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

Abstract

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 ...

Relaxation of a precipitate misfit stress state by creep in the matrix

“…However, the mechanical dissipation due to relaxation of the stress field around the precipitate is still an open issue and needs some further research. For an elastic-plastic matrix surrounding a spherical precipitate solutions are already available, see, e.g., the contributions by Fischer and Oberaigner (2001) or the recent paper by Song et al (2014) for precipitates. In this context, also the solutions for voids, see Fischer and Antretter (2009) and Levitas and Altukhova (2011), and for bubbles or melted zones are mentioned, see, e.g., Levitas and Altukhova (2012a) and Levitas (2012b).…”