A predictive strain-gradient model with no undetermined constants or length scales

Zhou, G.; Jeong, W.; Homer, E. R.; Fullwood, D. T.; Lee, M. G.; Kim, J. H.; Lim, H.; Zbib, H.; Wagoner, R. H.

doi:10.1016/j.jmps.2020.104178

Title: A predictive strain-gradient model with no undetermined constants or length scales

Abstract

A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

Authors:

Zhou, G. ^[1]; Jeong, W. ^[2]; Homer, E. R. ^[3]; Fullwood, D. T. ^[3]; Lee, M. G. ^[2]; Kim, J. H. ^[4]; Lim, H. ^[5]; Zbib, H. ^[6];

^[1]

The Ohio State Univ., Columbus, OH (United States)
Seoul National Univ. (Korea)
Brigham Young Univ., Provo, UT (United States)
Pusan National Univ., Busan (Korea)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Washington State Univ., Pullman, WA (United States)

Publication Date:: Wed Oct 07 00:00:00 EDT 2020

Research Org.:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1698022

Alternate Identifier(s):: OSTI ID: 1776117

Grant/Contract Number:: SC0012483; SC0012587; NA0003525

Resource Type:: Accepted Manuscript

Journal Name:: Journal of the Mechanics and Physics of Solids

Additional Journal Information:: Journal Volume: 145; Journal ID: ISSN 0022-5096

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Crystal Plasticity; Strain Gradient; GND; Stagnation; Anelasticity; Finite Element; Harmonization; Bauschinger effect; Ta

Citation Formats


                    Zhou, G., Jeong, W., Homer, E. R., Fullwood, D. T., Lee, M. G., Kim, J. H., Lim, H., Zbib, H., and Wagoner, R. H. A predictive strain-gradient model with no undetermined constants or length scales.  United States: N. p., 2020. 
Web.  doi:10.1016/j.jmps.2020.104178.

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                    Zhou, G., Jeong, W., Homer, E. R., Fullwood, D. T., Lee, M. G., Kim, J. H., Lim, H., Zbib, H., & Wagoner, R. H. A predictive strain-gradient model with no undetermined constants or length scales.  United States.  https://doi.org/10.1016/j.jmps.2020.104178

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                    Zhou, G., Jeong, W., Homer, E. R., Fullwood, D. T., Lee, M. G., Kim, J. H., Lim, H., Zbib, H., and Wagoner, R. H. Wed .  
"A predictive strain-gradient model with no undetermined constants or length scales".  United States.  https://doi.org/10.1016/j.jmps.2020.104178.  https://www.osti.gov/servlets/purl/1698022.

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@article{osti_1698022,

  title        = {A predictive strain-gradient model with no undetermined constants or length scales},

  author       = {Zhou, G. and Jeong, W. and Homer, E. R. and Fullwood, D. T. and Lee, M. G. and Kim, J. H. and Lim, H. and Zbib, H. and Wagoner, R. H.},

  abstractNote = {A general meso–scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. As a result, GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.},

  doi          = {10.1016/j.jmps.2020.104178},

  journal      = {Journal of the Mechanics and Physics of Solids},

  number       = ,

  volume       = 145,

  place        = {United States},

  year         = {Wed Oct 07 00:00:00 EDT 2020},

  month        = {Wed Oct 07 00:00:00 EDT 2020}

}

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Yoshida, Fusahito; Uemori, Takeshi
International Journal of Plasticity, Vol. 18, Issue 5-6
DOI: 10.1016/S0749-6419(01)00050-X

A model of large-strain cyclic plasticity and its application to springback simulation
journal, October 2003

Yoshida, F.; Uemori, T.
International Journal of Mechanical Sciences, Vol. 45, Issue 10
DOI: 10.1016/j.ijmecsci.2003.10.013

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Title: A predictive strain-gradient model with no undetermined constants or length scales

Abstract

Citation Formats

On the Microstructural Origin of Certain Inelastic Models journal, October 1984

Quantification of dislocation structures from anelastic deformation behaviour journal, August 2016

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

Latent hardening size effect in small-scale plasticity journal, May 2013

A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation journal, August 2014

Incompatibility and a simple gradient theory of plasticity journal, September 2001

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A three-dimensional dislocation field crystal plasticity approach applied to miniaturized structures journal, March 2007

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An RVE procedure for micromechanical prediction of mechanical behavior of dual-phase steel journal, May 2017

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An experimental statistical analysis of stress projection factors in BCC tantalum journal, October 2013

On the criteria for slip transmission across interfaces in polycrystals journal, January 1992

A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model journal, December 2004

Variation and consistency of Young’s modulus in steel journal, January 2016

The elastic–plastic transition of metals journal, August 2016

Inelastic effects on springback in metals journal, October 2002

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On modeling micro-structural evolution using a higher order strain gradient continuum theory journal, January 2016

