The role of crystal orientation and surface proximity in the self-similar behavior of deformed Cu single crystals

We report on novel 3D spatially resolved X-ray diffraction microscopy studies of self-affine behavior in deformed single crystals. This study extends surface profile measurements of self-affined morphology changes in single crystals during deformation to include local lattice rotations and sub-surface behavior. Investigations were made on the spatial correlation of the local lattice rotations in 8% tensile deformed Cu single crystals oriented with [1 2 3], [1 1 1] and [0 0 1] axes parallel to the tensile axis. The nondestructive depth-resolved measurements were made over a length scale of one to hundreds of micrometers. Self-affined correlation was found both at the surface and below the surface of the samples. A universal exponent for the power-law similar to that observed with surface profile methods is found at the surface of all samples but crystallographically sensitive changes are observed as a function of depth. Correlation lengths of the self-affine behavior vary with the [1 2 3] crystal exhibiting the longest self-affine length scale of 70 μ m with only 18 μ m for the [1 1 1] and [0 0 1] crystals. These measurements illuminate the transition from surface-like to bulk-like deformation behavior and provide new quantitative information to guide emerging models of self-organized structures in plasticity.