Delineating inertial and strain-rate hardening effects on dynamic hardness of elasto-viscoplastic materials

Indentation is a simple and one of the oldest small-scale test methods for characterizing the mechanical response of materials. Recently, there has been growing interest in dynamic indentation due to its potential to characterize the mechanical response of small volumes of materials at high strain rates. Herein, we focus on understanding the synergistic effects of materials’ inherent strain-rate sensitivity and inertia on the scaling of dynamic hardness with indentation strain rate. Specifically, we analyze the dynamic indentation response of elasto-viscoplastic materials over a wide range of indentation velocities, utilizing both finite element calculations and an analytical cavity expansion model. The analyses are carried out for a range of strain-rate sensitivity parameters, densities, and indenter geometries. Our results indicate that, below a critical indentation loading rate, dynamic hardness scales with indentation strain rate in a manner analogous to the material’s constitutive description. At these loading rates, dynamic hardness is independent of the material’s density. However, above a critical indentation loading rate, dynamic hardness is found to depend on the material’s density. Despite this, even at high loading rates, dynamic hardness continues to scale with indentation strain rate following a relation analogous to the material’s constitutive description, though the parameters of this relation are found to depend on indentation velocity and the material’s density. We also present possible normalization parameters for hardness and indentation strain rate to account for the effects of material density and indentation geometry.