Computational Homogenization of Polycrystals

Segurado, Javier; Lebensohn, Ricardo A.; Llorca, Javier

doi:10.1016/bs.aams.2018.07.001

Title: Computational Homogenization of Polycrystals

Abstract

This paper reviews the current state of the art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modeling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Lastly, current challenges and future research directionsmore » in this field are summarized.« less

Authors:

Segurado, Javier ^[1];

^[2]; Llorca, Javier ^[1]

IMDEA Materials Institute, Madrid (Spain); Polytechnic Univ. of Madrid, Madrid (Spain)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Wed Oct 17 00:00:00 EDT 2018

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

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

OSTI Identifier:: 1480031

Report Number(s):: LA-UR-18-23540
Journal ID: ISSN 0065-2156

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Advances in Applied Mechanics

Additional Journal Information:: Journal Volume: in press; Journal Issue: 0; Journal ID: ISSN 0065-2156

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Homogenization theory; Crystalline solids; Multiscale modeling; Crystal plasticity

Citation Formats


                    Segurado, Javier, Lebensohn, Ricardo A., and Llorca, Javier. Computational Homogenization of Polycrystals.  United States: N. p., 2018. 
Web.  doi:10.1016/bs.aams.2018.07.001.

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                    Segurado, Javier, Lebensohn, Ricardo A., & Llorca, Javier. Computational Homogenization of Polycrystals.  United States.  https://doi.org/10.1016/bs.aams.2018.07.001

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                    Segurado, Javier, Lebensohn, Ricardo A., and Llorca, Javier. Wed .  
"Computational Homogenization of Polycrystals".  United States.  https://doi.org/10.1016/bs.aams.2018.07.001.  https://www.osti.gov/servlets/purl/1480031.

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@article{osti_1480031,

  title        = {Computational Homogenization of Polycrystals},

  author       = {Segurado, Javier and Lebensohn, Ricardo A. and Llorca, Javier},

  abstractNote = {This paper reviews the current state of the art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modeling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Lastly, current challenges and future research directions in this field are summarized.},

  doi          = {10.1016/bs.aams.2018.07.001},

  journal      = {Advances in Applied Mechanics},

  number       = 0,

  volume       = in press,

  place        = {United States},

  year         = {Wed Oct 17 00:00:00 EDT 2018},

  month        = {Wed Oct 17 00:00:00 EDT 2018}

}

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Fig. 1: Digital representations of an RVE of a polycrystal. (A) Voxel-based representation and (B) Voronoi-based representation.

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journal, December 2016

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International Journal of Plasticity, Vol. 87
DOI: 10.1016/j.ijplas.2016.09.002

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journal, December 2016

Ghosh, Somnath; Shahba, Ahmad; Tu, Xiaohui
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journal, August 2015

Bertin, N.; Upadhyay, M. V.; Pradalier, C.
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Haouala, Sarra; Segurado, Javier; LLorca, Javier
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DOI: 10.1016/j.actamat.2018.01.024

Orientation dependent deformation by slip and twinning in magnesium during single crystal indentation
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Zambaldi, C.; Zehnder, C.; Raabe, D.
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DOI: 10.1016/j.actamat.2015.01.046

Measuring the critical resolved shear stresses in Mg alloys by instrumented nanoindentation
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Sánchez-Martín, R.; Pérez-Prado, M. T.; Segurado, J.
Acta Materialia, Vol. 71
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The Elasticity of an Isotropic Aggregate of Anisotropic Cubic Crystals
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Hershey, A. V.
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Works referencing / citing this record:

On the accuracy of spectral solvers for micromechanics based fatigue modeling
journal, July 2018

Lucarini, S.; Segurado, J.
Computational Mechanics, Vol. 63, Issue 2
DOI: 10.1007/s00466-018-1598-1

On the accuracy of spectral solvers for micromechanics based fatigue modeling
text, January 2018

Lucarini, Sergio; Segurado, Javier
arXiv
DOI: 10.48550/arxiv.1806.10599

On the accuracy of spectral solvers for micromechanics based fatigue modeling
text, January 2018

Lucarini, Sergio; Segurado, Javier
arXiv
DOI: 10.48550/arxiv.1806.10599

Modeling of One Inclusion in the Infinite Peristatic Matrix Subjected to Homogeneous Remote Loading
journal, March 2019

Buryachenko, Valeriy A.
Journal of Peridynamics and Nonlocal Modeling, Vol. 1, Issue 2
DOI: 10.1007/s42102-019-00006-w

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Title: Computational Homogenization of Polycrystals

Abstract

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Figures / Tables:

Three-dimensional investigation of grain orientation effects on void growth in commercially pure titanium journal, August 2016

A Critical Plane Approach to Multiaxial Fatigue Damage Including Out-Of-Phase Loading journal, March 1988

FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation journal, June 2018

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Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements journal, January 2016

A unified framework for polycrystal plasticity with grain boundary evolution journal, July 2018

