Colin Landon and Dr. Brent Adams, Mechanical Engineering
Plastic deformation of crystalline materials is accommodated by crystallographic slip, and the formation and motion of dislocations. Of particular interest to deformation predictions are the dislocation structures that form internal to grains (i.e. the cellular structures), because of their impact on the plastic behavior of the crystal. However, no generally acceptable models that link the dislocation structures and crystal plasticity exist, as is shown by the number of new theories emerging in the literature.
One of the most significant obstacles to a physical and robust theory for plasticity is the difficulty of observing dislocations and their interaction in crystals. Upon submitting this proposal we had developed a new technique for measuring and quantifying dislocation content [1]. The focus of this project was to refine our tool and apply it to an experiment in which we induced plastic deformation and monitored the dislocation behavior in a copper specimen. As we prepared the microscopy tool, it became apparent that there were significant advances that could be made, and that the resulting technology would be a much greater contribution to the materials science community than a simple study using the current tools. In response, the focus of the project became refining the new microscopy tool as described hereafter.
Electron backscatter diffraction (EBSD) analysis is the technique of measuring patterns of electrons as they refract along crystallographic planes and impact a phosphor screen. The resulting image contains bright and dark bands that correspond to the atomic planes in the material being interrogated (See Figure 1). Recently a cross-correlation based technique has been used to measure orientation and elastic strain to previously unachievable levels [2]. Unfortunately, direct experimental confirmation of the strain and rotation measurements to the resolution limits reported by the authors of the new methods is unachievable with traditional equipment and methods. Those resolution limits must be inferred from the statistics of many samplings.
On the other hand, in a computational environment all of the confounding variables of the EBSD pattern measurements can be fixed, and high fidelity electron backscatter patterns can be simulated for known lattice states. The absolute strain and rotation of a measured pattern can then be calculated by comparison to a pattern simulated for a known lattice state, rather than comparing it to an imprecisely characterized reference pattern. Because high-fidelity simulations are computationally costly, we implemented a simple method using Bragg’s Law based patterns as simulated reference patterns (See Figure 1). We then showed that by iteratively generating the simple patterns at each calculated deformation state of a measured pattern and then repeating the calculation with the new simulation, a high resolution result—approaching the levels of the standard cross-correlation based method—is rapidly found by convergence. While even the simple patterns significantly increase the analysis time of OIM they can still be reasonably computed offline and provide a practical avenue for a future OIM analysis system. Additionally the simulated pattern method provides access to high-resolution information about the microscope geometry and optical distortions.
The framework for extracting information about the lattice state from shift measurements was revaluated and refined, and a software tool for performing that analysis was written. The resulting system was presented at the International Conference on the Texture of Materials in June of 2008. Additionally, this simulated pattern method formed the basis of a patent application that is currently being processed as well as a journal article to be submitted shortly.
References
- Landon C, Adams B, Kacher J., 2008, “High resolution methods for characterizing mesoscale dislocation structures,” J. Eng. Mater. Tech., 130, pp. 40-45.
- Wilkinson, A. J., Meador, G., Dingley, D., 2006, “High-Resolution Elastic Strain Measurement from Electron Backscatter Diffraction Patterns: New Levels of Sensitivity,” Ultramicroscopy, 106, pp. 307-313.