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Hardness Testing
Hardness Testing The simplest definition of hardness is that it is a measure of the resistance offered by a material to being penetrated\indented by a much harder indenter. The resistance to indentation can be due to the plastic deformation (as in metals and alloys), elastic deformation (as in rubber), elastic–plastic deformation (as in ceramics), or even partly due to energy expended in crack formation and propagation (as in brittle materials like glass). The earliest method of hardness testing was based on Mohs scale, which consists of 10 minerals arranged in order from 1 (softest) to 10 (hardest), and in this scale each mineral will scratch the one below it. However, this qualitative method has given way to indentation methods, which measure either the depth of penetration or the dimension (diagonal or diameter) of the indentation. In the indentation method, the hardness is obtained as the ratio of the applied load to area of the indentation. The Mohs scale of hardness is related to indentation
hardness, Fig. 1, which explicitly shows the nonlinearity of Mohs scale. Given the fact that most of the currently available hardness testers are based on the indentation technique, this article will confine itself to presenting the features, advantages, and limitations of indentation-based hardness tests. 1. Macrohardness Testing 1.1 Rockwell Hardness Testing In a Rockwell hardness test, initially a minor load of 10 N is applied and the zero datum position is established. The major load (60, 100, or 150 N) is then applied for a specific period (a few seconds) and removed, leaving the minor load applied. The resulting Rockwell hardness number (as seen on the dial or as a digital output), is inversely related to the additional depth to which the indenter was forced by the major load, beyond the depth resulting from the previously applied minor load. The standard Rockwell hardness scales, along with information on the type of indenter, the magnitude of the major load, and also typical applications for each of the hardness scales, as defined by ASTM standard E18 (1984), are presented in Table 1. In all cases, the minor load is 10 N. It is clear from Table 1 that the hardness of a wide range of materials can be estimated using the Rockwell hardness tester. A widely used variant of the Rockwell hardness test is the superficial Rockwell test, wherein the minor load is 3 N and the major loads are 15, 30, or 45 N. Further details on the Rockwell superficial hardness scales are available in the relevant ASTM standards (ASTM 1984). The Rockwell hardness values are expressed as a combination of hardness number and a scale symbol representing the indenter and the minor and major loads. For example, 64 HRC represents the Rockwell hardness number of 64 on the Rockwell C scale (see Table 1), while 80 HRB represents a Rockwell hardness number of 80 on the Rockwell B scale. Similarly, 81 HR 30 N indicates a Rockwell hardness number of 81 on the Rockwell 30 N scale. Rockwell hardness tests are used for determining the hardness of most metals and alloys, ranging from the softest bearing materials to the hardest steels. 1.2 Brinell Hardness Testing The Brinell hardness test consists of applying a constant load, usually in the range 500–3000 N, for a specified period of time (10–30 s) using a 5 or 10 mm diameter hardened steel or tungsten carbide ball on the flat surface of a work piece. The Brinell hardness number (HB) is then obtained as:
Figure 1 Correlation of Mohs scratch hardness numbers with indentation hardness values.
HB l
P πD[Dk(D#kd #)"/#]
(1) 1
Hardness Testing Table 1 Rockwell standard hardness scales and applications. Scale symbol
Indenter
Major load (kgf )
Typical applications
60
B
Diamond (two scales—carbide and steels) 1.588 mm ball
100
C
Diamond
150
D
Diamond
100
E
3.175 mm ball
100
F
1.588 mm ball
60
G
1.588 mm ball
150
H K
3.175 mm ball 3.175 mm ball
60 150
L
6.35 mm ball
60
M
6.35 mm ball
100
P
6.35 mm ball
150
R
12.70 mm ball
60
S
12.70 mm ball
100
V
12.70 mm ball
150
Cemented carbides, thin steel, shallow case-hardened steel Copper alloys, soft steels, aluminum alloys, malleable iron Steel, hard cast irons, pearlitic malleable iron, titanium, deep case-hardened steel, other materials harder than HRB 100 Thin steel and medium case-hardened steel and pearlitic malleable iron Cast iron, aluminum and magnesium alloys, bearing metals Annealed copper alloy, thin soft sheet metals Phosphor bronze, beryllium copper, malleable irons. Upper limit HRG 92 to avoid possible flattening of ball Aluminum, zinc, lead Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect.
A
where D is the ball diameter (mm), d is the diameter of the resultant, recovered circular indentation (mm) and P is the applied load (kg). It is to be noted that HB is obtained by dividing the applied load by the surface area of the indentation (and not the projected area). The typical relationship between indentation diameter and HB is provided in Table 2. The standard ball for Brinell testing is 10 mm (p0.005 mm) in diameter and should have a minimum hardness of 850 HV. When balls of smaller size are used, the load as well as the ball size should be specified along with the 2
test result. Hardened steel balls can be used for testing material up to 444 HB, while tungsten carbide balls are recommended for measuring hardness values beyond 444 HB and up to 627 HB. Though loads of 500, 1000, 1500, 2000, 2500, and 3000 N are available in a typical Brinell hardness tester, a load of 500 N is used for testing relatively soft metals such as copper and aluminium alloys, while the 3000 N load is often used for testing harder materials such as steels and cast irons. However, the general rule is that the combination of test load and ball diameter
Hardness Testing Table 2 The relationship between indentation diameter and Brinell hardness. Brinell hardness no. (HB) Ball impression diameter (mm) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
500 kgf load 158.0 100.0 69.1 50.3 38.1 29.8 23.8 19.3 15.9 Ball diameter: 10 mm
3000 kgf load 945 601 415 302 229 179 143 116 96
load utilized. For example, the symbols HV5 and HV120 imply that the HV values have been obtained at loads of 5 and 120 kg, respectively. Further details on Vickers hardness testing can be obtained from ASTM standards E92 (1984). The Vickers hardness scale is unique in the sense that using the same indenter, just by varying the load (up to 120 N), virtually any material can be tested. Additionally, the same indenter can also be utilized at very low loads (1–500 N) to carry out microhardness measurements (see Sect. 2.1 for further details). Thus, the Vickers hardness tester is a versatile piece of equipment, and especially indispensable in research and testing laboratories. 1.4 Durometer Hardness Testing
should be such that the diameter of the indentation lies within the range of 25–60% of the ball diameter. Further details on the Brinell hardness test, especially concerning precautions to be taken while carrying out the test, can be obtained from ASTM standards E10 (1984). It must be kept in mind, however, that the Brinell test causes relatively large indentations to form on the work piece, and this may affect the subsequent use of the work piece. Thus the Brinell test, unlike the Rockwell test, may not qualify as a nondestructive test for measuring hardness of materials. Further, the hardness range that can be measured utilizing Brinell hardness test is much narrower than in the case of the Rockwell or Vickers hardness tests, since the latter tests utilize diamond indenters.
