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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the indenter that is indented into the plate, this plate can be considered as half-space. Many contact tasks can be solved analytically within the half-space approximation (Popov et al. (2019)). From the obtained analytical solutions contact forces, stress distribution in the contact area etc. can be found. Many classical theories, such as theory of the adhesive contact (Johnson et al. (1971), Derjaguin et al. (1975), Maugis (1992)), Hertz contact (Hertz (1882)) and others, use the half-space approximation. In real applications we often deal with situations, where thickness of contacting bodies is finite and limited by the technological conditions, and thus, solutions, obtained within half space approximation lead to incorrect results. Theories, that include the thickness of the contacting bodies generally are more complex and not give the solutions in simple analytical forms (Argatov et al. (2015)). One of the possible ways to resolve this problem is to use various methods of the computer simulation, such as Finite Element Method (FEM), Boundary Element Method (BEM), Movable Cellular Automaton method (MCA), Molecular Dynamics (MD), Method of Dimensionality Reduction (MDR) and others (Reddy (2006), Banerjee (1994), Pohrt and Li (2014), Psakhie et al. (1995), Popova and Popov (2020)). Mentioned methods become more and more effective with the growth of the computing power of modern computers. In the presented paper we perform several experiments concerning indention of the soft elastomer by a steel indenter. As it follows from the performed experiments, the thickness of the elastomer must significantly exceed the size of the contact area in order to validate the half-space approximation. This conclusion is not exactly match with classic theory, where simple condition for thickness of the elastomer to be larger than the size of the contact is enough to consider the elastomer as a half-space. Size effects have significant influence on the behaviour of almost every system, that is why to take them into account is one of the general problems of the science. As an example, we can refer to the process of alloy fragmentation under the severe plastic deformation, where the thickness of the obtained sample significantly affects its mechanical and physical properties (Khomenko et al. (2008)).

Nomenclature F N

normal force (N)

indentation depth (mm) critical indentation depth (mm) radius of the contact (mm) diameter of cylindrical indenter (mm) radius of spherical indenter (mm) velocity of indenter motion (mm/s)

d

d c

a

D R k z E v

contact stiffness (N/m) elastic modulus (Pa)

Poisson ratio

ν

reduced elastic modulus (Pa) specific work of adhesion (J/m 2 )

E * γ 12

dimensionless values of normal force, contact radius, and indentation depth units of normal force (N), contact radius (mm) and indentation depth (mm)

, , N F a d F 0 , a 0 , d 0

thickness of the elastomer (mm)

h

2. Experimental device and methodology Described in proposed work experiments were performed on the laboratory equipment that is shown in Fig. 1. Linear stage M-403.2DG (manufactured by PI) is denoted by number 1 in the figure and are operated by controller PI C-863 (number 9 in the figure). Stage move aluminium plate (2) with fixed three axes force sensor ME K3D40 (3), the sensor operates in the range ±10 N. Signals obtained from the sensor are amplified by 4-channel strain-gauge amplifier GSV-1A4 SubD37/2 and are transmitted to the computer through 16-bit multifunction input/output device NI USB-6211. Steel indenter (4) is mounted on the force sensor. In performed experiments indenter (4) is indented into the elastomer (5). Surface of the elastomer can be rotated in horizontal plane by tilt mechanism (7). Contact area is illuminated by all-sides LED lightening (6) with intensity that can be varied through regulated power supply (10).