Theoretical and numerical investigations on confined plasticity in micropillars

• The operation stress equation of single arm source in coated micropillar is proposed.
• Trapped dislocation density linearly increases with plastic strain.
• A relation between trapped dislocation density and back stress is built.
• Reveal the correlation between DDD results and high-order crystal plasticity theory.
• Theoretical model can conveniently and nicely predicts stress–strain curves.

Multiscale dislocation dynamic simulations are systematically carried out to reveal the dislocation mechanism controlling the confined plasticity in coated micropillar. It is found that the operation of single arm source (SAS) controls the plasticity in coated micropillar and a modified operation stress equation of SAS is built based on the simulation results. The back stress induced by the coating contributes most to the operation stress and is found to linearly depend on the ‘trapped dislocation’ density. This linear relation is verified by comparing with the solution of the current higher-order crystal plasticity theory and is used to determine the material parameters in the continuum back stress model. Furthermore, based on the linear back stress model and considering the stochastic distribution of SAS, a theoretical model is established to predict the upper and lower bound of stress–strain curve in the coated micropillars, which agrees well with that obtained in the dislocation dynamic simulation.