كتاب Mechanics of Sheet Metal Forming - Material Behavior and Deformation Analysis

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Mechanics of Sheet Metal Forming
Material Behavior and Deformation Analysis
Edited by
Donald P. Koistinen and Neng-ming Wang
General Motors Research Laboratories

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CONTENTS
Preface . v
SESSION I-State of the Art
Chairman: W. Johnson,
University of Cambridge
Sheet Metal Stamping TechnologyNeed for Fundamental Understanding
S. P. Keeler, National Steel Corporation 3
Discussion . 17
Experimental Studies of Material Behavior as
Related to Sheet Metal Forming
K. Yoshida and K. Miyauchi,
The Institute of Physical and Chemical Research
Discussion .
Plasticity Analysis of Sheet Metal Forming
P. B. Mellor and A. Parmar, University of Bradford
Discussion .
SESSION II-Constitutive Relations for Sheet Metal
Chairman: E. H. Lee,
Stanford University . 79
Plastic Deformation Behavior Under Conditions of Combined Stress
Y. Tozawa, Nagoya University. . . . 81
Discussion . 109Vlll CONTENTS
Sheet Necking-I. Validity of Plane Stress Assumptions of the
Long-Wavelength Approximation
J. W. Hutchinson, Harvard University
K. W. Neale, Universite de Sherbrooke
A. Needleman, Brown University 111
Sheet Necking-II. Time-Independent Behavior
J. W. Hutchinson, Harvard University
K. W. Neale, Universite de Sherbrooke 127
Discussion . 150
SESSION III-Role of Friction
Chairman: J. J. Jonas,
McGill University 155
Friction and Lubrication in Sheet Metal Forming
W. R. D. Wilson, University of Massachusetts . , 157
Discussion , 174
Drawbead Forces in Sheet Metal Forming
H. D. Nine, General Motors Research Laboratories 179
Discussion . 207
SESSION IV-Instability Processes
Chairman: S. S. Hecker,
Los Alamos Scientific Laboratory 213
Sheet Metal Forming Limits
Z. Marciniak, Technical University of Warsaw
Discussion .
Limits to Ductility Set by Plastic Flow Localization
A. Needleman and J. R. Rice, Brown University
Discussion .
Sheet Necking-III. Strain-Rate Effects
J. W. Hutchinson, Harvard University
K. W. Neale, Universite de Sherbrooke
Discussion
Plastic Flow Properties in Relation to Localized Necking in Sheets
A. K. Ghosh, Rockwell International . 287
Discussion . 311
SESSION V-Analysis of Deformation in Stamping Operations
Chairman: B. Budiansky,
Harvard University . 313
Deformation Analysis of Large Sized Panels in the Press Shop
H. Ishigaki, Toyota Motor Company . 315
Discussion . 338
Deformation Analysis of Axisymmetric Sheet Metal Forming
Processes by the Rigid-Plastic Finite Element Method
S. Kobayashi and J. H. Kim, University of California. . 341
Discussion . 363
Elastic-Viscoplastic Analyses of Simple Stretch Forming Problems
N.-M. Wang and M. L. Wenner, General Motors Research Laboratories 367
Discussion . 398
Symposium Summary
B. Budiansky, Harvard University 403
Participants . 407
Subject Index .
407
PARTICIPANTS
Agnew, W. G.
General Motors Research Laboratories
Warren, Michigan
Altan, T.
Battelle Laboratories
Columbus, Ohio
Amann, C. A.
General Motors Research Laboratories
Warren, Michigan
Armen, H. A.
Grumman Aerospace Corporation
Bethpage, New York
Astill, C. J.
National Science Foundation
Washington, DC
Ayres, R. A.
General Motors Research Laboratories
Warren, Michigan
Babcock, S. G.
General Motors Manufacturing Staff
Warren, Michigan
Bartell, B. E.
Chevrolet Motor Division, GMC
Parma, Ohio
Bathe, K.-J.
Massachusetts Institute of Technology
Cambridge, Massachusetts
Baxter, W. J.
General Motors Research Laboratories
Warren, Michigan
Beaman, R. T.
General Motors Research Laboratories
Warren, Michigan
Bowden, R. L.
Fisher Body Division, GMC
Warren, Michigan
Bidwell, J. B.
General Motors Research Laboratories
Warren, Michigan
Bird, J. E.
