An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression

Daphalapurkar, Nitin P.; Luscher, Darby J.; Versino, Daniele; Margolin, Len; Hunter, Abigail

doi:10.1016/j.jmps.2019.103818

Title: An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression

Abstract

In this report, we developed a thermodynamically-consistent, rate-dependent micromechanics model for brittle damage nucleated by dislocation plasticity applicable for large deformations. Dislocation substructure evolution was used to inform a nucleation criterion for a microcrack. Under global compression, the sliding of a microcrack induces formation of wing cracks. Effective stress drives dynamic growth of these cracks under a 3D stress state, resulting in an anisotropic material stiffness. The model was also advanced to predict grain size dependence of a polycrystalline solid. Internal variables were constrained based on the laws of thermodynamics. Material constants were calibrated for polycrystalline beryllium to demonstrate the applicability of the model to simulate dynamic failure under compression. We demonstrate the versatility of the model to capture brittle to ductile transition governed by temperature and strain rate. The predictive capability of the model to simulate failure stress and failure strain is compared with dynamic and quasistatic data on beryllium.

Authors:

^[1];

^[1]

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

Publication Date:: 2019-12-13

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1581276

Alternate Identifier(s):: OSTI ID: 1580118

Report Number(s):: LA-UR-19-25002
Journal ID: ISSN 0022-5096; TRN: US2100870

Grant/Contract Number:: 89233218CNA000001

Resource Type:: Accepted Manuscript

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

Additional Journal Information:: Journal Volume: 137; Journal Issue: C; Journal ID: ISSN 0022-5096

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; HCP; fracture; cracks; kinetics; damage; viscoplastic

Citation Formats


                    Daphalapurkar, Nitin P., Luscher, Darby J., Versino, Daniele, Margolin, Len, and Hunter, Abigail. An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression.  United States: N. p., 2019. 
Web.  doi:10.1016/j.jmps.2019.103818.

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                    Daphalapurkar, Nitin P., Luscher, Darby J., Versino, Daniele, Margolin, Len, & Hunter, Abigail. An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression.  United States.  https://doi.org/10.1016/j.jmps.2019.103818

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                    Daphalapurkar, Nitin P., Luscher, Darby J., Versino, Daniele, Margolin, Len, and Hunter, Abigail. Fri .  
"An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression".  United States.  https://doi.org/10.1016/j.jmps.2019.103818.  https://www.osti.gov/servlets/purl/1581276.

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@article{osti_1581276,

  title        = {An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression},

  author       = {Daphalapurkar, Nitin P. and Luscher, Darby J. and Versino, Daniele and Margolin, Len and Hunter, Abigail},

  abstractNote = {In this report, we developed a thermodynamically-consistent, rate-dependent micromechanics model for brittle damage nucleated by dislocation plasticity applicable for large deformations. Dislocation substructure evolution was used to inform a nucleation criterion for a microcrack. Under global compression, the sliding of a microcrack induces formation of wing cracks. Effective stress drives dynamic growth of these cracks under a 3D stress state, resulting in an anisotropic material stiffness. The model was also advanced to predict grain size dependence of a polycrystalline solid. Internal variables were constrained based on the laws of thermodynamics. Material constants were calibrated for polycrystalline beryllium to demonstrate the applicability of the model to simulate dynamic failure under compression. We demonstrate the versatility of the model to capture brittle to ductile transition governed by temperature and strain rate. The predictive capability of the model to simulate failure stress and failure strain is compared with dynamic and quasistatic data on beryllium.},

  doi          = {10.1016/j.jmps.2019.103818},

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

  number       = C,

  volume       = 137,

  place        = {United States},

  year         = {2019},

  month        = {12}

}

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Abstract

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Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys journal, October 2011

Theory of the tensile ductile-brittle behavior of poly-crystalline h.c.p. materials, with application to beryllium journal, March 1968

