A simple constitutive framework is proposed to take account of progressive changes in a stress-based criterion of yielding as plastic deformation accumulates. The analysis is relevant to a sheet of isotropic or orthotropic material which is subsequently loaded in its plane by biaxial tensions (σ1, σ2) in arbitrary fixed ratio. Under these circumstances there is evidence that texture development causes significant changes in the shapes of successive yield loci in (σ1, σ2) space. Here such departures from geometric similarity are explicitly linked to a presumed dependence on σ1/σ2 of the exponent m in a standard power-law representation of the stress-strain characteristic under each constant value of σ1/σ2. The linkage is formulated in detail for several types of representation, and it is shown how a family of yield loci associated with any conjectural dependence m(σ1/σ2) can be generated readily by computer graphics. Some typical examples are given, in particular when m (σ1/σ2) reflects the distinctive trends reported for certain kinds of brass and aluminum sheet (e.g., Wagoner, 1980; Stout and Hecker 1983).
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June 1992
Research Papers
Differential Hardening in Sheet Metal Under Biaxial Loading: A Theoretical Framework
R. Hill,
R. Hill
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, England
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J. W. Hutchinson
J. W. Hutchinson
Division of Applied Sciences, Harvard University, Cambridge, MA 02138
Search for other works by this author on:
R. Hill
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, England
J. W. Hutchinson
Division of Applied Sciences, Harvard University, Cambridge, MA 02138
J. Appl. Mech. Jun 1992, 59(2S): S1-S9
Published Online: June 1, 1992
Article history
Received:
April 12, 1991
Revised:
September 25, 1991
Online:
March 31, 2008
Citation
Hill, R., and Hutchinson, J. W. (June 1, 1992). "Differential Hardening in Sheet Metal Under Biaxial Loading: A Theoretical Framework." ASME. J. Appl. Mech. June 1992; 59(2S): S1–S9. https://doi.org/10.1115/1.2899489
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