Where are the geometrically necessary dislocations accommodating small imprints?
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Electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) analyses of small indentations in copper single crystals exhibit only slight changes of the crystal orientation in the surroundings of the imprints. Far-reaching dislocations might be the reason for these small misorientation changes. Using EBSD and TEM technique, this work makes an attempt to visualize the far-propagating dislocations by introducing a twin boundary in the vicinity of small indentations. Because dislocations piled up at the twin boundary produce a misorientation gradient, the otherwise far-propagating dislocations can be detected. I. INTRODUCTION
During indentation, the indenter causes a permanent plastic imprint on the originally flat material surface. Consequently, the material originally occupying the region of the plastic indent has to be pushed into the underneath substrate.1 The required material transport is thereby typically performed by defects, e.g., dislocations that are geometrically necessary.2 It was found that the density of these so-called geometrically necessary dislocations (GNDs) is proportional to the gradient of plastic strain.3,4 The concept of GNDs was used by many authors to explain the depth dependence of hardness.5–9 One of the most prominent approaches is those proposed by Nix and Gao.9 In their mechanism-based model Nix and Gao assumed that GNDs, which accommodate the plastic strain caused by the indenter, are contained in an approximately hemispherical volume below the imprint. The density of GNDs distributed in the hemisphere is thereby found to be proportional to the reciprocal indentation depth. As a consequence, at small indentation depths the GND density as well as the occurring strain gradient become very large. However, in reality such high strain gradients were not observed in the surroundings of small indentations. As electron backscatter diffraction (EBSD)10–12 and transmission electron microscopy (TEM)13–16 experiments show, the plastically deformed zone consists of far-reaching dislocation loops, which induce only slight misorientation changes. For a 1 mN indentation for example, the maximum misorientation change is in the order of 2 .10 Similar results were found by Minor et al.17 in in situ TEM nanoindentation experiments, where the generated dislocations are spread over a large volume in the bulk. a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0131 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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An appropriate dislocation model, which explains the indentation size effect of indentations with depths smaller than 500 nm and accounts for these experimental findings, was proposed by Rester et al.10 in a former work. To facilitate the following discussion, the dislocation model is presented briefly in Sec. II. However, up to now no experimental evidence for the proposed model is delivered. The present work makes an attempt to demonstrate the plausibility of this
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