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. 12k Downloads.AbstractThe Brinell, Vickers, Meyer, Rockwell, Shore, IHRD, Knoop, Buchholz, and nanoindentation methods used to measure the indentation hardness of materials at different scales are compared, and main issues and misconceptions in the understanding of these methods are comprehensively reviewed and discussed. Basic equations and parameters employed to calculate hardness are clearly explained, and the different international standards for each method are summarized. The limits for each scale are explored, and the different forms to calculate hardness in each method are compared and established.
The influence of elasticity and plasticity of the material in each measurement method is reviewed, and the impact of the surface deformation around the indenter on hardness values is examined. The difficulties for practical conversions of hardness values measured by different methods are explained. Finally, main issues in the hardness interpretation at different scales are carefully discussed, like the influence of grain size in polycrystalline materials, indentation size effects at micro- and nanoscale, and the effect of the substrate when calculating thin films hardness. The paper improves the understanding of what hardness means and what hardness measurements imply at different scales.
The hardness of a solid material can be defined as a measure of its resistance to a permanent shape change when a constant compressive force is applied. The deformation can be produced by different mechanisms, like indentation, scratching, cutting, mechanical wear, or bending. In metals, ceramics, and most of polymers, the hardness is related to the plastic deformation of the surface. Hardness has also a close relation to other mechanical properties like strength, ductility, and fatigue resistance, and therefore, hardness testing can be used in the industry as a simple, fast, and relatively cheap material quality control method.Since the Austrian mineralogist Friedrich Mohs devised in 1812 the first methodical test to measure the hardness , a large variety of methods have been established for determining the hardness of a substance. The first report of a machine to measure indentation hardness was done by William Wade in 1856 , where a specified load was applied to a pyramid-shaped hardened tool, and the hardness value was evaluated from the size of the deformed cavity on the surface.
At the beginning of the twentieth century, there were already commercially available machines for measuring indentation hardness because of the increasing demand for testing steels and rubbers. Mass production of parts in the new aeronautic, automotive, and machine tool industries required every item produced to be quality tested. During World War I and World War II, macroindentation and later micro-indentation tests had a big role for controlling gun production. However, it was only in 1951 when the scientific basis for the indentation hardness tests was settled in the seminal work of Tabor. It represented a revolutionary model based on theoretical developments and careful experiments which provided the physical insight for the understanding of the indentation phenomena.The arrival of the microelectronics and nanotechnology age pushed in the 1980s the development of novel methods for the measurement of hardness at nanoscale size. This development was possible thanks to advances in high-sensitive instrumentation controlling distances in tens of picometers, and loads below the micro-Newtons range.
This novel approach for indentation hardness is based on controlling and recording continuously the indenter position and load during the indentation. The measurement instruments, known as nanoindenters, have very sharp and small tips for the indentation of volumes at the nanoscale.Nowadays it is known that material hardness is a multifunctional physical property depending on a large number of internal and external factors. The transition from macroscale to microscale and from microscale to nanoscale indentation hardness measurement is accompanied by a decreasing influence of some of these factors and by an increasing contribution of others. Indentation hardness value also depends on the test used to measure it. In order to work with comparable measured values, international standard methods have been developed for different methods at macro-, micro-, and nanoscale ,.During the last 15 years, the indentation hardness methods have been discussed in many specialized books and papers.
A survey for the period 2001–2015 in the database Google Books using as keyword “indentation hardness” estimates 88 books or book chapters, and the same search in Google Scholar gives about 12,100 papers. However, if the same search is done including the names of the main indentation hardness methods discussed in this review (Brinell, Vickers, Meyer, Rockwell, Shore, IHRD, Knoop, and nanoindentation), the search result indicates that only one book but no papers containing all these methods have been published in the period 2001–2015. The book is, in fact, an edited book by Herrmann published in 2011 where all these methods are developed in unconnected chapters written by different authors, so no real correlation of comparison between methods at different scales is developed in the work.In this paper, the major methods used to measure the indentation hardness of materials at different scales are compared, and main issues and misconceptions in the understanding of these methods are compressively reviewed and discussed.
The indentation hardness methods at macro-, micro-, and nanoscale are examined in Sects., and, respectively. The basic equations and parameters employed to calculate hardness are clearly explained, and the different international standards for each method are summarized. Section critically discusses different issues related to indentation hardness at multiple scales.
