Abstract
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.Graphic abstract
Highlights
The macroscopic mechanical properties of materials have traditionally and generally been determined by uniaxial tensile/ compression and multiaxial tests, such as metals, concrete and polymer materials [1,2,3,4]
Further analysis has revealed that the deviation between the finite element method (FEM) and classical Sneddon model is correlated to the indentation depth and Poisson’s ratio
We have demonstrated that Sneddon model works well for materials with big Poison’s ratio, when the indentation depth is below 1% of sample height for a flat sample with sufficiently large width
Summary
The macroscopic mechanical properties of materials have traditionally and generally been determined by uniaxial tensile/ compression and multiaxial tests, such as metals, concrete and polymer materials [1,2,3,4]. These methods requires the samples with specific geometries which may not be always feasible [5]. Chen and Bull [39] found such a linear relationship works very well for a limited range of materials They have developed a nonlinear model to describe the relation between H/E and Wirr/Wt for a wide range of materials. Machine learning method using different algorithms [42,43,44] have been adopted to identify elastic–plastic properties of materials when the constitutive materials models may be unknown
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