磁性形状记忆合金力磁耦合行为的唯象模型研究

论文基于热力学及耗散概念,推导了一种磁性形状记忆合金(MSMA)的力磁耦合三维唯象本构关系.采用内变量模拟微观相结构及磁结构的演化,考虑了马氏体相变过程及马氏体重定向过程.同时,论文摒弃了传统的单畴假设,运用双畴模型来模拟循环加载下的磁畴结构演化.根据文献中的二维加载情况的实验数据确定本模型的参数.数值模拟结果表明:论文的模型可以很好的捕捉磁性形状记忆合金的形状记忆效应、应变及磁化响应的滞后性.应变及磁化响应模拟结果明显比文献中的理论模型更加吻合实验数据,低磁场时尤为明显.

A Phenomenological Model of MSMA with Magneto-mechanical Coupling Behavior

Upon magneto-mechanical loadings, magnetic shape memory alloys (MSMA), can exhibit significant magnetic field-induced strain as well as stress-induced change of magnetization. These features make MSMA an important smart material in the application of actuator and sensor, which calls for deep understanding of the constitutive behavior of MSMA. Based on thermodynamics and dissipation of energy, we developed a three-dimensional constitutive model of MSMA under magneto-mechanical loadings. The martensitic transformation and reorientation are considered simultaneously. The evolution of the crystallographic and magnetic microstructure is described by using internal state variables. As for the simulation of magnetic microstructure, the single-domain assumption is usually adopted in literature, implying that the magnetic structure has evolved into a single-domain when the reorientation process begins. The single-domain assumption is believed to be suitable for the loading stage of magnetic field, but no longer valid for the unloading process. In the present model, we use the dual-domain model to simulate the evolution of the domain structure under cyclic loading. An arcsine function is selected to describe the macro magneto-mechanical responses induced solely by the evolution of magnetic domain. The simulation given by a reduced two-dimensional version of the present model, where the parameters are determined in terms of the experimental data of Ni₂MnGa in literature, shows that the constitutive model developed in this paper is able to capture the magnetic shape memory effect and the hysteresis effect of strain as well as the magnetization response. The results predicted by the present model agree very well with experimental data, especially when the magnetic field is relatively low. It is believed that the present constitutive model can give good simulation for the strain and magnetization responses when MSMA is subjected to complex loading paths, especially the cases with unloading where the reverse reorientation is generally accompanied by the evolution of magnetic domains.