Inverse Method for Determination of Constitutive Behavior Using Spherical and Vickers Indentation

Background There exists no experimentally validated indentation method to uniquely determine the plastic properties of a material whose hardening behavior is defined with a three-parameter model. Objective The present work aims to systematically investigate non-unique solutions associated with existing and newly proposed indentation methods, and to study the possibility and implications of pressure-induced strengthening during indentation. Methods The residual profiles left by spherical indentation in four materials with different strain hardening behavior were measured with a profilometer. Inverse finite element analysis of the indentation, iterating over hardening parameters to fit the experimental residual indentation profile, was used to map non-unique solutions. The ability of additional spherical indents of varying depth and of post-mortem microhardness measurements to identify unique solutions was assessed. Results Non-unique solutions of high work-hardening materials had large differences in flow behavior, enabling their distinguishability by microhardness measurement after spherical indentation, but not by multiple indents to varying depth. Improved agreement with uniaxial tension data was achieved through inclusion of a pressure-dependent plasticity model over assumed pressure-independence. Conclusions A method was established to uniquely determine a three-parameter hardening model using indentation techniques combining spherical indentation, contact profilometry, and Vickers microhardness before and after spherical indentation. Constitutive properties obtained from indentation tests are suggested to overestimate material strength if pressure-induced strengthening is not accounted for.