Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale

Abstract

Under stress, many crystalline materials exhibit irreversible plastic deformation caused by the motion of lattice dislocations. In plastically deformed microcrystals, internal dislocation avalanches lead to jumps in the stress-strain curves (strain bursts), whereas in macroscopic samples plasticity appears as a smooth process. By combining three-dimensional simulations of the dynamics of interacting dislocations with statistical analysis of the corresponding deformation behavior, we determined the distribution of strain changes during dislocation avalanches and established its dependence on microcrystal size. Our results suggest that for sample dimensions on the micrometer and submicrometer scale, large strain fluctuations may make it difficult to control the resulting shape in a plastic-forming process.

Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution

“…The size distribution of the dislocation avalanches decreases by a universal power-law with exponent 1.5. The distribution was recovered by experiments [6,7], by two-(2D) and three-dimensional (3D) discrete dislocation dynamics (DDD) simulations [2,8], and by analytical modeling [9,10]. These findings indicate that intermittent dislocation avalanches are an intrinsic feature of the plasticity of crystals, and their size distribution is not affected by the details of the deformation.…”

“…Firstly, the increased relative size of the fluctuations makes difficult to control the plastic forming process [8]. Secondly, at small specimen sizes the yield stress is not well-defined any more.…”

“…Although irregular plastic response of submicron crystalline materials is by now conceived as a self-organized critical phenomenon [5,8,16,19], a physical understanding, that is, a phenomenology for plastic flow based on statistical properties of strain avalanches is still lacking. In this paper we present a statistical analysis of the fluctuating stress-strain response of individual specimens, and of the velocity distribution P (v) of short dislocation segments.…”

In situ nanoindentation study on plasticity and work hardening in aluminium with incoherent twin boundaries

“…Interestingly, MD simulations 14,31,32 also predicted serrated stress-strain curve in nt Al, drastically different from that in low SFE nt Cu or Ag. Discrete dislocation dynamics simulations predicted that dislocation avalanches are a universal phenomenon during deformation of single-crystal Al, and grain boundaries in polycrystalline Al would reduce avalanche frequency 33 . Micropillar compression tests on Al yield controversial results 34,35 presumably related to the orientation of grain boundaries.…”

Microscopic aspects of magnetic lattice demagnetizing factors

“…The demagnetizing problem in magnetic systems is a natural setting for exploring this question since it is accessible and of intrinsic importance in experiments, and constitutes a paragon for exploring the thermodynamics of long-range interacting systems [1]. Demagnetizing effects are also important in superconductors, while analogs occur, for example, in electric systems [8] (depolarizing factor), in the problem of strain fields around inclusions [9], and in the treatment of avalanching systems in confined geometries [10][11][12].…”