On the uniqueness and sensitivity of indentation testing of isotropic materials

• Sensitivity of various indentation techniques for experimental error is studied.
• Condition number is used to rank indentation techniques according to sensitivity.
• Guidelines regarding the selection of shape functions are provided.
• Some dual indentation techniques can be worse than single indentation techniques.
• Indentation experiments need to be very accurate to extract reliable properties.

Instrumented indentation is a popular technique to extract the material properties of small scale structures. The uniqueness and sensitivity to experimental errors determine the practical usefulness of such experiments. Here, a method to identify test techniques that minimizes sensitivity to experimental erros is in indentation experiments developed. The methods are based on considering “shape functions,” which are sets of functions that describe the force–displacement relationship obtained during the indentation test. The concept of condition number is used to investigate the relative reliability of various possible dual indentation techniques. Interestingly, it was found that many dual indentation techniques can be as unreliable as single indentation techniques. Sensitivity analyses were employed for further understanding of the uniqueness and sensitivity to experimental errors of indentation techniques. The advantage of the Monte Carlo approach over other procedures is established. Practical guidelines regarding the selection of shape functions of force–displacement relationship and geometric parameters, while carrying out indentation analysis are provided. The results suggest that indentation experiments need to be very accurate to extract reliable material properties.