Indentation experiment

Perhaps the most significant complication in the interpretation of nanoscale adhesion and mechanical properties measurements is the fact that the contact sizes are below the optical limit ( 1 t,im). Macroscopic adhesion studies and mechanical property measurements often rely on optical observations of the contact, and many of the contact mechanics models are formulated around direct measurement of the contact area or radius as a function of experimentally controlled parameters, such as load or displacement. In studies of colloids, scanning electron microscopy (SEM) has been used to view particle/surface contact sizes from the side to measure contact radius [3]. However, such a configuration is not easily employed in AFM and nanoindentation studies, and undesirable surface interactions from charging or contamination may arise. For adhesion studies (e.g. Johnson-Kendall-Roberts (JKR) [4] and probe-tack tests [5,6]), the probe/sample contact area is monitored as a function of load or displacement. This allows evaluation of load/area or even stress/strain response [7] as well as comparison to and development of contact mechanics theories. Area measurements are also important in traditional indentation experiments, where hardness is determined by measuring the residual contact area of the deformation optically [8J. For micro- and nanoscale studies, the dimensions of both the contact and residual deformation (if any) are below the optical limit. 

Fig. 3. (a) Illustration of various AFM cantilever configurations for indentation experiments and (b) simple mechanical model for AFM-based indentation (by sample displacement). 

Oliver, W.C. and Pharr, G.M., An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res.,1, 1564-1583 (1992). 

Oliver, W. C., and Pharr, G. M., An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, J. Mater. Res., Vol. 7,1992, pp. 1564-1583. 

Complementary to the indentation experiments, the lateral force microscope has been introduced to measure lateral forces exerted on the tip [388]. Somewhat latter, different modifications of contact-mode SFM have been developed to investigate indentation and wear in thin films [ 115]. On the lateral force measurement, one has to distinguish between operation at very small lateral displacements of the cantilever when the shear forces dominate in the net force, and a... 

Johnson, K.L. (1970), The correlation of indentation experiments , Journal of Mechanics and Physics of Solids, 18, 115-126. 

In a typical indentation experiment the indenter is pressed onto the surface under investigation and the load is successively increased up to a certain maximum load. In the so-called compliance approach both load and indenter displacement are recorded and plotted as a load-displacement curve, the so-called compliance curve. If the experiment is exclusively run in the compressive load regime, the curve is also referred to as the load-penetration curve. Upon loading, elastic deformations occur succeeded by plastic ones. Upon releasing the imposed stress, elastic strain recovers immediately. 

In analogy to indentation experiments, measurements of the lateral contact stiffness were used for determining the contact radius [114]. For achieving this, the finite stiffness of tip and cantilever have to be taken into account, which imposes considerable calibration issues. The lateral stiffness of the tip was determined by means of a finite element simulation [143]. As noted by Dedkov [95], the agreement of the experimental friction-load curves of Carpick et al. [115] with the JKR model is rather unexpected when considering the low value of the transition parameter A(0.2Further work seems to be necessary in order to clarify the limits of validity of the particular contact mechanics models, especially with regard to nanoscale contacts. 

Contact problems have their origins in the works of Hertz (1881) and Boussinesq (1885) on elastic materials. Indentation problems are an important subset of contact problems (17,18). The assessment of mechanical properties of materials by means of indentation experiments is an important issue in polymer physics. One of the simplest pieces of equipment used in the experiments is the scleroscope, in which a rigid metallic ball indents the surface of the material. To gain some insight into this problem, we consider the simple case of a flat circular cylindrical indentor, which presents a relatively simple solution. This problem is also interesting from the point of view of soil mechanics, particularly in the theory of the safety of foundations. In fact, the impacting cylinder can be considered to represent a circular pillar and the viscoelastic medium the solid upon which it rests. 

These data indicate that, under certain circumstances, the limitations of AFM indentation experiments have to carefully considered. This is particularly true, if quantitative data are sought. 

Schall et al. indented colloidal crystals using a needle with an almost hemispherical tip of diameter 40 dm, inducing a strain field in which tine maximum shear strain lies well below the contact surface. The tip diameter, particle radius and crystal thickness in their experiments were chosen to be similar to parameters in typical metallic nano-indentation experiments. The authors discussed their observations using a model that addresses the role played by thermal fluctuations in the nucleation and growth of dislocations. 

Figure 10.36 (a) The indentation of a thin film. The indentation area and depth will depend on the properties of the indenter and the substrate as well as the film being tested, (b) Schematic unloading curve for a nano-indentation experiment. Adapted from G.M. Pharr and W.C. Oliver, 1992, Measurement of Thin Film Mechanical Properties Using Nano-indentation , Materials Research Society Bulletin XVII (July) 28... 

Typical load-displacement curves obtained from instrumented indentation experiments are shown in Figure 39.13b. Results are shown for silica E = 72 GPa, v = 0.2) and polystyrene (PS, E = 2 GPa, V = 0.4). The load-displacement curve for PDMS E = 1.5 MPa, v 0.5) involve forces that are too low to appear on the scale used in Figure 39.13b, due to the fact its elastic modulus is three orders of magnitude lower than polystyrene. 

Lawn, B. and Wilshaw, T.R. (1975) Indentation fracture— principles and applications, J. Mater. Sci. 10, 1049. The paper that showed how to derive Ki from indenter experiments. 

A scanning force instrument also allows for the acquisition of force-distance curves to characterize the local mechanical properties of the sample. Well-defined indentation experiments on soft surfaces like swollen hydrogels in aqueous media are possible with the colloidal probe technique. Raw data are assessed, for example, according to the Hertz model, with the assumption... 

FIGURE 6.9 The dependence of reduced elasticity modulus E obtained in nano indentation experiment on plastic strain for nanocomposites BSR/TC. 

Usually, in such indentation experiments, plastic flow also arises in the substrate under the film as shown in Fig. 14.20(b). This has been analyzed by Swain and his colleagues." As the indenter was pressed into the surface, ring cracks were observed just outside the indenter contact region. Sometimes radial cracks were also seen in the film." Subsequently, the substrate was pushed down... 

This paper describes an indentation experiment to investigate in vivo the bulk mechanical properties of the composite of skin and underlying tissues on the anterior aspects of human forearms and thighs by applying constant pressures. Significant variations in tissue stiffness with sex, age and body site were also demonstrated. 

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