First, the limits for each scale are explored, and the different forms to calculate hardness in each method are compared and established. The influence of elasticity and plasticity of the material in each measurement method is reviewed, and the impact of the surface deformation around the indenter on hardness values is examined. The difficulties for practical conversions of hardness values measured by different methods are explained.
Finally, main issues in the hardness interpretation at different scales are carefully discussed, like the influence of grain size in polycrystalline materials, indentation size effects at micro- and nanoscale, and the effect of the substrate when calculating thin films hardness. 2 Macroindentation Tests. Macroindentation tests are characterized by indentations loads L in the range of 2 N. Proposed by Johan A. Brinell in 1900, this is from the historic point of view the first standardized indentation hardness test devised for engineering and metallurgy applications. In this test, a ball of diameter D (mm) is used to indent the material through the application of a load L, as shown in Fig. The diameter d (mm) of the indentation deformation on the surface is measured with an optical microscope, and the Brinell hardness number (BHN) is then calculated as the load divided by the actual area A c of the curved surface of the impression.
(1)In the original test proposed by Brinell, the load L is expressed in kilogram force. If L is measured in N (SI system), Eq. Should be divided by 9.8065. The full test load is applied for a period of 10–15 s. Two diameters of impression at right angles are measured (usually in the range 2–6 mm), and the mean diameter value is used for calculating the Brinell hardness number.
The standard from the American Society for Testing and Materials (ASTM) E10-15a and the International Organization for Standardization (ISO) standard 6506-1 explain the standard method for Brinell hardness of metallic materials, as well as the calibration of the testing machine and reference materials. The typical test uses a 10-mm (0.39 in)-diameter steel ball as an indenter with a 3000 kgf (29.4 kN) load. For softer materials, a smaller force can be used: 1500 kgf (14.7 N) load is usually used for Al, while Cu is tested using a 500 kg (4.9 kN) test force. For harder materials, a tungsten carbide ball substitutes the steel ball.
In the European ISO standards, Brinell testing is done using a much wider range of forces and ball sizes: it is common to perform Brinell tests on small parts using a 1-mm carbide ball and a test force as low as 1 kg (9.8 N), referred as “baby” Brinell test.When quoting a Brinell hardness number (BHN or more commonly HB), it is also necessary to mention the conditions of the test. There is a standard format for specifying tests: for instance, a value reported as “125 HB 10/1500/30” means that a Brinell hardness of 125 was obtained using a 10-mm-diameter ball with a 1500 kg load (14.7 kN) applied during 30 s.It is interesting to note that for steels, the hardness HB value divided by two gives approximately the ultimate tensile strength in units of kilo-pound per square inch (1 ksi = 6.9 MPa). This feature contributed to its adoption over competing hardness tests in the steel industry.
2.2 Meyer Test. The Vickers hardness test is 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. (UK) , the indenter is a square-based pyramid whose opposite sides meet at the apex with an angle of 136°, the edges at 148°, and faces at 68°. In designing the new indenter, they chose a geometry that would produce hardness numbers nearly identical to Brinell numbers within the range of both tests.
The Vickers diamond hardness number, HV, is calculated using the indenter load L and the actual surface area of the impression A c. Fig. 2Vickers micro-indentation testThe time for the initial application of the force is 2–8 s, and the test force is maintained during 10–15 s.
The applied loads vary from 1 to 120 kgf (9.8 N–1.2 kN), with standard values of 5, 10, 20, 30, 50, 100, and 120 kgf (1 kgf–9.8 N) ,. The size of the impression (usually no more than 0.5 mm) is measured with the aid of a calibrated microscope with a tolerance of ±1/1000 mm. The Vickers hardness can be related to the diagonal d or the penetration depth t which are related as d = 7 t. The Vickers contact area and the penetration depth are related as A c = 24.5 t 2 if the elastic recovery of the material is not important.The Vickers hardness is denoted as HV, and frequently, the units are also reported as kgf/mm 2, or in MPa (the value in kgf/mm 2 multiplied by 9.8065). 2.4 Rockwell TestThe Rockwell test determines the hardness by measuring the depth of penetration of an indenter under a large load compared to the penetration made by a smaller preload.
The differential-depth hardness measurement used in the method was conceived in 1908 by the Austrian professor Paul Ludwik in his book Die Kegelprobe (“the cone test”). The use of an initial low load in this method has the advantage to eliminate errors in measuring the penetration depth, like backlash and surface imperfections.
