Homogeneous nucleation of a solid-solid dilatational phase transformation

Moran, Brian; Chu, Yi-An; Olson, Gregory B.

doi:10.1016/0020-7683(95)00136-0

Cited by 11 publications

(27 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Quantity c=R introduces a``length scale'', and is neglected in this study, since it is mostly of relevance only in the case of nucleation, see e.g [8,9]. Finally, one can formulate a relation…”

Section: Jump Conditions Thermodynamic Force On the Interfacementioning

confidence: 99%

“…The question remains, which process is responsible for the generation of a nucleus with the radius R i or, in reality, the midrib of a plate or lens. We leave this question to the studies [8,9], which investigated the nucleation problem applying a Helmholtz free-energy function, supplemented by a strain-gradient term to bridge the gap to atomistic dimensions. Since the study dealt with a spherically symmetric con®guration, the accommodation of the transformation shear is not included in their approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Fischer¹,

Oberaigner²

2001

Archive of Applied Mechanics (Ingenieur Archiv)

View full text Add to dashboard Cite

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 ...

show abstract

Section: Jump Conditions Thermodynamic Force On the Interfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Fischer¹,

Oberaigner²

2001

Archive of Applied Mechanics (Ingenieur Archiv)

View full text Add to dashboard Cite

show abstract

“…This quantity decreases as the normalized In classical nucleation theory, the interfacial energy density and the misfit strain energy are constants independent driving force increases and is denoted by 0 at equilibrium of the normalized driving force ␣. [9] induced by the presence of gradient terms in Eq.…”

Section: Introductionmentioning

confidence: 99%

“…[8] Moran et sively studied within the framework of the so-called classical al. [9] use a strain-based finite-element method together with nucleation theory (based on linear elasticity for evaluation a perturbed Lagrangian algorithm to study nucleation of a of the self-energy associated with nucleation and on the dilatational phase transformation for materials governed by assumption of a sharp interface with a constant interfacial a Landau-Ginzburg potential. Chu and Moran [10] use a disfree energy).…”

Section: Introductionmentioning

confidence: 99%

“…is proportional to the nucleus volume has been demonstrated For a dilatational transformation with spherical symmetry, in the inclusion work of Eshelby. [16] This term is also proporthe 2-3-4 Landau-Ginzburg potential is written as [9] tional to the square of the misfit strain and depends on the nucleus shape in a fairly complicated way. [16,17,18] For the…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A model for nonclassical nucleation of solid-solid structural phase transformations

Chu

Moran²,

Reid³

et al. 2000

Metall Mater Trans A

Self Cite

View full text Add to dashboard Cite

A new model for homogeneous nucleation of structural phase transformations, which can span the range of nucleation from classical to nonclassical, is presented. This model is extended from the classical nucleation theory by introducing driving-force dependencies into the interfacial free energy, the misfit strain energy, and the nucleus chemical free-energy change in order to capture the nonclassical nucleation phenomena. The driving-force dependencies are determined by matching the asymptotic solutions of the new model for the nucleus size and the nucleation energy barrier to the corresponding asymptotic solutions of the Landau-Ginzburg model for nucleation of solid-state phase transformations in the vicinity of lattice instability. Thus, no additional material parameters other than those of the classical nucleation theory and the Landau-Ginzburg model are required, and nonclassical nucleation behavior can be easily predicted based on the well-developed analytical solutions of the classical nucleation model. A comparison of the new model to the Landau-Ginzburg model for homogeneous nucleation of a dilatational transformation is presented as a benchmark example. An application to homogeneous nucleation of a cubic-to-tetragonal transformation is presented to illustrate the capability of this model. The nonclassical homogeneous nucleation behavior of the experimentally studied fcc → bcc transformation in the Fe-Co system is examined by the new model, which predicts a 20 pct reduction in the critical driving force for homogeneous nucleation.

show abstract