The Durometer is specifically meant for measuring the indentation hardness of rubber and plastic products. The durometer is a pocket-sized instrument with a flat bottom and a dial which indicates the Durometer hardness numbers. During the test, the flat bottom of the durometer is pressed against the specimen and the hardness reading is taken within 1 second after firm contact has been established. During the pressing of the durometer against the test piece, the indenter attached to the end of the spring is forced into the test piece at a specified force by the spring. The Durometer hardness numbers, although arbitrary, are inversely related to the indentation depth.
2. Microhardness Testing 2.1 Knoop and Vickers Microhardness Testing
1.3 Vickers Hardness Testing In a Vickers hardness test, a pointed diamond pyramid with a square base is used as the indenter. The opposite faces of the pyramid have an included angle of 136m. This indenter is pressed against the work piece\test piece at a selected applied load (P) in the range 5–120 kg. The average diagonal length (L) of the resulting indentation on the test piece is measured and Vickers hardness number (VHN or HV) is computed using Eqn. (2) given below. HV l
KP L#
(2)
In Eqn. (2), K equals 1.854. It is to be noted that HV is also computed on the basis of surface area of the indentation and not the projected area. The selection of the load depends very much on the hardness of the work piece. The usual criterion is that the length of the diagonal should be of the order of at least 0.5 mm. It is therefore important that the Vickers hardness number is reported along with the
Microhardness testing can be defined as indentation hardness testing that involves applied loads of 1 N or less on the indenter or, more precisely, as tests which result in indentation depths of 70–100 µm. In the case of Vickers microhardness testing, a highly polished, pointed, square-based pyramidal diamond (already described earlier in Sect. 1.3) is used as the indenter and HV is given by Eqn. (2). The Knoop microhardness testing, in contrast, uses a highly polished, rhombic-based pyramidal diamond as the indenter. This indenter produces a diamond-shaped indentation wherein the ratio of long to short diagonals is 7:1. Unlike for the Vickers microhardness test, the Knoop hardness number (HK) is defined as the applied load divided by the projected area of the indentation. Thus, HK is given by Eqn. (2), where L is the length of the longer diagonal and the constant K is equal to 14.229. An advantage of Knoop microhardness testing as compared to the Vickers method is that the Knoop indentations can be spaced much closer to each other along the direction of the short diagonal, and this in turn increases the accuracy of the hardness vs. depth 3
Hardness Testing data required in the case of concentration gradients such as in carburized or nitrided samples. Specific applications of microhardness testing are as follows: $ Measuring hardness of miniature work pieces where the specimen size precludes the use of macrohardness tests; $ Measuring the hardness of thin samples like a foil or wire; $ Estimation of depth of carburizing, nitriding, boriding, etc., utilizing the microhardness vs. depth profile; $ Measuring hardness of individual micro constituents in a multiphase alloy, e.g., the hardness of pearlite and ferrite phases in steels; $ Measurement of hardness of coatings where the coating thickness is sufficiently low to preclude the use of macrohardness tests.
2.2 Ultrasonic Microhardness Testing In ultrasonic microhardness testing, a Vickers diamond is attached to one end of a magnetostrictive metal rod. The metal rod is excited to its natural frequency by a piezo electric converter. The Vickers diamond attached to the vibrating metal rod indents the test piece. The maximum indentation load is 800 mN and the indentation depths are usually in the range 4–20 µm. Unlike other microhardness testers, the area of contact between the diamond tip and the test piece surface (i.e., equal to the surface area of indentation) is derived from the measured resonant frequency, once the ultrasonic microhardness equipment has been calibrated for the known modulus of elasticity of the tested material. Since the area of contact is inversely related to the hardness, the measured frequency can be directly converted into a hardness number (either Vickers or Rockwell). The major advantage of ultrasonic microhardness testing is that it instantly measures the area of contact under indentation and hence the hardness. Additionally, since the area of indentation is measured under load in ultrasonic hardness testing, elastic recovery does not affect the results. A one-point calibration procedure, in conjunction with the ability to measure the contact area of even the smallest indentations, has made the ultrasonic microhardness testing a versatile and popular technique, especially for inspection of large parts and on-line, in-process inspection hardness testing.
2.3 Ultramicrohardness Testing Ultramicrohardness (UMH) testing is characterized by indentation depths in the range 0.1–1.0 µm. More importantly, UMH testers monitor the depth of 4
indentation as a function of applied load during the course of the indentation process itself. Depths of indentation as low as 10 nm can be reliably measured using this equipment. The basic UMH system consists of an optical head, an objective lens, a test piece stage, and an attachment for holding thin test specimens. The load is usually applied through an electromagnetic force generator (0.02–10 mN) and the indentation depth is measured using a differential transformer positioned near the indenter. Usually, a standard Berkovitz indenter (i.e., a triangular pyramid) is used. Typical load vs. depth of indentation data, obtained during an indentation test carried out using the UMH system, is illustrated in Fig. 2. In Fig. 2, the curve AB represents the loading curve, i.e., the variation of indentation depth with increasing applied load while the indenter is penetrating into the test piece. At point B, the indentation stops and the unloading begins. During this unloading, the load decreases along the curve BC and becomes zero at point C. AC represents the recovered depth of indentation, and AD the depth of indentation under maximum load (hmax). This value of hmax is then utilized to calculate the UMH. The UMH tester is especially suited for measuring the intrinsic hardness of coatings, miniature specimens (IC chips, etc.) and also very thin specimens. Since the system is capable of measuring indentation depths as low as 10 nm, the intrinsic hardness of coatings even as thin as 1 or 2 µm can be measured. In addition, evaluation of hardness vs. depth profiles in ionnitrided, ion-implanted, and plasma-nitrided samples, wherein the thickness of the modified surface layer is of the order of 10 µm, is also possible with the UMH system (see Thin Films: Mechanical Testing, Nanoindentation Techniques, and Sect. 3). 2.4 Scratch Hardness Scratch hardness is defined as the hardness of a material when it is scratched by a stylus dragged along its surface under a given load. Unlike pure indentation-based hardness tests, scratch hardness defines the resistance of material to plowing (i.e., a combination of indentation cum sliding) by a hard stylus. A typical scratch hardness tester consists of a stylus, a movable sample holding stage, load-applying device, and a data processing and display unit. During a scratch hardness test, at a chosen constant load, the stylus is allowed to plow into the test specimen up to a predetermined distance to form a groove. The scratch hardness (Hs) is then obtained as: Hs l
AFN b#
(3)
where FN is the applied constant load, b is the groove
Load (gf)
Hardness Testing
Figure 2 The loading–unloading curve typically obtained from ultramicro- and nanohardness tests.
width (measured using a microscope), and A is a numerical constant which equals 8\π for styli having conical, spherical, or parabolic tips and 4 for styli having a pyramidal tip. Many of the common tribological phenomena like sliding, abrasive, and cutting wear are characterized by a harder material plowing into the softer wearing material. Thus, for correlating the tribological performance of many materials, scratch hardness (Hs) is expected to be a better correlating parameter than the indentation hardness.
