Indentation hardness numbers

The flow stress in Figure 2.6 is given approximately by Y = Y0 + h8 where h is the deformation-hardening coefficient. It is assumed that the elastic strain is fully recovered in a hardness measurement, so it need not be considered further in this approximate treatment. Then H = 2.2h8, and since 8 = 2x/L = tan 0 = 0.414 then H = 0.89 h. Hence H — h. That is, the indentation hardness number approximately equals the deformation-hardening coefficient. 

Recall that an indentation hardness number does not measure an initial stress for deformation in metals. It measures the stress needed for further deformation after about 40 percent deformation has already occurred. 

In relatively recent years, it has been found that that indentations made in covalent crystals at temperatures below their Debye temperatures often result from crystal structure changes, as well as from plastic deformation via dislocation activity. Thus, indentation hardness numbers may provide better critical parameters for structural stability than pressure cell studies because indentation involves a combination of shear and hydrostatic compression and a phase transformation involves both of these quantities. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

Figure 8. Correlation of the metallization pressure as calculated from the Herzfeld model and Vicker s indentation hardness number (from Gilman29).

The principle of the Brinell hardness test is that the spherical surface area of a recovered indentation made with a standard hardened steel ball under specific load is direcdy related to the property called hardness. In the following, HBN = Brinell hardness number, P = load in kgf,... 

Because of the geometric limitations of the indenting ball the relationship between indentation area and computed hardness number deviates from linearity when the recovered indentation diameter of a 10-mm ball is less than 2.5 mm or greater than 6.0 mm. 

In practice it is stiU necessary to read the diameter of the Brinell impressions with a caUbrated microscope however, the computations to derive the Brinell hardness number are uimecessary for standard loads and indentors. Table 1 of ASTM ElO (2) contains the tabulated relation between indentation diameter and hardness number. 

Rockwell. The invention of the Rockwed hardness tester in 1919 was an advance over previous indentation tests requiring accurate indentation measurement and tabular reduction to derive a hardness number. In the Rockwed test the hardness number is read direcdy from the instmment dial (1,3). 

The principle of the Rockwed hardness test is that the depth of the indentation between a minor and a major load appHed through an indenter is inversely proportional to the hardness number. Using a minor load to set the indenter helps to reduce backlash in the measuring system. 

In the Rockwed test a spheroconical diamond (Brale) indenter or a hardened steel bad is used with various load ranges to achieve a series of scales identified by a suffix letter (Table 3). The suffix letter defines both load and indenter. The most popular scales used are "C" for hard materials and "B" for soft materials. A Rockwed hardness number is meaningless without the letter suffix, eg, HRC 54 or HRB 95. 

The Rockwed testing machine is thus a framework permitting stable support of the workpiece on one side and means to impress the indenter under specified load on the other. A dial indicator attached to the indenter spindle is used to read directly the depth of indentation in hardness numbers. 

The indenter/load combinations used for superficial Rockwell testing are Hsted in Table 5. As with the standard Rockwell test it is necessary to include the superficial load/indenter combination used for the hardness number to be meaningful, eg, HR30N 65 or HR30T 65. 

Vickers hardness numbers are calculated from measurement of the indentation diagonals as follows, where HV = Vickers hardness,... 

The Vickers hardness test is commonly made on a flat specimen on which the indenter is hydrauhcaHy loaded. When the desired number of indentations have been made, the specimen is removed and both diagonals of the indentations, measured using a caUbrated microscope, are then averaged. The Vickers hardness number may be calculated, or for standard loads taken from a precalculated table of indentation size vs VHN. The preferred procedures are described in ASTM E92 (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. 

Barcol Indenter. The Barcol hardness tester is a hand-held, spring-loaded instmment with a steel indenter developed for use on hard plastics and soft metals (ASTM D2583) (2). In use the indenter is forced into the sample surface and a hardness number is read direcdy off the integral dial indicator caUbrated on a 0 to 100 scale. Barcol hardness numbers do not relate to nor can they be converted to other hardness scales. The Barcol instmment is caUbrated at each use by indenting an aluminum ahoy standard disk suppHed with it. The Barcol test is relatively insensitive to surface condition but may be affected by test sample size and thickness. 

For erosive wear. Rockwell or Brinell hardness is likely to show an inverse relation with carbon and low alloy steels. If they contain over about 0.55 percent carbon, they can be hardened to a high level. However, at the same or even at lower hardness, certain martensitic cast irons (HC 250 and Ni-Hard) can out perform carbon and low alloy steel considerably. For simplification, each of these alloys can be considered a mixture of hard carbide and hardened steel. The usual hardness tests tend to reflect chiefly the steel portion, indicating perhaps from 500 to 650 BHN. Even the Rockwell diamond cone indenter is too large to measure the hardness of the carbides a sharp diamond point with a light load must be used. The Vickers diamond pyramid indenter provides this, giving values around 1,100 for the iron carbide in Ni-Hard and 1,700 for the chromium carbide in HC 250. (These numbers have the same mathematical basis as the more common Brinell hardness numbers.) The microscopically revealed differences in carbide hardness accounts for the superior erosion resistance of these cast irons versus the hardened steels. 

