摘要:
功能梯度形状记忆合金（Functionally graded shape memory alloy，FGSMA）兼具功能梯度材料和形状记忆合金材料的双重特性，广泛应用于微机电、航空航天等工程领域。为研究FGSMA复合梁的弯曲行为，本文对形状记忆合金（SMA）力学本构方程进行简化处理，并根据复合材料层合板理论建立了FGSMA复合梁的力学模型，据此研究了SMA体积分数沿厚度方向呈线性变化的FGSMA悬臂梁内SMA纤维铺设角度对悬臂梁横截面应变、中面轴向位移、中性面高度和相变层高度的影响以及悬臂梁中面应变、曲率、SMA马氏体相变临界层高度和中性面高度随弯矩载荷的变化规律。研究结果表明：在弯矩载荷作用下，悬臂梁中性面位置与中面位置不重合，且悬臂梁上下层SMA马氏体相变临界层位置不对称；截面轴向应变绝对值随铺设角度增大而增大，截面纵向应变绝对值随铺设角度增大先增大后减小，中面轴向位移随铺设角度增大先增大后减小；随着铺设角度增大，悬臂梁中性面高度逐渐增大，拉伸状态下相变结束临界层高度先减小后增大，压缩状态的趋势相反；随着弯矩载荷绝对值逐渐增大，中性面位置高度表现出先稳定后减小然后逐渐增大的趋势，相变临界层逐渐向中性面位置靠拢；中面正应变和挠曲率随着弯矩载荷绝对值逐渐增大而发生变化，且变化率先增大后减缓。
Abstract:
Functionally graded shape memory alloy (FGSMA) is widely used in micro-electromechanical systems, aerospace and other practical engineering regions due to its excellent properties of both functionally graded material and shape memory alloy(SMA) material. In order to investigate the bending behavior of FGSMA composite, the nonlinear constitutive model of SMA was simplified, and the mechanical model of FGSMA composite beam was established according to the composite laminated plate theory in this paper. The effects of the laying angle of SMA fiber in FGSMA cantilever beam with linear variation of SMA volume fraction along the thickness direction on the cross-section strain, the axial displacement of the middle plane, the height of the neutral plane and the height of the phase change layer were studied by using the established model. And the variation of mid-plane strain, curvature, critical layer height of SMA martensitic transformation and the height of neutral plane in cantilever beam with different bending moment loads were also discussed. The results indicate that the neutral plane does not coincide with the mid-plane of the cantilever beam, and the positions of the upper and lower martensitic transformation critical layers of SMA are asymmetrical. In the cross section, the absolute value of axial strain increases, but the absolute value of longitudinal strain increases first and then decreases with the increase of laying angle, as well as the axial displacement of the middle plane. With the increase of the laying angle, the height of phase transformation finish layer decreases first and then increases under tensile condition, but the trend is opposite under compression state. With the increasing of the absolute value of the moment load, the height of neutral plane position shows a tendency of first stabilizing, then decreasing and finally increasing, and the phase transformation critical layers moves gradually closer to the position of the neutral plane. The positive strain and flexural rate of the middle plane change with the increasing of the absolute value of the moment load, and the change rate increases first and then slows down.
百度学术
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