Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-orientated copper single crystals

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Abstract
Copper single crystals oriented for multiple slip with [001] axes have been deformed in tension and investigated by X-ray line-broadening measurements using {002} Bragg reflections. The intensity distributions of the broadened line profiles of the deformed crystals exhibit an asymmetry whose ‘sign’ depends on the particular reflection used. It is shown that the asymmetric line profiles are due to the superposition of two mutually displaced symmetrically broadened line profiles. These two sub-profiles can be ascribed to the material located in the cell walls and in the cell interiors of the dislocation cell structure, respectively. The mutual displacements of the sub-profiles are evaluated quantitatively in terms of deformation-induced long-range internal stresses, which aid the applied stress in the cell walls and oppose it in the cell interiors. It is shown by a simple model that the long-range internal stresses are a necessary consequence of the plastic strain mismatch between the soft cell interiors and the hard cell walls. Finally, it is shown that, with appropriate consideration of the long-range internal stresses, the macroscopic flow stress must be defined as a weighted average of the local flow stresses of the cell interiors and of the walls.