Transition from deterministic to stochastic deformation

Abstract

Theory predicts that deformation that occurs by emission of strain bursts falls into two regimes, one in which the burst emission remains a stochastic process as strain increases, and another in which the emission of bursts settles into a deterministic process for large strains. The stochastic regime occurs when the burst emission rate decreases with strain, and in this case, large statistical scatter persists in the stress–strain response on repeated measurements. The deterministic regime occurs when the emission rate increases with strain, and the scatter in the corresponding stress–stress behaviour diminishes at large strains. The strength at the same strain in the stochastic regime is also higher than in the deterministic regime. Factors that affect the burst emission rate include the number of sources as well as the stress dependence of the efficiency of the sources.

Keywords:

• statistical mechanics
• strength
• Monte Carlo simulation
• plastic deformation
• compression test

Acknowledgements

The work described in this paper was supported by grants from the Research Grants Council (Project No. HKU7156/08E) and the University Grants Committee (Project No. SEG HKU-06) of the Hong Kong Special Administration Region, P.R. China. We are grateful to Wolfgang Pantleon for helpful discussions.