3. Nanohardness Testing Nanohardness testing refers to hardness tests wherein the depth of indentation usually is less than about 50 nm or equivalently, the indentation diameter\ length is lower than about 150 nm. To obtain such low indentation depths, applied loads on the indenter are usually in the range 0.1–100 mN. The accuracies of nanohardness testers with regard to load and displacement (or depth) measurements are typically 1 µN and 0.2 nm, respectively. The indenter used is invariably a Berkovitz diamond indenter. This indenter has a pointed triangular pyramid shape and the profile of the tip of the indenter is measured a priori (or supplied by the manufacturer of the indenter), so that measured indentation depths can be converted to area of contact (A) between the indenter and the substrate material. During a typical nanohardness test, the pre-
determined load is slowly and steadily applied on the indenter. As a result, the indenter penetrates into the test piece, and AB in Fig. 2 represents the corresponding load (P) vs. indentation depth (h) curve. At point B, the resistance offered by the test piece being indented equals the applied load and no further penetration occurs. Next, as the applied load is removed, the deformed indentation elastically recovers resulting in the unloading curve BC (Fig. 2). Nanohardness testing is eminently suited for measuring the hardness of thin films\coatings (thickness of coatings 1 µm), the hardness of micro-constituents like fibers and particulates in composites, and the hardness of submicron powders. In addition, nanohardness testing is extensively used to characterize and evaluate quality of the various circuit components of modern IC chips. However, it should be noted that the nanoindenter system is high-technology, high-cost equipment. Further, it has to be installed with great care, since even minor vibrations will influence the test results. In view of the above, it is unlikely that the nanoindenter will ever attain the status of micro- or ultramicrohardness testers, i.e., a standard piece of equipment to measure hardness. It is more likely to remain a research tool which can also be utilized to measure the hardness of materials at indentation depths of the order of nanometers.
4. Scleroscope Hardness Testing The Scleroscope is a dynamic hardness tester invented in 1907. Scleroscope testing involves the dropping of a hammer of known weight from a predetermined height onto the work piece and measuring the rebound height of the hammer. The rebound height is then related to the Scleroscope hardness number, which in turn is relatable to Vickers, Brinell, or Rockwell hardness numbers. Two types of Scleroscope hardness testers are available. The Model C consists of a vertically disposed barrel containing a precision-base glass tube. A vertical scale graduated from 0 to 140 is set behind the tube. Hardness is read from this vertical scale. The operation of the pneumatic actuating head, affixed to the top of the barrel, allows the hammer to drop freely within the glass tube. After impacting the work piece, the hammer rebounds and the scale number corresponding to the maximum height of rebound is taken as the Scleroscope hardness number. Model C Scleroscope is also portable. The model D Scleroscope is similar to model C except for the fact that it uses a heavier hammer, which is dropped from a lower height. In addition, Model D also contains a clutch system to arrest the hammer at its maximum height of rebound. The Scleroscope hardness test can be carried out on large components and very rapidly. Further, a single scale is capable of 5
Hardness Testing covering the entire hardness range from the softest to hardest metals.
5. Hardness Testing at Elevated Temperatures Many of the room-temperature hardness tests like Rockwell, Brinell, and Vickers have been modified suitably to carry out hardness testing at elevated temperatures. In terms of equipment modification, the major requirement is the furnace with provisions for a controlled atmosphere (either vacuum or inert atmosphere). In addition, an indexing feature that makes it possible to bring any area of the test piece under the indent without contaminating the atmosphere or disturbing the temperature equilibrium is also commonly incorporated, so that several indentations can be made in a sequential fashion (see Creep by Indentation and Sect. 8.4). A major limitation of hardness testing at elevated temperatures, especially beyond 0.5 TM (TM l melting point of the test material in Kelvin), is the interference due to primary creep. Primary creep causes the indentation diameter to increase as a function of time even at constant load, and thus results in errors in measurement of indentation diameter and hence calculation of hardness. For this reason, some countries do not accept ‘‘hot hardness’’ above 0.3 TM. 6.
Further Problems in Hardness Testing
6.1 Brittle Materials Indentation of brittle materials like ceramics and glasses also leaves a residual impression, as in the case of metals. However, especially during the unloading phase of the indentation, cracks form and propagate from the indented area. Such cracks, apart from hindering the accurate measurement of indentation dimensions, also will have an influence on the nature of constraint experienced by the plastically deforming material beneath the indenter. Additionally, certain brittle materials show a greater tendency towards deformation in hydrostatic stress than they do in shear. Fused silica, for example, is known to undergo structural densification when subjected to confining pressure, as during the hardness test. Many crystalline ceramics also exhibit pressureinduced phase transformations which can result in volume expansion or contraction. Further, environmental factors like humidity can affect the friction behavior of ceramics like alumina, which in turn can alter the friction between the indenter and the indented material and thus influence hardness. Lastly, it should be noted that some of the ceramics are very hard, and thus it should be ensured that the hardness of the indenter material is at least 1.5 times that of the ceramic material being tested (see Mechanics of Subcritical Crack Growth in Brittle Materials). 6
6.2 Polymer Materials The indentation process in the case of polymers involves viscoelastic effects. The deformation is time dependent and often markedly temperature dependent. As a result, the loading rate and the dwell time employed during the hardness test will have an appreciable influence on the measured hardness value, and thus need to be properly controlled and calibrated prior to and during the hardness test. Another problem in the case of polymeric materials is the relaxation of indentation once the load is removed during the hardness test. At first only shallowing of the indentation occurs, but over prolonged periods the size of the indentation shrinks, especially when spherical indenters are used. Thus the indentation diameter has to be measured immediately after the test. A related problem is that the poor reflectivity of polymeric materials makes the accurate measurement of indentation size rather difficult. Additionally, some polymers like nylon readily absorb fluids, including water, from the environment, which may also affect the dimensional stability of the indentation and hence may result in inaccuracies of hardness measurement.
6.3 Coatings In the case of coatings, the intrinsic hardness value of the coating material can be obtained only if the depth of indentation is less than 10% of the thickness of the coating. The above statement is true irrespective of whether the coating is harder or softer than the substrate (Matsuda and Kaneta 1996). Thus, the intrinsic hardness of coatings of thickness 10 µm or more can be obtained using a microhardness tester, while coatings a few microns thick will require an ultramicrohardness tester. In contrast, measurement of the hardness of coatings having thicknesses in the submicron range will require the use of a nanoindentation facility. If the available hardness tester is such that the depth of indentation exceeds 10% of the coating thickness, the hardness values obtained should be reported as the composite hardness of the coating–substrate system. Various mathematical models have been developed to obtain the intrinsic hardness of the coating from the composite hardness values (e.g., see Korunsky et al. 1998).
