Papers

ICMCTF2010 Session E2-1: Mechanical Properties and Adhesion

Tuesday, April 27, 2010 8:00 AM in Room Pacific Salon 1

Tuesday Morning

Start	Invited?	Item
8:00 AM		E2-1-1 Strength: Size Matters in 1, 2 and 3 D William Gerberich, A.R. Beaber, L.M Hale, D.D. Stauffer (University of Minnesota) The fact that size matters for the strength of films, wires or pillars, and spheres is now well documented. Due to crystallography, microstructure or confinement, the reasons may vary. Confinement models may depend upon grain size or second effects which limits exhaustion of nucleation sites and the crystallography of BCC or FCC may be factors as well. Here, we consider mainly one system, silicon single crystals, and focus on the confinement issue. Considering contact mechanics, such as nanoindentation of thin films, the constraint between hard contacts and hard substrates leads to Taylor (forest dislocation) hardening of thin soft Au films. This gives a (1/h)1/2 length scale dependency for films in the 100 to 400nm thickness (h) range. For silicon pillars small in 2D, Taylor hardening is clearly inappropriate and the competition between exhaustion hardening and linear hardening remains unclear. Most work has considered silicon single crystal nanospheres in the 40 nm to 400 nm diameter (d) range. These spheres small in 3D follow a linear hardening model with strength proportional to (1/d). Regarding the controlling mechanism, this is dislocation nucleation with small activation volumes in the 2 to 10 b3 range. Resulting contact flow stresses approach 50 Gpa.
8:40 AM		E2-1-3 Some Unpleasant Truth About Dynamic/Oscillatory Indentation Measurement Procedures Norbert Schwarzer (Saxonian Institute of Surface Mechanics, Germany) The dynamic / oscillatory indentation method, where a supposedly small oscillation is superposed to the ordinary loading circle of an indentation experiment, is a widely used tool for the detection of internal surface respectively coating structures. Meaning, wherever there is suspicion that a coating is not homogeneous it was suggested to apply this method in order to find and analyze such an internal structure. However, little is known about the many flaws of this method leading to virtual structures where there was homogeneity in reality or giving completely wrong structural information where there is an internal structure. Depending on the example in question the deviation from the truth can be rather dramatic. The author will not only present and discuss these flaws but also show a few “every day examples” where the dynamic / oscillatory indentation method leads to severe misinterpretation.
9:00 AM		E2-1-4 On Hall-Petch Strengthening Below 10 nm Grain Size Alan Jankowski (Texas Tech University) The activity of dislocations provides the basis for the Hall-Petch mechanism of strengthening in crystalline materials. The loss of dislocation activity is routinely suggested as the domain size decreases below 10 nm wherein a transition occurs from an intra-granular dislocation-based behavior to an inter-granular boundary motion. A consequence is that Hall-Petch strengthening will be lost with further decrease in grain size. This transition in deformation behavior is dependent on the disorder found in the inter-granular boundaries as seen in the increasing role of triple junctions. However, the nature of the structural disorder in the boundary influences the deformation mechanism that results, and the change in strength that occurs with further decrease in domain size below 10 nm. We now examine the interplay between Hall-Petch type behavior for grain sizes below 10 nm, and those changes related to the activation volume for deformation. It can be derived from the consideration of plastic deformation as a thermally activated process, that a linear relationship should exist between the experimentally determined parameters of “dⁿ/m” and “v”. In the first parameter, the domain (i.e. grain) size (d) is raised to an exponent (n) and divided by the strain-rate sensitivity exponent (m). The n represents the power law fit of strength with domain size. For the case of Hall-Petch behavior, n equals negative one-half. The exponent (m) to the power law fit between the strength and strain rate represents the strain-rate sensitivity. The second parameter “v” is the activation volume for deformation that can be determined by a linear fit to the logarithmic change in strain rate with linear change in stress as the activation energy is a strong function of stress. Since these individual parametric components can be experimentally measured without an a priori assumption to value of the exponent n, an evaluation of Hall-Petch strengthening can be independently made for material behavior as it extends for grain sizes down to a few nanometers. The mechanical properties of electrodeposited nanocrystalline alloys are now assessed with regards to the behavior of the experimentally measured strain-rate sensitivity exponent (m) and activation volume (v*) for grain sizes (d) as small as 4 nm – a nanoscale regime that has here-to-fore gone without detailed examination. It is found from micro-scratch measurements that hardness (hence strength) approaches ideal values as the grain size decreases to 7 nm. Thereafter, softening in strength and departure from Hall-Petch behavior can be related to an increase in the activation volume for deformation as grain size decreases further.
