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The isothermal decomposition of austenite in the bainite region 1949

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THE ISOTHERMAL DECOMPOSITION OF AUSTENITE IN THE BAINITE REGION by David William Morgan A thesis submitted i n par t ia l fulfilment of the requirements for the degree of MASTER OF APPLIED SCIENCE i n the department of MINING AND METALLURGY The University of B r i t i s h Columbia A p r i l , 1949 ABSTRACT The isothermal decomposition of austenite i n the bainite region has been examined. The progress of the transformation i n several hypoeuteetoid and eutectoid steels was investigated metallographically from a qualitative point of view. A survey: was made of the information available on the i n i t i a t i o n , course, and end product of the transformation. The factors entering into the transformation were examined separately, their temperature-dependence and interactions investigated. A theory of the decom- position of austenite was proposed, and this theory examined i n the l igh t of the phenomena associated with the isothermal and anisothermal progress of the trans- formation. INEEX i I INTRODUCTION. • . .• 1 I I EXPERIMENTAL METHODS 3 I I I DISCUSSION (a) The Isothermal Transformation of Austenite i n the Bainite Region. 5 (b) The Stear Mechanism of Bainite Formation. . . 12 (c) L a t t i c e Coherency 12 d) The E f f e c t s of Residual Stresses 14 e) Behaviour of the Carbon. . . . . . . . . . . 13 (f) The Extension of F e r r i t e Regions Without Shear. 17 (g) The Energy Change i n Bainite Formation . . . 19 (h) Nucleatiom 20 ( i ) Growth * 22 (j) The Process of Reaction i n the Upper Temperature Region 24 (k) The Process of Reaction i n the Lower Temperature Region 2j? (1) E f f e c t of Grain Size 26 (m) Anisothermal Behaviour . . . . . 27 IY SUMMAHr. 32 Y ACKNOWLEDGEMENTS 36 VI BIBLIOGRAPHY 37 THE ISOTHERMAL DECOMPOSITION OF AUSTENITE IN THE BAINITE REGION I ~ INTRODUCTION Although there has been a great deal of information published on the theory of the demomposition of austenite i n the bainite region, and many theories have been advanced to explain d i f f e r e n t phenomena associated with t h i s decomposition, there has been no recent summary of the available knowledge i n t h i s f i e l d . The object of the present i n v e s t i g a t i o n i s to bring together and correlate the e x i s t i n g data, with a view to a s s i s t i n g i n providing a better understanding of the mechanism of the reaction. The nature of the transformation of austenite i n the bainite region renders i t s study p a r t i c u l a r l y d i f f i c u l t . Two interdependent mechanisms of transformation are av a i l a b l e ; (a) p r e c i p i t a t i o n and growth by d i f f u s i o n , and (b) phase change by • martensitic shear. Since both are temperature-dependent., the complications of the transformation are reduced i f the process i s carried out isothermally rather than during continuous cooling. As some of the factors involved,- such as va r i a t i o n i n carbon concentration on a micro scale, and 2 dis t r ibut ion of internal stress, may not be d i rec t ly observed, their importance must be deduced from the observable phenomena and results associated with the reactions occurring during transformation and other reactions of a s imilar nature. This res t r i c t ion prevents the quantitative evaluation of the rate and course of the transformation from basic principles but, from a knowledge of the reaction behaviour at different tempe- • ratures of transformation, the relat ive importance of the different factors may be estimated. In this investigation the different reactions have been examined individual ly from a thermodynamic and kinet ic viewpoint. Their variat ion with temperature has been indicated. The interaction between the individual reactions has been inves- tigated and a theory proposed, for the decomposition process. This theory has been applied to the experimental data available. Where the terms bainite and fer r i te are used i n many places interchangeably throughout this report, bainite generally i s taken to refer to the l ab i l e aggregate of carbide plus fer r i te (possibly supersaturated with carbom), and fe r r i t e to refer to the body-centered cubic form of i ron , whether supersat- urated with carbon or not, and whether formed by shear or by a diffusive growth. 3 II «. TJiYPgRiMENTAIi METHODS The structures of a number of low-alloy hypo:-eutectoid and eutectold steels have been examined microscopically a f t e r having been p a r t i a l l y transformed isothermally at various tempe- ratures i n the ba i n i t e region. The i n i t i a l stages of isothermal transformation have been investigated i n a series of steels with 0.55% Carbon, with and without 0.3,5% Molybdenum and with varying N i c k e l content. The preparation of these a l l o y s has been, described elsewhere 1)* A s i m i l a r series with higher carbon analysis (up to 0.80 weight percent), was investigated i n the region of ba i n i t e formation. Various low-alloy commercial steels have been examined to varying extents. The specimens were prepared as f l a t discs approximately 0.0.5 inches thick. A wire was attached to each to f a c i l i t a t e handling during heat treatment. The specimens were austenitized f o r 15 minutes at 1600° P. i n a neutral s a l t bath, quenched t o , and held f o r a measured time at, the isothermal transformation temperature i n a s a l t bath, and immediately brine-quenched to room temperature. The treated specimens were ground on emery to remove any possible surface effects and to prepare f o r p o l i s h i n g The specimens were polished e l e c t r o l y t i e a l l y using a mixture of perchloric and acetic aoids, 18^ ml. perchloric aoid, s p e c i f i c gravity 1 . 6 l gm./e.c, 165 ml. acetic a c i d , 10 ml. water, with some aluminum introduced into the s o l u t i o n 2 ) . The p r i n c i p a l ©tenant used was 2% n i t al<. containing 1% Zephiran Chloride.* This preparation of the specimen to be examined was found to produce a highly-detailed undisturbed surface. Structures shown i n the accompagnyimg micrographs were obtained by tre a t i n g commercial SAB 1 0 8 0 s t e e l containing 0 . 