A phase field approach for phase transition between austenite to martensitic variants and twinning between martensitic variants is presented with the main focus on the effects of interfacial stress on phase transformations. In this theory, each variant-variant phase transformations and twinnings within each martensitic variant can be represented by only one-order parameter. Thus, it allows us to get the analytical solution of the martensite-martensite interface profile, energy, and width. Moreover, this model allows us to include interface stress which is consistent with the sharp interface limit. The finite element method is utilized to solve the coupled phase field and elasticity equations for a cubic to tetragonal phase transformation in NiAl shape memory alloy. The stress fields are obtained and the effects of interfacial stress on the stress field at the interfaces are studied for both austenite–martensite and martensite–martensite interfaces in detail. Additionally, the temperature-induced growth of the martensitic phase inside austenite, martensitic phase transformation, and twining are solved. The evolution of the microstructure and stress fields are obtained and the effects of interfacial stress on the morphological evolution of martensitic nanostructures are examined. It is found that the interfacial stress is an important factor, influencing the stress distribution at interfaces and the phase field solution significantly. This theory can be extended for electric, reconstructive, and magnetic phase transformations.

中文翻译：

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NiAl形状记忆合金马氏体相变相场法中界面应力的影响

提出了一种用于奥氏体到马氏体变体之间的相变以及马氏体变体之间的孪晶的相场方法，主要关注界面应力对相变的影响。在该理论中，每个马氏体变体中的每个变体-变体相变和孪晶只能由一阶参数表示。因此，它使我们能够得到马氏体-马氏体界面轮廓、能量和宽度的解析解。此外，该模型允许我们包括与锐界面极限一致的界面应力。利用有限元方法求解NiAl形状记忆合金立方相到四方相变的耦合相场和弹性方程。获得了应力场，并详细研究了奥氏体-马氏体和马氏体-马氏体界面的界面应力对界面应力场的影响。此外，还解决了奥氏体内部马氏体相的温度诱导生长、马氏体相变和缠绕问题。获得了微观结构和应力场的演变，并检查了界面应力对马氏体纳米结构形态演变的影响。发现界面应力是一个重要因素，对界面应力分布和相场解有显着影响。该理论可以扩展到电、重构和磁相变。