Neural networks for tip correction of spherical indentation curves from bulk metals and thin metal films

Spherical indentation is widely used to determine a variety of important mechanical properties from small volumes. However, the available nanoindenter tips mostly deviate from the perfect spherical shape making the application of analysis methods developed for perfect spheres uncertain. In this paper, neural network-based methods are presented that are used to correct force–depth curves measured with such indenter tips. Finite element simulations for imperfect and perfect spherical tips with varying material behaviour are used to train the neural networks, which solve the inverse problem of mapping the true tip shape and the measured force–depth curve to one that corresponds to a perfect spherical indenter. Solutions are provided for bulk materials and thin films. The method has been verified experimentally on nanocrystalline nickel and a copper film on a titanium substrate for different spherical tips.