instance, rather than pearlite, in the Fe-C-Mo alloys studied, t2~

Although Figure 17 of Reference 20 shows only a boundary between "stasis" and "no stasis" percent C vs percent Mo regions, the foregoing description of the other overall reaction kinetics behaviors observed indicates that additional regions must be present in this diagram. These have been added in Figure 10 with dashed lines. Use of Roman numerals I through IV indicates the highest numbered kinetics observed at any reaction temperature in such alloys. Although we are confident that the dashed lines in Figure 10 are more or less correct in a schematic sense, it must be emphasized that they have yet to be determined in a quantitative fashion. Clearly, though, it would now be highly desirable to do so, and particularly to accomplish these evaluations in sufficient detail so that the presence or absence of curvature in the various boundaries can be delineated.

Another important result from the work of Reynolds et al. ~2~ on Fe-C-Mo alloys is that Type IV kinetics do not continue to occur with decreasing reaction temperature until the fraction transformed at transformation stasis reaches unity. Thus, in these alloys, the concept of a


- - . . , - ---....

%C

Fig. 10- -Schemat ic of pct Mo vs pct C regions in which the indicated type of overall reaction kinetics behavior is the highest numbered type appearing at any reaction temperature below the kinetic B , .

bainite finish (By) temperature, denoting the reaction temperature at which f-at-stasis reaches unity, is meaningless. Instead, at a reaction temperature corresponding to some appreciably lower f , Type IV kinetics are replaced by Type III kinetics. Hence, the traditional plot off-at-stasis v s reaction temperature in Figure 11 (a) should be replaced, at least in Fe-C-Mo alloys, by the curve in Figure 1 l(b), in which this plot simply termi- nates at some f < 1.

None of the foregoing aspects of incomplete transformation or of overall reaction kinetics behavior below kinetic B, has been previously reported. The circumstance that they have been identified in Fe-C-Mo alloys probably speaks much more for the accuracy and sensitivity of the quantitative optical metallographic technique than it does for the more remote possibility that Fe-C-Mo alloys are unique! These results also point

strongly toward the need to redocument, in much greater detail than was practicable for the alloy systems to be discussed next, overall reaction kinetics behavior in other Fe-C-X systems.

Investigations of two Fe-C-Mn alloys are reported in other papers by Reynolds and co-workers with quantitative optical metallography: Fe-0.38 wt pct C-3.11 wt pct Mn [2~4] and Fe-0.10 wt pct C-2.99 wt pct Mn. ~j The former alloy did not exhibit stasis. Overall reaction kinetics curves describing ferrite/bainite formation were entirely of Type I. At the highest temperature studied, both pearlite and bainite were formed. These two con- stituents were accordingly point-counted separately. It was clear, though, that the ferrite/bainite reaction was able to develop to a sufficient extent in this alloy so that pearlite could be morphologically prevented from obscuring ferrite/bainite formation. In particular, pearlite nucleates reluctantly at the interface of grain boundary ferrite allotriomorphs from which Widmanst/itten ferrite sideplates have developed and even less rapidly at well- formed intragranular ferrite plates. [165,2~5] Thus, regions transformed predominantly to pearlite were well segregated from those in which ferrite/bainite extensively developed (see Figure 1 in Reference 214), and the opinion that pearlite formation under these circumstances could have materially interfered with the evolution of incomplete transformation [2|61 is incorrect. [2~7l

On the other hand, the Fe-0.10 wt pct C-2.99 wt pct Mn alloy did exhibit stasis. Figure 13(b) of Reference 21 in this issue shows Type IV overall reaction kinetics at 550 ~ with a zero slope in the middle region. In Figure 13(c), Type III behavior is obtained at 500 ~ whereas Type I kinetics develop at 450 ~ (Figure 13(d)).

Fe-0.11 wt pct C-1.83 wt pct Si t2~1 and Fe-0.38 wt pct C-1.73 wt pct Si [2~4] alloys did not develop stasis nor did Fe-0.41 wt pct C-3.01 wt pct Cu, Fe-0.12 wt pct C-3.28 wt pct Ni, or Fe-0.42 wt pct C-7.25 wt pct Ni. [2~] In- spection of the micrographs provided for these alloys [21,2171 will again verify that even though their TTT diagrams are all of the type shown in Figure 8(a),

09 . m 09

09 !

,,2.

09 09

09 !

,,2.

0 0

Reaction Temperature (a)

Reaction Temperatu re (b)

Fig. 1 1 - - ( a ) Presently accepted view of the maximum fraction of austenite transformable to bainite as a function of temperature below the kinetic B,. (b) Proposed new version of (a), based upon the experimental results of Reynolds e t al . t2~ in Fe-C-Mo alloys.


pearlite formation could not have prevented detection of incomplete transformation. However, two observations of transformation stasis have been made in Si steels. One was made on an Fe-0.60 pct C-1.98 pct Si-0.30 pct Cr steel taj and may have resulted from Si-Cr interactions. The other, reported by Papadimitriou and Genin ~2~81 on a high-purity Fe-0.9 pct C-3.85 pct Si alloy, in w h i c h f was measured by quantitative metallography at higher temperatures and M6ssbauer spectroscopy at lower temperatures, does appear to demonstrate the presence of incomplete transformation. This finding appears to con- flict with the results of dilatometric determinations o f f , made continuously as a function of reaction time. The latter f vs time curves show mainly Type I overall reaction kinetics behavior, with only local "blips" suggestive of Type III or IV kinetics. In a similar alloy, Stark et al. [99] reported f values (qualitatively determined with optical microscopy and TEM) of 0.7 to 0.8, presumably during incomplete transformation, which could well be consistent with the paraequilibrium proportion of ferrite at the temperatures employed. No kinetic data were reported, thereby preventing distinction of Type IV from any other type of overall reaction kinetics. While transformation stasis in higher C, higher Si, Fe-C-Si alloys remains a definite possibility, its existence has yet to be proved.

These results thus demonstrate that incomplete transformation is not a general phenomenon in steel. Even in Fe-C-X systems which do display incomplete transformation, evidence provided for the Fe-C-Mo and Fe- C-Mn systems indicates that incomplete transformation develops only in certain percent C-percent X regions. One reason why previous workers have considered this phenomenon to occur generally in steel is that the alloys utilized in many of their experiments, particularly in earlier years, contained significant proportions of more than one alloying element. As an illustration of the ability of a quaternary steel to produce incomplete transformation even though its component ternary alloys cannot, on the basis of weak dilatometric evidence and very limited metallographic observations, an Fe-0.43 pct C-3.00 pct Mn-2.12 pct Si alloy tlg~ appears to display incomplete transformation. This finding and the resultant Figure 8(b)- type T T T diagram contrast sharply with the absence of incomplete transformation and Figure 8(a)-type TTT diagrams for Fe-0.38 wt pct C-3.11 wt pct Mn t2~4J and Fe-0.38 wt pct C-1.73 wt pct S i [2141 alloys. The potential synergism of substitutional alloying elements in producing (or discouraging) incomplete transformation remains a seriously underexplored research topic!

In addition to failing to occur in a number of alloy steel systems, incomplete transformation has yet to be reported in any purely substitutional alloy system, either ferrous or nonferrous. Termination of the proeutectoid a reaction in hypoeutectoid Ti-Cr alloys prior to complete decomposition of the/3 matrix does not constitute a demonstration of incomplete transformation, since the metastable equilibrium proportion of proeutectoid a was found to precipitate at each temperature studied prior to the cessation of reaction. [219] Completion of/3 matrix decomposition did not occur until after precipitation of the TiCr2 phase had begun, t173,2191 This mode of transformation is found in a number of Ti-X systems in which X markedly

depresses the eutectoid temperature below the a / f l equilibrium temperature in pure Ti.t~741 The lack of generality of this essential component of the overall reaction kinetics definition of bainite thus demonstrates that it is not appropriate to attach a generic name such as "bainite" to this group of phenomena, m

D. Ferrite Morphology above and below the Kinetic B, Temperature

In the absence of incomplete transformation and at lower C and/or X concentrations, such that an appreciable bay does not develop in the T T T curve for the initiation of transformation, the microstructure of proeutectoid ferrite and the ferritic component of bainite (temporarily as microstructurally defined) follows expectation for Fe-C alloys and plain carbon steels. I~7~ Once grain boundary allotriomorphs are replaced as the dominant ferrite morphology by Widmanst~itten plates, the Widmanst/itten structure remains predominant down to and below I22~ the M, temperature unless its formation is prevented at intermediate temperatures (and higher carbon concentrations) by the pearlite reaction, tlTj Although the Widmanstfitten ferrite morphologies often do not appear as parallel, slightly tapering plates at lower temperatures in the proeutectoid ferrite region, the degenerate versions of these plates develop in only a limited number of "modes," which are usually both crystallographic and reproducible.t 152j

However, when a substantial T T T diagram bay and especially incomplete transformation develop, a quite different temperature dependence of ferrite/bainite morphology develops. As described by Boswell et al. c1961 and further by Tsubakino and Aaronson t1931 and Reynolds et al. t2~ in Fe-C-Mo alloys, changes begin to appear just below the upper nose in the TTT curve for initiation of transformation--as indicated schematically in Figure 12. Whereas the highest temperature at which appreciable numbers of Widmanst~itten ferrite plates appear, termed the IV, temperature, t~96,22u usually lies above the upper nose in the TTT diagram and the frequency with which sideplates form increases with decreasing temperature, below the upper nose, the frequency of plate formation diminishes, t1961 When the C and Mo concentrations are sufficiently high, sideplate formation entirely disappears at temperatures somewhat above that of the bay in the TTT diagram, i.e., the kinetic B~ temperature. L19,:~ Grain boundary and also twin boundary allotriomorphs are then the only ferrite/bainite morphologies present. 119,2~ The higher the proportions of C and Mo present, the wider the temperature range in which this situation is obtained. At Mo concentrations of approximately 2 wt pct, the allotriomorphs are often quite prominently faceted, as if sideplates were attempting to emerge from t hem. [2~ When the Mo concentration is in the 3 to 4 wt pct range, however, the broad faces of allotriomorphs tend to be smoother, now without a marked tendency toward the development of protuberances, t191

Whereas at temperatures above that of the bay, ferrite microstructures vary slowly with decreasing temperature, reduction in the reaction temperature by only 5 ~ to 10 ~ below the bay temperature causes drastic


