Phase-field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part 2. simulations of phase transformations Si I<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo>↔</mml:mo></mml:math>Si II

Babaei, Hamed; Levitas, Valery I.

doi:10.1016/j.ijplas.2018.04.006

Cited by 22 publications

(28 citation statements)

References 33 publications

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“…In addition, atomistic simulation provided information, material functions and parameters for developing and calibrating our phase field models. 37,38)…”

Section: Crystal Lattice Instability Criteria: Phase Fieldmentioning

confidence: 99%

High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

Levitas

2019

Mater. Trans.

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Numerous experiments have documented that combination of severe plastic deformation and high mean pressure during high-pressure torsion in rotational metallic, ceramic, or diamond anvils produces various important mechanochemical effects. We will focus here on four of these: plastic deformation (a) significantly reduces pressure for initiation and completion of phase transformations (PTs), (b) leads to discovery of hidden metastable phases and compounds, (c) reduces PT pressure hysteresis, and (d) substitutes a reversible PT with irreversible PT. The goal of this review is to summarize our current understanding of the underlying phenomena based on multiscale atomistic and continuum theories and computational modeling. Recent atomistic simulations provide conditions for initiation of PTs in a defect-free lattice as a function of the general stress tensor. These conditions (a) allow one to determine stress states that significantly decrease the transformation pressure and (b) determine whether the given phase can, in principle, be preserved at ambient pressure. Nanoscale mechanisms of phase nucleation at plastic-strain-induced defects are studied analytically and by utilizing advanced phase field theory and simulations. It is demonstrated that the concentration of all components of the stress tensor near the tip of the dislocation pileup may decrease nucleation pressure by a factor of ten or more. These results are incorporated into the microscale analytical kinetic equation for strain-induced PTs. The kinetic equation is part of a macroscale geometrically-nonlinear model for combined plastic flow and PT. This model is used for finite-element simulations of plastic deformations and PT in a sample under torsion in a rotational anvil device. Numerous experimentally-observed phenomena are reproduced, and new effects are predicted and then confirmed experimentally. Combination of the results on all four scales suggests novel synthetic routes for new or known high-pressure phases (HPPs), experimental characterization of strain-induced PTs under high-pressure during torsion under elevated pressure.

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“…In addition, atomistic simulation provided information, material functions and parameters for developing and calibrating our phase field models. 37,38)…”

Section: Crystal Lattice Instability Criteria: Phase Fieldmentioning

confidence: 99%

High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

Levitas

2019

Mater. Trans.

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“…In Section 2, the complete systems of equations for PFA to martensitic PTs for the largestrain kinematic model are presented. A single martensitic variant is considered, similar to that which was observed in atomistic simulations in [33,34] and described in theory by [4,26].…”

Section: Introductionmentioning

confidence: 88%

“…Thus, new conditions must be introduced to make the PFA instability criteria consistent with the lattice instability conditions obtained by atomistic simulations. These conditions were introduced in [4,26] and is implemented in this work.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic aspects and finite element solutions for advanced phase field approach to martensitic phase transformation under large strains

Babaei

Basak

2019

Comput Mech

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A new problem formulation and numerical algorithm for an advanced phase-field approach (PFA) to martensitic phase transformation (PT) are presented. Finite elastic and transformational strains are considered using a fully geometrically-nonlinear formulation, which includes different anisotropic elastic properties of phases. The requirements for the thermodynamic potentials and transformation deformation gradient tensor are advanced to reproduce crystal lattice instability conditions under a general stress tensor obtained by molecular dynamics (MD) simulations. The PFA parameters are calibrated, in particular, based on the results of MD simulations for PTs between semiconducting Si I and metallic Si II phases under complex action of all six components of the stress tensor (Levitas et al. in Phys Rev Lett 118:025701, 2017a; Phys Rev B 96:054118, 2017b). The independence of the PFA instability conditions of the prescribed stress measure is demonstrated numerically for the initiation of the PT. However, it is observed that the PT cannot be completed unless the stress exceeds the stress peak points that depend on which stress measure is prescribed. Various 3D problems on lattice instability and following nanostructure evolution in single-crystal Si are solved. The effect of stress hysteresis on the nanostructure evolution is studied through analysis of the local driving force and stress fields. It is demonstrated that variation of internal stress fields due to differing boundary conditions may lead to completely different PT mechanisms.

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“…(2.19)-(2.21). Thus we obtain 27) where using Eq. (3.6) we determine g(λ a , λ a , λ b ) = g(λ a , λ b , λ a ) = g(λ b , λ a , λ a ) and…”

Section: Second Derivatives Of U T and Some Related Termsmentioning

confidence: 99%

“…. In [26,27] a new nonlinear interpolation function was introduced to describe a new instability criteria related to phase transformations between silicon-I↔silicon-II.…”

Section: Introductionmentioning

confidence: 99%

An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations

Basak

Levitas

2020

Mathematics and Mechanics of Solids

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A general theoretical and computational procedure for dealing with an exponential-logarithmic kinematic model for transformation stretch tensor in a multiphase phase field approach to stress- and temperature-induced martensitic transformations with N martensitic variants is developed for transformations between all possible crystal lattices. This kinematic model, where the natural logarithm of transformation stretch tensor is a linear combination of natural logarithm of the Bain tensors, yields isochoric variant–variant transformations for the entire transformation path. Such a condition is plausible and cannot be satisfied by the widely used kinematic model where the transformation stretch tensor is linear in Bain tensors. Earlier general multiphase phase field studies can handle commutative Bain tensors only. In the present treatment, the exact expressions for the first and second derivatives of the transformation stretch tensor with respect to the order parameters are obtained. Using these relations, the transformation work for austenite ↔ martensite and variant ↔ variant transformations is analyzed and the thermodynamic instability criteria for all homogeneous phases are expressed explicitly. The finite element procedure with an emphasis on the derivation of the tangent matrix for the phase field equations, which involves second derivatives of the transformation deformation gradients with respect to the order parameters, is developed. Change in anisotropic elastic properties during austenite–martensitic variants and variant–variant transformations is taken into account. The numerical results exhibiting twinned microstructures for cubic to orthorhombic and cubic to monoclinic-I transformations are presented.

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Phase-field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part 2. simulations of phase transformations Si I↔Si II

Cited by 22 publications

References 33 publications

High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

Algorithmic aspects and finite element solutions for advanced phase field approach to martensitic phase transformation under large strains

An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations

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