9:20 AM		E2-1-5 The Effect of Microstructure on the Mechanical Properties of Submicron Thin Films and Nanostructured Devices Steve Bull (Newcastle University, United Kingdom) The manufacture of mechanical devices such as MEMS from thin films can lead to circumstances where the scale of the mechanical deformation induced by device operation is comparable to the scale of the microstructure of the materials from which they are made. A similar observation occurs when using indentation tests to assess the properties of thin films where the plastic zone dimensions may be comparable to the grain size. For the purposes of design based on continuum mechanics approaches it is usually required that the grain size is very much smaller than the deforming volume which is not always observed in practice. Considerable differences between predicted and observed performance can be seen depending on the material tested and its grain size. This presentation will highlight the effect of grain size, shape and orientation on the mechanical response of metallic thin films used as protective coatings and for semiconductor metallisation. The conditions under which continuum mechanics may be used successfully will be discussed and the effect of crystallographic anisotropy on the choice of appropriate design data will be highlighted for copper and zinc coatings.
9:40 AM		E2-1-6 The Effect of Surface Roughness on Nanoindentation of Hard Coatings: Simulation and Experiment Claudia Walter, Christian Mitterer (Montanuniversität Leoben, Austria) In this work finite element modeling (FEM) is applied to investigate the influence of surface roughness on nanoindentation results. Surface roughness may pose a problem when indentation depth is limited e.g. for the indentation of thin films. It causes scatter of the measured data and makes it difficult to evaluate reliable mechanical properties from the measured load-displacement data. Indentation with spherical indenter tips of CrN thin films with an arithmetic surface roughness Ra measured by atomic force microscopy of 3, 5, and 11 nm is investigated. Here, the different Ra values arise from differences in asperity height as well as different lateral extensions of the asperities. Additionally, artificial surface topographies are investigated by simulation, where only the vertical dimension of the asperities has been changed. Load-displacement curves have been generated for these samples by experimental measurement, 2-D FEM simulations and 3-D FEM simulations. The Oliver and Pharr method is then applied to analyse the load-displacement curves from all three methods. This allows for a critical discussion of the evaluated elastic modulus and its scatter as a function of the surface roughness. A comparison for different indenter radii is also shown. The general trend of lower measured elastic modulus and larger data scatter with increasing surface roughness can be observed by all three methods. This can be explained by the fact that the surface area for the rough coatings can be a factor 2 smaller compared to the case of smooth surfaces in contact under the applied conditions. This will lead to a significant underestimation of the elastic modulus evaluated from the load-displacement data applying the assumption of smooth surfaces in contact. The FEM simulations visualise nicely the real contact area under maximum load. The deviation from the true elastic modulus increases with increasing roughness values. It is also shown that a full 3-D simulation is needed, while a 2-D axisymmetric approach is not sufficient to capture the contact conditions adequately. Surface profiles will be represented as an assembly of concentric rings in the 2-D model, while the 3-D model captures the complete topography resulting in a large number of randomly distributed asperity tips in contact with the indenter. Visualized with FEM it becomes intuitive to understand that the concentric-ring setup will give artificial stiffness and scatter.
10:00 AM		E2-1-7 Size Effects in Ceramics - The influence of Yield Stress on the Effect of Size Sandra Korte, Robert Stearn, William Clegg (University of Cambridge, United Kingdom) Size effects are commonly observed in mechanical tests at the micrometer scale. Extensive experimental work has been reported in the literature describing size effects in soft metals where the yield or flow stress at the micron scale is related to the specimen dimensions by a relation of the form τ~d^-0.6. Experiments on harder materials such as bcc metals or semiconductors have shown that the size effect is less pronounced in these materials, but in contrast to fcc metals little data is available in the literature. This paper presents experimental data obtained on a wide range of materials in order to identify the relationship between bulk yield stress and magnitude of the size effect. A direct relationship is found implicating that a simple description of the size effect of the form τ=τ₀+Bd^-x is not sufficient and different mechanisms need to be considered if the origin of the effect of size is to be studied for materials other than soft metals.
