A variational multiscale constitutive model for nanocrystalline materials

Gürses, Ercan; Sayed, Tamer S. El

doi:10.1016/j.jmps.2010.10.010

Cited by 17 publications

(28 citation statements)

References 96 publications

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“…Based on transmission electron microscopy observations [38,41,48], the thinnest and the thickest of the three Pd films were found to have similar distribution of the in-plane grain diameter D. The grain size distribution is represented in this study using a lognormal distribution, as commonly used in numerical approaches [28,51,52]. The probability density function P(D) of a log-normal grain size distribution is given by: …”

Section: Lab-on-chip Uniaxial Tensile Test Resultsmentioning

confidence: 99%

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

et al. 2016

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Section: Lab-on-chip Uniaxial Tensile Test Resultsmentioning

confidence: 99%

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

et al. 2016

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“…Note that as a consequence of the growth rule (4) the grains initially greater than the mean grain size D 0 coarsen, whereas the grains smaller than D 0 shrink in accord with experimental observations and MD simulations. The scale transition from the single grain level to the polycrystalline level is achieved through a conventional Taylor averaging, i.e., all the grains are subject to the same deformation and, therefore, the compatibility among grains is satisfied a priori and the macroscopic stress is computed by volume averaging; see [2] for details. Furthermore, we assume that the initial grain size has a lognormal distribution through the polycrystalline sample.…”

Section: Description Of Grain Growth Modelmentioning

confidence: 99%

Softening in Nanocrystalline Metals: Modeling of Grain Growth Induced Creep and Relaxation

Gürses

Sayed

2011

Proc Appl Math and Mech

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A variational multiscale model is presented for grain growth in face-centered cubic nanocrystalline (nc) metals. In particular, grain-growth-induced stress softening and the resulting relaxation and creep phenomena are addressed. The behavior of the polycrystal is described by a conventional Taylor-type averaging scheme in which the grains are treated as two-phase composites consisting of a grain interior phase and a grain boundary affected zone. Furthermore, a grain growth law that captures the experimentally observed characteristics of the grain coarsening phenomena is proposed. The model is shown to provide a good description of the experimentally observed grain-growth-induced relaxation in nc-copper. Description of Grain Growth ModelFollowing the classical multiplicative decomposition framework, the deformation gradient F = F e F p is assumed to decompose into an elastic part F e and a plastic partTreating each grain as a composite material composed of a grain interior (GI) phase and a grain boundary (GB) phase, the free energy function can be expressed as a simple volume average W = ξW gi + (1 − ξ)W gb , where ξ is the volume fraction of the grain core region, W gi and W gb denote the free energies of the grain interior and boundary phases, respectively. The average first Piola-Kirchhoff stress P reads similarly P = ξP gi + (1 − ξ)P gb . The volume average stress P, the GI stress P gi and the GB stress P gb are computed from Coleman's relations by evaluating the partial derivatives of corresponding energies with respect to F. Assuming cubical grains and a constant thickness d gb of the GB phase, the volume fraction is evaluated as ξ = (d − d gb ) 3 /d 3 . Following [2], the flow rule for the GB phase is assumed to bė

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“…We refer to [3] for further details. Following the classical multiplicative decomposition framework, the deformation gradient F = F e F p is assumed to decompose into an elastic part F e and a plastic part F p .…”

Section: Description Of Multiscale Model For Nanocrystalline Metalsmentioning

confidence: 99%

“…We make use of the classical hardening matrix h αβ (γ) = [q + (1 − q)δ αβ ]h(γ), whereγ = α γ α is the accumulated plastic slip on slip systems, q is the latent hardening coefficient and δ αβ is the Kronecker delta. The hardening function h(γ) reads from [3]. The scale transition from the single grain level to the polycrystalline level is achieved through a conventional Taylor averaging and the macroscopic stress is computed by volume averaging; see [3] for details.…”

Section: Description Of Multiscale Model For Nanocrystalline Metalsmentioning

confidence: 99%

“…The hardening function h(γ) reads from [3]. The scale transition from the single grain level to the polycrystalline level is achieved through a conventional Taylor averaging and the macroscopic stress is computed by volume averaging; see [3] for details. Furthermore, the initial grain size distribution is assumed to be lognormal.…”

Section: Description Of Multiscale Model For Nanocrystalline Metalsmentioning

confidence: 99%

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Multiscale Modeling of Nanocrystalline Materials: A Variational Approach

Sayed

Gürses

2011

Proc Appl Math and Mech

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This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior (GI) phase and a grain boundary (GB) phase. A rate-independent isotropic porous plasticity model is employed to describe the GB phase, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the GI phase. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization. It is shown that the proposed model is able to capture the inverse Hall-Petch effect. Description of Multiscale Model for Nanocrystalline MetalsIn the sequel the proposed multiscale model is briefly outlined. We refer to [3] for further details. Following the classical multiplicative decomposition framework, the deformation gradient F = F e F p is assumed to decompose into an elastic part F e and a plastic part F p . Treating a particular grain as a composite material composed of a grain interior (GI) phase and a grain boundary (GB) phase, the free energy function can be expressed as a simple volume average W = ξW gi + (1 − ξ)W gb , where ξ is the volume fraction of the GI phase, W gi and W gb denote the free energies of the GI and GB phases, respectively. The average first Piola-Kirchhoff stress P reads similarly P = ξP gi + (1 − ξ)P gb . The volume average stress P, the GI stress P gi and the GB stress P gb are computed from Coleman's relations by evaluating the partial derivatives of corresponding energies with respect to F. Assuming cubical grains and a constant thickness d gb of the GB phase, the volume fraction is evaluated as Following [3], the flow rule for the GB phase readṡ

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A variational multiscale constitutive model for nanocrystalline materials

Cited by 17 publications

References 96 publications

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

Softening in Nanocrystalline Metals: Modeling of Grain Growth Induced Creep and Relaxation

Multiscale Modeling of Nanocrystalline Materials: A Variational Approach

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