Phenomenological Analysis of Plastic Spherical Indentation

Abstract

Functional relationships describing the “expected” deformation behavior of a spherically indented surface are obtained by statistical analysis of published data. The representative strain εR of the indentation, the ratio ψ of mean contact pressure to representative flow stress YR (εR ), the shape of the interfacial pressure distribution p(r), the plastic boundary dimensions, and the displacement at the contact circumference can each be expressed, with specified precision, as functions of the altitude to base radius ratio h/b of the displaced spherical segment, the flow stress to Young’s modulus ratio YR /E (a measure of elastic strain capacity), and the Meyer index m (a measure of strain-hardening rate). Only εR and ψ are independent of m. Whereas εR = 0.43h/b, all other variables are predicted more precisely by φ = (h/b)/(YR /E) than by h/b. After plastic flow commences (φ = 1.15), ψ = 1.1 + 0.53 lnφ until φ = 27, beyond which ψ = 2.87. The extent of plastic flow during unloading can be predicted from p(r), which becomes flatter as φ and/or m increase.