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Energy Barriers and Hysteresis in Martensitic Phase Transformations
MINNESOTA UNIV MINNEAPOLIS DEPT OF AEROSPACE ENGINEERING AND MECHANICS
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We report results from a systematic program of changing composition of alloys in the system TiNiX, X Cu, Pt, Pd, Au, to pursue certain special lattice parameters that have been identified previously with low hysteresis. We achieve lambda sub 2 1, where lambda sub 2 is the middle eigenvalue of the transformation strain matrix, for alloys with X Pt, Pd, Au. In all cases there is a sharp drop of the graph of hysteresis vs. composition at the composition where lambda sub 2 1. When the size of the hysteresis is replotted vs. lambda sub 2 we obtain an universal graph for these alloys, which also agrees with trends in an earlier combinatorial study of alloys in the system TiNiCu. Motivated by these experimental results, we present a new theory for the size of the hysteresis based on the growth from a small scale of fully developed austenite martensite needles. In this theory the energy of the transition layer plays a critical role. New methods for calculation the optimal layer are developed that rely on Gamma-convergence arguments, the small parameter being lamba sub 2 - 1. The limiting energy of the transition layer is found to be governed by a nonstandard linear elasticity problem. Overall, the results point to a simple systematic method of achieving low hysteresis and a high degree of reversibility in transforming materials.
APPROVED FOR PUBLIC RELEASE