Transition theories of elastic-plastic deformation of metallic polycrystals

Lipiński, P.; Berveiller, M.; Reubrez, Eric; Morreale, J.

doi:10.1007/bf00789222

Cited by 64 publications

(38 citation statements)

References 34 publications

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“…Then, for the purely mechanical loading (b 0) Eqs. (16) and (19) formally coincide with the analogous relations obtained in [111] by the use of Green's functions for a bounded domain w. Its implementation is not trivial because the ®nite-body Green's function G w is generally not known, and the replacement of G w by G c in (10) if w is large enough leads to well-known convergence dif®culties as discussed in detail, [68]. For homogeneous boundary conditions (5), (6), and for b 0, Eqs.…”

Section: Appendix: Comparison With Related Equationssupporting

confidence: 72%

Local effective thermoelastic properties of graded random structure matrix composites

Buryachenko

Rammerstorfer

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coef®cient, as well as ®rst statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective ®eld method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective ®eld homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated.

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Section: Appendix: Comparison With Related Equationssupporting

confidence: 72%

Local effective thermoelastic properties of graded random structure matrix composites

Buryachenko

Rammerstorfer

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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“…The derivation of polycrystal constitutive equations is based on a self-consistent scheme. Only the main lines of this approach are recounted here; the details of the entire scheme are developed in previous reports [9,14,23,24].…”

Section: Scale-transition Scheme-polycrystalline Behaviormentioning

confidence: 99%

Impact of intragranular microstructure development on ductility limits of multiphase steels

Franz¹,

Abed‐Meraim

Zineb

et al. 2011

Materials Science and Engineering: A

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a b s t r a c tIn this paper, the effects of microstructure and deformation mechanisms on the ductility of multiphase steels are investigated. To this end, a formability criterion based on loss of ellipticity of the boundary value problem is coupled with an advanced multiscale model accounting for intragranular microstructure development and evolution. The spatially heterogeneous distribution of dislocations inside the grain is represented by three types of local dislocation densities. The resulting large strain elastic-plastic single crystal constitutive law (based on crystal plasticity) is incorporated into a self-consistent scale-transition scheme. The present contribution focuses on the relationship between the intragranular microstructure of B.C.C. steels and their ductility. The model allows interesting comparisons in terms of formability limits for different dislocation networks, during monotonic loading tests applied to polycrystalline aggregates.

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“…Only the main lines of this scheme are presented in the current section. Further details on this model are provided in [8]. Compared to the full-constraint Taylor model, which is much more commonly used due to its simplicity, the self-consistent scheme presents a number of advantages.…”

Section: Constitutive Equations At the Polycrystalline Scalementioning

confidence: 99%

Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory

Bettaieb

Abed‐Meraim

2018

Int J Mater Form

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Abstract. In this paper, both the bifurcation theory and the initial imperfection approach are used to predict localized necking in substrate-supported metal layers. The self-consistent scale-transition scheme is used to derive the mechanical behavior of a representative volume element of the metal layer from the behavior of its microscopic constituents (the single crystals). The mechanical behavior of the elastomer substrate follows the neo-Hookean hyperelastic model. The adherence between the two layers is assumed to be perfect. Through numerical results, it is shown that the limit strains predicted by the initial imperfection approach tend towards the bifurcation predictions when the size of the geometric imperfection in the metal layer vanishes. Also, it is shown that the addition of an elastomer layer to a metal layer enhances ductility.

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Transition theories of elastic-plastic deformation of metallic polycrystals

Cited by 64 publications

References 34 publications

Local effective thermoelastic properties of graded random structure matrix composites

Local effective thermoelastic properties of graded random structure matrix composites

Impact of intragranular microstructure development on ductility limits of multiphase steels

Ductility prediction of substrate-supported metal layers based on rate-independent crystal plasticity theory

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