7 5 % Carbon* The micrographs were taken using an oil-immersion objective of N.A. 1 . J 5 2 . In i n t e r p r e t i n g these micrographs i t should be noted that the magnifications are s u f f i c i e n t l y large that the observed structure i n the f i e l d shown may not be t r u l y representative of the degree of transformation throughout the specimen. In the following discussion, the r e s u l t s of t h i s metallographic i n v e s t i g a t i o n are given together with a survey of the published r e s u l t s of other investigations. Leading references have been given f o r r e s u l t s drawn from the l i t e r a t u r e . In some oases references have been c i t e d f o r evidence supporting the results of t h i s i n v e s t i g a t i o n . 8 $ aqueous solution, d i s t r i b u t e d by Winthrop Chemical Company, Inc., New York, N.Y. 5 I H - DISCUSSION (a) The Isothermal Transformation of Austenite i n the Bainite Region. . In the early stages of formation, bainite oceurs as lamellae nucleated on the grain boundaries^) ( F i g . I ) . These lamellae consist of f e r r i t e , possibly supersaturated with]: carbon at lower temperatures^ -), and carbide p a r t i c l e s , p r e c i p i - tated, on the f e r r i t e - a u s t e n i t e interface i n the early stages^). Svidence has been given that the habit plane of the bainite i n r e l a t i o n to the parent austenite changes with temperature of transformation^), and that the orientation of the f e r r i t e i n bainite i s independent of temperature of formation^), being the same as proeutectoid f e r r i t e . The cementite i s i n a f i n e state of dispersion, X-ray l i n e i n t e n s i t i e s being considered comparable with those of tempered martensite^). The r e s u l t s of magneto- metric investigations have been interpreted to indicate that i n a l l o y s t e e l s , the carbides tend to be closer to the simpler Fe^G composition as the temperature of transformation i s lower!9). During transformation i n the upper temperature regions the lamellae when i n i t i a l l y formed are i r r e g u l a r , often occuring i n groups of lamellae with s i m i l a r orientation ( F i g . X). These lamellae grow as bloeky formations (Fig. IX) or, sometimes, i n lens shapes which are more concave at higher temperatures (Fig. I I I ) . Nucleation apparently stops soon a f t e r the i n i t i a l period, and the lamellae agglomerate by side-growth. The transformation at high temperatures goes to completion by the agglomeration of e x i s t i n g plates followed by the extension of regions so formed, r e s u l t i n g i n an aggregate of f e r r i t e and cementite. Bainite formed i n the lower temperature range i s f i n e r i n structure, l e s s i r r e g u l a r i n cross-section, and more uniform (Tig. 17). As the temperature of transformation i s lowered the tendency of the lamellae of the same orienta t i o n to group together becomes less apparent^) ( F i g . 17). The decompo- s i t i o n of the austenite i n the lower range goes to completion by the formation of new lamellae, apparently nucleated by e x i s t i n g plates. Analysis of the o v e r - a l l transformation r a t e s 7 ) has shown a progress from three-dimensional towards two-dimensional growth as the temperature of isothermal transformation i s lowered. There i s ev idence3»8) that carbon enrichment of the untransformed austenite occurs with the formation of b a i n i t e . This has "been shown to be thermodynamically l i k e l y ? ) . The enrichment of the austenite by carbon from the ba i n i t e i s oountered by carbon depletion during carbide formation 1^). Figure I SAE 1080, pa r t i a l ly transformed isothermally at 700° F. 2000x. Electropolished. Etched i n 2% n i t a l with Zephiran Chloride. The two micrographs above show the appearance of the i n i t i a l high-temperature bainite formation. The bainite i s i n groups of irregular similarly-oriented lamBllae. The grain-boundary or igin of the bainite may heisbe observed. Figure I I SAE 1080, pa r t i a l ly transformed isothermally at 800° F. 2000 x . Electropolished. Etched i n 2% n i t a l with Zephiran Chloride. This micrograph shows an extreme form of high-temperature bainite. The growth i s acicular , but the rate of agglomeration of the lamellae by sidewise growth i s rapid, therefore only the advancing edges of the plates i n a group are separate. This specimen was cooled to the isothermal trans- formation temperature slowly enough to permit the formation of some nodular pear l i te . Figure I I I SAE 1080, pa r t i a l ly transformed isothermally at 600° F . 2000 x . Electropolished. Etched im 2% n i t a l with Zephiran Chloride. These micrographs i l l u s t r a t e the intermediate-temperature bainite growth. Pa ra l l e l lamellae occur i n groups i n the early stages. The lamellae thicken as they grow, often becoming lens-ehaped as i l l u s t r a t ed . Few new bainite plates appear i n the la ter stages of growth, the transformation going to completion by agglomeration. (a) <b) Figure 17 SAE 1080, pa r t i a l ly transformed isothermally at (a) 4J?0° F . , and (b) 500° F. 2000 x. Electropolished. Etched i n 2% n i t a l with Zephiran Chloride. Low-temperature bainite i s finer and more regular than that formed at higher temperatures. The tendency for para l le l lamellae to occur i n groups i s less , as i s here shown. New plates are formed throughout the course of the reaction. 11 Figure V SAE 1080, pa r t i a l ly transformed isothermally at 700° F . 2000 x . Electropolished. Etched i n 2% n i t a l with Zephiran Chioride. The above structure follows a grain boundary. The irregular agglomerated structure with associated lamellae i s typical of the high-temperature reaction i n the early stages of growth. 