A micromechanics-based model is developed to capture the grain-size dependent superelasticity of nanocrystalline shape memory alloys (SMAs). Grain-size effects are incorporated in the proposed model through definition of dissipative length scale and energetic length scale parameters. In this paper, nanocrystalline SMAs are considered as two-phase composites consisting of the grain-core phase and the grain-boundary phase. Based on the Gibbs free energy including the spatial gradient of the martensite volume fraction, a new transformation function determining the evolution law for transformation strain is derived. Using micromechanical averaging techniques, the grain-size-dependent superelastic behavior of nanocrystalline SMAs can be described. The internal length scales are calibrated using experimental results from published literature. In addition, model validation is performed by comparing the model predictions with the corresponding experimental data on nanostructured NiTi polycrystalline SMA. Finally, effects of the internal length scales on the critical stresses for forward and reverse transformations, the hysteresis loop area (transformation dissipation energy), and the strain hardening are investigated.

开发了一种基于微力学的模型来捕捉纳米晶形状记忆合金 (SMA) 的晶粒尺寸相关超弹性。通过定义耗散长度尺度和能量长度尺度参数，将晶粒尺寸效应纳入所提出的模型中。在本文中，纳米晶 SMA 被认为是由晶核相和晶界相组成的两相复合材料。基于包括马氏体体积分数空间梯度在内的吉布斯自由能，推导出一种新的确定转变应变演化规律的转变函数。使用微机械平均技术，可以描述纳米晶 SMA 与晶粒尺寸相关的超弹性行为。内部长度标度使用来自已发表文献的实验结果进行校准。此外，通过将模型预测与纳米结构 NiTi 多晶 SMA 的相应实验数据进行比较来进行模型验证。最后，研究了内部长度尺度对正向和反向转换的临界应力、磁滞回线面积（转换耗散能）和应变硬化的影响。