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

Strain gradient plasticity: Theory and experiment journal, February 1994

Mechanism of the Bauschinger effect in Al-Ge-Si alloys journal, January 2017

Mechanism-based strain gradient plasticity? I. Theory journal, April 1999

Taylor-based nonlocal theory of plasticity journal, April 2001

Second-order crystal plasticity: internal stress effects and cyclic loading journal, December 2006

Local Ratcheting Phenomena in the Cyclic Behavior of Polycrystalline Tantalum journal, June 2019

A microcantilever investigation of size effect, solid-solution strengthening and second-phase strengthening for 〈a〉 prism slip in alpha-Ti journal, September 2011

〈a〉 Prismatic, 〈a〉 basal, and 〈c+a〉 slip strengths of commercially pure Zr by micro-cantilever tests journal, September 2015

A physically-based constitutive model for metal deformation journal, November 1980

A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations journal, January 2002

Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector journal, January 2005

Gradient single-crystal plasticity with free energy dependent on dislocation densities journal, September 2007

Gradient single-crystal plasticity within a Mises–Hill framework based on a new formulation of self- and latent-hardening journal, August 2014

Mechanism-based strain gradient crystal plasticity—I. Theory journal, May 2005

Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization journal, January 2020

“Region of constant flow stress” during compression of aluminium polycrystals prestrained by tension journal, August 1974

Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium journal, January 1975

Mechanism-based strain gradient plasticity—II. Analysis journal, January 2000

Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field journal, February 2003

Crystallographic texture evolution in bulk deformation processing of FCC metals journal, January 1992

Laws for Work-Hardening and Low-Temperature Creep journal, January 1976

Studies of scale dependent crystal viscoplasticity models journal, September 2006

A finite deformation theory of higher-order gradient crystal plasticity journal, August 2008

On the formulations of higher-order strain gradient crystal plasticity models journal, April 2008

Nonuniform and localized deformation in single crystals under dynamic tensile loading journal, April 2019

A new strategy to describe nonlinear elastic and asymmetric plastic behaviors with one yield surface journal, November 2017

A dislocation density-based single crystal constitutive equation journal, July 2010

Simulation of polycrystal deformation with grain and grain boundary effects journal, September 2011

A Practical Meso-Scale Polycrystal Model to Predict Dislocation Densities and the Hall–Petch Effect journal, January 2014

Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals journal, September 2014

Investigation of grain-scale microstructural variability in tantalum using crystal plasticity-finite element simulations journal, May 2016

Investigating active slip planes in tantalum under compressive load: Crystal plasticity and slip trace analyses of single crystals journal, February 2020

Numerical study of the size-dependent deformation morphology in micropillar compressions by a dislocation-based crystal plasticity model journal, December 2016

A dislocation dynamics based higher-order crystal plasticity model and applications on confined thin-film plasticity journal, February 2011

Stress/strain gradient plasticity model for size effects in heterogeneous nano-microstructures journal, October 2017

A comparison of Gurtin type and micropolar theories of generalized single crystal plasticity journal, June 2014

Continuous distribution of moving dislocations journal, May 1963

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Indentation size effects in crystalline materials: A law for strain gradient plasticity journal, March 1998

On the Finite Element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility journal, October 2016

On the role of higher-order conditions in distortion gradient plasticity journal, September 2018

On an implementation of the strain gradient plasticity with linear finite elements and reduced integration journal, October 2012

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Finite element approximation of field dislocation mechanics journal, January 2005

Dislocation pile-up and grain boundary interactions in 304 stainless steel journal, June 1986

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Consistent tangent operators for rate-independent elastoplasticity journal, February 1985

Complex unloading behavior: Nature of the deformation and its consistent constitutive representation journal, July 2011

On the nonlinear anelastic behavior of AHSS journal, October 2018

Sample Dimensions Influence Strength and Crystal Plasticity journal, August 2004

On the Microstructural Origin of Certain Inelastic Models
journal, October 1984

Quantification of dislocation structures from anelastic deformation behaviour
journal, August 2016

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

Latent hardening size effect in small-scale plasticity
journal, May 2013

A computational study of a model of single-crystal strain-gradient viscoplasticity with an interactive hardening relation
journal, August 2014

Incompatibility and a simple gradient theory of plasticity
journal, September 2001

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

A three-dimensional dislocation field crystal plasticity approach applied to miniaturized structures
journal, March 2007

Experimental and finite element analysis on oscillating cold forming in consideration of nonlinear loading-unloading-reloading behavior
journal, December 2018

Dynamic explicit solution for higher-order crystal plasticity theories
journal, February 2014

An RVE procedure for micromechanical prediction of mechanical behavior of dual-phase steel
journal, May 2017

Gradient-dependent deformation of two-phase single crystals
journal, November 2000

An experimental statistical analysis of stress projection factors in BCC tantalum
journal, October 2013

On the criteria for slip transmission across interfaces in polycrystals
journal, January 1992

A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model
journal, December 2004

Variation and consistency of Young’s modulus in steel
journal, January 2016

The elastic–plastic transition of metals
journal, August 2016

Inelastic effects on springback in metals
journal, October 2002

Consistent determination of geometrically necessary dislocation density from simulations and experiments
journal, October 2018

