Nanoindentation with spherical indenters: finite element studies of deformation in the elastic–plastic transition regime

Abstract Finite element simulation techniques were used to examine spherical indentation in the elastic–plastic transition regime and characterize the development of the constraint factor—the ratio of the mean pressure to the flow stress—with penetration depth for a wide variety of materials with different yield strengths and work hardening behavior. The simulations showed that the initial portion of the transition at small penetration depths is essentially independent of the work hardening behavior because plastic deformation in the subsurface plastic zone is constrained by surrounding elastic material. This is a potentially useful result in that it implies that some material properties may be measured from the indentation load–displacement data without prior knowledge of the work hardening behavior. At larger depths, the constraint factor diverges and the indentation behavior becomes dependent on the work hardening characteristics. These observations serve to divide the elastic–plastic transition into elastically-dominated and plastically-dominated parts. Insights gained about the behavior are presented and discussed.