Size effect of nickel-based single crystal superalloy revealed by nanoindentation with low strain rates

Size effect of the nickel-based single crystal superalloy DD6 is investigated in this study by performing nanoindentation experiments and finite element (FE) simulations by emphasizing the strain rate effect. An analytical method is proposed to identify whether a material has the indentation size effect (ISE) based on incremental formulations of the indentation strain rate. By taking ISE as a critical factor, the contact area is further described by considering the curvature radius of non-ideal indenters due to wear issues in practice. In order to emphasize the strain rate effect during indentations, the material parameters dominating mechanical properties are adopted from the strain rate dependent Johnson–Cook model, particular for the nickel-based single crystal superalloy. Consequently, the dimensional ISE analysis is performed by proposing a theoretical framework to establish the relationship among the indentation strain rate, the indenter tip curvature radius and the applied load–penetration depth (P–h) curve for characterizing nanoindentation responses. By identifying the indenter curvature radii and loading time as the important external factors of hardness measurement, FE simulations are validated to achieve good agreement with experimental data. The validated FE predictions are reliably employed to calibrate the dimensionless model of hardness with different indenter curvature radii and loading rates. In the proposed form of the dimensional hardness model, it is found that the indenter curvature radius can be perfectly independent of the material constitutive properties and loading rates. It reveals the potential and advantageous determination of characteristic length of materials by using nanoindentation.