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arXiv · 1401.3571

A probabilistic explanation for the size-effect in crystal plasticity

Peter M. Derlet·Robert Maass
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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.

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Peter M. Derlet, Robert Maass. 2014-01-15. A probabilistic explanation for the size-effect in crystal plasticity. https://doi.org/10.1080/14786435.2014.932502

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