D urometer hardness An arbitrary numerical value that measures the resistance to intention of a blunt indenter point of the durometer. The higher the number, the greater indention hardness. 

The Brinell test uses an indentor of 10 mm diameter hardened steel ball, and applies a load which is usually 3000 kg. The Brinell hardness number (BHN) is defined as the load, F (kilogrammes), divided by the surface area of the indentation. The expression given below describes the definition. 

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. 

An alternative to the measurement of the dimensions of the indentation by means of a microscope is the direct reading method, of which the Rockwell method is an example. The Rockwell hardness is based on indentation into the sample under the action of two consecutively applied loads - a minor load (initial) and a standardised major load (final). In order to eliminate zero error and possible surface effects due to roughness or scale, the initial or minor load is first applied and produce an initial indentation. The Rockwell hardness is based on the increment in the indentation depth produced by the major load over that produced by the minor load. Rockwell hardness scales are divided into a number of groups, each one of these corresponding to a specified penetrator and a specified value of the major load. The different combinations are designated by different subscripts used to express the Rockwell hardness number. Thus, when the test is performed with 150 kg load and a diamond cone indentor, the resulting hardness number is called the Rockwell C (Rc) hardness. If the applied load is 100 kg and the indentor used is a 1.58 mm diameter hardened steel ball, a Rockwell B (RB) hardness number is obtained. The facts that the dial has several scales and that different indentation tools can be filled, enable Rockwell machine to be used equally well for hard and soft materials and for small and thin specimens. Rockwell hardness number is dimensionless. The test is easy to carry out and rapidly accomplished. As a result it is used widely in industrial applications, particularly in quality 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). 

For interpreting indentation behavior, a useful parameter is the ratio of the hardness number, H to the shear modulus. For cubic crystals the latter is the elastic constant, C44. This ratio was used by Gilman (1973) and was used more generally by Chin (1975) who showed that it varies systematically with the type of chemical bonding in crystals. It has become known as the Chin-Gilman parameter (H/C44). Some average values for the three main classes of cubic crystals are given in Table 2.1. 

Since the surfaces of crystals have specific symmetries (usually triangular, square, or tetragonal) and indenters have cylindrical, triangular, square, or tetragonal symmetries, the symmetries rarely match, or are rotationally misaligned. Therefore, the indentations are often anisotropic. Also, the surface symmetries of crystals vary with their orientations relative to the crystallographic axes. A result is that crystals cannot be fully characterized by single hardness numbers. 

In textbooks, plastic deformation is often described as a two-dimensional process. However, it is intrinsically three-dimensional, and cannot be adequately described in terms of two-dimensions. Hardness indentation is a case in point. For many years this process was described in terms of two-dimensional slip-line fields (Tabor, 1951). This approach, developed by Hill (1950) and others, indicated that the hardness number should be about three times the yield stress. Various shortcomings of this theory were discussed by Shaw (1973). He showed that the experimental flow pattern under a spherical indenter bears little resemblance to the prediction of slip-line theory. He attributes this discrepancy to the neglect of elastic strains in slip-line theory. However, the cause of the discrepancy has a different source as will be discussed here. Slip-lines arise from deformation-softening which is related to the principal mechanism of dislocation multiplication a three-dimensional process. The plastic zone determined by Shaw, and his colleagues is determined by strain-hardening. This is a good example of the confusion that results from inadequate understanding of the physics of a process such as plasticity. 

Indentation data for the sulfides could not be found in the literature. However, Mohs scratch hardness numbers were found (Winkler, 1955). They were converted to Vickers numbers using a correlation chart. The hardnesses are shown in Figure 9.10. Since they all have the same number of valence electrons, this is the same as plotting the hardnesses versus the valence electron densities. 

So, the physical hardness density, = B. (In Parr s notation, the indentation hardness, H (kg/mm2) = (M/p)B, where (p/M) is the number density of the atoms, but this does not agree very well with measured values, most solids being anisotropic.)... 

The influence of fillers has been studied mostly at hl volume fractions (40-42). However, in addition, it is instructive to study low volume fractions in order to test conformity with theoretical predictions that certain mechanical properties should increase monotonlcally as the volume fraction of filler is Increased (43). For example, Einstein s treatment of fluids predicts a linear increase in viscosity with an increasing volume fraction of rigid spheres. For glassy materials related comparisons can be made by reference to properties which depend mainly on plastic deformation, such as yield stress or, more conveniently, indentation hardness. Measurements of Vickers hardness number were made after photopolymerization of the BIS-GMA recipe, detailed above, containing varying amounts of a sllanted silicate filler with particles of tens of microns. Contrary to expectation, a minimum value was obtained (44.45). for a volume fraction of 0.03-0.05 (Fig. 4). Subsequently, similar results (46) were obtained with all 5 other fillers tested (Table 1). 

In the most used Rockwell tests, the hardness number does not measure total indentation but only the irreversible portion after a heavy load is applied for a given time and reduced to a... 

Hardness was measured on the Rockwell hardness scale according to the method described in ASTM D785-93. Test results are reported as a Rockwell hardness number, which is directly related to the indentation hardness of a plastic material where higher values reflect greater hardness. Measurements were done on the R scale using a minor load of 10 kg or major load of 60 kg. Testing results are provided in Table 1. 

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