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Abstract: Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of
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sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model
is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and
die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted
results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when
the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of
bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface
shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed
that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-
lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to
that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.
Key words: Springback, V-bending, Contact pressure, Neutral surface shifting, Transverse stress, Bending ratio 9344
doi:10.1631/jzus.2007.A0237 Document code: A CLC number: TG386.3
INTRODUCTION
As an important manufacturing method, bending
has been widely used in modern industries to produce
stamping parts such as frames, channels, braces,
brackets and other structural parts. The understanding
and development of bending mechanics are aimed at
achieving two kinds of information which are very
important for industrial production. One is to predict
springback for dies design and compensation in order
to obtain high dimension accuracy of bending parts.
The other is to determine the limit bending ratio Ri/t0
for a given sheet thickness and material properties.
Different methods such as analytical method,
semi-analytical method and finite element method
(FEM) have been applied to analyze the bending
process (Gerdeen and Duncan, 1986; Huang and
Gerdeen, 1994). FEM is a time-consuming method
and also is very sensitive to numerical parameters
such as element type and size, algorithms, contact
definition and convergence criterion for solution, etc.
(Li and Wagoner, 1998; Hamouda et al., 2004). Ana-
lytical method is a time-saving method and has been
widely used for predicting springback of bending
parts. But most of these researches ignored the effects
of contact pressure, transverse stress, neutral surface
shifting and thickness thinning on sheet springback of
bending parts. Gardiner (1957) presented a
mathematical model to calculate the springback of
pure bending for perfect plastic material. Johnson and
Yu (1981a; 1981b; 1982) further developed
Gardiner’s work on tension-bending problem, using
linearly and exponentially hardening material model.
Based on plane strain condition, Wang et al.(1993)
established a mathematical model for predicting the
springback, bend ability, strain and stress distribu-
tions, and maximum loads on the punch for
air-bending problem. By using three rules for material