PSI - Issue 36

Iakov Lyashenko et al. / Procedia Structural Integrity 36 (2022) 394–400 Iakov Lyashenko, Vadym Borysiuk / Structural Integrity Procedia 00 (2021) 000 – 000

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elastic sample, located on the absolutely rigid substrate are shown in the Fig. 3 c . Dashed line shows the theoretical solution within half-space approximation. Lines from top to bottom relate to the thickness of the elastic layer from h = 15 mm to h = 60 mm with increment of Δ h = 5 mm. As it can be seen from the figure, obtained dependencies are characterized by fast approaching to theoretical solution for smaller thicknesses with following slowing down with the growth of h. Closest to the dashed line dependence was obtained for the thickness h = 150 mm, which is 10 times larger than the diameter of the indenter. Even for these parameters the difference between theory and simulation is noticeable. Thus, we can conclude, that thickness of the elastic layer must be 10 times larger than diameter of the indenter in order to use half-space approximation. However, from the performed simulations we cannot obtain the sizes of rubber substrate in the direction parallel to the contact area. To study the effect of the lateral sizes of rubber sample on the obtained results, series of additional experiments were performed. The results of these experiments are shown in Fig. 4.

Fig. 4. Dependence of the elastic normal force F N on indentation depth d during the indentation of cylindrical indenter with the diameter D = 4 mm into the rubber sample at different position of the indenter related to the centre of the sample.

Results of the five experiments are presented in the figure. The difference between the performed experiments is the position of the indenter with respect to the centre of the rubber sample. Let us recall, that rubber sample was a cylinder with a diameter of 45 mm and a thickness of 15 mm (see Fig. 1). Top curve in the Fig. 4 corresponds to the position of the indenter in the centre of the rubber sample. This experiment completely matches with the experiment that was shown by curve 4 in Fig. 3 b . All remaining dependencies in Fig. 4 correspond to the consecutive radial approaching of the centre of the indenter to the edge of the rubber block with increment of 5 mm. As it was mentioned above, results of the 5 experiments are shown in the figure. First two experiments show similar dependencies that are barely distinguished in the figure scale (indenter positioned at the centre of rubber sample, and shifted from its centre on 5 mm). Dependence at the bottom of figure related to the indenter positioned at 20 mm from the centre, i.e. almost at the edge of rubber block. As it follows from the figure, obtained data depends on the position of indentation. Therefore, to use half-space approximation it is important to operate the sample, not only thick enough, but also with large enough length in all directions. 4. Conclusions We described the series of experiments concerning indentation of the spherical and cylindrical indenters with different radii into the elastic elastomer. Elastic modulus of the indenter by several orders of magnitude exceeds the elastic modulus of the elastomer, thus only elastomer undergoes strains. In the case of cylindrical indenter, area of the contact and its rigidity remain constant. At these conditions effective elastic modulus of the elastomer ’s material can be estimated. Calculated elastic parameter depends on the radius of the indenter, as elastomer has limited thickness and it cannot be considered as a half-space. Both experiments and simulations show that for the half-space approximation to be valid the thickness of the elastomer must several times (preferably more than 10 times) exceed the diameter of the contact.