The general asymptotic method proposed in Part I is applied to the investigation of the puckering instability in the hemispherical cup test. Both a membrane and a shell stress state for the principal axisymmetric solution have been considered. Due to the possibility of strong deviations from proportional loading in some cases, a corner theory of plasticity is also employed, in addition to the standard J2 deformation theory which is often used in plastic buckling calculations. Results are compared to a previous experimental investigation for brass specimens. [S0021-8936(00)00904-1]

Issue Section:
Technical Papers
Keywords:
asymptotic stability, buckling, plastic deformation, stress analysis, forming processes, metals
Topics:
Buckling, Deformation, Membranes, Shells, Stability, Tooling, Stress, Corners (Structural elements), Plasticity, Sheet metal work, Brass (Metal), Kinematics
1.
Devons, J. D., 1941, The Metallurgy of Deep Drawing and Pressing, Chapman Hall, London.
2.
Triantafyllidis
,
N.
,
1985
, “
Puckering Instability in the Hemispherical Cup Test
,”
J. Mech. Phys. Solids
,
33
, pp.
117
–
139
.
3.
Donoghue
,
M.
,
Stevenson
,
R.
,
Kwon
,
Y. J.
, and
Triantafyllidis
,
N.
,
1989
, “
An Experimental Verification of the Hemispherical Cup Puckering Problem
,”
ASME J. Eng. Mater. Technol.
,
111
, pp.
248
–
254
.
4.
Triantafyllidis
,
N.
, and
Samanta
,
S. K.
,
1986
, “
Bending Effects on Flow Localization in Metallic Sheets
,”
Proc. R. Soc. London, Ser. A
,
406
, pp.
205
–
226
.
5.
Christoffersen
,
J.
, and
Hutchinson
,
J. W.
,
1979
, “
A Class of Phenomenological Corner Theories of Plasticity
,”
J. Mech. Phys. Solids
,
27
, pp.
465
–
487
.
6.
Goetz, A., 1970, Introduction to Differential Geometry, Addison-Wesley, New York.
7.
Hutchinson
,
J. W.
,
1974
, “
Plastic Buckling
,”
Adv. Appl. Mech.
,
14
, pp.
67
–
144
.
Copyright © 2000
 by ASME
You do not currently have access to this content.