Summary
Strips of copper, brass and mild steel, horizontally and freely supported in a circular die, were formed using a matching punch. The developments of clearance between the strip and the punch pole, and of primary and secondary bottoming of the strips against the die with consequent multi-point bending are described. The associated punch load-travel curves are shown and compared with the results of a theoretical analysis. The effects of tensile forces and strain-hardening on bending and springback are also summarized.
Representative results are presented concerning the stamping of rectangular plates into doubly-curved dies by matching punches in order to examine the effects of die curvature ratio, specimen dimension and the largest punch load applied. Photographs are shown of the contact regions which develop between plate, die and punch. Rigid/plastic deformation models with appropriate hinge lines are proposed and the experimental results are seen to be in good accord throughout.
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Abbreviations
- a1, a2 :
-
half side-lengths of rectangular plate
- D:
-
diameter
- E:
-
Young’s modulus
- Ep :
-
strain-hardening modulus
- h:
-
thickness
- L:
-
half length of strip
- Me :
-
largest elastic bending moment
- Mp :
-
fully plastic bending moment
- P:
-
punch load
- P*:
-
largest punch load applied
- R:
-
radius of curvature
- S:
-
area of plate
- s:
-
arc length
- Y:
-
yield stress
- Δ:
-
punch travel
- η:
-
non-dimensional parameter, μm /μm.
- κ:
-
curvature
- λ:
-
non-dimensional parameter, L/R
- μb, μm :
-
non-dimensional parameters
- ξ:
-
standard deviation of curvature distribution
- ρ:
-
non-dimensional parameter, YR/Eh
- ω:
-
curvature-ratio of die, κ D1 /κ D2
References
Johnson, W.: The mechanics of some industrial pressing, rolling and forging processes, in “Mechanics of Solids: The Rodney Hill 60th Anniversary Volume” (Eds. H. G. Hopkins and M. J. Sewell), Pergamon Press (1982), pp. 303–356.
Johnson, W.; Singh, A. N.: Springback after cylindrically bending metal strips, Conference on Large Deformation, Delhi, December, 1979, see ‘Large Deformations’, Edited by N. K. Gupta and S. Sengupta, South Asian Publishers (1982), pp. 236–250.
Yu, T. X.; Johnson, W.: Experiments on the cylindrical bending of metal strips, to be published in Metals Technology.
Yu, T. X.; Johnson, W.: A theoretical analysis on the cylindrical bending of strips, to be published in Metal Technology.
Johnson, W.; Yu, T. X.: The large elastic deflection on thin strips in V-die bending and the onset of plasticity, to be published in Proceedings of Institution of Mechanical Engineers.
Yu, T. X.; Johnson, W.: Influence of axial force on the elastic-plastic bending and springback of a beam, Journal of Mechanical Working Technology, (1982), 6, 5–21.
Yu, T. X.; Johnson, W.: The press-brake bending of rigid/linear work-hardening plates, Int. J. Mech. Sci., (1981), 23, 307–318.
Oh, S. I.; Kobayashi, S.: Finite element analysis of plane-strain sheet bending, Int. J. Mech. Sci., (1980), 22, 583–594.
Yu, T. X.; Johnson, W.; Stronge, W. J.: The stamping of rectangular plates into doubly-curved dies, to be published in the Int. J. Mech. Sci.
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© 1983 Springer-Verlag, Berlin, Heidelberg
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Johnson, W., Yu, T.X. (1983). The Cylindrical Bending of Strips and the Biaxial Stamping of Rectangular Plates into Curved Dies. In: Grundlagen der Umformtechnik — Stand und Entwicklungstrends / Fundamentals of Metal Forming Technique — State and Trends. Berichte aus dem Institut für Umformtechnik der Universität Stuttgart, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82186-8_1
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DOI: https://doi.org/10.1007/978-3-642-82186-8_1
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