How is hardness determined?
Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Stiffness
where
Hard and soft light
The softness of a light source can also be determined by the angle between the illuminated object and the 'length' of the light source (the longest dimension that is perpendicular to the object being lit). The larger this angle is, the softer the light source.
Blade
Typically blades are made from a material that is about as hard, though usually harder, than the material to be cut. Insufficiently hard blades will be unable to cut a material or will wear away quickly as hardness is related to a material's ability to resist abrasion. However, blades must also be tough enough to resist the dynamic load of impact and as a general rule the harder a blade the less tough (the more brittle) a material. For example, a steel axehead is much harder than the wood it is intended to cut and is sufficiently tough to resist the impact resulting when swung against a tree while a ceramic kitchen knife, harder than steel, is very brittle (has low toughness) and can easily shatter if dropped onto the floor or twisted while inside the food it is cutting or carelessly stored under other kitchen utensils. This creates a tension between the intended use of the blade, the material it is to be made from, and any manufacturing processes (such as heat treatment in the case of steel blades that will affect a blade's hardness and toughness). A balance must be found between the sharpness and how well it can last. Methods that can circumvent this include differential hardening. This method yields an edge that can hold its sharpness as well as a body that is tough.
Fracture toughness
The problem can also be formulated in terms of stress instead of energy, leading to the terms stress intensity factor "K" (or "K" for mode I) and critical stress intensity factor "K" (and "K"). These "K" and "K" (etc.) quantities are commonly referred to as fracture toughness, though it is equivalent to use "G". Typical values for "K"are 150 MN/m for ductile (very tough) metals, 25 for brittle ones and 1–10 for glasses and brittle polymers. Notice the different units used by "G" and "K". Engineers tend to use the latter as an indication of toughness.
Toughness
Tensile toughness (or, "deformation energy", "U") is measured in units of joule per cubic metre (J·m) in the SI system and inch-pound-force per cubic inch (in·lbf·in) in US customary units.
1.00 N·m.m ≃  in·lbf·in and 1.00 in·lbf·in ≃ 6.89 kN·m.m.
Hardness
In glasses, hardness seems to depend linearly on the number of topological constraints acting between the atoms of the network. Hence, the rigidity theory has allowed predicting hardness values with respect to composition.
Toughness
Toughness can also be defined with respect to regions of a stress–strain diagram. Toughness is related to the area under the stress–strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses and high strains. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.
Iron
The mechanical properties of iron and its alloys can be evaluated using a variety of tests, including the Brinell test, Rockwell test and the Vickers hardness test. The data on iron is so consistent that it is often used to calibrate measurements or to compare tests. However, the mechanical properties of iron are significantly affected by the sample's purity: pure, single crystals of iron are actually softer than aluminium, and the purest industrially produced iron (99.99%) has a hardness of 20–30 Brinell. An increase in the carbon content will cause a significant increase in the hardness and tensile strength of iron. Maximum hardness of 65 R is achieved with a 0.6% carbon content, although the alloy has low tensile strength. Because of the softness of iron, it is much easier to work with than its heavier congeners ruthenium and osmium.
Soil structure
Hardsetting has been defined this way: ""A hardsetting soil is one that sets to an almost homogeneous mass on drying. It may have occasional cracks, typically at a spacing of >0.1 m. Air dry hardset soil is hard and brittle, and it is not possible to push a forefinger into the profile face. Typically, it has a tensile strength of 90 kN. Soils that crust are not necessarily hardsetting since a hardsetting horizon is thicker than a crust. (In cultivated soils the thickness of the hardsetting horizon is frequently equal to or greater than that of the cultivated layer.) Hardsetting soil is not permanently cemented and is soft when wet. The clods in a hardsetting horizon that has been cultivated will partially or totally disintegrate upon wetting. If the soil has been sufficiently wetted, it will revert to its hardset state on drying. This can happen after flood irrigation or a single intense rainfall event.""