O3

s

8_ E

g

rr

7 / (a + 7) Temperature Grain boundary allotriomorphs

reased number of Widmanst~tten o~ plates

Diminishing number of Widmanst~tten o~ plates

dmanst~itten o~ plates no longer present

"%•rain boundary and

twin boundary allotriomorphs are the sole Ierrite morphologies

erate o~ plates appear

Large numbers of degenerate (z plates

Degeneracy diminishing

N Normal Widmanst~tten oc morphology largely restored

Log (reaction time)

Fig. 12--Schematic of the variation of ferrite or bainite morphology with position on the TTT curve for initiation of transformation in Fe- C-Mo alloys.

alterations in the microstructure. 12~ While allotriomorphs continue to form at grain and twin boundaries for a few tens of degrees Celsius below the bay temperature, the predominant component of the microstructure is now a strikingly degenerate form of the W i d m a n s t / i t t e n s t ruc tu re . 12~ As indicated by the asymmetric shape of the T T T curve for the beginning of transformation (Figures 8(b) and (12)), development of the degenerate Widmanst~itten structure takes place with great rapidity. As illustrated in Figure 12 of the paper on Fe-C-Mo alloys by Reynolds e t a l . ,1201 this morphology has a bizarre appearance and is probably extensively interconnected in three dimensions. Transmission electron microscopy studies show that sympathetic nucleation plays a major role in building these degenerate structures (see Figure 2(d) in Reference 20). The individual crystals comprising these structures are in the 0.5 to 3 /xm size range and are equivalent to the "subunits" of bainite sheaves described by Oblak and Hehemann, t''61 though with considerably less regular shapes. However, many of the extreme irregularities in these crystals occur on a finer scale, probably resulting from the presence of many superledges.I2~ Examination of sideplates of hcp a in the retained/3 matrix of a Ti-6 wt pct A1-4 wt pct V alloy 12231 with TEM showed that a : a boundaries formed by sympathetic nucleation are fertile sites for the generation of superledges in this alloy. Examination with TEM of the interfacial structure of degenerate ferrite plates in a steel alloyed so that martensite does not form even in thin foils in the carbon-enriched regions between closely spaced ferrite crystals should permit this explanation to be tested in a considerably more decisive manner than is possible when the austenite matrix is destroyed by the martensite reaction, as invariably happened in the Fe-C-

Mo and other alloys on which these observations were made.

With further decreases in reaction temperature below that of the bay, degeneracy is progressively diminished but remains greater than it would be in an Fe-C alloy or in an Fe-C-X alloy in which X does not strongly dimin- ish the activity of carbon in austenite. At later reaction times, degeneracy is reduced, primarily through concealment by extensive local impingement. I193j Re- ducing the Mo concentration in an Fe-0.11 pct C-X alloy from 1.95 to 0.90 wt pct causes replacement of a deep bay in the T T T curve for the beginning of transformation with a shallow " n o t c h , "I1961 as shown in Figure 23 of Reference 196. At the temperature of the "notch," grain boundary and twin boundary allotriomorphs are replaced by a nearly normal microstructure consisting of thin allotriomorphic ferrite layers along the grain boundaries and a dense tangle of only moderately degenerate plates, probably predominantly of the sideplate variety. Fe-C- Cr alloys with nearly 3 wt pct Cr but containing 0.092 and 0.13 wt pct C, respectively, exhibited a "notched" TTT curve for the beginning of transformation and a moderately deep bay in this curve, respectively. Reac- tion at the "notch" temperature of the former alloy yielded a microstructure similar to that of its Fe-C-Mo counterpart, whereas reaction at the bay temperature of the latter produced a severely degenerate Widmanst~itten structure atop grain boundary allotriomorphs, instead of only allotriomorphs as in the deeper bayed 1.95 wt pct Mo alloy. Hence, there appears to be a good qualitative correlation between the depth of the bay and the degeneracy of the Widmanst/itten structure formed at this temperature, leading in the no-bay limit to complete disappearance of this morphology. Similarly, in the Reynolds e t a l . [21] paper in which stasis is sought in a variety of Fe-C-X alloys, the one alloy which did exhibit stasis at one of the temperatures studied, Fe-0.10 wt pct C-2.99 wt pet Mn, developed a similar (though somewhat more crystallographic) type of degenerate ferrite morphology at that temperature (see Figure 14 of Reference 21).

Although complexities are involved, a clear association between degeneracy of Widmanst~itten ferrite morphologies, and in extreme cases, elimination of this morphology, and the occurrence of incomplete transformation has now been established. Correlation among incomplete transformation, morphological degeneracy of ferrite, and a notch or a bay in the T T T diagram is generally good, except for the Fe-0.10 wt pct C-2.99 wt pct Mn alloy. However, inspection of Figure 13(b) of Reference 21 suggests that this apparent contradiction arose because f-at-stasis is nearly 0.5 at the one temperature where stasis was observed and also because transformation kinetics were not explored at slightly higher temperatures, where stasis should have developed at lower levels at these temperatures, with this approach possibly producing a bay in t h e f = 0.01 TTT curve. In support of this view, Russell and McGuire I224] showed that a shallow bay is present in the initiation TTT curve of an Fe-0.53 wt pct C, 4.05 wt pct Mn steel. A bulge in the T T T curve for completion toward longer times at lower temperatures (which was not established with certainty) is suggestive of the presence of the incomplete transformation phenomenon at these temperatures.


E. Carbide Precipitation in Association with Ferrite above and below the Kinetic Bs

Much of the material in this section could have been equally well fitted into the section on microstructurally def'med bainite. However, the ultimate focus will be seen to be the temperature and composition effects upon carbide precipitation as they develop in association with the bay in the T T T diagram and the incomplete transformation phenomenon. Hence, the material initially presented should be viewed in the present context as a background against which the special effects on carbide precipitation produced by the overall reaction kinetics phenomena may be appreciated.

In high-purity Fe-C alloys and probably also in plain carbon steels, cementite is associated with (microstructurally defined) upper bainite and epsilon carbide (Fez.4C) and/or cementite precipitate with lower bainite. t4J As substitutional alloying elements are added, these elements tend first to replace some of the iron atoms in these carbides. However, the presence of an element such as Si, which has very little solubility in cementite tz251 but evidently considerably more in epsilon carbide, leads to expansion of the temperature region in which the latter carbide is associated with bainite at the expense of the former.[4] Further increases in the concentration of a substitutional alloying element, identified generically as X, cause alloy carbides to replace (Fe, X)3C, especially but not only at high temperatures, t~82,222,2261 Early work, e.g., that of Hultgren, t~82,2261 led to the generalization that such replacement occurs in pearlite but not in (upper) bainite. A simple rationalization of this result is that interphase boundary transport of substitutional solute should play a more important role in pearlite than in bainite because both phases are continuously in contact with the austenite matrix only in pearlite. Cahn and Hagel t227~ provided the major early analysis of alloying element redistribu- tion during the edgewise growth of pearlite.

Still higher X concentrations, particularly when X is a strong carbide former, bring about important changes in the familiar low-alloy steel pattern. With decreasing reaction temperature, carbide-free proeutectoid ferrite is replaced by carbide-containing upper bainite and then by carbide-containing lower bainite in such steels. Espe- cially when optical microscopy is supplemented with extraction replication and thin foil TEM in steels containing sufficient proportions of carbide-forming alloy element, it is found that carbide-free proeutectoid ferrite is replaced by carbide-containing proeutectoid ferrite, converting it to bainite or "rod pearlite" even at temperatures just below the eutectoid range, t198~ Some of these carbides precipitate on dislocations in the interiors of proeutectoid ferrite crystalsJ ~981 Most carbides, though, precipitate at a : y boundaries under these circumstances. One mode for so doing is on the terraces of growth ledges with widely spaced risers as "sheets" of isolated carbides. I197! Another mode probably occurs on the terraces of more closely spaced ledges, I2281 permitting the carbides to grow synchronously with the surrounding ferrite and thereby forming the needle or rod equivalent of lamellar pearlite3229,23~ The former carbide distribution has been termed "interphase boundary carbides," while the latter is described as "fibrous carbides. "1198.229,23~

The ferrite morphology upon which both distributions of alloy carbide develop is overwhelmingly that of grain boundary allotriomorphs when X is a strong carbide- forming element, i198j However, interphase boundary carbides have also been observed, albeit much less frequently, in Fe-C-X alloys in which X is a non-carbide former, e.g., Ni and Si. I2311 While sideplates were present in such microstructures, the interphase boundary carbides were again more frequently associated with grain boundary ferrite allotriomorphs.

All of the ferrite + carbide structures discussed in this section have morphologies which are clearly proeutectoid ferrite-dominated, as described in Section I I I -C-2 . In Section IV-D, the marked changes in proeutectoid ferrite morphology which occur when a sufficient proportion of a strong carbide-forming substitutional alloying element is added were described. It now appears clear, however, that these morphological changes are not the result of carbide precipitation at a : y boundaries. In- stead, the changes in ferrite morphology and in carbide morphology and distribution are due to effects of alloying elements on ferrite formation, with the carbide effects being at least partially subsidiary to those upon ferrite, rather than causes. As will be argued in Section I V - H - 3 , the basic cause of these marked kinetic and morphological changes is a solute drag-like effect (SDLE) exerted by alloying elements, such as Mo and Cr, which markedly reduce the activity of carbon in austenite. Al- though other types of alloy carbide sometimes do precipitate at the same time as or even before grain boundary ferrite allotriomorphs, e.g., M6C, II9'2131 in the main, the ferrite allotriomorph morphology is well established, and the evolution of sideplates therefrom has been inhibited prior to the onset of either interphase boundary carbide or fibrous carbide precipitation. ~228j As in the more familiar cases of upper and lower bainite formation, precipitation of these two distributions and morphologies of alloy carbides merely serves to enlarge the ferrite crystals at whose interphase boundaries they form without markedly changing their shapes. However, the association of interphase boundary and/or fibrous carbide with ferrite from a very early stage of growth over substantial ranges of reaction temperature and alloy composition tl9'2~ does indicate that further consideration of the influence of carbide precipitation at a : y boundaries upon ferrite morphology is warranted.

