﻿ 基于自由胀形的弯曲管材变形行为<sup>*</sup>
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1. 北京航空航天大学 机械工程及自动化学院, 北京 100083;
2. 北京航空航天大学 先进航空发动机协同创新中心, 北京 100083

Deformation behavior of a bent tube based on free expansion
KONG Deshuai1, LANG Lihui1,2, RUAN Shangwen1
1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Collaborative Innovation Center of Advanced Aero-Engine, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-06-20; Accepted: 2016-09-21; Published online: 2016-10-11 17:33
Foundation item: National Science and Technology Major Project (2014ZX04002041); National Natural Science Foundation of China (51175024)
Corresponding author. LANG Lihui, E-mail:lang@buaa.edu.cn
Abstract: As the development of lightweight design in manufacture industry, the application of thin-walled bent hollow tubes with various sections is expanding widely. In order to study the deformation behavior of bent tubes during hydroforming process and have a reliable process design, a theoretical model of free-expansion bent tubes based on membrane theory and plastic theory was put forward, and the model was verified by finite element (FE) analysis. The FE analysis results show good agreement with the theoretical model. The stresses distribution and deformation behavior were revealed. Finally, the work-hardening behavior during rotary draw bending was analyzed, and meanwhile, the fracture site of pre-bent tubes with different work-hardening states during free-expansion process was explored. The experimental results show good agreement with the FE analysis results.
Key words: hydroforming     bending     deformation behavior     work-hardening     fracture

1 管材弯胀理论模型 1.1 内压作用下环壳的应力应变表达

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 A、B、C、D——管材截面在水平和竖直方向上的顶点。 图 1 环壳胀形理论模型 Fig. 1 Theoretical model of an internally pressurized torus

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1.2 内压作用下环壳的应力应变的变化规律

 图 2 参数k随相对弯曲半径的变化规律 Fig. 2 Parameter k's variation pattern with relative bending radius

 图 3 参数k沿截面圆环向的变化规律 Fig. 3 Parameter k's variation pattern in circumferential direction

 图 4 应变增量沿截面圆环向的变化规律 Fig. 4 Strain increment variation pattern in circumferential direction
2 理论模型的有限元分析验证

 图 5 应力分布的理论分析与有限元结果对比 Fig. 5 Comparison of stress distribution between theoretical analysis and FE results
 图 6 环壳与弯管自由胀形状态下的应力分布 Fig. 6 Stress distribution of torus and bent tube in free-expansion state
3 考虑弯曲影响的管材自由胀形失效分析 3.1 管材弯曲过程的变形特点

 图 7 典型的弯曲模具结构 Fig. 7 Typical bending mold structure

 图 8 典型位置沿轴向等效应变分布规律 Fig. 8 Equivalent strain distribution rule in axial direction at typical location
3.2 弯曲管材胀形过程失效形式分析

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 图 9 管材弯胀过程中所需内压力及各截面应变增量分布 Fig. 9 Internal pressure needed during tube bending and expansion process and strain increment distribution at cross-sections of a bent tube

 图 10 弯管胀形典型单元的应变路径 Fig. 10 Strain paths at different typical points of a pressurized bent tube
 图 11 弯管的自由胀形实验 Fig. 11 Free-expansion experiment of bent tubes

 图 12 过度弯曲的管材自由胀形过程中的应变路径 Fig. 12 Strain paths of a bent tube losing most of formability during free expansion process
 图 13 过度弯曲的管材自由胀形过程典型截面上的等效应力和应变增量分布 Fig. 13 Equivalent stress and strain increment distribution of a bent tube losing most of formability at typical cross-section during free expansion process
 图 14 过度弯曲的管材自由胀形过程实验样件 Fig. 14 Experimental sample of a bent tube losing most of formability during free expansion process
4 结论

1) 对于等壁厚理想的弯管在自由胀形过程中，其环向应力沿截面圆从弯曲最内侧至弯曲最外侧呈递减分布，且弯曲内侧的变化率大于弯曲外侧。而轴向应力则在截面圆上的分布一致。

2) 理想等壁厚弯管自由胀形过程中弯曲内侧的环向应力分布随着弯曲半径的增大而减小，而弯曲外侧随着相对弯曲半径的增加而增加。当ζ < 2.5时弯曲内侧的应力分布对相对弯曲半径的敏感程度比弯曲外侧高。

3) 理想等壁厚弯管的自由胀形过程中，弯曲外侧是环向和轴向双向受拉减薄的变形。而弯曲内侧则是环向受拉轴向受压壁厚减薄的变形。

4) 在管材绕弯工艺过程中，弯曲外侧的最大变形区域位于弯曲的中间段，而对于弯曲内侧和中性层上最大变形则发生在弯曲端部靠近压模处。

5) 考虑弯曲影响的管材自由胀形的破裂位置通常位于弯曲的端部靠近夹模的中性层处，而过度弯曲时管材胀形的破裂位置则位于弯曲的外侧。

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#### 文章信息

KONG Deshuai, LANG Lihui, RUAN Shangwen

Deformation behavior of a bent tube based on free expansion

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(7): 1395-1402
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0525