The dynamics of configurational forces at phase-transition fronts

Maugin, Gérard A.; Trimarco, Carmine

doi:10.1007/bf01557088

Cited by 39 publications

(17 citation statements)

References 15 publications

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“…However, a special case of that extended expression of the relative power in the conservative case emerges from the extension of Nöther's theorem, presented in de Fabritiis and Mariano (2005), to the elasticity of complex materials endowed with structured discontinuity surfaces. Different approaches can be followed to analyze the mechanics of structured discontinuity surfaces, with other assumptions and different procedures (Gurtin, 2000a;Gurtin & Struthers, 1990;Maugin & Trimarco, 1995;Simha & Bhattacharya, 2000). The reader will be able to distinguish the procedure requiring the smallest number of assumptions, a peculiarity allowing it to be a flexible tool to tackle nonstandard situations.…”

Section: Perspectives: Low-dimensional Defects Strain-gradient Matermentioning

confidence: 98%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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Section: Perspectives: Low-dimensional Defects Strain-gradient Matermentioning

confidence: 98%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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“…In practice, the uniformity of the chemical potential is substituted by the non-zero driving force, which in the case of homothermal phase transition can be represented as (Maugin, 1997;Maugin and Trimarco, 1995) …”

Section: Jump Relations At a Frontmentioning

confidence: 99%

Moving singularities in thermoelastic solids

Berezovski

Maugin

2007

Int J Fract

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The solution of the evolution problem of a discontinuity requires the formulation of a kinetic law of the progress relating the driving force and the velocity of the singularity. In the case of a crack, the energy-release rate can be computed (in quasi-statics and in the absence of thermal and intrinsic dissipations) by means of the celebrated Jintegral of fracture that is known to be path-independent and, therefore, provides a very convenient estimation of the driving force once the field solution is known. However, the velocity at the crack tip remains undetermined. A similar situation holds for a displacive phase-transition front propagation. The driving force acting on the phase boundary can be determined, but not the velocity of the displacive phasetransition front.From the thermodynamic point of view, both the phase transition and the crack propagation are non-equilibrium processes; entropy is produced at the evolving discontinuity. Therefore, stress jumps are determined by means of non-equilibrium jump relations at the discontinuity. Then the kinetic relations can be obtained depending on the choice of excess stress behavior. The procedure is illustrated on the example of a phase-transition front propagation in a shape-memory alloy bar.

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“…[12], for the full dynamical case and large deformations. We refer here to the papers [13,14], and report some important jump conditions.…”

Section: Jump Conditions Thermodynamic Force On the Interfacementioning

confidence: 99%

A micromechanical model of phase boundary movement during solid-solid phase transformations

Fischer¹,

Oberaigner²

2001

Archive of Applied Mechanics (Ingenieur Archiv)

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Understanding the kinetics of phase boundary movement is of major concern in e.g. martensitic transformation in related engineering applications. The main goal of this paper is to develop such kinetics on the basis of thermodynamic principles at the material microlevel. After a short literature survey in the introduction, the jump condition and thermodynamic force on the interface are discussed based on laws of conservation and thermodynamics. This leads to a relation for the driving force of the transformation front. In particular, the propagating front of a phase-transforming sphere within an elastic-plastic medium is considered. Due to density change, which is implicitly expressed in the transformation volume strain, strains and accompanying stresses are induced which hamper the propagation and in¯uence the transformation kinetics. Together with the latent heat, the heat due to plastic dissipation occurs as a source term in the heat conduction equation. Since kinetics are in¯uenced by temperature, the heat conduction equation and the kinetics equation are coupled. Using Green's function techniques, an integral equation is derived and solved numerically. The results of a parameter study are discussed. IntroductionWe study the propagation of a solid±solid transformation front in an elastic±plastic medium. The phase transformation is thermally induced. The front motion is controlled by the thermodynamic force F D acting on the front. This force will be discussed below. Such a consideration is typical for a martensitic transformation if the movement of the front is not controlled by a diffusional process.The assumption of no change in the composition is kept throughout this paper. To allow for a broad discussion of the in¯uencing parameters, we select a model as simple as possible. Therefore, we assume as the transforming phase a sphere with radius r R, starting from a nucleus with the radius R i . The front velocity x is _ R. Although martensite typically appears in a plate or lens form, for sake of simplicity we assume a spherically transformed region embedded in an elastic±plastic in®nite solid. This has the advantage that analytical relations for the temperature ®eld and the stress ®eld can be deduced. Indeed, spherical inclusions may be realistic, e.g. in ceramics and composites. These change their volume during a martensitic transformation with a nearly totally compensated shearing.The transformation is accompanied by a dilatational volume change 3e o . Since both the temperature at the interface and the local stress state, which occurs due to the accommodation of the dilatational volume change 3e o , contribute to the thermodynamic force F D , both ®elds must be known. It is important to note that the local stress ®eld decreases with the distance r from the origin. If one assumes a transforming layer (a plate) in an in®nite solid, the stress state would be homogeneous in space everywhere. This is, however, extremely unrealistic and would mean that the transforming of a microregion is perceptible everywhere ...

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The dynamics of configurational forces at phase-transition fronts

Cited by 39 publications

References 15 publications

Mechanics of Material Mutations

Mechanics of Material Mutations

Moving singularities in thermoelastic solids

A micromechanical model of phase boundary movement during solid-solid phase transformations

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