Thermomechanical Instabilities in M-Lattices with Application to Shape Memory Materials

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THERMOMECHANICAL INSTABILITIES IN M-LATTICESWITH APPLICATIONS TO SHAPE MEMORY ALLOYSNicolas Triantafyllidis and John A. ShawDepartment of Aerospace EngineeringThe University of Michigan1. Project SummaryShape memory alloys (SMAs) are technologically important materials, because of twouseful features: the shape memory effect and the pseudoelastic effect. Their interesting thermomechanicalresponse makes them attractive as low frequency robust actuators and passive devicesfor a variety of novel applications. The thermo-mechanical behavior of SMAs is due to displacive,first-order phase transformations (or martensitic transformations), which produce complex, finescalemicrostructures. This feature is at the heart of modeling difficulties encountered in thecontinuum descriptions of these materials. Existing work on continuum modeling of SMAs isbased on finite thermoelasticity theory and requires the use of phenomenological strain energydensity functions. Solutions of boundary value problems based on these functions are successful inpredicting many features of the experimentally observed fine scale microstructures. This approach,however, leaves a host of other problems unanswered, such as the lattice-level origin of theinstabilities, the number of coexisting phases and the characteristic wavelengths of the observedmicrostructures.The novel feature of the proposed investigation is the use of atomic lattice simulations ofSMAs, and in particular for NiTi, the most technologically promising material in its class. Our goalis to generate realistic energy densities and to simulate and understand the stability phenomena atthe nanometer scale. Specifically, we intend to find all equilibrium phases for temperature and stressand their corresponding microstructures (twinning and crystal interfaces) and study their stabilitywith the ultimate objective to bridge the scales between the nano-(lattice) phenomena and micro-(single crystal) behavior. Besides advancing a fundamental understanding of SMAs at the nanoscale,the work has the potential to help answer why certain intermetallic alloys exhibit shapememory phenomena and other do not, and this work could eventually be used to guide the searchfor new SMAs.The research team consists of two investigators, Professors Nicolas Triantafyllidis and JohnShaw, who bring complementary expertise to the project. The requested funds will fund onedoctoral student over a period of three years plus a one year post-doctoral appointment for Mr.Ryan Elliott, who is working with the PI's on this area. Collaboration with the Theoretical Physicsgroup of Los Alamos National Labs is underway through hosting of the graduate students duringthe summers. Results of this research will be used in a new graduate level, cross-disciplinary courseon atomistic modeling in solid mechanics.Broader Impact of the proposed work: This work fits well within the current nanomechanicsinitiative at NSF, since it pertains to the study of underlying lattice stability phenomenaof m-crystals from atomistic considerations. Understanding these phenomena will eventually beuseful in the conception of novel materials with shape memory effects. The proposed work not onlyaddresses a fundamental problem in mechanics, but it also requires input from other disciplines, i.e.condensed matter physics and applied mathematics. The existing collaboration with Los AlamosNational Labs provides a natural framework for the interaction with these disciplines and for thedissemination of the knowledge to be created.