Dislocation-density based size-dependent crystal plasticity framework accounting for climb of piled up dislocations at elevated temperature

Abstract

In this paper, a climb-enabled scale-dependent crystal plasticity (CP) framework with geometrically necessary dislocation (GND) and statistically stored dislocation (SSD) effects was proposed. A simple dislocation pile-up model, which can capture the long-range back stress due to the micro-structural constraint effect (i.e. grain-size effect, nano-layer thickness effect, nano-twin effect, etc.) and micro-deformational constraint effect (i.e. micro-bending, micro-torsion, micro-indentation, etc.), was developed. As an application of this framework, the size effect on the bending strength of cantilever micro-beams at elevated temperature was investigated. The long-range back stress from dislocation pile-ups near the neutral plane of bent micro-beams was specially considered, with the stress relaxation due to climb of piled up dislocations involved. The simulation results illustrated that thickness effect on the bending strength of micro-beams observed in experiments could be well captured by this CP framework. Dislocation climb, which can collapse the dislocation pile-ups near the neutral plane, plays a significant role in the thickness effect at high temperature. The stress relaxation due to dislocation pile-ups collapsing is stronger in thinner micro-beams, which contributes to the climb-affected thickness effect at high temperature. These are helpful for us to understand the temperature dependence of the second-order size effects induced by GNDs and dislocation pile-ups at various interfaces.