PSI - Issue 36

Iakov Lyashenko et al. / Procedia Structural Integrity 36 (2022) 24–29

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Iakov Lyashenko, Vadym Borysiuk / Structural Integrity Procedia 00 (2021) 000 – 000

1. Introduction Contact mechanics and investigation of the processes between contacting solids developed rapidly during last few decades. Even though the most known classic work in this field was published more than 130 years ago (Hertz, 1882), an active development of a contact mechanics has begun just recently. Reasons for recent progress are the appearance of the new methods of computational analysis and dramatic increasing of the computational power of modern computers as well as the improvement of experimental methods of studies. Modern computational methods for simulation of the mechanical contacts include Finite Element Method (FEM) (Reddy, 2006), Boundary Element Method (BEM) (Banerjee, 1994; Pohrt and Li, 2014), Method of Dimensionality Reduction (MDR) (Popova and Popov, 2020) and Movable Cellular Automaton method (MCA) (Psakhie et al., 1995). All mentioned methods allow one to calculate the strains in the material if the type of load is known. In recent works (Pohrt and Popov, 2015; Popov, Pohrt and Li, 2017) boundary element method for description of the mechanical contacts was modified so the adhesion forces can be taken into account. It is worth to mention, that studies of the adhesive processes also lasts for several decades (Johnson, Kendall and Roberts, 1971; Derjaguin, Muller and Toporov, 1975; Maugis, 1992). However, there are still some open questions in this field, which continue give rise to the active discussions in the leading scientific groups. Namely, mechanisms and peculiarities of the adhesive interaction between rough surfaces (Ciavarella and Papangelo, 2018; Pepelyshev et al., 2018) and how exactly adhesion affects the motion in tangential contact (Popov, 2018; Popov, Lyashenko and Filippov, 2017; Parent and Adams, 2016) remain among open and actively discussed issues. Moreover, neither of this problem have final solution in both quasi-static approximation and dynamic case if viscoelastic effects appear. In work (Popov, Pohrt and Li, 2017) authors developed and described experimental setup, that was used to perform the series of experiments concerning detachment of the flat surfaces of different geometrical shape from the surface of material with strong adhesive properties, while hardened water solution of gelatin was used as the latest. We will refer to this material as elastomer, as it consists mainly of water which makes it practically incompressible (like all elastomers) with Poisson ratio ν ≈ 0.5. Also in mentioned paper, simulation of the process of detachment was performed within boundary elements method (Pohrt and Popov, 2015). It is important to note that motion only in normal direction was considered. Elastomer sample had a cylindrical shape with a diameter of 4.5 cm and height up to 3 cm to study the indentation of the samples with small contact areas. To compare the results of the experiment and simulations the half-space approximation must be valid in both cases, when the strain at the edges of elastomer is negligible. To ensure this conditions the experimental equipment developed in (Popov, Pohrt and Li, 2017) must be modified. In the proposed work we describe the modified equipment, outlining its peculiarities and options. We also present the results of the performed experiment that can qualitatively explain the mechanism leading to the superplasticity effect in metallic samples with defects such as grain boundaries.

Nomenclature ν

Poisson ratio

indentation depth (mm)

D V F

velocity of indenter motion (mm/s)

contact force (N) normal force (N) tangential force (N) friction coefficient

F N F x

µ x R

tangential coordinate of indenter

radius of indenter