On modeling micro-structural evolution using a higher order strain gradient continuum theory
journal, January 2016

Energetic dislocation interactions and thermodynamical aspects of strain gradient crystal plasticity theories
journal, November 2009

A critical assessment of theories of strain gradient plasticity
journal, March 2009

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

Strain gradient plasticity: Theory and experiment
journal, February 1994

Mechanism of the Bauschinger effect in Al-Ge-Si alloys
journal, January 2017

Mechanism-based strain gradient plasticity? I. Theory
journal, April 1999

Taylor-based nonlocal theory of plasticity
journal, April 2001

Second-order crystal plasticity: internal stress effects and cyclic loading
journal, December 2006

Local Ratcheting Phenomena in the Cyclic Behavior of Polycrystalline Tantalum
journal, June 2019

A microcantilever investigation of size effect, solid-solution strengthening and second-phase strengthening for 〈a〉 prism slip in alpha-Ti
journal, September 2011

〈a〉 Prismatic, 〈a〉 basal, and 〈c+a〉 slip strengths of commercially pure Zr by micro-cantilever tests
journal, September 2015

A physically-based constitutive model for metal deformation
journal, November 1980

A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
journal, January 2002

Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector
journal, January 2005

Gradient single-crystal plasticity with free energy dependent on dislocation densities
journal, September 2007

Gradient single-crystal plasticity within a Mises–Hill framework based on a new formulation of self- and latent-hardening
journal, August 2014

Mechanism-based strain gradient crystal plasticity—I. Theory
journal, May 2005

Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization
journal, January 2020

“Region of constant flow stress” during compression of aluminium polycrystals prestrained by tension
journal, August 1974

Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium
journal, January 1975

Mechanism-based strain gradient plasticity—II. Analysis
journal, January 2000

Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field
journal, February 2003

Crystallographic texture evolution in bulk deformation processing of FCC metals
journal, January 1992

Laws for Work-Hardening and Low-Temperature Creep
journal, January 1976

Studies of scale dependent crystal viscoplasticity models
journal, September 2006

A finite deformation theory of higher-order gradient crystal plasticity
journal, August 2008

On the formulations of higher-order strain gradient crystal plasticity models
journal, April 2008

Nonuniform and localized deformation in single crystals under dynamic tensile loading
journal, April 2019

A new strategy to describe nonlinear elastic and asymmetric plastic behaviors with one yield surface
journal, November 2017

A dislocation density-based single crystal constitutive equation
journal, July 2010

Simulation of polycrystal deformation with grain and grain boundary effects
journal, September 2011

A Practical Meso-Scale Polycrystal Model to Predict Dislocation Densities and the Hall–Petch Effect
journal, January 2014

Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals
journal, September 2014

Investigation of grain-scale microstructural variability in tantalum using crystal plasticity-finite element simulations
journal, May 2016

Investigating active slip planes in tantalum under compressive load: Crystal plasticity and slip trace analyses of single crystals
journal, February 2020

Numerical study of the size-dependent deformation morphology in micropillar compressions by a dislocation-based crystal plasticity model
journal, December 2016

A dislocation dynamics based higher-order crystal plasticity model and applications on confined thin-film plasticity
journal, February 2011

Stress/strain gradient plasticity model for size effects in heterogeneous nano-microstructures
journal, October 2017

A comparison of Gurtin type and micropolar theories of generalized single crystal plasticity
journal, June 2014

Continuous distribution of moving dislocations
journal, May 1963

Computational strain gradient crystal plasticity
journal, January 2014

Indentation size effects in crystalline materials: A law for strain gradient plasticity
journal, March 1998

On the Finite Element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility
journal, October 2016

On the role of higher-order conditions in distortion gradient plasticity
journal, September 2018

On an implementation of the strain gradient plasticity with linear finite elements and reduced integration
journal, October 2012

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

Modeling of surface effects in crystalline materials within the framework of gradient crystal plasticity
journal, March 2018

A physically based yield criterion I. Determination of the yield stress based on analysis of pre-yield dislocation behaviour
journal, April 2016

Finite element implementation of gradient plasticity models Part I: Gradient-dependent yield functions
journal, September 1998

Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity finite-element predictions with experiments
journal, June 2014

Finite element approximation of field dislocation mechanics
journal, January 2005

Dislocation pile-up and grain boundary interactions in 304 stainless steel
journal, June 1986

Dislocation and grain boundary interactions in metals
journal, December 1988

Consistent tangent operators for rate-independent elastoplasticity
journal, February 1985

Complex unloading behavior: Nature of the deformation and its consistent constitutive representation
journal, July 2011

On the nonlinear anelastic behavior of AHSS
journal, October 2018

Sample Dimensions Influence Strength and Crystal Plasticity
journal, August 2004

Grain boundary interfacial plasticity with incorporation of internal structure and energy
journal, November 2015

Gradient plasticity theory with a variable length scale parameter
journal, July 2005

Strain gradient continuum plasticity theories: Theoretical, numerical and experimental investigations
journal, October 2019