A Study of the Indentation Size Effect in Copper

A simple model for an expanding array of screw dislocations is developed to evaluate the size of the containment zone of the geometrically necessary dislocations as it relates to the indentation size effect. The model as developed predicts the same functional form as the Nix-Gao model, H²=H₀²(1+h^*/h), but a new relation for h^* applies that depends only on the Burgers vector and the Taylor constant, where as the Nix-Gao model predicts a strong dependence of the macroscopic hardness and the tip angle. The continuous stiffness method, CSM, is critically examined using experimental measurements of varying harmonic displacement. Large errors are identified at small depths in soft metals which have important consequences for interpretation of the indentation size effect. A model is developed to predict the depths of which CSM breaks down, and corrections are proposed for CSM measurements that account for most of the error caused by the CSM. Indentations in single crystal (100) electropolished copper were made using three-sided pyramidal tips of varying centerline-to-face angle. Using this, we explore the prediction of the Nix-Gao model, that the characteristic depth is very strongly dependent on the included indenter angle, and of the Strader-Pharr model, that it is independent of depth. The Strader-Pharr model is found to account for the experimental observations more accurately than the Nix-Gao model.