For a perforated sheet with circular holes, used in shadow masks, the diameter of the circular hole varies through the thickness, and the nonuniform circular holes are arranged in a triangular pattern. In order to simplify the analysis, a perforated sheet with equivalent circular holes of uniform diameter is proposed such that its plastic behavior is similar to that with the given nonuniform circular holes. In this study, a yield criterion is discussed for the perforated sheet with uniform circular holes by employing an equivalent continuum approach, which is then applied to examine the plastic deformation of the perforated sheet with nonuniform circular holes. The analytical results predicted by the theory, including those for the apparent yield stresses and strain ratios, are verified by the results obtained from the finite element analysis and also from experiments.

Issue Section:
Technical Papers
Keywords:
yield stress, plastic deformation, finite element analysis, plasticity, stress analysis
Topics:
Deformation, Finite element analysis, Stress, Yield stress, Flow (Dynamics), Shades and shadows
1.
Gardner
,
K. A.
,
1948
, “
Heat Exchanger Tube Sheet Design
,”
ASME J. Appl. Mech.
,
70
, pp.
377
–
385
.
2.
Doerschuk
,
E. E.
,
Moscony
,
J. J.
, and
Weber
,
D. M.
,
1948
, “
Shadow-mask Etching for Data-display Tubes
,”
RCA Eng.
,
29
(
2
), pp.
67
–
73
.
3.
O’Donnell
,
W. J.
, and
Langer
,
B. F.
,
1962
, “
Design of Perforated Plates
,”
ASME J. Ind.
,
84
, pp.
307
–
320
.
4.
Horvey
,
G.
,
1952
, “
The Plane-stress Problem of Perforated Sheet
,”
ASME J. Appl. Mech.
,
74
, pp.
355
–
360
.
5.
O’Donnell
,
W. J.
, and
Porowski
,
J.
,
1973
, “
Yield Surface for Perforated Materials
,”
ASME J. Appl. Mech.
,
37
, pp.
260
–
268
.
6.
Sawczuk
,
A.
,
O’Donnell
,
W.
, and
Porowski
,
J.
,
1975
, “
Plastic Analysis of Perforated Plates for Orthotropic Yield Criteria
,”
Int. J. Mech. Sci.
,
17
, pp.
411
–
421
.
7.
Chen
,
F. K.
,
1993
, “
Analysis of Plastic Deformation for Sheet Metals with Circular Perforations
,”
J. Mater. Process. Technol.
,
37
, pp.
175
–
188
.
8.
Baik
,
S. C.
,
Oh
,
K. H.
, and
Lee
,
D. N.
,
1995
, “
Forming Limit Diagram of Perforated Sheet
,”
Scr. Metall. Mater.
,
33
, pp.
1201
–
1207
.
9.
Baik
,
S. C.
,
Oh
,
K. H.
, and
Lee
,
D. N.
,
1996
, “
Analysis of the Deformation of a Perforated Sheet Under Uniaxial Tension
,”
J. Mater. Process. Technol.
,
58
, pp.
139
–
144
.
10.
Baik
,
S. C.
,
Han
,
H. N.
,
Lee
,
S. H.
,
Oh
,
K. H.
, and
Lee
,
D. N.
,
1997
, “
Plastic Behavior of Perforated Sheets Under Biaxial Stress State
,”
Int. J. Mech. Sci.
,
39
, pp.
781
–
793
.
11.
Isida
,
M.
, and
Igawa
,
H.
,
1991
, “
Analysis of a Zig-zag Array of Circular Holes in an Infinite Solid Under Uniaxial Tension
,”
Int. J. Solids Struct.
,
27
, pp.
849
–
864
.
12.
Lee
,
Y. C.
, and
Chen
,
F. K.
,
2000
, “
Yield Criterion for a Perforated Sheet with a Uniform Triangular Pattern of Round Holes and a Low Ligament Ratio
,”
J. Mater. Process. Technol.
,
103
, pp.
353
–
361
.
13.
Nadai, A., 1950, Theory of Flow and Fracture of Solids, McGraw-Hill, New York.
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 by ASME
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