Fig. 3: The stages of an Eshelby inclusion avalanche.
From: Time limited self-organised criticality in the high rate deformation of face centred cubic metals
After a number of small slip events, an arbitrary forest of individually pinned dislocations form a population of volumetric Eshelby inclusions (a) bound by a surface of dislocations. The volumetric slip of the inclusion is capable of imparting much greater strain and activating at much lower applied stress than an individual dislocation, as all dislocations involved contribute to overcoming the obstacle; the red sphere in (a). In order to slip collectively, the dislocations binding the inclusion must synchronise their motion against the obstacle, requiring the propagation of information between the organising dislocations (a). The scaling of the surface and the transverse oscillation period of the binding dislocations will cause the synchronisation time to scale in approximate proportion to the inclusion volume. Avalanches that manage to synchronise collectively slip as shown in (b), both expanding and tilting the inclusion, imparting a large volumetric strain into the lattice that scales with inclusion size. The side profiles of the inclusion are shown (not to scale) before slip in (c) and after in (d). The volumetric shear, combined with the mobility of screw dislocations in the interface, enables the avalanche axes to depart from the crystal plane. The projection of applied stresses on to secondary systems eventually activates them, anchoring the band1.