7. Hardness Testing: General Considerations In this section, important guidelines are described which should be followed while selecting the appropriate hardness test, and also while carrying out the hardness tests. The choice of the appropriate hardness test depends
Hardness Testing on a number of factors. The productivity (tests per hour) of the ultrasonic hardness tester is the highest, and the Rockwell hardness tester comes second. While a machined and ground surface is enough for Rockwell hardness testing, a smoother surface is required for other hardness testers. Microhardness and ultramicrohardness tests require well-polished surfaces. The minimum thickness of the test piece\work piece required for carrying out valid hardness measurement depends on the type of hardness tester. The general rule is that the thickness of the test piece\work piece should be at least 10 times the depth of indentation. This criterion can be incorporated in the hardness– diameter\depth of indentation relationship valid for various hardness tests, to obtain the minimum specimen thickness (Tmin) required for the hardness data obtained using a given hardness test to be valid. The spacing of the indenters should be such that the distance from the center of one indentation to another must be at least three times the indentation diameter or the longer diagonal. Similarly, the distance from the center of the indentation to the edge of the specimen should be a minimum of 2.5 times the diameter or longer diagonal of the indentation. At low loads, especially in the case of micro-, ultramicro-, and nanohardness testing, the hardness may itself become a function of indentation size. This is usually referred to as the size effect and the phenomenon is not completely understood. From a practical standpoint, the load selected should be as large as practically possible (keeping in mind the limitations due to specimen thickness) to circumvent the size effect.
8. Use of Hardness Testing for Obtaining Other Properties 8.1 Determination of Elastic Modulus The elastic modulus of the near surface region of a bulk test piece, or of the coating deposited on a substrate, can be obtained using depth-sensing hardness tests like the ultramicro- and nanohardness testers. The elastic modulus is obtained from the loading–unloading curve discussed earlier and shown in Fig. 2. The slope of the initial portion of the unloading curve equals the contact stiffness S ( l dP\dh where P l load and h l depth of indentation). Once S is obtained as above and the contact area (A) between the indenter and the test piece is calculated on the basis of the known relationship between the indentation depth and contact area, the elastic modulus of the test material is obtained using the relation (Pharr et al. 1992): El
1kν# (0.89S\A"/#)k(1kν#i \Ei)
(4)
In the above equation, Ei and νi represent the elastic modulus and Poisson’s ratio of the indenter material, respectively, while E and ν correspond to the elastic modulus and Poisson’s ratio of the test material. Since Ei and νi are known (especially for the commonly used indenter material, i.e., diamond), by assuming a reasonable value for the Poisson’s ratio of the test material (ν), the elastic modulus of the test material can be computed. The indentation-based technique for estimating elastic modulus is especially useful for estimating the modulus of thin coatings.
8.2 Determination of Flow Stress–Strain Behaior of Metallic Materials and Coatings The concept of using the indentation test with a spherical ball as the indenter, to evaluate the flow stress–strain behavior of the indented material, was pioneered as early as 1951 by Tabor. The relevant equations which relate the indentation diameter (d ) and the corresponding applied load (P) with the flow stress (σ) and the corresponding plastic strain (ε) are as follows: σl
4P πd #C
(5)
εl
0.2d D
(6)
where C is the constraint factor (usually having a value of around 3) and D is the indenter (ball) diameter. Thus, indentation tests carried out over a range of load will result in the flow stress (σ) data being obtained over a range of plastic strain (ε). The above concept has been demonstrated to be valid even under dynamic indentation (DI) conditions, thereby allowing the σ(ε) curves to be obtained even at dynamic strain rates of the order of 10% s−". The above technique is particularly suitable for obtaining the stress–strain behavior of coatings and thin films (invariably spherical tip indenters are used for the above purpose), and also of very thin specimens.
8.3 Indentation Toughness of Brittle Materials In the case of brittle materials, indentation testing has been successfully utilized to evaluate their toughness. In this technique, the fracture resistance is related to the scale of the crack pattern. Over the years, a large number of models have been developed relating toughness of the test piece (Kc) to the measured postindentation crack size (C ) (see Fig. 3 for details). 7
Hardness Testing ranking of a large number of materials on the basis of their creep resistance, the indentation creep technique has proved useful (see Creep by Indentation).
8.5 Adhesion of Coatings The scratch hardness tester described in Sect. 2.4 can also be utilized for measuring the adhesion strength of coatings. For this purpose, the stylus is dragged across the surface of the coating to be tested, under progressively increasing loads, until either the coating peels off or the coating–substrate interface starts cracking. The peeling off of the coating can be observed under a microscope, while the formation of the crack at the interface is usually detected using an acoustic signal detector and processor (normally supplied with the scratch hardness tester). The load (Fc) at which the coating peels off or the interface cracks is usually defined as the ‘‘adhesion strength’’ of the coating. The above technique has been standardized so far only for thin coatings (a few micrometers thick). Figure 3 A photomicrograph of the crack pattern formed around a Vickers indenter.
9. Concluding Remarks However, all these models invariably lead to an equation of the form: E
KC l β F
E H
G
E
H
n F
P C$/#
G
(7) H
In the above equation, β is a constant, H is the Vickers hardness of the test material, P is the applied load, E is the elastic modulus of the test material, and n is a constant usually in the range 0.4–0.5 (McColm 1990). The KC values of a large number of ceramic materials have been determined using the above technique.