Based on this method, the brothers Hugh M. Rockwell and Stanley P.
Rockwell from USA patented a “Rockwell hardness tester,” which was a differential-depth machine. There are several L 1 loads: 60, 100, and 150 kgf (1 kgf–9.8 N), and several ball diameters: 1/2, 1/4, 1/8, and 1/16 inch (1 inch–2.52 cm) that can be used, as established in the standards ISO 6508-1 and ASTM E18 for metallic materials, and ISO 2039-2 for plastics. These methods are named with letters: (scales A, B, C, D, E, F, G, H, K, L, M, P, R, S, and V), and the most used ones are explained in Table. The correct notation for a Rockwell hardness value is HR followed by the scale (e.g., 62 HRC) where C is the letter for the scale used. The durometer scale was defined by Albert Ferdinand Shore in 1927 when he filed a patent for a device to measure hardness. The device consists of a calibrated spring applying a specific pressure to an indenter foot, which can be either cone or sphere shaped (Fig. An indicating needle in a dial measures the depth of indentation in a scale from 0 (for full penetration of the indenter) to 100 (corresponding to no penetration of the indenter).
The method measures, in fact, the maximum penetration at the applied load and not the deformation of the material. As this method is used to measure viscoelastic materials, it requires to measure also the movement of the indenter during a specific time. The determination of the final durometer hardness is achieved by visually reading the dial within 1 s of the “moment of cessation” of the numerical increase in the indication, which is generally agreed upon a specific reference time. The introduction of electronics, digital displays, and miniaturization has allowed the construction of durometers using load cells and pressure–force transducers, replacing springs, mechanical dials, and visual guess. Durometers are available in a variety of models, according to the maximum applied load (78, 113, 197, 822, and 4536 gf, where 1 gf 9.8 mN) and the size and kind of indenter (cone, truncated cone, disc, and sphere) which are normalized within 12 scales by the standard ASTM D2240. The indenter should be manufactured from hardened steel 500HV10. According also to ASTM D2240, this test method is an empirical test intended primarily for control purposes.
No simple relationship exists between indentation hardness determined by this test method and those obtained with another type of durometer or other instruments used for measuring hardness. The shore durometer is used mainly for measuring the indentation hardness of rubbers, thermoplastic elastomers, and soft plastics such as polyolefin, fluoropolymer, and vinyl. Fig. 5Basic scheme of a Shore durometerThe Barber–Colman Impressor, or shortly known as Barcol Impressor, is a handheld portable durometer developed by Walter Colman during World War II to check the hardness of aircraft rivets. Fifty years later, the same Barcol product has been used to perform hardness testing on repairs to the USA Space Shuttle.
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The governing standard for the Barcol hardness test is ASTM D 2583. This method is used nowadays to determine the hardness of reinforced and non-reinforced rigid plastics and to determine the degree of cure of resins and plastics. 2.6 International Rubber Hardness Degree (IRHD). (8)with a = 0.34 and σ = 0.7. This relation is chosen in a way that IHRD = 0 represents a material having an elastic modulus E = 0 and IHRD = 100 represents a material of infinite elastic modulus.According to Morgans et al. , there are some reports of using the IRHD method in the 1920s, but the first standard was introduced as a British Standard BS in 1940.
The modern test procedure in ISO 48 contains three macroscale methods for the determination of the hardness on flat surfaces: normal ( N), high ( H), and low ( L) hardness, and three for curved surfaces (CN, CH, and CL). The three methods differ primarily in the diameter of the indenting ball: 2.5, 1, and 5 mm for N, H, and L, respectively. There is also a corresponding international ASTM norm D1415.
3 Micro-indentation Tests. Micro-indentation tests are characterized by indentations loads L in the range of L 0.2 µm. There are two main tests used at this scale: Vickers and Knoop. These indentation hardness tests determine the material resistance to the penetration of a diamond indenter with a shape of a pyramid. Like in the case of macroindentation tests, the hardness is correlated with the depth which such indenter will sink into the material, under a given load, within a specific period of time. 3.1 Micro-Vickers TestThe micro-indentation Vickers test is similar to the macroindentation test explained in Sect. The difference is the use of a lower applied load range.
