Geometrical effect of pyramidal indenters on the elastoplastic contact behaviors of ceramics and metals

Depth-sensing indentation measurements were performed using the three trihedral pyramid indenters with the specific inclined face angles βB (βB=11.4°, 24.7° (Berkovich) and 43.7°), three tetrahedral pyramid indenters with βV (βV=10°, 22° (Vickers) and 40°) and a Knoop indenter (βK=25.2°). The materials tested ranged from ductile metals to brittle ceramics, including soda-lime glass, Si3N4, MgO, copper/zinc alloy, and high-carbon chromium bearing steels. The loading paths were conformed to the quadratic relations of P=k1h2, and the unloading paths were well approximated with P=k2(h−hr)2, in terms of the indentation load P, penetration depth h, and the residual depth hr of impression. All of the indentation-related parameters were calculated from the loading/unloading P–h hysteresis curves, and then correlated well with the nondimensional plastic strain E′ tan βC/H (elastic modulus E′, true hardness H and the inclined face angle βC of equivalent cone indenter). The concept of “equivalent cone” provided an efficient analytical method, by which all of the indentation behaviors for the Vickers-type, Berkovich-type and the Knoop indenters were described in a unified manner. The quadratic approximation for the unloading path combined with the concept of “effective shape of indenter” was successfully utilized to estimate the elastic modulus E′ of the materials indented.