A continuum dislocation-based model of wedge microindentation of single crystals

Po, Giacomo; Huang, Yue; Ghoniem, Nasr

doi:10.1016/j.ijplas.2018.10.008

Title: A continuum dislocation-based model of wedge microindentation of single crystals

Abstract

Recent Electron Backscatter Diffraction (EBSD) experiments have revealed the emergence of heterogeneous dislocation microstructures forming under a wedge indenter in fcc crystals, where micro-meter dislocation patterns challenge the predictions of traditional models of plasticity. In order to explain the formation of these features and develop a relationship between the force-displacement curve and the dislocation substructure, here we present a model of wedge indentation based on the continuum theory of dislocations. The model accounts for large deformation kinematics through the multiplicative split of the deformation gradient tensor, where the incompatible plastic component of deformation results from the flux of dislocations on different and interacting slips systems. Constitutive equations for dislocation fluxes are determined from a dissipative variational principle. As a result, each dislocation density satisfies an initial-boundary value problem with convective-diffusive character, which is coupled to the macroscopic stress and displacement fields governing the deformation process. Solution to the self-consistent continuum formulation is found using the finite element method. Computer simulations mimic the experimental conditions of wedge micro-indentation experiments into Ni single-crystals used by Kysar et al. (2010a). A comparison of overall dislocation density distribution and macroscopic mechanical response shows good overall agreement with the experimental results in terms of themore »« less

Authors:

Po, Giacomo ^[1]; Huang, Yue ^[1];

^[1]

University of California, Los Angeles, CA (United States)

Publication Date:: Fri Oct 26 00:00:00 EDT 2018

Research Org.:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); US Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF)

OSTI Identifier:: 1612981

Alternate Identifier(s):: OSTI ID: 1636863

Grant/Contract Number:: SC0018410; FA9550-16-1-0444; CMMI-1563427

Resource Type:: Accepted Manuscript

Journal Name:: International Journal of Plasticity

Additional Journal Information:: Journal Volume: 114; Journal Issue: C; Journal ID: ISSN 0749-6419

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; 42 ENGINEERING; dislocation density tensor; finite deformation; indentation; dislocation patterns

Citation Formats


                    Po, Giacomo, Huang, Yue, and Ghoniem, Nasr. A continuum dislocation-based model of wedge microindentation of single crystals.  United States: N. p., 2018. 
Web.  doi:10.1016/j.ijplas.2018.10.008.

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                    Po, Giacomo, Huang, Yue, & Ghoniem, Nasr. A continuum dislocation-based model of wedge microindentation of single crystals.  United States.  https://doi.org/10.1016/j.ijplas.2018.10.008

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                    Po, Giacomo, Huang, Yue, and Ghoniem, Nasr. Fri .  
"A continuum dislocation-based model of wedge microindentation of single crystals".  United States.  https://doi.org/10.1016/j.ijplas.2018.10.008.  https://www.osti.gov/servlets/purl/1612981.

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@article{osti_1612981,

  title        = {A continuum dislocation-based model of wedge microindentation of single crystals},

  author       = {Po, Giacomo and Huang, Yue and Ghoniem, Nasr},

  abstractNote = {Recent Electron Backscatter Diffraction (EBSD) experiments have revealed the emergence of heterogeneous dislocation microstructures forming under a wedge indenter in fcc crystals, where micro-meter dislocation patterns challenge the predictions of traditional models of plasticity. In order to explain the formation of these features and develop a relationship between the force-displacement curve and the dislocation substructure, here we present a model of wedge indentation based on the continuum theory of dislocations. The model accounts for large deformation kinematics through the multiplicative split of the deformation gradient tensor, where the incompatible plastic component of deformation results from the flux of dislocations on different and interacting slips systems. Constitutive equations for dislocation fluxes are determined from a dissipative variational principle. As a result, each dislocation density satisfies an initial-boundary value problem with convective-diffusive character, which is coupled to the macroscopic stress and displacement fields governing the deformation process. Solution to the self-consistent continuum formulation is found using the finite element method. Computer simulations mimic the experimental conditions of wedge micro-indentation experiments into Ni single-crystals used by Kysar et al. (2010a). A comparison of overall dislocation density distribution and macroscopic mechanical response shows good overall agreement with the experimental results in terms of the detailed features of dislocation patterns and lattice rotations as well as the macroscopic force-displacement response.},

