OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 max 1 max 2 ( ) , m f r c h h dF S km h h E A dH − = = = − = π (4) 2 2 1 1 1 , i r i E E E − ν − ν = + (5) where v and vi are Poisson’s ratios for the material and indenter, respectively; Er is the reduced elastic modulus; Ei is the elastic modulus of the indenter tip. The equation that describes the reduced elastic modulus is as follows: 1 , 2 r c E S A π = (6) where Аc is the actual contact area of the spherical indenter tip with regard to the height of the plastic pile-up hpile and the elastic contact depth hd. The real contact area Аc is determined with respect to the actual contact radius а and is the function hc of the contact depth and the material: ( ). c c À f h = (7) The contact depth at the current penetration force can be obtained from the analysis of the unloading curve (fig. 4) using the indenter geometry, elastic strain, and morphology of deformed surface. In figs. 4 and 5, the following notations are used: Fmax: Maximum penetration force; hp: Residual indentation depth after Fmax removal from the specimen; hr: Point of intersection of the tangent to curve at Fmax with the indentation depth-axis; Fig. 4. Schematic “loading/unloading” curves of indentation for a single cycle
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