In practical applications, TiNi shape memory alloys (SMAs) exhibit behavior that can pose a challenge with current constitutive models and their implementations in finite element method (FEM) software. TiNi SMA devices typically operate in the forward or reverse martensitic transformation regime, which is known as subloop loading. During such cyclic loading–unloading, the hysteresis stress–strain loop changes because of material damage, which can be considered the fatigue of TiNi SMAs. During both the loading and unloading processes, the stress plateau decreases. At the same time, the accumulated (residual) martensitic transformation strain increases. In this study, the experimental investigation results and observations of the aforementioned phenomena are presented. Next, the phase-field damage model is employed, along with a modified Lagoudas constitutive model, to simulate the change in stress–strain hysteresis. Furthermore, a fatigue function is used to simulate the accumulation of martensitic transformation strain. The experimental stress–strain response is compared with the simulation results, and good quantitative and qualitative agreement is obtained. The damage and martensitic volume fraction with respect to strain are discussed for full-loop and subloop loading. The observations and conclusions, as well as open questions, are presented. Possible directions for future research are provided.

中文翻译：

---

TiNi SMA 子环加载的相场损伤模拟

在实际应用中，TiNi 形状记忆合金 (SMA) 表现出的行为可能对当前本构模型及其在有限元法 (FEM) 软件中的实现构成挑战。 TiNi SMA 设备通常在正向或反向马氏体转变状态下运行，这称为子循环加载。在这种循环加载-卸载过程中，由于材料损伤，滞后应力-应变环发生变化，这可以被认为是TiNi SMA的疲劳。在加载和卸载过程中，应力平台都会降低。同时，累积的（残余）马氏体转变应变增加。在本研究中，提出了上述现象的实验研究结果和观察结果。接下来，采用相场损伤模型以及改进的 Lagoudas 本构模型来模拟应力应变滞后的变化。此外，使用疲劳函数来模拟马氏体转变应变的积累。将实验应力应变响应与模拟结果进行比较，获得了良好的定量和定性一致性。针对全循环和子循环加载，讨论了相对于应变的损伤和马氏体体积分数。提出了观察结果和结论以及悬而未决的问题。提供了未来研究的可能方向。