Abstract
Understanding the strength of metals has been a scientific challenge for many decades. In recent years, much progress has been made toward understanding the plastic strength of metals, thanks to the method of discrete dislocation dynamics (DDD) simulations. This method simulates the evolution of dislocation ensembles in crystals thus revealing how the dislocation mechanisms collectively translate to the observed plastic behavior. The method also has the potential of accounting for alloy strengthening mechanisms caused by solute and particles. However, the DDD method is limited to probing the deformation behavior of metals in the small strain range of only few percent. Practical levels of crystal deformation encountered in experiments require the development of dislocation-based models of plasticity that capture the deformation behavior to higher strain levels. The method of continuum dislocation dynamics (CDD) is believed to meet this objective. This method casts the dislocations dynamics problem in the form of transport-reaction equations for crystal dislocations after expressing them in terms of density fields. Coupled with crystal mechanics, these transport equations provide the plastic closure required solve the crystal deformation problem self-consistently. At present time, however, the method faces theoretical challenges having to do with properly coarse graining the dislocation system, and incorporating dislocation reactions, mobility, and short-range interactions in a density-based framework. Key to resolving these issues is the proper modelling of the spatial, line-direction, and temporal statistics of large dislocation systems and their elastic fields. In this presentation, we will review the recent progress related to continuum modelling of dislocation dynamics, with emphasis on its statistical underpinning: internal stress fluctuations, dislocation correlations, line-direction statistics. We will also highlight the novel adoption of graph theory and data science methods in bringing continuum models of dislocation dynamics to fruition. Computational results associated with these developments will be presented.
About the Speaker
Dr. El-Azab is a professor of Materials Science and Engineering at Purdue University. He obtained his doctoral degree in Engineering at the University of California, Los Angeles. Prior to coming to Purdue, he joined Pacific Northwest National Laboratory as a research scientist, and was a professor of Mechanical Engineering, Materials Science and Engineering and Computational Science at Florida State University. His current research focuses on the mechanics and physics of defects in materials and the influence of defects on materials properties. His latest research covers statistical modeling of dislocations and continuum dislocation dynamics, microstructure evolution in materials including thin films, radiation effects in nuclear materials, and thermal transport in defective solids. Part of his research is dedicated to the development of theoretical formalisms and computational and data science methods for multiscale and multi-physics modeling of materials, as well as the development of algorithms for bridging modeling and experiments in materials research.
Host: Professor Nikhil Admal