Returning to the context of the overall reaction kinetics definition of bainite, Berry and Honeycombe 12131 showed that grain boundary allotriomorphs containing predominantly fibrous carbides, but also interphase boundary carbides, are the principal morphology of ferrite at temperatures below that of the (upper) nose in the T T T diagram in Fe-C-Mo alloys containing approximately 0.2 wt pct C and 2 to 4 wt pct Mo. Both interphase boundary and fibrous carbides were MozC. These findings are extended down to the temperature of the bay in an accompanying paper by Shiflet and Aaronson, I191 in which alloys containing 0.15 to 0.25 wt pct C and 2.3 to 4.3 wt pct Mo were employed. While there is little doubt that both interphase boundary and fibrous carbide structures are ferrite-nucleated, during the latter study, no ferrite crystals which did not contain carbides were observed with TEM.


These studies were later extended to temperatures well below that of the bay in a single alloy containing 0.19 wt pct C and 2.3 wt pct Mo. [193] The bay temperature in this alloy lies between 610 ~ and 615 ~ Although fibrous carbides predominate above the bay, they disappear almost entirely immediately below this temperature. Interphase boundary carbides, on the other hand, continue to form down to 550 ~ Additionally, large laths of Mo2C, 4- to 5-fold thicker and more widely spaced than either fibrous or interphase boundary carbides, appear below the bay and remain a noticeable feature of the microstructure down to 575 ~ Many of these laths appear to be nucleated at and parallel to the broad faces of ferrite plates; others, oriented orthogonal to them, may have nucleated at either facets on the leading edges of ferrite plates or at dislocations within these plates. The size of Mo2C precipitates shrinks rapidly with decreasing temperature. When the reaction temperature is decreased to the 500 ~ to 525 ~ range, large carbides reappear but now as cementite (presumably (Fe, Mo)3C ). At a given temperature, they are about 10 times longer than their M02C counterparts.

It should finally be noted that M02C needles or plates nucleated within ferrite are a usual feature of these microstructures both above and below the bay temperature. [193[ While their numbers are not necessarily large, they are a persistent feature of carbide precipitation in association with ferrite.

The various patterns of carbide precipitation described have attracted much attention. [193.198,228.232-2341 The mechanism(s) which presently appear to be responsible for each of them will now be considered. Planar arrays of interphase boundary carbides were correctly ascribed to carbide nucleation on the terraces of ledges on the broad faces of grain boundary ferrite allotriomorphs. [1971 How- ever, curvilinear arrays of interphase boundary carbides were proposed to have nucleated at disordered-type a: "y boundaries,/232,2331 since no special orientation relationship was found among ferrite, austenite, and the carbides in this situation. I235,236,2371 A theoretical analysis of this problem t9~ demonstrated that nucleation on a continuously moving disordered a: 3' boundary is infeasible unless the driving force for the movement of such a boundary has been nearly exhausted. Consistent with this deduction, a subsequent investigation showed that in a Ti-Cr alloy, the interfaces between hcp proeutectoid ct allotriomorphs and the bcc/3 matrix grain, toward which the allotriomorphs do not bear a Burgers orientation relationship, are also ledged and, hence, must also be partially coherent. [2381 The suggestion was therefore made [234] that the carbides in the curvilinear arrays also nucleate on the terraces of short ledges that undergo frequent changes in their conjugate habit planes or are components of triatomic structural ledges, which (unlike monatomic and biatomic structural ledges) can step up or down at bcc:fcc interfaces. [138,2381 Both interfacial structures will appear to be smoothly curved if they are revealed only by the formation of very few carbides on each terrace. [2341

Whereas rational orientation relationships were reported between bcc M02C fibers and ferrite [213~ and between fcc Cr23C6 fibers and felTite, [239] at least in the former situation, the fiber axis was found to be neither rational

nor unique. In the latter, the ferritic component of the fiber structure did not have a rational orientation relationship with respect to retained austenite, and the fibers themselves did not display the usual cube :cube orientation relationship to this austenite. However, the fibers are in contact with austenite. [213] That the fibrous and interphase boundary carbide structures are not wholly separate is indicated by the observation of Barbacki and Honeycombe [24~ that an Fe-C-Mo alloy yielded interphase boundary carbides when partially transformed at 850 ~ but that these were replaced by fibrous carbides during further reaction (prior to quenching) at 725 ~ This change in carbide morphology was accompanied by a replacement of ledged by apparently smoothly curved a: y boundaries between the eutectoid ferrite and the parent austenite. However, at much higher levels of resolution, such boundaries are only too likely to be partially coherent and ledged. An analysis of the ledgewise growth of two eutectoid phases, summarized in Section I l l -B , thus led to the suggestion that the fibrous carbides of rod pearlite may also grow by shared growth ledges, as does lamellar pearlite. [1661 This would again ensure that the ferrite and carbide phases grow at exactly the same rate, even though both are partially coherent with respect to austenite. The irrational crystallography evidently exhibited by the components of rod pearlite/fibrous structure is now understood to be no longer indicative of substantial areas of disordered interphase boundaries. [238[

The disappearance of the fibrous structure coincides with the onset of severe ferrite degeneracy, tl931 The tor- tuous path of a: 3' boundaries in this morphology would be expected to prevent fibrous growth by a shared ledge mechanism, t17] Continuation of the interphase boundary carbide morphology until about 60 ~ below the bay temperature is consistent with the appearance of this type of carbide distribution only at later stages of ferrite growth, when degeneracy is ameliorated by impingement, planar boundaries of appreciable length have begun to develop, and the lateral velocity of the risers of ledges is low enough so that the overrunning of carbide embryos is less frequent. [1931 At lower temperatures, however, growth kinetics of the degenerate structure appear fast enough to inhibit the development of the large numbers of carbides on the terraces of ledges, and thus, the interphase boundary carbide structure is absent. [193~

Nucleation of large M02C laths parallel to the broad faces of ferrite plates at temperatures just below the bay and of (Fe, Mo)3C laths at lower temperatures presumably results from carbide nucleation oriented so that the habit plane of the carbides is parallel to that of the terraces of the ledges. It is not clear, though, why nucleation in this presumably favorable orientation should produce such a small number density of carb ides- -unless lateral impingement is obscuring the presence of initially much larger numbers of carbides. Figure 6 in Reference 193 provides some support for the "composite" nature of lath carbides and suggests that they may be another form of interphase boundary carbide precipitation in which the apparently far greater height of the growth ledges in degenerate ferrite structures makes the spacing between successive sheets of interphase boundary carbides more than an order of magnitude larger than is usually encountered. Replacement of MozC by


( F e , M o ) 3 C laths at lower temperatures follows directly from the rapidly diminishing diffusivity of Mo in both austenite and ferrite.

F. Growth Kinetics in the Vicinity o f the Kinetic Bs

Two ferrite morphologies are present in the temperature region of interest: grain boundary allotriomorphs*

*Twin boundary allotriomorphs are also available, but too few twin boundaries are present in a typical austenite grain to permit solution of the stereological problem of ascertaining the angle between the twin plane and the plane of polish and thus determining the true thickening rate normal to the twin boundary.

and degenerate Widmanst~itten structure, t~961 The "tech- nology" for measuring the thickening kinetics of grain boundary allotriomorphs has been available for some time. I241J However, as Figures 2(b) through (d) in an accompanying paper by Reynolds et al. I2~ demonstrate, measurements of any type on the degenerate Widmanstfitten morphology made upon a plane of polish which can be realistically translated into significant data in three dimensions appear to be impossible. Unfortu- nately, transformation stasis develops during the formation of the degenerate structureY ~ Hence, a direct connection between growth kinetics and transformation stasis cannot presently be established. However, measurements of allotriomorph thickening kinetics will be seen to provide useful indirect information as to the origin of transformation stasis as well as more direct knowledge about the reduction in growth kinetics which precedes stasis in time and in reaction temperature.

The initial clue as to the involvement of growth kinetics in the development of the bay in the TTT diagram and the incomplete transformation phenomenon appeared during THEEM measurements of allotriomorph thickening kinetics in an Fe-0.11 wt pct C-1.95 wt pct Mo alloy. [242] Thickening kinetics were parabolic, as expected for volume diffusion control, but the parabolic growth rate constant passed through a maximum at about the temperature of the upper nose in the TTT curve for transformation initiation, whereas calculation of this constant from a relationship appropriate to a planar, disordered b o u n d a r y [243,244] indicated that this rate constant should have increased continuously throughout the temperature regime in which the intensity of thermionic emission was high enough so that THEEM data could be collected. This regime ended about halfway between the upper nose and the bay temperature. Hence, the suggestion could be made, but not tested, that the bay in the T T T diagram is directly associated with a minimum in growth kinetics.

Boswell et al.[196] developed a room-temperature measurement technique for evaluating the growth kinetics of ferrite allotriomorphs and applied it to four Fe-C-2 pet Mo alloys in the carbon concentration range of 0.055 to 0.26 wt pct. In three of the four alloys studied, the parabolic rate constant did indeed pass through a minimum at the bay temperature, while in the fourth, it did so somewhat below this temperature. Log-log plots of all the growth kinetics data obtained by Boswell et al. yield a time-law exponent of 0.50 - 0.02.

In one of the following papers in this issue, Shiflet

and Aaronson I19! report the same type of data for Fe-C- Mo alloys in the 0.15 to 0.25 wt pct C and 2.3 to 4.3 wt pct Mo range, with emphasis now being placed upon measurements made from the bay temperature to about 50 ~ above this temperature at small intervals of reaction temperature. Results quite different from those of Boswell e ta / . 11961 w e r e obtained. As illustrated schematically in Figure 13, I191 four different types of behavior are found when the logarithm of the half-thickness of grain boundary allotriomorphs, S / 2 , is plotted as a function of the logarithm of the reaction time.* Type 1

*Although use of growth time rather than reaction time would have been preferable, the former usage was found to make little difference in the results obtained and also to introduce additional uncertainty. Hence, the reaction time convention was retained.

