Finite element study for nanoindentation measurements on two-phase materials

Finite element simulations of conical indentations in two-phase elastic–plastic materials were used to investigate the influence of the shape and the aspect ratio of particles embedded in a matrix material on the deformation behavior and hardness during depth-sensing indentation. Starting with single-phase materials, pile-up behavior and its influence on the contact area was studied. Particle–matrix systems were simulated for elastic–perfectly plastic particles embedded in a matrix, with a yield-strength ratio of 2 or 0.5, respectively. The simulations were motivated by indentation experiments in precipitation hardened nickel-base superalloy with a nanoindenting atomic force microscope. In the studied alloys, the matrix formed channels with a thickness of about 100 nm around the precipitates with diameters of about 500 nm. The simulations explained an experimentally observed transition from particle to matrix deformation behavior during indentation. Depth limits in hardness testing in particle–matrix systems were evaluated. Depending on the aspect ratio, soft and hard particles were tested reliably up to a normalized contact radius of about 70% particle diameter.