8.4 Indentation Creep Over the years, many investigators have attempted to correlate the hardness behavior of materials at elevated temperatures (beyond 0.5 times the absolute melting point of the test material) with the tensile creep behavior. In many systems, depending on the time of application of load, there is a change in the size of the indentation diameter. This results in an apparent reduction of the hardness of materials. The effect is known as indentation creep. However, this technique is not very popular, mainly because the stress state underneath the indenter is complex and multiaxial, and also not uniform. Thus the correlation of the indentation creep rate with the tensile creep rate is not straightforward. However, for assessing the relative 8
In this article, the salient features of all the available indentation-based hardness test techniques have been described. In addition, the use of hardness test equipment to evaluate properties other than hardness of the test material has been described. Hardness testing has stood the test of time and has retained its recognition and usefulness amongst the engineering and scientific community. There can be no doubt that hardness testing will be an important tool in the coming years as well. However, with the drive towards automation encompassing all fields, it is likely that hardness testers of the future will be invariably based on the measurement of indentation depth, rather than indentation diameter or length. This is so because sensor-based measurement, integral to any automated system, is much easier and more accurate in the case of depth of indentation. An added advantage of depthbased hardness measurement, which is likely to be exploited in the coming years, is that the load-depth of indentation curves can be deconvoluted, to provide hardness vs. depth data on the basis of a single test. See also: Thin Films: Mechanical Testing
Bibliography ASTM 1984 Standard test methods for Rockwell hardness and Rockwell superficial hardness of metallic materials. Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA, Sects. E10, E18, E92 Blau P J, Lawn B R 1986 Microindentation Techniques in
Hardness Testing Materials Science and Engineering. ASTM STP 889. American Society for Testing and Materials, Philadelphia, PA Korunsky A M, McGurk M R, Bull S J, Page T F 1998 On the hardness of coated systems. Surf. Coat. Technol. 99, 171–83 Matsuda K, Kaneta M 1996 Analysis of the Vickers hardness of electroplated coatings. Phil. Mag. A 74, 1171–84
McColm I J 1990 Ceramic Hardness. Plenum, New York Pharr G M, Oliver W C, Brotzen F R 1992 On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613–17
G. Sundararajan and M. Roy
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 3728–3736 9
hardness, Fig. 1, which explicitly shows the nonlinearity of Mohs scale. Given the fact that most of the currently available hardness testers are based on the indentation technique, this article will confine itself to presenting the features, advantages, and limitations of indentation-based hardness tests. 1. Macrohardness Testing 1.1 Rockwell Hardness Testing In a Rockwell hardness test, initially a minor load of 10 N is applied and the zero datum position is established. The major load (60, 100, or 150 N) is then applied for a specific period (a few seconds) and removed, leaving the minor load applied. The resulting Rockwell hardness number (as seen on the dial or as a digital output), is inversely related to the additional depth to which the indenter was forced by the major load, beyond the depth resulting from the previously applied minor load. The standard Rockwell hardness scales, along with information on the type of indenter, the magnitude of the major load, and also typical applications for each of the hardness scales, as defined by ASTM standard E18 (1984), are presented in Table 1. In all cases, the minor load is 10 N. It is clear from Table 1 that the hardness of a wide range of materials can be estimated using the Rockwell hardness tester. A widely used variant of the Rockwell hardness test is the superficial Rockwell test, wherein the minor load is 3 N and the major loads are 15, 30, or 45 N. Further details on the Rockwell superficial hardness scales are available in the relevant ASTM standards (ASTM 1984). The Rockwell hardness values are expressed as a combination of hardness number and a scale symbol representing the indenter and the minor and major loads. For example, 64 HRC represents the Rockwell hardness number of 64 on the Rockwell C scale (see Table 1), while 80 HRB represents a Rockwell hardness number of 80 on the Rockwell B scale. Similarly, 81 HR 30 N indicates a Rockwell hardness number of 81 on the Rockwell 30 N scale. Rockwell hardness tests are used for determining the hardness of most metals and alloys, ranging from the softest bearing materials to the hardest steels. 1.2 Brinell Hardness Testing The Brinell hardness test consists of applying a constant load, usually in the range 500–3000 N, for a specified period of time (10–30 s) using a 5 or 10 mm diameter hardened steel or tungsten carbide ball on the flat surface of a work piece. The Brinell hardness number (HB) is then obtained as:
Figure 1 Correlation of Mohs scratch hardness numbers with indentation hardness values.
HB l
P πD[Dk(D#kd #)"/#]
(1) 1
Hardness Testing Table 1 Rockwell standard hardness scales and applications. Scale symbol
Indenter
Major load (kgf )
Typical applications
60
B
Diamond (two scales—carbide and steels) 1.588 mm ball
100
C
Diamond
150
D
Diamond
100
E
3.175 mm ball
100
F
1.588 mm ball
60
G
1.588 mm ball
150
H K
3.175 mm ball 3.175 mm ball
60 150
L
6.35 mm ball
60
M
6.35 mm ball
100
P
6.35 mm ball
150
R
12.70 mm ball
60
S
12.70 mm ball
100
V
12.70 mm ball
150
Cemented carbides, thin steel, shallow case-hardened steel Copper alloys, soft steels, aluminum alloys, malleable iron Steel, hard cast irons, pearlitic malleable iron, titanium, deep case-hardened steel, other materials harder than HRB 100 Thin steel and medium case-hardened steel and pearlitic malleable iron Cast iron, aluminum and magnesium alloys, bearing metals Annealed copper alloy, thin soft sheet metals Phosphor bronze, beryllium copper, malleable irons. Upper limit HRG 92 to avoid possible flattening of ball Aluminum, zinc, lead Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect. Bearing metals and other very soft or thin materials. Use smallest ball and heaviest load that do not produce anvil effect.
A
where D is the ball diameter (mm), d is the diameter of the resultant, recovered circular indentation (mm) and P is the applied load (kg). It is to be noted that HB is obtained by dividing the applied load by the surface area of the indentation (and not the projected area). The typical relationship between indentation diameter and HB is provided in Table 2. The standard ball for Brinell testing is 10 mm (p0.005 mm) in diameter and should have a minimum hardness of 850 HV. When balls of smaller size are used, the load as well as the ball size should be specified along with the 2
test result. Hardened steel balls can be used for testing material up to 444 HB, while tungsten carbide balls are recommended for measuring hardness values beyond 444 HB and up to 627 HB. Though loads of 500, 1000, 1500, 2000, 2500, and 3000 N are available in a typical Brinell hardness tester, a load of 500 N is used for testing relatively soft metals such as copper and aluminium alloys, while the 3000 N load is often used for testing harder materials such as steels and cast irons. However, the general rule is that the combination of test load and ball diameter
Hardness Testing Table 2 The relationship between indentation diameter and Brinell hardness. Brinell hardness no. (HB) Ball impression diameter (mm) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
500 kgf load 158.0 100.0 69.1 50.3 38.1 29.8 23.8 19.3 15.9 Ball diameter: 10 mm
3000 kgf load 945 601 415 302 229 179 143 116 96
load utilized. For example, the symbols HV5 and HV120 imply that the HV values have been obtained at loads of 5 and 120 kg, respectively. Further details on Vickers hardness testing can be obtained from ASTM standards E92 (1984). The Vickers hardness scale is unique in the sense that using the same indenter, just by varying the load (up to 120 N), virtually any material can be tested. Additionally, the same indenter can also be utilized at very low loads (1–500 N) to carry out microhardness measurements (see Sect. 2.1 for further details). Thus, the Vickers hardness tester is a versatile piece of equipment, and especially indispensable in research and testing laboratories. 1.4 Durometer Hardness Testing
should be such that the diameter of the indentation lies within the range of 25–60% of the ball diameter. Further details on the Brinell hardness test, especially concerning precautions to be taken while carrying out the test, can be obtained from ASTM standards E10 (1984). It must be kept in mind, however, that the Brinell test causes relatively large indentations to form on the work piece, and this may affect the subsequent use of the work piece. Thus the Brinell test, unlike the Rockwell test, may not qualify as a nondestructive test for measuring hardness of materials. Further, the hardness range that can be measured utilizing Brinell hardness test is much narrower than in the case of the Rockwell or Vickers hardness tests, since the latter tests utilize diamond indenters.
The Durometer is specifically meant for measuring the indentation hardness of rubber and plastic products. The durometer is a pocket-sized instrument with a flat bottom and a dial which indicates the Durometer hardness numbers. During the test, the flat bottom of the durometer is pressed against the specimen and the hardness reading is taken within 1 second after firm contact has been established. During the pressing of the durometer against the test piece, the indenter attached to the end of the spring is forced into the test piece at a specified force by the spring. The Durometer hardness numbers, although arbitrary, are inversely related to the indentation depth.
