Computer simulation of microstructure
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I.
INTRODUCTION
IT is often the case that the most important consequence of a martensitic transformation is the complex microstructure that results from it. It is, therefore, important to understand how these microstructures develop. To do so, it is necessary to understand the elastic strains that are produced as the transformation proceeds. A martensitic transformation t~,2,31 is a spontaneous, mechanical distortion of the parent lattice that ordinarily induces a substantial local elastic strain. The elastic energy associated with that strain decreases the net thermodynamic driving force for the transformation. The martensite phase grows in a pattern that keeps the elastic strain energy at a tolerable level. Several topological mechanisms can be used to minimize the elastic strain. They appear naturally in martensitic transformations. These involve the shape and habit of the martensite, its crystallographic variant, and its nucleation site. The elastic energy of a coherent inclusion is ordinarily minimized if the inclusion has the shape of a thin plate parallel to the crystallographic plane that minimizes the strain within the inclusion, t41 For that reason, elastic martensites tend to grow as thin plates or thin, lens-shaped particles. A typical martensitic transformation also offers several distinct crystallographic variants that differ in the orientation of the crystallographic axes of the product phase and, hence, in the principal axes of the transformation strain. If the parent matrix is locally stressed (as it always is once a martensitic transformation has begun), PING XU, Research Assistant and Ph.D. Candidate, and J.W. MORRIS, Jr., Professor of Metallurgy, are with the Center for Advanced Materials, Lawrence Berkeley Laboratory, and the Department of Materials Science and Mineral Engineering, University of California-Berkeley, Berkeley, CA 94720. Manuscript submitted March 16, 1992. METALLURGICAL TRANSACTIONS A
then the possible crystallographic variants have different elastic energies. The variant that is most effective in relaxing the local stress is preferred. This effect often leads to microstructures that are complex mixtures of several crystallographic variants whose transformation strains compensate one another. When the transformation strain is suitable, the individual martensitic plates may be composite particles in which compensating variants alternate. The twinned martensite found in carbon steel is the classic example. The bulk of the theoretical work that addresses the microstructure of martensite concerns the shape, habit, and internal state of isolated martensite plates. Two approaches have been useful. The older is the "crystallographic theory" of Wechsler et al. ,[51 which predicts the preferred twin fraction and crystallographic habit of a thin plate of twinned martensite. The method identifies an undistorted "invariant plane" of the transformation on which the martensite and matrix structures fit without distortion, so that a martensite plate parallel to this plane is nearly strain-f
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