(single-slope) behavior was obtained at lower C and Mo concentrations and at the highest temperatures studied. With increasing percent C and percent Mo and as the bay temperature was approached, thickening kinetics behavior passed successively through Types II, HI, and then IV. The latter behavior is of especial interest and importance, for it consists of three stages, of which the middle stage has a zero slope. This cessation of growth was termed "growth stasis," in order to distinguish it from the long known tl~ "transformation stasis," wherein transformation ceases everywhere in a specimen. Al- though Type IV growth kinetics are similar to Type IV overall transformation kinetics (Figure 9), growth stasis above the bay failed to produce transformation stasis, because the ranges of time during which ferrite allotriomorphs were nucleated were longer than the growth stasis times. Hence, the first nucleated allotriomorphs were emerging from growth stasis before those last nucleated had entered this middle stage of growth.* Type III growth,

*Growth kinetics measurements were always made on allotriomorphs which were among those first nucleated, since the metallographic procedure employed was based on measurement of the thickness of the thickest allotriomorph in the plane of polish.

it should be noted, also includes a middle stage in which growth kinetics are slower than in either the initial or final stages but nonetheless remain finite. Even during Type 1 growth in this temperature-composition regime and also in the first stage of Types II through IV, the time exponent was no longer 1/2 but instead varied from 0.1 to 1. The final stages of Types II through IV had time exponents near unity. Inasmuch as growth kinetics were reasonably slow and the allotriomorphic layers tended to develop in a fairly uniform manner, considerable confidence can be placed in the accuracy of these data. Interphase boundary and fibrous carbide structures were measured indiscriminantly during these studies since they could not be distinguished from one another with optical microscopy. However, repeated TEM and carbon extraction replication electron microscopy examination of the microstructures of these alloys provided convincing evidence that the thickening kinetics of allotriomorphs containing the two types of carbide dispersion are essentially the same.

Reynolds et a l Y ~ succeeded in extending these measurements slightly below the bay temperature in the lowest Mo alloy in which transformation stasis developed.


Cq

0") 0

J 10g (time)

Fig. 13--Schematic of four types of log (allotriomorph half-thickness) v s log (growth time) plots for ferrite allotriomorphs obtained in Fe- C-Mo alloys at temperatures from the kinetic Bs to about 50 ~ higher, t~9~

Both at the bay temperature (650 ~ in this Fe-0.24 wt pct C-0.93 wt pct Mo alloy and at two temperatures, 640 ~ and 630 ~ below the bay, two-stage growth appeared. Whereas at the two higher temperatures the kinetics corresponded to those of Type II in Figure 13, at 630 ~ the first stage had a steeper slope than the second stage. The second stage of thickening at the two higher temperatures and the first stage at the lowest temperature displayed approximately t 1/2 growth kinetics; the remaining stages of thickening yielded time exponents in the 0.2 to 0.3 range.

A number of different possibilities have been explored for explaining these growth kinetics data. t191 None of the quantitative models examined contains the possibility for explaining multistage kinetics. Particularly in view of the invariable presence of carbides among the ferrite allotriomorphs and the presence of two solutes, C and Mo, with vastly different diffusivities in austenite, however, analyses of the types now to be summarized were clearly necessary.

The obvious first choice of a model for allotriomorph thickening kinetics is that of a planar, disordered boundary whose motion is governed by the diffusion of carbon in austenite, with phase boundary compositions appropriate to paraequilibrium. Although assuming that the broad faces of allotriomorphs have considerable areas of disordered interfacial structure has long seemed reason- able, ~152,2451 the demonstration by Furuhara et al. I2381 that both interfaces of allotriomorphs are partially coherent in a hypoeutectoid Ti-Cr alloy supports the contrary deduction made earlier from considerations of nucleation theory 11491 and which may now be presumed to be generally applicable. However, Enomoto 1246'2471 and Enomoto and Aaronson I2481 have shown that once a critical growth time has been exceeded, planar ledged interphase boundaries grow with very nearly the kinetics of planar disordered boundaries. (The critical time is dependent upon

supersaturation, temperature, rate-controlling volume diffusivity, the interledge spacing/ledge height ratio, and even the number of ledges in a given set. t2481) Para- equilibrium is an accurately definable unstable equilibrium wherein the ratio of the X concentration to that of Fe is the same in ferrite as it is in austenite, and the carbon concentrations in the two phases are adjusted so that their partial molar free energies are equal. [2431 When Boswell et a l . 11961 applied this model, they found that at the bay temperature, it predicted a parabolic rate constant 1.5 orders of magnitude higher than that measured experimentally. This difference was rapidly reduced below the kinetic Bs and also at temperatures at and above that of the upper nose in the T T T diagram. Reynolds et al. t2~ found that this model accounts fairly well for their data, though, of course, it cannot predict either the two-stage growth kinetics they obtained or the time exponent less than 1/2 applicable at one of these stages at each temperature. However, the Shiflet and Aaronson [191 growth kinetics data, having been measured in alloys containing at least 2.3 wt pct Mo and concentrated in and just above the bay region, fell orders of magnitude below the rate constants calculated from the paraequilibrium model.

The parabolic rate constant was also calculated, on the basis of planar disordered boundaries, from a model assuming equilibrium partition of Mo between austenite and ferrite and thus control of growth by Mo diffusion in austenite. Even though electron probe data indicate the absence of bulk partition of Mo between austenite and f e r r i t e , 1249] a s did earlier data obtained through careful measurements of the ferrite lattice parameter, I25~ this model yielded growth kinetics which were too slow for Type I growth but gave agreement with experiment which improved with successively higher types, yielding a fair accounting (except during growth stasis) for Type IV growth. Hence, Mo diffusion through austenite does appear to play some role in determining the growth kinetics of these ferrite + M02C aggregates at temperatures above the bay region.

The growth of the fibrous structure was first modeled as if it were controlled by Mo volume diffusion from ferrite through austenite to the M02C fibers and then as if kinetics were determined by Mo diffusion along the advancing interphase boundaries. The volume diffusion version of this mechanism predicted kinetics too slow for Type I growth but increasingly closer to the experimental kinetics through successively higher numbered types. Both the time law and the rate constant agreed mainly with the final stage of growth but not with earlier stage kinetics. On the other hand, the interphase boundary diffusion mechanism led to kinetics about l 0 4 faster than those measured.

The "collector plate mechanism" t2511 for the growth of individual interphase boundary carbides yielded kinetics 10 6 tOO rapid. A mechanism for the growth of the interphase boundary structure as a whole, based upon volume diffusion of Mo through austenite, predicts kinetics at least 102 slower than those observed.

The observation that despite their obviously different mechanisms, diffusion paths, and distances, the growth kinetics of fibrous and interphase boundary carbide structures are nearly the same suggests that a factor common to both exerts a major influence upon their growth

METALLURGICAL TRANSACTIONS A VOLUME 21A, JUNE 1990 1367

kinetics and plays a significant role in producing slower than predicted growth rates. This factor is suggested to be a SDLE upon the growth of the ferritic component of both ferrite and carbide structures. This possibility will be discussed in detail in Section IV-H, after the experimental evidence on a necessary component of the SDLE, i .e . , nonequilibrium segregation of X to mobile areas of a:3 ' boundaries, is discussed in the following section.

G. Segregat ion o f Substi tutional Alloying E lement to t~: 3, Boundaries in Overal l React ion Kinetics Bainite

This type of segregation is an essential element of SDLE theories of substitutional alloying element effects upon the growth kinetics of ferrite. A number of direct investigations of such segregation have accordingly been made. Before considering the results obtained, however, some problems associated with these measurements should be noted.

If bulk partition of X between austenite and ferrite attends the growth of ferrite, measurements of X segregation to a : 3, boundaries should still be feasible, though more difficult to measure experimentally and evaluate theoretically. Such partition has been observed at high reaction temperatures (usually, but not always, well above those of interest here) in Fe-C-Mn, Fe-C-Ni, and Fe-C- Pt alloys, t2581 As discussed in Reference 19, partition of X between ferrite and carbide can occur behind and up to the advancing ct: 3, boundaries. Particularly since carbides in contact with a : ) , boundaries should be able to drain X from them, this ought to be a particularly un- favorable situation in which to evaluate experimentally X segregation to these boundaries. An even more serious and less correctable problem is that, as discussed in Section I l l -A, the mobile areas of interphase boundaries formed during precipitation are confined not only to the risers of ledges but probably also to kinks on these risers. Because the segregated solute is likely to be confined to the width of a : y boundaries, the field ion microscope/atom probe seems best suited to measuring the concentration of such solute. However, the "field of view" provided by the field ion microscope is only about 20 nm in diameter, whereas growth ledges at c~:? boundaries can be microns apart, t551 Hence, the proba- bility of conducting measurements on the riser of a growth ledge, much less upon kinks on a riser, with a field ion microscope/atom probe seems quite small. Since segregation of X to the terraces of growth (and, of course, also structural) ledges is presumably much less than to areas of a : ? boundaries which are sufficiently disordered to be mobile, it seems likely that data obtained by means of the FIM/AP technique may provide no more than a rough lower limit to the segregation actually of interest.

X segregation at a:3, boundaries should now be detectable, if present, with both scanning transmission electron microscopy (STEM) and FIM/AP instruments. Most studies so far reported, however, have been made with the field ion microscope/atom probe. A disturb- ingly mixed pattern of results has been reported. Bach et al.t2521 made the first such study but did so on a complex commercial Cr-Mo steel, in which Mn, Si, and V

were also present. Their finding of enrichment in both of these elements on either side of the boundary, but depletion of them within the boundary itself, is very difficult to explain. Although perhaps a result of a technique problem, this strange profile might also have resulted from complex interactions among the many alloying elements present. Bhadeshia and Waugh t97,981 conducted imaging atom probe studies on simpler alloys, Fe-C-Mn-Si and Fe-C-Ni-Si. No enrichment in Si was found at a : ? boundaries in either alloy, and no enrichment was observed in Ni in the second alloy; Mn segregation could not be evaluated, because Fe and Mn atoms could not be distinguished with the instrument employed. This mode of analysis is also not capable of de- tecting small enrichments, e .g . , by a factor of 2, of elements present at low bulk concentrations. Stark et al. t991 subsequently reported limited studies on an Fe-C-Si and on two Fe-C-Mn-Si alloys; the instrument used now permitted detection of Mn atoms. Absence of Si enrichment at ~:~, boundaries was claimed. In the Mn-containing alloys, absence of Mn segregation at these boundaries was suggested by their data during what may have been an early stage of incomplete transformation, while two- to fourfold enrichment was suggested after prolonged holding at the transformation temperature. These results also appear to be quite uncertain, even though each study in this series of investigations was conducted in the absence of carbide precipitation.