12 (b) The Shear Mechanism of Bainite Formation. From crystallographic.and s t r u c t u r a l considerations bai n i t e i s generally considered to be formed, i n the early stages at l e a s t , by a l a t t i c e shearing process, comparable to martensite formation. Such a mechanism i s to be expected at temperatures where the s e l f - d i f f u s i o n rate of the i r o n i s low; the shear process requires only a small movement of atoms from the positions i n the parent phase to the positions i n the new phase, and hence w i l l take place e a s i l y 1 1 ) . The formation of b a i n i t e takes place as a time-dependent growth process, as opposed to martensite formation, which, disregarding r e l a x a t i o n e f f e c t s , is.;essentially independent of time. Martensite f o r - mation i n t h i s respect, resembles mechanical t w i n n i n g 1 2 ) . Since bainite formation i s a shear-type reaction, i t w i l l produce res i d u a l shear stresses. Also, since the s p e c i f i c volume of bainite i s greater than that of austenite, shear stresses aire set up by the formation of b a i n i t e because of t h i s increase i n volume. The r e l a t i o n - s h i p of b a i n i t e to the parent austenite i s such that coherency of the l a t t i c e s at the interfaces may exist i f the bainite i s compressed and/or the austenite stretched within l i m i t s outlined i n the subsequent discussion. (c) L a t t i c e Coherency. The problem of forced l a t t i c e coherency has been investigated i n the case of preeipitatiom of lamellar structures from s o l i d s o l u t i o n 1 ? ) . The reasoning and r e s u l t s may be applied to b a i n i t e formation to y i e l d a rough estimate of the 13 maximum size of bainite which may be coherent with the parent austenite* The plate thickness increases u n t i l the s t r a i n energy i s equal to that required f o r the formation of a disordered i n t e r f a c e . This thickness i s of the order of 100/d atom diameters, where ! d ! i s the percentage m i s f i t between the two l a t t i c e s on the interface plane. In addition to the assump- tions used i n reference 13),(namely: that the material i s i s o t r o p i c ; that a l l the s t r a i n i s taken up i n the p r e c i p i t a t e ; that the e l a s t i c equations of a continuous medium may be applied; that Hooked Law w i l l hold over the large s t r a i n s involved), we have neglected i n our application the eff e c t of the shear stresses associated with bainite formation and the e f f e c t , probably not small, of carbon i n s o l u t i o n i n the b a i n i t e . Coherent Interface Disordered Interface This estimate i s s u f f i c i e n t to ind- i c a t e , however, that coherency w i l l be probable only i n those regions wherein the austenite s t r a i n i s less restricted^as at the grain, boundaries, and near the advancing edge of a bainite plate. We may expect the advancing edge i t s e l f to be coherent with the austenite, since the movement of an atom from i t s p o s i t i o n i n the austenite to i t s p o s i t i o n i n the bainite i s small enough (approximately 1/3 of the interatomic distance) that Figure VI 14 l o c a l d i s t o r t i o n w i l l take up the discontinuity without breaking coherency. A graphical representation of the s t r a i n s produced near the growing edge of a bainite plate because of l a t t i c e coherency i s given i n Figure VI. (d) The E f f e c t s of Residual Stresses. Assuming a badnite plate to have formed, the shear . stresses thereby produced w i l l oppose a s i m i l a r shear reaction with the same orienta^on,, and a s s i s t shear reactions i n other 14\ s p e c i f i e d complementary d i r e c t i o n s / . Considering Figure VII, i f the bainite arises from a shear i n the d i r e c t i o n of the dotted arrows i t w i l l produce shear stresses i n the matrix as shown by the f u l l arrows. Since the shear may occur i n one d i r e c t i o n o n l y 1 ^ ) , the residual stresses act so as to oppose, any bainite formation Figure VII of s i m i l a r o r i e n t a t i o n . There are, however, i n any c r y s t a l of austenite several planes and directions along which the bainite formation may take place, and therefore tJae shear stresses may a s s i s t the formation of bainite along a d i f f e r e n t d i r e c t i o n . The formation of bainite of such a comple- 15 mentary orientation would serve as a means of relax a t i o n f o r the stresses set up by the f i r s t plate. Also, the stresses produced by a foreign p a r t i c l e or phase i n a matrix are strongest near the p a r t i c l e , as may be deduced from the phenomenon of dispersed p r e c i p i t a t e . The fact that p a r a l l e l plates do not form so r e a d i l y at lower temperatures can be accounted f o r by t h i s process of reasoning. (e) Behaviour of the Carbon. I t i s considered that during the formation of b a i n i t e whole groups of atoms may move simultaneously from the old to the new phase, entrapping the carbon atoms9). This method of growth i s to be expected, where possible, since the growth rate i s f a s t e r and the a c t i v a t i o n energy i s lower than f o r an ordered i n d i v i d u a l d i f f u s i o n 1 ^ ) . I t does not, however, exclude the advancement of the bainite by a proaess of growth wherein the carbon i s not trapped, but diffuses away or prec i p i t a t e s as carbide. higher rate of d i f f u s i o n i n the bainite than i n the austenite. Taking a c t i v a t i o n energies of 18,000 oal/mol f o r carbon i n f e r r i t e 1 ^ ) , and 3>2,000 cal/mol f o r carbon i n a u s t e n i t e ! 7 ) , and the average time between basic acts of d i f f u s i o n as being given s t r e s s - r e l i e f by agglomeration i n a l l o y s having a highly- Any carbon atoms entrapped i n bainite w i l l have a approximately by h N e' H/TR h - Planck 1s constant H - a c t i v a t i o n energy t - fo r a d i f f u s i o n movement N - Avogadro*s number R - gas constant T - temperature 16 we may oalculate that at a temperature of 400° C. a carbon atom i n f e r r i t e i s l i k e l y to have about 10,000 times as many ohanges of p o s i t i o n i n any given time as a carbon atom i n austenite. This unbalance of d i f f u s i o n rates, coupled with the large free energy change of carbon between austenite and f e r r i t e w i l l r e s u l t i n a rapid increase i n carbon concentration i n the austenite adjacent to a newly-formed block of b a i n i t e . There i s considerable s t r a i n i n the l a t t i e e near the i n t e r f a c e , and i f the b a i n i t e has l o s t coherency with the austenite we may expect a high m o b i l i t y of d i f f u s i n g atoms at the interface 1**). The heat of reaction w i l l a s s i s t a higher l o c a l m o b i l i t y . Such conditions promote rapid nucleation of carbide, and hence w i l l tend to p r e c i p i t a t e the carbide i n a very f i n e form. The f i n e size of the carbide w i l l r e s u l t i n i t having a lower a l l o y content than the equilibrium conditions at that temperature require, as has been observed and f u l l y discussed 1?). That the carbide of the simple Fe^C structure should p r e c i p i t a t e i n preference to a more complex a l l o y carbide may also be deduced from consideration of the r e l a t i v e p r o b a b i l i t i e s of forming . c r i t i c a l size n u c l e i of the a l t e r n a t i v e carbides. The problem of