Deformation-induced long-range internal stresses and lattice plane misorientations and the role of geometrically necessary dislocations

Abstract The goal of this study is to develop a unified picture of the role of geometrically necessary dislocations (GNDs) in the evolution of long-range internal stresses and lattice plane misorientations in the heterogeneous dislocation pattern of deformed crystals. For this purpose, X-ray diffraction techniques are considered as the pertinent experimental tools. On the modelling side, the composite models of single/multiple slip serve to interpret the experimentally measured long-range internal stresses quantitatively in terms of densities of GNDs. However, in order to be able to deduce from experiment the evolution of those GNDs that are responsible for the observed lattice plane misorientations, the composite model must be refined. Quite generally, the same GND array can give rise to both long-range internal stresses and lattice plane misorientations. On this basis, available experimental data obtained on cyclically and tensile-deformed copper (and copper–manganese) single crystals were analyzed quantitatively. The stresses acting locally in the "hard" dislocation cell walls and in the "soft" cell interiors and the magnitude of the internal stresses are found to increase approximately linearly with the applied stress. In spite of the fact that the density of the GNDs always amounts to only a few per cent of the total dislocation density, they are responsible for the long-range internal stresses and/or for the misorientations. An analysis of the evolution of the lattice plane misorientations shows that the kink walls and the dislocation sheets/grids in stage II are geometrically necessary boundaries (GNBs), whereas the dislocation cell walls formed by multiple slip are incidental dislocation boundaries (IDBs). Acknowledgments It is a pleasure to thank Professor Frank Nabarro for constructive criticism and for most inspiring discussions over many years. Sincere thanks go to Dr. Ellen Hieckmann for making available unpublished data. The present work rests on the valuable experience gained more than two decades ago at the Max-Planck-Institut für Metallforschung in Stuttgart under the guidance of the late Dr. Manfred Wilkens and Professor Alfred Seeger to whom I express my gratitude.