A modified single-arm source model for the size-dependent strain-hardening behavior of metallic micropillars

Abstract

The recent theoretical and experimental studies indicate that a strong size effect of strain hardening exists in small-sized metallic pillars. To better predict the size-dependent strain-hardening behavior in micropillars, a new physical model is proposed. This model is based on the classical single-arm source (SAS) model but has several important developments: (1) The experimentally determined Weibull-type scale parameter and shape parameter are used; (2) The interactions between the dislocations of different slip systems, i.e. anisotropic dislocation interaction produced by the back stress, are taken into account. (3) A size-dependent kinetic equation for the dislocation density evolution is introduced. The validity and applicability of the proposed model are examined by comparison studies with the experiment data in available literatures. The predicted results show that the size effect and stochastic characteristic in the strain hardening of micropillars is mainly controlled by the average longest SAS length. Present study is expected to be helpful for theoretical modeling of strain-hardening mechanisms for micron samples, and may be beneficial to the safety design of micro-sized devices.