carbide p r e c i p i t a t i o n i s rendered more complex by the i n e q u a l i t i e s of concentration, that i s , i f by d i f f u s i o n from a region of r a p i d l y formed b a i n i t e p a high- carbon region i s formed, under the conditions of rapid nucleation outlined above most of the n u c l e i w i l l be of c r i t i c a l or near- e r i t i c a l s i z e f o r that concentration of carbon. The concentration of carbon i n the region where the carbides are precipitated i s 17 reduced by d i f f u s i o n towards the unreacted austenite, which i s of lower carbon content, and by p r e c i p i t a t i o n onto the carbides* Wow, as the carbon concentration i s reduced, the c r i t i c a l s i z e of the carbide nucleus, below which the nucleus i s unstable, increases. At temperatures of rapid d i f f u s i o n , i t i s qiuite conceivable that the c r i t i c a l s i z e of nucleus could increase at a greater rate than the increase in. size by growth of the carbids p a r t i c l e s present, and so could exceed the size of many of these, rendering them unstable. The unstable carbides would then redissolve. The r e s u l t would be an increased carbon con- centration i n the unreacted austenite. The carbide p a r t i c l e s remaining a f t e r the carbon con- centration has become more uniform continue to grow i n a normal fashion. The growth of carbides implies a reduction i n the carbon concentration of the surrounding austenite. This process acts simultaneously with the carbon-enrichment by bainite f o r - mation. At any one temperature of reaction, whether or not the unreacted austenite i s enriched or depleted with regard to carbon w i l l depend upon the r e l a t i v e rates of the bainite and the carbide reactions.i One may expect that carbon-enrichment w i l l occur when the bainite reaction i s more rapid, depletion when slower. This i s indicated experimentally8,10). (f) The Extension of f e r r i t e Regions Without Shear. I f an a u s t e n i t e - f e r r i t e interface i s considered a f t e r i t has l o s t coherency, i t may be seen that i n d i v i d u a l i r o n atoms could jump from positions i n the austenite to more stable positions 18 i n the f e r r i t e without increasing the shear stresses associated with the shear mechanism of ba i n i t e formation. Such a method of phase growth has been shown to be dependent upon the d i f f u s i o n rate of carbon away from the i n t e r f a c e 9 ) . As a r e s u l t of the concentration gradient caused by bainite formation, d i f f u s i o n may increase the carbon concentration i n the unreacted austenite. The amount of the enrichment w i l l be influenced by the degree of carbide p r e c i p i t a t i o n . Therefore three factors w i l l l a r g e l y control the rate of transformation of austenite to f e r r i t e i n t h i s manner: the carbon concentration i n the austenite remote from the interface, the a c t i v a t i o n energy of i r o n transfering across the inte r f a c e , and the d i f f u s i o n rate of carbon. The carbon concentration i s dependent upon the degree of transform.-*- ation, increasing i n the upper bainite range, showing l i t t l e change at lower temperatures.' The temperature-dependence of the rate of growth at t r i b u t a b l e to the i r o n and carbon a c t i v a t i o n requirements w i l l be of the' form ezp(-A/RT), where A i s propor- t i o n a l to the a c t i v a t i o n energies. Since the carbon d i f f u s i o n rate i s the predominant.factor i n such a r e a c t i o n 9 ) , the rate of growth w i l l decrease approximately exponentially with temperature.. Growth i n t h i s manner w i l l f a c i l i t a t e the segregation of any a l l o y i n g elements, those such as n i c k e l and manganese which have lower free energy when dissolved i n austenite tending to diffuse away from the boundary so as to stay i n the austenite, and those elements such as chromium which have lower free energy when dissolved i n f e r r i t e tending to enter the b a i n i t e . Such segregation has been advanced as an explanation f o r the abnormally 19 long times f o r completion of transformation i n the upper bainite region i n c e r t a i n a l l o y s t e e l s ^ ) . (g) The Energy Change i n Bainite Formation. A phase change i s possible only i f the free energy i s decreased by the reaction. Considering bainite formed by shear, with entrapped carbon, four factors determine the free energy changer, the free energy change of the i r o n i n going from the face- centered structure to the body-centered, dG|,Q; the difference i n free energy between carbon i n a face-centered cubic l a t t i c e , and carbon i n the body-centered cubic l a t t i c e dG^; the change i n entropy of the carbon, dS; and the change in. s t r a i n energy assoc- iated with the transformation, dU. This may he written a s 9 ) : dG = dGpe • CdGc - CTdS * dU. ' C - carbon concentration T - temperature There i s no need to consider surface energy i f the l a t t i c e s are assumed coherent at the time of transformation. In any transformation there i s a c e r t a i n a c t i v a t i o n energy which controls the rate of reaction. Tor martensitic- shear reactions with small movements t h i s i s i n s i g n i f i c a n t , however, and may be neglected. Thus assuming that the transformation w i l l occur when- ever the free energy change i s negative, we w i l l examine the factors involved to account f o r the time-dependence of the bainite reaction. dGj,Q, dG c, and dS are independent of time, but C, the carbon concentration, and dU, the s t r a i n energy change, w i l l 20 fluctuate w i t l i time and with the degree of transformation. The carbon concentration w i l l fluctuate by chance d i f f u s i o n , by the effect .of nearby bainite formation, by p r e c i p i t a t i o n of carbides as described, and by variations i n i n t e r n a l stress conditions. References 1 8 , 2 0 , 2 1 ) . The i n t e r n a l stress w i l l be very high under the i n i t i a l effect of quenching, and w i l l be raised by bainite transformation. I t w i l l r elax at an appreciable rate i n the temperature range of bainite formation. The rel a x a t i o n rate i s temperature dependent exponentially, of the form exp(-B/T), where B i s dependent upon the amount of i n t e r n a l stress. I f we consider a single bainite plate growing edgewise by shear, we may see that the rate w i l l be r e s t r i c t e d by the relaxation rate of the opposing residual stresses. As the tempe- rature of transformation i s lowered the decrease i n free energy by the change of i r o n from the face-centered cubic to the body- centred cubic form increases r a p i d l y , p a r t i a l l y o f f s e t t i n g the decrease i n the relaxation rate of the i n h i b i t i n g stresses. (h) Nucleation. Metallographic examination has shown that bainite tends to nucleate p r e f e r e n t i a l l y on the grai n boundaries?