Strain hardening at high strain in aluminum alloys and its effect on strain localization
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6 d4
-
Z,
[11
where Z is a constant for a particular type of process and flow instability, 6 is effective stress, and ~ is effective strain. In imperfection models which have developed out of the concept proposed by Marciniak, strain localization develops from the growth of strain gradients which are produced by the imperfection. H In certain processes, such as the stretching of a sheet over the surface of a hemispherical punch in the presence of friction, strain gradients develop spontaneously during flow and it is not necessary to assume an initial imperfection in order to account for strain localization, m3 In the development and experimental testing of these
J. E. BIRD, 3218 Hawthorne Court, Murrysville, PA 15668 was formerly with Alcoa Laboratories, Alcoa Center, PA 15069, U.S.A.J. L. DUNCAN is Professor, Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4L7. Manuscript submitted October 11, 1979.
models a simple description of the material behavior which is often used is, o = KC~"m
[21
where ~ is the true strain rate; uniaxial tensile data are frequently used to provide values for the material parameters, K, n and m. Experimental tests have shown that while the imperfection models indicate the correct trends in the results, they often fail to predict localization strains accurately. It has been stated that quantitative agreement is poor in some materials unless unrealistically large imperfections ~4or large values of friction are assumed. ~5Various concepts have been introduced to improve agreement, including alternative theories of plasticity, ~6a7kinematic hardening, 18damage functions, ~9,2~alternative macroscopic anisotropy models, 21 probabilistic analyses, = ductile fracture criteria, 23,24 and imperfections due to surface rougheningY Relatively little attention, however, has been given to a careful comparison of the material description used and the experimentally observed mechanical behavior of the sheet, particularly with respect to the stress, strain, strain rate relation used. In studying strain localization in aluminum alloys, it has become apparent that material descriptions such as Eq. [2] are inadequate to describe the strain hardening behavior of a number of commercial sheet alloys. These alloys show decreasing values of n at higher strains in tensile testing, and undergo rapid strain localization at high strains in tensile testing or punch stretching. Punch stretching involves strains which are much higher than the uniform flow which is conventionally studied in tensile testing, and so appropriate strain hardening data are generally not available. If strain hardening were to continue to drop with increasing strain at a rate more rapid than suggested by tensile results, then agreement between existing models and experiment might be improved. Further, this might help to explain why some materials which show fairly similar tensile properties behave quite dissimilarly in punch stretching. The purpose of this work is to measure strain
ISSN 0360-2133/
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