Theoretical study on nanoindentation hardness measurement of a particle embedded in a matrix

The finite element method was used to simulate indentation tests on a particle embedded in a matrix, to investigate the influence of the properties of the particle and the matrix, and the indentation depth on the measured hardness. The particle's work-hardening exponent and the mismatch in particle and matrix yield strength have a significant influence on the measured hardness. A particle-dominated indentation depth was identified, within which the measured nanoindentation hardness agrees very well with the true hardness of the particle material. Numerical results from the simulations of a wide range of material properties determined that the measured hardness is within 5% difference of the particle's true hardness when the indentation depth is less than 13.5% of the particle's radius. The results can be used in practice as a guideline to measure the hardness of a particle embedded in a matrix and provides the theoretical basis to develop a particle-embedded method to measure the hardness of individual particles.