Depinning transition of dislocation assemblies: Pileups and low-angle grain boundaries

Abstract

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low-angle grain boundaries interacting with a disordered stress landscape provided by solute atoms, or by other immobile dislocations present in nonactive slip systems. Using linear elasticity, we compute the stress originated by small deformations of these assemblies and the corresponding energy cost in two and three dimensions. Contrary to the case of isolated dislocation lines, which are usually approximated as elastic strings with an effective line tension, the deformations of a dislocation assembly cannot be described by local elastic interactions with a constant tension or stiffness. A nonlocal elastic kernel results as a consequence of long-range interactions between dislocations. In light of this result, we revise statistical depinning theories of dislocation assemblies and compare the theoretical results with numerical simulations and experimental data.

Grain boundaries in vortex matter

“…In this limit, the same result predicted by the isotropic theory 39 is thus obtained. The nonlocal character of the elastic kernel ͑ϰk͒ manifests that long-range interactions between dislocations stiffen the grain boundary, and that a surface tension approximation is not suitable for a correct description of its elastic properties.…”

“…Its contribution to the elastic Hamiltonian is known since it is the same as for straight dislocations in isotropic lattices. 39 In the following this contribution will be referred to as H 0 .…”

“…While ideally a grain boundary minimizes its energy by remaining flat, the action of external perturbations leads to deformations that can be described by the theory of elasticity. 39 We compute the self-interaction of a deformed grain boundary extending the results obtained for isotropic elasticity 39 to the case of the vortex lattice. Grain boundaries are much stiffer than isolated dislocations, possessing a nonlocal long-range surface tension and, in presence of disorder, they are expected to be less rough than isolated dislocations.…”

Universal fluctuations and extreme statistics of avalanches near the depinning transition

“…Crystal plasticity as a critical phenomenon has also been confirmed by other experimental techniques such as highresolution extensometry [17] and compression of nanopillars and micro-pillars [19,20], as well as by numerical simulations of discrete dislocation dynamics [7,[21][22][23]. Moreover, the statistics of slip avalanches-i.e.…”

Avalanche statistics from data with low time resolution

“…Avalanches are observed in a variety of dynamical systems, including magnetic materials [1,2], charge density waves [3,4], vortices in superconductors [5], earthquakes [6,7], crystal plasticity [7][8][9][10][11], and amorphous plasticity [7,8,[12][13][14][15][16][17]. For these last two cases, deformation occurs through small jumps caused by slipping weak spots in the material.…”