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1. 兰州理工大学 机电工程学院, 兰州 730050;
2. 河南理工大学 机械与动力工程学院, 焦作 454000;
3. 北京航空航天大学 机械工程及自动化学院, 北京 100083

Test method of elliptical hydraulic bulging based on constant strain rate
SUN Zhijia1,2 , YANG Xiying3 , LANG Lihui3
1. Mechanical and Electrical Engineering Institute, Lanzhou University of Technology, Lanzhou 730050, China ;
2. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454000, China ;
3. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-10-09; Accepted: 2015-12-31; Published online: 2016-05-25 12: 00
Foundation item: National Natural Science Foundation of China (51175024)
Corresponding author. E-mail:sunzhijia2004@163.com
Abstract: To determine the forming limit curves (FLCs) of 2A16-O aluminum alloy sheet at various temperatures and strain rates, a modified Hollomon equation is put forward to acquire the fitted true stress-true strain curve. Through finite element analysis (FEA), the fracture position in elliptical hydraulic bulging with different ovality was obtained. The forming limit data in specified strain path were determined by optimizing the process parameters. The quantitative relation between pressure rate and strain rate was derived by establishing the formula of liquid pressure, equivalent strain and strain rate. By combining the uniaxial tensile with elliptical hydraulic bulging which is controlled by the constant strain rate, the FLCs of 2A16-O aluminum alloy sheet at different temperatures and strain rates were acquired. The above method provides the criterion for quantitatively analyzing the influence rule of strain rate on FLCs and evaluating which theoretical method is more accurate to predict FLCs.
Key words: aluminum alloy sheet     forming limit curve     elliptical hydraulic bulging     strain rate     pressure variation rate

1 椭圆凹模胀形适用性论证 1.1 试验原理

 (1)
 (2)
 (3)
 图 1 胀形顶点处微元体示意图 Fig. 1 Schematic of infinitesimal unit at dome apex

1.2 真实应力-应变曲线

 (4)
 图 2 不同温度和应变率下真实应力-真实应变曲线 Fig. 2 True stress-true strain curves at different temperatures and strain rates

1.3 工艺参数选取

 图 3 1/4椭圆凹模胀形有限元模型示意图 Fig. 3 Schematic of finite element method in 1/4 elliptical hydro-bulging

 T/℃ 20 160 210 300 r 0.69 0.77 0.85 1.04

 图 4 等效应变分布趋势 Fig. 4 Distribution trends of equivalent strain
 图 5 不同椭圆度的等效应变分布 Fig. 5 Distribution of equivalent strain with different ovalities

 图 6 凹模圆角半径对最大等效应变的影响 Fig. 6 Influence of die corner radius on maximum equivalent strain

 图 7 不同椭圆度的第一、二主应变路径 Fig. 7 Major and minor strain paths with different ovalities
2 应变率与压力变化率转换

χ=0.6为例,拟合的液体压力-等效应变曲线与模拟结果比较如图 8所示,在胀形过程中,液体压力与等效应变呈单调增函数,且符合幂指数形式。

 图 8 拟合的液体压力-等效应变曲线与模拟结果比较 Fig. 8 Comparison of fitted results and simulation results for fluid pressure-equivalent strain

 (5)

 (6)

 (7)

ε=tt,代入式(7)中,得到

 (8)

 图 9 压力变化率与应变率关系 Fig. 9 Relation between pressure variation rate and strain rate
3 试验分析

 图 10 椭圆凹模胀形用试验工装和凹模 Fig. 10 Test setup and die for elliptical hydraulic bulging

 图 11 不同椭圆度下胀形试验件(210℃、应变率0.001 s-1) Fig. 11 Bulged samples with different ovalities (210℃, strain rate 0.001 s-1)

 图 12 不同温度和应变率下的2A16-O铝合金成形极限曲线 Fig. 12 Forming limit curves for 2A16-O aluminum alloy sheet at different temperatures and strain rates

4 结 论

1) 改进Hollomon公式如式(4)所示,该式可获取满足外插可靠度的拟合应力应变,提高有限元分析的精度。

2) χ=1,0.8,0.6,0.4时,最大等效应变均出现在胀形顶点处,与理论分析相符;而χ=0.15时,等效应变的最大值出现在椭圆凹模胀形曲面的侧壁部位。为避免试件提前破裂而影响成形极限获取,椭圆凹模胀形应满足R≥15 mm。

3) 建立了应变率与压力变化率的关系,如式(8)所示,通过控制压力变化以实现板材的恒定应变率加载。同时,结合椭圆凹模胀形和单拉试验,得到不同温度和应变率下的2A16-O铝合金板材成形极限曲线,验证了恒应变率控制的适用性。

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文章信息

SUN Zhijia, YANG Xiying, LANG Lihui

Test method of elliptical hydraulic bulging based on constant strain rate

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(5): 899-905
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0653