In the same conference proceedings, Stark and Smith ~253j reported on FIM/AP and X-ray analyses with field- emission STEM of interfaces in Fe-C-Mo alloys. Anal- yses of t~: 3' boundaries were reported only with the STEM technique on an Fe-0.20 wt pct C-0.52 wt pct Mo alloy reacted for 15 seconds at 595 ~ and on an Fe-0.32 wt pct C-2.05 wt pct Mo alloy reacted for 23 hours at the same temperature. A TTT curve was shown only for an alloy closely similar to the higher Mo one; this curve indicates that 595 ~ lies just below the bay temperature of this alloy. According to Figure 17 of Reference 20, transformation stasis would be expected to develop only in the higher Mo alloy. Approximately twofold segregation appears to have occurred at c~: 3' boundaries in this alloy but effectively none in the lower Mo alloy, in qualitative accord with expectation from the SDLE concept. t2~ Further, no correction was reported for the volumes of bulk ferrite and austenite presumably included in these analyses; hence, they should presumably be regarded as minimum levels of enrichment. (Field ion microscopy/atom probe data were provided only for bulk ferrite and austenite and for a high-angle a : a boundary.)

Reynolds et al. I1~176 have reported an FIM/AP analysis of interfaces in an Fe-0.19 wt pct C-1.81 wt pct Mo alloy reacted for 30 seconds at 585 ~ a temperature not far below that of the bay in this alloy. Because a:~, boundaries (which became a: martensite boundaries after quenching) quickly fractured under the high electric field applied during FIM analysis, only one such boundary was successfully analyzed. Data were also obtained on 16 a : a boundaries. Inasmuch as the segregation levels measured were essentially the same, despite the Stark- Smith f253j finding of much more extensive segregation at an ~ : a boundary, it was concluded that the a : a boundaries had actually been a: 3, boundaries until sympathetic


nucleation occurred at them shortly before quenching and that insufficient time had elapsed to permit readjustment of interracial segregation. A correction was made for bulk phase(s) included in these analyses. Again, an enrichment of approximately 2 was found. Whereas it is uncertain as to whether or not M02C precipitation affected the segregation data reported by Stark and Smith, Reynolds et al. I~~176 used a reaction time shorter than that required to enter the transformation stasis regime at the reaction temperature employed. Hence, MozC precipitation was not observed at any of the a: a or a : y boundaries examined.

Of the still meager harvest of interracial composition data thus summarized, only that on Mo is directly relevant to incomplete transformation in ternary alloys. Among quaternary alloys, Mn segregation to a: y boundaries is said to be absent initially during incomplete transformation in Fe-C-Mn-Si alloys, t991 However, Chen et al. t2541 are finding the opposite result during current research.

H. Theories of Incomplete Transformation

Although three of the following papers in this issue t19,2~ deal with incomplete transformation, it will nonetheless be useful in this overview paper to provide a compact summary of attempts which have been made to explain this phenomenon. A relatively recent explanation, ~2551 not discussed in the other papers, will also be examined here in more detail. The SDLE theory, which the present authors favor, will then be summarized in its present form, and an effort (largely not undertaken in the other papers) will be made to delineate and respond to objections which have been made to this theory.

1. Summary and critique of earlier theories The earliest explanation, that incomplete transforma-

tion results from accumulation of transformation strain energy which can be progressively overcome by increasing the undercooling below the kinetic B, and thus the driving force for the bainite reaction, Iz56,2571 continues periodically to reappear in the literature. ~4,2581 This view, closely analogous to the usual explanation for the temperature dependence of the proportion of martensite formed in C- or Ni-containing steels, t259~ fails to explain, however, the sensitivity of the occurrence of this phenomenon to carbon and alloying element concentrations and especially to alloying element identity, as presented in Section IV-C. Embryos of ferrite quenched-in from the austenite region, which become critical nuclei either within austenite ~26~ or at a :y boundaries during the en- largement of sheaves of bainite by sympathetic nucleation, I41 have also been invoked. The lower the reaction temperature, the smaller the embryos which become larger than critical nuclei and, thus, the greater the number of balnite plates that can form. However, the quenching rates usually applied have been shown to be insufficient to permit the quenching-in of ferrite embryos. I26u "Unmix- ing" in the austenite phase prior to ferrite formation is a familiar means of making shear thermodynamically feasible in local areas and also provides a mechanism for producing more solute-poor areas as the reaction temperature is d e c r e a s e d . [257'262'2631 However, at least on current models of the austenite solid solution, the spi-

nodal process is thermodynamically impossible, tsvl Zener ts61 has proposed that the kinetic Bs temperature is also the To temperature, at which stress-free austenite and ferrite (or counterpart phases in a nonferrous system) with the same composition have the same free energy. How- ever, thermodynamic calculations indicate that this pos- tulate is often not correct, tu Also, on this mechanism, ferrite should grow with the velocities appropriate to a massive or even a martensitic transformation. As discussed in Sections I I I -D and IV-F , there is no valid evidence for such swift growth kinetics of the ferritic component of bainite. On a more localized basis, termination of the growth of a bainite plate is sometimes ascribed to carbon enrichment of the austenite by carbon diffused out of supersaturated fe r r i t e . [8'264'2651 However, carbon enrichment of austenite is initially highly localized, ~1861 and stasis can even occur in the absence of enrichment. [ 115,222]

2. Summary and critique of the Bhadeshia-Edmonds theory The carbon-enrichment explanation has been revived

fairly recently by Bhadeshia and Edmonds t2551 and continues to be promoted by them. t23,z6J Bainitic ferrite is considered on their variant of this theory to form by high- velocity shear with very little carbon partition to austenite. "The bulk of the partitioning of carbon into the residual austenite must occur after the initial formation event. If this represents the true nature of events, the bainite reaction can be expected to cease as soon as the austenite carbon content reaches a critical value, the magnitude of which would be near the To curve, de- pending on the exact degree of partitioning occurring simultaneously with transformation. Such an interpretation would also explain the incomplete reaction phenomenon since, with decreasing temperature, the austenite can tol- erate successively greater amounts of carbon before the formation of supersaturated ferrite becomes thermodynamically impossible. "t2551 It is immediately clear, however, that this model postulates the implausible sequence of events sketched in Figure 14(a) in the form of composition-penetration curves through a particular bainite plate drawn at successively longer reaction times. This sequence requires that carbon diffusion from ferrite into austenite across a: y boundaries take place with a sharp discontinuity in partial molar free energy at the boundary, despite the circumstance that the interfacial structure barrier to growth at this boundary (which Bhadeshia and Edmonds reject) is necessarily "porous" to interstitial diffusion of carbon. This sequence also appears to require that carbon diffuse through austenite in the absence of carbon activity gradients in this phase! The sequence sketched in Figure 14(b) at three different post- growth reaction times would not require a discontinuity in partial molar free energy and is thus much more likely to approximate the actual consequence of the fast shear- then-stop growth model. On the diffusional growth model, these curves would appear as portrayed in Figure 14(c). On the mechanism employed by Bhadeshia and Edmonds, further formation of bainitic ferrite by shear would therefore be thermodynamically prohibited almost instantly after the cessation of growth-by-shear in the immediate vicinity of the bainite p l a t e s - - but could continue to take


x 7

x~(To)

X 7

t3

t2 tl

(X.

t 1

t2

t3

t3

t2

tl

Distance (a)

t3>t2>t 1

x./

xT(T~

x~ t / t2 tl

t x~ x

or,

t 1

I I Distance

(b)

7

tl t2 t3

t3>t2>t I

x 7

x~(To)

X.~

_ 7

t2

J t2

tl tl

t2

Distance

~ . t2>tl

(c)

Fig. 14--Concentration-penetration curves through a bainite plate and the surrounding austenite at successively greater isothermal reaction times: (a) as deduced from the Bhadeshia-Edmonds [2553 mechanism of incomplete transformation; (b) as expected from a high-velocity-shear- stop mechanism; and (c) anticipated from purely diffusional growth.

place well outside of this region. Hence, the implied gradual increase in carbon concentration, more or less uniformly throughout the untransformed austenite, until the concentration which makes the reaction temperature equivalent to the To temperature is achieved, is inconsistent not only with the elementary thermodynamics of the situation but also with the elementary diffusion kinetics applicable. Particularly at the comparatively low reaction temperatures involved (generally less than approximately 600 ~ the penetration of the carbon re- jected from the supposedly more or less fully supersaturated ferrite plates into the surrounding austenite is far slower than the Bhadeshia-Edmonds mechanism clearly implies.

The differences between Figures 14(b) and (c) are directly relevant to the interpretation given by Bhadeshia and Edmonds of their attempts to estimate the average carbon concentration in the untransformed austenite dilatometrically, as reproduced in Figure 15(a), and by FIM/ AP analysis, as reproduced in Figure 15(b). The finding that these average carbon concentrations* lie close to the

*These data are of questionable accuracy and relevancy, respectively. See a critique of the dilatometric procedure by Liu et al . t~4]

and of the F IM/AP measurements in Section I V - G and in Reynolds et al. I~~176 The FIM/AP data, it should be emphasized, must also be highly nonrepresentative because of the very small sampling area allowed by an FIM/AP measurement relative to that of the austenite or austenite + martensite regions remaining between bainite plates.

"no-partitioning" (To) curve and below various versions of the Ae3 curve in Figure 15(a) and closer to the To curve in Figure 15(b) was taken as evidence supporting the Bhadeshia-Edmonds model. However, on Figure 14(c), since they can only be random points on varying, and sometimes steeply sloped, concentration curves, these data have little significance in the present context. It is instead necessary to provide complete curves of this type across the regions between bainite plates, and especially, to extrapolate these data to the a:3 ' boundaries insofar as this can be achieved.

