Inertial effect on dynamic hardness and apparent strain-rate sensitivity of ductile materials Articles uri icon

publication date

  • November 2023

volume

  • 180

International Standard Serial Number (ISSN)

  • 0022-5096

Electronic International Standard Serial Number (EISSN)

  • 1873-4782

abstract

  • 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.

keywords

  • constitutive behavior; dynamic cavity expansion; dynamics; elastic-viscoplastic material; finite elements; indentation and hardness