Size-dependent crystal plasticity: From micro-pillar compression to bending

• Size dependent crystal plasticity model is developed.
• Accounts for first order effects: captured via uniaxial experiments.
• Accounts for second order effects: captured via heterogeneous loading experiments.
• Practical extension of a strain-gradient theory without extra parameters.

Size-dependent crystal plasticity of metal single crystals is investigated using finite-element method based on a phenomenological crystal-plasticity model, incorporating both first-order and second-order effects. The first-order effect is independent of the nature of the loading state, and described by three phenomenological relationships based on experimental results. The second-order effect is considered in terms of storage of geometrically necessary dislocations, affected significantly by the loading state. The modelling approach is shown to capture the influence of loading conditions on the sample size effect observed in compression and bending experiments. A modelling study demonstrates the subtleness and importance of accounting for first-order and second-order effects in modelling crystalline materials in small length-scales.