Static elastic and thermoelastic field fluctuations in multiphase composites

Bobeth, M.; Diener, G.

doi:10.1016/0022-5096(87)90033-0

Cited by 63 publications

(60 citation statements)

References 7 publications

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“…Indeed, the homogenization procedure also delivers estimates of the field fluctuations. More precisely, the second moment of the intraphase field distribution can be obtained by considering partial derivatives of the effective elastic energy with respect to the local elastic behaviour (see Bergman, 1978;Bobeth and Diener, 1987;Kreher, 1990;Ponte Castañeda and Suquet, 1998). This result follows from the quadratic dependence of the elastic energy on the stress and strain fields.…”

Section: Self-consistent Estimatementioning

confidence: 99%

Elastic anisotropy and yield surface estimates of polycrystals

Brenner

Lebensohn

Castelnau

2009

International Journal of Solids and Structures

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a b s t r a c t Homogenization estimates based on the self-consistent scheme are customarily used to describe the plastic yielding of polycrystals. Such estimates of the initial micro yield surface of a polycrystal depend on the morphologic and crystallographic textures, the slip system geometry, the corresponding critical resolved shear stresses and the single crystal elastic anisotropy. The usual approach relies on a rather crude description of the stress field induced by the local elastic anisotropy. This deficiency is addressed and a new concept, i.e. a ''probability" yield surface is proposed. Based on a statistical description of the local fields, the latter makes use of the average and the standard deviation of the resolved shear stress on the different slip systems within a given crystalline orientation. By comparing the homogenization estimates with full-field results, it is shown that the self-consistent scheme does not present intrinsic shortcomings regarding the prediction of the micro yield stress of polycrystals with anisotropic elastic constitutive behaviour. On the contrary, it delivers realistic estimates if the local field fluctuations are taken into account in the yield criterion. The quantitative results obtained for cubic elasticity show a strong influence of the intragranular stress heterogeneity on the estimate of the micro yield stress.

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Section: Self-consistent Estimatementioning

confidence: 99%

Elastic anisotropy and yield surface estimates of polycrystals

Brenner

Lebensohn

Castelnau

2009

International Journal of Solids and Structures

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“…The LCC is then homogenized using a MFH scheme valid in linear elasticity, providing a purely elastic effective stiffness C el . This enables us to estimate the second moment of the total strain increment in each phase (Bobeth and Diener, 1987;Buryachenko, 2001):…”

Section: Elastic Predictor In Each Phasementioning

confidence: 99%

A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites

Doghri

Brassart

Adam³

et al. 2011

International Journal of Plasticity

129

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“…Indeed, the heterogeneity of stress and strain rate within a given lattice orientation (so-called ''intraphase'' heterogeneity) can be partially characterized by an appropriate derivation of the effective potentials [Bobeth and Diener, 1987;Kreher, 1990;Brenner and Masson, 2005].…”

Section: A1 Exact Solution For Linear Elastoviscoplasticitymentioning

confidence: 99%

Elastoviscoplastic micromechanical modeling of the transient creep of ice

et al. 2008

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[1] A salient feature of the rheology of isotropic polycrystalline ices is the decrease of the strain rate by more than 2 orders of magnitude during transient creep tests to reach a secondary creep regime at a strain which is systematically of $1%. We use a recent (socalled ''affine'') version of the self-consistent mean-field theory to model the elastoviscoplastic behavior of ice. The model aims at bridging scales between the rheology of single grain and the one of polycrystals by evaluating the intergranular interactions. It takes into account the long-term memory effects, which manifests itself by the fact that local stress and strain rate in grains depend on the whole mechanical history of the polycrystal. It is shown that the strong hardening amplitude during the transient creep is entirely explained by the stress redistribution within the specimen, from an almost uniform stress distribution upon instantaneous loading (purely elastic response) to strong interphase and intraphase heterogeneities in the stationary regime (purely viscoplastic response). The experimental hardening kinetic is much too slow to be explained by the same process; it is attributed to the hardening of hard glide slip systems (prismatic slip) in the transient regime. Moreover, the model very well reproduces the permanent creep rate of several highly anisotropic specimens of the Greenland Ice Core Project ice core (pronounced crystallographic textures), when accounting for a single-grain rheology that well matches the experimental one. Our results are consistent with recent findings concerning dislocation dynamics in ice.

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Static elastic and thermoelastic field fluctuations in multiphase composites

Cited by 63 publications

References 7 publications

Elastic anisotropy and yield surface estimates of polycrystals

Elastic anisotropy and yield surface estimates of polycrystals

A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites

Elastoviscoplastic micromechanical modeling of the transient creep of ice

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