A numerical study on the nanoindentation response of a particle embedded in a matrix

An indentation test is an experimental method whereby an indenter is pressed into a specimen in order to create a contact impression. Based on experimental input and the mechanical response of a specimen, an indentation test can be used to measure material properties of a specimen. A nanoindentation test is an instrumented indentation test where the indentation depth is at the submicron scale, utilising the interpretation of recorded load-displacement data. Nanoindentation tests have proven to be popular commercially due to their non-destructive nature, with the Oliver-Pharr method being one of the most prominent analysis methods applied. In this research, nanoindentation tests on a semi-spherical particle embedded in a semi-infinite matrix were simulated using the finite element method. Dimensional analysis was utilised to conduct a numerical study of the nanoindentation response obtained from finite element simulations. The Oliver-Pharr method to estimate contact area from a nanoindentation test is unsuitable for the cases with pile-up deformation. In an indentation of a hard particle embedded in a soft matrix, the mismatch of material properties will cause the particle to indent itself into the matrix, which creates a secondary indentation effect. This makes it difficult to investigate the pile-up and sink-in behaviour for hard particle reinforced composites because the definition of pile-up for monolithic materials is no longer valid. In this research, a feasible method to quantify pile-up and sink-in for particle-matrix systems is proposed. Using a reference height, it was found that particle pile-up and sink-in can be quantified when the maximum indentation depth is less than 15% of the particle’s radius. The influence of particle and matrix material property on pile-up and sink-in was explored. Within the maximum indentation depth, which is less than 15% of the particle’s radius, it was found that only the mechanical properties of the particle represented by particle’s elastic modulus, particle’s yield strength, and particle’s work-hardening exponent, have a significant influence on the degree of pile-up and sink-in from a nanoindentation test. In a nanoindentation test of a particle embedded in a matrix, the matrix material properties may influence the measured indentation hardness of the particle. A numerical study was carried out to identify the influence of particle and matrix material properties on the measured hardness. Results reveal that a mismatch in material properties is more sensitive on the measured hardness of a hard particle embedded in a soft matrix than a soft particle embedded in a hard matrix. Finally, a parametric study was carried out to identify a particle-dominated depth, within which the particle’s hardness obtained from a nanoindentation test can be measured with confidence. Simulation results from the finite element analysis of a variety of material properties determined that when the maximum indentation depth is less than 13.5% of the particle’s radius, the measured hardness is in good agreement with the particle’s true hardness, with a maximum error of 5%. This finding can be applied in practice as a guideline to measure the hardness of a particle embedded in a matrix from a nanoindentation test and provide the theoretical basis to develop a particle-embedded method to measure the hardness of individual particles.