Vickers hardness test
The Vickers hardness test was developed in 1921 by Robert L. Smith and George E. Sandland at Vickers Ltd as an alternative to the Brinell method to measure the hardness of materials. The Vickers test is often easier to use than other hardness tests since the required calculations are independent of the size of the indenter, and the indenter can be used for all materials irrespective of hardness. The basic principle, as with all common measures of hardness, is to observe a material's ability to resist plastic deformation from a standard source. 
The Vickers test can be used for all metals and has one of the widest scales among hardness tests. 
The unit of hardness given by the test is known as the Vickers Pyramid Number (HV) or Diamond Pyramid Hardness (DPH). The hardness number can be converted into units of pascals, but should not be confused with pressure, which uses the same units. The hardness number is determined by the load over the surface area of the indentation and not the area normal to the force, and is therefore not pressure.
Specific strength
Tenacity is the customary measure of strength of a fiber or yarn. In the U.S. it is usually defined as the ultimate (breaking) force of the fiber (in gram-force units) divided by the denier.
Because denier is a measure of the linear density, the tenacity works out to be not a measure of force per unit area, but rather a quasi-dimensionless measure analogous to specific strength. 
A tenacity of formula_1 corresponds to: formula_2
Paper and ink testing
% of moisure content in the paper is known as relative moisure content.High moisure content will increase the weight of the paper and increase the cost of paper. At the same time low moisure content will make the paper brittle and increases the chances of break in production.Roughness indicates varying degree of porosity of the paper. Porosity is a direct indication of paper to accept ink or water.
Types of cheese
Categorizing cheeses by moisture content or firmness is a common but inexact practice. The lines between soft, semi-soft, semi-hard and hard are arbitrary, and many types of cheese are made in softer or firmer variants. The factor that controls cheese hardness is moisture content, which depends on the pressure with which it is packed into moulds, and upon aging time.
Nanoindentation
In a traditional indentation test (macro or micro indentation), a hard tip whose mechanical properties are known (frequently made of a very hard material like diamond) is pressed into a sample whose properties are unknown. The load placed on the indenter tip is increased as the tip penetrates further into the specimen and soon reaches a user-defined value. At this point, the load may be held constant for a period or removed. The area of the residual indentation in the sample is measured and the hardness, formula_1, is defined as the maximum load, formula_2, divided by the residual indentation area, formula_3:
Thickness (geology)
Thickness is measured at right angles to the surface of the seam or bed and thus independently of its spatial orientation. The concept of thickness came originally from mining language, where it was used mainly to indicate the workability of seams. It has since become an established term in earth science, for example in geology, for the depth of sedimentary rocks, in hydrogeology for the vertical extent of groundwater – i.e. the distance from the base of the groundwater layer to its surface – or in soil science for the vertical extent of soil horizons.
Fracture toughness
In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor (formula_1) at which a thin crack in the material begins to grow. It is denoted K and has the units of formula_2 or formula_3. Plastic-elastic fracture toughness is denoted by J, with the unit of J/cm or lbf-in/in, and is a measurement of the energy required to grow a thin crack.
Hardness
Scratch hardness is the measure of how resistant a sample is to fracture or permanent plastic deformation due to friction from a sharp object. The principle is that an object made of a harder material will scratch an object made of a softer material. When testing coatings, scratch hardness refers to the force necessary to cut through the film to the substrate. The most common test is Mohs scale, which is used in mineralogy. One tool to make this measurement is the sclerometer.
Toughness
The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to strike a notched specimen of defined cross-section and deform it. The height from which the pendulum fell, minus the height to which it rose after deforming the specimen, multiplied by the weight of the pendulum is a measure of the energy absorbed by the specimen as it was deformed during the impact with the pendulum. The Charpy and Izod notched impact strength tests are typical ASTM tests used to determine toughness.
