考虑磁场影响的磁性形状记忆合金分段线性化超弹性本构模型研究

磁性形状记忆合金(Magnetic Shape Memory Alloy，MSMA)作为一种新型智能材料，同传统温控形状记忆合金一样具有形状记忆效应和超弹性效应。现有的MSMA本构模型大多存在理论性强、形式繁杂、参数较多等问题，不利于实际工程应用。为此，该文借助线性化方法，建立了超弹性MSMA分段线性化应力-应变关系；引入应力择优取向马氏体变体体积分数作为内变量，基于塑性理论框架，构建了MSMA分段线性化超弹性本构模型；提出了描述临界应力与环境磁场关系的Logistic关系函数，并基于试验数据拟合了关键参数；利用所建立的本构模型对考虑磁场影响下的MSMA超弹性进行了数值模拟，并从滞回曲线形状和滞回耗能两个方面与试验结果对比。结果表明:所提出的临界应力与环境磁场关系函数拟合优度可达0.993；材料本构模型预测曲线与试验结果较为接近，理论耗能能力与试验结果误差平均为11.9%。因此，模型能够较为准确地模拟MSMA的超弹性变形过程和耗能能力，为预测考虑磁场影响的MSMA超弹性特性提供了一种简便方法。

INVESTIGATION ON A SEGMENT LINEARIZED SUPER-ELASTIC CONSTITUTIVE MODEL OF MAGNETIC SHAPE MEMORY ALLOY CONSIDERING THE INFLUENCE OF MAGNETIC FIELD

Magnetic Shape Memory Alloy (MSMA), as a new smart material, has both shape memory effect and super-elastic effect as traditional temperature-controlled Shape Memory Alloy. Most of the existing MSMA constitutive models have some problems, e.g., theoretically oriented, complex forms, and multiple parameters, which may affect their engineering application. The segment linearized stress-strain relationship of super-elastic MSMA is established using the linear method. The segment linearized super-elastic constitutive model is established based on the plasticity theory frame for the MSMA, which considers the volume fraction of the stress-preferred orientation martensite variants. The Logistic function is proposed to predict the relationship between critical stress and environment magnetic field, and the parameters of this function are fitted using experimental data. The constitutive model is used to simulate the super-elasticity of MSMA considering the influence of magnetic field, and the results are compared with the experimental results in terms of hysteretic curve shape and hysteretic energy consumption. The results show that the goodness of fit, which reflects the relationship between critical stress and environmental magnetic field, can reach 0.993. The proposed model results are close to the test results, and the average error between theoretical energy consumptions and test results is 11.9%. Therefore, the proposed model can accurately simulate the super-elastic deformation and energy dissipation capacity of MSMA, and can provide a simple method to predict MSMA's super-elastic characteristics considering the magnetic field's influence.