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.