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TECHNICAL PAPERS

Asymptotic Stability Analysis for Sheet Metal Forming—Part II: Application

[+] Author and Article Information
W. Scherzinger

Sandia National Laboratories, P.O. Box 5800, MS 0847, Albuquerque, NM 87185  

E. Chu

ALCOA Inc., Alcoa Technical Center, Alcoa Center, PA 15069-0001  

N. Triantafyllidis

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140

J. Appl. Mech 67(4), 691-696 (Jan 30, 2000) (6 pages) doi:10.1115/1.1325013 History: Received September 24, 1999; Revised January 30, 2000
Copyright © 2000 by ASME
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References

Figures

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Schematic drawing for hemispherical cup test
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Kinematics for axisymmetric shell and membrane theories. C is the meridian for the sheet in the undeformed (reference) configuration, and C̄ is the meridian for the sheet in the deformed (current) configuration.
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Stress history for material points initially at a radius of 48.12 mm for the 0.508 mm sheet. Stress history is shown for the bottom, middle, and top surfaces of the shell.
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Stress history for material points initially at a radius of 48.12 mm for the 1.016 mm sheet. Stress history is shown for the bottom, middle and top surfaces of the shell.
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Effect of sheet thickness on the critical punch height for a brass sheet with RL/RA=1.7, the S1 tooling, BHF=41.316 kN a coefficient of friction μ=0.04. The membrane prestress underpredicts the shell theory results for the same constitutive relations. Using a corner theory, and varying its corner geometry so as to approach a flow theory, the critical punch height increases. It is noted that the BHF used for all the numerical calculations is the experimental value corresponding to the thickest blank. Experimental results are marked by (♦).
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Effect of friction on the critical punch height for 1.016 mm brass sheet with RL/RA=1.7, the S1 tooling and a BHF=41.316 kN. The trend in the results is the same as that seen in Fig. 5, and it shows the great dependence of the results on the friction boundary conditions, which are often difficult to measure. The experimental result for this case is shown by the dashed line.

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