An extension of the self-consistent scheme to plastically-flowing polycrystals

Berveiller, M.; Zaoui, A.

doi:10.1016/0022-5096(78)90003-0

Cited by 686 publications

(298 citation statements)

References 9 publications

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“…This model does not need any additional parameter to define the scale transition rule. It can then be easily applied to calibrate the single crystal material parameters on the tensile test [19]. Since the model is valid for tensile tests only, the identification has then to be refined for cyclic tests.…”

Section: Materials Parameters Identificationmentioning

confidence: 99%

Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates

Guilhem

Basseville

Curtit³

et al. 2013

Computational Materials Science

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The aim of the present paper is to investigate the consequences of the loading on the free surface response in polycrystalline aggregates. The study is made on a 316L stainless steel. Finite element computations using a crystal plasticity model are performed to simulate a polycrystalline aggregate submitted to different cyclic loadings. A statistical analysis of the results is carried out to extract information concerning the local stress and local strain fields at the free surface. The analysis of plastic strain localization on surface maps and inside the bulk through transparent volumetric views allows to exhibit the effects of the grain orientation and of the loading on local mechanical fields. The computation of an indicator characterizing extrusion/intrusion steps give some information on the initiation sites.

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Section: Materials Parameters Identificationmentioning

confidence: 99%

Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates

Guilhem

Basseville

Curtit³

et al. 2013

Computational Materials Science

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“…[3,4,12,[14][15][16]), (ii) the two-phase self-consistent model (e.g., Refs. [15,17,18]), (iii) the generalized self-consistent scheme (e.g., Refs. [3,[19][20][21]), and (iv) the more recent third-order approximation models of Torquato [12].…”

Section: Introductionmentioning

confidence: 99%

Simplified prediction of the monotonic uniaxial stress–strain curve of non-linear particulate composites

Mueller

Mortensen

2006

Acta Materialia

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“…He noticed that, for power-law creep, Hill's formulation may be integrated into a`total' one making use of`secant' creep compliances. Other secant moduli or compliances have also been de®ned (Berveiller and Zaoui, 1979;Tandon and Weng, 1988) leading to a (classical)`secant formulation', closely related to Hill's incremental formulation.…”

Section: Introductionmentioning

confidence: 99%

An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals

Masson¹,

Bornert²,

Suquet³

et al. 2000

Journal of the Mechanics and Physics of Solids

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285

214

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Variational approaches for nonlinear elasticity show that Hill's incremental formulation for the prediction of the overall behaviour of heterogeneous materials yields estimates which are too sti and may even violate rigorous bounds. This paper aims at proposing an alternative `a ne' formulation, based on a linear thermoelastic comparison medium, which could yield softer estimates. It is ®rst described for nonlinear elasticity and speci®ed by making use of Hashin±Shtrikman estimates for the linear comparison composite; the associated a ne self-consistent predictions are satisfactorily compared with incremental and tangent ones for power-law creeping polycrystals. Comparison is then made with the second-order procedure (Ponte CastanÄ eda, P., 1996. Exact second-order estimates for the e ective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids, 44 (6), 827±862) and some limitations of the a ne method are pointed out; explicit comparisons between di erent procedures are performed for isotropic, two-phase materials. Finally, the a ne formulation is extended to history-dependent behaviours; application to the self-consistent modelling of the elastoplastic behaviour of polycrystals shows that it o ers an improved alternative to Hill's incremental formulation.

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An extension of the self-consistent scheme to plastically-flowing polycrystals

Cited by 686 publications

References 9 publications

Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates

Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates

Simplified prediction of the monotonic uniaxial stress–strain curve of non-linear particulate composites

An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals

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