Conditions of applying Oliver–Pharr method to the nanoindentation of particles in composites

The indentation test is a popular experimental method to measure a material’s mechanical properties such as elastic modulus and hardness, and the Oliver–Pharr method is commonly used in commercial indentation instruments to obtain these two quantities. To apply the Oliver–Pharr method correctly in all of these cases, it is essential to know the limitations of this method. The present study focuses on the applicability of the Oliver–Pharr method to measure the mechanical properties of particles in composites. The finite element method is used to undertake virtual indentation tests on a particle embedded in a matrix. In our numerical studies, the indentation “pile-up” phenomenon is generally observed in our numerical case studies, which indicates that the contact area used for predicting the elastic modulus should be measured directly, not be estimated from the indentation curve. The Oliver–Pharr method based on the real contact area is applied to estimate the elastic modulus of the particles by using the indentation curve from the numerical simulation, with the estimated elastic modulus being compared with the input value. Applying the real contact area value (not the one predicted from the indentation curve) we show that the Oliver–Pharr method can still be applied to measure the elastic modulus of the particle with sufficient accuracy if the indentation depth is smaller than the particle-dominated depth, a value defined in this work. The influences of the matrix and particle properties on the particle-dominated depth are studied using a dimensional analysis and parametric study. Our results provide guidelines to allow the practical application of the Oliver–Pharr method to measure the elastic modulus of particles in composites. This could be particularly important where particles are formed in situ in a matrix (as opposed to being preformed and subsequently incorporated in a matrix), or when the modulus of individual performed particles is required such as for subsequent modelling, but the modulus of individual material particles (or its material) cannot readily be determined.