> 2 2). This i s supported by the examination of proeutectoid f e r r i t e , which has a cl o s e l y - r e l a t e d mode of formation, and which, because of i t s l e s s e r tendency towards lamellar growth, shows more c l e a r l y i t s region of nucleation. There i s evidence that nucleation and growth of b a i n i t e are greatly assisted by p l a s t i c f l o w 2 ? ) . Nucleation of bainite i n the grain boundaries i s to be expected. 21 The contribution to the s t r a i n energy by volume change i s smaller at the grain boundaries 1^). Amongst the disordered material there i s a higher p r o b a b i l i t y of f i n d i n g s i t e s p a r t i c - u l a r l y suited to n u c l e a t i o n 2 ^ ) . Regions having a favourable i n t e r n a l stress f o r nucleation may be expected because of the constraining e f f e c t of the grain boundaries, the v a r i a t i o n i n i n t e r n a l stress being p a r t i c u l a r l y great during the t<ime when quenching stresses are operative. Conditions of p l a s t i c flow produce both a large number of nucleation s i t e s and a wide v a r i a t i o n i n i n t e r n a l s t ress. Better defined evidence of the e f f e c t of stress conditions i s found i n the ease of transfor- mation below the M g l i n e 2 - ? ) . Here, bain i t e nucleates on the martensite needles, the transformation proceeding more quickly adjacent to the martensite than i n the untransformed matrix. From t h i s evidence i t would be expected that grain s i z e would greatly a f f e c t the number of s i t e s of possible nucleation. In general, the p r o b a b i l i t y that a preferred s i t e of nucleation w i l l transform into a nucleus i s dependent i n some manner upon the degree of transformation i n the surrounding m a t e r i a l 2 ^ ) . In the bainite transformation the p r o b a b i l i t y i s affected by three f a c t o r s . F i r s t l y , when the s t e e l i s quenched to the transfor- mation temperature the stresses produced by the quenching w i l l promote nucleation where they are, by chance, so oriented as to a s s i s t the bainite shear on any plane under consideration. This factor w i l l be e f f e c t i v e only at the beginning of transformation. Secondly, any increase i n carbon concentration caused by previous bainite formation w i l l i n h i b i t nucleation. This factor w i l l be 22 of greater importance at higher temperatures, and w i l l be dependent upon the amount of bainite and precipitated carbide near to the nucleation s i t e . Thirdly, stresses set up by the previous formation of bainite w i l l i n h i b i t nucleation of bainite of a s i m i l a r o r i e n t a t i o n , as described, but may a s s i s t nucleation of bainite of a complementary o r i e n t a t i o n 1 * * 2 ^ ) . The effect of t h i s l a s t factor w i l l increase with the amount of transformation. I t w i l l have i t s greatest effect i n the same regions, those near to previously formed lamellae, i n which the carbon-enrichment factor w i l l be strongest, but since stress relaxation decreases with temperature, the stress factor w i l l increase with decreasing temperature. From these considerations i t may be seen that the rate of formation of n u c l e i w i l l be very high i n i t i a l l y , but w i l l decrease r a p i d l y , the rate of decrease being l e s s at lower temperatures, f u r t h e r , the rate of nucleation w i l l be affected by a change i n the number of s i t e s of possible nucleation, as by a change im the amount of grain boundary material. Direct observation of nucleation rates of bainite i s not p r a c t i c a l , but i t i s to be noted that at higher temperatures the reaction tends to go to completion by agglomeration, whereas at lower temperatures i t progresses by the formation of new lamellae throughout the reaction period. ( i ) Growth. The isothermal transformation of austenite i n the bainite region must be considered to take place by twocdifferent processes,; one martensitic i n nature, the other d i f f u s i v e . The 23 former i s strongly affected by the rate of stress r e l a x a t i o n , and both are affected by the behaviour of the carbon. The martensitic-type reaction i s nucleated on the grain, boundaries. During growth i t creates high residual stresses which i n h i b i t the growth of s i m i l a r l y - o r i e n t e d lamellae, and promote growth along c e r t a i n other planes. The edgewise rate of growth i s high, favouring continued extension i n the same plane. The stress conditions may be expected to be analogous to those set up by martensite formation, and i t may thus be assumed that the rate of transformation through shear i s i n t h i s way controlled by the rate of stress relaxation. A re l a t i o n s h i p has been sug- gested between the induction period of bainite and the creep strength of the austenite27). The formation of bainite causes rapid carbon p r e c i p i t a t i o n and i f the temperature i s i n the up- per range raises the carbon concentration of the unreacted aus- t e n i t e . This increase i n carbon i n h i b i t s the transformation?). The d i f f u s i o n reaction may be considered as the addition of single atoms of ir o n to a nucleus of f e r r i t e across a disrupted interface. The rate of a reaction dependent upon d i f f u s i o n has been shown.to decrease exponentially with temperature. At any one temperature of reaction the rate of transformation of auste- n i t e by t h i s process w i l l depend upon the area of f e r r i t e - a u s t e - n i t e interface. The f l a t plates formed by the shear reaction provide a large interface area, and so i t i s evident that the amount of transformation by diffusion, increases r a p i d l y as the amount of sheared product increases. I 24 (j) The Process of Reaction i n the Upper Temperature Region, At higher temperatures the rate of d i f f u s i o n and the rate of stress relaxation are greater. The change i n free energy of the i r o n i n going from the austenite to the f e r r i t e i s l e s s , and carbon enrichment