Martensite Formation

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O n the Theory of the Formation of Martensiteby M. S. Wechsler, D. S. Lieberman, and T. A. ReadA theoretical analysis of the austenite-martensite transformation is presented which predicts the habit plane, orientation relationships, and macroscopic distortions from a knowledge only of the crystal structures of the initial and final phases.

HIS a new of the formaTtion paper presentsaustenitetheorymakeswhich the of martensite. This theory possible the calculation of the planes on martensite plates form, the orientation relationship between the austenite and martensite crystal axes, and the macroscopic distortions which are observed. The only input data needed are the crystal structures and lattice parameters of the austenite and martensite. Considerable effort has been devoted over the past thirty years to the development of an understanding of the crystallographic features of martensite reactions. Much of this work has been done on steels and iron-nickel alloys, for which a great deal of data has been accumulated concerning the shape and orientation of the martensite plates, the relative orientations of the austenite and martensite crystal axes, and the observable distortions which result from transformation. These observations are reviewed in refs. 1, 2, and 3. The first major step toward an understanding of these phenomena was made in 1924 by Bain,' who showed that the a body-centered cubic structure can be produced from the 7 face-centered cubic structure by a contraction of about 17 pct in the direction of one of the austenite cube axes and an expansion of 12 pct in all directions perpendicular to it. Since that time, most of the efforts at further interpretation have been made by investigators who have worked from the phenomenological data, incorporating some of the information from the lattice properties, and have sought an analysis into likely deformations which would produce the observed results."-"11 but the three most recent papers on the subject have already been reviewed in some detail." Machlin and Cohenl0 measured the components of the distortion matrix and verified that the habit plane is a plane of zero distortion and rotation for the (259) case. They showed that the measured distortion matrix, when applied to the parent lattice, does not yield the product lattice and hence some inhomogeneous distortion must occur. Frank,u working from the lattice properties and taking some clues from the observations, considered the correspondence of close-packed rows and planes in theM . 5. WECHSLER, D. S. LIEBERMAN, and T. A. READ, Member AIME, are associated with the Dept. of Metallurgy, School of Mines, Columbia University, New York. Discussion on this paper, TP 3632E. may be sent, 2 copies, to AIME by Jan. 1, 1954. Manuscript, April 20, 1953. Cleveland Meeting, October 1953. This paper is based on a thesis by M . S. Wechsler submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy to the Faculty of Pure Science, Columbia University. TRANSACTIONS AlME

austenite and martensite. He predicted substantially the observed lattice relationship and habit plane for certain steels which have a (225) habit. Geisler" suggested that there is a natural tendency for the habit plane to be a (111) and postulated certain slip processes to account for the fact that the experimentally observed habit plane is irrational and deviates from the assumed one. The present work differs from previous treatments of martensite formation in that it permits calculation of all the major manifestations of the process. Habit plane indices, orientation relationships, and observable distortions are all calculated from a knowledge of the crystal structures of the initial and final phases alone. The calculations contain no adjustable parameters. The agreement found between calculated results and the observations reported in the literature constitutes powerful evidence in favor of the mechanism of martensite formation proposed. The theory is applicable to systems other than steel (as is discussed later in this paper) which exhibit a diffusionless phase change but because of the wide-spread interest in the austenite-martensite transformation, particular attention will be given to the iron-base alloys. For other systems which undergo a similar face-centered cubic to face-centered tetragonal transformation, the mathematical treatment is identical with that presented here. Hence the theory successfully describes the transformation in the indium-thallium alloy.'"Homogeneous Transformation to Martensite The distortion which any homogeneously transforming volume of austenite undergoes in order to become martensite is shown in Fig. 1, as was first suggested by Bain.' (This distortion will hereafter be referred to as the "Bain distortion.") This specification of a contraction along one cube axis ;ombined with an expansion in all directions perpendicular to this axis describes what is properly called the "pure" distortion associated with this transformation. The distinction between a "pure" and an "impure" distortion plays an important part in the discussion which follows. A "pure" distortion is characterized by the existence of at least one set of orthogonal axes fixed in the body which are not rotated by the distortion. (These are called the "principal axes" of the distortion.) No such set of axes exists in the case of an "impure" distortion. On the other hand, an impure distortion can always be represented as the result of a pure distortion combined with the rotation of the specimen as a rigid body. For a given impure distortion the corresponding pure distortionNOVEMBER 1953, JOURNAL OF METALS-1503

Fig. 1-(A) Body-centered tetragonal cell delineated in face-centered cubic structure. The Bain distortion takes (8) into (C).

and rigid body rotation are unique." It is to be par* More precisely, there are two combinations of pure distortion and rotation, one of which corresponds to a distortion followed by a rotation and the other to a rotation followed by a distortion. In this discussion it is simpler to use the formulation where the distortion is considered to occur first.-

stretched is the one which had come from one of the original face-centered cubic cube axes, then the combination of Bain distortion followed by twinning simply gives the Bain distortion over again, with a different choice of axes. If, however, the body-centered cubic cube axis which is stretched during twinning is one which before transformation was a face-centered cubic face diagonal direction, then the total increase in length in this direction produced by the Bain distortion followed by twinning is 59 pct. This is to be compared with a maximum extension of 12 pct which is produced by the Bain distortion alone. The discussion above brings out the fact that the Bain distortion produces a body-centered cubic structure from a face-centered cubic one by means of much less drastic changes in interatomic distances than any other distortion which accomplishes the same change in structure. Another illuminating way of comparing alternate distortions is by considering nearest neighbor relationships for the atoms in the two crystal structures. In the face-centered cubic structure each atom has twelve nearest neighbors, whereas in the body-centered cubic structure it has only eight. After the Bain distortion, each atom's eight nearest neighbors are eight of the twelve it had previously had when the crystal structure was face-centered cubic. In contrast with this, the next simplest distortion leads to the result that two of the nearest neighbors of each atom in the body-centered cubic crystal had been only nextnearest neighbors before transformation. There are, therefore, strong physical grounds for concluding that the Bain distortion is the pure distortion which describes what actually happens in any small region which transforms homogeneously from austenite to martensite. A complete description requires in addition, of course, a specification of the rigid body rotation of the region.Mechanism of Martensite Formation

titularly noted that these statements are not re-

stricted in validity to the small distortions and rotations dealt with by elasticity theory. The distortion which occurs during the complete transformation of an austenite single crystal to martensite is both impure and inhomogeneous. But if the transformation of sufficiently small volumes of austenite, still large compared with the unit cell, is considered, the distortion of these, while still impure, will be homogeneous (otherwise X-ray diffraction patterns could not reveal the martensite structure). The distortion specified by Bain gives this homogeneous pure distortion of a small volume of material, without saying anything about the rigid body rotation which accompanies it. It is particularly to be noted that while many distortions will generate a body-centered cubic (or body-centered tetragonal) structure from a facecentered cubic one, the Bain distortion involves considerably less distortion than any of the others. Any distortion which converts a face-centered cubic lattice into a body-centered cubic one can be represented as the Bain distortion followed by a distortion which carries the body-centered cubic lattice into another body-centered cubic lattice with the same lattice parameter. The smallest of these additional distortions is the one involved in the familiar mechanical twinning of the body-centered cubic lattice. In this case, the maximum extension is in the direction of one of the cube axes of the bodycentered cubic structure. If the cube axis which is1504-JOURNAL

Several investigators have shown that the distortion which occurs as martensite is formed is inhomogeneous even within a single martensite plate. The most complete study of this aspect of martensite formation was carried out by Machlin and Cohen,'" who demons