1. WHAT IS HARDNESS?
The Metals Handbook defines hardness as "Resistance of metal to plastic deformation, usually by indentation. However, the term may also refer to stiffness or temper, or to resistance to scratching, abrasion, or cutting. It is the property of a metal, which gives it the ability to resist being permanently, deformed (bent, broken, or have its shape changed), when a load is applied. The greater the hardness of the metal, the greater resistance it has to deformation.
In mineralogy the property of matter commonly described as the resistance of a substance to being scratched by another substance. In metallurgy hardness is defined as the ability of a material to resist plastic deformation.
The dictionary of Metallurgy defines the indentation hardness as the resistance of a material to indentation. This is the usual type of hardness test, in which a pointed or rounded indenter is pressed into a surface under a substantially static load.
2. HARDNESS MEASUREMENT
Hardness measurement can be defined as macro-, micro- or nano- scale according to the forces applied and displacements obtained .
Measurement of the macro-hardness of materials is a quick and simple method of obtaining mechanical property data for the bulk material from a small sample. It is also widely used for the quality control of surface treatments processes. However, when concerned with coatings and surface properties of importance to friction and wear processes for instance, the macro-indentation depth would be too large relative to the surface-scale features.
Where materials have a fine microstructure, are multi-phase, non-homogeneous or prone to cracking, macro-hardness measurements will be highly variable and will not identify individual surface features. It is here that micro-hardness measurements are appropriate.
Microhardness is the hardness of a material as determined by forcing an indenter such as a Vickers or Knoop indenter into the surface of the material under 15 to 1000 gf load; usually, the indentations are so small that they must be measured with a microscope. Capable of determining hardness of different microconstituents within a structure, or measuring steep hardness gradients such as those encountered in casehardening. Conversions from microhardness values to tensile strength and other hardness scales (e.g. Rockwell) are available for many metals and alloys.
Micro-indenters works by pressing a tip into a sample and continuously measuring: applied load, penetration depth and cycle time.
Nano-indentation tests measure hardness by indenting using very small, on the order of 1 nano-Newton, indentation forces and measuring the depth of the indention that was made. These tests are based on new technology that allows precise measurement and control of the indenting forces and precise measurement of the indentation depths. By measuring the depth of the indentation, progressive levels of forcing are measurable on the same piece. This allows the tester to determine the maximum indentation load that is possible before the hardness is compromised and the film is no longer within the testing ranges. This also allows a check to be completed to determine if the hardness remains constant even after an indentation has been made.
There are various mechanisms and methods that have been designed to complete nano-indentation hardness tests. One method of force application is using a coil and magnet assembly on a loading column to drive the indenter downward. This method uses a capacitance displacement gauge. Such gages detect displacements of 0.2 to 0.3 NM (nanometer) at the time of force application. The loading column is suspended by springs, which damps external motion and allows the load to be released slightly to recover the elastic portion of deformation before measuring the indentation depth. This type of nano-indentation machine can be seen in Figure 1.
Another method of nano-indentation uses a long-range piezo driver and an elastic element as shown in Figure 2. When the indenter is moved downward by the piezo driver, the elastic element resists the movement and establishes a force. This force is measurable by knowing the distance that the indenter moved downward after touching the film surface. An LVDT (linear variable differential transform) records the position of the shaft, thereby measuring the indentation depth and the spring force applied at one time.
3. HARDNESS MEASUREMENT METHODSThere are three types of tests used with accuracy by the metals industry; they are the Brinell hardness test, the Rockwell hardness test, and the Vickers hardness test. Since the definitions of metallurgic ultimate strength and hardness are rather similar, it can generally be assumed that a strong metal is also a hard metal. The way the three of these hardness tests measure a metal's hardness is to determine the metal's resistance to the penetration of a non-deformable ball or cone. The tests determine the depth which such a ball or cone will sink into the metal, under a given load, within a specific period of time. The followings are the most common hardness test methods used in today`s technology:
- Rockwell hardness test
- Brinell hardness
- Knoop hardness
3.1. Rockwell Hardness Test
The Rockwell Hardness test is a hardness measurement based on the net increase in depth of impression as a load is applied. Hardness numbers have no units and are commonly given in the R, L, M, E and K scales. The higher the number in each of the scales means the harder the material.
