Effect of temperature and strain rate on indentation size effect at shallow indentation depths

• Indentation size effect deviates from the Nix-Gao model at shallow (submicron) indentation depths. • The deviation is temperature and strain rate dependent in bcc metals. • Higher temperatures and strain rates act against the deviation from the Nix-Gao model via lowering the escape of dislocations far from the indentation process zone. This study investigates the indentation size effect in a bcc silicon iron single-crystal tested at different temperatures and strain rates. The classical Nix-Gao model based on strain gradient plasticity and geometrically necessary dislocations starts to deviate from experimental data at small depths due to dislocation interactions not accounted for. Using a modified Nix-Gao model that incorporates lattice friction and the effective plastic zone effect, the indentation response can be more accurately captured. The study found that at depths exceeding approximately 1 µm, the increase in hardness due to Taylor hardening is independent of temperature and strain rate and can be well captured by the Nix-Gao model with temperature- and strain rate-dependent lattice friction parameter. However, at submicron depths, the deviation from the Nix-Gao model is temperature and strain rate dependent and can be accounted for using the concept of the effective plastic zone. Higher temperatures and strain rates result in less GNDs escaping from the indentation process zone, leading to an apparently more pronounced indentation size effect compared to room temperature and/or slow strain rates.