Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

Lebensohn, Ricardo A.

doi:10.1007/978-3-319-42913-7_15-1

Title: Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

Abstract

We review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. Finally, the assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.

Authors:

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Tue Aug 07 00:00:00 EDT 2018

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE; LANL Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1480022

Report Number(s):: LA-UR-17-31125

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Handbook of Materials Modeling

Additional Journal Information:: Journal Name: Handbook of Materials Modeling

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    Lebensohn, Ricardo A. Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations.  United States: N. p., 2018. 
Web.  doi:10.1007/978-3-319-42913-7_15-1.

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                    Lebensohn, Ricardo A. Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations.  United States.  https://doi.org/10.1007/978-3-319-42913-7_15-1

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                    Lebensohn, Ricardo A. Tue .  
"Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations".  United States.  https://doi.org/10.1007/978-3-319-42913-7_15-1.  https://www.osti.gov/servlets/purl/1480022.

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@article{osti_1480022,

  title        = {Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations},

  author       = {Lebensohn, Ricardo A.},

  abstractNote = {We review two crystal plasticity methodologies based on Green’s functions for the prediction of microstructure-property relations in polycrystalline aggregates. The first, known as the viscoplastic self-consistent (VPSC) formulation, is a mean-field theory. The second, known as the viscoplastic fast Fourier transform-based (VPFFT) formulation, is a full-field method. Finally, the assumptions and main equations of these Green’s function-based crystal plasticity formulations are presented using a unified notation, pointing out their similarities and differences and cross-validating their predictions.},

  doi          = {10.1007/978-3-319-42913-7_15-1},

  journal      = {Handbook of Materials Modeling},

  number       = ,

  volume       = ,

  place        = {United States},

  year         = {Tue Aug 07 00:00:00 EDT 2018},

  month        = {Tue Aug 07 00:00:00 EDT 2018}

}

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Title: Polycrystal Plasticity Models Based on Green’s Functions: Mean-Field Self-Consistent and Full-Field Fast Fourier Transform Formulations

Abstract

Citation Formats

A fast numerical scheme for computing the response of composites using grid refinement journal, April 1999

Mechanical behavior of Mg subjected to strain path changes: Experiments and modeling journal, October 2015

A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys journal, April 2015

Elastic anisotropy and yield surface estimates of polycrystals journal, August 2009

Effects of grain interaction on deformation in polycrystals journal, November 1998

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A self-consistent approach for modelling texture development of two-phase polycrystals: Application to titanium alloys journal, September 1997

A numerical method for computing the overall response of nonlinear composites with complex microstructure journal, April 1998

A deformation-based model for recrystallization of anisotropic materials journal, August 1997

Three-dimensional finite element simulation of a polycrystalline copper specimen journal, July 2007

On the thermostatics of composite materials journal, January 1973

Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations journal, August 2007

Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals journal, February 2004

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications journal, February 2010

Fourier-based schemes for computing the mechanical response of composites with accurate local fields journal, March 2015

Average intragranular misorientation trends in polycrystalline materials predicted by a viscoplastic self-consistent approach journal, February 2016

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms journal, December 2016

Intra-grain orientation distributions in hot-deformed aluminium: Orientation dependence and relation to deformation mechanisms journal, November 2015

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An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials journal, May 2012

Analysis of texture evolution in channel die compression—I. Effects of grain interaction journal, June 1991

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The problem of two plastic and heterogeneous inclusions in an anisotropic medium journal, January 1987

Residual stresses and stored elastic energy of composites and polycrystals journal, January 1990

Mechanical response of zirconium—I. Derivation of a polycrystal constitutive law and finite element analysis journal, September 2001

Continuum micro-mechanics of elastoplastic polycrystals journal, April 1965

Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations journal, May 2006

Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening journal, September 2006

FFT-based methods for the mechanics of composites: A general variational framework journal, September 2010

Modeling void growth in polycrystalline materials journal, October 2013

Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons journal, October 2006

Study of the antiplane deformation of linear 2-D polycrystals with different microstructures journal, October 2005

Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper journal, September 2008

Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements journal, January 2012

Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials journal, February 1976

A spectral method solution to crystal elasto-viscoplasticity at finite strains journal, July 2013

Multiscale modeling of the mechanical behavior of IN718 superalloy based on micropillar compression and computational homogenization journal, October 2015

