Modeling of reconstructive phase transformations through Atomistically informed Landau theory with Infinite Symmetry – ALIS
A general continuum modeling framework to describe the kinetics of reconstructive martensitic phase transformation (MT) coupled with crystal plasticity (CP) at the scale of dislocations is still lacking. In this project, we propose to use the geometrically nonlinear elasticity theory as a single unified framework to model reconstructive MT and CP together. The theory is capable of distinguishing the behavior of different crystal symmetries and dealing with nucleation, and propagation of martensitic variants and their interaction with dislocations without ad-hoc assumptions.
Nonlinear elasticity theory can be used to model crystal plasticity and martensitic phase transformations if the global invariance of the elastic energy in the space of finite strain tensors is taken into account. In this approach, continuum elasticity takes the form of Landau theory with an infinite number of equivalent energy wells whose configuration is controlled by the symmetry group GL(n, Z). To regularize such a highly degenerate model we use lattice-based discretization which brings a finite cut off length representing a Ginzburg- like characteristic superatomic scale. The model is mesoscopic in nature, in that it is formulated in terms of mesoscopic quantities such as stresses and strains, and at the same time fully incorporates the underlying symmetry of the crystal lattice. Our model shows that crystal plasticity together with phase transitions naturally arises from nonlinear elasticity if the symmetry of the crystal lattice is properly accounted for. It correctly describes plastic slip and displacive martensitic transformations at the atomic scale and long-range interactions between dislocations and different phases; the dislocations cores and phase boundaries are regularized and blurred on the scale of the unit cell. In order to perform quantitative simulations, we will calculate the strain energy by making use of the Cauchy-Born hypothesis, which is capable of bridging information from the atomistic scale to macro-scale and it consists of coupling of the continuum with molecular theories. More precisely, we will deform a homogeneous lattice formed by atoms interacting via an atomistic potential in order to obtain the homogenous strain energy density in the undeformed configuration as a sum of the interactions of the atoms for a given macroscopic deformation gradient.
We will apply the model to study the microstructural evolution during reconstructive martensitic transformations observed in materials such as titanium, zirconium and their alloys. They are of substantial interest for several applications in the nuclear, aeronautic and bio-medical fields.
Monsieur Umut Salman (Laboratoire des Sciences des Procédés et des Matériaux)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
LSPM Laboratoire des Sciences des Procédés et des Matériaux
Help of the ANR 160,855 euros
Beginning and duration of the scientific project: March 2020 - 42 Months