ASM Metals HandBook Vol. 14 - Forming and Forging
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Fig. 17 Comparisons of theoretical and practical limiting strains at each node point for (a) cup 1 and (b) cup 2.
Example 5: Vent Forming.
The same procedure used for cup forming will be followed for the vent forming analysis. Photographs of the formed vent
1 part and the finite-element geometry model corresponding to the round section of the formed part are shown in Fig. 18.
An obvious difference between the two is the side flange, which is not axisymmetric in the formed part. The effect of
assuming a circular flange section in the analysis will be discussed when the analytical result is compared with the
experimental data.
Fig. 18 (a) Photograph of the formed part and (b) finite element model for the circular section in (a) for vent.
Following the same procedure used in the cup analysis, the computed results are compared with the safe/marginal/failure
FLD criteria shown in Fig. 19. Vent 1 can be formed without any difficulty. Laboratory forming of vent 1 did not cause
any necking, which is consistent with the finite-element analysis results.
Fig. 19 Comparisons of theoretical and practical major and minor strains at each node point for vent 1.
Example 6: Square Box Forming.
The three-dimensional square-box forming process was modeled following an analytical procedure similar to that used in
Examples 4 and 5. Here again, two assumptions were made: First, the plane stress condition is valid, and, second, the
deformation theory of plasticity is applicable. The unknowns, then, are the initial location of the element nodal
coordinates as well as the blank shape. These unknowns are computed by applying the principle of minimum potential
energy. The basic mathematical approach is summarized in Ref 118.
A summary of the details of square-box geometry and loading boundary conditions include:
• Material: aluminum-killed steel
• Stress-stain curve: σ= 739 ε
0.3
MPa
• Punch size: 40 × 40 mm (1.6 × 1.6 in.)
• Die size: 42.5 × 42.5 mm (1.7 × 1.7 in.)
• Punch radius: 5 mm (0.2 in.)
• Die radius: 5 mm (0.2 in.)
• Corner radius: 3.2 mm (0.125 in.)
• Blank size (undeformed): 110 × 110 mm (4.3 × 4.3 in.)
• Coefficient of friction: 0.2 at the punch and 0.04 at the die
• Blank holding pressure: 500 kgf (1100 lbf)
The deformed sheet domain used in the square-cup simulation is shown in Fig. 20. Eight noded isoparametric membrane-
type elements were used. The solution was converged within 25 iterations to increments of nodal displacements of <25
m (0.001 in.). Figures 21 and 22 show the major strain distributions across the diagonal and transverse generators of the
square cup, respectively. The experimental results obtained by T.R. Thomson (Ref 119) were also included for
comparison. Although a considerable discrepancy of the results is seen under the flat punch profile, good correlation
between the predicted finite-element model and the experimental results is observed. In particular, the experimental and
predicted results match most closely at the critical areas of the punch and die profile radii where the highest strains are
observed.
Fig. 20 (a) Major and (b) minor strain distributions superimposed on the finite-element mesh representing one-
quarter of the square box.
Fig. 21 Comparison of the numerical solutions wit
h experimental results for major and minor strain
distributions along the diagonal generator of a square box. Punch depth: 30 mm (1.18 in.).
Fig. 22
Comparison of the numerical solutions with experimental results for major and minor strain
distributions along the transverse generator of a square box. Punch depth: 30 mm (1.18 in.).
References cited in this section
118.
J. Amoedo, "Development of Sheet Metal Forming Analysis Method for Symmetric Three-
Dimensional Parts,"
Masters of Engineering thesis, Rensselaer Polytechnic Institute, 1987
119.
T.R. Thomson, Influence of Material Properties in the Forming of Square Shells, J. Australian Inst. Met.,
Vol 20,
1975, p 106-113
Process Modeling and Simulation for Sheet Forming
D. Lee, S.A. Majlessi, and J. H. Vogel, Department of Mechanical Engineering, Rensselaer Polytechnic Institute
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