Inertial effect on dynamic hardness and apparent strain-rate sensitivity of ductile 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 a growing interest in dynamic indentation due to its potential to characterize the mechanical response of small volume 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 ductile materials over a wide range of indentation velocities, utilizing both finite element calculations and an analytical cavity expansion model. The materials are assumed to follow isotropic elastic- viscoplastic constitutive relations, with the viscoplastic part described by either an overstress or a simple power-law model. Our results show that below a critical indentation strain-rate, the scaling of dynamic hardness with indentation strain-rate is the same as the viscoplastic constitutive description. Therefore, at these strain-rates, dynamic hardness can effectively characterize a material's strain-rate sensitivity, provided its viscoplastic constitutive description is known beforehand. However, above the critical indentation strain-rate, the dynamic hardness increases rapidly with indentation strain-rate. This phenomenon indicates an apparent strain-rate sensitivity that exceeds the expected response of the viscoplastic constitutive description. Moreover, above the critical indentation strain-rate, the indentation depth acts as a natural length-scale, with higher hardness observed at greater depths due to increased inertial effects. In other words, above the critical indentation strain-rate, dynamic hardness cannot be taken as an intrinsic material property.