Self-consistent experimental determination of the dislocation line tension and long-range internal stresses in deformed copper crystals by analysis of dislocation curvatures

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The present TEM study on deformed copper single crystals had several objectives. In a first step, the line tensions of near-edge and near-screw dislocations were determined directly by a statistical analysis of the radii of curvature of dislocation segments that had been pinned in the stress-applied state. Next, using the experimentally determined values of the line tensions, the locally acting shear stresses and their spatial variations were evaluated. Finally, the local values of the deformation-induced long-range internal stresses and their spatial variation were analysed in terms of the differences between the applied stress and the local stresses. The whole analysis was done in a self-consistent manner. Based on the experimentally established values of the line tensions, equilibrium shapes of dislocation loops, approximated by ellipses, were constructed. It was found that the dislocation loops are much less elliptical, i.e. rounder, than in the classical “line tension” model of de Wit and Koehler. Comparison of the results with those of later theoretical studies in the so-called “relaxation” model yielded significantly better agreement. The magnitudes of the long-range internal stresses were generally found to be of the order of the applied stress with stress enhancement in the dense dislocation walls and back stresses in the areas with lower dislocation densities in between. These results are in line with the predictions of the composite model.