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Jeffrey Kysar's blog

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Measurements of Geometrically Necessary Dislocation Densities on Individual Slip Systems

We have recently published a paper on measurements of the density of geometrically necessary dislocations (GND) associated with wedge indentation of a single face-centered cubic crystal. The deformation field is two-dimensional and there are three effective in-plane slip systems that contribute to the plastic slip. We determine the lower bound on the total GND density with a three micrometer spatial resolution. We also show that in certain regions of the domain, the lower bound on total GND density corresponds to the exact total GND density.

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Analytical solutions for plastic deformation around voids in anisotropic single crystals

It is well established that the growth of microscopic voids near a crack tip plays a fundamental role in establishing the fracture behavior of ductile metals. Mechanics analyses of plastic void growth have typically assumed the plastic properties of the surrounding metal to be isotropic. However voids are typically of the order of magnitude of one micron so that they exist within individual grains of the metal, or along grain boundaries, at least at the initial growth stage. For that reason, the plastic properties of the material surrounding the void are most properly treated as being anisotropic, rather than isotropic.

In the uploaded preprint, the stress state and deformation state are derived around a cylindrical void in a hexagonal close packed single crystal. The orientation of the cylindrical void and the loading state relative to the crystal are chosen so that the deformation state is one of plane strain. The active slip systems reduce to a total of three slip systems which act within the plane of plane strain. The solution shows that the deformation state consists of angular sectors around the void within which only one slip system is active. Further, it is shown that the stress state and deformation state exhibit self-similarity both radially and circumferentially, as well as periodicity along certain logarithmic spirals which emanate from the void surface.

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