Measuring, elastic indentation

By determining its resistance to a rigid indentor to which a force is applied, the hardness measurement is obtained, giving the measure of the elastic modulus of the rubber. Hardness may be regarded as depending simply on Young s modulus, as the cured rubber is perfectly elastic. Indentation involves deformation in tension, shear, and compression. 

It is customary to characterize the modulus, stiffness, or hardness of rubbers by measuring their elastic indentation by a rigid die of prescribed size and shape under specified loading conditions. Various nonlinear scales are employed to derive a value of hardness from such measurements (Soden, 1952). Corresponding values of shear modulus G for two common hardness scales are given in Figure 1.18. 

In atomic force microscopy (AFM) indentation measurements, thin films of Ca " -PA gels displayed an apparent elastic modulus of 200 MPa, whereas HCl-PA gels had an elastic modulus of 100 MPa (Fig. 5d) [168]. The mesh size of Ca " -PA gels was calculated according to the MacKintosh model for sterically entangled semiflexible networks. The persistence length and the mesh size were estimated to be 102 and 20 nm, respectively [182]. 

Indentation Measurements. Indentation force measurements utilize the indentation part of a f-d curve (compare Figs. 4 and 5). In the case of a noncom-pliant sample surface, the SFM tip does not indent significantly the sample, and hence the deflection vs piezo position curve in the contact region has a slope of 1.0. For compliant samples, the slope is <1.0 (Fig. 9) and can be used to obtain the elastic modulus of the sample by fitting the measured indentation to a suitable model. Knowledge of the tip shape/geometiy and elastic constants of the tip is required to obtain the desired materials properties. 

By performing a cumbersome integration or by employing dimension analysis, we can come up with the same mean values of the work of elastic indentation as a function of the measured radius, a, of a hole. This free energy excess is proportional to a . The precision of the estimated mean values is within an order of magnitude, or sometimes even within the precision of dimensionless... 

Force-Curves and Force-Modulation Calibration. In figure l(a b), typical force-indentation curves obtained respectively on a rigid ( = 610 MPa) and a soft (E = 27 MPa) polymer are presented. The elastic modulus derived from the analysis of the force-indentation curves is compared to the bulk elastic modulus measured by DMA in figure 1(c). For this analysis, the used tip geometry was adapted to the maximum indentation depth reached during the experiment, Smax- For Smax Rj the spherical geometry was considered while, for Smax the conical one was used. For intermediate values, the paraboloid model was used. 

The elasticity of the skin shell of the pore is always higher than the bulk interior because the elasticity is proportional to the energy density though the total energy stored in the shell may be lower than the entire sphere beyond the critical size. For plastic deformation, the hollow sphere could be tougher than the ideal bulk because of the long-distance effect in the indentation measurement. On the other hand, the thermal stability of the hollow sphere is always lower than the solid sphere [71]. 

The technological importance of thin films in snch areas as semicondnctor devices and sensors has led to a demand for mechanical property infonnation for these systems. Measuring the elastic modnlns for thin films is mnch harder than the corresponding measurement for bnlk samples, since the results obtained by traditional indentation methods are strongly perturbed by the properties of the substrate material. Additionally, the behaviour of the film under conditions of low load, which is necessary for the measnrement of thin-film properties, is strongly inflnenced by surface forces [75]. Since the force microscope is both sensitive to surface forces and has extremely high depth resolntion, it shows considerable promise as a teclnhqne for the mechanical characterization of thin films. 

Hardness is a measure of a material s resistance to deformation. In this article hardness is taken to be the measure of a material s resistance to indentation by a tool or indenter harder than itself This seems a relatively simple concept until mathematical analysis is attempted the elastic, plastic, and elastic recovery properties of a material are involved, making the relationship quite complex. Further complications are introduced by variations in elastic modulus and frictional coefficients. 

A hardness indentation causes both elastic and plastic deformations which activate certain strengthening mechanisms in metals. Dislocations created by the deformation result in strain hardening of metals. Thus the indentation hardness test, which is a measure of resistance to deformation, is affected by the rate of strain hardening. 

