Mechanics and geometry of indentation

The first section involves a general description of the mechanics and geometry of indentation with regard to prevailing mechanisms. The experimental details of the hardness measurement are outlined. The tendency of polymers to creep under the indenter during hardness measurement is commented. Hardness predicitions of model polymer lattices are discussed. The deformation mechanism of lamellar structures are discussed in the light of current models of plastic deformation. Calculations... 

Another largely unexplored area is the change of dynamics due to the influence of the surface. The dynamic behavior of a latex suspension as a model system for Brownian particles is determined by photon correlation spectroscopy in evanescent wave geometry [130] and reported to differ strongly from the bulk. Little information is available on surface motion and relaxation phenomena of polymers [10, 131]. The softening at the surface of polymer thin films is measured by a mechanical nano-indentation technique [132], where the applied force and the path during the penetration of a thin needle into the surface is carefully determined. Thus the structure, conformation and dynamics of polymer molecules at the free surface is still very much unexplored and only few specific examples have been reported in the literature. 

The development of indentation fracture mechanics has also allowed fracture toughness to be determined using indentation cracks. Indeed, the ease with which these cracks can be introduced and the simple specimen preparation involved has popularized this approach. Moreover, it has allowed crack behavior to be studied for cracks in a size range that is close to that found in practice. There are two main approaches for determining fracture toughness from indentation cracks. In the first approach, the size of the radial cracks that emanate from the hardness impression are measured. It is recognized that the parameter x depends on the elastic properties of the indented material. It has been proposed that x=P E H), where )8 is a constant that depends only on the indenter geometry and H is hardness. Equation (8.64) can, therefore, be written as... 

Force-Curves Measurements In force curve measurements, a vertical displacement of the sample, z, is imposed and the subsequent tip displacement, d, is measured. The tip-sample interaction force, F, is deduced by means of the Hooke s relation, F = -kcd, where is the cantilever stiffness. Force curves arc generally divided into different regions (7). If the part where the electrostatic repulsion forces are dominant is only considered, with silicon tips much stiffer than polymers, tips penetrate the sample surface and an indentation depth, 5, equal to Z d, can be measured. The lower the sample elastic modulus, the greater will be the indentation depth. By using the Hertz mechanical model adapted to the geometry of the tip-sample system (8,9) surface elastic modulus could be deduced from the following equations corresponding respectively to a spherical, a paraboloid and a conical tip ... 

Abstract This chapter gives a brief description of special mechanical tests for various types of materials and sample geometries, such as blister tests for membranes/adhesives/coatings, tensile tests and shear tests for sealants/foam adhesives, indentation and scratch tests for coatings, tack tests for pressure-sensitive adhesives (PSAs), and bimaterial curvature tests for characterizing residual stress, stress-free temperature (SFT), and coefficient of thermal expansion (CTE) of adhesives bonded to substrates of interest. In addition, some applications of these tests, including the nano-/micrometric scale, are also described in this chapter. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

From a more fundamental point of view, the selection of different inden-ter geometries and loading conditions offer the possibility of exploring the viscoelastic/viscoplastic response and brittle failure mechanisms over a wide range of strain and strain rates. The relationship between imposed contact strain and indenter geometry has been quite well established for normal indentation. In the case of a conical or pyramidal indenter, the mean contact strain is usually considered to depend on the contact slope, 0 (Fig. 2a). For metals, Tabor [32] has established that the mean strain is about 0.2 tanG, i.e. independent of the indentation depth. A similar relationship seems to hold for polymers although there is some indication that the proportionality could be lower than 0.2 for viscoelastic materials [33,34], In the case of a sphere, an... 

The technological advances and the recent researches provide new alternatives for manufacturing processes based on conventional processes [1], This paper studies the indentation process from the point of view of manufacturing. There are a variety of studies on the indentation process. However in most of them, indentation is used to obtain mechanical properties of the material such as hardness [2, 3, 4], In the present study, the indentation process is analyzed as a unitary compression process [5], This unitary operation studies the influence of technological parameters such as the friction and the workpiece geometry [6],... 

AFM has become the method of choice for measuring cellular elasticity. Harris and Charras et al. [8] have shown that in AFM elasticity measurements, experimental force-indentation curves are analyzed using contact mechanics models that infer the tip-cell contact area from the tip geometry and indentation depth. However, values of cellular elasticity reported in AFM measurements are large compared to those reported by other methods, and measurements affected using spherical tips give significantly lower elasticity than pyramidal tips [8]. 

With these complications in mind, research in this area has blossomed rapidly. Two main foci of research in this area are on (1) how external conditions (such as levels of loadings, the use of different indenters, and scratch rate) and (2) intrinsic materials properties (such as modulus and crystallinity) affect the tribological behaviors of the polymers. Apart from examining the scratch resistance of polymers, a closely related quantity which is of interest would be changes in coefficient of friction. Studies relating mechanical properties (3-5,9,36,71,75,76), deformation patterns (18,33,63,71,77-81), fabrication process (3,5,35,72,77,82-86) with respect to experimental parameters, snch as temperature (18), loading effect (24,71,72,87-96), indenter geometry (21,33,75,82,95,97), and scratch velocity (21,56,57,59,64,65,96,98) have been carried ont. In addition, scratch maps for different polymers have been produced (32,33), and various scratch resistance properties estimated (33,37,56,58,59,99). 

For depth-sensing nanoindentation, a controlled, variable force is applied to a sample by the indenter and the resulting displacement of the indenter is measured. The resulting load vs. displacement data, together with the indenter geometry, can be analyzed to obtain hardness and elastic modulus using well established mechanical models (14). The simultaneous measurement of load and displacement also allows study of creep (time dependent strain response due to a step change in stress) (15,16). 

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