Crystal Plasticity of Single Crystal and Film on Substrate Probed by Nano-indentation: Simulations and Experiments
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Crystal Plasticity of Single Crystal and Film on Substrate Probed by Nano-indentation: Simulations and Experiments Sinh Vu-Hoang, Guillaume Parry, Marc Verdier SIMAP, 1130 Rue de la Piscine, F-38402 Saint Martin d’Hères Cedex, FRANCE. ABSTRACT Thin films are the building blocks of small devices technology. The mechanical characterization of layers is a central step for their integration in industrial process. Instrumented indentation is an experimental measurement technique well suited to small scales. In the film on substrate geometry, the deformation pattern during indentation is modified as compared to semi infinite homogenous solid. In this work, the effect of the constrained geometry on the indentation test is investigated on model material: Cu single crystal. The constitutive laws for the materials are based on a crystal plasticity model. This is not a strain gradient model as in [1] since no material length scale is introduced. The approach is similar to [2], except that the hardening is physically based, using dislocations densities on the 12 slip systems of the FCC crystal as internal variables. This modelling strategy gave good quantitative agreements with experiments in the case of various bulk Cu single crystals. It is used here in order to explore the geometry effect due to the finite thickness of elastic-plastic films deposited on elastic substrates. The criteria of comparison between the finite thickness films and the bulk samples are curves of indentation forces and stiffness versus indentation depth on the one hand, surface deformation on the other hand; it is straightforward to get these data from the finite elements simulations and from the atomic force microscopy (AFM). The simulations are compared to experimental data obtained on Cu films deposited on Si and Cu single crystals. INTRODUCTION Nanoindentation is a well suited method for locally evaluating the properties of materials, especially thin films. Nevertheless, the deformation field is non uniform and three-dimensional. Hence, the interpretation of experimental data is difficult, as it involves physical parameters associated to the plastic deformations, as critical shear stresses and hardening parameters. Simulation can be very helpful in order to determine those parameters from experimental data. The aim of the present work is to extend our results [3,7] to the case of micron range thick single crystal film on substrate. In these conditions, a size effect is observed due to the finite film thickness, which is an additional characteristic length to the geometrical problem. The deformation occurs at room temperature (T/Tmelting ~ 0.3), where crystal plasticity is restricted to slip systems {111} in CFC crystals. The two criteria for comparison between simulations and experiments are the loading curves of indentation (load versus depth) and the indentation imprint (“pile up” or “sink-in”) observed with AFM. MODELING The simulations are carried out using the finite element method (ABAQUS software), with a material user subroutine specially ad
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