Hardness has been variously defined as resistance to local penetration, scratching, machining, wear or abrasion, and yielding. The multiplicity of definitions, and corresponding multiplicity of hardness measuring instruments, together with the lack of a fundamental definition, indicates that hardness may not be a fundamental property of a material, but rather a composite one including yield strength, work hardening, true tensile strength, modulus of elasticity, and others. In the Rockwell method of hardness testing, the depth of penetration of an indenter under certain arbitrary test conditions is determined. The indenter may either be a steel ball of some specified diameter or a spherical diamond-tipped cone of 120° angle and 0.2 mm tip radius, called Brale. The type of indenter and the test load determine the hardness scale(A, B, C, etc).
A minor load of 10 kg is first applied, which causes an initial penetration and holds the indenter in place.Then, the dial is set to zero and the major load is applied. Upon removal of the major load, the depth reading is taken while the minor load is still on. The hardness number may then be read directly from the scale.
The hardness of ceramic substrates can be determined by the Rockwell hardness test, according to the specifications of ASTM E-18. This test measures the difference in depth caused by two different forces, using a dial gauge. Using standard hardness conversion tables, the Rockwell hardness value is determined for the load applied, the diameter of the indentor, and the indentation depth.
The hardness testing of plastics is most commonly measured by the Rockwell hardness test or Shore (Durometer) hardness test. Both methods measure the resistance of the plastic toward indentation. Both scales provide an empirical hardness value that doesn't correlate to other properties or fundamental characteristics. Rockwell hardness is generally chosen for 'harder' plastics such as nylon, polycarbonate, polystyrene, and acetal where the resiliency or creep of the polymer is less likely to affect the results.
The results obtained from this test are a useful measure of relative resistance to indentation of various grades of plastics. However, the Rockwell hardness test does not serve well as a predictor of other properties such as strength or resistance to scratches, abrasion, or wear, and should not be used alone for product design specifications.
The Rockwell hardness tester to measure the hardness of metal measures resistance to penetration like the Brinell test, but in the Rockwell case, the depth of the impression is measured rather than the diametric area. With the Rockwell tester, the hardness is indicated directly on the scale attached to the machine. This dial like scale is really a depth gauge, graduated in special units. The Rockwell hardness test is the most used and versatile of the hardness tests.
For soft materials such as copper alloys, soft steel, and aluminum alloys a 1/16" diameter steel ball is used with a 100-kilogram load and the hardness is read on the "B" scale. In testing harder materials, hard cast iron and many steel alloys, a 120 degrees diamond cone is used with up to a 150 kilogram load and the hardness is read on the "C" scale. The Rockwell test uses two loads, one applied directly after the other. The first load, known as the "minor", load of 10 kilograms is applied to the specimen to help seat the indenter and remove the effects, in the test, of any surface irregularities. In essence, the minor load creates a uniformly shaped surface for the major load to be applied to. The difference in the depth of the indentation between the minor and major loads provides the Rockwell hardness number. There are several Rockwell scales other than the "B" & "C" scales, (which are called the common scales). The other scales also use a letter for the scale symbol prefix, and many use a different sized steel ball indenter. A properly used Rockwell designation will have the hardness number followed by "HR" (Hardness Rockwell), which will be followed by another letter which indicates the specific Rockwell scale. An example is 60 HRB, which indicates that the specimen has a hardness reading of 60 on the B scale. There is a second Rockwell tester referred to as the "Rockwell Superficial Hardness Tester". This machine works the same as the standard Rockwell tester, but is used to test thin strip, or lightly carburized surfaces, small parts or parts that might collapse under the conditions of the regular test. The Superficial tester uses a reduced minor load, just 3 kilograms, and has the major load reduced to either 15 or 45 kilograms depending on the indenter, which are the same ones used for the common scales. Using the 1/16" diameter, steel ball indenter, a "T" is added (meaning thin sheet testing) to the superficial hardness designation. An example of a superficial Rockwell hardness is 15T-22, which indicates the superficial hardness as 22, with a load of 15 kilograms using the steel ball. If the 120Ў diamond cone were used instead, the "T" would be replaced with "N".
instead, the "T" would be replaced with "N". The ASTM (American Society for Testing & Materials) has standardized a set of scales (ranges) for Rockwell hardness testing. Each scale is designated by a letter.
3.2. Brinell Hardness Test
Brinell hardness is determined by forcing a hard steel or carbide sphere of a specified diameter under a specified load into the surface of a material and measuring the diameter of the indentation left after the test.The Brinell hardness number, or simply the Brinell number, is obtained by dividing the load used, in kilograms, by the actual surface area of the indentation, in square millimeters.The result is a pressure measurement, but the units are rarely stated .