2. Microhardness Testing 2.1 Knoop and Vickers Microhardness Testing
1.3 Vickers Hardness Testing In a Vickers hardness test, a pointed diamond pyramid with a square base is used as the indenter. The opposite faces of the pyramid have an included angle of 136m. This indenter is pressed against the work piece\test piece at a selected applied load (P) in the range 5–120 kg. The average diagonal length (L) of the resulting indentation on the test piece is measured and Vickers hardness number (VHN or HV) is computed using Eqn. (2) given below. HV l
KP L#
(2)
In Eqn. (2), K equals 1.854. It is to be noted that HV is also computed on the basis of surface area of the indentation and not the projected area. The selection of the load depends very much on the hardness of the work piece. The usual criterion is that the length of the diagonal should be of the order of at least 0.5 mm. It is therefore important that the Vickers hardness number is reported along with the
Microhardness testing can be defined as indentation hardness testing that involves applied loads of 1 N or less on the indenter or, more precisely, as tests which result in indentation depths of 70–100 µm. In the case of Vickers microhardness testing, a highly polished, pointed, square-based pyramidal diamond (already described earlier in Sect. 1.3) is used as the indenter and HV is given by Eqn. (2). The Knoop microhardness testing, in contrast, uses a highly polished, rhombic-based pyramidal diamond as the indenter. This indenter produces a diamond-shaped indentation wherein the ratio of long to short diagonals is 7:1. Unlike for the Vickers microhardness test, the Knoop hardness number (HK) is defined as the applied load divided by the projected area of the indentation. Thus, HK is given by Eqn. (2), where L is the length of the longer diagonal and the constant K is equal to 14.229. An advantage of Knoop microhardness testing as compared to the Vickers method is that the Knoop indentations can be spaced much closer to each other along the direction of the short diagonal, and this in turn increases the accuracy of the hardness vs. depth 3
Hardness Testing data required in the case of concentration gradients such as in carburized or nitrided samples. Specific applications of microhardness testing are as follows: $ Measuring hardness of miniature work pieces where the specimen size precludes the use of macrohardness tests; $ Measuring the hardness of thin samples like a foil or wire; $ Estimation of depth of carburizing, nitriding, boriding, etc., utilizing the microhardness vs. depth profile; $ Measuring hardness of individual micro constituents in a multiphase alloy, e.g., the hardness of pearlite and ferrite phases in steels; $ Measurement of hardness of coatings where the coating thickness is sufficiently low to preclude the use of macrohardness tests.
2.2 Ultrasonic Microhardness Testing In ultrasonic microhardness testing, a Vickers diamond is attached to one end of a magnetostrictive metal rod. The metal rod is excited to its natural frequency by a piezo electric converter. The Vickers diamond attached to the vibrating metal rod indents the test piece. The maximum indentation load is 800 mN and the indentation depths are usually in the range 4–20 µm. Unlike other microhardness testers, the area of contact between the diamond tip and the test piece surface (i.e., equal to the surface area of indentation) is derived from the measured resonant frequency, once the ultrasonic microhardness equipment has been calibrated for the known modulus of elasticity of the tested material. Since the area of contact is inversely related to the hardness, the measured frequency can be directly converted into a hardness number (either Vickers or Rockwell). The major advantage of ultrasonic microhardness testing is that it instantly measures the area of contact under indentation and hence the hardness. Additionally, since the area of indentation is measured under load in ultrasonic hardness testing, elastic recovery does not affect the results. A one-point calibration procedure, in conjunction with the ability to measure the contact area of even the smallest indentations, has made the ultrasonic microhardness testing a versatile and popular technique, especially for inspection of large parts and on-line, in-process inspection hardness testing.
2.3 Ultramicrohardness Testing Ultramicrohardness (UMH) testing is characterized by indentation depths in the range 0.1–1.0 µm. More importantly, UMH testers monitor the depth of 4
indentation as a function of applied load during the course of the indentation process itself. Depths of indentation as low as 10 nm can be reliably measured using this equipment. The basic UMH system consists of an optical head, an objective lens, a test piece stage, and an attachment for holding thin test specimens. The load is usually applied through an electromagnetic force generator (0.02–10 mN) and the indentation depth is measured using a differential transformer positioned near the indenter. Usually, a standard Berkovitz indenter (i.e., a triangular pyramid) is used. Typical load vs. depth of indentation data, obtained during an indentation test carried out using the UMH system, is illustrated in Fig. 2. In Fig. 2, the curve AB represents the loading curve, i.e., the variation of indentation depth with increasing applied load while the indenter is penetrating into the test piece. At point B, the indentation stops and the unloading begins. During this unloading, the load decreases along the curve BC and becomes zero at point C. AC represents the recovered depth of indentation, and AD the depth of indentation under maximum load (hmax). This value of hmax is then utilized to calculate the UMH. The UMH tester is especially suited for measuring the intrinsic hardness of coatings, miniature specimens (IC chips, etc.) and also very thin specimens. Since the system is capable of measuring indentation depths as low as 10 nm, the intrinsic hardness of coatings even as thin as 1 or 2 µm can be measured. In addition, evaluation of hardness vs. depth profiles in ionnitrided, ion-implanted, and plasma-nitrided samples, wherein the thickness of the modified surface layer is of the order of 10 µm, is also possible with the UMH system (see Thin Films: Mechanical Testing, Nanoindentation Techniques, and Sect. 3). 2.4 Scratch Hardness Scratch hardness is defined as the hardness of a material when it is scratched by a stylus dragged along its surface under a given load. Unlike pure indentation-based hardness tests, scratch hardness defines the resistance of material to plowing (i.e., a combination of indentation cum sliding) by a hard stylus. A typical scratch hardness tester consists of a stylus, a movable sample holding stage, load-applying device, and a data processing and display unit. During a scratch hardness test, at a chosen constant load, the stylus is allowed to plow into the test specimen up to a predetermined distance to form a groove. The scratch hardness (Hs) is then obtained as: Hs l
AFN b#
(3)
where FN is the applied constant load, b is the groove
Load (gf)
Hardness Testing
Figure 2 The loading–unloading curve typically obtained from ultramicro- and nanohardness tests.
width (measured using a microscope), and A is a numerical constant which equals 8\π for styli having conical, spherical, or parabolic tips and 4 for styli having a pyramidal tip. Many of the common tribological phenomena like sliding, abrasive, and cutting wear are characterized by a harder material plowing into the softer wearing material. Thus, for correlating the tribological performance of many materials, scratch hardness (Hs) is expected to be a better correlating parameter than the indentation hardness.
