Islam A B M Rezaul, Karadoğan Ernur
Robotics and Haptics Lab, School of Engineering and Technology, Central Michigan University, Mount Pleasant, MI 48859, USA.
Materials (Basel). 2019 May 24;12(10):1687. doi: 10.3390/ma12101687.
A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models' sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.
形状记忆合金（SMA）能够记住其原始形状，并在受热时从因加载产生的应变中恢复（形状记忆效应）。形状记忆合金在完成向奥氏体转变的特征温度以上，对应力也表现出弹性响应（伪弹性或超弹性）。形状记忆合金的形状记忆效应和伪弹性已通过几种微观热力学和宏观唯象学模型，采用不同的建模方法进行了研究。田中模型和梁 - 罗杰斯模型是描述形状记忆合金行为最广泛使用的两个宏观唯象学本构模型。在本文中，我们针对田中模型和梁 - 罗杰斯模型，在不同的工作温度和加载条件下，使用索博尔方法和扩展傅里叶振幅灵敏度测试（eFAST）方法进行了灵敏度和不确定性分析。分析了应力相关灵敏度指标和平均灵敏度指标，以确定这些模型中最具影响力的参数。结果表明，变异性主要是由工作温度和加载条件的变化引起的。这两个模型似乎都受到材料弹性模量不确定性的显著影响。本文所进行的分析旨在通过加深对这些模型对输入参数的灵敏度以及由于相同输入参数的不确定性导致输出变异性原因的理解，为使用形状记忆合金设计应用提供更好的见解。