  doi          = {10.1016/j.ijplas.2018.10.008},

  journal      = {International Journal of Plasticity},

  number       = C,

  volume       = 114,

  place        = {United States},

  year         = {Fri Oct 26 00:00:00 EDT 2018},

  month        = {Fri Oct 26 00:00:00 EDT 2018}

}

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Title: A continuum dislocation-based model of wedge microindentation of single crystals

Abstract

Citation Formats

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Experimental lower bounds on geometrically necessary dislocation density journal, August 2010

Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals journal, August 2005

High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities journal, July 2007

Elastic-Plastic Deformation at Finite Strains journal, March 1969

Simulation of micro-indentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity journal, October 2010

Atomistic mechanisms governing elastic limit and incipient plasticity in crystals journal, July 2002

A review of nanoindentation continuous stiffness measurement technique and its applications journal, February 2002

Fracture mechanisms of thin amorphous carbon films in nanoindentation journal, November 1997

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation journal, May 2003

Theory of Dislocation Mobility in Pure Slip journal, June 1962

Thermodynamic coarsening of dislocation mechanics and the size-dependent continuum crystal plasticity journal, March 2010

Size effects in indentation response of thin films at the nanoscale: A molecular dynamics study journal, November 2008

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

Some geometrical relations in dislocated crystals journal, March 1953

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments journal, June 1992

Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys journal, March 2005

An X-ray investigation of pure iron-nickel alloys. Part 4: the variation of lattice-parameter with composition journal, May 1937

Length-scale effect due to periodic variation of geometrically necessary dislocation densities journal, February 2013

Hardness measurement at penetration depths as small as 20 nm journal, April 1983

The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations journal, June 2010

Stacking fault energy and indentation size effect: Do they interact? journal, February 2008

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

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

Resolving geometrically necessary dislocation density onto individual dislocation types using EBSD-based continuum dislocation microscopy journal, January 2016

Crystal plasticity analysis of cylindrical indentation on a Ni-base single crystal superalloy journal, December 2013

Wedge indentation into elastic–plastic single crystals. 2: Simulations for face-centered cubic crystals journal, January 2012

Nanoindentation studies of materials journal, May 2006

High cycle fatigue of thin silver films investigated by dynamic microbeam deflection journal, September 1999

Views on multiplicative elastoplasticity and the continuum theory of dislocations journal, December 1996

A new method for estimating residual stresses by instrumented sharp indentation journal, October 1998

Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations journal, June 2002

On the continuum thermodynamic rate variational formulation of models for extended crystal plasticity at large deformation journal, September 2010

Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals journal, May 2015

Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals journal, November 2012

The Influence of Indenter Tip Radius on the Micro-Indentation Hardness journal, June 2002

A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations journal, February 2004

On the origin of deformation-induced rotation patterns below nanoindents journal, January 2008

Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations journal, April 2006

Indentation of a hard film on a soft substrate: Strain gradient hardening effects journal, January 2007

Lattice rotation caused by wedge indentation of a single crystal: Dislocation dynamics compared to crystal plasticity simulations journal, August 2014

A model of crystal plasticity based on the theory of continuously distributed dislocations
journal, April 2001

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements
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On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals
journal, June 2004

Dislocation structure during microindentation
journal, September 2015

Discrete dislocation plasticity analysis of the wedge indentation of films
journal, November 2006

Continuum theory of dislocations revisited
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Dynamic aspects of dislocation motion: atomistic simulations
journal, July 2005

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

Scaling, dimensional analysis, and indentation measurements
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Application of thermomechanical principles to the modelling of geotechnical materials
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Geometrically necessary dislocation density measurements associated with different angles of indentations
journal, March 2014

The direction of the force on a dislocation and the sign of the Burgers vector
journal, November 1965

Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography
journal, January 2009

Continuum simulation of the evolution of dislocation densities during nanoindentation
journal, November 2012

