Rate-dependent, finite elasto-plastic deformation of polycrystals
10.1098/rspa.1986.0101
Crossref journal-article
The Royal Society
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences (175)
Abstract

Based on Hill’s method, a self-consistent averaging scheme is proposed for estimating the overall, finite deformation response of polycrystalline aggregates consisting of single crystals which undergo plastic flow by rate-dependent crystallographic slip, accompanied by elastic lattice distortion. First, constitutive relations for such single crystals are developed assuming that the slip-rate and the associated resolved shear stress are governed by: (1) a power-law relation, and (2) a viscoplastic relation. Then, Hill’s idea that the constraint imposed on a single crystal by the remaining aggregates may be represented by embedding the single crystal in a homogeneous, infinitely extended matrix having the instantaneous overall moduli, is used to formulate a completely self-consistent averaging procedure, valid for rate-dependent materials at finite strains and rotations. This method includes both the Hill and the Krӧner‒Budiansky‒Wu (K. B. W.) methods as limiting cases; when rate-effects are negligible, it reduces to Hill’s self-consistent method as formulated by Iwakuma and Nemat-Nasser for finite deformations, while it reduces to a generalized finite deformation version of the K. B. W. method for strongly rate-dependent materials. Illustrative numerical examples are presented for a plane uniaxial deformation, using a two-dimensional poly crystalline model. These examples clearly show that the rate-dependent crystallographic slip on the level of single crystals produces a more stable overall behaviour of poly crystals. This supports similar results arrived at by other investigators for single crystals and for polycrystals, by using the Taylor averaging scheme. It is shown that, while Taylor’s averaging scheme gives accurate estimates of the incremental quantities at large strains, the total overall quantities differ considerably from the ones obtained by the self-consistent method.

Bibliography

Rate-dependent, finite elasto-plastic deformation of polycrystals. (1986). Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 407(1833), 343–375.

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Dates
Type When
Created 18 years, 8 months ago (Dec. 18, 2006, 6:11 p.m.)
Deposited 4 years, 6 months ago (Feb. 19, 2021, 1:35 p.m.)
Indexed 11 months, 2 weeks ago (Sept. 19, 2024, 11:07 a.m.)
Issued 38 years, 10 months ago (Oct. 8, 1986)
Published 38 years, 10 months ago (Oct. 8, 1986)
Published Online 28 years, 8 months ago (Jan. 1, 1997)
Published Print 38 years, 10 months ago (Oct. 8, 1986)
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@article{1986, finite elasto-plastic deformation of polycrystals_1986, volume={407}, ISSN={0080-4630}, url={http://dx.doi.org/10.1098/rspa.1986.0101}, DOI={10.1098/rspa.1986.0101}, number={1833}, journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1986}, month=oct, pages={343–375} }