Probability Density Function of Dislocation Free Path Length: Experimental Determination through GND Measurements

Columbia University, New York NY

Investigators

Abstract

TECHNICAL SUMMARY: The dislocation mean free path length is a unifying concept in understanding plastic deformation across all pertinent length scales. Plasticity formulations that account directly for the motion of dislocations are stochastic processes because of the non-deterministic behavior of dislocations combined with the otherwise deterministic equations of solid mechanics. The mean free path length (MFPL) succeeds only partially in quantifying the dislocation free path length. It is also necessary to quantify the probability density function (PDF) of the dislocation free path length. The overall research objective of this proposal is to measure experimentally the MFPL and the PDF of dislocation free path length and relate them experimentally to the deformation quantity of plastic shear strain in individual crystallographic slip systems. The concept of making such measurements has existed for several decades, but the capabilities to perform such experiments have not existed until now. This program will develop and use the methods and procedures to make these experimental measurements. In that context, the overall educational objective of this proposal is to promulgate not only the results from the research objective, but also the underlying mechanics concepts as well as experimental methods and procedures necessary to perform research of this type to the larger research community. NON-TECHNICAL SUMMARY: The safety and reliability of the nation's infrastructure and transportation systems depend upon the ability of scientists and engineers to predict the behavior of materials, especially metals, used to build that infrastructure. Metals experience mechanical failure due to the presence of defects called dislocations that cause permanent deformation as they move throughout the interior of the metal. The goal of this project is to measure the average distance and the variation in distances that dislocations travel as metals are deformed permanently and to relate these quantities to the amount of deformation that occurred. These quantities are very important for the development and validation of theories that predict the failure of metals. New fundamental understanding of the motion of defects in metals has the potential to lead to better theories that predict the behavior of materials in the nation's infrastructure with greater fidelity. The main educational goal of this project is to introduce the novel concepts and methods necessary to make the measurements to engineers and scientists through technical articles as well as teaching seminars at scientific conferences. A Ph.D. student will be supported in this project, thus enhancing the nation's human resources.