Trans. Indian Inst. Met.
TP 2182
Vol. 61, No. 1, February 2008, pp. 39-43
Study Of Effect Of Load On Springback In Sheet Metal Bending S.K. Panthi, N. Ramakrishnan, R. Das Gupta and J.S. Chouhan * Advanced Materials and Processes Research Institute (AMPRI), Bhopal-26 (MP) India * Civil engineering department, S.A.T.I, Vidisha 464001(M.P.) India E-mail:
[email protected] (Received 31 May 2007 ; in revised form 25 February 2008)
ABSTRACT Springback remains a major concern in sheet metal bending in fabricating any final product within the permissible tolerance. Apart from the geometrical and material parameters, springback is significantly affected by the forming load also and the present study is focused on it. Sheet metal bending process involves large rotation and strain as well as large springback due to elastic recovery of the material. Therefore, a large deformation algorithm based Finite Element software was used to model a typical sheet metal bending process employed in manufacturing cylindrical structures. A Total-ElasticIncremental-Plastic (TEIP) algorithm has been incorporated in an in-house software to handle large deformation and the elastic recovery during the unloading process. In addition, experiments have been performed on aluminum, brass, copper and mild steel sheets and substantiated with the FEM analysis.
1. INTRODUCTION In sheet metal bending process, a blank is plastically deformed between tools to obtain the desired final configuration. The process is very important in automobile and aerospace industries in manufacturing curved parts, large spherical & cylindrical pressure vessels etc. The accuracy in dimension, always remains a major concern in sheet metal bending process owing to the considerable elastic recovery during unloading which leads to springback. Springback is normally measured in terms of the difference between the dimensions of the fully loaded and unloaded final configurations. The elastic recovery is influenced by a combination of various process parameters, such as tool shape & dimension, material properties and thickness of the sheet. Apart from these parameters, elastic recovery is significantly influenced by the forming load. The determination of springback by means of trial and error technique is expensive and time consuming1. The prediction of springback using numerical simulation based on Finite Element Method (FEM) has been proved to be a powerful tool and used extensively. Prediction of the springback during bending operation has been addressed by several investigators in the past. Cho et al. 2 carried out numerical investigation on springback characteristics in plane strain ‘U’ bending process by thermoelastoplastic FEM. Li et al 3 mainly dealt with material hardening and Modulus to analyze ‘V’ bending by simulation and showed that the material-hardening characteristics directly affect the springback. Chaudhary and Lee4 accounted
for inertial effects in the FEM of sheet metal forming process. Papeleux and Ponthot5 discussed numerically the effect of blank holder force, friction etc. on the forming response. Chou and Hung 6 carried out FEM of several springback reduction techniques such as over bending, stretching, arc bottoming, pinching die, spanking and movement (double bend) techniques, used in ‘U’ channel bending. Math and Grizelj7 reported springback and residual stresses of bent plates designed for assembling spherical tanks made of steel using elastic-plastic incremental FE calculations. Esat et al.8 carried out springback analysis of different aluminum sheets with different thicknesses and FEM results were compared with empirical ones. Lei et al.9 analyzed the free bending and square cup deep drawing to predict the springback, stress distribution etc. for stainless steel with FEM. In this investigation, an elasto-plastic analysis of sheet metal bending process was carried out using experiments to predict the springback and substantiated with FEM. The main feature of this study is to investigate the influence of load on the springback pertaining to arc type sheet bending. The experimental data on aluminum, copper, brass and mild steel sheets were presented and results were compared with FEM ones, which shows a reasonable agreement.
