A modified Sneddon model for the contact between conical indenters and spherical samples

Indentation techniques have proven to be effective to characterize the mechanical properties of materials. For the elastic deformation, the commonly used models are Hertz model and Sneddon model. However, neither of them works for indenting the spherical samples using the pyramid or conical indenter. Therefore, one modified Sneddon model has been developed to determine the Young's modulus of spherical samples from indentation results. In this study, the effects of sample diameter and indenter angles on indentation tests were investigated by finite element method (FEM). The empirical correction parameters in the new mathematical model were introduced based on dimensional analysis and determined by the numerical fitting to FEM results. Experimental tests with different conical indenters have demonstrated that the new model is capable to reliably determine the Young's modulus of the spherical samples. The new model can fill the gap of the contact mechanics and enrich the experimental solid mechanics for the interpretation of indentation results.