Indentation elastic

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. 

Elastic indentation modulus Ell Er Ej 77 dF 2 Calculated from the slope of the tangent to the unloading curve at maximum load. 

FIGURE 4.25 Force versus displacement curves on PNiPAAm gel in pure water at 10 and 35°C and on mica in pure water at room temperature. The same z-piezo displacement results in a smaller cantilever deflection on the soft gel surface in comparison with the hard mica sample because of elastic indentation. Source Matzelle et al. [55]. Reproduced with permission of American Chemical Society. 

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... 

Figure 1337 Schematic comparison of the brittle-ductile temperature transition in four different tests ( ) Hertzian indentation (lower transition), (2) plastic-elastic indentation (upper transition), (3) Double cantilever beam (lower transition) and (4) notched bar (upper transition). (Reproduced from Puttick, K.E. (1980) The correlation of fracture transitions. ). Phys. D, 13, 2249. Copyright (1980) Institute of Physics.)...

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. 

Many types of hardness tests have been devised. The most common in use are the static indentation tests, eg, Brinell, Rockwell, and Vickers. Dynamic hardness tests involve the elastic response or rebound of a dropped indenter, eg, Scleroscope (Table 1). The approximate relationships among the various hardness tests are given in Table 2. 

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. 

Because the indentation varies with time, the modulus must be specified for a certain indentation time, eg, a 10-s modulus. The Hertz equation holds only for purely elastic materials. However, it has been appHed to viscoelastic materials, including polymers and coatings, with excellent results (249—256). Indentation hardness vs temperature curves are shown in Figure 40 (249,251). 

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. 

Fig. 9. (a) Depth-sensing nanoindenter model and (b) simple mechanical model for force controlled indentation assuming purely elastic contact mechanics. 

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). 

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. 

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