The phenomenological theory of martensite crystallography: Interrelationships
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I.
INTRODUCTION
IN one of the most classical metallurgical articles of the century, tll Bain published "The Nature of Martensite" in 1924. Some 70 years later, this article still provides fascinating reading about its crystallography, morphology, kinetics, and mechanical properties. Indeed, on the subject at hand here, it may be said that Bain laid some crucial cornerstones of the presently accepted phenomenological theory of martensite crystallography (PTMC). This theory became fully developed, more or less, in the 1950s, following much intervening work of increasing degrees of sophistication and definitiveness. Today, "the Bain strain" is common knowledge, even outside metallurgical circles. It is the purpose of the present article to review the development and assess the validity of the PTMC. As other articles from this conference will suggest, the theory may transcend its original intent, and an important aspect of the theory, the invariant line strain, is coming into closer scrutiny. II.
THE LATTICE CORRESPONDENCE
All martensitic transformations involve a correspondence by means of which lattice points in the parent phase are uniquely related on a one-by-one basis to those in the product (martensite). The original proposal by Bain tll is drawn to scale and copied from the original paper. Bain's correspondence relates the body-centered tetragonal (bct) cell (heavy lines) within two unit face-centered cubic (fcc) cells to the body-centered cubic (bcc) unit cell of a-iron. A simple upsetting of the former produces the bcc lattice (it was then thought that martensite was C.M. WAYMAN, Professor, is with the Department of Materials Science and Engineering, University of Illinois, Urbana, IL 61801. This article is based on a presentation made at the Pacific Rim Conference on the "Roles of Shear and Diffusion in the Formation of Plate-Shaped Transformation Products," held December 18-22, 1992, in Kona, Hawaii, under the auspices of ASM INTERNATIONAL's Phase Transformations Committee.
METALLURGICAL AND MATERIALS TRANSACTIONS A
cubic a-iron). This contraction along the c-axis and expansion along the a axis is almost obvious from inspection, but there are many possible fcc-bcc correspondences, another case in point given in Figure 2. Jaswon and Wheelert21 considered many such correspondences between the two lattices and showed mathematically that of all considered, Bain's correspondence involved the smallest principal strains. For this, and other reasons as well, the Bain strain has gained universal acceptance as a model for the fcc-bcc transformations; and even in other alloy systems involving different crystal structures and correspondences, the pure strain effecting the structural change is most frequently referred to as the Bain strain. Bain argued in favor of his distortion by further noting that "there are also extensions and compressions locally developed as shown by the roughening of a polished surface of austenite (fcc parent) after martensitization is brought about by cooling to liquid-air temperatures".
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