Experimental characterization of the intragranular strain field in columnar ice during transient creep journal, May 2012

Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory journal, April 2002

Modeling texture, twinning and hardening evolution during deformation of hexagonal materials journal, April 2007

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling journal, April 2010

A self consistent approach of the large deformation polycrystal viscoplasticity journal, December 1987

Static elastic and thermoelastic field fluctuations in multiphase composites journal, January 1987

The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity journal, January 2015

Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations journal, March 2000

Plastic flow of γ-TiAl-based polysynthetically twinned crystals: micromechanical modeling and experimental validation journal, August 1998

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Micromechanical and macromechanical effects in grain scale polycrystal plasticity experimentation and simulation journal, October 2001

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A fast numerical scheme for computing the response of composites using grid refinement
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Mechanical behavior of Mg subjected to strain path changes: Experiments and modeling
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A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys
journal, April 2015

Elastic anisotropy and yield surface estimates of polycrystals
journal, August 2009

Effects of grain interaction on deformation in polycrystals
journal, November 1998

Numerical implementation of static Field Dislocation Mechanics theory for periodic media
journal, March 2014

A self-consistent approach for modelling texture development of two-phase polycrystals: Application to titanium alloys
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A numerical method for computing the overall response of nonlinear composites with complex microstructure
journal, April 1998

A deformation-based model for recrystallization of anisotropic materials
journal, August 1997

Three-dimensional finite element simulation of a polycrystalline copper specimen
journal, July 2007

On the thermostatics of composite materials
journal, January 1973

Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations
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Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals
journal, February 2004

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
journal, February 2010

Fourier-based schemes for computing the mechanical response of composites with accurate local fields
journal, March 2015

Average intragranular misorientation trends in polycrystalline materials predicted by a viscoplastic self-consistent approach
journal, February 2016

Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms
journal, December 2016

Intra-grain orientation distributions in hot-deformed aluminium: Orientation dependence and relation to deformation mechanisms
journal, November 2015

An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals
journal, June 2000

An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials
journal, May 2012

Analysis of texture evolution in channel die compression—I. Effects of grain interaction
journal, June 1991

Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model
journal, January 2001

The problem of two plastic and heterogeneous inclusions in an anisotropic medium
journal, January 1987

Residual stresses and stored elastic energy of composites and polycrystals
journal, January 1990

Mechanical response of zirconium—I. Derivation of a polycrystal constitutive law and finite element analysis
journal, September 2001

Continuum micro-mechanics of elastoplastic polycrystals
journal, April 1965

Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations
journal, May 2006

Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening
journal, September 2006

FFT-based methods for the mechanics of composites: A general variational framework
journal, September 2010

Modeling void growth in polycrystalline materials
journal, October 2013

Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons
journal, October 2006

Study of the antiplane deformation of linear 2-D polycrystals with different microstructures
journal, October 2005

Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper
journal, September 2008

Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements
journal, January 2012

Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials
journal, February 1976

A spectral method solution to crystal elasto-viscoplasticity at finite strains
journal, July 2013

Multiscale modeling of the mechanical behavior of IN718 superalloy based on micropillar compression and computational homogenization
journal, October 2015

Experimental characterization of the intragranular strain field in columnar ice during transient creep
journal, May 2012

Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory
journal, April 2002

Modeling texture, twinning and hardening evolution during deformation of hexagonal materials
journal, April 2007

Anisotropic response of high-purity α-titanium: Experimental characterization and constitutive modeling
journal, April 2010

A self consistent approach of the large deformation polycrystal viscoplasticity
journal, December 1987

Static elastic and thermoelastic field fluctuations in multiphase composites
journal, January 1987

The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity
journal, January 2015

Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations
journal, March 2000

Plastic flow of γ-TiAl-based polysynthetically twinned crystals: micromechanical modeling and experimental validation
journal, August 1998

N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform
journal, August 2001

A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics
journal, November 2014

Micromechanical and macromechanical effects in grain scale polycrystal plasticity experimentation and simulation
journal, October 2001

Predicting intragranular misorientation distributions in polycrystalline metals using the viscoplastic self-consistent formulation
journal, November 2017

A dislocation-based constitutive law for pure Zr including temperature effects
journal, May 2008

Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements
journal, March 2013

A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys
journal, September 1993

Dilatational viscoplasticity of polycrystalline solids with intergranular cavities
journal, August 2011