Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

Levitas, Valery I.; Chen, Hao; Xiong, Liming

doi:10.1103/PhysRevB.96.054118

Title: Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

Abstract

A continuum/atomistic approach for predicting lattice instability during crystal-crystal phase transformations (PTs) is developed for the general loading with an arbitrary stress tensor and large strains. It is based on a synergistic combination of the generalized Landau-type theory for PTs and molecular dynamics (MD) simulations. The continuum approach describes the entire dissipative transformation process in terms of an order parameter, and the general form of the instability criterion is derived utilizing the second law of thermodynamics. The feedback from MD allowed us to present the instability criterion for both direct and reverse PTs in terms of the critical value of the modified transformation work, which is linear in components of the true stress tensor. It was calibrated by MD simulations for direct and reverse PTs between semiconducting silicon Si i and metallic Si ii phases under just two different stress states. Then, it describes hundreds of MD simulations under various combinations of three normal and three shear stresses. Finally, in particular, the atomistic simulations show that the effects of all three shear stresses along cubic axes on lattice instability of Si i are negligible, which is in agreement with our criterion.

Authors:

Levitas, Valery I. ^[1]; Chen, Hao ^[2]; Xiong, Liming ^[2]

Iowa State Univ., Ames, IA (United States). Dept. of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering; Ames Lab., Ames, IA (United States)
Iowa State Univ., Ames, IA (United States). Dept. of Aerospace Engineering

Publication Date:: 2017-08-29

Research Org.:: Ames Lab., Ames, IA (United States)

Sponsoring Org.:: National Science Foundation (NSF); USDOE; US Army Research Office (ARO)

OSTI Identifier:: 1418498

Grant/Contract Number:: CMMI-1536925; DMR-1434613; W911NF-17-1-0225; N00014-16-1-2079

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Levitas, Valery I., Chen, Hao, and Xiong, Liming. Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevB.96.054118.

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                    Levitas, Valery I., Chen, Hao, & Xiong, Liming. Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion.  United States.  https://doi.org/10.1103/PhysRevB.96.054118

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                    Levitas, Valery I., Chen, Hao, and Xiong, Liming. Tue .  
"Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion".  United States.  https://doi.org/10.1103/PhysRevB.96.054118.  https://www.osti.gov/servlets/purl/1418498.

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@article{osti_1418498,

  title        = {Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion},

  author       = {Levitas, Valery I. and Chen, Hao and Xiong, Liming},

  abstractNote = {A continuum/atomistic approach for predicting lattice instability during crystal-crystal phase transformations (PTs) is developed for the general loading with an arbitrary stress tensor and large strains. It is based on a synergistic combination of the generalized Landau-type theory for PTs and molecular dynamics (MD) simulations. The continuum approach describes the entire dissipative transformation process in terms of an order parameter, and the general form of the instability criterion is derived utilizing the second law of thermodynamics. The feedback from MD allowed us to present the instability criterion for both direct and reverse PTs in terms of the critical value of the modified transformation work, which is linear in components of the true stress tensor. It was calibrated by MD simulations for direct and reverse PTs between semiconducting silicon Si i and metallic Si ii phases under just two different stress states. Then, it describes hundreds of MD simulations under various combinations of three normal and three shear stresses. Finally, in particular, the atomistic simulations show that the effects of all three shear stresses along cubic axes on lattice instability of Si i are negligible, which is in agreement with our criterion.},

  doi          = {10.1103/PhysRevB.96.054118},

  journal      = {Physical Review B},

  number       = 5,

  volume       = 96,

  place        = {United States},

  year         = {2017},

  month        = {8}

}

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https://doi.org/10.1103/PhysRevB.96.054118

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Figure 1: Phase transformation process for Si I→Si II under uniaxial loading. (A) heterogeneous nucleation of Si II due to stress fluctuation. (B) and (C) due to internal stresses caused by the transformation strain, complete Si II and residual Si I reshape into bands. Note that Si I bands aremore »

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Similar Records

Title: Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

Abstract

Citation Formats

Figures / Tables:

Ab initio study of the high-pressure phase transition from the cubic-diamond to the β-tin structure of Si journal, November 2001

Shear-induced phase transition of nanocrystalline hexagonal boron nitride to wurtzitic structure at room temperature and lower pressure journal, November 2012

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Low-pressure phase transformation from rhombohedral to cubic BN: Experiment and theory journal, February 2002

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Ab initio calculations of mechanical properties: Methods and applications journal, August 2015

Theoretical bcc ⇆ fcc Transitions in Metals via Bifurcations under Uniaxial Load journal, April 1995

The internal stability of an elastic solid journal, December 2000

Phase field approach to martensitic phase transformations with large strains and interface stresses journal, October 2014

Molecular dynamics with coupling to an external bath journal, October 1984

Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy journal, February 1996

Crystal instabilities at finite strain journal, December 1993

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

Fast Parallel Algorithms for Short-Range Molecular Dynamics journal, March 1995

Polymorphic transitions in single crystals: A new molecular dynamics method journal, December 1981

Twin Boundaries in Ferroelastic Media without Interface Dislocations journal, September 1984

Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool journal, December 2009

Comparative study of silicon empirical interatomic potentials journal, July 1992

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Principles of stability analysis of ideal crystals journal, March 1977

Phase-field theory for martensitic phase transformations at large strains journal, October 2013

Ideal crystal stability and pressure-induced phase transition in silicon journal, November 1994

Atomistic basis for the plastic yield criterion of metallic glass journal, June 2003

Dynamics of viscoplastic deformation in amorphous solids journal, June 1998

Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations journal, January 2007

Towards a nonlinear elastic representation of finite compression and instability of boron carbide ceramic journal, August 2012

Continuum interpretation of virial stress in molecular simulations journal, July 2008

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Introduction to lattice dynamics journal, August 1994

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Shear-induced phase transition of nanocrystalline hexagonal boron nitride to wurtzitic structure at room temperature and lower pressure
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Theoretical bcc $⇆$ fcc Transitions in Metals via Bifurcations under Uniaxial Load
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The internal stability of an elastic solid
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Phase field approach to martensitic phase transformations with large strains and interface stresses
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Molecular dynamics with coupling to an external bath
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Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy
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Comparative study of silicon empirical interatomic potentials
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Reversible stress-induced martensitic phase transformations in a bi-atomic crystal
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Atomistic basis for the plastic yield criterion of metallic glass
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