OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 25 No. 4 2023 Fig. 5. Morphology of deformed surface of the material hmax: Maximum indentation depth at Fmax; hc: Depth of the contact of the indenter with the test piece at Fmax; hpile*: Height of plastic pile-up; hd: Depth of elastic contact; R: Radius of spherical tip; а: Actual contact radius; а*: Contact radius without pule-up. We thus obtain: * * * max , c c pile d pile h h h h h h = + = − + (8) max max ( ) 0, 75 / , d r h h h F S = ω − = (9) where ω is the indenter shape index equaling 0.75 for spherical tip. Therefore, * * * max max (0, 7 , 5 / ) c pile pile h h h F S h + = − + (10) * max * , . pile IT c h h f n R h = (11) The plastic pile-up can be expressed through the constant с and connected with the strain hardening n of the material by the empirical relation 2 2 *2 5(2 ) , 2(4 ) à n ñ n à − = = + (12) where a is the actual contact radius; а* is the contact radius without pile-up. Based on the geometry of the spherical indenter, the actual contact radius is expressed as hc and the indenter radius R: ( ) 2 * *2 5(2 ) 2 . 2(4 ) c c n à Rh h n − = − + (13) The actual contact area Ac is determined by the actual contact depth hc correlating with hpile* and hc*: ( ) 2 2 . c c c A Rh h = π − (14)
RkJQdWJsaXNoZXIy MTk0ODM1