Now consider how such data might be interpreted. Figures 16(a) through (d) are schematic carbon concentration-penetration curves through two parallel ferrite plates, constructed perpendicular to their broad faces, and the austenite region between them. (In each sketch, the atom fraction of carbon in ferrite in metastable equilibrium with austenite, x~ ~, has been set at too high a level for the purpose of clarity.) Carbides are assumed to be absent, and the proportion of substitutional sites occupied by X atoms is taken to be the same in ferrite as in austenite. In Figures 16(a) and (b), the a: 3' boundaries are taken to have either a disordered or a glissile dislocation structure in order that they offer no barrier to either diffusional or martensitic growth. Figure 16(a) shows the concentration-penetration curve when sufficient time has elapsed for the carbon diffusion fields associated with the two ferrite plates to have overlapped; however, the concentration gradients in austenite have not yet been eliminated, and less than the metastable equilibrium proportion of ferrite is present. Figure 16(b) shows the concentration-penetration curve at a later time, when these gradients have been eliminated and the metastable equilibrium proportion of ferrite has precipitated. In both figures, the atom fraction


500

.,_, (.S0

,oc

~ 35C

3 0 (

0

I I I I I I I

~, "\\\

002 004 006 008 010 012 01(. MOLE FRACTION 0f CARBON IN AUSTENITE

(a)

i

J

~.00

350

T t

3OO

2S0

To' ", To Ae3" "".

o o~ o~8 0~z mole fraction C in austenlte

T~ To'' iTo Ae~ ',

39O

300~

0

mole fraction C in austenite

(b)

Fig. 1 5 - - ( a ) Carbon concentration in austenite during transformation stasis vs reaction temperature determined dilatometrically, as well as calculated To ("No Partitioning") and paraequilibrium 7 / ( a + 3') ("No Substitutional Partitioning") curves, p55j (b) F IM/AP data on carbon concentration in austenite in: (a) Fe-0.43 wt pct C-2.2 wt pct Si-2.8 wt pct Mn and (b) Fe-0.83 wt pct C-3.05 wt pct Si steels. 1991 (T~, Ae3 ' , Ae3" notation follows usage of Aaronson et al.1286]).

of carbon in austenite at the a : 7 boundaries, x ~ , is given by the paraequilibrium "y/(a + 7) phase boundary. In Figure 16(c), movement of the a : T boundaries is assumed to have been halted by the incomplete transformation phenomenon. Whether this stoppage is produced by exhaustion of growth ledges, jamming of a glissile dislocation interfacial structure, or an SDLE operating at either type of boundary, the resulting concentration- penetration curve is qualitatively the same. Note that

~" and x~ r have both been replaced by smaller atom X7 ~ and ~ and that the proportion of ferrite fractions, xrl x~,,

formed is smaller (though not drawn to scale). The post- transformation stasis reaction time is here taken to be long enough for the carbon diffusion fields associated with the two ferrite plates to have overlapped and for an effective average carbon concentration in austenite at a : 7 boundaries to have become applicable at the ledged boundaries. When the reaction time has been further extended to the point where the carbon concentration gradients in the remaining austenite have been eliminated while transformation stasis is still in effect, the situation represented by Figure 16(d) is obtained. Since the pro-

portion of ferrite has not been increased, the atom fraction of carbon in austenite in contact with the boundaries

w ~ Each of the three mecha- diminishes from xv~ to xv2. nisms for halting the movement of the a : 7 boundaries

~ and or However, will produce different values of xv2 x~2. calculation of these compositions is either not yet feasible or requires information (on ledge heights and interledge spacings) not readily obtained in steel. However, since Figures 16(c) and (d) should be qualitatively the same for all of these mechanisms, the claim of Bhadeshia and co-workers 197'99] that the mechanism through which the ferritic component of bainite was formed can be deduced from either data on the carbon concentration in austenite taken at random locations in the austenite, as they have done, or from complete concentration- penetration curves is clearly invalid.

3. Summary and critique of an SDLE theory This explanation for the incomplete transformation

phenomenon, and, more generally, for reduced and more complex overall transformation kinetics (Figure 9) and for the introduction of a bay in the T T T diagram, has undergone a number of changes since it was introduced


x~ ~

X 1

x~ ~

0~

x~ ~'

X 7

x,~ "t

(a) (b)

ya X,y1

X~,

x~ ~

B

B

m

7 (~

~

Xy2

Xy

ay X a

0t ~'

(c) (d)

0r

Fig. 16--Concentrat ion-penetrat ion through a ferrite/bainite plate and the surrounding austenite. (a) and (b) sketched in the absence of a growth barrier, (a) prior to achievement of metastable equilibrium and (b) after metastable equilibrium has been reached. (c) and (d) sketched in the presence of a growth barrier such as produces transformation stasis, (c) prior to elimination of carbon concentration gradients and (d) after these gradients have been removed.

in 1967. [z4zl* The present incarnation of the SDLE con-

*Hillert t2~) has also proposed an explanation of this general t y p e , and other investigators have alluded to such an effect (~67] when explaining slower than anticipated transformation kinetics not ascribed to interfacial structure effects.

cept is discussed in detail in a paper by Reynolds et al. [2~ in this issue. After summarizing the present status of this concept and its ramifications here, attention will be fo- cused upon some of the more important criticisms made of the SDLE and of our responses to them.

During the familiar solute drag effect upon grain growth, [268'269] when the binding energy of solute atoms to grain boundaries is sufficiently high relative to the operative driving force these boundaries are required to drag the solute atoms along with them as the boundaries migrate. The dragging process is tantamount to one involving volume diffusion. When an interphase boundary is migrating by diffusional processes during precipitation from solid solution, on the other hand, long-range volume diffusion must normally accompany such migration. Hence, solute dragging will perceptibly slow boundary migration kinetics only if the volume diffusiv-

ity controlling growth is several orders of magnitude higher than the volume diffusivity determining the kinetics of the solute dragging process. This difference in diffusivities can usually be achieved only in an alloy system in which the long-range diffusivity is interstitial and the dragging diffusivity is substitutional. The proeutectoid ferrite reaction in Fe-C-X alloys is the prototype of this type of diffusional transformation. When X markedly reduces the activity of carbon in austenite, segregation of X to a : 7 boundaries is to be expected, particularly in view of the high carbon concentration in austenite in contact with these boundaries. Comparison of experimentally measured growth kinetics in these alloys with the maximum distance X can diffuse during growth readily establishes that in the absence of growth stasis, X cannot volume diffuse to a : y boundaries. 127~ Hence, X must be swept up by these boundaries during growth, t27~ Thus, retardation of c~:y boundary growth kinetics is termed a solute drag-like effect, rather than simply a solute drag effect. It now appears that the concentration of X at the mobile areas of these boundaries is determined primarily by kinetic rather than by the usual thermodynamic factors tz~ and, hence, is very difficult to estimate a priori. However, as long as this solute


concentration has a nonequilibrium value,* the possibil-

*In view of the presence of paraequilibrium between austenite and ferrite under most circumstances of interest here, it seems nearly impossible for any level of X segregation to an a : y boundary to be in equilibrium with both bulk phases forming the boundary; a compromise non-equilibrium value with respect to both phases seems more likely.

ity arises that the activity of carbon in austenite in contact with the boundary will be markedly reduced by the presence of a suitable X element, thereby decreasing the driving force for growth. [L73'2421 When this activity reduction is sufficient to make the carbon activity in bulk austenite in contact with the a: 3' boundary the same as that of carbon far away from the boundary, i .e. , to produce a zero carbon activity gradient in austenite, growth stasis OCCURS. 11'19] Preferential adsorption of X at disordered areas of t~:7 boundaries should also reduce the boundary orientation dependence of growth prior to stasis so that the Widmanst~itten structure no longer develops. [~96] Only growth preferentially along grain boundaries (and for reasons unknown, also along twin boundaries) occurs when the SDLE is sufficiently strong. [19,29A93,196,222] Since the carbon concentration at the 7 / ( a + 7) phase boundary increases about linearly with decreasing temperature [87'27~] and entropic contri- butions tending to drive X away from the boundaries simultaneously decrease, strengthening of the SDLE with decreasing temperature is expected. [242]

Earlier, it was predicted that the bay would appear at that temperature at which a : 7 boundaries are saturated with X. ]11 As reviewed in Section IV-G, however, at least in Fe-C-Mo alloys, this does not appear to occur; enrichment of the boundaries appears to be only by a factor of 2 ]~~176 one must still be concerned that the FIM/AP measurements are presumably not being made at the risers of growth ledges and especially at kinks on these risers. In another paper in this issue, Reynolds et al. [2~ have therefore proposed a different explanation for the bay, based upon their TEM studies of the morphology of degenerate ferrite formed at temperatures just below that of the bay. This study demonstrated that the degenerate Widmanst~itten morphology is actually com- posed of large numbers of successively sympathetically nucleated ferrite crystals. The proposal was accordingly made that at the undercooling where the SDLE becomes

"yet sufficiently strong so that x~ (SDLE) (the averaged atom fraction of carbon in austenite in contact with ledged a: 7 boundaries in the presence of the SDLE) is far enough

74 below x v to create a sufficient driving force for ferrite nucleation, sympathetic nucleation [591 begins to occur to a significant extent at a:3, boundaries. This undercooling, which is usually appreciably greater than that needed to inhibit development of sideplates and intragranular plates, tends to maximize the driving force for critical nucleus formation by slowing down ledge motion to the point where the bulk composition of the alloy is approached over much of the area of the terraces. Hence, ferrite embryos forming on the terraces are less frequently overrun by succeeding ledges.

The swift acceleration of transformation kinetics below the bay temperature is partly due to the usual sharp temperature dependence of (sympathetic) nucleation kinet-

ics. However, the repeated renucleation of ferrite also provides repeated opportunities to escape the SDLE, since a finite amount of growth is evidently required to acquire the X concentration in the boundary needed to produce the SDLE of the strength characteristic of a particular reaction temperature and alloy composition. Incomplete transformation develops shortly after the increase in carbon concentration in the remaining austenite reduces the driving force for sympathetic nucleation to the level where this process is effectively halted. Provided that nucleation at austenite grain boundaries or at intragranular sites has ceased as the combined result of site saturation and diminished driving force, the SDLE is then able to complete termination of transformation by stopping further growth of the ferrite crystals already formed. If the reaction temperature is just below that of the bay, only a small increase in the carbon concentration in the remaining austenite is needed to prevent further sympathetic nucleation; hence, incomplete transformation begins at a low proportion of ferrite. With decreasing reaction temperature, however, the increased driving force for sympathetic nucleation requires more carbon enrichment in order to produce the same result, leading to formation of increasing proportion~ of ferrite prior to the onset of incomplete transformation. At any given reaction temperature, carbide precipitation at a: 7 boundaries termi- nates growth stasis, t2~ presumably by draining a significant proportion of the X in these boundaries and carbon in the adjacent austenite, thereby diminishing the SDLE. [19j

A number of objections have been raised to earlier versions of the SDLE. [23,26'272] Many have already been answered. [273] Here the most important criticisms are summarized together with our response to each.

