Elastic–plastic spherical indentation: Deformation regimes, evolution of plasticity, and hardening effect

Abstract

Deformation of an elastic–plastic half-space by a rigid spherical indenter was examined with the finite element method. Simulation results show that the post-yield deformation behavior comprises four deformation regimes: linear elastic–plastic, nonlinear elastic–plastic, transient fully plastic, and steady-state fully plastic, representing different stages of the plastic zone evolution. Equations for the boundaries between neighboring deformation regimes are given in terms of the dimensionless mean contact pressure and indentation depth. The development of the plastic zone in the nonlinear elastic–plastic deformation regime is interpreted in terms of two characteristic modes of evolution that depend on the effective elastic modulus-to-yield strength ratio. General constitutive relations of the dimensionless mean contact pressure and contact area are derived for each deformation regime from finite element simulation results. The effect of strain hardening on the indentation behavior is shown to be significant for indentation depths larger than those corresponding to linear elastic–plastic deformation. An equation of the effective strain is introduced, and generalized constitutive relations are obtained using the effective yield strength, which accounts for the effect of strain hardening on the yield strength. The constitutive relations of the deformation behavior at the asperity scale derived in this study can be incorporated in contact analyses of elastic–plastic rough surfaces.