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

M-LATTICESWITH应用于形状记忆的热机械不稳定性[美国密歇根大学航空航天工程系尼古拉斯·特里安塔菲利迪斯和约翰·A·肖]形状记忆合金(SMA)具有形状记忆效应和伪弹性效应两大特点，是一种具有重要技术价值的材料。其有趣的热机械响应使其成为各种新型应用的低频强健执行器和无源器件。SMA的热机械行为是由于位移型的一级相变(或马氏体相变)，它产生了复杂的、细小的微观组织。这一特点是在对这些材料的连续描述中遇到的建模困难的核心。现有的SMA连续介质建模工作是基于有限热弹性理论的，需要使用唯象应变能密度函数。基于这些函数的边值问题的解成功地预测了实验观察到的精细微结构的许多特征。然而，这种方法留下了许多其他问题的答案，例如不稳定性的晶格级来源，共存相的数量和观察到的微结构的特征波长。拟议的研究的新特点是使用SMA的原子晶格模拟，特别是对于NiTi，这是同类材料中最有技术前景的材料。我们的目标是产生真实的能量密度，并在纳米尺度上模拟和理解稳定性现象。具体地说，我们打算找到温度和应力的所有平衡相及其相应的微观结构(孪晶和晶体界面)，并研究它们的稳定性，最终目的是在纳米(晶格)现象和微米(单晶)行为之间架起一座桥梁。除了在纳米尺度上促进对SMAs的基本理解外，这项工作还有可能帮助解释为什么某些金属间合金表现出形状记忆现象，而其他金属间合金则不表现出形状记忆现象，这项工作最终可能被用于指导寻找新的SMAs。研究团队由两名研究人员组成，Nicolas Triantafyllidis教授和JohnShaw教授，他们为该项目带来了互补的专业知识。申请的资金将在三年内资助一名博士生，外加瑞安·埃利奥特先生一年的博士后职位，他正与PI在这一领域合作。与洛斯阿拉莫斯国家实验室的理论物理小组的合作正在进行中，方法是在夏季接待研究生。这项研究的结果将用于一门新的研究生水平的跨学科课程--固体力学中的原子建模。拟议工作的广泛影响：这项工作非常适合目前NSF的纳米力学倡议，因为它涉及从原子角度研究m晶体潜在的晶格稳定性现象。了解这些现象最终将有助于构思具有形状记忆效应的新材料。这项拟议的工作不仅解决了力学中的一个基本问题，而且还需要其他学科的投入，即凝聚态物理和应用数学。与洛斯阿拉莫斯国家实验室的现有合作为与这些学科的互动和将要创造的知识的传播提供了一个自然的框架。

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.