The plastic anisotropy of two-phase aluminium alloys—I. Anisotropy in unidirectional deformation

Bate, P. S.; Roberts, W. T.; Wilson, D. V.

doi:10.1016/0001-6160(81)90106-1

Cited by 94 publications

(53 citation statements)

References 15 publications

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“…Alternatively, ( Q j ; A j ) could be directly related to the stress-strain pair ( P; E p ), which would also be consistent in a thermo-mechanical sense. The back stress is, however, often related to the internal stresses of the precipitates contained in common alloys [16,17] relating ( Q j ; A j ) to ( S; E e ).…”

Section: Clausius-duhem Inequalitymentioning

confidence: 99%

“…The evolution of the internal strain-like variables A j are obtained with (17). By choosing the terms in brackets in (17) to be positive proportional to the stress-like variable D p + A j ∼ṡ Q j , evolution equations of Armstrong-Frederick type [23] are obtained for the kinematic hardening with (10) as…”

Section: Evolution Of Plastic Strain Rate and Internal Variablesmentioning

confidence: 99%

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Integration algorithms for planar anisotropic shells with isotropic and kinematic hardening at finite strains

Han

Lee

Chung

et al. 2003

Commun. Numer. Meth. Engng.

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SUMMARYAn elasto-plastic formulation at ÿnite strains was considered with isotropic and kinematic hardening and anisotropic yield functions. In order to ÿnd a simple but thermomechanically consistent continuum mechanical basis for stress integration algorithms of shell problems, evolution equations of the plastic strain rate and internal variables were derived. This was performed in the stress-free intermediate conÿguration with the Mandel stress and corresponding back stress tensors. The resulting relations were then transformed into the current conÿguration and restricted to small elastic strains. For an algorithmic treatment of this material formulation for shell problems, the kinematic hardening was reformulated in stress-related terms to obtain a set of equations for planar anisotropic elasto-plastic materials. Finally, an updated iterative treatment for the elasto-plastic shell at ÿnite strains was derived utilizing the cutting plane algorithm.

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Section: Clausius-duhem Inequalitymentioning

confidence: 99%

Section: Evolution Of Plastic Strain Rate and Internal Variablesmentioning

confidence: 99%

Integration algorithms for planar anisotropic shells with isotropic and kinematic hardening at finite strains

Han

Lee

Chung

et al. 2003

Commun. Numer. Meth. Engng.

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“…It indicated that the strength depends not only on the individual precipitate strength and volume fraction (or number density) but also on the morphology such as shape, density, spatial distribution and orientation distribution of the precipitates for a given volume fraction. Previous continuum mechanics models Ð the plastic inclusion model [24] and the elastic inclusion model [25] Ð have been proposed to address the plate-orientation effect on the anisotropy of mechanical properties. Since the complicated stress and strain distribution around and between plates were simplified, the influence of the spatial and/or orientation distribution was not explicitly incorporated in these microscopic elastic and plastic models.…”

Section: Precipitate Structuresmentioning

confidence: 99%

The Intelligent Design of Age Hardenable Wrought Aluminum Alloys

et al. 2002

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“…This strain Combining the compliance constants and the external state is rotated around l 2 by , the angle between the stress strain state, the accommodation tensor terms are defined as axis and the habit plane normal of the inclusion. A schematic of the orientation of the inclusion, stress axis, coordinate [8] system, and rotation angle, , is presented in Figure 1. This ϩ SЈ ij22 Ϫ 2SЈ ij33 ]/2 construction generates the following strain state: The magnitude of the accommodation tensor is defined still periodic, predicts weaker strengthening at 0 deg than as the magnitude of ␥ 33 , the resolved strain in the inclusion at 90 deg.…”

Section: A Plastic Inclusion Modelmentioning

confidence: 99%

“…In the elastic inclusion model, the cos 2 term represents [8] to resolve the inclusion strain along the stress axis: the dependence of the strain state in the inclusion on Pois-␥ 33 ϭ [2 Ϫ (3/2) * cos 4 Ϫ 6 sin 2 cos 2 [10] son's ratio and the compliance constants of the inclusion. Due to the compliance constants specific to a plate-shaped ϩ (cos 2 )/2]/2 inclusion, the trace of the strain state in the precipitate is Simplifying to allow comparison with the solution for the not a constant, as seen in Table I.…”

Section: A Plastic Inclusion Modelmentioning

confidence: 99%

Precipitate-induced plastic anisotropy: Explicit solutions of the plastic anisotropy due to plate-shaped precipitates

Lyttle

Wert

1999

Metall Mater Trans A

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In some aluminum alloys, the observed plastic anisotropy cannot be explained solely by the measured Taylor factor variation. Qualitatively, it has been suggested that this difference results from a secondary effect due to plate-shaped precipitates. Models addressing the effect of plastically-deforming and elastically-deforming precipitates have been previously proposed. In the present article, explicit solutions of the anisotropic strengthening increment are presented for the case of plate-shaped precipitates. These solutions allow a quantitative consideration of the effect of precipitates on different habit planes and of the effect due to stress aging. Generally, in fcc materials, precipitates on {100} habit planes are predicted to minimize the anisotropy due to texture; precipitates on {111} habit planes are predicted to accentuate the anisotropy due to texture; and precipitates on other habit planes are predicted to produce a minor effect resulting from an averaging over a greater number of crystallographically equivalent habit planes. Stress aging to alter the relative orientation distribution of a single precipitate type is predicted to produce only slight changes in the plastic anisotropy. Larger effects on the yield variation will be observed when stress aging alters the relative volume fractions of two precipitate types on different habit planes.

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The plastic anisotropy of two-phase aluminium alloys—I. Anisotropy in unidirectional deformation

Cited by 94 publications

References 15 publications

Integration algorithms for planar anisotropic shells with isotropic and kinematic hardening at finite strains

Integration algorithms for planar anisotropic shells with isotropic and kinematic hardening at finite strains

The Intelligent Design of Age Hardenable Wrought Aluminum Alloys

Precipitate-induced plastic anisotropy: Explicit solutions of the plastic anisotropy due to plate-shaped precipitates

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