Coupled glide-climb diffusion-enhanced crystal plasticity journal, October 2014

Experimental characterisation for micromechanical modelling of CoCr stent fatigue journal, January 2014

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

Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading journal, July 2010

Shear band bifurcations in ductile single crystals journal, January 1983

Grain Size Strengthening in Microcrystalline Copper: A Three-Dimensional Dislocation Dynamics Simulation journal, December 2009

The relation between macroscopic and microscopic strain hardening in F.C.C. polycrystals journal, October 1984

Continuum micro-mechanics of elastoplastic polycrystals journal, April 1965

Challenges in the prediction of twin transmission at grain boundaries in a magnesium alloy journal, October 2016

Overview no. 42 Texture development and strain hardening in rate dependent polycrystals journal, June 1985

A numerical approximation to the elastic properties of sphere-reinforced composites journal, October 2002

On the characterization of geometrically necessary dislocations in finite plasticity journal, July 2001

A combined grain scale elastic–plastic criterion for identification of fatigue crack initiation sites in a twin containing polycrystalline nickel-base superalloy journal, January 2016

Deformation twinning in AZ31: Influence on strain hardening and texture evolution journal, November 2010

Computational micromechanics of composites: The effect of particle spatial distribution journal, August 2006

Non-local crystal plasticity model with intrinsic SSD and GND effects journal, October 2004

Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density journal, March 1999

Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations journal, November 2017

Microstructure-sensitive HCF and VHCF simulations journal, December 2013

Augmenting the 3D Characterization Capability of the Dual Beam FIB-SEM journal, August 2004

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

Grain neighbour effects on twin transmission in hexagonal close-packed materials journal, December 2016

In situ observation of collective grain-scale mechanics in Mg and Mg–rare earth alloys journal, November 2014

Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals journal, May 2017

Deformation twinning journal, January 1995

Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results journal, January 2001

A computational procedure for rate-independent crystal plasticity journal, April 1996

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

The Deformation and Ageing of Mild Steel: III Discussion of Results journal, September 1951

Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp journal, July 2014

Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100 journal, March 2010

Grain boundaries and interfaces in slip transfer journal, August 2014

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

Crystal plasticity FE study of the effect of thermo-mechanical loading on fatigue crack nucleation in titanium alloys: Crystal Plasticity FE Study journal, February 2016

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet journal, October 2010

Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach journal, October 2007

In situ analysis of the tensile and tensile-creep deformation mechanisms in rolled AZ31 journal, February 2012

Quantifying deformation processes near grain boundaries in α titanium using nanoindentation and crystal plasticity modeling journal, November 2016

Three-dimensional investigation of grain boundary–twin interactions in a Mg AZ31 alloy by electron backscatter diffraction and continuum modeling journal, December 2013

Generalized constitutive relations for incremental deformation of metal crystals by multislip journal, March 1966

Dislocation Mean Free Paths and Strain Hardening of Crystals journal, June 2008

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

Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique journal, September 2005

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

High– and low–cycle fatigue crack initiation using polycrystal plasticity journal, July 2004

Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials: COMPARISON OF THREE ACCELERATED FFT-BASED SCHEMES journal, January 2014

Microstructure-sensitive computational modeling of fatigue crack formation journal, September 2010

Structural composites for multifunctional applications: Current challenges and future trends journal, August 2017

Microstructure based fatigue life prediction framework for polycrystalline nickel-base superalloys with emphasis on the role played by twin boundaries in crack initiation journal, April 2016

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

A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations journal, January 2006

A self-consistent mechanics of composite materials journal, August 1965

On the thermostatics of composite materials journal, January 1973

Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls journal, August 1958

Exponential map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals journal, October 1996

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

Finite strain FFT-based non-linear solvers made simple journal, May 2017

Derivation of F=FeFp as the continuum limit of crystalline slip journal, April 2016

Three-dimensional investigation of grain orientation effects on void growth in commercially pure titanium
journal, August 2016

A Critical Plane Approach to Multiaxial Fatigue Damage Including Out-Of-Phase Loading
journal, March 1988

FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation
journal, June 2018

Incorporating physically-based microstructures in materials modeling: Bridging phase field and crystal plasticity frameworks
journal, April 2016

An analysis of nonuniform and localized deformation in ductile single crystals
journal, June 1982

Evolution of grain-scale microstructure during large strain simple compression of polycrystalline aluminum with quasi-columnar grains: OIM measurements and numerical simulations
journal, July 2001

A model-reduction approach to the micromechanical analysis of polycrystalline materials
journal, January 2016

Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti–6Al–4V
journal, January 2012

Generation of statistically representative synthetic three-dimensional microstructures
journal, March 2018

A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity
journal, November 2006

Modeling of discontinuous dynamic recrystallization of a near-α titanium alloy IMI834 during isothermal hot compression by combining a cellular automaton model with a crystal plasticity finite element method
journal, November 2013

Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics
journal, August 2010

The physics of fatigue crack initiation
journal, December 2013

The elastic field outside an ellipsoidal inclusion
journal, October 1959

Is stored energy density the primary meso-scale mechanistic driver for fatigue crack nucleation?
journal, February 2018

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

Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements
journal, January 2016

A unified framework for polycrystal plasticity with grain boundary evolution
journal, July 2018

Coupled glide-climb diffusion-enhanced crystal plasticity
journal, October 2014

Experimental characterisation for micromechanical modelling of CoCr stent fatigue
journal, January 2014

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

Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading
journal, July 2010

Shear band bifurcations in ductile single crystals
journal, January 1983

Grain Size Strengthening in Microcrystalline Copper: A Three-Dimensional Dislocation Dynamics Simulation
journal, December 2009

The relation between macroscopic and microscopic strain hardening in F.C.C. polycrystals
journal, October 1984

Continuum micro-mechanics of elastoplastic polycrystals
journal, April 1965

Challenges in the prediction of twin transmission at grain boundaries in a magnesium alloy
journal, October 2016

Overview no. 42 Texture development and strain hardening in rate dependent polycrystals
journal, June 1985

A numerical approximation to the elastic properties of sphere-reinforced composites
journal, October 2002

On the characterization of geometrically necessary dislocations in finite plasticity
journal, July 2001

A combined grain scale elastic–plastic criterion for identification of fatigue crack initiation sites in a twin containing polycrystalline nickel-base superalloy
journal, January 2016

Deformation twinning in AZ31: Influence on strain hardening and texture evolution
journal, November 2010

Computational micromechanics of composites: The effect of particle spatial distribution
journal, August 2006

Non-local crystal plasticity model with intrinsic SSD and GND effects
journal, October 2004

Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density
journal, March 1999

Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations
journal, November 2017

Microstructure-sensitive HCF and VHCF simulations
journal, December 2013

Augmenting the 3D Characterization Capability of the Dual Beam FIB-SEM
journal, August 2004

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

Grain neighbour effects on twin transmission in hexagonal close-packed materials
journal, December 2016

In situ observation of collective grain-scale mechanics in Mg and Mg–rare earth alloys
journal, November 2014

Estimating the slip resistance from spherical nanoindentation and orientation measurements in polycrystalline samples of cubic metals
journal, May 2017

Deformation twinning
journal, January 1995

Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results
journal, January 2001

A computational procedure for rate-independent crystal plasticity
journal, April 1996

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

The Deformation and Ageing of Mild Steel: III Discussion of Results
journal, September 1951

Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp
journal, July 2014

Microstructure-sensitive extreme value probabilities for high cycle fatigue of Ni-base superalloy IN100
journal, March 2010

Grain boundaries and interfaces in slip transfer
journal, August 2014

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

Crystal plasticity FE study of the effect of thermo-mechanical loading on fatigue crack nucleation in titanium alloys: Crystal Plasticity FE Study
journal, February 2016

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet
journal, October 2010

Estimating fatigue sensitivity to polycrystalline Ni-base superalloy microstructures using a computational approach
journal, October 2007

In situ analysis of the tensile and tensile-creep deformation mechanisms in rolled AZ31
journal, February 2012

Quantifying deformation processes near grain boundaries in α titanium using nanoindentation and crystal plasticity modeling
journal, November 2016

Three-dimensional investigation of grain boundary–twin interactions in a Mg AZ31 alloy by electron backscatter diffraction and continuum modeling
journal, December 2013

Generalized constitutive relations for incremental deformation of metal crystals by multislip
journal, March 1966

Dislocation Mean Free Paths and Strain Hardening of Crystals
journal, June 2008

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

Mechanical properties of micro-sized copper bending beams machined by the focused ion beam technique
journal, September 2005

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

High– and low–cycle fatigue crack initiation using polycrystal plasticity
journal, July 2004

Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials: COMPARISON OF THREE ACCELERATED FFT-BASED SCHEMES
journal, January 2014

Microstructure-sensitive computational modeling of fatigue crack formation
journal, September 2010

Structural composites for multifunctional applications: Current challenges and future trends
journal, August 2017

Microstructure based fatigue life prediction framework for polycrystalline nickel-base superalloys with emphasis on the role played by twin boundaries in crack initiation
journal, April 2016

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

A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations
journal, January 2006

A self-consistent mechanics of composite materials
journal, August 1965

On the thermostatics of composite materials
journal, January 1973

Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls
journal, August 1958

Exponential map Algorithm for Stress Updates in Anisotropic Multiplicative Elastoplasticity for Single Crystals
journal, October 1996

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

Finite strain FFT-based non-linear solvers made simple
journal, May 2017

Derivation of F=FeFp as the continuum limit of crystalline slip
journal, April 2016

Grain-scale measurement of slip resistances in aluminum polycrystals using spherical nanoindentation
journal, May 2015

Strain gradient plasticity: Theory and experiment
journal, February 1994

Numerical Modeling of Twinning Induced Plasticity in Austenite Based Advanced High Strength Steels
journal, January 2016

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