薄壁圆管膨胀变形行为的量纲分析及理论研究

通过有限元数值方法及已有圆管膨胀试验对金属圆管膨胀的变形行为进行研究，研究发现圆管膨胀后的几何尺寸h和D₁主要受圆管和压模初始几何结构参数影响，而受圆管材料和摩擦因数的影响较小；基于量纲分析，得到膨胀后圆管的几何尺寸h和D₁与主要影响因素之间的量纲一关系式.结合量纲一关系式与能量守恒定律，提出圆管稳态膨胀过程中稳态下压力的预测模型，模型中考虑了材料的应变强化效应和压模外径对膨胀管弯曲区域曲率的影响，结果表明该模型的预测值与试验结果、仿真结果能较好地吻合. 

Dimensional Analysis and Theoretical Study on the Expansion Deformation Behaviors of Thin-Walled Circular Tube

The expansion behavior of thin-walled circular tube was studied by the finite element method and the existing expansion experiments. It was found that the geometric dimensioning h and D₁ of the expanded tube were mainly affected by the initial geometric parameters of the tube and die, but less affected by the metallic materials and friction coefficient. According to the dimensional analysis, the dimensionless relationships between the geometrical dimensioning (h, D₁) and the main influencing factors were obtained. Then, based on the above dimensionless relationships and the law of conservation of energy, a new prediction model of the steady compression force was put forward, in which the effects of strain hardening and die diameter on the curvature of the bending regions of expanded tube were also taken into account, and the predictions of the current model are in good agreement with experiment and simulation data.