Implications of linear relationships between local and macroscopic flow stresses in the composite model

Abstract

Abstract Earlier results obtained by X-ray diffraction studies on tensile-deformed [001]-orientated copper single crystals have recently been re-assessed with respect to the evolution of the long-range internal stresses and the local flow stresses of the dislocation cell walls and the cell interiors. It was noted that the magnitudes of the long-range internal stresses and of the local flow stresses increase in good approximation linearly with the applied macroscopic flow stress. In the present work, the results of a similar analysis of earlier published X-ray data, which were obtained on tensile-deformed [001]-orientated Cu–Mn single crystals, are reported. When the friction stress of the alloy is taken into account, similar linear relationships to the case of deformed [001]-orientated copper single crystals were obtained. The implications of these results are analyzed in the framework of the composite model of crystal plasticity. It is shown that linear relationships of the type considered imply, in terms of the composite model, that the ratio between the local dislocation densities in the dislocation cell walls and the cell interiors must remain constant during deformation. This result is discussed with respect to the experimentally obtained data on local dislocation densities.