Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale

Constitutive laws are critical in the investigation of mechanical behavior of single crystal or polycrystalline materials in applications spanning from microscale to macroscale. In this investigation, a combined FEM simulation and experimental nanoindentation approach was taken to determine the mechanical behavior of single crystal copper incorporating the mesoplastic constitutive model. This model was implemented in a user-defined subroutine in 3D ABAQUS/Explicit code. Nanoindentation was modeled using the multiscale modeling technique involving mesoplasticity and elasticity, i.e., mesoplastic constitutive model was used near the local nanoindentation region (where the dislocations are generated) while elastic constitutive model was used in rest of the region in the workmaterial. The meso-mechanical behavior of the crystalline structure and the effect of the mesoplastic parameters on the nanoindentation load–displacement relationships were investigated in the FEM analysis. Nanoindentation tests were conducted on single crystal copper to determine load–displacement relationships. Appropriate mesoplastic parameters were determined by fitting the simulated load–displacement curves to the experimental data. The mesoplastic model, with appropriate parameters, was then used to determine the stress–strain relationship of a single crystal copper at meso-scale. The effect of indenter radius (3.4–1000μm) on material hardness under nanoindentation was simulated and found to match the experimental data for several indenter radii (3.4, 10 and 500μm). A comparison of the topographies of nanoindentation impressions in the experiments with FEM results showed a reasonably good agreement.