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## 形状记忆合金超弹性螺旋弹簧的力学模型

(1.中国石油大学 (华东) 储运与建筑工程学院, 青岛 266580)
【知识点链接】形状记忆合金

【摘要】结合普通金属螺旋弹簧的弹性变形理论和形状记忆合金 (SMA) 的力学本构模型, 分析与描述SMA螺旋弹簧的簧丝横截面上应变、应力分布规律, 进而推导SMA螺旋弹簧的相变临界参数计算公式。基于SMA螺旋弹簧的宏观试验现象和推导的相变临界参数计算公式, 建立描述SMA螺旋弹簧的轴向变形和轴向外力间关系的力学模型。理论计算与试验结果的对比表明, 建立的SMA螺旋弹簧力学模型能准确预测SMA螺旋弹簧的轴向外力和轴向变形间的关系, 并克服有限单元法模拟计算SMA螺旋弹簧时在几何建模和数值收敛等方面的局限性, 可为研究SMA螺旋弹簧的力学行为和基于SMA螺旋弹簧的结构设计提供必要的理论基础和技术参考。

【关键词】 形状记忆合金;螺旋弹簧;相变临界参数;力学模型;

【DOI】

【基金资助】 国家重点研发计划资助项目 (2017YFC0307604) ;

## Mechanical Model for Super-elastic Helical Spring of Shape Memory Alloy

ZHOU Bo1 WANG Zhiyong1 XUE Shifeng1

(1.College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266580)
【Knowledge Link】shape memory alloy

【Abstract】The distributions of strain and stress in the section of the shape memory alloy (SMA) wire of a helical spring are analyzed and described based on the deformation theory of ordinary helical springs and the constitutive model of SMAs. Then the formulas are derived to calculate the phase-transition critical parameters of SMA helical springs. A mechanical model, which expresses the relation between axial force and axial deformation of SMA helical springs, is developed based on the experimental phenomena and the formulas of phase-transition critical parameters of SMA helical springs. Results show that the developed mechanical model is able to predict the relation between axial force and axial deformation of SMA helical springs and overcome the limitations of the finite element method in geometric modeling and numerical convergence. Therefore, it can serve as a theoretical basis and technical reference for the investigation on the mechanical behavior of SMA helical springs and the structural design based on SMA helical springs.

【Keywords】 shape memory alloy; helical spring; phase transition critical parameter; mechanical model;

【DOI】

【Funds】 National Key R&D Program of China (2017YFC0307604);

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ISSN:0577-6686

CN: 11-2187/TH

Vol 55, No. 08, Pages 56-64

April 2019

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