Nanoindentation testing is an established method for the measurement of indentation hardness, modulus and other materials parameters. Since many years exits the aim to extract the same parameters from indentation tests in metals that can be obtained from tensile tests because this would allow to get such data from finished parts and from small volumes. This was partially successful in the macro-range with indents of mm size and material models without time dependency. However, in the micro and nano range stain rate dependency and creep behavior play a larger role as well as the local grain structure of the metal. Therefore, now a material model was applied that includes creep effects and rate sensitivity. Further, a special experimental method was developed to address the influence of grain sizes and orientations.
The basic idea of our approach is to simulate the indentation process using known process parameters and iteratively optimize the initially unknown material properties until a minimum error between numerical and experimental results is achieved. Using the time-dependent material model, a large dataset of numerically generated data was produced. To improve the precision of the analysis, both, the force-displacement curve as well as the shape of the indent profile have been modeled and analyzed. Such data forms the basis for the training of a numerically very efficient surrogate model for the finite element simulation of the indentation process with up to eight material parameters. The advantage of the surrogate model based on an artificial neural network is that the training effort is only required once, and the machine learning algorithm can then be used to execute the inverse methods for different materials, provided their properties lie within the range of the training parameters. The numerical efficiency of this approach also allows the use of powerful optimization methods that require a relatively large number of iterations but deliver more robust results than the direct inverse method based on finite element simulations. The combination of computer simulation, machine learning and experiment represents a significant improvement in the inverse material parameter determination based on indentation measurements.
Finally, the precision of the method was tested by the analysis of micro-indentation test results from different aluminum and copper alloys as well as different steels and the comparison with tensile test results from the same materials.