Aluminum Company of America
New Kensington, Pennsylvania
Bragard, M. A.
Centre de Recherches Metallurgiques
Liege, Belgium
Brazier, W. G.
Fisher Body Division, GMC
Warren, Michigan
Bucher, J. H.
Jones & Laughlin Steel Corporation
Pittsburgh, Pennsylvania
Budiansky, B.
Harvard University
Cambridge, Massachusetts
Butterworth, A. V.
General Motors Research Laboratories
Warren, Michigan
Buzan, L. R.
General Motors Research Laboratories
Warren, Michigan408
Caddell, R. M.
University of Michigan
Ann Arbor, Michigan
Chang, D. C.
General Motors Research Laboratories
Warren, Michigan
Chatfield, D. A.
National Steel Corporation
Weirton, West Virginia
Chen, K.-K.
General Motors Research Laboratories
Warren, Michigan
Chenea, P. F.
General Motors Research Laboratories
Warren, Michigan
Conrad, H.
University of Kentucky
Lexington, Kentucky
Devenpeck, M. L.
U.S. Steel Corporation
Monroeville, Pennsylvania
Dodd, G. G.
General Motors Research Laboratories
Warren, Michigan
Dubey, R. N.
University of Waterloo
Waterloo, Canada
Duncan, J. L.
McMaster University
Hamilton, Canada
Eary, D.
General Motors Institute
Flint, Michigan
Ebert, L. J.
Case Western Reserve University
Cleveland, Ohio
PARTICIPANTS
Elliott, W. A.
General Motors Engineering Staff
Warren, Michigan
Fredericks, D. R.
AC Spark Plug Division, GMC
Flint, Michigan
Frey, W. H.
General Motors Research Laboratories
Warren, Michigan
Furubayashi, T.
Nissan Motor Company Ltd.
Yokohama, Japan
Gardels, K. D.
General Motors Research Laboratories
Warren, Michigan
Gegel, H. L.
Air Force Materials Laboratory
Dayton, Ohio
Ghosh, A. K.
Rockwell International
Thousand Oaks, California
Gibala, R.
Case Western Reserve University
Cleveland, Ohio
Goodwin, G. M.
Chrysler Corporation
Detroit, Michigan
Grube, W. L.
General Motors Research Laboratories
Warren, Michigan
Hall, C.
University of Pittsburgh
Pittsburgh, Pennsylvania
Hall, D. A.
Chevrolet Motor Division, GMC
Warren, MichiganPARTICIPANTS
Hart, D. E.
General Motors Research Laboratories
Warren, Michigan
Havner, K.
North Carolina State University
Raleigh, North Carolina
Hays, D. F.
General Motors Research Laboratories
Warren, Michigan
Hecker, S. S.
Los Alamos Scientific Laboratory
Los Alamos, New Mexico
Heimbuch, R. A.
General Motors Manufacturing Staff
Warren, Michigan
Henry, A. K.
Fisher Body Division, GMC
Warren, Michigan
Hiam, J. R.
Dominion foundries and Steel Ltd.
Hamilton, Canada
Hilsen, R. R.
Inland Steel Company
East Chicago, Indiana
Hockett, J. E.
Los Alamos Scientific Laboratory
Los Alamos, New Mexico
Hodge, P. G., Jr.
University of Minnesota
Minneapolis, Minnesota
Hollyer, R. N.
General Motors Research Laboratories
Warren, Michigan
Holzwarth, J. C.
General Motors Research Laboratories
Warren, Michigan
Hook, R. E.
Armco Steel Corporation
Middletown, Ohio
Hosford, W. F.
University of Michigan
Ann Arbor, Michigan
Hunter, J. E.
409
General Motors Research Laboratories
Warren, Michigan
Hutchinson, J. W.
Harvard University
Cambridge, Massachusetts
Ishigaki, H.
Toyota Motor Company
Toyota, Japan
Jalinier, J. M.
Universite de Metz
Metz, France
Jamerson, F. E.
General Motors Research Laboratories
Warren, Michigan
James, K. F.
General Motors Manufacturing Staff
Warren, Michigan
Johnson, W.
University of Cambridge
Cambridge, England
Jonas, J. J.
McGill University
Montreal, Canada
Justusson, J. W.
General Motors Research Laboratories
Warren, Michigan
Kaftanoglu, B.
