Quasistatic propagation of steps along a phase boundary

Sharma, Basant Lal; Vainchtein, Anna

doi:10.1007/s00161-007-0059-4

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…In fact, calculations of Sharma and Vainchtein (2007) for a quasistatic stepped phase boundary show that a sequential one-by-one propagation of steps involves significantly smaller energy barriers than simultaneous motion. Numerical simulations presented in the second part of this paper (Zhen and Vainchtein, 2007), henceforth referred to as Part II, show that the sequential propagation of steps is also preferred in dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution

Zhen

Vainchtein

2008

Journal of the Mechanics and Physics of Solids

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We study the motion of steps along a martensitic phase boundary in a cubic lattice. To enable analytical calculations, we assume antiplane shear deformation and consider a phase transforming material with a stress-strain law that is piecewise linear with respect to one component of shear strain and linear with respect to another. Under these assumptions we derive a semi-analytical solution describing a steady sequential motion of the steps under an external loading. Our analysis yields kinetic relations between the driving force, the velocity of the steps and other characteristic parameters of the motion. These are studied in detail for the two-step and three-step configurations. We show that the kinetic relations are significantly affected by the material anisotropy. Our results indicate the existence of multiple solutions exhibiting sequential step motion.

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Section: Introductionmentioning

confidence: 99%

Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution

Zhen

Vainchtein

2008

Journal of the Mechanics and Physics of Solids

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“…The two wells represent two different twin variants and are separated by a spinodal region where the potential is non-convex. This is an extension of the model with bilinear interactions that was used in [8, 9] to study high-velocity dynamics of steps along a phase boundary and in [10], where their quasistatic evolution was considered. Piecewise linear interactions were assumed by many authors to describe propagation of phase boundaries, fracture and dislocations in a crystal lattice (see [11–24] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Kinetics of a twinning step

Liu

Vainchtein

Wang

2013

Mathematics and Mechanics of Solids

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We study the kinetics of a step propagating along a twin boundary in a cubic lattice undergoing an antiplane shear deformation. To model twinning, we consider a piecewise quadratic double-well interaction potential with respect to one component of the shear strain and harmonic interaction with respect to another. We construct semi-analytical traveling wave solutions that correspond to a steady step propagation and obtain the kinetic relation between the applied stress and the velocity of the step. We show that this relation strongly depends on the width of the spinodal region where the double-well potential is non-convex and on the material anisotropy parameter. In the limiting case when the spinodal region degenerates to a point, we construct new solutions that extend the kinetic relation obtained in the earlier work of Celli, Flytzanis and Ishioka into the low-velocity regime. Numerical simulations suggest stability of some of the obtained solutions, including low-velocity step motion when the spinodal region is sufficiently wide. When the applied stress is above a certain threshold, nucleation and steady propagation of multiple steps are observed.

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A Brief Review on Discrete Modelling of Martensitic Phase Transformations

Uchimali,

Sittner

2023

Shap. Mem. Superelasticity

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Quasistatic propagation of steps along a phase boundary

Cited by 6 publications

References 14 publications

Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution

Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution

Kinetics of a twinning step

A Brief Review on Discrete Modelling of Martensitic Phase Transformations

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