A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates journal, January 2011

The effective compliance of spatially evolving planar wing-cracks journal, February 2018

Fracture toughness of CIP-HIP Beryllium at elevated temperatures journal, February 1987

A reduced-order crystal model for HCP metals: Application to Mg journal, July 2016

Energy of periodic discrete dislocation networks journal, December 2018

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

Comparison of dislocation density based approaches for prediction of defect structure evolution in aluminium and copper processed by ECAP journal, April 2015

In Situ Neutron Diffraction Measurements During Annealing of Deformed Beryllium With Differing Initial Textures journal, August 2013

A non-singular continuum theory of dislocations journal, March 2006

Atomistic modeling of dislocation cross-slip in nickel using free-end nudged elastic band method journal, April 2019

A geometric framework for the kinematics of crystals with defects journal, November 2005

The missing term in the decomposition of finite deformation journal, January 2014

Finite polycrystalline elastoplasticity and damage: multiscale kinematics journal, October 2003

Orientation dependence of the nucleation and growth of partial dislocations and possible twinning mechanisms in aluminum journal, February 2012

Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws journal, February 2011

Kinetics of a fast moving twin boundary in nickel journal, April 2014

Dislocation evolution during plastic deformation: Equations vs. discrete dislocation dynamics study journal, February 2018

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model journal, October 2008

A Constitutive Description of the Inelastic Response of Ceramics: Inelastic Response of Ceramics journal, April 2011

Coalescence of fractures under shear stresses in experiments journal, April 1995

XLI. The equilibrium of linear arrays of dislocations. journal, April 1951

Local strain hardening and nonuniformity of plastic deformation journal, December 1986

A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable journal, January 1988

Crack propagation in an elastic solid subjected to general loading—II. Non-uniform rate of extension journal, June 1972

Overview no. 5 journal, October 1979

Crack initiation at dislocation cell boundaries in the ductile fracture of metals journal, July 1977

Effective elasticity of fractured rocks: A snapshot of the work in progress journal, November 2006

Plastic anisotropy and fracture in beryllium journal, January 1961

The temperature and strain rate dependence of the flow stress of tantalum journal, August 1977

A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading journal, May 2015

Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids journal, June 2003

Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures journal, January 1985

Crack nucleation in magnesium oxide bi-crystals under compression journal, January 1962

Dislocation Multiplication in Lithium Fluoride Crystals journal, April 1960

Cleavage in zinc journal, February 1971

A scaling law for the dynamic strength of brittle solids journal, May 2013

Pressure-shear impact and the dynamic viscoplastic response of metals journal, December 1985

A statistical theory of flow stress and work-hardening journal, March 1966

Physics and phenomenology of strain hardening: the FCC case journal, January 2003

Kinetics of shear-activated indentation crack initiation in soda-lime glass journal, September 1983

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging journal, September 2018

Plane wave simulation of elastic-viscoplastic single crystals journal, September 2014

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine journal, January 2017

A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals journal, July 2004

Kinetics of flow and strain-hardening journal, November 1981

Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory journal, April 1983

Elastic moduli of beryllium versus temperature: Experimental data updating journal, August 2010

Discussion of Geometric probability approach to the characterization and analysis of microcracking in rocks journal, December 1985

A Microcrack Model of Dilatancy in Brittle Materials journal, March 1988

Probability density distribution of the orientation of strength-controlling flaws from multiaxial loading using the unit-sphere stochastic strength model for anisotropy journal, November 2013

On the mechanisms of work hardening and flow-stress saturation journal, June 2000

A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals journal, November 2017

Micromechanical constitutive model for low-temperature constant strain rate deformation of limestones in the brittle and semi-brittle regime journal, July 2017

Length scales and scaling laws for dislocation cells developed during monotonic deformation of (001) nickel single crystal journal, March 2016

An interacting micro-crack damage model for failure of brittle materials under compression journal, March 2008

Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression journal, September 2010

