Interaction energy between martensitic variants
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I. INTRODUCTION
SOLID-TO-SOLID phase transformations such as forming precipitates or martensitic transformation alter the local stress state both inside the transformed phase (the inclusion) and in the surrounding parent phase (the matrix) if an eigenstrain is associated with the phase transformation. The change in the stress state and the resulting change in the strain energy play an important role in the thermodynamics of the phase transformation in solids.[1] The stress state strongly influences the transformation kinetics as well as the microstructure of the evolving composite.[2] For a proper thermodynamic description, it is essential in many cases to perform a stress analysis, because the local stress acts as a mechanical driving force, whereas the constraint imposed by the surrounding matrix on the deformation due to the transformation strain yields a dragging force.[2–6] The analytic solutions for the stress analysis available apply mainly to purely elastic materials. The solution given by Eshelby is appropriate for problems that can be described by a single ellipsoidal inclusion in an infinitely large elastic matrix.[7,8] Several researchers investigating the stress-assisted martensitic transformation use either the Mori–Tanaka[9–13] method or the self-consistent approach to determine the strain energy associated with the phase transformation.[14] In the elastic-plastic regime, only few analytical solutions exist, e.g., for the problem of a growing sphere in an elastic, ideally plastic matrix;[15] for a discussion, see, e.g., Reference 16. To study the interaction of several inclusions in a more realistic situation (e.g., Transformation Induced Plasticity (TRIP)), numerical approaches have to be pursued such as e.g., the finite element G. REISNER, Senior Research Associate, is with the Department of Mechanics, Technical University of Munich, 85747 Garching, Germany. F.D. FISCHER, Professor, is with the Institute of Mechanics, University of Leoben, 8700 Leoben, Austria. Y.H. WEN, Postdoc, formerly with the Institute of Mechanics, University of Leoben, is with the Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA. E. A. WERNER, Professor, is with the Christian Doppler ¨ ¨ ¨ Laboratorium fur Moderne Mehrphasenstahle, Technische Universitat ¨ Munchen. Manuscript submitted March 16, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
method.[17–20] The importance of the interaction of several inclusions was reported repeatedly.[10,14,21–23] Fassi-Fehri et al. introduce the concept of an interaction matrix for the martensitic variants.[21,22] In the present work, we investigate the interaction energy among martensitic variants in an elastic-plastic material considering external load stress states and the spatial arrangement of the formed martensitic plates. The finite element method allows determination of the stress and strain distribution in a representative volume element. We systematically study the interaction of two martensitic variants in order to enrich th
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