The use of forces below 1 kgf (9.8 N) with the Vickers test was first evaluated in 1932 at the National Physical Laboratory in the UK. Four years later, Lips and Sack constructed the first micro-hardness Vickers tester designed for applied forces ≤1 kgf (9.8 N). The test is normalized by ASTM E384 and ISO 6507. 3.2 Knoop Test. (9)where d is the length of the longest diagonal (in mm). L was originally measured in kgf; if L is measured in N, Eq.
Should be divided by 9.8065. The process measurement consists in pressing the indenter by a load which is maintained by 10–15 s. After the dwell time is complete, the indenter is removed leaving an elongated diamond shaped indent in the sample. Knoop tests are mainly done at test forces from 10 to 1000 g (98 mN to 9.8 N), so a high-magnification microscope is necessary to measure the indent size ,.
3.3 Buchholz Test. This test method was developed originally to analyze the indentation hardness of paints with plastic deformation behavior. The indenter is a sharp doubly beveled disk indenting tool made in steel, as shown in Fig.
The indentation procedure consists on applying a 500 gf load L (4.9 N) during 30, and 35 s later the indentation length d (mm) is measured with the help of a precision 20× magnification microscope. The indentation resistance Buchholz (IRB) is then calculated according to the following equation. (10)The disk dimensions are standardized: diameter of 30 mm, thickness of 5 mm, and 120° bevel angle. The test is particularly sensitive to the positioning and removal of the apparatus, as well as to the recovery time before measuring the indentation length. The standard ISO 2815 describes the measurement method which is valid for single coating or a multicoating system of paints, varnishes, or related products. The norm also establishes values for the equivalent penetration h of the indenter, the limits of the indentation mark 0.75. In the nanoindentation test, the indenter is pushed into the surface of the sample producing both elastic and plastic deformation of the material (Fig.
The first difference with macro- or micro-indentation tests is that, in the nanoindentation machines, the displacement h and the load L are continuously monitored with high precision, as schematically shown in Fig. During the nanoindentation process, the indenter will penetrate the sample until a predetermined maximum load L max is reached, where the corresponding penetration depth is h max. When the indenter is withdrawn from the sample, the unloading displacement is also continuously monitored until the zero load is reached and a final or residual penetration depth h f is measured.
The slope of the upper portion of the unloading curve, denoted as S = d L/d h, is called the elastic contact stiffness. Fig. 10Load–unload during nanoindentationThere are mainly two indenter shapes of choice in nanoindentation: Berkovich and cube corner.
The Berkovich indenter is a three-sided pyramid with a face angle of 65.3° with respect to the indentation vertical axis, and its area-to-depth function is the same as that of a Vickers indenter. The cube corner is also a three-sided pyramid which is precisely the corner of a cube.In nanoindentation, the hardness of the material is defined as H = L/ A pml, where A pml is the projected area of contact at the maximum load. In this method, the maximum load ranges between few µN and about 200 mN, while penetrations will vary from few nm to about few µm. The indented area results to be very small (nanometer or few micrometers size), and as a consequence, the use of optical microscopy is not possible like in macro- and micro-indentation tests. The only way for observing so small areas is by using a scanning electron microscopy (SEM), which is not very practical.
However, methods have been developed to calculate the area directly from the load–unload curve. Unfortunately, a perfect Berkovich indenter is a utopia. Even if they are carefully manufactured, the indenter tips are usually blunted and/or can have other defects, or they become imperfect after few nanoindentations. However, the method of Oliver and Pharr also shows how to calculate the projected contact area at maximum load A pml by evaluating an empirically determined indenter area function A pml = f( h c).
The area function f( h c) is also called the shape function or tip function because it relates the cross-sectional area of the indenter A p to the distance h c from its tip. A general polynomial form is used.
(16)The first term of the polynomial fit corresponds to the ideal Berkovich indenter, and the remaining terms take into consideration the deviations from the ideal geometry.The fitting parameters C i can be obtained by performing nanoindentation tests on materials with known elastic modulus. The most used material used for the fitting is fused quartz, with a known hardness H = 9.25 GPa. Fused quartz material used for calibration has a very smooth surface, is amorphous, and presents no pileup.The number of terms in Eq. ( ) is chosen to give a good fit over the entire range of analyzed depths, using a weighted fitting procedure to assure that data from all depths have equal importance. (18)with E and ν are the elastic modulus and Poisson’s ratio of the sample and E i and ν i the elastic modulus and Poisson’s ratio of the indenter.Equation ( ) is based on the classical problem of the axisymmetric contact of a smooth, rigid, circular punch with an isotropic elastic half-space whose elastic properties E and ν are constants. For indenters with triangular cross section such as the Berkovich pyramid, B = 1.034.The reduced modulus in Eq. ( ) is used to take into consideration that both sample and indenter have elastic deformation during the nanoindentation. For a diamond indenter, the values E i = 1140GPa and ν i = 0.07 are frequently used. Equation ( ) requires to know the Poisson’s ratio of the sample which is usually unknown.