Material properties of diamond
Unlike hardness, which denotes only resistance to scratching, diamond's toughness or tenacity is only fair to good. Toughness relates to the ability to resist breakage from falls or impacts. Because of diamond's perfect and easy cleavage, it is vulnerable to breakage. A diamond will shatter if hit with an ordinary hammer. The toughness of natural diamond has been measured as 2.0 MPa m, which is good compared to other gemstones, but poor compared to most engineering materials. As with any material, the macroscopic geometry of a diamond contributes to its resistance to breakage. Diamond has a cleavage plane and is therefore more fragile in some orientations than others. Diamond cutters use this attribute to cleave some stones, prior to faceting.
Brinell scale
The typical test uses a diameter steel ball as an indenter with a force. For softer materials, a smaller force is used; for harder materials, a tungsten carbide ball is substituted for the steel ball. The indentation is measured and hardness calculated as:
Barcol hardness test
The Barcol hardness test is generally used on soft materials such as rigid plastics. It measures hardness based on indentation of a sharp point with a flat tip. The test is performed using a similar method and indentation device as that used to measure Shore D hardness, however the Shore D indentor has a round tip. Barcol hardness is not a valid hardness measure for curved surfaces.
Toughness
In the SI system, the unit of tensile toughness can be easily calculated by using area underneath the stress–strain ("σ"–"ε") curve, which gives tensile toughness value, as given below:
Indentation hardness
The term "macroindentation" is applied to tests with a larger test load, such as 1 kgf or more. There are various macroindentation tests, including:There is, in general, no simple relationship between the results of different hardness tests. Though there are practical conversion tables for hard steels, for example, some materials show qualitatively different behaviors under the various measurement methods. The Vickers and Brinell hardness scales correlate well over a wide range, however, with Brinell only producing overestimated values at high loads.
Complexity
The complexity measures broadly cover:
Instance hardness is a bottom-up approach that first seeks to identify instances that are likely to be misclassified (or, in other words, which instances are the most complex). The characteristics of the instances that are likely to be misclassified are then measured based on the output from a set of hardness measures. The hardness measures are based on several supervised learning techniques such as measuring the number of disagreeing neighbors or the likelihood of the assigned class label given the input features. The information provided by the complexity measures has been examined for use in meta learning to determine for which data sets filtering (or removing suspected noisy instances from the training set) is the most beneficial and could be expanded to other areas.
Toughness
where
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
List of blade materials
The hardness of steel is usually stated as a number on the Rockwell C scale (HRC). The Rockwell scale is a hardness scale based on the resistance to indentation of a material, as opposed to other scales such as the Mohs scale (scratch resistance) testing used in mineralogy. As hardness increases, the blade becomes capable of taking and holding a better edge, but is more difficult to sharpen and more brittle (commonly called less "tough"). Laminating a softer steel between a harder one is an expensive process that to some extent gives the benefits of both types (see Damascus steel).
Hot hardness
In materials engineering and metallurgy, hot hardness or red hardness (when a metal glows a dull red from the heat) corresponds to hardness of a material at high temperatures. As the temperature of material increases, hardness decreases and at some point a drastic change in hardness occurs. The hardness at this point is termed the "hot" or "red" hardness of that material. Such changes can be seen in materials such as heat treated alloys.
SAE steel grades
An "H" suffix can be added to any designation to denote hardenability is a major requirement. The chemical requirements are loosened but hardness values defined for various distances on a Jominy test.
Vickers hardness test
It was decided that the indenter shape should be capable of producing geometrically similar impressions, irrespective of size; the impression should have well-defined points of measurement; and the indenter should have high resistance to self-deformation. A diamond in the form of a square-based pyramid satisfied these conditions. It had been established that the ideal size of a Brinell impression was of the ball diameter. As two tangents to the circle at the ends of a chord 3"d"/8 long intersect at 136°, it was decided to use this as the included angle between plane faces of the indenter tip. This gives an angle from each face normal to the horizontal plane normal of 22° on each side. The angle was varied experimentally and it was found that the hardness value obtained on a homogeneous piece of material remained constant, irrespective of load. Accordingly, loads of various magnitudes are applied to a flat surface, depending on the hardness of the material to be measured. The HV number is then determined by the ratio "F/A", where "F" is the force applied to the diamond in kilograms-force and "A" is the surface area of the resulting indentation in square millimeters. "A" can be determined by the formula.
