ICMCTF2007 Session E2-3: Mechanical Properties and Adhesion

Nanoindentation is widely accepted as the preferred technique to study localized mechanical deformation phenomena in materials. However, the mechanisms of deformation can only be inferred from the load-displacement data obtained during a typical instrumented nanoindentation test. In order to elucidate the underlying physics of these process, we have developed and exploited a new technique, that of in-situ nanoindentation in a transmission electron microscope (TEM). In this technique, a voltage-actuated piezoceramic tube is used to position a sharp diamond in-plane with the edge of an electron transparent sample. The tip is then driven into the material using a three-plate capacitive transducer which allows direct measurement of load and displacement data to be recorded concomitant with real time images of the indentation response of the material. In this paper we will briefly review the details of our experimental technique, as well as summarize our result from aluminum thin metal films. We have found that the onset of plasticity in these materials does not occur via sub-surface nucleation of dislocations at the point of ultimate strength, but is rather induced by surface forces.¹ Detailed studies of grain boundary motion and grain size effects have shown that indentation loading conditions result in stress-induced coalescence, and thus grain growth.^2,3

¹A.M. Minor, A.M. Minor, S.A. Syed Asif, Z.W. Shan, E.A. Stach, E. Cyrankowski, T. Wyrobek and O. Warren, Nat. Mat., 5, 697, 2006.

²A.M. Minor, E.T. Lilleodden, E.A. Stach and J.W. Morris, Jr., J. Elect. Mat., 31 (10), 958, 2002.

³M. Jin, A.M. Minor, E.A. Stach and J.W. Morris, Jr., Acta Mat. 52(18), 5381, 2004.

Reliability of MEMS devices can be limited by stiction forces that develop in use. It is desirable to alter the mechanical and interfacial behaviour of the silicon surfaces and this can be done by the application of thin (10-100 nm), low surface energy and low stress coatings. The closed field unbalanced magnetron sputtering deposition process (CFUBMS) is capable of producing dense, low stress coatings. Optimisation of the performance of sub-100 nm coatings by CFUBMS is made possible by recent advances in nanotribological (nano-scratch and nano-wear) and nanomechanical (nanoindentation) test methods in a commercial instrument. The CFUBMS thin films did not undergo stress-related delamination that can occur behind the moving probe during nano-scratching of thicker, more stressed films. Nanowear results correlate with nano-scratch critical loads. High resolution nanoindentation can be used to probe thin film mechanical properties at depths ~ 5 nm. A novel nanoscale reciprocating wear technique (Nano-fretting[TM]) was found to have potential for evaluating local fatigue performance of ultra-thin coatings. The deposition of <100 nm films on Si appears to be a promising strategy for improving reliability of Si-based MEMS devices [1].

[1] Funding from the UK Department of Trade and Industry - BTIA Programme - Project CHBL/C/019/00024 is acknowledged.

The analysis of nanoindentation data always requires physical models allowing the extraction of mechanical coating parameters. Only the model chosen appropriate to the experimental set up assures high quality and correct parameter identification. Thus, the paper will treat the following topics:

- Limits of the Hertzian and the extended Hertzian theory for blunt indenters with respect to the mechanical and geometrical parameters of layered materials.

- Limits of the concept of the effectively shaped indenter in connection with the extended Hertzian theory.

- How to extract mechanical coating parameters from the effective half space values classical procedures like Oliver and Pharr do provide?

- Normal and lateral minima for the sample size in dependence on the Young's moduli of the layered structure.

- Normal, lateral, rotating and tilting loads for the next generation of nanoindenters.

The effect of the surface roughness on nanoindentation results was investigated instancing a series of CrN thin films deposited by unbalanced magnetron sputtering. The arithmetic roughness (R_a) of the films ranged between 2 and 10 nm and was measured by atomic force microscopy (AFM). The measured surface topography was incorporated into a finite element model, which allowed to simulate the indentation of an axisymmetric sample by a rigid spherical indenter. At the applied load of 15 mN it was found that plastic deformation could be neglected and thus purely elastic material behaviour was assumed. For roughness values of R_a = 2, 5, and 10 nm a number of 100 indents each were simulated. Subsequently, the software Elastica was used to evaluate Young's modulus of the CrN thin films from the simulated load-displacement curves.

Under the applied conditions, which should be representative for a wide range of magnetron sputtered thin films, the increasing roughness causes a reduction of the contact area and leads to an underestimation of Young's modulus. The mean Young's modulus of all simulated indents on the rough surfaces lies 8-14 % below the Young's modulus determined for a perfectly smooth surface. This deviation seems to be independent of R_a, although the data scatter increases significantly with increasing roughness. Additionally an influence of the lateral extension of the surface texture on the data scatter was observed which is not accounted for in roughness measures such as R_a.

In this paper, limiting factors for contact modelling of layered materials using finite element solutions are presented. Finite element calculations are frequently used as an established and trusted method for mechanical contact analyses. Additionally, several commercial contact models are available. One has to note that a fundamental problem is attributed to the normal and lateral domain boundaries of the finite element model. On the one hand, it is necessary to reduce the CPU time by a properly chosen mesh size. On the other hand, a decrease of the model size results in a systematic deviation due to the boundaries.

The underlying parameters, which influence the finite element results of the elastic stress field, are identified based on comparison to the complete analytical solution of layered materials. Therefore, layered systems have been studied having different elastic moduli and film thicknesses. Secondly, the influence of the normal and lateral dimensions of the finite element model on the contact solution has been considered. It was found, e.g. that the elastic modulus configuration of layer and substrate leads to a dramatic deviation of the resulting finite element contact force from the analytical solution under certain conditions. These deviations are enhanced or extenuated by the varying geometry parameters of the film and model, respectively. Based on these results, empirical relations for a properly sized finite element model will be given. This should help to improve mechanical contact solution using finite models for samples, which in reality can be rather considered as infinite half spaces.

Recently, a developed FEM-supported method enabled the continuous simulation of nanoindentation and based on that a stepwise determination of materials' stress-strain laws. Furthermore, an accurate description of the contact geometry between the material and the indenter during its penetration into the tested specimen, as well as of the remaining impression were possible.

Various materials such as coatings, Silicon (100), glass BK7, fused silica, tungsten, steels, etc. were tested by the previous methods and the results were used to establish the materials' stress-strain characteristics and the indenter area functions. Additionally, load versus displacement diagrams were calculated by appropriately developed FEM-based algorithms considering spherical indenter tip geometries along with various radii.

In ISO 14577, various indenter tip calibration procedures are proposed for determining the indenter area functions, based on either the Young's modulus or the hardness of reference materials. The indenter calibration procedure, based on the hardness of a reference material, led almost to the same indenter surface area versus the contact depth, as the one determined by the developed FEM-supported algorithm. The indenter surface area functions established by the indenter calibration procedure based on the Young's modulus of a reference material, are deviating from the FEM calculated ones. On the other hand, taking into account spherical indenter tip geometries did not lead to a convergence with the experimental results.