Fractal Dislocation Patterning in Plastically Deformed NaCl Polycrystals

Abstract

Introduction In severely deformed metals, strain hardening goes along with the formation of cellular dislocation patterns. When many slip systems are active, these patterns exhibit multiscale behaviour: they are characterized by power-law distributions of cell sizes [1] and the cell arrangement has features of a self-similar 'hole fractal'. Fractal cell patterning has been observed in fcc metals deformed in tension or compression along the [100] and [111] axes [1, 2] as well as in fcc polycrystals [3,4]. For a general discussion of different types of dislocation patterns see [5].In the present research note we report results of a fractal dimension analysis performed on dislocation cell patterns developing during severe deformation of polycrystalline NaCl. (For sample preparation and work-hardening behavior see [6].) The samples were deformed in compression at room temperature at a strain rate of 10 À5 s À1 . Cellular patterns were observed inside the grains after deformation to a flow stress of 35.2 MPa (Fig. 1). The statistical characterization of these patterns is the subject of the present note.

Role of discrete intragranular slip on lattice rotations in polycrystalline Ni: Experimental and micromechanical studies

“…The atomic force microscope allows determination of the spatial positions and the heights of steps on the sample surface which can be analyzed as post-treatments using different techniques (see e.g. Zaiser [21], using gap width distribution, box counting and correlation integral, or Konstandinidis and Aifantis [41], using the wavelet method). In this work, a Veeco Dimension 3000 atomic force microscope is used.…”

“…From experimental studies of deformed single crystals and polycrystals, plastic strain within grains is known to be strongly heterogeneous and intermittent [21]. As a consequence of the collective motion of dislocations, slip lines and slip bands appear as glide traces on the surface reliefs of the sample [18].…”

“…Consequently, local incompatibilities (and local lattice orientation), such as those introduced by Nye [17] and Krö ner [14], can be perturbed by the discrete nature of intragranular slip. Experimental observations of deformed polycrystalline samples in fact show that the plastic process is strongly heterogeneous inside grains, which corresponds to discrete space-time mechanisms (creation and movement of dislocations) observable on surfaces as slip lines/bands [18][19][20][21][22][23][24] and in the bulk by transmission electron microscopy [25]. Physically, some intragranular dislocations forming slip bands pile-up on grain boundaries and grains may be split into sub-grains bounded by dislocation networks (dislocation cells and dislocation walls [26,27]).…”

“…The main advantage of this method is that it gives us a record of the dislocation movement during deformation [21]. The atomic force microscope allows determination of the spatial positions and the heights of steps on the sample surface which can be analyzed as post-treatments using different techniques (see e.g.…”

Relaxation of creep strain in paper

“…Examples for such generality can be found from the crackling noise or intermittent response by which many systems -magnets (Barkhausen noise), dislocation assemblies (strain avalanches), foams, granular systems, fracture and creep deformation etc. -react to external forces or influences [1,2,3,4,5,6]. Likewise, universal behavior is found in "aging" and "rejuvenation", two concepts first introduced in the theory of spin glasses where at the simplest these can be taken to imply that the correlation or response properties of the system are found to be dependent on the observation or waiting time scale [7].…”