Length-scale effect due to periodic variation of geometrically necessary dislocation densities

Strain gradient plasticity theories have been successful in predicting qualitative aspects of the length scale effect, most notably the increase in yield strength and hardness as the size of the deforming volume decreases. However new experimental methodologies enabled by recent developments of high spatial resolution diffraction methods in a scanning electron microscope give a much more quantitative understanding of plastic deformation at small length scales. Specifically, geometrically necessary dislocation densities (GND) can now be measured and provide detailed information about the microstructure of deformed metals in addition to the size effect. Recent GND measurements have revealed a distribution of length scales that evolves within a metal undergoing plastic deformation. Furthermore, these experiments have shown an accumulation of GND densities in cell walls as well as a variation of the saturation value of dislocation densities in these cell walls and dislocation structures. In this study, a strain gradient plasticity framework is extended by incorporating the physical quantities obtained from experimental observations: the quasi-periodicity and the saturation value of GND densities. The proposed model is tested with constrained shear and pure bending problems. The results show a change in overall mechanical response depending on the prescribed initial spatial variation of the saturation values. (C) 2012 Elsevier Ltd. All rights reserved.