The Middle East Technical University
Ankara, Turkey410
Kalpakjian, S.
Illinois Institute of Technology
Chicago, Illinois
Kamal, M. M.
General Motors Research Laboratories
Warren, Michigan
Kasper, A. S.
Chrysler Corporation
Detroit, Michigan
Keeler, S. P.
National Steel Company
Ecorse, Michigan
Key, S. W.
Sandia Laboratories
Albuquerque, New Mexico
Kobayashi, S.
University of California
Berkeley, California
Kocks, U. F.
Argonne National Laboratory
Argonne, Illinois
Koistinen, D. P.
General Motors Research Laboratories
Warren, Michigan
Laukonis, J. V.
General Motors Research Laboratories
Warren, Michigan
Lee, D.
General Electric Company
Schenectady, New York
Lee, E. H.
Stanford University
Stanford, California
LeRoy, G.
McMaster University
Hamilton, Canada
Levy, B. S.
Inland Steel Company
East Chicago, Indiana
Lindholm, U. S.
PARTICIPANTS
Southwest Research Institute
San Antonio, Texas
Litzke, H.
Fried. Krupp Huttenwerke AG
Bochum, West Germany
Magee, C. L.
Ford Motor Company
Dearborn, Michigan
Mancewicz, T. A.
General Motors Manufacturing Staff
Warren, Michigan
Marciniak, Z.
Technical University of Warsaw
Warsaw, Poland
Mattavi, J. N.
General Motors Research Laboratories
Warren, Michigan
McClintock, R.
General Motors Research Laboratories
Warren, Michigan
McCullough, D. G.
Pontiac Motor Division, GMC
Pontiac, Michigan
McDonald, G. C.
General Motors Research Laboratories
Warren, Michigan
McDonald, R. J.
General Motors Research Laboratories
Warren, Michigan
McLaughlin, B. D.
Alean International Ltd.
Kingston, CanadaPARTICIPANTS
McMillan, M. L.
General Motors Research Laboratories
Warren, Michigan
Mellor, P. B.
University of Bradford
Bradford, England
Miller, E. J.
General Motors Research Laboratories
Warren, Michigan
Miyauchi, K.
The Institute of Physical and Chemical
Research, Tokyo, Japan
Morris, L.
Alcan International Ltd.
Kingston, Canada
Muench, N. L.
General Motors Research Laboratories
Warren, Michigan
Neale, K. W.
Universite de Sherbrooke
Sherbrooke, Canada
Needleman, A.
Brown University
Providence, Rhode Island
Neimeier, B. A.
Reynolds Metals Company
Richmond, Virginia
Nemat-Nasser, S.
Northwestern University
Evanston, Illinois
Ni, C.-M.
General Motors Research Laboratories
Warren, Michigan
Nimmer, R. P.
General Electric Company
Schenectady, New York
411
Nine, H. D.
General Motors Research Laboratories
Warren, Michigan
Oh, H. L.
General Motors Research Laboratories
Warren, Michigan
Rashid, M. S.
General Motors Research Laboratories
Warren, Michigan
Rasmussen, G. K.
AC Spark Plug Division, GMC
Flint, Michigan
Rhodes, C. J.
GMC Truck & Coach Division
Pontiac, Michigan
Rice, J. R.
Brown University
Providence, Rhode Island
Robinson, G. H.
General Motors Research Laboratories
Warren, Michigan
Rogers, H. C.
Drexel University
Philadelphia, Pennsylvania
Sajewski, V. F.
Fisher Body Division, GMC
Warren, Michigan
Sang, H.
Alcan International Ltd.
Kingston, Canada
Shabaik, A.
University of California
Los Angeles, California
Smith, E. J.
National Steel Corporation
Weirton, West Virginia412
Smith, G. W.
General Motors Research Laboratories
Warren, Michigan
Sorensen, E. P.
General Motors Research Laboratories
Warren, Michigan
Stevenson, R.
General Motors Research Laboratories
Warren, Michigan
Stine, P. A.
General Electric Company
Louisville, Kentucky
Tanaka, T.
Nippon Kokan K.K.
New York City, New York
Tang, S. C.
Ford Motor Company
Dearborn, Michigan
Taylor, B.
General Motors Manufacturing Staff
Warren, Michigan
Thomas, J. F., Jr.
Wright State University
Dayton, Ohio
Tozawa, Y.
