Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms

Kalidindi, Surya R.; Knežević, Marko; Niezgoda, Stephen R.; Shaffer, Joshua

doi:10.1016/j.actamat.2009.04.055

Cited by 60 publications

(25 citation statements)

References 25 publications

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“…These are well established in literature with numerous applications in predicting monotonic deformations as standalone codes (Al-Harbi et al, 2010;Fast et al, 2008;Fromm et al, 2009;Kalidindi et al, 2009;Knezevic et al, 2009;Knezevic et al, 2014b;Knezevic and Kalidindi, 2007;Knezevic et al, 2008a;Knezevic and Landry, 2015;Knezevic and Savage, 2014 MANUSCRIPT 5 et al, 2010;Van Houtte, 1982;Van Houtte et al, 2002;Wu et al, 2007) or non-monotonic within finite elements (Barton et al, 2008;Beaudoin et al, 1993;Knezevic et al, 2014d;Knezevic et al, 2013c;Knezevic et al, 2013d;Knezevic et al, 2012b;Zecevic et al, 2015b, c).…”

Section: Figurementioning

confidence: 96%

A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model

Ardeljan

Knežević

Nizolek

et al. 2015

International Journal of Plasticity

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140

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Section: Figurementioning

confidence: 96%

A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model

Ardeljan

Knežević

Nizolek

et al. 2015

International Journal of Plasticity

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140

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“…The developed procedure is fully automated; however, to facilitate calculations involving thousands of grains, significant increases in computation speed are necessary. To this end, we plan to explore the use of non-iterative numerical methods that are based on fast Fourier transforms [20,33,[72][73][74][75][76][77] and utilization of specialized computer hardware [18,78] that involves graphic hardware.…”

Section: Application: a Case Study Of Twinning In Uraniummentioning

confidence: 99%

Explicit incorporation of deformation twins into crystal plasticity finite element models

Ardeljan

McCabe

Beyerlein

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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137

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Highlights• Morphology and crystallography of deformation twinning are implemented in crystal plasticity finite element models.• Intrinsic twinning transformation shear strain is enforced to correspond to the plastic strain accommodated by the twin lamella.• Heterogeneities in spatial mechanical fields are correlated with microstructural changes during twin formation and thickening.• Multiple thin twin lamellae are predicted to be more favorable than a single thick twin lamella in uranium. AbstractDeformation twinning is a subgrain mechanism that strongly influences the mechanical response and microstructural evolution of metals especially those with low symmetry crystal structure. In this work, we present an approach to modeling the morphological and crystallographic reorientation associated with the formation and thickening of a twin lamella within a crystal plasticity finite element (CPFE) framework. The CPFE model is modified for the first time to include the shear transformation strain associated with deformation twinning. Using this model, we study the stress-strain fields and relative activities of the active deformation modes before and after the formation of a twin and during thickening within the twin, and in the parent grain close to the twin and away from the twin boundaries. These calculations are carried out in cast uranium (U), which has an orthorhombic crystal structure and twins predominantly on the {130} <310> systems under ambient conditions. The results show that the resolved shear stresses on a given twin system on the twin-parent grain interface and in the parent are highly inhomogeneous. We use the calculated mechanical fields to determine whether the twin evolution occurs via thickening of the existing twin lamella or formation of a second twin lamella. The analysis suggests that the driving force for thickening the existing twin lamella is low and that formation of multiple twin lamellae is energetically more favorable. The overall modeling framework and insight into why twins in U tend to be thin are described and discussed in this paper.

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“…The viability and the computational benefits of using the DFT approach (for facilitating crystal plasticity solutions) have already been highlighted in prior work (cf. Knezevic et al, 2008Knezevic et al, , 2009Kalidindi et al, 2009;Alharbi et al, 2010;Knezevic and Savage, 2014;Mihaila et al, 2014;Savage and Knezevic, 2015;Alharbi and Kalidindi, 2015;Zecevic et al, 2015;Eghtesad et al, 2017;Knezevic and Kalidindi, 2017). In particular, the accuracy and computational savings of the DFT database approach compared to the conventional Taylor-type approach have been demonstrated by Knezevic et al (2009) and Alharbi and Kalidindi (2015) for both monotonic and non-monotonic strain paths.…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

Gupta

Bettaieb

Abed‐Meraim

et al. 2018

International Journal of Plasticity

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/13136 To cite this version :Akash GUPTA, Mohamed BEN BETTAIEB, Farid ABED-MERAIM, Surya KALIDINDIComputationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database -International Journal of Plasticity -Vol. 103, p.168-187 -2018 Any correspondence concerning this service should be sent to the repository A B S T R A C TThe present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak-Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).

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Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms

Cited by 60 publications

References 25 publications

A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model

A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model

Explicit incorporation of deformation twins into crystal plasticity finite element models

Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

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