Residual stresses and stored elastic energy of composites and polycrystals

Kreher, W.

doi:10.1016/0022-5096(90)90023-w

Cited by 149 publications

(82 citation statements)

References 9 publications

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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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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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“…where the second moment per phase of the stress field σ e reads as (Bobeth and Diener, 1987;Kreher, 1990;Suquet, 1995;Ponte Castañeda and Suquet, 1998)…”

Section: Local Response Of the Composite To A Creep Test At Short Andmentioning

confidence: 99%

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Brenner

Suquet

2013

International Journal of Solids and Structures

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This paper is devoted to the effective behavior of linear viscoelastic heterogeneous materials with a particular emphasis on their transient response. First, two new asymptotic relations for the overall creep function are derived at short and large times. They are related to the retardation spectrum of the composite and involve second-order moments per phase of the stress field for the purely elastic and purely viscous problems. In the context of harmonic loadings, these relations provide exact frequential asymptotic conditions on the overall storage and loss moduli. Second, by making use of these asymptotic results, an approximate model is proposed. It consists in approximating the retardation spectrum of the composite by a single discrete Dirac mass. Its accuracy is assessed by comparison with exact analytical results, fullfield simulations and collocation results for several classes of composites and polycrystals.

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“…Combination of perturbation method and variational principle (Bergman 1978), which is based on the estimation of the perturbation of an energetic function due to a variation of the material properties, was developed for estimation of stress fluctuations for RVEs with isotropic components (Bobeth and Diener 1986;Kreher 1990). Xu (Xu et al 2009) employed the generalized variational principles to decompose a boundary value problem with random microstructure into a slow scale deterministic problem and a fast scale stochastic one using a Green's function based multiscale method.…”

Section: Statistical Characterization Of Local Stress and Strain Fieldsmentioning

confidence: 99%

Statistical methods for mechanical characterization of randomly reinforced media

Tashkinov

2017

Mech Adv Mater Mod Process

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Advanced materials with heterogeneous microstructure attract extensive interest of researchers and engineers due to combination of unique properties and ability to create materials that are most suitable for each specific application. One of the challenging tasks is development of models of mechanical behavior for such materials since precision of the obtained numerical results highly depends on level of consideration of features of their heterogeneous microstructure. In most cases, numerical modeling of composite structures is based on multiscale approaches that require special techniques for establishing connection between parameters at different scales. This work offers a review of instruments of the statistics and the probability theory that are used for mechanical characterization of heterogeneous media with random positions of reinforcements. Such statistical descriptors are involved in assessment of correlations between the microstructural components and are parts of mechanical theories which require formalization of the information about microstructural morphology. Particularly, the paper addresses application of the instruments of statistics for geometry description and media reconstruction as well as their utilization in homogenization methods and local stochastic stress and strain field analysis.

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Residual stresses and stored elastic energy of composites and polycrystals

Cited by 149 publications

References 9 publications

Elastoviscoplastic micromechanical modeling of the transient creep of ice

Elastoviscoplastic micromechanical modeling of the transient creep of ice

Overall response of viscoelastic composites and polycrystals: exact asymptotic relations and approximate estimates

Statistical methods for mechanical characterization of randomly reinforced media

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