The Brinell hardness test  uses a desk top machine to press a 10mm diameter, hardened steel ball into the surface of the test specimen. The machine applies a load of 500 kilograms for soft metals such as copper, brass and thin stock. A 1500 kilogram load is used for aluminum castings, and a 3000 kilogram load is used for materials such as iron and steel. The load is usually applied for 10 to 15 seconds. After the impression is made, a measurement of the diameter of the resulting round impression is taken. It is measured to plus or minus .05mm using a low-magnification portable microscope. The hardness is calculated by dividing the load by the area of the curved surface of the indention, (the area of a hemispherical surface is arrived at by multiplying the square of the diameter by 3.14159 and then dividing by 2). To make it easier, a calibrated chart is provided, so with the diameter of the indentation the corresponding hardness number can be referenced. A well structured Brinell hardness number reveals the test conditions, and looks like this, "75 HB 10/500/30" which means that a Brinell Hardness of 75 was obtained using a 10mm diameter hardened steel with a 500 kilogram load applied for a period of 30 seconds. On tests of extremely hard metals a tungsten carbide ball is substituted for the steel ball. Among the three hardness tests discussed, the Brinell ball makes the deepest and widest indentation, so the test averages the hardness over a wider amount of material, which will more accurately account for multiple grain structures, and any irregularities in the uniformity of the alloy.
The Brinell hardness test was one of the most widely used hardness tests during World War II . For measuring armour plate hardness the test is usually conducted by pressing a tungsten carbide sphere 10mm in diameter into the test surface for 10 seconds with a load of 3,000kg, then measuring the diameter of the resulting depression. The BHN is calculated according to the following formula:
BHN = the Brinell hardness number
F = the imposed load in kg
D = the diameter of the spherical indenter in mm
Di = diameter of the resulting indenter impression in mm
Several BHN tests are usually carried out over an area of armour plate. On a typical plate each test would result in a slightly different number. This is due not only to minor variations in quality of the armour plate (even homogenous armour is not absolutely uniform) but also because the test relies on careful measurement of the diameter of the depression. Small errors in this measurement will lead to small variations in BHN values. As a result, BHN is usually quoted as a range of values (e.g. 210 to 245, or 210-245) rather
than as a single value.
The BHN of face hardened armour uses a back slash ?\? to separate the value of the face hardened surface from the value of the rear face. For example, a BHN of 555\353-382 indicates the surface has a hardness of 555 and the rear face has a hardness of 353 to 382.
The Brinell Hardness Test described above is called ?HB 10/3000 WC? and was the type of test used by the Germans in World War II. Other types of hardness tests use different materials for the sphere and/or different loads. Softer materials deform at high BHN which is why tungsten carbide (a very hard material) is used to measure armour plate. Even so, as the BHN goes above 650 the tungsten carbide ball begins to flatten out and the BHN values indicate a greater difference in hardness than there actually is, while above 739 the ball flattens out so badly that it cannot be used.
When there are widely different values for quoted BHN then the cause may be use of a Poldi Hardness Tester instead of the Brinell Hardness Test. The Poldi Hardness Tester is less accurate but could be used in the field. The Poldi Hardness Test has the advantage that the testing unit is portable, so measurements can be carried out in the field, e.g. on captured enemy vehicles after a battle. The Poldi portable unit relies on a hammer blow impression in a standardized sample. This test is much less accurate than the Brinell Hardness Test.
ASTM E-10 is a standard test for determining the Brinell hardness of metallic materials. The load applied in this test is usually 3,000, 1,500, or 500 kgf, so that the diameter of the indentation is in the range 2.5 to 6.0 mm. The load is applied steadily without a jerk. The full test load is applied for 10 to 15 seconds. Two diameters of impression at right angles are measured, and the mean diameter is used as a basis for calculating the Brinell hardness number (BHN), which is done using the conversion table given in the standard .
3.3. Vickers Hardness Test
It is the standard method for measuring the hardness of metals, particularly those with extremely hard surfaces: the surface is subjected to a standard pressure for a standard length of time by means of a pyramid-shaped diamond. The diagonal of the resulting indention is measured under a microscope and the Vickers Hardness value read from a conversion table 
Vickers hardness is a measure of the hardness of a material, calculated from the size of an impression produced under load by a pyramid-shaped diamond indenter. Devised in the 1920s by engineers at Vickers, Ltd. in the United Kingdom, the diamond pyramid hardness test, as it also became known, permitted the establishment of a continuous scale of comparable numbers that accurately reflected the wide range of hardnesses found in steels.
The indenter employed in the Vickers test is a square-based pyramid whose opposite sides meet at the apex at an angle of 136є. The diamond is pressed into the surface of the material at loads ranging up to approximately 120 kilograms-force, and the size of the impression (usually no more than 0.5 mm) is measured with the aid of a calibrated microscope. The Vickers number (HV) is calculated using the following formula:
HV = 1.854(F/D2),
with F being the applied load (measured in kilograms-force) and D2 the area of the indentation (measured in square millimetres). The applied load is usually specified when HV is cited.
