PSI - Issue 36

Iakov Lyashenko et al. / Procedia Structural Integrity 36 (2022) 24–29 Iakov Lyashenko, Vadym Borysiuk / Structural Integrity Procedia 00 (2021) 000 – 000

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coefficient increases monotonically. At the beginning of motion, as the crack opens, tangential force decreases, causing decreasing of µ value with its following growth. When x > 10 mm monotonic increasing of coefficient µ is not observable, as the crack no longer affects the system. Fig. 2d shows enlarged fragment of Fig. 2c, where periodic changes in the friction coefficient is clearly visible. This behavior relates to the phases of slip, when tangential force F x decreases while normal force F N remains constant. This situation explains the decreasing of the µ = F x / F N value. Presented in Fig. 2 stick-slip mode, exists in the system because the shear stresses periodically exceed certain critical value, which lead to the slip of the surfaces of contacting bodies. In considered case surface of the gelatin slips over steel indenter, as the elastic modulus of the steel is significantly larger than those of the gelatin and indenter can be considered as absolutely rigid. Described phenomena often can be observed in multicontacting system, where friction force can be expressed as a certain average value (Zaskoka, 2017; Scheibert, Riad and Michel, 2020). In the case when number of connected contacts is high enough, saw-edged dependence of the friction force F x ( x ) on the displacement may not be observed at macroscopic scale, although every single contact exhibits non-continuous movement (Bayart, Svetlitzky and Fineberg, 2016). Example of such multicontacting system is the fragmented metallic sample with grain boundaries as defects. When the sample is loaded the slips may occur over these defects. Every single contact in the area of grain boundary in such system behaves similarly to the behavior with slips shown in Fig. 2 (Khomenko, Lyashenko and Metlov, 2008). As a result collective behavior leads to the new physical phenomena, known as superplasticity (Kaibyshev, 1984; Kaibyshev and Pshentchnyuk, 2012; Chuvil’ deev, 2004). 4. Conclusions We presented the results of the experiment concerning the indentation of the steel sphere into the soft elastic elastomer with the following tangential movement of the indenter. It is shown that in stationary case, system exhibit the stick-slip mode of movement with the destruction of the elastomer surface. Single contact is considered in details. In multicontact systems similar processes lead to collective behavior with different properties due to the large number of contacts. Namely, metallic samples with large number of defects such as grain boundaries, exhibit superplasticity phenomena caused by slips on grain boundaries. Studying of the slips on grain boundaries in the volume of the sample directly is impossible, thus for general understanding of the processes occurring during superplasticity model system similar to the one, studied in the proposed must be developed. Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (DFG), project PO 810-55-3; it partially contains results of investigations carried out within the scope of Scholarship work within the framework of the nominal scholarship of the Verkhovna Rada of Ukraine for young scientists – doctors of sciences (Resolution of the Verkhovna Rada of Ukraine of 14.07.2021 No. 1641-IX). References Bayart, E., Svetlitzky, I., Fineberg, J., 2016. Slippery But Tough – The Rapid Fracture of Lubricated Frictional Interfaces. Physical Review Letters 116 (19), 194301. Banerjee, P. K., 1994. The Boundary Element Methods in Engineering, 2nd ed. (London, etc.: McGraw - Hill); ISBN 0 - 07 - 707769 - 5. Ciavarella, M., Papangelo, A., 2018. A Generalized Johnson Parameter for Pull - Off Decay in the Adhesion of Rough Surfaces. Physical Mesomechanics 21 (1), 67–75. Chuvil’deev, V. N., 2004. Nonequilibrium Grain Boundaries in Metals: Theory and Applications. (Fizmatlit, Moscow) [in Russian]. Derjaguin, B. V., Muller, V. M., Toporov, Y. P., 1975. Effect of Contact Deformations on the Adhesion of Particles. Journal of Colloid and Interface Science 53 (2), 314–326. Hertz, H., 1882. Ueber die Berührung Fester Elastischer Körper. Journal für die reine und angewandte Mathematik 92, 156–171. Johnson, K. L., Kendall, K., Roberts, A. D., 1971. Surface Energy and the Contact of Elastic Solids. Proceedings of the Royal Society A 324 (1558), 301–313. Kaibyshev O. A., 1984. Superplasticity of Commercial Alloys. (Metallurgiya, Moscow) [in Russian]. Kaibyshev O. A., Pshentchnyuk A. I., 2000. To Theory of Superplasticity. Vest. UGATU 1 (1), 53–60 [in Russian]. Khomenko, A. V., Lyashenko, Ya. A., Metlov, L. S., 2008. Phase Dynamics and Kinetics of Intensive Plastic Deformation. Metallofizika i Noveishie Tekhnologii 30(6), 859–872 [in Russian].