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

Abstract

Abstract Depth-sensing indentation measurements were performed using the three trihedral pyramid indenters with the specific inclined face angles β B ( β B =11.4°, 24.7° (Berkovich) and 43.7°), three tetrahedral pyramid indenters with β V ( β V =10°, 22° (Vickers) and 40°) and a Knoop indenter ( β K =25.2°). The materials tested ranged from ductile metals to brittle ceramics, including soda-lime glass, Si 3 N 4 , MgO, copper/zinc alloy, and high-carbon chromium bearing steels. The loading paths were conformed to the quadratic relations of P = k 1 h 2 , and the unloading paths were well approximated with P = k 2 ( h − h r ) 2 , in terms of the indentation load P , penetration depth h , and the residual depth h r 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 β C / H (elastic modulus E ′, true hardness H and the inclined face angle β C 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.