of the unreacted austenite i s more l i k e l y . Afeer the i n i t i a l quenching stresses have relaxed the v a r i a t i o n i n stress conditions i n the material w i l l be very l i m i t e d , since relaxation i s rapid. For t h i s reason sheared b a i n i t e i s i n i t i a t e d upon quenching which, since the stress conditions promoting nuc- l e a t i o n w i l l often p r e v a i l over . distances of a si z e comparable to grain r a d i i , w i l l tend to form i n groups of p a r a l l e l lamellae. Any plate w i t h i n such a group w i l l not i n h i b i t independent growth of adjacent plates by reason of residual stresses,except when very close toggther^because of the rapid r e l a x a t i o n rate. As indicated under Nucleation, page 20, the number of nu c l e i formed a f t e r the i n i t i a l stages w i l l be very l i m i t e d . The plates w i l l extend edgewise hy a continued shear action and sidewise by a di f f u s i o n reaction. The edgewise growth w i l l stop at such discon- t i n u i t i e s as grain boundaries, Figure I . The amount of austenite transformed by sidewise growth increases as the a u s t e n i t e - f e r r i t e Interface area increases by the shear reaction, and decreases as the interface area i s decreased by the decrease of unreacted austenite, fhe rate of growth sidewise decreases as the carbon content of the austenite i s increased by reaction The type of growth curve indicated by t h i s process i s i n accordance with those observed7). 25 (k) The Process of Reaction i n the Lower Temperature Region. At lower temperatures d i f f u s i o n and r e l a x a t i o n rates are lower. The free energy change of the iron transformation i s greater, and le s s carbon enrichment of the austenite i s l i k e l y . Because of increased free energy change the shear re- action i s more l i k e l y to occur, and larger blocks of atoms may be expected to transform at one time, r e s u l t i n g i n greater en- trapment of carbon*). The stresses set up w i l l be larger as the temperature i s lower since the relaxation rate i s lower, and there higher stresses w i l l i n h i b i t nearby growth of a s i m i l a r orientation, thereby both reducing the tendency to form .groups of s i m i l a r lamellae, and a s s i s t i n g growth of a complementary nature, which acts to r e l i e v e the stress, r e s u l t i n g i n a cr i s s - c r o s s pattern. Sidewise growth i s l i m i t e d ; the thermal energy being lower, the d i f f u s i o n reaction w i l l be i n h i b i t e d by i t s activationi. energy. Sidewise growth by shear i s i n h i b i t e d by the contrary r e s i d u a l stress. The edgewise growth i s such as to tend to keep the plates f l a t • The growth rate curve w i l l be ofatwo-dimensional nature, as has been experimentally indicated*?). This theory of growth explains s a t i s f a c t o r i l y the struc- tures observed metallographically during the isothermal transform- ation of austenite: i n the upper temperature range i r r e g u l a r coarse b a i n i t e , showing groups of p a r a l l e l lamellae (Figs. I , I I I ) tending to thicken as they grow, transforming only p a r t i a l l y by formation of plates, and completing transformation by a thickening, d i f f u s i v e process; as the temperature of transformation i s lowered the bainite becomes more regular, f i n e , s i m i l a r l y - o r i e n - 26 -.r.ted lamellae are leas l i k e l y to occur i n groups (F i g . IT), reaction proceding to completion by the continued formation of new plates. (1) Effect of Grain Size. The effect of grain-size variance on the behaviour of the transformation 2 2* 28) i s i n agreement with the proposed theory of decomposition. Grain size i n the lower range has no appreci- able e f f e c t , in. the upper range has very l i t t l e e f fect on the i n i t i a l stages of transformation but tends to accelerate the l a t e r stages of transformation. The lamellar structure of bain- i t e i s better defined when formed i n austenite of large grain s i z e 2 0 * ) . The number of nu c l e i which grow w i l l be determined by the stress conditions.- set up by t h e i r growth, not by the number of possible s i t e s of nucleation. Therefore, although more s i t e s may be activated during the i n i t i a l stage before the quenching stresses have been relaxed, many of these w i l l become inoperative because of the growth of nearby plates, and the growth rate of a l l plates w i l l be reduced i f the density of lamellae i s greater. The o v e r a l l transformation by shear w i l l also be retarded by the constraining action of the grain boundaries 2?)• Some more n o t i - ceable acceleration of the transformation occurs towards the £pper temperatures 2^). The 1% transformation time i s not appreci- ably altered, since the products appearing up to that stage are nearly a l l sheared, but that f o r 99% transformation i s reduced, since the sheared products are spread out over more grain boundary area, and hence give a greater a u s t e n i t e - f e r r i t e interface area., 27 allowing more rapid transformation by the d i f f u s i o n mechanism. (m) Anisothermal Behaviour, Much useful information may be gained from a study of the effect of p a r t i a l transformation at one temperature on the transformation at a d i f f e r e n t temperature level22»?°»?!). P a r t i a l transformation to f e r r i t e (less than 1%) accelerates beyond additivity?~subsequent bainite formation {!%). I t i s indicated that holding a f i x e d time i n the f e r r i t e range a c c e l - erates formation of bainite by a percentage which i s independ- ent of the temperature at which the bainite forms? 0). Considering temperatures above and below the nose of the f e r r i t e nC* curve when the f e r r i t e transformation i s d i s t i n c t from the bainite transformation, holding at a higher temperature i n the f e r r i t e region has a greater effect than holding at a lower temperature f o r which the time f o r 1% transformation i s the same. An explanation of t h i s has been put f o r t h ? 