When using the Oliver–Pharr method, the indented specimen is assumed to be a perfectly flat surface, thus ignoring the influences of surface roughness that might be encountered in experiment. For nanoindentation measurements, a flat surface is fabricated from curved specimens by mechanical polishing. However, the position of the polished curved surface cannot be controlled. There are no reliable theoretical or experimental methods to evaluate the mechanical behavior during nanoindentation of an elastic–plastic microsphere. Therefore, it is necessary to conduct reliable numerical simulations to evaluate this behavior. This article reports a systematic computational study regarding the instrumented nanoindentation of elastic–plastic microspherical materials. The ratio between elastic modulus of the microsphere and the initial yield stress of the microsphere was systematically varied from 10 to 1000 to cover the mechanical properties of most materials encountered in engineering. The simulated results indicate that contact height is unsuitable to replace contact depth for obtaining the indentation elastic modulus of microspherical materials. The extracted elastic modulus of a microsphere using the Oliver–Pharr method with the simulated unloading curve depends on the indentation depth. It demonstrates that nanoindentation on microspherical materials exhibits a “size effect”.

The understanding of the mechanical indentation on a curved specimen (e.g., microspheres and microfibers) is of paramount importance in the characterization of curved micro-structured materials, but there has been no reliable theoretical method to evaluate the mechanical behavior of nanoindentation on a microsphere. This article reports a computational study on the instrumented nanoindentation of elastic-plastic microsphere materials via finite element simulation. The finite element analyses indicate that all loading curves are parabolic curves and the loading curve for different materials can be calculated from one single indentation. The results demonstrate that the Oliver-Pharr formula is unsuitable for calculating the elastic modulus of nanoindentation involving cured surfaces. The surface of the test specimen of a microsphere requires prepolishing to achieve accurate results of indentation on a micro-spherical material. This study provides new insight into the establishment of nanoindentation models that can effectively be used to simulate the mechanical behavior of a microsphere.