Nagoya University
Nagoya, Japan
Tracy, J. C.
General Motors Research Laboratories
Warren, Michigan
PARTICIPANTS
Vail, C. F.
General Motors Engineering Staff
Warren, Michigan
VanderVeen, P.
Bethlehem Steel Corporation
Bethlehem, Pennsylvania
Vigor, C. W.
General Motors Research Laboratories
Warren, Michigan
Wang, N.-M.
General Motors Research Laboratories
Warren, Michigan
Webbere, F. J.
General Motors Research Laboratories
Warren, Michigan
Weber, B. C.
Fisher Body Division, GMC
Warren, Michigan
Wenner, M. L.
General Motors Research Laboratories
Warren, Michigan
Wilson, W. R. D.
University of Massachusetts
Amherst, Massachusetts
Woo, D. M.
University of Sheffield
Sheffield, England
Zimmerer, R.
Cadillac Motor Car Division, GMC
Detroit, Michigan413
SUBJECT INDEX
Anisotropy
- normal (or orthotropic), 65, 344, 371.
- planar, 56, 62, 86, 101.
- prestrained sheets, 36.
Artisan system, 7.
Bauschinger effect, 103.
Bending, 82.
Biaxial compression test, 93.
Biaxial tension
- Hill's yield criterion, 67.
- strain hardening, 30, 65, 66, 69, 301.
- Yoshida's X-value, 29, 67.
Bifurcation, see Strain localization.
Circle grid analysis, 34, 316.
Coefficient of friction, 170, 195, 354, 371.
Combined stretch-draw forming, 26.
Complex deformation paths, 325.
Constitutive relations
- deformation theory, 130, 270.
- dilatant plasticity, 242.
- elastic-viscoplastic theory, 371.
- flow theory, 129, 270.
- porous solids, 244.
- pressure sensitive yielding, 242.
- thermally activated dislocation
model, 300.
- vertex model, 131, 240.
Critical hardening rate, see Strain localization.
Critical surface roughness, see Forming
limits.
Deep drawing
- anisotropy, 56.
- elliptical shells, 43.
- flange wrinkling, 43, 59.
- high pressure fluid, 58.
- limiting drawing ratio, 28, 55.
- lubrication, 168.
- strain distribution, 62, 360.
- strain hardening, 57.
Deformation analysis system
- characteristics, 10.
- economic impact, 15.
Deformation increment
- effect of initial imperfection, 248.
- onset of bifurcation, 250.
Deformation theory, see Constitutive
relations.
Drawbead forces
- cyclic strain, 189.
- deformation, 183.
- friction, 194.
- strain rate effect, 191.
Ductility ratio, 253.
Excessive hardening phenomenon, see Yield
surface.
Finite element method
- deep drawing, 357.
- elastic-viscoplastic formulation, 391.
- hemispherical punch stretching, 350, 384.
- hydrostatic bulging, 347.414
- in-plane, plane-strain deformation, 124.
- plane strain punch stretching, 377.
- rigid-plastic formulation, 344.
Flat-bottomed punches
- size effect on strain distribution, 32.
Flow theory, see Constitutive relations.
Forming complex shapes
- eccentric forces, 31.
Forming limit diagram, see Forming limits.
Forming limits (also see Strain localization)
- change of strain path, 36, 325.
- critical surface roughness, 318, 321.
- defect simulation, 309.
- effect of prestrain, 36, 325.
- fracture limit, 231, 295.
- Marciniak-Kuczynski model, 294.
- material imperfections, 307.
- strain rate effect, 299.
Fracture
- material instability, 230, 295.
- void growth, 256, 263.
Friction coefficient
- in drawbeads, 196.
Friction stress
- characterization, 170.
- friction factor, 171.
- lubricant shear, 158.
- regime transition, 171.
Galling
- drawbeads, 200.
Hemispherical punch stretching
- forming limits, 63.
- strain distribution, 355, 384.
Hill's yield criterion
- anisotropic materials, 67.
- application to prerolled sheet, 8p.
Hydraulic bUlging
- anisotropic sheets, 86.
- balanced biaxial stress-strain curve,
29,64,89.
- finite element analysis, 347.
- rigid-plastic and elastoplastic solutions, 62.
- strain distribution, 349.
- Yoshida's X-value, 29.
SUBJECT INDEX
In-plane forming limits
- defect simulation, 309.
