PSI - Issue 59

Hryhorii Habrusiev et al. / Procedia Structural Integrity 59 (2024) 494–501 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

499

6

 2 1



E 



2

2  1

k



.



     1



1

2  



1

cr  are different for different materials, because they depend on  . In

In this case, the critical values

0.3   , the “resonance” phenomena are observed as 1

.

particular, at

0.565

cr    

1 k on the parameter of linear elongation

1  for the Bartenev –

In fig. 2, we illustrate the dependence of

Khazanovich elastic potential (curve 1 ) and harmonic-type potential (curve 2 ).

Fig. 2 . Dependence of 1 k on 1 

The performed numerical analysis enables us to assert that the influence of initial strains on the vertical dis- placements for compressible and incompressible bodies is significantly greater in the case of presence of preliminary compressive strains, 1 1   , than in the case of preliminary tensile strains, 1 1   .

Fig. 3 . Distributions of contact stresses ( a ) and vertical displacements ( b ) for various values of a r We analyzed the influence of presence of a plane domain at the indenter footing on the distribution of contact stresses and the character of vertical displacements. In fig. 3, we show the graphs of functions     * ,0 zz r r P    and     * ,0 z u r u r P  for a parabolic indenter, in the absence of residual strains in the layer 1 1   , constant contact domain radius 1 a  and different values of r a : 0 a r  – curve 1, 0.2 a r  – curve 2, 0.5 a r  – curve 3. It is noticeable that the indenter shape affects substantially the level and character of distribution of contact stresses. In particular, for a parabolic indenter, where there is no plane part at the footing, the extreme values