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

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

doi:10.3390/ma9050335

Cited by 9 publications

(3 citation statements)

References 39 publications

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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%

“…In the grain volume average based model, the inherent length-scale appears explicitly through the parameters γ GB and ρ GB as a function of δ GB (Eqs. ( 23) and (24) in the phenomenological formulation, and Eqs. ( 27) and ( 28) in the dislocation based formulation).…”

Section: Simplified Model Based On the Grain Boundary Effects On An Average Sense Over The Grain Volumementioning

confidence: 99%

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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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Section: General Crystal Plasticity Frameworkmentioning

confidence: 99%

Section: Simplified Model Based On the Grain Boundary Effects On An Average Sense Over The Grain Volumementioning

confidence: 99%

Grain size-dependent crystal plasticity constitutive model for polycrystal materials

Moghaddam

Achuthan

Bednarcyk

et al. 2017

Materials Science and Engineering: A

Self Cite

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show abstract

“…A practical way for the analysis of a composite structure is to take an approach of a multi-scale framework (MSF) [ 68 , 69 , 70 , 71 , 72 , 73 , 74 ]. As shown in Figure 1 in the MSF the models at different scales are built independently but are combined organically so that loads and material data can be transferred between the models.…”

Section: Introductionmentioning

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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Micromechanical Analysis for Iron-Based Composites Under Large Deformations

Dodla

2021

Journal of Elec Materi

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

Cited by 9 publications

References 39 publications

Grain size-dependent crystal plasticity constitutive model for polycrystal materials

Grain size-dependent crystal plasticity constitutive model for polycrystal materials

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

Micromechanical Analysis for Iron-Based Composites Under Large Deformations

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