Time-dependent relaxation processes continue after forming of sheet metal components. Mechanical properties and even the shape of the part may evolve with time. Beverage can ends, made of an aluminum-magnesium alloy, provide one example of relaxation in a metal product. Ends are manufactured in a series of forming operations, and the can end buckle pressure plays an important role in the design. It has been established that buckle pressure decreases with time in service. In this work, we outline a simple bending test to study relaxation at stress levels well below the usual 0.2 percent offset yield stress. The evolution of stress and development of plastic strain with time are assessed through a simple analysis of springback. The microplastic processes that lead to permanent deformation of the bent beam are well characterized by a model developed by Garmestani and Hart.
Issue Section:
Technical Papers
1.
MacEwen, S. R., 1999, “Stress Relaxation in Beer Cans: Deformation of AA 5182 at Rather Low Strain Rates,” in The Physical Basis of Plasticity, A Symposium to Honor Dr. U. F. Kocks, Los Alamos National Laboratory.
2.
Wagoner, R. H., Carden, W. D., Carden, W. P., and Matlock, D. K., 1997, “Springback After Drawing and Bending of Metal Sheets,” in IPMM ’97—Intelligent Processing and Manufacturing of Materials, 1, University of Wollongong, pp. 1–10.
3.
Hart
, E. W.
, and Solomon
, H. D.
, 1973
, “Load Relaxation Studies of Polycrystalline High Purity Aluminum
,” Acta Metall.
, 21
, pp. 295
–307
.4.
Hart
, E. W.
, and Garmestani
, H.
, 1993
, “Mechanical Testing Using Direct Control of the Inelastic Strain Rate
,” Exp. Mech.
, 1
, pp. 1
–6
.5.
Yamada
, H.
, and Li
, C. Y.
, 1974
, “Stress Relaxation and Mechanical Equation of State in B.C.C. Metals in Monotonic Loading
,” Acta Metall.
, 22
, pp. 249
–253
.6.
Saimoto
, S.
, and Kuo
, R.-C.
, 1991
, “Simulation of the Effect of Solute Drag: 2. During Load Relaxation
,” Scr. Metall. Mater.
, 25
, pp. 2797
–2802
.7.
Diak, B. J., Upadhyaya, K. R., and Saimoto, S., 1998, “Characterization of Thermodynamic Response by Materials Testing,” in M. F. Ashby, B. Cantor, J. W. Christian, and T. B. Massalski, eds., Progress in Materials Science, 43, Pergamon Press Ltd., Oxford, England.
8.
Garmestani
, H.
, Vaghar
, M. F.
, and Hart
, E. W.
, 2001
, “A Unified Model for Inealstic Deformation of Polycrystalline Materials—Application to Transient Behavior in Cyclic Loading and Relaxation
,” Int. J. Plast.
, 17
, pp. 1367
–1391
.9.
Follansbee
, P. S.
, and Kocks
, U. F.
, 1988
, “A Constitutive Description of the Deformation of Copper Based on the Use of the Mechanical Threshold Stress as an Internal State Variable
,” Acta Metall.
, 36
, pp. 81
–93
.10.
Chen, S. R., Kocks, U. F., MacEwen, S. R., Beaudoin, A. J., and Stout, M. G., 1998, “Constitutive Modeling of a 5182 Aluminum as a Function of Strain Rate and Temperature,” in Hot Deformation of Aluminum Alloys II, The Minerals, Metals & Materials Society, Warrendale, PA, pp. 205–216.
11.
Kocks
, U. F.
, and Mecking
, H.
, 2002
, “Physics and Phenomenology of Strain Hardening: The FCC Case
,” Prog. Mater. Sci.
, 48
, pp. 171
–273
.12.
Hart
, E. W.
, 1976
, “Constitutive Relations for the Nonelastic Deformation of Metals
,” J. Eng. Mater. Technol.
, 98
, pp. 193
–202
.13.
Feltham
, P.
, 1963
, “Stress Relaxation and Dynamic Recovery in Cobalt at Low Temperatures
,” Philos. Mag.
, 8
, pp. 989
–996
.14.
Sargent
, G. A.
, 1965
, “Stress Relaxation and Thermal Activation in Niobium
,” Acta Metall.
, 13
, pp. 663
–671
.15.
Korhonen, M. A., Hannula, S. P., and Li, C. Y., 1987, “State Variable Theories Based on Hart’s Formulation,” in Unified Constitutive Equations for Creep and Plasticity, Elsevier, pp. 89–137.
16.
Hart
, E. W.
, 1978
, “Constitutive Relations for Non-Elastic Deformation
,” Nucl. Eng. Des.
, 46
, pp. 179
–185
.17.
Kumar
, V.
, Morjaria
, M.
, and Mukherjee
, S.
, 1980
, “Numerical Integration of Some Stiff Constitutive Models of Inelastic Deformation
,” ASME J. Eng. Mater. Technol.
, 102
, pp. 92
–96
.18.
Kocks, U. F., Argon, A. S., and Ashby, M. F., 1975, “Thermodynamics and Kinetics of Slip,” in Progress in Materials Science, B. Chalmers, J. W. Christian, and T. B. Massalski, eds., 19, Pergamon Press Ltd., Oxford, England.
19.
Kocks, U. F., 1987, “Constitutive Behavior Based on Crystal Plasticity,” in Unified Constitutive Equations for Creep and Plasticity, Elsevier, pp. 1–88.
20.
Saimoto, S., 1989, “Examination of the Hart-Li State Variable Parameters in Terms of Thermally Activated Dislocation—Defect Interaction,” in Materials Architecture Proceedings of the Riso International Symposium on Metallurgy and Materials Science, Riso Natl Lab., pp. 557–564.
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