3. Nanohardness Testing Nanohardness testing refers to hardness tests wherein the depth of indentation usually is less than about 50 nm or equivalently, the indentation diameter\ length is lower than about 150 nm. To obtain such low indentation depths, applied loads on the indenter are usually in the range 0.1–100 mN. The accuracies of nanohardness testers with regard to load and displacement (or depth) measurements are typically 1 µN and 0.2 nm, respectively. The indenter used is invariably a Berkovitz diamond indenter. This indenter has a pointed triangular pyramid shape and the profile of the tip of the indenter is measured a priori (or supplied by the manufacturer of the indenter), so that measured indentation depths can be converted to area of contact (A) between the indenter and the substrate material. During a typical nanohardness test, the pre-
determined load is slowly and steadily applied on the indenter. As a result, the indenter penetrates into the test piece, and AB in Fig. 2 represents the corresponding load (P) vs. indentation depth (h) curve. At point B, the resistance offered by the test piece being indented equals the applied load and no further penetration occurs. Next, as the applied load is removed, the deformed indentation elastically recovers resulting in the unloading curve BC (Fig. 2). Nanohardness testing is eminently suited for measuring the hardness of thin films\coatings (thickness of coatings 1 µm), the hardness of micro-constituents like fibers and particulates in composites, and the hardness of submicron powders. In addition, nanohardness testing is extensively used to characterize and evaluate quality of the various circuit components of modern IC chips. However, it should be noted that the nanoindenter system is high-technology, high-cost equipment. Further, it has to be installed with great care, since even minor vibrations will influence the test results. In view of the above, it is unlikely that the nanoindenter will ever attain the status of micro- or ultramicrohardness testers, i.e., a standard piece of equipment to measure hardness. It is more likely to remain a research tool which can also be utilized to measure the hardness of materials at indentation depths of the order of nanometers.
4. Scleroscope Hardness Testing The Scleroscope is a dynamic hardness tester invented in 1907. Scleroscope testing involves the dropping of a hammer of known weight from a predetermined height onto the work piece and measuring the rebound height of the hammer. The rebound height is then related to the Scleroscope hardness number, which in turn is relatable to Vickers, Brinell, or Rockwell hardness numbers. Two types of Scleroscope hardness testers are available. The Model C consists of a vertically disposed barrel containing a precision-base glass tube. A vertical scale graduated from 0 to 140 is set behind the tube. Hardness is read from this vertical scale. The operation of the pneumatic actuating head, affixed to the top of the barrel, allows the hammer to drop freely within the glass tube. After impacting the work piece, the hammer rebounds and the scale number corresponding to the maximum height of rebound is taken as the Scleroscope hardness number. Model C Scleroscope is also portable. The model D Scleroscope is similar to model C except for the fact that it uses a heavier hammer, which is dropped from a lower height. In addition, Model D also contains a clutch system to arrest the hammer at its maximum height of rebound. The Scleroscope hardness test can be carried out on large components and very rapidly. Further, a single scale is capable of 5
Hardness Testing covering the entire hardness range from the softest to hardest metals.
5. Hardness Testing at Elevated Temperatures Many of the room-temperature hardness tests like Rockwell, Brinell, and Vickers have been modified suitably to carry out hardness testing at elevated temperatures. In terms of equipment modification, the major requirement is the furnace with provisions for a controlled atmosphere (either vacuum or inert atmosphere). In addition, an indexing feature that makes it possible to bring any area of the test piece under the indent without contaminating the atmosphere or disturbing the temperature equilibrium is also commonly incorporated, so that several indentations can be made in a sequential fashion (see Creep by Indentation and Sect. 8.4). A major limitation of hardness testing at elevated temperatures, especially beyond 0.5 TM (TM l melting point of the test material in Kelvin), is the interference due to primary creep. Primary creep causes the indentation diameter to increase as a function of time even at constant load, and thus results in errors in measurement of indentation diameter and hence calculation of hardness. For this reason, some countries do not accept ‘‘hot hardness’’ above 0.3 TM. 6.
Further Problems in Hardness Testing
6.1 Brittle Materials Indentation of brittle materials like ceramics and glasses also leaves a residual impression, as in the case of metals. However, especially during the unloading phase of the indentation, cracks form and propagate from the indented area. Such cracks, apart from hindering the accurate measurement of indentation dimensions, also will have an influence on the nature of constraint experienced by the plastically deforming material beneath the indenter. Additionally, certain brittle materials show a greater tendency towards deformation in hydrostatic stress than they do in shear. Fused silica, for example, is known to undergo structural densification when subjected to confining pressure, as during the hardness test. Many crystalline ceramics also exhibit pressureinduced phase transformations which can result in volume expansion or contraction. Further, environmental factors like humidity can affect the friction behavior of ceramics like alumina, which in turn can alter the friction between the indenter and the indented material and thus influence hardness. Lastly, it should be noted that some of the ceramics are very hard, and thus it should be ensured that the hardness of the indenter material is at least 1.5 times that of the ceramic material being tested (see Mechanics of Subcritical Crack Growth in Brittle Materials). 6
6.2 Polymer Materials The indentation process in the case of polymers involves viscoelastic effects. The deformation is time dependent and often markedly temperature dependent. As a result, the loading rate and the dwell time employed during the hardness test will have an appreciable influence on the measured hardness value, and thus need to be properly controlled and calibrated prior to and during the hardness test. Another problem in the case of polymeric materials is the relaxation of indentation once the load is removed during the hardness test. At first only shallowing of the indentation occurs, but over prolonged periods the size of the indentation shrinks, especially when spherical indenters are used. Thus the indentation diameter has to be measured immediately after the test. A related problem is that the poor reflectivity of polymeric materials makes the accurate measurement of indentation size rather difficult. Additionally, some polymers like nylon readily absorb fluids, including water, from the environment, which may also affect the dimensional stability of the indentation and hence may result in inaccuracies of hardness measurement.
6.3 Coatings In the case of coatings, the intrinsic hardness value of the coating material can be obtained only if the depth of indentation is less than 10% of the thickness of the coating. The above statement is true irrespective of whether the coating is harder or softer than the substrate (Matsuda and Kaneta 1996). Thus, the intrinsic hardness of coatings of thickness 10 µm or more can be obtained using a microhardness tester, while coatings a few microns thick will require an ultramicrohardness tester. In contrast, measurement of the hardness of coatings having thicknesses in the submicron range will require the use of a nanoindentation facility. If the available hardness tester is such that the depth of indentation exceeds 10% of the coating thickness, the hardness values obtained should be reported as the composite hardness of the coating–substrate system. Various mathematical models have been developed to obtain the intrinsic hardness of the coating from the composite hardness values (e.g., see Korunsky et al. 1998).
