Quantifying the Uncertainty of Critical Resolved Shear Stress Values Derived from Nano-Indentation in Hexagonal Ti Alloys

Background Inverse indentation analysis (IIA) optimizes the adjustable parameters in a chosen constitutive description of crystal plasticity until the load–depth response and the residual surface topography match between real and simulated nanoindentation into one (or multiple) grains. Based on synthetic data, past work demonstrated that initial critical resolved shear stress (CRSS) values of hexagonal crystals could be extracted with good reproducibility from indenting a single strategically chosen crystal orientation. Objective The goal of the present contribution is to more deeply assess the IIA method using measured (instead of synthetic) topography and load–depth data sets that were acquired for three different Ti alloys at ambient and elevated temperature, and fitted based on a size-independent phenomenological power-law constitutive description of crystal plasticity. Methods The uncertainties in measuring surface topography and load–depth response and the uncertainties resulting from choices made in the setup of the finite element indentation simulation are quantified and linked to the reliability of the ultimately identified CRSS values. Results Surface topography uncertainties largely outweigh those of the load–depth response. Optimization can be accelerated by upscaling of shallower indentation simulations but only to a limited degree, i.e., to about an upscaling factor of 2 to 3. The physical interpretation of identified CRSS values needs careful consideration of the effect of limited indentation depth. Conclusions The present work demonstrates that reliable identification of CRSS values is possible when the combined relative deviations in topography and load–depth response inherent in the actual indentation experiment and in the practical constraints of the corresponding simulations stay below around 20 %. Consequently, the applicability of the IIA method requires pre-assessment of the uncertainties outlined in this work to determine the feasibility of extracting constitutive parameters and their expected validity.