2. SHEET BENDING EXPERIMENT A standard 400 tonne hydraulic press was used to carry out the experiment of sheet metal bending process. It has two parallel platens of tungsten carbide with facilities for measuring loads, displacements as well as the speed of the platen. Figure 1 shows the setup of bending process with the
Fig. 1 : Experimental setup of the bending process
40 | Panthi et al. : Study of effect of load on springback in sheet metal bending
die, punch and sheet on the hydraulic press. The die radius was 200 mm, radius of the punch was 195 mm and sheet thickness was 5 mm. Aluminum, copper, brass and mild steel sheets were used, to carry out the experiments. Mild steel die and punch, with well polished surfaces, were used in the experiment. The initial size of the sheet was 240 mm in length, 50 mm in width and 5 mm in thickness. The sector angle was kept as 600 in all these experiments. The sheet was freely placed on the bottom die without any pre-stress or any external influence. Downward displacement was given to the upper platen of the press at a speed of 0.5 mm/sec to bend the sheet. The exact gap between the lower surface of the sheet and the bottom die surface was 27.46 mm. In the first trial of bending, a total downward displacement of 27.5 mm was given to the upper platen to bend the sheet and the load was recorded. To release the forming load, upward displacement was given to the upper platen and the sheet was allowed to elastically relax itself without any external influence. The experiment was repeated for different load conditions. Figure 2 shows the bent shape of the mild steel sheet with different radii at different forming loads. The spring back values were calculated by measuring the radius of the deformed sheet as shown in Fig. 3; assuming the bent sheet to conform to an arc of a circle, the final radius of the bent sheet was calculated as,
rf
X 2 h2 2h
(1)
Where, x = half of the chord length, h = the distance between the chord line and the sheet at the center, rf = final radius of the bent sheet after spring back as shown in Fig. 3. The experiments were carried out in the unlubricated condition. Load was applied at a slow rate so as to disregard from inertial effects on the test results and the magnitude was kept low so as to keep thickness change minimal. The experiment was performed at room temperature under normal atmospheric pressure and biaxial homogeneity was assumed with regard to the sheet metal. In order to compare the
Fig. 3 : Calculation of final radius of the bent sheet from the experiment
experimental results with the simulated results, the ratios of rf ri
and
rf t
, where rf is the final radius, ri is the radius of
the die and t is the thickness of the sheet, were plotted.
3. NUMERICAL SIMULATION OF SHEET METAL BENDING The initial FE mesh geometry used for the simulation is shown in Fig. 4. A FORTRAN coded software was developed to generate the FE mesh parametrically. Thickness of the sheet, radius of the die, number of elements in x and y directions, number of elements in the die and the punch, and sector angle are parametrically input to generate the mesh. The geometrical parameters as in the experiment were assigned in the FEM. The initial mesh configuration consisting of bilinear quadrilateral elements is shown in Fig. 4. Symmetry is used in imposing the boundary conditions. The details are shown in Fig. 4. The process is simulated for the plane strain condition. The elements representing the die and the punch are assumed rigid and these elements formed the master surfaces. The elements representing the sheet are treated as deformable
Fig. 2 : Bent sheet of mild steel at different load of forming Trans. Indian Inst. Met., Vol. 61, No. 1, February 2008
Fig. 4 : Initial geometry of the process used for the simulation
Panthi et al. : Study of effect of load on springback in sheet metal bending | 41
rf
X 2 X1 2 Y2 Y1 2 2 Y2 Y1
(2)
To establish the relaxed configuration to be an arc of a circle, different sets of points were taken and the radii were computed and the mean difference does not exceed about 1%.
Table 1 Material Properties of Material Material
Young’s modulus (GPa)
Yield stress (MPa)
Strain hardening exponent
Poisson’s Ratio
Aluminum
72
210
0.26
0.33
Copper
117
190
0.10
0.36
Brass
110
75
0.49
0.34
Mild Steel
200
190
0.22
0.3
The prediction of springback by FE simulation is carried out for copper, brass, aluminum and mild steel sheets. The mechanical properties used for the simulation 10-12 are presented in Table 1. Fig. 5 : The deformation shapes for the bending process at various stages of the punch displacement
body and the surfaces formed the slave surfaces. The displacement of the nodes of the slave surface is constrained by the contact boundary condition imposed by the rigid master surface. Suitable downward ‘y’ displacement is assigned to the nodes representing the punch and the same are constrained in ‘x’ direction. The nodes forming the stationary die are constrained in both ‘x’ and ‘y’ directions. The sheet is placed on the bottom die and the punch is moved downward gradually. The sheet metal bends gradually as the deformation is induced in the sheet after making contact with the punch. This is numerically carried out by assigning the necessary total punch displacement. Figures 5a to 5c presents the bent shape of the sheet during the bending process at the stages of 15, 75 and 100 % of the assigned total punch displacement. After the complete depression, the punch is gradually elevated to free the plate and the plate is allowed to elastically relax itself incrementally and iteratively in each increment. The final relaxed shape of the bent sheet after the release of the forming load is shown in Fig. 5d. The simulation is carried out from the minimal load condition to saturation condition. In this study, the “minimal load condition” refers to the depression of the punch at which the sheet metal just takes the shape of the die. Any subsequent displacement of the punch from minimal load condition increases the load steeply. In the literature, some times, it is referred to as ‘overstress’ or ‘overloading’ condition 7 . The springback is characterized in terms of change in radius of the bent sheet with respect to die radius. The final radius of the bent sheet is calculated as follow: If (x1, y1) and (x2, y2) are the co-ordinates of two distant nodal points on the bent sheet, its radius (rf) is calculated by the following equation
