Kinetics of lattice phase transitions

University Of Pittsburgh, Pittsburgh PA

Investigators

Abstract

Vainchtein DMS-1007908 This project focuses on development and analysis of physically-motivated models of materials undergoing martensitic phase transition, a diffusionless deformation of a crystal lattice from the high-symmetry parent austenite phase to the low-symmetry martensite phase, which can exist in several symmetry-related twin variants. Under mechanical or thermal loading, these materials form finely layered twinning microstructures. The unique properties of martensites, such as their ability to accommodate large deformations and the marked hysteresis they exhibit under cyclic loading, are determined by the kinetics of phase and twin boundaries. Understanding how dynamics of the interfaces depends on their orientation, microstructural configuration, and properties of the crystal lattice involves challenging open problems in modeling of martensites. The project seeks to advance the understanding of these phenomena from the perspective of mesoscopic lattice models. Building on her prior work, the investigator focuses on several prototypical discrete models with the goal of capturing the essential features of interface kinetics and microstructure evolution and an emphasis on higher-dimensional phenomena and rate effects. The main ingredients of the models are nonconvex interactions between nearest neighbors allowing for the existence of two stable homogeneous states and the long-range interactions. Among the outcomes of this project are prediction of nucleated microstructural patterns and derivation of interfacial kinetic laws that can be used to solve problems involving temporal and spatial inhomogeneities. The results are compared to experimental observations and molecular dynamics simulations. By focusing on the interface kinetics, this project helps determine how the dissipative properties of martensites and related active materials depend on the material structure and the loading conditions. This is important in emerging civil, aerospace and industrial applications that require significant passive damping, such as damage and vibration control in composite structures and attenuation of earthquake- and wind-induced vibrations in buildings and bridges. Results of this project may also help design new materials with desired properties. Mathematical methods developed during the project can be used to solve similar problems encountered in dislocation theory, fracture mechanics, DNA modeling, image recognition, and numerical analysis. The broader impacts of this program are also achieved through training of graduate and undergraduate students in an interdisciplinary research program, as well as educational and high-school outreach activities.