Inverse Problems in Microstructural Evolution of Polycrystalline Materials

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

The vast majority of the solid materials used in engineered systems are polycrystalline. They are composed of many single crystals joined together by a three dimensional network of internal interfaces called grain boundaries. In many cases, the performance and integrity of a material are determined by the structure of the grain-boundary network. Examples of such materials are nano-twinned copper whose strength is dominated by coherent twin boundaries; fine-scale interconnects in microelectronics whose resistivity is dominated by grain boundaries. While these material present extremely attractive properties, the fundamental mechanisms that underlie them are poorly-understood thus presenting a challenge to further development. Efforts to meet this challenge have led to new directions of research in experiment, theory, modeling and simulation. The goal of this work is to develop the mathematical tools and its software implementation and to provide a toolbox for extracting these material properties based on experimental data. The investigator and his colleagues will achieve these goals using inverse problem formulations in conjunction with recently developed experimental technique - The High Energy Diffraction Microscopy (HEDM) - to identify energy and mobility in materials ubiquitously used in applications. Grain boundary energy and mobility, which are defined on a five dimensional space, are the physical parameters that govern the evolution of grain boundaries under thermal loading where the most acceptable model is the Mullins equation. The advent of the HEDM technique opens new possibilities for probing the evolution of polycrystalline materials and will enable us the direct calculation of grain boundary velocities. This in conjunction with inverse problems governed by Mullins equation will lead us to accurate estimates of both energy and mobility. The mathematical techniques that we use in this work include Optimal Transport, Numerical solution of PDEs and Optimization Techniques for solving the inverse problems. This work deals with novel mathematical and computational approaches for meeting important challenges in materials science. In particular, understanding microstructure evolution under mechanical and thermal loading. Microstructure affects materials reliability and failure and is strongly dependent on physical parameters - the energy and mobility. We will develop techniques for accurate identification of these properties in materials of engineering applications. This is pivotal for better design and reliability of electronic, structures and combustion components. These studies will pave the road to deal with response to thermo-mechanical loading in polycrystalline materials. The applications of these results will have broader impact in essentially all the other branches of engineering where mechanical loads occur (bridges, cars, planes, MEMS devices, prostheses), as well as the study of geological materials.