One possibility is to use a value ν = 0.25 which produces in most materials about a 5% uncertainty in the calculated value of E. Most of publications, however, report the value of the reduced elastic modulus E r to avoid guessing a value for the Poisson’s ratio. The main international standards for nanoindentation are ISO 14577 and ASTM E2546.Improvements to measurement and calibration procedures have been facilitated in the last decade by the continuous stiffness measurement (CSM) technique, in which the stiffness is measured continuously during the loading of the indenter by imposing a small oscillation on the force (or displacement) signal and measuring the amplitude and phase of the corresponding displacement (or force) signal by means of a frequency-specific amplifier. New advances in nanoindentation hardware have also allowed the possibility to make nowadays in situ experiments in a wide range of temperatures of up to 700 °C , to characterize small features as standing alone nanowires and nanorods , , or to adapt nanoindenters to measure piezoelectricity at the nanoscale. 5 Tests Comparison.
5.1 The Scales of Hardness Indentation TestsWhile in the field of tribology the limits of macro-, micro-, and nanoscale experiments are still blurry , there is some consensus in the indentation mechanics area about which tests can be considered to belong to each scale. Brinell and Rockwell tests are considered to be in the macroscale, due to the high loads (5 N–30 kN), high deformation areas, and high penetrations (more than 1 mm). Vickers and IHRD are considered to be a macro- or microscale, according to the applied load. Knoop test is considered to be a microscale test, with low loads and low penetration depths (up to 0.1 mm). Buchholz is also a microscale test because of the low penetration depth into the coatings (15–35 µm).
Finally, indentations made with nanoindenters or atomic force microscopes are considered as nanoscale tests, with loads L. There is also some disagreement in the standards regarding the load range applicable to microscale testing. ASTM Specification E384, for example, states that the load range for microscale testing is 1–1000 gf (9.8 mN to 9.8 N). On the other hand, the ISO 14577-1 norm specifies that the microscale indentation is for loads lower than 200 gf (1.96 N). In fact, this ISO norm gives the ranges of loads and penetrations for determining the indentation hardness at the three scale definitions , as shown in Table. Figure shows an estimation of the number of scientific publications dealing with indentation hardness of materials in the period of years going from 1910 to 2015.
Each indicated year data in the figure include all publications in the precedent period of 15 years. The survey separates the publications according to the macro-, micro-, or nanoscale where the indentation hardness has been measured. The estimation was done with the database from Google Scholar, using as keywords: “indentation hardness,” “micro-indentation,” and “nanoindentation,” through a Boolean logic search to exclude publications dealing simultaneously with two or three scale measurements in the same publication. It is observed a huge increase trend of publications in the nanoscale area during the last 15 years, surpassing the number of publications at microscale.
Fig. 11Number of publications reporting results of indentation hardness at macro- ( filled triangle), micro- ( filled circle), and nanoscale ( filled square). The estimation was done using the database Google Scholar. Each data point reports number of publications in the previous 5-year period 5.2 Indentation Hardness DefinitionsThe indentation hardness in the aforementioned methods is defined in three different ways. Brinell and Vickers define hardness as the applied load L divided by the actual area A c of the impressed curved surface. Meyer, Knoop, and the nanoindentation hardness are defined as the ratio of the applied load L to the projected areas ( A p or A pml) of the indent. Finally, the Rockwell, Shore, IHRD, and Buchholz tests determine the hardness by measuring the depth of penetration of an indenter under a large load.There are some authors who explain that there is just a geometrical difference between the actual area A c of the curved surface of the impression and the projected area A p of the indent. However, this geometrical approximation is valid if the indentation produces a 100% plastic deformation.Elastic the material changes temporarily its shape, but returns to the original shape when the stress is removed.