Alloying elements which increase the activity of carbon in austenite, such a s S i [2741 and N i , [275'2761 produce a bay in the T T T diagram and incomplete transformation, thereby contradicting the SDLE theory. 14'23,74] In the ex- amples cited, however, the Si steel contained 0.30 wt pct Cr; Si-Cr interactions could be responsible for these effects. In the Fe-C-Ni alloys ]2771 noted, the bay arose in hypereutectoid steels and reflected replacement of proeutectoid carbide by bainite rather than a change in the kinetics of transformation products nucleated by ferrite both above and below the bay. In a related situation, Rao and Winchell t278] reported that the lengthening kinetics of bainite plates in Fe-C-10 at. pct Ni alloys were 100-fold slower than carbon diffusion kinetics in austenite would allow. This result has often been cited as evidence against the existence of an SDLE.[23,74.272] Sub- sequent recalculation of these lengthening rates using the Trivedi [~~ analysis of plate lengthening reduced this dis- crepancy to a factor of less than 5. [279] This difference was postulated to be caused by an increase in the average interledge spacing at the edges of bainite plates as a result of the presence of Ni. I2791 This mechanism was suggested because grain boundary ferrite allotriomorphs in Fe-C-Ni alloys thicken at essentially the rates predicted by carbon diffusion control under paraequilibrium conditions. [2701

No incomplete transformation or a bay in the T T T diagram was detected in either an Fe-0.11 pct C-1.83 pct Si or an Fe-0.38 pct C-1.73 pct Si alloy, t2~,2~4] No anom- alies were found in the morphology of ferrite or bainite


in these alloys. However, Papadimitriou and Genin [a181 have reported a bay in the TTT curve for the beginning of transformation and also incomplete transformation in an Fe-0.90 pct C-3.85 pct Si alloy of good purity. This alloy is also distinctly hypereutectoid.128~ Insufficient information is supplied to ascertain whether or not the explanation offered for the bay in Fe-C-Ni alloys is also applicable here. However, incompleteness of transformation, in the absence of carbides at higher temperatures and in their presence down to Ms, was established. The fraction of the austenite remaining untransformed is roughly 1.5 times that allowed by the paraequilibrium ~//(a + 7) phase boundary at the highest temperature at which incomplete transformation was observed. Inspec- tion of the micrographs published with this paper suggests that a combination of reduced sympathetic nucleation kinetics resulting from substantial enrichment of the remaining austenite and a low density of ledges on the ferrite plates present may have been responsible for premature cessation of transformation. Interestingly, the authors' micrographs show little indication of the heavily degenerate Widmanst~itten ferrite morphology characteristic of incomplete transformation in Fe-C-Mo, 12~ Fe-f-Cr, ~222[ and Fe-C-Mn 1211 alloys. Nonetheless, the results of Papadimitriou and Genin do represent a distinct chal- lenge to the SDLE theory of incomplete transformation and require further investigation.

Hultgren [226[ has provided good evidence for incomplete transformation in an Fe-C-Si-Mn alloy; Bhadeshia and Edmonds tl9~ may also have identified this phenomenon in an alloy containing higher proportions of Si and Mn. This result also has been claimed to disprove the SDLE theory, because Si raises the activity of C in austenite. [281J Liu et al. [214] suggested that Si may increase segregation of Mn to a : T boundaries and thereby en- courage stasis; inasmuch as Si and Mn exert opposite effects upon carbon activity in austenite, mutual repul- sion of these elements should not be unexpected. Al- though this proposal has been dismissed as "completely speculative,'[216[ Chen et a1.[254] have recently secured preliminary evidence in direct support of it.

The complaint has been made that the influence of carbide precipitation upon the occurrence of incomplete transformation was not considered, t2721 However, Shiflet e t a l . I2311 demonstrated that within the composition- temperature-time region within which Bradley and Aaronson I27~ reported alloWiomorph growth kinetics data supporting the SDLE theory, either very little or no carbide precipitation at a: T boundaries was observed. In another paper in this issue, Reynolds et al. [2~ demonstrate that transformation stasis occurs in an Fe-C-Mo alloy in the absence of interphase boundary carbide precipitation, and that stasis ends when such carbide precipitation begins. Finally, it should be pointed out that both theoretical [9~ and experimental t2281 studies support the original proposal that interphase boundary carbide precipitation can usually occur only on the immobile terraces of ledges I1971 and is only rarely feasible on mobile areas of interphase boundaries.J9~ The view that such precipitation can also take place on disordered a: T boundaries 1232,2331 has recently been challenged, as described in Section IV-E.

Field ion microscopy/atom probe analysis has been re-

peatedly claimed to demonstrate that the segregation to a : 'y boundaries required by the SDLE theory does not o c c u r . [26'97-991 In Section IV-G, the inadequacy and/or irrelevancy of the FIM/AP data cited in support of this claim are discussed. Recent FIM/AP measurements demonstrated Mo segregation at a : 7 boundaries in Fe- C-Mo alloys [1~176 exhibiting transformation stasis but not in an Fe-C-Mo alloy where stasis appeared to be absent.~253]

The claimed hindrance to growth by the SDLE was dismissed by calling attention to recent analyses of data on ferrite and bainite plate lengthening kinetics in plain carbon and alloy steels in which these kinetics were found to be much faster than volume diffusion control allows. [ll0"llll In Section I I -C-1, these analyses were shown to be inappropriate and also to have been misinterpreted. It is further noted here that the measurements analyzed are unlikely to have been made in connection with either stasis or prestasis phenomena or in the vicinity of a noticeable (or still deeper) bay in a TTT diagram. Under these conditions, ferrite/bainite plates are either absent or are severely degenerate. As summarized in Section IV- F, under these circumstances, one either makes growth kinetics measurements on grain boundary allotrio- m o r p h s - - o r not at all. The Fe-C-Si alloy studied by Papadimitrou and Genin I218[ is the one exception so far found to this generalization; it remains to be seen if diminished kinetics of ledge formation (or some other effect) is responsible for the premature cessation of transformation, as now appears to be the cause for too slow bainite plate lengthening kinetics in Fe-C-10 at. pct Ni a l l o y s . 1278'279[

The implication of the SDLE theory that ferrite- controlled transformation predominates above as well as below the kinetic Bs has been denied by both Bhadeshia t26[ and Christian and Edmonds. r231 Following the views of earlier investigators, as has been well summarized by Hehemann and Troiano, [6[ pearlite was taken to predominate above the kinetic Bs and bainite below; a demonstration of separate C-curves for these two reactions in a near-eutectoid Fe-C-Mn alloy [~81[* was noted in sup-

*As discussed in the paper by Spanos et at. 1171 in this issue, at least some of the nodular structures published for this alloy are probably nodular bainite, not pearlite.

port of this view by Christian and Edmonds./231 The evidence in favor of the precedence of ferrite both above and below the kinetic Bs in lower carbon alloy steels [2221 was not considered, even though some of it has long been available. It was also not recognized that in near- eutectoid steels, the sorting out of small amounts of ferrite allotriomorphs which were subsequently immersed in large volumes of eutectoid transformation product is virtually impossible. Nicholson t282[ thus used indirect evidence to prove that pearlite is nucleated predominantly by proeutectoid ferrite even in slightly hypereutectoid steels.

The series of micrographs published by Boswell et a / . [1961 o n Fe-C-Mo and Fe-C-Cr alloys and by Shiflet and Aaronson [t9j and by Reynolds et al. [2~ in this issue on Fe-C-Mo alloys should provide convincing evidence that the "classical picture" of pearlite predominating at temperatures above the bay and bainite at temperatures


below the bay is greatly in error in pronouncedly hypoeutectoid alloys and, on the above cited reasoning, is probably incorrect in near-eutectoid alloys as well. Hence, the simple explanation for the bay (that it is a natural result of the intersection of the transformation-start T T T curves for pearlite and bainite when the temperature ranges of these transformations are sufficiently separated by alloying element additions) should now be viewed with considerable reserve.

V. C ONFLICTS AMONG T H E THREE DEFINITIONS OF BAINITE

A. Introduction

The view that there are three incongruent definitions of bainite presently in use was first suggested in 1969. I11 However, except in a review published by Hehemann I4] in 1970, not until recently has much notice been taken of this view; considerable (largely unsupported) oppo- sition to it has now appeared. [23'26'19~ In this section, the main items of experimental evidence for the essential differences between the phenomena encompassed by these definitions will be summarized.

B. Surface Relief vs Generalized Microstructural Definitions of Bainite

(1) Widmanstiitten plates which produce an IPS relief effect when formed at a free surface are described as bainite even in alloys whose composition and reaction temperatures do not lie in the vicinity of the phase fields associated with a eutectoid reaction, e.g., al Cu-Zn, [421 al Ag-Cd, (431 and AuCu II. (441 (2) Widmanst~itten plates producing an IPS surface relief effect are often formed above the To in substitutional alloys, even though shear requires the absence of a composition change in such alloys, e.g., a Ti-Cr, ml a Ti-Fe, (841 a Ti-V, (841 "y A1Ag2, I491 o/l Cu-Zn, 1421 and og 1 Cu_Zn_AI.( 120] (3) Carbide-containing grain boundary allotriomorphs in plain carbon 0831 and alloy steels [1,198,2321 which are bainite on the generalized microstructural definition cannot be on the surface relief definition, since allotriomorphs do not appear tO produce IPS or even related surface reliefs. [2831 (4) Degenerate Widmanstiitten bainite in Fe-C-Mo alloys does not produce an IPS relief but instead only slightly rumples the specimen surface. 12~ (5) At a given reaction temperature in an Fe-C-Cr alloy, Widmanstiitten plates containing a nonlamellar carbide dispersion were replaced by grain boundary allotriomorphs, also containing carbides, merely by reducing markedly the austenite grain size. Ill (6) Carbides are often absent from Widmanstiitten ferrite and also from ferrite crystals configured (through sympathetic nucleation) in upper bainitic and even in lower bainitic morphological arrangements. 1196] (7) The B,, is in principle, the eutectoid temperature for the generalized microstructural definition, even if some competing eutectoid reaction, such as lamellar or rod pearlite, develops instead. The Ws temperature repre-

sents the surface relief B~. However, the W~ temperature tends to lie roughly parallel to the phase boundary of the proeutectoid phase involved t152'194'284! and thus intersects the eutectoid temperature (range) at but a single composition or over a narrow range of compositions.

