Simulation of micro-indentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity

The size effect observed in the micro-indentation of FCC single crystal copper is modelled by the employment of mechanism-based strain gradient crystal plasticity (MSG-CP). The total slip resistance in each active system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. The MSG-CP constitutive model is implemented into the Abaqus/Standard FE platform by developing the User MATerial subroutine UMAT. The simulation of micro-indentation hardness on (0 0 1) and (1 1 1) single crystal copper, with a conical indenter having a sharp tip, a conical indenter with a spherical tip and a three-sided Berkovich indenter, is undertaken. The phenomena of pile-up and sink-in have been observed in the simulation and dealt with by appropriate use of the contact analysis function in Abaqus. These phenomena have been taken into account in the determination of the contact areas and hence the average indentation depth for anisotropic single crystals. The depth dependence of the micro-indentation hardness, the size effect, is calculated. The micro-hardness results from the simulation are compared with those of the published experimental ones in the literature and a good agreement is found.