Deformation in the elastic region is linear, as described by the stress–strain curve. In this region, the definition of indentation hardness as the ratio of applied load divided by the permanent deformed area is not applicable. Penetration methods to measure hardness, like the Shore durometer, IHRD, or Buchholz tests, must be used to measure meaningful hardness values.Plastic the material has a permanent change shape in response to the stress, but remains in one piece.
The yield strength is the point at which elastic deformation gives way to plastic deformation. Deformation in the plastic region is nonlinear, as described by the stress–strain curve.
Indentation hardness measurements in this region can be done using permanent deformation areas or indenter penetration, as described above.Fracture the material cracks and separates into two or more pieces. The fracture property in indentation methods can be used to calculate other mechanical properties like indentation toughness.When the material is indented, there will be elastic and plastic deformations according to the applied level of stress. All macro- and micro-indentation tests using A c or A p measure the plastic deformed area after the material has recuperated elastically. The calculation of hardness can give different values by different methods, even applying the geometrical correction. The difference will depend on how much the applied stresses in each method will deform the material into the elastic and plastic zones, giving place to more or less elastic recovery. Furthermore, behaviors of sink-in or pileup around the indented area are usually neglected, even if they were already studied in the early development of the methods.
Norbury et al. published a pioneering study of the piling-up and sinking-in during Brinell indentation hardness tests where they found a large effect on hardness measurement. Of course, these differences could fall inside the measurement error if the deformed areas are measured with microscopes of low magnification. The case is different for nanoindentation.
First, the contact area A pml is calculated, and not directly measured. The calculation of A pml developed by Oliver and Pharr is, however, only valid for materials where the surface around the indenter sinks in, as shown in Figs. If the opposite indentation deformation phenomenon of ‘‘pileup’’ occurs (i.e., the surface of the sample around the indenter is at a higher level than its surroundings as shown in Fig.
B), the predicted contact area is smaller than the real one. Therefore, the contact area supporting the indenter at L = L max increases and the measured elastic modulus and hardness can be significantly overestimated up to 50%. Fig. 13Schematics of a sink-in and b pileup around the indenterOliver and Pharr have shown that the amount of pileup or sink-in depends on h f/ h max and the work-hardening behavior.
Specifically, pileup is large only when h f/ h max is close to 1 and the degree of work hardening is small. It should also be noted that when h f/ h max. Until recent years, it was common to speak in Europe about the calculation of the “Universal Hardness” (UH). For instance, the original draft of the ISO 14577 prepared in the year 2000 was using the term UH when referring to the hardness calculated by instrumented indentation tests. Another term used in the document was “Hardness under Test Force” referring to the way that hardness is calculated: the applied maximum force L max divided by the contact area calculated at the maximum load A s (see Fig. A for the comparison of A c, A p, A pml and A s).
According to Wilde et al. , many discussions in the ISO committee took place, as the denomination of “universal” could be confusing.
Finally, it was decided to call it “Martens Hardness” (HM) in honor of the German Professor Adolf Martens, a leading researcher of steel characterization at the end of the nineteenth century. Adolf Martens was the first researcher to describe the steel structure that carries his name (martensitic) and also was the first to build an indentation machine at the macroscale measuring the penetration of the indenter at maximum load.
Martens Hardness is defined only for the symmetric pyramidal indenters Vickers and Berkovich. For a Vickers indenter with apex angle of 136°, the area A s as function of the penetration h is given. (22)Martens hardness values are determined from load and depth readings during the application of the test force, and the norm established that a penetration greater than 0.2 µm depth is required. The Martens hardness value is denoted by the symbol HM, followed by the test conditions that specify the indenter, the test force, the time of application of the test force, and the number of load steps applied if not a continuous application of force. For example, “HM (Berkovich) 0.5/20/30 = 6500 N/mm 2” represents a Martens hardness value of 6500 N/mm 2, determined with a test force of 0.5 N, applied during 20 s in 30 steps. The main difference of HM with the standard Vickers hardness is that A s take into consideration both elastic and plastic deformation because it is measured under the load, while A p only is influenced by plastic deformation because it is measured after the indentation.After our discussion regarding the ways to calculate hardness trough different kind of areas (contact area A c, projected area A p, projected area at maximum load A pml, contact area at maximum load A s) or penetrations depths, one question still remind: which one is more reasonable to define hardness? According to Tabor, macro- and micro-indentation hardness measurements in metals are essentially a me.