10:20 AM		E2-1-9 Dimensionality of Plasticity Size Effects- the ‘Thinness’ Effect Nigel Jennett, Xiaodong Hou (National Physical Laboratory, United Kingdom); Rudy Ghisleni, Johann Michler (Empa, Switzerland); Andy Bushby (Queen Mary University of London, United Kingdom) The indentation size effect is now well-established, with many examples in the literature of “smaller being harder.” Strain gradient plasticity has often been used to explain the size effect in indentation and in other loading geometries involving non-uniform deformation. However, it is now clear that a strain gradient is not a necessary condition for size effects. This paper reports spherical nanoindentation data and circular cross-section micro-pillar compression data from the same crystal. Taking the contact pressure in the indentation tests to be 3 times the stress, the magnitude of the size effect is found to be exactly the same in both cases, i.e. with and without a plastic strain gradient. These two results can, however, be fitted by a slip distance model using the same set of material parameters and very few assumptions. In both cases the slip distance can be represented by a single value due to axisymmetry. The slip distance model is based on the principle that plasticity in small structures requires small radius indentation loops, which take more strain energy to form; resulting in higher yield stresses. One way to investigate this theory further is to determine the dimensionality of plasticity size effects by looking at non-axisymmetric structures. Therefore, a series of tungsten micro-pillars with different geometries, ranging from square pillars to rectangular ‘walls,’ were compressed in a Nanoindenter and dimensionally characterised in an SEM. This clearly showed that the shortest dimension dominated the strength of the pillars, ruling out a surface area to volume effect (suggested by dislocation starvation models) and reinforcing the hypothesis that a minimum source size or slip distance is governing behaviour. Yield stress is determined by wall width; the length of the wall making little or no difference. The implication of this is that thin structures exhibit the same enhanced yield strength regardless of total size (volume) or surface to volume ratio; nano-layers are as strong as nanoparticles. This is good news for the surface engineering and coatings communities as it means that thin layers and multilayers may be the most cost effective solution, especially where 3-D dispersion of nano-particles to separate a matrix material into small elements is difficult, or there is resistance, using the precautionary principle, to the use of nano-particles at all.
11:00 AM		E2-1-11 Mechanical Properties Extraction of Bulk Materials and Thin Films Based on Vickers Instrumented Indentation Tests Sara Aida Rodriguez, María Cristina Farias, Roberto Souza (University of São Paulo, Brazil) In this work, the applicability of a new algorithm for the calculation of mechanical properties from instrumented indentation test was studied for thin films with different architectures. The proposed algorithm was based on one previously suggested by Rodríguez et al for Berkovich indentation. In this work, the algorithm coefficients for Vickers indentations on bulk materials were obtained and the proposed algorithm considers the effect of friction at the indenter-specimen contact. The feasibility of the algorithm for thin films was analyzed with the aid of both three-dimensional finite elements simulations and the analysis of experimental indentation tests. The equation coefficients for mechanical properties calculations correspond to the best fit to the simulated data, obtained from the numerical procedure. The numerical approach was also selected to analyze how the calculated mechanical properties of the film were affected by the mechanical properties of the substrate and by the ratio between film thickness and maximum indentation depth l/h_max. The experimental indentation tests were conducted on AISI H13 tool steel specimens, plasma nitrated and coated with thin films of TiN, TiC or TiC-TiN-TiC multi-layers. Although experimental variations, residual stresses and substrate effect limited the capability of mechanical properties estimation, the proposed algorithm allow more accurate calculation of mechanical properties when the value of the ratio of the residual indentation depth to maximum indentation depth h_r/h_max is low and when the strain hardening exponent n is high.
11:20 AM		E2-1-12 Effects of Mechanical Properties, Residual Stress and Indenter Tip Geometry on Instrumented Indentation Data in Thin Films Carlos Mady, Sara Aida Rodriguez, Adriana Gómez, Roberto Souza (University of São Paulo, Brazil) In this work, an axisymmetric two dimensional finite element model was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrate. The indenter was modeled as a rigid cone (half angle of 70.3^o) and two ratios between indenter tip radius and maximum penetration depth (R/h_max) were considered. The level of film residual stress (σ_r), the film elastic modulus (E) and the film work hardening exponent (n) were varied to analyze their effects on instrumented indentation data. Results indicated that all variables (R, σ_r, E, n) have effects on indentation morphology (pile-up and sink-in), on the maximum load necessary to achieve a given penetration depth and on the proportional curvature constant during loading. On the other hand, the load curve exponent was only affected by the indenter tip radius. These numerical results were used to analyze experimental data that were obtained with titanium nitride coated specimens, in which the substrate bias applied during deposition was modified to obtain films with different levels of residual stress. Good qualitative correlation was obtained when numerical and experimental results are compared, as long as all film properties are considered in the analyses, and not only the film residual stress level, due to the influence of all mechanical properties on the results.