Stress-measure dependence of phase transformation criterion under finite strains: Hierarchy of crystal lattice instabilities for homogeneous and heterogeneous transformations

Babaei, Hamed

doi:10.26226/morressier.5f5f8e69aa777f8ba5bd5fef

Cited by 3 publications

(3 citation statements)

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“…For dislocations, twins, and cracks, described by the corresponding order parameters 43,[58][59][60] , defect nucleation at the nanoscale occurs at reaching theoretical strength in shear and tension, i.e., at large elastic strains. While theory is developed for higher-order energies, the second-order elasticity is used currently 47,48,[59][60][61] , due to lack of reliable data. Utilizing higher-order elastic energy developed in the current paper will significantly improve phase fields models for phase transformations, dislocations, and fracture, and their interaction.…”

Section: Stress-strain Curves For Triaxial Loadingmentioning

confidence: 99%

“…In particular, higher-order elasticity is required for determination of the stress-strain states and optimization of the diamond anvil cell for reaching maximum possible pressures 21 . This approach is general and will significantly improve phase-field models for phase transformations, in contrast to the second-order elasticity used currently 47,48,61 . It also provides a basis for the description of the competition between different instabilities at different loadings.…”

Section: Stress-strain Curves For Triaxial Loadingmentioning

confidence: 99%

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Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

et al. 2020

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Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

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Section: Stress-strain Curves For Triaxial Loadingmentioning

confidence: 99%

Section: Stress-strain Curves For Triaxial Loadingmentioning

confidence: 99%

Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

et al. 2020

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show abstract

“…In particular, higherorder elasticity is required for determination of the stressstrain states and optimization of the diamond anvil cell for reaching maximum possible pressures [21]. This approach is general and will significantly improve phase fields models of phase transformations, in contrast to second-order elasticity used currently [39,40,45]. It also provides a basis for the description of the competition between different instabilities at different loadings.…”

Section: Introductionmentioning

confidence: 99%

Fifth-degree elastic potential for predictive stress-strain relations and elastic instabilities under large strain and complex loading in Si

Chen¹,

Zarkevich²,

Levitas³

et al. 2020

Preprint

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Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we represent Si I under large strain in terms of Lagrangian strains by an 5 th -order elastic potential found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress -Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I→II phase transformation (PT) and the shear instabilities. PT conditions for Si I→II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such elastic potential permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum simulations of crystal behavior under extreme loading.

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Multiphase Phase-Field Approach for Virtual Melting: A Brief Review

Roy

2021

Mat. Sci. Res. India

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A short review on a thermodynamically consistent multiphase phase-field approach for virtual melting has been presented. The important outcomes of solid-solid phase transformations via intermediate melt have been discussed for HMX crystal. It is found out that two nanoscale material parameters and solid-melt barrier term in the phase-field model significantly affect the mechanism of PTs, induces nontrivial scale effects, and changes PTs behaviors at the nanoscale during virtual melting.

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Stress-measure dependence of phase transformation criterion under finite strains: Hierarchy of crystal lattice instabilities for homogeneous and heterogeneous transformations

Cited by 3 publications

References 0 publications

Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Fifth-degree elastic potential for predictive stress-strain relations and elastic instabilities under large strain and complex loading in Si

Multiphase Phase-Field Approach for Virtual Melting: A Brief Review

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