Institute of Metals Division - On the Theory of the Formation of Martensite

A 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. THIS paper presents a new theory of the formation of martensite. This theory makes possible the calculation of the austenite planes on which the 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 the austenite and martensite. He predicted substantially the observed lattice relationship and habit plane for certain steels which have a (225) habit. Geisler12 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 distortion