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基于已有实验得到的形状记忆合金非线性的应力-应变关系,引入拉压不对称系数研究了形状记忆合金纯弯曲梁的力学性能。在平截面假定下,建立了梁在不同弯矩作用下截面应力、相变百分含量、相边界的解析表达式。对两端受弯的简支梁进行数值分析,结果表明:纯弯曲的过程中,平截面假定仍然成立,中性层的移动和表层材料相变状况有关;表层材料发生相变后,中性层偏离截面中心向受压侧移动,直至受压侧表层材料相变完成,完全转变为马氏体相;之后随弯矩的增大,中性层开始反向移动。材料本身的拉压不对称性使得形状记忆合金纯弯曲梁截面应力的分布以及相边界的移动呈现出明显的不对称性。
Based on the existing stress-strain relationship of shape memory alloys, the mechanical properties of the shape memory alloy pure bending beam were studied by introducing the asymmetric coefficient of tension and compression. Under the assumption of flat section, the analytic expression of the cross-section stress, phase change percentage and phase boundary under different bending moment is established. The numerical analysis of the simply supported beams with both ends flexed showed that in the process of pure bending, the assumption of flat section still holds, and the movement of the neutral layer is related to the phase change of the surface material. After the surface material is transformed, the neutral The layer moves away from the center of the cross section toward the pressure side until the transformation of the material on the pressure side is completed and completely changes to the martensite phase. After that, the neutral layer starts to move backward. Asymmetric tension and compression of the material itself make the stress distribution and the phase boundary shift of the pure bending beam of shape memory alloy show obvious asymmetry.