Molecular dynamics analysis of temperature effects on nanoindentation measurement
journal, September 2003

Critical review of analysis and interpretation of nanoindentation test data
journal, April 2006

Three-dimensional modeling of indent-induced plastic zone at a mesoscale1This paper is dedicated to Gilles Canova whose untimely death occurred on 28 July 1997 at the age of 43.1
journal, November 1998

3D simulation of a nanoindentation test at a mesoscopic scale
journal, August 1997

Numerical and experimental studies of deep indentation on single crystals
journal, October 2008

Indentation across size scales and disciplines: Recent developments in experimentation and modeling
journal, July 2007

Variational approach in dislocation theory
journal, September 2010

Dynamics of coarse grained dislocation densities from an effective free energy
journal, March 2007

Continuum dislocation dynamics: Towards a physical theory of crystal plasticity
journal, February 2014

Collective behaviour of dislocations in a finite medium
journal, April 2014

Microscopically derived free energy of dislocations
journal, May 2015

Free energy of dislocations in a multi-slip geometry
journal, March 2016

Experimental lower bounds on geometrically necessary dislocation density
journal, August 2010

Cylindrical void in a rigid-ideally plastic single crystal. Part I: Anisotropic slip line theory solution for face-centered cubic crystals
journal, August 2005

High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities
journal, July 2007

Elastic-Plastic Deformation at Finite Strains
journal, March 1969

Simulation of micro-indentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity
journal, October 2010

Atomistic mechanisms governing elastic limit and incipient plasticity in crystals
journal, July 2002

A review of nanoindentation continuous stiffness measurement technique and its applications
journal, February 2002

Fracture mechanisms of thin amorphous carbon films in nanoindentation
journal, November 1997

Atomistic simulations of elastic deformation and dislocation nucleation during nanoindentation
journal, May 2003

Theory of Dislocation Mobility in Pure Slip
journal, June 1962

Thermodynamic coarsening of dislocation mechanics and the size-dependent continuum crystal plasticity
journal, March 2010

Size effects in indentation response of thin films at the nanoscale: A molecular dynamics study
journal, November 2008

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

Some geometrical relations in dislocated crystals
journal, March 1953

An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments
journal, June 1992

Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
journal, March 2005

An X-ray investigation of pure iron-nickel alloys. Part 4: the variation of lattice-parameter with composition
journal, May 1937

Length-scale effect due to periodic variation of geometrically necessary dislocation densities
journal, February 2013

Hardness measurement at penetration depths as small as 20 nm
journal, April 1983

The Indentation Size Effect: A Critical Examination of Experimental Observations and Mechanistic Interpretations
journal, June 2010

Stacking fault energy and indentation size effect: Do they interact?
journal, February 2008

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

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

Resolving geometrically necessary dislocation density onto individual dislocation types using EBSD-based continuum dislocation microscopy
journal, January 2016

Crystal plasticity analysis of cylindrical indentation on a Ni-base single crystal superalloy
journal, December 2013

Wedge indentation into elastic–plastic single crystals. 2: Simulations for face-centered cubic crystals
journal, January 2012

Nanoindentation studies of materials
journal, May 2006

High cycle fatigue of thin silver films investigated by dynamic microbeam deflection
journal, September 1999

Views on multiplicative elastoplasticity and the continuum theory of dislocations
journal, December 1996

A new method for estimating residual stresses by instrumented sharp indentation
journal, October 1998

Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations
journal, June 2002

On the continuum thermodynamic rate variational formulation of models for extended crystal plasticity at large deformation
journal, September 2010

Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals
journal, May 2015

Coarse-grained atomistic simulations of dislocations in Al, Ni and Cu crystals
journal, November 2012

The Influence of Indenter Tip Radius on the Micro-Indentation Hardness
journal, June 2002

A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations
journal, February 2004

On the origin of deformation-induced rotation patterns below nanoindents
journal, January 2008

Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations
journal, April 2006

Indentation of a hard film on a soft substrate: Strain gradient hardening effects
journal, January 2007

Lattice rotation caused by wedge indentation of a single crystal: Dislocation dynamics compared to crystal plasticity simulations
journal, August 2014