Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation

Abstract

The evolution of the plastic zone underneath the indenter is challenging to be described during nanoindentation, which is recently known to be crucial to establish a constitutive model that features the plastic properties of the substrate materials based on their indentation responses. Using molecular dynamics and axisymmetric finite element (FE) simulations in this study, we show that the plastic zone shape in the elastoplastic materials is hemispherical in a broad range of length scales under a three-sided pyramid-shaped Berkovich indenter. By considering the critical factors of the applied load–penetration depth (P–h) curve, dimensional analysis is performed to derive dimensionless functions regarding the radius of the hemispherical plastic zone. For the loading and unloading stages in extensive FE simulations, a set of polynomial functions are proposed by associating the instantaneous and residual plastic zone radii with constitutive parameters. In addition to Young's modulus and the hardening exponent, the ratio of the representative stress to the reduced modulus is found to be crucial for predicting the plastic deformation. Lastly, the proposed dimensionless function reveals that the plastic zone radii are drastically different for three representative materials with identical P–h curves as confirmed by three independent methods. This result suggests that the proposed plastic zone radius in the dimensionless analysis helps to overcome the challenging uniqueness issue for decades to determine the unique elastoplastic properties of materials based on nanoindentation responses.