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NiTi形状记忆合金多尺度本构模型研究

A MULTI-SCALE CONSTITUTIVE MODEL OF NiTi SHAPE MEMORY ALLOYS

  • 摘要: 为了描述NiTi形状记忆合金的宏观变形行为并反映变形过程中微观结构演化特性, 本文按照“自下而上”(晶粒尺度-多晶尺度-宏观尺度)的本构建模思路, 提出了一个多尺度本构模型. 在晶粒尺度上, 该模型考虑了马氏体相变和相变诱发塑性这两种非弹性变形机制及其交互作用. 通过构建系统的Helmholtz自由能结合Clausius-Duhem不等式, 推导了上述两种非弹性变形机制的热力学驱动力, 提出了满足热力学约束的内变量演化方程. 进一步采用等变形梯度准则度量晶粒之间的交互作用, 实现模型从晶粒尺度向多晶尺度的过渡. 在此基础上, 将本构模型与有限元方法相结合, 实现了多晶模型的有限元移植. 进一步地, 本文开展了系列实验, 针对具有不同几何构型的NiTi形状记忆合金薄板(矩形、梯形、抛物线形、沙漏形)以及带孔薄板, 测定了不同薄板在不同位移幅值下的整体力-位移曲线. 将模型模拟结果与实验数据进行对比发现, 所提出的多尺度本构模型不但能够很好地描述薄板结构宏观变形行为, 还能同步预测不同空间尺度下的变形及微结构演化信息.

     

    Abstract: To characterize the macroscopic deformation behavior of NiTi shape memory alloys and capture the microstructural evolution during the deformation, a multiscale constitutive model is proposed by employing a "bottom-up" modeling strategy (including grain scale, polycrystalline scale and macroscopic scale). At the grain scale, two different inelastic deformation mechanisms, i.e., martensite transformation, transformation-induced plasticity and their interactions are considered. The thermodynamic driving forces for these two inelastic deformations mechanisms are derived based on the constructed Helmholtz free energy and Clausius-Duhem inequality. Thermodynamics-consistent evolution equations for internal variables are proposed. To estimate the interactions among the grains in the polycrystalline aggregate and obtain the scale transition rule from grain scale to polycrystalline scale, a uniform deformation gradient criterion is employed. Then, The polycrystalline model is implemented into the finite element framework by combining the constitutive model with the finite element method. And a series of experiments are performed to characterize the deformation behaviors of on NiTi shape memory alloy thin plates (including the rectangular, trapezoidal, parabolic, hourglass-shaped plates and the plate with holes). The global force-displacement responses under various displacement amplitudes are measured. Comparing the simulated results obtain by the proposed model with the experimental data, it is shown that the proposed multiscale model not only accurately describes the macroscopic deformation behavior of the plates but also reveals the deformation and microstructural evolution information at different spatial scales.

     

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