Physical-based Nano Indentation Simulation of Single Crystals

Abstract

In this article, a loading process of the micro/Nano-indentation test is simulated based on physical plasticity. The total energy of process is obtained by evaluating different terms such as dislocations density energy, energy caused by contact of indenter to the material and other terms of classic mechanic’s. The physical domain of region beneath the indenter is mapped to a unit cubic domain as a computational domain by using a homographic mapping formulation. For the first time by using the principle of minimum energy differential equations of the micro-indentation process is evaluated for a FCC crystal. Three main coupled differential equations, twelve necessary robin boundary conditions and eight physical boundary conditions are solved by using a generalized differential quadrature method based on the Gauss-Chebyshev-Lobato polynomials. It is seen that the applied method is more efficient and gets closer results to experiments. Finally, material behavior to different conical angles of indenter for the FCC crystal is compared.