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

397

4

Fig. 2. Dependence of the normal force F N on indentation depth d during the indentation into the rubber layer TARNAC CRG N0505: (a) Cylindrical indenter with the diameter D = 10 mm; (b) spherical indenter with radius R = 11 mm; (c) spherical indenter with radius R = 22 mm. As it follows from Fig. 2 a , in the positive range of indentation depth dependence F N ( d ) is almost linear. To estimate elastic parameters of the elastomer we will use the half-space approximation. With the use of definition of the incremental contact stiffness k z = ∂ F N / ∂ d , we obtain k z ≈ 741.7 N/m. Contact stiffness is defined as:

* 2 z k E a ,

(1)

hence, elastic modulus of the elastomer (radius of the contact a = 5 mm) E * = 74.17 kPa. Critical value of the indentation depth d (distance between the surface of the indenter and the surface of the half-space, at which total disappearance of the contact occurs), is defined by well-known expression:

* a E ,

(2)

c d

12 2 /

from equation (2) surface energy γ 12 can be calculated. Calculated from the dependence F N ( d ) in Fig. 2 a critical indentation depth is d c ≈ – 0.32 mm, which lead to the value γ 12 ≈ 0.242 J/m 2 . According to JKR theory (Johnson et al. (1971)) if the spherical (parabolic) profile is indented into elastic half-space, dependencies of the indentation depth and normal elastic force are defined by the equations:

3 3/2 2 N F a a ,

(3)

2 1/2 3 4 d a a ,

0 / N N F F F ,

0 / a a a and

0 / d d d are measured as follows:

where dimensionless parameters

1/3

1/3

2

2 2

R

R E

9

3

2 R

3

(4)

,

,

.

12

12

a

d

12

F

0

0

0

*

*2

E

8

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Dashed lines in Fig. 2 b and c represent theoretical curves, calculated according to the equations (3). As it can be seen from the figure, the experimental results match with the theory in some regions of the dependencies, at the same time certain disagreements are also observed. These disagreements are caused by the fact that theoretical relations (3) are valid within half-space approximation, while in experiment elastomer with finite sizes was used. Thus theoretical (dashed) curves show larger contact stiffness. In the following series of experiments contact between elastomer and cylindrical indenters with different diameters was investigated. Results of the performed experiments are shown in Fig. 3.