Homogeneity and heterogeneity in channel-die compressed Al–1%Mn single crystals: Considerations on the activity of the slip systems

Darrieulat, Michel; Poussardin, Jean-Yves; Fillit, R.Y.; Desrayaud, Christophe

doi:10.1016/j.msea.2006.09.094

Cited by 13 publications

(16 citation statements)

References 20 publications

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“…The values (rounded) are 0.279 (Cu) and 0.337 (Al). In the only experiments (to my knowledge) in which lateral stresses have been determined at b ¼ 1, the ranges are 0.30-0.36 in Cu (Wonsiewicz et al [32], Figure 5) and 0.25-0.38 in Al (Darrieulat et al [33], Figure 5, after 10% strain). If instead one were to adopt b ¼ b E (from elastoplastic transition analysis) in Equation (F3) 1 and solve for n for each crystal, an extreme rate-sensitivity would result: n ¼ 0:560 in Al and n ¼ 0:470 in Cu.…”

Section: Viscoplastic Results At B =mentioning

confidence: 97%

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: Viscoplastic Results At B =mentioning

confidence: 97%

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 my knowledge, all carefully done experiments on fcc crystals in (1 1 0) compression, from Chin et al (1966a) through Darrieulat et al (2007), clearly demonstrate that stability. However, in the series of papers (Havner (2007a(Havner ( ,b, 2008a), covering ranges I, II, and III, load-axis stability has not been assumed.…”

Section: General Stress and Kinematic Equations In (1 1 0) Compressiomentioning

confidence: 84%

“…(The increase above the elastic value conceivably could be attributed to the adjustable jaw having very slightly compressed the crystal laterally as deformation proceeded, but of course that is merely speculation.) Not since Wonsiewicz et al (1971), to my knowledge, was there another experimental determination of the constraint stress in channel die compression until Darrieulat et al (2007) for Al-1%Mn crystals (see their Fig. 2 showing the measuring device).…”

Section: Investigation Of a Critical Strain For Possible Loss Of Lattmentioning

confidence: 99%

Analysis of fcc crystals in two singular orientations in (110) channel die compression

Havner

2010

Mechanics of Materials

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“…With X, Y and Z, the loading, lateral constraint and channel-axis directions (figure 1), and ι, κ, μ unit vectors in the respective directions (such that ικμ constitutes a rigid orthogonal triad fixed in the channel frame), the general kinematic and constraint equations in (110) compression may be expressed (eqns (12), (30) and (9) in [20]) d xx = ιDι = −ė L , d xy = ιDκ = 0, d yy = κDκ = 0, d xz = ιDμ, d yz = κDμ, D = N jγj +ε, N j = sym(b ⊗ n) j , (tan χ x ) • = 2d yz +ė L tan χ x , (tanχ y ) • = 2d xz + 2ė L tan χ y andφ = (κ · b j )(μ · n j )γ j +ε yz ,…”

Section: General Equations In (110) Compressionmentioning

confidence: 99%

“…Let f , g denote the 'true' compressive load and lateral constraint stresses corresponding to a uniform stress and deformation state in the crystal (well away from the end faces). The general equations for resolved shear stress τ k and its rate-of-change in the kth slip-system, for any orientation, are (eqns (2) and (9) in [14], and eqn (8) in [20]) τ k = m k f + r k g, m k = −ιN k ι, r k = −κN k κ, N k = sym(b ⊗ n) k , τ k = m kḟ + r kġ +ṁ k f +ṙ k g,ṁ k = −2ιN kι ,ṙ k = −2κN kκ…”

Section: General Equations In (110) Compressionmentioning

confidence: 99%

An anisotropic, viscoplastic power law for face-centred cubic crystals: comparative evaluations in the Goss and Brass orientations of channel die compression

Havner

2016

Proc. R. Soc. A.

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ResearchCite this article: Havner KS. 2016 An anisotropic, viscoplastic power law for face-centred cubic crystals: comparative evaluations in the Goss and Brass orientations of channel die compression. Proc. R. Soc. A 472: 20150568. http://dx.An anisotropic, viscoplastic power law is introduced and applied to analysis of the Goss and Brass orientations, and compared with predictions from rate-independent theory and experiment. The structure of the new power law is so chosen that it has the capability of approaching rate-independent results for lattice rotation and crystal shearing, after finite rotation about the load axis, in the range of unstable lattice orientations in (110) channel die compression. (Rate-independent predictions of shear and lattice rotation are in good to very good agreement with experiments on aluminium and copper in that range, whereas classic isotropic power-law results are not.) It is established that, for sufficiently large power-law exponent n, the new anisotropic, elasto-viscoplastic theory predicts: (i) lattice stability in each of the Goss and Brass orientations, consistent with both experiment and rate-independent theory; (ii) zero crystal shear in the Goss orientation, also consistent with both; (iii) finite shear in the Brass orientation, in very good agreement with experiment and rateindependent theory; and (iv) a lateral-constraint stress that remains essentially elastic in both orientations, as predicted by rate-independent theory and close to experimental measurements for aluminium and copper in the Brass orientation.

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Homogeneity and heterogeneity in channel-die compressed Al–1%Mn single crystals: Considerations on the activity of the slip systems

Cited by 13 publications

References 20 publications

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

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

Analysis of fcc crystals in two singular orientations in (110) channel die compression

An anisotropic, viscoplastic power law for face-centred cubic crystals: comparative evaluations in the Goss and Brass orientations of channel die compression

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