Kinematic Description of Damage journal, March 1998

Dependence of room temperature fracture strength on strain-rate in sapphire journal, November 1973

Beryllium fracture observed by in situ high voltage electron microscopy journal, October 1983

Prismatic Slip in Beryllium and the Relative Ease of Glide in H.C.P. Metals journal, January 1970

Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals journal, July 1998

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks journal, June 1968

A Review of the Stages of Work Hardening journal, September 1993

Work hardening in heterogeneous alloys—a microstructural approach based on three internal state variables journal, November 2000

On the micromechanical theories of stressinduced cleavage microcracking in crystalline solids journal, January 1987

A continuum framework for finite viscoplasticity journal, August 2001

Influence of strain rate on mechanical properties and deformation texture of hot-pressed and rolled beryllium journal, July 2010

Crack Nucleation in Crystalline Solids journal, January 1967

A constitutive model for metals applicable at high‐strain rate journal, March 1980

Crack formation in magnesium oxide single crystals journal, July 1958

The Cleavage of Metal Single Crystals journal, June 1958

Tensile deformation modes in polycrystalline beryllium near the ductile-brittle transition journal, January 1964

Influence of Grain Size and Age-Hardening on Dislocation Pile-Ups and Tensile Fracture for a Ti-AI Alloy journal, July 1982

Influence of copper additions on the basal cleavage in beryllium single crystals at room temperature journal, May 1976

The ductile fracture of metals: A microstructural viewpoint journal, May 1983

Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys
journal, October 2011

Theory of the tensile ductile-brittle behavior of poly-crystalline h.c.p. materials, with application to beryllium
journal, March 1968

A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates
journal, January 2011

The effective compliance of spatially evolving planar wing-cracks
journal, February 2018

Fracture toughness of CIP-HIP Beryllium at elevated temperatures
journal, February 1987

A reduced-order crystal model for HCP metals: Application to Mg
journal, July 2016

Energy of periodic discrete dislocation networks
journal, December 2018

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

Comparison of dislocation density based approaches for prediction of defect structure evolution in aluminium and copper processed by ECAP
journal, April 2015

In Situ Neutron Diffraction Measurements During Annealing of Deformed Beryllium With Differing Initial Textures
journal, August 2013

A non-singular continuum theory of dislocations
journal, March 2006

Atomistic modeling of dislocation cross-slip in nickel using free-end nudged elastic band method
journal, April 2019

A geometric framework for the kinematics of crystals with defects
journal, November 2005

The missing term in the decomposition of finite deformation
journal, January 2014

Finite polycrystalline elastoplasticity and damage: multiscale kinematics
journal, October 2003

Orientation dependence of the nucleation and growth of partial dislocations and possible twinning mechanisms in aluminum
journal, February 2012

Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws
journal, February 2011

Kinetics of a fast moving twin boundary in nickel
journal, April 2014

Dislocation evolution during plastic deformation: Equations vs. discrete dislocation dynamics study
journal, February 2018

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model
journal, October 2008

A Constitutive Description of the Inelastic Response of Ceramics: Inelastic Response of Ceramics
journal, April 2011

Coalescence of fractures under shear stresses in experiments
journal, April 1995

XLI. The equilibrium of linear arrays of dislocations.
journal, April 1951

Local strain hardening and nonuniformity of plastic deformation
journal, December 1986

A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable
journal, January 1988

Crack propagation in an elastic solid subjected to general loading—II. Non-uniform rate of extension
journal, June 1972

Overview no. 5
journal, October 1979

Crack initiation at dislocation cell boundaries in the ductile fracture of metals
journal, July 1977

Effective elasticity of fractured rocks: A snapshot of the work in progress
journal, November 2006

Plastic anisotropy and fracture in beryllium
journal, January 1961

The temperature and strain rate dependence of the flow stress of tantalum
journal, August 1977

A 3D mechanistic model for brittle materials containing evolving flaw distributions under dynamic multiaxial loading
journal, May 2015

Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids
journal, June 2003

Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures
journal, January 1985

Crack nucleation in magnesium oxide bi-crystals under compression
journal, January 1962

Dislocation Multiplication in Lithium Fluoride Crystals
journal, April 1960

Cleavage in zinc
journal, February 1971

A scaling law for the dynamic strength of brittle solids
journal, May 2013

Pressure-shear impact and the dynamic viscoplastic response of metals
journal, December 1985

A statistical theory of flow stress and work-hardening
journal, March 1966

Physics and phenomenology of strain hardening: the FCC case
journal, January 2003

Kinetics of shear-activated indentation crack initiation in soda-lime glass
journal, September 1983

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging
journal, September 2018

Plane wave simulation of elastic-viscoplastic single crystals
journal, September 2014

A dislocation density-based continuum model of the anisotropic shock response of single crystal α-cyclotrimethylene trinitramine
journal, January 2017

A constitutive model for fcc single crystals based on dislocation densities and its application to uniaxial compression of aluminium single crystals
journal, July 2004

Kinetics of flow and strain-hardening
journal, November 1981

Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory
journal, April 1983

Elastic moduli of beryllium versus temperature: Experimental data updating
journal, August 2010

Discussion of Geometric probability approach to the characterization and analysis of microcracking in rocks
journal, December 1985

A Microcrack Model of Dilatancy in Brittle Materials
journal, March 1988

Probability density distribution of the orientation of strength-controlling flaws from multiaxial loading using the unit-sphere stochastic strength model for anisotropy
journal, November 2013

On the mechanisms of work hardening and flow-stress saturation
journal, June 2000

A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals
journal, November 2017

Micromechanical constitutive model for low-temperature constant strain rate deformation of limestones in the brittle and semi-brittle regime
journal, July 2017

Length scales and scaling laws for dislocation cells developed during monotonic deformation of (001) nickel single crystal
journal, March 2016

An interacting micro-crack damage model for failure of brittle materials under compression
journal, March 2008

Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression
journal, September 2010

Kinematic Description of Damage
journal, March 1998

Dependence of room temperature fracture strength on strain-rate in sapphire
journal, November 1973

Beryllium fracture observed by in situ high voltage electron microscopy
journal, October 1983

Prismatic Slip in Beryllium and the Relative Ease of Glide in H.C.P. Metals
journal, January 1970

Models for long-/short-range interactions and cross slip in 3D dislocation simulation of BCC single crystals
journal, July 1998

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
journal, June 1968

A Review of the Stages of Work Hardening
journal, September 1993

Work hardening in heterogeneous alloys—a microstructural approach based on three internal state variables
journal, November 2000

On the micromechanical theories of stressinduced cleavage microcracking in crystalline solids
journal, January 1987

A continuum framework for finite viscoplasticity
journal, August 2001

Influence of strain rate on mechanical properties and deformation texture of hot-pressed and rolled beryllium
journal, July 2010

Crack Nucleation in Crystalline Solids
journal, January 1967

A constitutive model for metals applicable at high‐strain rate
journal, March 1980

Crack formation in magnesium oxide single crystals
journal, July 1958

The Cleavage of Metal Single Crystals
journal, June 1958

Tensile deformation modes in polycrystalline beryllium near the ductile-brittle transition
journal, January 1964

Influence of Grain Size and Age-Hardening on Dislocation Pile-Ups and Tensile Fracture for a Ti-AI Alloy
journal, July 1982

Influence of copper additions on the basal cleavage in beryllium single crystals at room temperature
journal, May 1976

The ductile fracture of metals: A microstructural viewpoint
journal, May 1983

Shock wave compression of hexagonal-close-packed metal single crystals: Time-dependent, anisotropic elastic-plastic response of beryllium
journal, July 2014

A note on the propagation behavior of a crack nucleated by a dislocation pileup
journal, January 1990