Characterizing short-range vs. long-range spatial correlations in dislocation distributions

On the evaluation of dislocation densities in pure tantalum from EBSD orientation data

“…Further, the power-law is better defined at moderate deformation in the 25% cold rolled sample than at very large deformation in the 92% cold rolled sample. Such a tendency was also observed in ref [16], where it could be attributed to the existence of more complex spatial correlations at large strains, involving not only long-range elastic correlations between dislocations but also short-range correlations such as cross-slip. In this context, we now discuss the main features of the methods used in the present paper for the determination of dislocation density distributions in a benchmark test on tantalum samples.…”

“…At even smaller length scales, dislocation densities reflect accurately particular dislocation patterns, such as dislocation pile-ups or subgrain boundaries, but they are found in such wide ranges that no single-valued characteristic density is available. Such strongly varying dislocation density distributions, where average dislocation density values can hardly be defined, have been characterized in ice single crystals oriented for basal slip in torsion creep by their scaleinvariant character [16], meaning that dislocation density fluctuations are scaling as power-laws of their spatial frequency. Scale-invariance was assigned in the first place to the long-range spatial correlations arising from lattice incompatibility and the associated stored energy, although short-range correlations could be concurrently detected at large strains [16].…”

“…Such strongly varying dislocation density distributions, where average dislocation density values can hardly be defined, have been characterized in ice single crystals oriented for basal slip in torsion creep by their scaleinvariant character [16], meaning that dislocation density fluctuations are scaling as power-laws of their spatial frequency. Scale-invariance was assigned in the first place to the long-range spatial correlations arising from lattice incompatibility and the associated stored energy, although short-range correlations could be concurrently detected at large strains [16]. Similarly, the distributions of the dislocation density in the present polycrystalline tantalum samples were plotted in Figure 11 in relation with the various microstructures shown in Figure 3.…”

Computational Methods for Microstructure-Property Relationships

“…Hard X-ray diffraction analyses performed on slices extracted from the strained samples show that plasticity is almost exclusively due to polar dislocations of screw character gliding in basal planes, with very few mobile statistical dislocations (Montagnat et al 2003;Chevy et al 2010). The initial density of dislocations In each sample, height and diameter are equal (their common value is given in millimeter), in order to avoid any bias due to end effects.…”

“…In addition, the analyses reveal a scale invariant arrangement of polar dislocations along the torsion axis suggesting propagation of slip in this direction. The latter can be explained by the occurrence of double cross-slip of screw dislocations driven by the internal stress field through prismatic planes (Chevy et al 2010;Montagnat et al 2006).…”