Mechanical Analysis of Shape Memory Alloy Beams under Asymmetric Bending

形状记忆合金梁非对称弯曲问题的力学分析

School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Received: 14 October 2019

Abstract

Based on the bending theory of beams, combining with the constitutive relationship of shape memory alloy materials, the asymmetric bending of shape memory alloy beams under concentrated load was studied. Considering tension-compression asymmetry on both sides of the tension and compression in the process of bending, tension-compression asymmetry coefficient was introduced, by using the step-by-step method. The stress distribution, neutral axis displacement, curvature and phase boundary of the beam sections of the I-shaped cross-section shape memory alloy beam were analyzed. The results show that under the same load, the maximum offset of the neutral axis displacement increases with the increase of tension-compression asymmetry coefficient. Under the same tension-compression asymmetry coefficient, the displacement and curvature of the neutral axis increased with the increase of load; as tension-compression asymmetry coefficient increased, the proportion of mixed phase increased gradually, the proportion of martensite phase decreased, and the asymmetry of phase boundary became more obvious. Under the same conditions, the rectangular section is more suitable. The cross section of I shaped cross section was prone to occur phase transformation.

摘要

基于梁的弯曲理论，结合形状记忆合金材料的本构关系，研究了集中载荷作用下形状记忆合金梁的非对称弯曲问题。考虑到弯曲变形过程中拉压两侧相变的不对称性，特引入拉压不对称系数，采用分阶段分步骤的方法，分析得到了工字形截面形状记忆合金梁相变各阶段梁截面上的应力分布、中性轴位移、曲率及相边界的变化情况。结果表明：当载荷相同时，中性轴位移的最大偏移量随着拉压不对称系数增大而增大；当拉压不对称系数相同时，中性轴位移和曲率随着载荷的增大而增大；随着拉压不对称系数增大，混合相占比逐渐增大，马氏体相占比减小，相边界不对称性表现越明显；在相同条件下，矩形截面较工字形截面易发生相变。