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Crystal Plasticity of Single Crystal and Film on Substrate Probed by Nano-indentation: Simulations and Experiments

  • Sinh Vu-Hoang (a1), Guillaume Parry (a1) and Marc Verdier (a1)

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.

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[1]Feng, G., Budiman, A.S., Nix, W.D., Tamura, N. and Patel, J. R., Indentation size effects in single crystal copper as revealed by x-ray microdiffraction, Journal of Applied Physics, 104 (2008) 043501.
[2]Casals, O. and Forest, S., finite element crystal plasticity analysis of spherical indentation in bulk single crystals and coatings, Computational Materials Science 45 (2009) 774782
[3]Verdier, M., Chang, H.J., Fivel, M.: Indentation Crystal Plasticity: Experiments and Multiscale Simulations, in Mechanical Behavior at Small Scales — Experiments and Modeling, edited by Lou, J., Lilleodden, E., Boyce, B., Lu, L., Derlet, P.M., Weygand, D., Li, J., Uchic, M.D., Le Bourhis, E. (Mater. Res. Soc. Symp. Proc. Vol. 1224, Warrendale, PA, 2010), 1224-GG02-05.
[4]Kocks, U.F., Mecking, H., Physics and phenomenology of strain hardening: the FCC case, Prog. Mat. Sci. 48 (2003) 171273.
[5]Huang, Y., A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program, Mech Report, Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, 1991.
[6]Tabourot, L., Fivel, M., Rauch, E., Generalised constitutive laws for f.c.c. single crystals, Mater. Sci. Eng. A, 234-236 (1997), 639642.
[7]Chang, H.Y., Analysis of Nano indentation Size effect based on Dislocation Dynamics and Crystal Plasticity, PhD thesiss, Institut National Polytechnique de Grenoble, France, 2009.
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  • EISSN: 1946-4274
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