Ultrasonic Microhardness. A new microhardness test using ultrasonic vibrations has been developed and offers some advantages over conventional microhardness tests that rely on physical measurement of the remaining indentation size (6). The ultrasonic method uses the DPH diamond indenter under a constant load of 7.8 N (800 gf) or less. The hardness number is derived from a comparison of the natural frequency of the diamond indenter when free or loaded. Knowledge of the modulus of elasticity of the material under test and a smooth surface finish is required. The technique is fast and direct-reading, making it useful for production testing of similarly shaped parts. 

A fully automated microscale indentor known as the Nano Indentor is available from Nano Instmments (257—259). Used with the Berkovich diamond indentor, this system has load and displacement resolutions of 0.3 N and 0.16 nm, respectively. Multiple indentations can be made on one specimen with spatial accuracy of better than 200 nm using a computer controlled sample manipulation table. This allows spatial mapping of mechanical properties. Hardness and elastic modulus are typically measured (259,260) but time-dependent phenomena such as creep and adhesive strength can also be monitored. 

Indentation has been used for over 100 years to determine hardness of materials [8J. For a given indenter geometry (e.g. spherical or pyramidal), hardness is determined by the ratio of the applied load to the projected area of contact, which was determined optically after indentation. For low loads and contacts with small dimensionality (e.g. when indenting thin films or composites), a new way to determine the contact size was needed. Depth-sensing nanoindentation [2] was developed to eliminate the need to visualize the indents, and resulted in the added capability of measuring properties like elastic modulus and creep. 

Although hardness is a somewhat nebulous term, it can be defined in terms of the tensile modulus of elasticity. From a more practical side, it is usually characterized by a combination of three measurable parameters (1) scratch resistance (2) abrasion or mar resistance and (3) indentation under load. To measure scratch resistance or hardness, an approach is where a specimen is moved laterally under a loaded diamond point. The hardness value is expressed as the load divided by the width of the scratch. In other tests, especially in the paint industry, the surface is scratched with lead pencils of different hardnesses. The hardness of the surface is defined by the pencil hardness that first causes a visible scratch. Other tests include a sand-blast spray evaluation. 

The present review shows how the microhardness technique can be used to elucidate the dependence of a variety of local deformational processes upon polymer texture and morphology. Microhardness is a rather elusive quantity, that is really a combination of other mechanical properties. It is most suitably defined in terms of the pyramid indentation test. Hardness is primarily taken as a measure of the irreversible deformation mechanisms which characterize a polymeric material, though it also involves elastic and time dependent effects which depend on microstructural details. In isotropic lamellar polymers a hardness depression from ideal values, due to the finite crystal thickness, occurs. The interlamellar non-crystalline layer introduces an additional weak component which contributes further to a lowering of the hardness value. Annealing effects and chemical etching are shown to produce, on the contrary, a significant hardening of the material. The prevalent mechanisms for plastic deformation are proposed. Anisotropy behaviour for several oriented materials is critically discussed. 

It has been shown that the anisotropy depends on the orientation of the diagonals of indentation relative to the axial direction 14). At least two well defined hardness values for draw ratios A. > 8 emerge. One value (maximum) can be derived from the indentation diagonal parallel to the fibre axis. The second one (minimum) is deduced from the diagonal perpendicular to it. The former value is, in fact, not a physical measure of hardness but responds to an instant elastic recovery of the fibrous network in the draw direction. The latter value defines the plastic component of the oriented material. 

Since the early 1980s, the study of mechanical properties of materials on the nanometre scale has received much attention, as these properties are size dependent. The nanoindentation and nanoscratch are the important techniques for probing mechanical properties of materials in small volumes. Indentation load-displacement data contain a wealth of information. From the load-displacement data, many mechanical properties such as hardness and elastic modulus can be determined. The nanoindenter has also been used to measure the fracture toughness and fatigue properties of ul-... 

The two mechanical properties measured most frequently using indentation techniques are the hardness, H, and the elastic modulus, E. A t5pical load-displacement curve of an elastic-plastic sample during and after indentation is presented in Fig. 30, which also serves to define some of the experimental quantities involved in the measurement. 

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