0 ) i n terms of nucleation. Because, as has been shown, the transformation to bainite. i s l e s s controlled by the number of n u c l e i than by the stress conditions, i t i s f e l t that t h i s evidence should be discussed with regard to carbon behaviour and stress conditions*. The proeutectoid f e r r i t e reaction may be considered as an ext- ended bainite reaction i n which the carbon migrates away from X A reaction i s considered additive for a given amount of trans- formation i f that amount of transformation oecurs when the t o t a l f r a c t i o n a l time integrated over the various temperatures of the reaction i s equal to one, where the f r a c t i o n a l time at a temperature i s defined as the actual time at the temperature divided by the time necessary at that temperature to produce the given amount of transformation. 28 the fer r i te into the austenite. Because of the relationship of the fer r i te to the austenite some stress w i l l arise from volume expansion and possibly from shear formation of f e r r i t e . Consid- er .a. fraction of 1% transformation at three temperatures, two i n the fe r r i te region, at. a higher and lower temperature where the time for 1% transformation i s the same, and one i n the bain- . i t e region. ThB:, structures w i l l be comparable i n that they consist of fe r r i te having a similarly-determined orientation with regard to the parent austenite. The bainite w i l l have associated with i t residual stresses, some entrapped carbon and a carbon-enriched region surrounding i t containing precipitated carbides. The fe r r i te w i l l have associated residual stresses, much smaller, and less at the higher temperature, few prec ip i - tated carbides, and a carbon concentration i n the surrounding austenite much less above that of the remainder of the matrix, since diffusion rates are higher i n the fe r r i t e range. When the fer r i te i s produced at the upper temperature there w i l l be least local ized increase In carbon. From this i t may be seen that, i f austenite, pa r t i a l ly transformed to fer r i te i s quenched into the bainite range we may consider the fer r i te as baini te , without the high associated stresses and l o c a l increase i n carbon concai- t rat ion, and hence the reaction w i l l go to 1% i n a time less than that required by isothermal transformation at the bainite temperature alone. Pa r t i a l bainite formation (less than 1%) accelerates subsequent fer r i te formation (lf») but the effect i s less than that corresponding to a d d i t i v i t y ^ 0 ) . This i s explained i n the 29 preceding paragraph, since the stresses and carbon enrichment associated with the bainite w i l l reduce the rate of fe r r i te formation u n t i l the stresses are relaxed and the carbon d i f - fused, away at the higher temperature. Pa r t i a l bainite reaction at a higher temperature retards subsequent transformation at a lower temperature, and vice versa. . The effect i s more noticeable i n higher-carbon s t ee l? 0 ) . This effect i s . sa t i s fac tor i ly explained by the be*-. haviour of the carbon? 0). At higher temperatures the austenite adjacent to a bainite plate i s enriched with carbon and so retards the bainite formation at ,a lower temperature, where such enrichment i s not so great. Transformation at a lower temperature leaves less carbon nearby and so accelerates the transformation at a higher temperature. The differences i n residual stresses i n the temperature range for which data i s available, are of less importance than the carbon effect, ,as i s evidenced by the larger variat ion with steel of higher carbon content. Holding i n the carbide range apparently retards s l igh t ly the subsequent formation of ba in i t e? 0 *? 1 ) . This has been explained as carbide nucleating at severe discontinuit ies and so rendering them unavailable for bainite nucleation? 0 ) . While this might be a contributing effect i t must be noted also that the precipitaion of carbides w i l l harden the matrix,as ini age hardening, and so make the shear reaction more d i f f i c u l t . A relationship has been suggested between the strength of the austenite and i t s s t a b i l i t y i n the lower transformation range?2). 30 Some data has been advanced30) on the ef f e c t of p a r t i a l transformation on subsequent cementite p r e c i p i t a t i o n . The data, given indicate that holding i n the bainite range f o r moderate fr a c t i o n s of the time necessary f o r 1% bainite to form retards the subsequent carbide p r e c i p i t a t i o n , while holding f o r shorter times accelerates the p r e c i p i t a t i o n . The l a t t e r e f f e c t appears more predominant with holding at a lower temperature i n the bainite range. The retarding effect of moderate quantities of bainite has been explained3°) by the u t i l i z a t i o n of nucle- ation s i t e s by the b a i n i t e , reducing the number available f o r cementite nucleation. To explain why cementite was not nucle- ated on the cementite p a r t i c l e s precipitated i n conjunction with the*; b a i n i t e , the p o s s i b i l i t y of d i f f e r i n g orientations of bain- i t l c and proeutectoid cementite was advanced. Since there i s no experimental evidence concerning the o r i e n t a t i o n of the cementite t h i s must he considered as a p o s s i b i l i t y because of the different modes of formation. Accepting the depletion of nucleation s i t e s by b a i n i t e , the effect of the carbides already present may be considered i n the l i g h t of the mechanism of growth here advanced. When the bainite i s formed, the carbon content i s increased i n the adjacent region. Carbides are then precipitated at the interface, some of which at higher temperatures may redissolve. The remaining carbides w i l l grow and cause a carbon depletion of the surrounding austenite, allowing the growth of the bainite near them. In t h i s manner the cementite, o r i g i n a l l y on the a u s t e n i t e - f e r r i t e interface, w i l l become surrounded by f e r r i t e . This process w i l l occur more rapi d l y at higher temperatures. 