Quantitative determination of contact depth during spherical indentation of metallic materials—A FEM study

The continuous indentation technique, because it is fast, precise and nondestructive, has been widely used to determine such mechanical properties as flow properties, residual stress, fracture properties, viscoelastic properties and hardness of materials and structural units. In particular, continuous indentation by a spherical indenter can provide hardness and flow properties, such as yield strength, tensile strength and work-hardening exponent, using the characteristic that strain from the loaded indenter changes with indentation depth. Since the stress and strain values on the flow properties are defined based on the contact area between the indenter and material in the loaded state, accurate determination of the contact area is essential. Determination of the contact area is closely connected with the pile-up/sink-in behavior.In this study, the pile-up/sink-in phenomenon is considered as two independent behaviors, elastic deflection and plastic pile-up, which can be respectively described by a formula. The formulas can be obtained from FE simulation with conditions reflecting real indentation tests for materials used for various purposes and with a wide range of material properties. By analyzing indentation morphology from the FE simulation, the two phenomena were quantified as formulas. In particular, plastic pile-up behavior was formulated in terms of work-hardening exponent and indentation ratio.