Modelling nano-indentation of ion-irradiated FCC single crystals by strain-gradient crystal plasticity theory

In this work, a strain-gradient crystal plasticity theory with irradiation effect is proposed for the surface nano-indentation of ion-irradiated FCC metals. In order to characterize the indentation size effect and irradiation hardening of ion-irradiated materials indented by the Berkovich indenter, the hardening contributions of geometrically necessary dislocations and non-uniformly distributed defects are incorporated into the classical crystal plasticity theory. The constitutive equations are implemented into ABAQUS through the user material subroutine VUMAT to numerically simulate the surface nano-indentation of ion-irradiated single crystal copper. The theoretical model is calibrated by comparing the numerical results with experimental data. Both the simulated force-depth relationship without irradiation effect and hardness-depth relationship with/without irradiation effect can match well with corresponding experimental data. The dominant features as observed in the nano-indentation of ion-irradiated materials can be effectively characterized by the proposed theoretical framework, which include the indentation size effect, depth-dependent irradiation hardening, and unirradiated substrate softening effect. Moreover, the evolution of different hardening mechanisms during the surface nano-indentation is systematically analyzed to help understand the macroscopic deformation behavior.