31 The cementite p a r t i c l e s surrounded by f e r r i t e may be thought of as being made inactive as nucleation s i t e s by the envel- oping f e r r i t e . This provides an explanation of the accelera- t i o n of subsequent cementite by short periods of holding i n the bainite region, f o r , although the bainite w i l l remove some s i t e s of possible nucleation, i t w i l l provide many others i f the time of reaction i s not long enough to permit envelopment of the precipitated carbides. This effect i s expected to be more n o t i - ceable at lower temperatures where the enveloping growth i s much slower... In t h i s regard i t must be noted that the number of carbides precipitated i n the i n i t i a l stages of bainite formation i s much greater than the number subsequently precipitated at the growing edges of the b a i n i t e . The accelerating effect of the quenching stresses w i l l allow the effect of I n i t i a l b ainite form- ation by shear to predominate over the effect of the growing edges of b a i n i t e , since the amount of carbon entrapped (and hence the number of carbides precipitated at the interface') w i l l be greater when the stresses promoting the shear are l a r g e r . As the i n t e r n a l stress becomes: l e s s controlled by the quench and more by the bainite formation the fluctuations i n carbon may be expected to a s s i s t i n the reaction, that i s , the bainite w i l l form i n a region when the cafbon concentration i n that region fluctuates towards lower values. The formation of bainite under these conditions w i l l tend l e s s to cause adjaeent regions of increased carbon concentration conduiiive to rapid oarbide p r e c i p i t a t i o n . 22 17 - SUMMARY The i n i t i a t i o n and course of the isothermal decom- posi t i o n of austenite i n the ba i n i t e region has been i n v e s t i - gated, and a theory proposed to account f o r the observed phenomena associated, with t h i s transformation.. In the bainite region decomposition may take place by two mechanisms, (a) p r e c i p i t a t i o n and growth by d i f f u s i o n , and (b) phase change by martensitic shear. Since the shear reaction sets up residual stresses i n the surrounding auste- n i t e and entraps carbon atoms, the free energy change of a region of austenite transforming to bainite by shear i s of the form dG = dGjpe f CdGQ CTdS t dU where ^-^je * s * n e f r e e energy change of the i r o n i n going from the f . c c . structure to the b.c.c. dG c i s the difference i n free energy between carbon i n the f.c.c. l a t t i c e and carbon i n the b.c.c. l a t t i c e . C i s the carbon concentration T i s the temperature dS i s the change i n entropy of the carbon dU i s the s t r a i n energy associated with the transformation The s t r a i n energy dU i s such as to i n h i b i t further transformation by shear along planes of s i m i l a r o r i e n t a t i o n i n the same aus- teni t e grain, and to a s s i s t transformation' by shear along planes of certain complementary orientations. Since the a c t i v a t i o n energy of martensite-like reactions i s n e g l i g i b l e , the extension _o£ A growing edge of a bainite plate by shear i s assumed to occur 33 whenever the free energy of the adjacent austenite i n the d i r - ection of growth may be reduced by the reaction, At any temp- erature, dGj,Q, dGg, and dS are independent of time, but C and dU are functions of the time and the progress of the transfor- mation. dU I n i t i a l l y varies widely throughout the specimen because of quenching, i s relaxed at a rate dependent upon the temperature, and i s increased by the shear transformation. The progress of the shear reaction i s thereby dependent upon the rate of stress relaxation. The carbon concentraion w i l l f l uc - tuate with time by chance diffusion and by variations i n in ter- nal stress conditions, w i l l be increased by diffusion of carbon entrapped i n bainite and decreased by precipi tat ion of carbon as carbide. / l a t t i c e coherency between bainite and the parent aus- tenite i s improbable except near the advancing edge of a bainite plate. After the formation by shear of a region of baini te , carbon w i l l diffuse out of the bainite into the surrounding austenite, l oca l ly enriching the austenite and precipi tat ing highly-dispersed carbides at the disordered austenite-bainite interface. The carbon-enrichment w i l l be greater at higher temperatures. The decomposition of austenite i n addition takes place through the growth of fer r i te regions by diffusion of individual iron atoms from austenite to f e r r i t e . Such a reaction has an associated activation energy, and i t s rate of reaction i s rest- r ic ted by the rate of diffusion of carbon away from the austenite- 34 fe r r i te interface. The rate of transformation of austenite by this means i s proportional to the area of austenite-ferrite interface, and hence i s highly dependent upon the amount of previously-formed sheared product. Bainite i s nucleated on the grain boundaries. The quenching stresses promote rapid i n i t i a l nucleation. The shear reaction sets up inh ib i t ing residual stress conditions which res t r i c t the growth rate and number of operative nucle i . The decomposition «Sf austenite i n the bainite region begins as a shear transformation. The lamellae formed by shear grow edgewise by continued shear u n t i l obstructed, as by grain boundaries, and sidewise by a diffusive process which causes them to agglomerate. The rate of the diffusive process decreases more rapidly with temperature than does the rate of the shear process.. At higher temperatures the decomposition of austentjebe i s i n i t i a l l y by shear, but goes to completion by the diffusive reaction. At lower temperatures the decomposition progresses by the continued formation of new lamellae throughout the reac- t ion period. The internal stresses set up by the shear trans- formation i n l i b i t the growth of s imi la r ly orieh^ited lamellae, which as the temperature i s lowered and hence relaxation rate i s decreased, reduces the tendency of para l le l plates of bainite to occur i n groups, as i s to be expected from the effect of internal stress on nucleation. A decrease i n grain size accelerates the la ter stages of the decompesition of austenite i n the upper bainite region, but has a negligible effect i n the lower regions because the 35 rate of growth by shear i s determined by the i n t e r n a l stress, not by the number of n u c l e i . ,The larger area of grain bound- ary provides a larger a u s t e n i t e - f e r r i t e interface area, accel- erating the decomposition by. the d i f f u s i v e process, which i s predominant i n the l a t e r stages of decomposition i n the upper bainite range. The proposed theory has been applied to account f o r the effects i n the early stages of transformation observed with anisothermal transformation procedures. ?6 V - ACKNOWLEDGEMENTS The author i s grateful to Mr. F. A. Forward, Head of the Department of Mining and Metallurgy for his consideration and interest, and to Associate Professor W. M. Armstrong for his c r i t i c i sm and generous encouragement during the past year. 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