X-ray microbeam measurements of individual dislocation cell elastic strains in deformed single-crystal copper

Abstract

The distribution of elastic strains (and thus stresses) at the submicrometre length scale within deformed metal single crystals has remarkably broad implications for our understanding of important physical phenomena. These include the evolution of the complex dislocation structures that govern mechanical behaviour within individual grains, the transport of dislocations through such structures, changes in mechanical properties that occur during reverse loading (for example, sheet-metal forming and fatigue), and the analyses of diffraction line profiles for microstructural studies of these phenomena. We present the first direct, spatially resolved measurements of the elastic strains within individual dislocation cells in copper single crystals deformed in tension and compression along <001> axes. Broad distributions of elastic strains are found, with important implications for theories of dislocation structure evolution, dislocation transport, and the extraction of dislocation parameters from X-ray line profiles.

A statistical analysis of the elastic distortion and dislocation density fields in deformed crystals

“…The development of submicron resolution three-dimensional x-ray microscopy (3DXM) has provided the capability to perform nondestructive spatially resolved measurements of both local lattice orientations and elastic strain fields in 3D over mesoscopic length scales (Larson et al, 2002;Yang et al, 2003;Levine et al, 2006;Larson and Levine, 2013). Nondestructive measurements of the Nye dislocation density tensor were reported for a (2D) cross-sectional plane in elastically and plastically bent silicon plates, demonstrating that the 2D dislocation density tensor for an elastically bent Si plate vanishes and that the Nye tensor for a plastically deformed Si plate contains GND traces predicted for thin plate plastic deformation (Cleveringa et al, 1999).…”

Erratum: Anodes sliced with ions

“…In addition, the diff raction spots provide the local lattice spacing and lattice-spacing distribution. Th e spatial resolution is still far from what TEM provides routinely, but it is close to what can be achieved today [1][2][3][4][5]6 .…”

“…In addition, the diff raction spots provide the local lattice spacing and lattice-spacing distribution. Th e spatial resolution is still far from what TEM provides routinely, but it is close to what can be achieved today [1][2][3][4][5]6 .Th e fundamentals of plastic deformation of crystals containing a dislocation cell structure were developed more than twenty years ago and are described in the so-called composite model 7 . Th e basic idea is that the cell-wall regions of high dislocation density are harder than the cell-interior regions of low dislocation density.…”

“…Th e recent studies by several groups that made use of the diff erent high-performance synchrotron facilities [1][2][3][4][5] have demonstrated the potential of these techniques as powerful tools in the advanced microstructural analysis of deformed crystalline materials. In principle, it is now possible to analyse dislocation structures, also in deeply embedded regions 3,4 , with respect to dislocation densities, internal stresses and lattice misorientations on a submicrometre scale [1][2][3][4][5] .…”

“…In principle, it is now possible to analyse dislocation structures, also in deeply embedded regions 3,4 , with respect to dislocation densities, internal stresses and lattice misorientations on a submicrometre scale [1][2][3][4][5] . Furthermore, fi rst attempts to follow in situ the characteristics of the dislocation distributions evolving during plastic deformation have been encouraging 4 .…”