Stochastic theory for jerky deformation in small crystal volumes with pre-existing dislocations

Abstract

A statistical theory is proposed to describe the jerky deformation of micron-sized crystal pillars. The probability for a specimen surviving the applied load without generating a strain burst of a given order is analytically expressed in terms of the nucleation rate of that burst. The survival probability can be measured from an ensemble of macroscopically similar deformation experiments to obtain the nucleation rate. From experiments on aluminium pillars, the nucleation rate is found to increase with the pillar size and to decrease with the burst order, indicating that more sources are present in a larger specimen and that the available nucleating sources are progressively exhausted by the occurrence of bursts. The activation volume measured is roughly independent of the pillar size and burst order, indicating a constant mechanism for burst nucleation.

Keywords:

• aluminium
• deformation
• nanoindentation
• statistical mechanics
• dislocations

Acknowledgments

This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region, China (Project no. HKU7162/06E).