Application of a modified slip-distance theory to the indentation of single-crystal and polycrystalline copper to model the interactions between indentation size and structure size effects

Plasticity size effects offer both measurement challenges and opportunities for material engineering. We have used nano-indentation to study the relationship between different size effects. Hardness varies significantly with indent size in single crystals, and also in polycrystals, whenever indent sizes and structure sizes are within an order of magnitude of each other. We exploit the geometric self-similarity of a Berkovich indenter and apply slip distance theory to indents of different sizes at a constant indentation strain. We show that indent size, grain size and pinning defects combine in a single, length-scale-dependent deformation mechanism, to determine the yield strength (hardness) of a material. This provides an excellent foundation for: improved grain size determination by indentation, design rules for combining different methods of yield stress enhancement and using indentation to probe local stress–strain properties of a material, or for mapping residual stress.