Insights into the Role of Mechanics on Diffusion-Controlled Phase Transformations using Phase Field Models
Benoît Appolaire (1,2), Yann Le Bouar (2), Alphonse Finel (2), Maeva Cottura (3), Samuel Forest (4), Kais Ammar (4), Elisabeth Aeby-Gautier (1)
(1) Institut Jean Lamour, Université de Lorraine/Cnrs
(2) Laboratoire d'Étude des Microstructures, Cnrs/Onera
(3) University of Berkeley
(4) Centre des Matériaux, Mines ParisTech/Cnrs
The role played by the microstructures ensuing from phase transformations on the mechanical properties is now very well documented and thoroughly studied, in particular in metallic alloys. Although there is also a large number of works devoted to the reverse, i.e. the influence of mechanics on the microstructure formation and evolution, a general picture is still lacking, in particular when the phase transformations are diffusion-controlled. Indeed, drawing such a general picture requires to address at the same time the issues related to both mechanical behavior and phase transformations, as well as to address new issues arising from the tight coupling between evolving interfaces and evolving strain/stress fields.
Besides the well-known modification of two-phase thermodynamic equilibrium by elasticity, as explored by Larché and Cahn (e.g. [10]) and Voorhees and Johnson (e.g. [9]), the trends are less obvious concerning the morphological evolutions when the chemical and mechanical driving forces are competing to reduce the overall free energy of the materials.
In this contribution, an attempt will be made to draw some trends by examining several situations in different types of alloys where the different contributions that mechanics encompasses are decoupled. For that purpose, we will resort to extensive calculations with phase field models that have been specifically developed [1,7].
First we will discuss the role of elasticity on the shape selection of precipitates, beyond the classical results of hard precipitates in a soft matrix against soft precipitates in a hard matrix, that are relevant only for isotropic elasticity.
Indeed, we will show how the anisotropy of the elastic energy arising from either the moduli or the eigenstrain is crucial for the shape selection, even for diffusion-controlled transformation at high temperatures where it is usually believed that elasticity is totally relaxed by plasticity. The examples supporting our analysis will concern cuboidal ordered precipitates in Ni-base superalloys [6] and acicular structures in alloys exhibiting allotropic transformation such as Ti alloys, steels or brass [3].
In a second part, we will show that in many cases, plasticity does not relax totally the elastic strain associat ed with the phase transformations [4]. As a direct consequence, plasticity may not change qualitatively the shape evolutions driven by elasticity, as it will be illustrated on the rafting of the ordered precipitates in Ni -base superalloys [5] and on the acicular structures [4], although it can change the kinetics of the processes. However, we will show that in some cases, plasticity may induce shape bifurcations [5,8] that are difficult to infer with simplified qualitative arguments, as usually done in the literature on diffusion-controlled phase transformations.
We will conclude with a few open questions that we have been able to identify thanks to our phase field calculations, such as the inheritance of plastic strain by the growing phases [2].
Prof. Benoît Appolaire
Institut Jean Lamour
2 allée André Guinier
Campus Artem
54000 Nancy
France
Prof. B. Appolaire | |
Http | Université de Lorraine |
Institut Jean Lamour | |
Laboratoire d'Étude des Microstructures |