4. RESULTS & DISCUSSION The experiment was carried out for a die radius of 200 mm, sheet thickness of 5mm, punch radius of 195mm with a sector angle of 60 degrees. The experiment was performed on aluminum, copper, brass and mild steel sheets and springback ratio was determined. The experimental results are presented in Fig. 6 as a plot between the springback ratio
rf ri
and
rf
, where rf , ri and t represent t final radius of the bent sheet, radius of the die and the thickness of the sheet respectively. The abscissa is taken as
normalized design radius
rf t
for purely design convenience, since the input to the
Fig. 6 : Comparison of experiment and simulation results
Trans. Indian Inst. Met., Vol. 61, No. 1, February 2008
42 | Panthi et al. : Study of effect of load on springback in sheet metal bending
designer is given in terms of final radius of the bent sheet. The load is varied as 20, 40, 60, 80, 100 KN. It can be seen rf ri
and
rf t
is
linear for, the range of applied load and any of the sheet
rf/ri
from Fig. 6 that the relationship between
rf
< 70. The springback ratio is t extremely sensitive to the amount of load. The springback ratio is high at the minimal load and it decreases with increase in load. In Fig. 6, point ‘A’ corresponds to the minimal load while ‘B’ corresponds to the higher load condition. material in the range 0 <
The simulation was carried out for the same dimensions of the die, the punch, thickness of the sheet and the sector angle for the sheet materials, aluminum, copper, brass and mild steel. The load was increased to such a level, that further increase in load does not significantly affect the springback, which is referred to in this paper as saturation condition. FEM results compared to experimental results show a considerable agreement and have a linear relation rf ri
rf
and
A plot between
t
rf ri
.
and the compression depth is shown in
rf/ri
Fig. 7 for different materials, where, the displacement of the punch from the minimal load condition is designated as ‘compression depth’ in this investigation. It can be seen from Fig. 7 that the springback ratio is very high at the minimal load condition and it gradually decreases with increase in load. Beyond a certain compression, it was observed that there is no significant influence of loading on the springback. This is termed as saturation condition in this presentation. It was also demonstrated by Math and Grizelj7 experimentally that greater the force, smaller is the springback and beyond some limiting value of loading, any additional loading doesn’t affect the springback. Springback ratio was observed very high in sheet of aluminum compared to copper, brass and mild steel sheets.
rf/ri
between
Fig. 8 : Effect of load on springback ratio on 20 mm thick sheet by FE simulation for a range of die radii
Fig. 9 : Effect of load on springback for different frictional conditions
In addition, the simulation was carried out for 20 mm thick sheet with varying radius of die from 120 mm to 6100 mm taking the sheet material as structural steel with the following mechanical material properties; Yield stress 295 MPa, Young’s Modulus 190 GPa, strain hardening exponent 0.17 and Poisson’s ratio 0.3. It was carried out for a sector angle of 90 degrees with frictionless condition. Figure 8 presents a plot between the springback ratio
rf ri
and compression
depth for die radii. The springback ratio increases with increase in radius of the die. Therefore, a large amount of load is required for high radius of the die to get the final product within the desired shape and dimensions.
Fig. 7 : Effect of load on springback for different materials by FE simulation
Trans. Indian Inst. Met., Vol. 61, No. 1, February 2008
The effect of friction is presented in Fig. 9 for the coefficient of friction from zero to 0.24. It is understand from the figure that lower friction (zero to 0.24) has negligible effect on springback. It is also supported by the literature13,14.
Panthi et al. : Study of effect of load on springback in sheet metal bending | 43
5. CONCLUSIONS
3.
The following conclusions emerge from this study. rf z The relationship between the springback ratio (final ri radius/ die radius) and the final radius normalized with rf is found to be linear (in the range thickness rf t < 70) by experiment as well as FE simulation of 0 < t carried on aluminum, copper, brass and mild steel sheets.
4. 5. 6. 7.
This linear relation appears to be independent of the
8.
type of material and the magnitude of load.
9.
z
The springback is significantly affected by the load but not beyond a certain saturation limit.
10.
z
Springback increases with die radius and therefore for larger die radii, the load is to be high for reducing the springback.
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Trans. Indian Inst. Met., Vol. 61, No. 1, February 2008
