Phase transformation mechanical behavior of functionally graded shape memory alloy beams

功能梯度形状记忆合金梁的相变力学行为

Received: 23 March 2021

Abstract

Based on the bending deformation theory of the beam, combined with stress-strain relationship and the critical stress-temperature relationship of the shape memory alloy materials, the nonlinear governing equation of the functionally graded shape memory alloy statically indeterminate beam was obtained, and its mechanical behavior under the thermal-mechanical load was investigated. The phase transformation process of the beam was analyzed by a step-by-step method, and the influence of mechanical load, the tension-compression asymmetry coefficient, power exponent and temperature on the displacement of the neutral axis, curvature and phase boundary were obtained. The results draw that as the increase of the load, the displacement of neutral axis and the curvature become larger and the phase boundary is farther away from the edge of the section; the more the temperature and the power exponent are, the smaller the displacement of neutral axis and curvature will be, and the phase boundary become closer to the edge of the section; the tension-compression asymmetry coefficient has a greater influence on the phase boundary of the compressive side, but it has a weak influence on the phase boundary of the tensile side.

摘要

基于梁的弯曲变形理论，结合形状记忆合金材料的应力-应变关系和临界应力-温度关系，得到了功能梯度形状记忆合金超静定梁的非线性控制方程，研究了梁在热-机械载荷作用下的力学行为。采用分阶段分步骤的方法分析了梁的相变过程，得到了机械载荷、拉压不对称系数、幂指数和温度对中性轴位移、曲率和相边界的影响。结果表明：载荷越大，中性轴位移和曲率越大，相边界越远离截面边缘；温度和幂指数越大，中性轴位移和曲率越小，相边界越靠近截面边缘；拉压不对称系数对受压侧相边界影响较大，而对受拉侧相边界影响较小。