In this work, a multiscale constitutive model is established to describe the deformation behaviors of magnesium-shape memory alloy (Mg-SMA) composite in a wide temperature range and reveal the strengthening mechanism of SMA reinforcement on Mg. The model is established at the grain scale firstly and gradually transited to the macroscopic scale by employing a newly developed three-level scale transition rule. At the grain scale, the thermodynamic-consistent constitutive models of Mg and SMA are, respectively, constructed by addressing different inelastic deformation mechanisms. The basal, prismatic, pyramidal, slip systems and extension twinning system are considered for the Mg phase, and the martensite transformation (MT) and austenitic plasticity are addressed for SMA reinforcement. Thermodynamic driving forces of each inelastic deformation mechanism are derived from the dissipative inequality and the constructed Gibbs free energies. At the polycrystalline scale, to evaluate the interactions among the grains and pores, and obtain the whole responses of the polycrystalline Mg and SMA, a thermo-mechanically coupled self-consistent homogenization scheme is employed. At the mesoscopic scale, a modified thermo-mechanically coupled Mori-Tanaka's homogenization scheme is adopted to evaluate the interaction between the Mg phase and SMA phase, and predict the whole responses for the representative volume element (RVE) of the composite. According to the geometrical features and mechanical loadings applied on the specimen, a hypothesis of homogeneous stress and strain fields at the macroscopic scale is adopted to achieve the scale transition from the RVE of the composite to the whole specimen. The capacity of the multiscale model is verified by comparing the predictions with the existing experimental data (Aydogmus, 2015). Moreover, the influences of characteristic information for the microstructures at different spatial scales on the deformation behaviors of the composite are predicted and discussed.

中文翻译：

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镁形状记忆合金复合材料的多尺度本构模型


在这项工作中，建立了多尺度本构模型来描述镁形状记忆合金（Mg-SMA）复合材料在宽温度范围内的变形行为，并揭示了SMA增强镁的强化机制。该模型首先在颗粒尺度上建立，并采用新开发的三级尺度转换规则逐步过渡到宏观尺度。在晶粒尺度上，通过解决不同的非弹性变形机制，分别构建了 Mg 和 SMA 的热力学一致本构模型。 Mg 相考虑基底、棱柱、金字塔、滑移系统和延伸孪晶系统，SMA 强化则考虑马氏体相变 (MT) 和奥氏体塑性。每个非弹性变形机制的热力学驱动力均由耗散不等式和构造的吉布斯自由能导出。在多晶尺度上，为了评估晶粒和孔隙之间的相互作用，并获得多晶镁和SMA的整体响应，采用了热机械耦合自洽均质化方案。在介观尺度上，采用改进的热机械耦合 Mori-Tanaka 均质化方案来评估 Mg 相和 SMA 相之间的相互作用，并预测复合材料的代表体积单元 (RVE) 的整体响应。根据试件的几何特征和施加的机械载荷，采用宏观尺度上均匀应力应变场的假设，实现从复合材料的RVE到整个试件的尺度过渡。 通过将预测与现有实验数据进行比较来验证多尺度模型的能力（Aydogmus，2015）。此外，还预测并讨论了不同空间尺度微观结构特征信息对复合材料变形行为的影响。