On the critical nature of plastic flow: one and two dimensional models

Abstract

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with an overdamped one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws.

72 pages, 40 Figures, International Journal of Engineering Science for the special issue in honor of Victor Berdichevsky, 2012

References in corpus (13)

• Power-law distributions in empirical data
• Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
• Strain bursts in plastically deforming Molybdenum micro- and nanopillars
• Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
• Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution
• Driving-induced crossover: from classical criticality to self-organized criticality
• $1/f$ noise and avalanche scaling in plastic deformation
• Training-induced criticality in martensites
• Avalanche Spatial Structure and Multivariable Scaling Functions; Sizes, Heights, Widths, and Views through Windows
• Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum plasticity theory
• Discrete models of dislocations and their motion in cubic crystals
• Atomic-scale avalanche along a dislocation in a random alloy
• Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model

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• Atomistic mechanisms of intermittent plasticity in metals: Dislocation avalanches and defect cluster pinning
• Origin of scale-free intermittency in structural first-order phase transitions
• Variety of scaling behaviors in nanocrystalline plasticity
• Fluctuations in crystalline plasticity
• Inelastic rotations and pseudo-turbulent plastic avalanches in crystals
• Homogeneous nucleation of dislocations as a pattern formation phenomenon
• Normality condition in elasticity
• Dislocation avalanches from strain-controlled loading: A discrete dislocation dynamics study
• Modelling avalanches in martensites
• Avalanches and rate effects in strain-controlled discrete dislocation plasticity of Al single crystals
• Exact results for a toy model exhibiting dynamic criticality
• Reconstructive martensitic phase transitions: intermittency, anti-trasformation, plasticity, irreversibility
• Quantized plastic deformation
• Slip-dominated structural transitions
• Depinning as a coagulation process
• On dissipation in crackling noise systems
• Navigating with Stability: Local Minima, Patterns, and Evolution in a Gradient Damage Fracture Model