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A New Framework for the Interpretation of Modulated Martensites in Shape Memory Alloys

Banff International Research Station for Mathematical Innovation and Discovery

Shape memory alloys (SMAs) are a class of materials with unusual properties that have been attributed to the material undergoing a Martensitic Phase Transformation (MPT). An MPT consists of the material’s crystal structure evolving in a coordinated fashion from a high symmetry austenite phase to a low symmetry martensite phase. Often in SMAs,\\r\\nthe austenite is a B2 cubic configuration that transforms a Modulated Martensite (MM) phase. MMs are long-period stacking order structures consisting of [110]cubic basal planes. First-principles computational results have shown that the minimum energy phase for these materials is not a MM, but a short-period structure called the Ground State Martensite.\\r\\nIt is commonly argued that energy contributions associated with kinematic compatibility constraints at the austenite-martensite interface explain the experimental observation of meta-stable MMs, as opposed to the expected Ground State Martensite phase. To date, a general approach for predicting the properties of the MM structure that will be observed for a particular material has not been available.\\r\\nIn this work, we develop a new framework for the interpretation of MMs as natural features of the material’s energy landscape (expressed as a function of the lattice parameters and individual atomic positions within a perfect infinite crystal). From this energy-based framework, a new understanding of MMs as a mixture of two short-period Base Martensite phases is developed. Using only a small set of input data associated with the two Base Martensites, this MM Mixture Model (M4) is capable of accurately predicting the energy, lattice constants, and structural details of an arbitrary Modulated Martensite phase. This is demonstrated by comparing the M4 predictions to computational results from a particular\\r\\nempirical atomistic model.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Applied analysis / inverse problems

video/mp4

Author affiliation: University of Minnesota

2014-08-06

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/49257

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/