Comparative evaluation of a viscoplastic power-law and rate-independent crystal plasticity in channel die compression

Havner, Kerry S.

doi:10.1016/j.mechmat.2012.09.004

Cited by 6 publications

(37 citation statements)

References 29 publications

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“…In Section 2, general kinematic equations applicable to any elastic-plastic crystal theory in (1 1 0) compression are given. Section 3 includes resolved shear stress equations and a brief review of the elastoplastic transition (from [1] and [2]). In Section 4, the slip-systems hardening moduli and inequalities (from [9]) of anisotropic rate-independent theory are given.…”

Section: Philosophical Magazine 1925mentioning

confidence: 99%

“…(The anisotropic compliance s A is identically zero for elastic isotropy.) The lattice rotation-rate about load-axis X may be expressed in terms of only two slip-rates as ( [1], Equation (7))…”

Section: Philosophical Magazine 1927mentioning

confidence: 99%

“…Equation (4) for lattice rotation-rate and Equation (5) for crystal shear-rate are applicable to both rate-independent and viscoplastic theories, and apply to rigid/plastic analyses as well merely by equating all compliances to zero. However, it should be noted Philosophical Magazine 1929 that these equations (and the constraint equations) derived in [1] and [2] were simplified there from more complex equations that included a contribution of lattice rotation-rate to lattice strain-rate (see Equation (4) in either [1] or [2]). (Of course the effect of lattice rotation on overall, slip-produced finite deformations was retained.)…”

Section: Philosophical Magazine 1927mentioning

confidence: 99%

“…The two theories are compared in Havner [1] (Section 5) for the elastoplastic transition that precedes the onset of finite multiple-slip, corresponding to an experimental strain-range of order 10 À3 . Only one pair of slip systems is active in rate-independent theory during this transition (Havner [2]), and elastic strains must be included.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, in the series of papers Havner [3][4][5][6][7][8], presenting rate-independent finite-deformation analyses covering the full 90°range of distinct lattice orientations in (1 1 0) channel die compression, and based on the slip-systems hardening inequalities introduced in Havner [9], it always was assumed that elastic strains were negligible. Moreover, lattice straining was not included in rate-independent theory for finite deformation comparisons in [1], and crystal shearing was not investigated.…”

Section: Introductionmentioning

confidence: 99%

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On crystal shear, lattice rotation and constraint stress in (1 1 0) channel die compression: rate-independent and viscoplastic analyses and predictions compared

Havner

2014

Philosophical Magazine

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To cite this article: Kerry S. Havner (2014) On crystal shear, lattice rotation and constraint stress in (1 1 0) channel die compression: rate-independent and viscoplastic analyses and predictions compared, Philosophical Magazine, 94:17, 1924Magazine, 94:17, -1955 Rate-independent crystal plasticity theory and a classic viscoplastic power-law are investigated, contrasted and compared for finite deformation analysis of fcc crystals in channel die compression, including full consideration of lattice straining. Both experiment-based anisotropic and isotropic (Taylor) hardenings are evaluated in rate-independent theory; and an unlimited range of power-law exponent n is considered in viscoplasticity. The focus is on predictions of lateral constraint stress, lattice rotation and crystal shear, and their comparison with experiment. General elastic-plastic equations (for both theories) are given for the range of unstable lattice orientations in (1 1 0) compression ('range I') and evaluated before and after a finite rotation of the lattice about the load axis. Equations also are given and evaluated for the 'Brass' orientation. It is shown that the theories can be in close agreement at the onset of finite deformation in range I, but that viscoplasticity gives results (for any n) after finite rotation that are in sharp contrast to rate-independent theory. The latter's predictions for crystal shear and lattice rotation are in good to very good agreement with finite deformation experiments on aluminium and copper. The inclusion of lattice elasticity is found to have a negligible effect in range I. In contrast, for finite deformation in the stable Brass orientation, elastic-viscoplastic theory can be made to agree very closely with rate-independent theory and with experiment.

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Section: Philosophical Magazine 1925mentioning

confidence: 99%

Section: Philosophical Magazine 1927mentioning

confidence: 99%