In-plane plane-strain analysis
- criterion for strain localization, 125.
- growth rate of thickness nonuniformity, 114.
- long wavelength approximation, 116,
136.
- plane stress assumptions, 112.
In-plane stretching
- Marciniak-Kuczynski analysis, 63, 112.
- strain localization, 293.
Limit strain, see Forming limits.
Limiting cup depth
- combined stretch-draw, 26.
- punch stretching, 24, 387.
- Yoshida's X-value, 29.
Limiting drawing ratio, see Deep drawing.
Lubrication
- boundary films, 165, 167.
- film thickness, 158.
- Reynolds equation, 158.
surface roughness effects, 164.
Lubrication regimes
- boundary, 166.
- deep drawing, 168.
- ironing, 169.
- mixed, 165.
- thick film, 158.
- thin film, 164.
Marciniak-Kuczynski model, 63, 136, 270, 29(
Material imperfections
- effect on strain localization, 307.
- work hardening, 306.
Material instability
- bifurca~ion analysis, 250.
Necking, see Strain localization.
Normal anisotropy, 344.
Numerical analysis (see Finite element metho(
Overstress model, 300.SUBJECT INDEX
Planar anisotropy
- effect of strain state, 86.
Plane-strain stretching
- finite element method, 376.
- fracture, 218.
- instability development, 217.
- quasi-stable deformation, 221.
- strain localization, 125, 142, 273, 379.
Plane strain test, 89.
Predictive capability
- potential uses, 13.
Press performance
- assessment system, 45.
Punch stretching
- deformation analysis, 350.
- effect of strain hardening, 23.
- forming geometry and friction, 23, 293.
- forming limit diagram, 63.
Punch velocity
- in viscoplastic finite element method, 376.
Quasi-stable deformation
- factors affecting, 221.
Schuler Hydro-mechanical process, 58.
Shear band formation
- bifurcation, 132, 247.
- Hill's formula, 134.
- plane strain stretching, 218.
Shrink flanging, 28.
Solid lubricants, 163.
Stability loss
- in stretching, 217.
Strain composition diagram, 328.
- die geometry, 329.
- wrinkling, 331.
Strain distribution, (also see Hemispherical
punch stretching and Hydraulic bulging).
- large panels, 328.
- plane strain punch stretching, 378.
- square and elliptical shells, 32.
Strain hardening
- cyclic strain, 194.
- variation with strain states, 30.
Strain localization, (also see In-plane planestrain analysis and plane-strain
415
stretching).
- biaxial stretching, 145, 259, 277.
- bifurcation analysis, 259.
- critical hardening rate, 251.
- deformation theory, 140, 272.
- flow theory, 138, 272.
- forming limits, 147.
- geometric non-uniformity, 136.
- governing process, 215, 220.
- imperfection, 146, 222.
- Marciniak-Kuczynski analysis, 136,
259, 270, 290, 294.
- material imperfections, 148, 247.
- normal anisotropy, 142, 273, 379.
- strain hardening, 148, 223.
- strain rate effect, 225, 269.
- stress states, 223.
- tool forces, 227.
- void growth, 231, 260.
- yield vertex, 259.
Strain-rate effects, 189, 191, 225, 270, 273,
298, 307, 371, 378.
Strain states
- change of deformation path, 317.
Strength differential effect
- in tension and compression, 242.
Stretch forming
- instability modes, 217.
- instability strain, 62, 64.
Through thickness compression test, 89.
Variational principle, 342, 391.
Viscoplasticity
- overstress model, 300, 372.
- power law model, 270, 298, 373.
Void growth
- critical conditions, 256.
- experimental observations, 263.
- nucleation, 245.
Work-hardening, see Strain hardening.
Wrinkling, 41, 46, 331.416
Yield surface
- aluminum killed (or stabilized) steel, 99.
- annealed aluminum, 99.
- annealed steel, 94.
- brass, 94.
- excessive hardening phenomenon, 104.
- Hill's criterion for anisotropic sheets,
56, 67, 86, 88, 302, 344, 371.
- prestrain direction, 100.
- prestrained sheets, 99, 101, 102, 107.
- Tresca criterion, 92.
- vertex model, 238.
- von Mises criterion, 92.
Yield vertex
- bifurcation, 291.
- effect on critical hardening rate, 251.
Yoshida's X-value, 29, 67.
SUBJECT INDEX

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