A probabilistic explanation for the size-effect in crystal plasticity

Abstract

In this work, the well known power-law relation between strength and sample size, $d^{-n}$, is derived from the knowledge that a dislocation network exhibits scale-free behaviour and the extreme value statistical properties of an arbitrary distribution of critical stresses. This approach yields $n=(\tau +1)/(\alpha +1)$, where $\alpha$ reflects the leading order algebraic exponent of the low stress regime of the critical stress distribution and $\tau$ is the scaling exponent for intermittent plastic strain activity. This quite general derivation supports the experimental observation that the size effect paradigm is applicable to a wide range of materials, differing in crystal structure, internal microstructure and external sample geometry.

22 pages, 4 figures, to be published in Phil. Mag

References in corpus (3)

• Strain bursts in plastically deforming Molybdenum micro- and nanopillars
• Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution
• Slip avalanches in crystal plasticity: scaling of the avalanche cutoff

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• The stress statistics of the first pop-in or intermittent plastic event in cyrstal plasticity
• The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity
• Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations
• Plastic strain is a mixture of avalanches and quasi-reversible deformations: Study of various sizes
• Dynamic Length Scale and Weakest Link Behavior in Crystal Plasticity
• Critical stress statistics and a fold catastrophe in intermittent crystal plasticity
• Micro-plasticity and recent insights from intermittent and small-scale plasticity
• Avalanche Dynamics and the Effect of Straining in Dislocation Systems with Quenched Disorder