The Vickers test is reliable for measuring the hardness of metals, and also used on ceramic materials. The Vickers testing method  is similar to the Brinell test. Rather than using the Brinell's steel ball type indenter, and have to calculate the hemispherical area of impression, the Vickers machine uses a penetrator that is square in shape, but tipped on one corner so it has the appearance of a playing card "diamond". The Vickers indenter is a 136 degrees square-based diamond cone, the diamond material of the indenter has an advantage over other indenters because it does not deform over time and use. The impression left by the Vickers penetrator is a dark square on a light background. The Vickers impression is more easily "read" for area size than the circular impression of the Brinell method. Like the Brinell test, the Vickers number is determined by dividing the load by the surface area of the indentation (H = P/A). The load varies from 1 to 120 kilograms. To perform the Vickers test, the specimen is placed on an anvil that has a screw threaded base. The anvil is turned raising it by the screw threads until it is close to the point of the indenter. With start lever activated, the load is slowly applied to the indenter. The load is released and the anvil with the specimen is lowered. The operation of applying and removing the load is controlled automatically.
Several loadings give practically identical hardness numbers on uniform material, which is much better than the arbitrary changing of scale with the other hardness machines. A filar microscope is swung over the specimen to measure the square indentation to a tolerance of plus or minus 1/1000 of a millimeter. Measurements taken across the diagonals to determine the area, are averaged. The correct Vickers designation is the number followed "HV" (Hardness Vickers). The advantages of the Vickers hardness test are that extremely accurate readings can be taken, and just one type of indenter is used for all types of metals and surface treatments. Although thoroughly adaptable and very precise for testing the softest and hardest of materials, under varying loads, the Vickers machine is a floor standing unit that is rather more expensive than the Brinell or Rockwell machines .
3.4. Knoop hardness
The relative microhardness of a material is determined by the Knoop indentation test. In this test, a pyramid-shaped diamond indenter with apical angles of 130° and 172°30? (called a Knoop indenter) is pressed against a material. Making a thombohedral impression with one diagonal seven times longer than the other. The hardness of the material is determined by the depth to which the Knoop indenter penetrates .
This test method was devised in 1939 by F. Knoop and colleagues at the National Bureau of Standards in the United States. By using lower indentation pressures than the Vickers hardness test, which had been designed for measuring metals, the Knoop test allowed the hardness testing of brittle materials such as glass and ceramics.
The diamond indenter employed in the Knoop test is in the shape of an elongated four-sided pyramid, with the angle between two of the opposite faces being approximately 170є and the angle between the other two being 130є. Pressed into the material under loads that are often less than one kilogram-force, the indenter leaves a four-sided impression about 0.01 to 0.1 mm in size. The length of the impression is approximately seven times the width, and the depth is 1/30 the length. Given such dimensions, the area of the impression under load can be calculated after measuring only the length of the longest side with the aid of a calibrated microscope. The final Knoop hardness (HK) is derived from the following formula:
HK = 14.229(F/D2),
with F being the applied load (measured in kilograms-force) and D2 the area of the indentation (measured in square millimetres). Knoop hardness numbers are often cited in conjunction with specific load values.
ASTM D-1474 deals with standard test methods for indentation hardness of organic coatings. In this test, Knoop hardness determinations are made at 23 ± 2° C and 50 ± 5% relative humidity. The specimens are equilibrated under these conditions for at least 24 hours. They are then rigidly attached to the movable stage so that the surface to be measured is normal to the direction of the indentation. The apparatus is preset to apply a 25 g load. The time the indentor is in contact with the specimen should be 18 ± 0.5 seconds. The length of the long diagonal of the impression is measured with the filar micrometer eyepiece. The procedure is repeated until at least five impressions have been made at widely spaced locations. The Knoop hardness number is then calculated by
where 0.0025 is the load applied in kg to the indentor, l is the length of the long diagonal of the indentation in mm, and Cp is the indentor constant, equal to 7.028 x 10-2.
ASTM D-785 is the standard test for determining the Rockwell hardness of plastics and electrical insulating materials. A minor load of 10 kg, which is built into the machine, is first applied without shock. Within 10 seconds after applying the minor load and immediately after set position if obtained, the major load is applied on the specimen. The major load is removed 15 seconds after its application. The Rockwell hardness is read off the scale on the machine. Care should be taken in choosing the proper scale, as Rockwell hardness values are reported as a letter, indicating the scale, and a number, indicating the reading .
