A multi-scale computational model using Generalized Method of Cells (GMC) homogenization for multi-phase single crystal metals

Moghaddam, Masoud Ghorbani; Achuthan, Ajit; Bednarcyk, Brett A.; Arnold, Steven M.; Pineda, Evan J.

doi:10.1016/j.commatsci.2014.08.045

Cited by 21 publications

(6 citation statements)

References 40 publications

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“…In this article, GMC is evaluated as a potential method of homogenization to develop a multiscale model that can capture microscale plastic deformation in polycrystal metals and metallic alloys. This work is an extension of a previous study by authors [ 38 , 39 ] on the applicability of GMC homogenization for studying two-phase materials, e.g., Ni-base superalloys, characterized by crystal plasticity framework at microstructures. Polycrystalline materials, with several randomly oriented grains, demonstrate high material anisotropy; this anisotropy introduces its own challenges and is the focus for this study.…”

Section: Introductionmentioning

confidence: 71%

A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals

et al. 2016

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A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the stand-alone GMC is applied for studying simple material microstructures such as a repeating unit cell (RUC) containing single grain or two grains under uniaxial loading conditions. For verification, the results obtained by the stand-alone GMC are compared to those from an analogous FEA model incorporating the same single crystal plasticity constitutive model. This verification is then extended to samples containing tens to hundreds of grains. The results demonstrate that the GMC homogenization combined with the crystal plasticity constitutive framework is a promising approach for failure analysis of structures as it allows for properly predicting the von Mises stress in the entire RUC, in an average sense, as well as in the local microstructural level, i.e., each individual grain. Two–three orders of saving in computational cost, at the expense of some accuracy in prediction, especially in the prediction of the components of local tensor field quantities and the quantities near the grain boundaries, was obtained with GMC. Finally, the capability of the developed multiscale model linking FEA and GMC to solve real-life-sized structures is demonstrated by successfully analyzing an engine disc component and determining the microstructural scale details of the field quantities.

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Section: Introductionmentioning

confidence: 71%

A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals

et al. 2016

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“…To tackle this issue, a number of numerical micromechanics models with reduced computational effort have been developed. Examples include the Voronoi Cell Finite Element Method (VCFEM) [ 147 , 148 , 149 ], the Generalized Method of Cells (GMC) [ 131 , 150 , 151 , 152 ], the Finite Volume Direct Averaging Micromechanics (FVDAM) [ 153 , 154 , 155 , 156 , 157 , 158 , 159 , 160 , 161 ], and the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) [ 86 , 162 , 163 , 164 , 165 , 166 ]. Reviews on them for nonlinear analysis of a composite can be found in Kanouté et al [ 70 ] and Saeb et al [ 98 ], among others.…”

Section: Review On Micromechanics Modelsmentioning

confidence: 99%

Analytical Micromechanics Models for Elastoplastic Behavior of Long Fibrous Composites: A Critical Review and Comparative Study

Wang

Huang

2018

Materials

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Elasto-plastic models for composites can be classified into three categories in terms of a length scale, i.e., macro scale, meso scale, and micro scale (micromechanics) models. In general, a so-called multi-scale model is a combination of those at various length scales with a micromechanics one as the foundation. In this paper, a critical review is made for the elastoplastic models at the micro scale, and a comparative study is carried out on most popular analytical micromechanics models for the elastoplastic behavior of long fibrous composites subjected to a static load, meaning that creep and dynamic response are not concerned. Each model has been developed essentially following three steps, i.e., an elastic homogenization, a rule to define the yielding of a constituent phase, and a linearization for the elastoplastic response. The comparison is made for all of the three aspects. Effects of other issues, such as the stress field fluctuation induced by a high contrast heterogeneity, the stress concentration factors in the matrix, and the different approaches to a plastic Eshelby tensor, are addressed as well. Correlation of the predictions by different models with available experimental data is shown.

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“…Following the classical approach, the kinematics of elastic-plastic deformation is split into two multiplicative operations; a plastic deformation followed by an elastic deformation. The plastic deformation describes the slipping of lattices without any lattice stretching, while the elastic deformation describes the stretching and rotation of the lattices [23,24,35]. The total deformation gradient F is then given by,…”

Section: General Crystal Plasticity Frameworkmentioning

confidence: 99%

“…The validation was performed for both the phenomenological formulation (Eqs. ( 6), ( 8), (23), and ( 24)) and the dislocation based formulation (Eqs. ( 6), ( 27) and ( 28)).…”

Section: Grain Size-dependent Constitutive Modelmentioning

confidence: 99%

Grain size-dependent crystal plasticity constitutive model for polycrystal materials

Moghaddam

Achuthan

Bednarcyk

et al. 2017

Materials Science and Engineering: A

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Consideration of a core and mantle configuration for individual grains is a prominent method to capture the grain size-dependence in the constitutive models for polycrystal material. The mantle represents a region of the grain volume near the grain boundary where mechanical deformation is influenced by the grain boundaries, while the core represents the inner region of the grain volume. The grain size-dependence is then realized by assigning a set of values for the mechanical properties in the mantle that are different from those of the core region. However, these values for the mechanical properties of the mantle region are typically chosen arbitrarily, guided solely by the quality of the agreement between a model's predicted stress-strain behavior with that obtained experimentally. In the present study, a physics-based method to develop the grain size-dependent crystal plasticity constitutive model on the core and mantle configuration for polycrystal materials is presented. The method is based on the assumption that any resistance to dislocation nucleation and motion in a material manifests as an increase in yield strength and a decrease in strainhardening modulus, and the mutual relationship between yield strength and strain-hardening is an inherent material property that determines the plasticity of that specific material. Accordingly, the same single crystal plasticity constitutive model that describes the behavior of the material under loading can be used to capture the increased resistance to dislocation nucleation and motion in the grain boundary influence region. The physics-based modeling is facilitated by introducing a shear flow strain distribution in the phenomenological formulation and a pile-up of dislocation density distribution in the dislocation based formulation, such that, the resulting variations in the yield strength and the strain-hardening modulus are identical to that produced by the increased resistance in the grain boundary influence region. Thus, the increase in strength and the decrease in the strain-hardening modulus, determined as spatially varying local material properties in the mantle, are mutually related through the grain size-independent inherent plastic properties specific to the material. A simplified model that considers the grain boundary effect averaged over the grain volume is also developed under this general framework. Implementation of this simplified model is demonstrated by considering the case of a power law flow rule and a hyperbolic-secant hardening rule for the phenomenological formulation, and Taylor strength relation for the dislocation based formulation. Finally, the grain size-dependent constitutive model is validated by *

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A multi-scale computational model using Generalized Method of Cells (GMC) homogenization for multi-phase single crystal metals

Cited by 21 publications

References 40 publications

A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals

A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals

Analytical Micromechanics Models for Elastoplastic Behavior of Long Fibrous Composites: A Critical Review and Comparative Study

Grain size-dependent crystal plasticity constitutive model for polycrystal materials

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