C. Overall Reaction Kinetics vs Generalized Microstructural Definitions o f Bainite

It is useful to begin this section by noting that Christian and Edmonds, I23] adopting the Oblak-Hehemann tll61 view that a dense dislocation substructure in the ferritic component of upper bainite but not in Widmanstiitten ferrite marks the microstructural B, temperature, noted that this feature also characterizes the overall reaction kinetic Bs. However, Tsubakino and Aaronson [1931 measured dislocation density above and below the kinetic B, in an Fe- C-Mo alloy and found only a mild increase below this temperature. They pointed out that increased transformation kinetics and, hence, less time available for an- nealing out dislocations introduced by the volume strain energy associated with transformation from austenite to ferrite could account for both this effect and its temperature dependence. It should also be pointed out in this connection that the Fe-C-Mo microstructures presented in two other papers in this issue I19,2~ show neither upper bainite nor lower bainite sheaves at or near the kinetic Bs; instead, there is a transition from grain boundary ferrite allotriomorphs to highly degenerate Widmanstiitten ferrite. Hence, this example of congruence between these two definitions of bainite does not appear to be generally meaningful. The following items of evidence support the view that there are basic distinctions between these two definitions:

(1) The kinetic Bs, which corresponds to the temperature of the bay in the TTT diagram, or in the absence of a bay, to the lowest temperature at which the fraction of the austenite matrix transformed to bainite is zero, tends to lie I00 ~ to 300 ~ below the eutectoid temperature (the microstructurai B~) in steels. (2) Incomplete transformation has yet to be observed during the microstructural bainite reaction in any purely substitutional alloy system in which microstructural bainite forms. (3) Incomplete transformation is absent over an appreciable range of carbon and Mo concentrations in Fe-C- Mo alloys I2~ and also in some Fe-C-Mn, Fe-C-Ni, Fe-C-Si, and Fe-C-Cu alloys, t2q However, the microstructural bainite reaction is present in all of these alloys. [20.21] (4) In an Fe-C-Mo alloy studied in detail by Reynolds et al.,t2~ carbide precipitation in association with ferrite formed below the kinetic Bs did not begin until transformation stasis came to an end. Hence, incomplete transformation is exhibited by what the microstructural definition terms (degenerate) Widmanst~tten ferrite, rather than bainite. Similar sequences are appearing in other alloy steels J 21~ (5) In Fe-C-Mo rIg] and Fe-C-Cr [236[ alloys, interphase boundary carbides, which are associated with grain boundary bainite allotriomorphs on the generalized microstructural definition, form at temperatures high above that of the kinetic B,.


D. Surface Relief vs Overall Reaction Kinetics Definitions of Bainite

(1) The surface relief Bs, corresponding to the highest temperature at which plate-shaped crystals of the product phase producing an invariant plane strain surface relief effect can form, usually lies high above the kinetic Bs in Fe-C-X alloys. I213,221,222,2361 (2) In appreciably alloyed Fe-C-Mo tl96j and Fe-C-Cr t'96,2z2~ steels, "surface relief bainite" disappears somewhere below the upper nose in the TTT diagram and does not reappear until an appreciable temperature interval below the kinetic B~, presumably at the temperature at which the ferritic component of bainite forms sufficiently regular plates to yield reliefs detectable with optical interference microscopy. It is important to recognize that neither allotriomorphs formed above and just below the kinetic Bs nor degenerate ferrite formed further below this temperature produce detectable IPS or IPS-related reliefs.t20j (3) Surface relief bainite forms in any alloy system which produces precipitate plates. Except in steel, there is no evidence in any of these systems for the phenomena described by the overall reaction kinetics definition of bainite.

VI. SUMMARY

The three principal definitions of bainite now in use are further considered, mainly upon the basis of experimental information and interpretations thereof which have recently become available. In present form, these definitions are the following. On the surface relief definition, bainite consists of precipitate plates which produce an IPS relief effect when formed at a free surface and are therefore considered to grow by a shear or martensitic mechanism. The unit atomic process is the glide of atoms across the advancing interphase boundaries in closely coordinated and sequenced fashion. The generalized microstructural definition currently describes bainite as the diffusional, noncooperative, I1641 and competitive ledgewise formation of the two precipitate phases formed during eutectoid decomposition, t168~ The unit atomic process is the thermally activated diffusional jumping of individual atoms across interphase boundaries in the style of biased random walk. However, transfer across interphase boundaries is limited by the details of the operative ledge mechanism. The overall reaction kinetics definition confines bainite to a temperature region 100 ~ to 300 ~ below the eutectoid temperature. Transfor- mation to bainite is increasingly incomplete as the upper limit of the bainite C-curve on a TTT diagram is approached; this limit is termed the kinetic Bs temperature. Bainite defined in this manner is often considered to form by shear.

In respect of the surface relief definition of bainite, Wayman TM has made clear that all requirements of the PTMC must be met, in a self-consistent manner, in order that a transformation product can be considered to have formed by shear. Particularly among ferrite and bainite plates formed during the decomposition of austenite, vi- olations of one or more of these formal requirements often occur. Additionally, three important derivative require-

ments must also all be satisfied by the product of a shear transformation. These include the absence of a change in the proportion of substitutionally dissolved solutes, the absence of a change in long-range order (particularly in substitutional alloys), and the presence of an interphase boundary structure capable of supporting growth by a shear mechanism. Four model phase transformations in substitutional alloys, which are surface relief bainite on the basis of satisfaction of the formal requirements of the PTMC, are shown not to take place by shear when these derivative requirements are applied. The formation of bainite and ferrite in steel by shear is similarly ruled out, but the growth of/3 VH0.45 plates by shear cum hydrogen diffusion t5~ remains an open, though questionable possibility. The surface relief definition of bainite thus increasingly appears to represent a serious misreading of experimental realities. Recognition that IPS surface reliefs can be produced by the diffusion-limited movement of ledges 128'49'52'72,731 and that an interphase boundary containing an invariant line of a transformation tlSa,~55j can represent the boundary orientation at which the kinetics of ledge generation are a minimum t221 is increasingly making possible accounting for fulfillment of the formal crystallographic requirements of the PTMC entirely through the ledge mechanism of diffusional growth.

The key to the present view of the generalized microstructural definition of bainite is that partial coherency is the predominant structure of interphase boundaries during diffusional growth. E7~,151,2381 Simple modifications of a treatment by Hillert t~691 have shown that (assuming initially that the equilibrium proportions of both eutectoid phases are continuously present) unless the ratio of the ledge height to the average interledge spacing at the precipitate: matrix boundaries of both eutectoid phases is the same, the phase whose ratio is larger will grow more rapidly and thus almost inevitably cut off the slower growing eutectoid phase from further access to the matrix phase. I'681 Hence, the slower growing phase will have to be renucleated repeatedly at the interphase boundaries of the faster growing phase, ljrst

Recent research has made substantial changes in the experimental phenomenology of overall reaction kinetics bainite. While the absence of incomplete transformation above the kinetic Bs has been confirmed by quantitative optical metallography in Fe-C-Mo alloys, 1~9~ the presence of this phenomenon below the kinetic Bs has been shown not to be general. In Fe-C-Mo alloys, for example, critical proportions of carbon and Mo must be exceeded in order that incomplete transformation may develop, t2~ Also in these alloys, intervals of transformation stasis are terminated by carbide precipitation at ~ : y boundaries, and the bainite reaction then re- sumes. ~2~ Evidently, termination of incomplete transformation by the pearlite reaction is not the fundamental process through which this occurs. Overall reaction kinetics which produce incomplete transformation exhibit three different kinetic behaviors in succession, of which the middle one represents cessation of reaction. With decreasing temperature below that of the kinetic Bs or with decreasing percent C and/or percent Mo, these kinetics are successively replaced by three-stage behavior, in which the middle stage has slow but finite


kinetics, by two-stage behavior, and finally, by single- stage Johnson-Mehl-type t2851 overall reaction kinetics, t2~

Between the upper nose in the TTT curve for beginning of transformation and the kinetic B~ in Fe-C-Mo and Fe-C-Cr alloys, particularly when there is a deep bay in the TTT curve, Widmanst~itten plates are largely eliminated and replaced by grain boundary and twin boundary allotriomorphs, t19,2~ Especially in Fe-C-Mo alloys, pearlite is not observed in this temperature range, t19,2~31 Below the kinetic Bs, these morphologies are swiftly replaced by highly degenerate ferrite sideplates and intragranular plates, t19,193,1961 With decreasing temperature, the average level of degeneracy is gradually reduced. [193,1961 Marked changes in carbide distribution and morphology accompany these changes in morphology of ferrite.

Above the kinetic Bs, up to four different types of thickening behavior of grain boundary allotriomorphs are observed in Fe-C-Mo alloys, t~91 paralleling those of overall reaction kinetics behavior below the kinetic Bs. I2~ Allotriomorphs formed just below kinetic B~ exhibit two different forms of two-stage behavior, t2~ However, the predominance of degenerate ferrite below the kinetic B~, inability to measure the growth kinetics of this complex morphology, and the circumstance that it is this morphology which ceases to grow during transformation stasis have so far prevented direct correlation between growth kinetics and overall reaction kinetics.

Although a fair amount of data on the composition of a: y boundaries has been acquired, particularly with the field ion microscope/atom probe, use of complex steels and/or inadequate experimental technique prevents application of these data to experimental evaluation of the SDLE hypothesis I1,19,2~ for the incomplete transformation phenomenon. Recently, two sets of more reliable data indicate that about twofold enrichment of these boundaries occurs during transformation stasis in Fe-C- Mo alloys. I1~176 Further development of the SDLE hypothesis is considerably handicapped by inability to acquire information on the thermodynamic properties of the mobile areas of a: y boundaries.

The extensive conflicts among the three definitions of bainite are reviewed and are demonstrated again to be major and very serious. Attempts to deny the existence of these conflicts are easily refuted or are of little value, because these denials are largely undocumented.

The overall reaction kinetics definition of bainite is clearly insufficiently general to warrant definitional status. m However, the set of special phenomena which it encompasses is of considerable scientific and technolog- ical importance and is certainly worth substantial further research efforts. On the other hand, the surface relief definition of bainite should finally be discarded, m

ACKNOWLEDGMENTS

The following sponsorships of the preparation of this review are gratefully acknowledged: HIA--AFOSR Grant No. AFOSR84-0303; GJS - - Department of Energy Grant No. DE-FG0585ER45 18 1; WTR, Jr. --Materials Engineering Department of Virginia Polytechnic Institute and State University; and GS- -Nava l Research Laboratory.

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Documents

Bainite viewed three different ways