The objective of this work is to develop and demonstrate the fundamentals of a predictive, next-generation, computational tool for microstructure-sensitive design of metallic components of modern machines that are subjected to mechanical stress and deformation. The generally irreversible deformation of metallic materials at the macroscopic scale called plastic deformation arises due to the motion of vast numbers of defects in their underlying regular crystalline structure under applied loading. Such defect motions lead to special spatial patterns of organization of multiple defects called microstructure, and it is known that this defect microstructure has significant effect on the material's macroscopic properties like strength and ductility. The individual defect motions occur at much smaller length scales and much faster time scales than those of macroscopically observed plastic deformation, thus requiring a mathematical process of averaging to define the macroscopic model of collective behavior of defects from the microscopic dynamics. This award supports the development and validation of such a macroscopic model from microscopic fundamentals through multiscale mathematical and computational modeling. The project addresses a key scientific question with significant impact on society. A great deal of modern manufacturing, design of light-weight, high-strength structural materials and materials for gas turbines for energy and aerospace applications all depend upon understanding of microstructure evolution and its effect on material properties. Widely used industrial design codes do not at present make use of microstructure sensitive material models. This research will develop a truly material microstructure-sensitive model for plastic strength and dislocation microstructure evolution that has the potential to revolutionize the way metallic materials are designed in many industries, bringing about significant cost and energy savings for the US economy. The research tightly integrates the fields of Applied Mathematics, Mechanics of Materials, and Materials Science, and this will lead to fruitful interdisciplinary interplay of ideas between these fields, all directed to very practical outcomes, including the training of students which will enhance the US workforce in science and technology. Efforts will be made to archive developed computer codes at the NSF supported Pittsburgh Supercomputing Center to enable systematic, free, widespread access to interested practitioners.
The challenge of this work is to develop a novel computational tool for accurate multi-scale simulations of plasticity and dislocation microstructure evolution in crystalline materials. The tasks addressed will be the computation of plastic strength and associated microstructure of a material at the meso and macroscale directly from the underlying motion of crystal defects. This application is a paradigmatic complex system, with immense practical relevance. Specifically, an exact, but non-closed, partial differential equation based theory representing the evolution of space-time averaged dislocation dynamics will be utilized, that contains well-defined place-holders for microscopic dislocation dynamics based input. These inputs, typically prescribed as phenomenological constitutive assumptions, will be replaced in this work by a carefully designed coupling, on the "slow" time-scale of meso-macro response, with time-averaged response of "fast", local (on the macroscopic scale) Discrete Dislocation Dynamics simulations. The overall strategy is based on novel and sound continuum mechanical principles like a conservation statement for topological charge carried by crystal defects coupled to macroscopic elasticity as well as modern mathematical tools like Young Measure theory for averaging multi-time scale response of nonlinear Ordinary Differential Equations. Interestingly, this approach for solving a patently practical problem involves finite dimensional dynamical system input into an overarching infinite dimensional dynamical system.