7. Hardness Testing: General Considerations In this section, important guidelines are described which should be followed while selecting the appropriate hardness test, and also while carrying out the hardness tests. The choice of the appropriate hardness test depends
Hardness Testing on a number of factors. The productivity (tests per hour) of the ultrasonic hardness tester is the highest, and the Rockwell hardness tester comes second. While a machined and ground surface is enough for Rockwell hardness testing, a smoother surface is required for other hardness testers. Microhardness and ultramicrohardness tests require well-polished surfaces. The minimum thickness of the test piece\work piece required for carrying out valid hardness measurement depends on the type of hardness tester. The general rule is that the thickness of the test piece\work piece should be at least 10 times the depth of indentation. This criterion can be incorporated in the hardness– diameter\depth of indentation relationship valid for various hardness tests, to obtain the minimum specimen thickness (Tmin) required for the hardness data obtained using a given hardness test to be valid. The spacing of the indenters should be such that the distance from the center of one indentation to another must be at least three times the indentation diameter or the longer diagonal. Similarly, the distance from the center of the indentation to the edge of the specimen should be a minimum of 2.5 times the diameter or longer diagonal of the indentation. At low loads, especially in the case of micro-, ultramicro-, and nanohardness testing, the hardness may itself become a function of indentation size. This is usually referred to as the size effect and the phenomenon is not completely understood. From a practical standpoint, the load selected should be as large as practically possible (keeping in mind the limitations due to specimen thickness) to circumvent the size effect.
8. Use of Hardness Testing for Obtaining Other Properties 8.1 Determination of Elastic Modulus The elastic modulus of the near surface region of a bulk test piece, or of the coating deposited on a substrate, can be obtained using depth-sensing hardness tests like the ultramicro- and nanohardness testers. The elastic modulus is obtained from the loading–unloading curve discussed earlier and shown in Fig. 2. The slope of the initial portion of the unloading curve equals the contact stiffness S ( l dP\dh where P l load and h l depth of indentation). Once S is obtained as above and the contact area (A) between the indenter and the test piece is calculated on the basis of the known relationship between the indentation depth and contact area, the elastic modulus of the test material is obtained using the relation (Pharr et al. 1992): El
1kν# (0.89S\A"/#)k(1kν#i \Ei)
(4)
In the above equation, Ei and νi represent the elastic modulus and Poisson’s ratio of the indenter material, respectively, while E and ν correspond to the elastic modulus and Poisson’s ratio of the test material. Since Ei and νi are known (especially for the commonly used indenter material, i.e., diamond), by assuming a reasonable value for the Poisson’s ratio of the test material (ν), the elastic modulus of the test material can be computed. The indentation-based technique for estimating elastic modulus is especially useful for estimating the modulus of thin coatings.
8.2 Determination of Flow Stress–Strain Behaior of Metallic Materials and Coatings The concept of using the indentation test with a spherical ball as the indenter, to evaluate the flow stress–strain behavior of the indented material, was pioneered as early as 1951 by Tabor. The relevant equations which relate the indentation diameter (d ) and the corresponding applied load (P) with the flow stress (σ) and the corresponding plastic strain (ε) are as follows: σl
4P πd #C
(5)
εl
0.2d D
(6)
where C is the constraint factor (usually having a value of around 3) and D is the indenter (ball) diameter. Thus, indentation tests carried out over a range of load will result in the flow stress (σ) data being obtained over a range of plastic strain (ε). The above concept has been demonstrated to be valid even under dynamic indentation (DI) conditions, thereby allowing the σ(ε) curves to be obtained even at dynamic strain rates of the order of 10% s−". The above technique is particularly suitable for obtaining the stress–strain behavior of coatings and thin films (invariably spherical tip indenters are used for the above purpose), and also of very thin specimens.
8.3 Indentation Toughness of Brittle Materials In the case of brittle materials, indentation testing has been successfully utilized to evaluate their toughness. In this technique, the fracture resistance is related to the scale of the crack pattern. Over the years, a large number of models have been developed relating toughness of the test piece (Kc) to the measured postindentation crack size (C ) (see Fig. 3 for details). 7
Hardness Testing ranking of a large number of materials on the basis of their creep resistance, the indentation creep technique has proved useful (see Creep by Indentation).
8.5 Adhesion of Coatings The scratch hardness tester described in Sect. 2.4 can also be utilized for measuring the adhesion strength of coatings. For this purpose, the stylus is dragged across the surface of the coating to be tested, under progressively increasing loads, until either the coating peels off or the coating–substrate interface starts cracking. The peeling off of the coating can be observed under a microscope, while the formation of the crack at the interface is usually detected using an acoustic signal detector and processor (normally supplied with the scratch hardness tester). The load (Fc) at which the coating peels off or the interface cracks is usually defined as the ‘‘adhesion strength’’ of the coating. The above technique has been standardized so far only for thin coatings (a few micrometers thick). Figure 3 A photomicrograph of the crack pattern formed around a Vickers indenter.
9. Concluding Remarks However, all these models invariably lead to an equation of the form: E
KC l β F
E H
G
E
H
n F
P C$/#
G
(7) H
In the above equation, β is a constant, H is the Vickers hardness of the test material, P is the applied load, E is the elastic modulus of the test material, and n is a constant usually in the range 0.4–0.5 (McColm 1990). The KC values of a large number of ceramic materials have been determined using the above technique.
8.4 Indentation Creep Over the years, many investigators have attempted to correlate the hardness behavior of materials at elevated temperatures (beyond 0.5 times the absolute melting point of the test material) with the tensile creep behavior. In many systems, depending on the time of application of load, there is a change in the size of the indentation diameter. This results in an apparent reduction of the hardness of materials. The effect is known as indentation creep. However, this technique is not very popular, mainly because the stress state underneath the indenter is complex and multiaxial, and also not uniform. Thus the correlation of the indentation creep rate with the tensile creep rate is not straightforward. However, for assessing the relative 8
In this article, the salient features of all the available indentation-based hardness test techniques have been described. In addition, the use of hardness test equipment to evaluate properties other than hardness of the test material has been described. Hardness testing has stood the test of time and has retained its recognition and usefulness amongst the engineering and scientific community. There can be no doubt that hardness testing will be an important tool in the coming years as well. However, with the drive towards automation encompassing all fields, it is likely that hardness testers of the future will be invariably based on the measurement of indentation depth, rather than indentation diameter or length. This is so because sensor-based measurement, integral to any automated system, is much easier and more accurate in the case of depth of indentation. An added advantage of depthbased hardness measurement, which is likely to be exploited in the coming years, is that the load-depth of indentation curves can be deconvoluted, to provide hardness vs. depth data on the basis of a single test. See also: Thin Films: Mechanical Testing
Bibliography ASTM 1984 Standard test methods for Rockwell hardness and Rockwell superficial hardness of metallic materials. Annual Book of ASTM Standards. American Society for Testing and Materials, Philadelphia, PA, Sects. E10, E18, E92 Blau P J, Lawn B R 1986 Microindentation Techniques in
Hardness Testing Materials Science and Engineering. ASTM STP 889. American Society for Testing and Materials, Philadelphia, PA Korunsky A M, McGurk M R, Bull S J, Page T F 1998 On the hardness of coated systems. Surf. Coat. Technol. 99, 171–83 Matsuda K, Kaneta M 1996 Analysis of the Vickers hardness of electroplated coatings. Phil. Mag. A 74, 1171–84
McColm I J 1990 Ceramic Hardness. Plenum, New York Pharr G M, Oliver W C, Brotzen F R 1992 On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res. 7, 613–17
G. Sundararajan and M. Roy
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 3728–3736 9