The shore scleroscope measures hardness in terms of the elasticity of the material. A diamond-tipped hammer in a graduated glass tube is allowed to fall from a known height on the specimen to be tested, and the hardness number depends on the height to which the hammer rebounds; the harder the material, the higher the rebound .
Shore hardness  is a measure of the resistance of material to indentation by 3 spring-loaded indenter. The higher the number, the greater the resistance.
The hardness testing of plastics is most commonly measured by the Shore (Durometer) test or Rockwell hardness test. Both methods measure the resistance of the plastic toward indentation. Both scales provide an empirical hardness value that doesn't correlate to other properties or fundamental characteristics. Shore Hardness, using either the Shore A or Shore D scale, is the preferred method for rubbers/elastomers and is also commonly used for 'softer' plastics such as polyolefins, fluoropolymers, and vinyls. The Shore A scale is used for 'softer' rubbers while the Shore D scale is used for 'harder' ones. The shore A Hardness is the relative hardness of elastic materials such as rubber or soft plastics can be determined with an instrument called a Shore A durometer. If the indenter completely penetrates the sample, a reading of 0 is obtained, and if no penetration occurs, a reading of 100 results. The reading is dimensionless.
The Shore hardness is measured with an apparatus known as a Durometer and consequently is also known as 'Durometer hardness'. The hardness value is determined by the penetration of the Durometer indenter foot into the sample. Because of the resilience of rubbers and plastics, the hardness reading my change over time - so the indentation time is sometimes reported along with the hardness number. The ASTM test number is ASTM D2240 while the analogous ISO test method is ISO 868.
The results obtained from this test are a useful measure of relative resistance to indentation of various grades of polymers. However, the Shore Durometer hardness test does not serve well as a predictor of other properties such as strength or resistance to scratches, abrasion, or wear, and should not be used alone for product design specifications.
Figure 5. Shore A vs. Shore D
Figure 6. Shore D vs. Rockwell M 
Figure 7. Hardness comparison scale of some materials 
3.6.1. Mohs Hardness:
Mohs hardness is defined by how well a substance will resist scratching by another substance . It is rough measure of the resistance of a smooth surface to scratching or abrasion, expressed in terms of a scale devised (1812) by the German mineralogist Friedrich Mohs. The Mohs hardness  of a mineral is determined by observing whether its surface is scratched by a substance of known or defined hardness.
To give numerical values to this physical property, minerals are ranked along the Mohs scale, which is composed of 10 minerals that have been given arbitrary hardness values. The minerals contained in the scale are shown in the Table; also shown are other materials that approximate the hardness of some of the minerals. As is indicated by the ranking in the scale, if a mineral is scratched by orthoclase but not by apatite, its Mohs hardness is between 5 and 6. In the determination procedure it is necessary to be certain that a scratch is actually made and not just a "chalk" mark that will rub off. If the species being tested is fine-grained, friable, or pulverulent, the test may only loosen grains without testing individual mineral surfaces; thus certain textures or aggregate forms may hinder or prevent a true hardness determination. For this reason the Mohs test, while greatly facilitating the identification of minerals in the field, is not suitable for accurately gauging the hardness of industrial materials such as steel or ceramics. (For these materials a more precise measure is to be found in the Vickers hardness or Knoop hardness;) Another disadvantage of the Mohs scale is that it is not linear; that is, each increment of one in the scale does not indicate a proportional increase in hardness. For instance, the progression from calcite to fluorite (from 3 to 4 on the Mohs scale) reflects an increase in hardness of approximately 25 percent; the progression from corundum to diamond, on the other hand (9 to 10 on the Mohs scale), reflects a hardness increase of more than 300 percent.
3.6.2. Barcol Hardness
Barcol hardness is a method that a hardness value obtained by measuring the resistance to penetration of a sharp steel point under a spring load. The instrument, called the Barcol impressor, gives a direct reading on a 0 to 100 scale. The hardness value is often used as a measure of the degree of cure of a plastic.
ASTM D2583 Barcol Hardness test method is used to determine the hardness of both reinforced and non-reinforced rigid plastics. The specimen is placed under the indentor of the Barcol hardness tester and a uniform pressure is applied to the specimen until the dial indication reaches a maximum. The depth of the penetration is converted into absolute Barcol numbers.
Barcol hardness values are also used to determine degree of cure of resin. Resin is considered cured when it has a hardness value greater than or equal to 90% of the surface hardness value.
4. HARDNESS OF ELECTRONIC PACKAGING MATERIALS:
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