Indentation hardness area measured

Most instmments make use of a probe geometry which gives an increasing area of contact as penetration proceeds. In this way, at some depth of penetration, the resisting force can become sufficient to balance the appHed force on the indentor. Unfortunately, many geometries, eg, diamonds, pyramids, and cones, do not permit the calculation of basic viscoelastic quantities from the results. Penetrometers of this type include the Pfund, Rockwell, Tukon, and Buchholz testers, used to measure indentation hardness which is dependent on modulus. 

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. 

Indentation studies on different polymeric materials suggest that the hardness values derived from continuous depth-sensing recording compare fairly well with the hardness numbers derived from the direct measurement of the size of indentation (35,43,44). This result suggests that hardness numbers determined from the contact area imder load are comparable to post-indentation hardness values. 

The actual trend in hardness testing is to use the nanoindentation instruments in conjimction with atomic force microscopes (45). Load-displacement measurements are used to derive hardness and elastic modulus data while the atomic force microscope yields additional topographic information of the indentation area. Measurements at depths of 1 nm can be performed. 

Scratch Hardness. One of the more commonly used scratch resistance measures is the so-called scratch hardness (10,21,54). This is a concept borrowed from static indentation Hardness. Like indentation hardness, scratch hardness is often a measure of force experienced by the sample per unit area. The frequently used deflnitions for scratch hardness, Hs, and ploughing hardness, Hp, are given in Reference (10) ... 

Hardness measures the plastic resistance of a surface to contact loading, that is, its resistance to permanent deformation. Most experiments are carried out using a Vickers diamond pyramid. When a Vickers diamond (four-sided) pyramid is loaded over the plastic threshold, one can determine, after the test, the mean pressure or hardness FI defined by the ratio between the applied load and the projected surface Ap of the permanent deformation left by the indenter. This area can be determined from the mark diagonals (Ap = 2a, a half the mean size of the diagonal Figure 8.10) observed under elevated loads by means of optical microscopy. Hardness is... 

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. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

The Vickers hardness measurement uses a square based pyramid of about 100 pm height as the indenter. The included angles between opposite faces are a = 136°. This corresponds to the tangential angle of an ideal ball impression, considered to have a diameter equal to 0.375 times that of the ball1 . The hardness value is equal to the applied force P in newtons divided by the actual area of impression in mm2. 

The Knoop test is a microhardness test. In microhardness testing the indentation dimensions are comparable to microstructural ones. Thus, this testing method becomes useful for assessing the relative hardnesses of various phases or microconstituents in two phase or multiphase alloys. It can also be used to monitor hardness gradients that may exist in a solid, e.g., in a surface hardened part. The Knoop test employs a skewed diamond indentor shaped so that the long and short diagonals of the indentation are approximately in the ratio 7 1. The Knoop hardness number (KHN) is calculated as the force divided by the projected indentation area. The test uses low loads to provide small indentations required for microhardness studies. Since the indentations are very small their dimensions have to be measured under an optical microscope. This implies that the surface of the material is prepared approximately. For those reasons, microhardness assessments are not as often used industrially as are other hardness tests. However, the use of microhardness testing is undisputed in research and development situations. 

A fixed force is applied to the axis of the indenter which makes an irreversible indentation into the specimen s surface. The projected length, or area, of this indentation is measured, and the ratio of the applied load to this projection is formed to obtain the hardness number which has the dimensions of stress (also expressable as energy/volume).The sizes of the indentations vary, depending on the indenter s shape and the amount of load applied to it. The size range is from macro- (millimeters), through micro- (microns), to nano-(nanometers). 

This model is not precise, but does identify some of the factors that are important to indentation. Like the model, the hardness measurement process is not precise. At the micro-hardness level, the projected areas of indentations are measured, but this can only be done with about 10% accuracy. At the nano-indentation level, relative values can determined accurately, but absolute values are probably only about 10% accurate. 

An unfortunate aspect of hardness is that it is difficult to quantify in an absolute manner. Most hardness scales are relative and fairly qualitative, and there is a proliferation of different hardness scales. Some of the more common scales are shown in Figure 5.19. In a typical hardness test, a hard indenter of a standard shape is pressed into the surface of a material under a specified load, causing first elastic and then plastic deformation. The resulting area of the indentation or depth of indentation is measured and assigned a numerical value. The value depends upon the apparatus and scale used. 

Brinell method. The measurement is made by driving a calibrated hardened steel ball of diameter D into a flat and smooth sample under variable pressure P, perpendicular to the surface, and then measuring the diameter of the indentation d left on the surface (CMEA ST. 468-77 ISO R 79-68). Brinell hardness HB is the ratio of pressure P to area S of a spherical cup-shaped indentation... 

It follows from the above that deviations from parallel variation in abrasiveness and hardness are the outcome of the inaccuracy of measurement, increasing with hardness. Attention should be paid in particular to the microstructure of the material under test in the area of the indentation, and the degree of brittleness should be estimated on morphological analysis... 

Lawn et al. (1975, 1978), and Lawn and Marshall (1978) distinguish two types of indenter whose action on the tested surface differs significantly (1) a blunt indenter (e.g., a hard ball) distinguished by an ideal elastic contact, so that the crack initiation is controlled by previously present defects (usually on the sample surface), and (2) a sharp indenter (e.g., a cone or pyramid) distinguished by partially plastic contact, so that the original defects start to grow as the result of the indentation process itself. In practice, the contact situations can therefore be seen as intermediate between the two cases. Within this area all typical indenters used for hardness measurement are contained. 

A No known as Diamond Pyramid Hardness. Indcnter is a square-hased diamond pyramid with included angle between faces of 136°. Loads may vary1 from 1 to I 20 kilograms with 10. 30. and 50 kilograms in common use. Hardness is equal to load (kilogramsi divided hy surface area (square millimeter) of the permanent indentation, ll is determined directly from oplical measurements of the diagonals of the indentation, which appear square at Ihe surface of the metal. 

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