Estimation of the elastic modulus and the work of adhesion of soft materials using the extended Borodich-Galanov (BG) method and depth sensing indentation

The depth-sensing indentation (DSI) is currently one of the main experimental techniques for studying elastic properties of materials of small volumes. Usually DSI tests are performed using sharp pyramidal indenters and the load-displacement curves obtained are used for estimations of elastic moduli of materials, while the curve analysis for these estimations is based on the assumptions of the Hertz contact theory of non-adhesive contact. The Borodich–Galanov (BG) method provides an alternative methodology for estimations of the elastic moduli along with estimations of the work of adhesion of the contacting pair in a single experiment using the experimental DSI data for spherical indenters. The method assumes fitting the experimental points of the load-displacement curves using a dimensionless expression of an appropriate theory of adhesive contact. Earlier numerical simulations showed that the BG method was robust. Here first the original BG method is modified and then its accuracy in the estimation of the reduced elastic modulus is directly tested by comparison with the results of conventional tensile tests. The method modification is twofold: (i) a two-stage fitting of the theoretical DSI dependency to the experimental data is used and (ii) a new objective functional is introduced which minimizes the squared norm of difference between the theoretical curve and the one used in preliminary data fitting. The direct experimental validation of accuracy and robustness of the BG method has two independent steps. First the material properties of polyvinyl siloxane (PVS) are determined from a DSI data by means of the modified BG method; and then the obtained results for the reduced elastic modulus are compared with the results of tensile tests on dumbbell specimens made of the same charge of PVS. Comparison of the results of the two experiments showed that the absolute minimum in relative difference between individual identified values of the reduced elastic modulus in the two experiments was 3.80%; the absolute maximum of the same quantity was 27.38%; the relative difference in averaged values of the reduced elastic modulus varied in the range 16.20 ... 17.09% depending on particular settings used during preliminary fitting. Hence, the comparison of the results shows that the experimental values of the elastic modulus obtained by the tensile tests are in good agreement with the results of the extended BG method. Our analysis shows that unaccounted factors and phenomena tend to decrease the difference in the results of the two experiments. Thus, the robustness and accuracy of the proposed extension of the BG method has been directly validated