Indentation hardness
Scratch tests at low loads, such as the Bierbaum microcharacter test, performed with either 3 gf or 9 gf loads, preceded the development of microhardness testers using traditional indenters. In 1925, Smith and Sandland of the UK developed an indentation test that employed a square-based pyramidal indenter made from diamond. They chose the pyramidal shape with an angle of 136° between opposite faces in order to obtain hardness numbers that would be as close as possible to Brinell hardness numbers for the specimen. The Vickers test has a great advantage of using one hardness scale to test all materials.The first reference to the Vickers indenter with low loads was made in the annual report of the National Physical Laboratory in 1932. Lips and Sack describes the first Vickers tester using low loads in 1936.
There is some disagreement in the literature regarding the load range applicable to microhardness testing. ASTM Specification E384, for example, states that the load range for microhardness testing is 1 to 1000 gf. For loads of 1 kgf and below, the Vickers hardness (HV) is calculated with an equation, wherein load ("L") is in grams force and the mean of two diagonals ("d") is in millimeters:
Scratch hardness
Scratch hardness tests are used to determine the hardness of a material to scratches and abrasion. The earliest test was developed by mineralogist Friedrich Mohs in 1820 (see Mohs scale). It is based on relative scratch hardness, with talc assigned a value of 1 and diamond assigned a value of 10. Mohs' scale had two limitations; it was not linear, and most modern abrasives fall between 9 and 10.
Heat treating
Only hardness is listed for through hardening. It is usually in the form of HRC with at least a five-point range.
Fracture toughness
When a material of unknown fracture toughness is tested, a specimen of full material section thickness is tested or the specimen is sized based on a prediction of the fracture toughness. If the fracture toughness value resulting from the test does not satisfy the requirement of the above equation, the test must be repeated using a thicker specimen. In addition to this thickness calculation, test specifications have several other requirements that must be met (such as the size of the shear lips) before a test can be said to have resulted in a K value.
Scratch hardness
Raymond R. Ridgway, a research engineer at the Norton Company, modified the Mohs scale by giving garnet a hardness of 10 and diamond a hardness of 15. Charles E. Wooddell, working at the Carborundum Company, extended the scale further by using resistance to abrasion, and extrapolating the scale based on seven for quartz and nine for corundum, resulting in a value of 42.4 for South American brown diamond bort. Resistance to abrasion is less affected by surface variations than other methods of indentations.
Hardenability
The hardenability of a metal alloy is the depth to which a material is hardened after putting it through a heat treatment process. The unit of hardenability is length. It is an indication of how deep into the material a certain hardness can be achieved. It should not be confused with hardness, which is a measure of a sample's resistance to indentation or scratching. It is an important property for welding, since it is inversely proportional to weldability, that is, the ease of welding a material.
Diamond-like carbon
Within the "cobblestones", nodules, clusters, or "sponges" (the volumes in which local bonding is sp) bond angles may be distorted from those found in either pure cubic or hexagonal lattices because of intermixing of the two. The result is internal (compressive) stress that can appear to add to the hardness measured for a sample of DLC. Hardness is often measured by nanoindentation methods in which a finely pointed stylus of natural diamond is forced into the surface of a specimen. If the sample is so thin that there is only a single layer of nodules, then the stylus may enter the DLC layer between the hard cobblestones and push them apart without sensing the hardness of the sp bonded volumes. Measurements would be low. Conversely, if the probing stylus enters a film thick enough to have several layers of nodules so it cannot be spread laterally, or if it enters on top of a cobblestone in a single layer, then it will measure not only the real hardness of the diamond bonding, but an apparent hardness even greater because the internal compressive stress in those nodules would provide further resistance to penetration of the material by the stylus. Nanoindentation measurements have reported hardness as great as 50% more than values for natural crystalline diamond. Since the stylus is blunted in such cases or even broken, actual numbers for hardness that exceed that of natural diamond are meaningless. They only show that the hard parts of an optimal "ta-C" material will break natural diamond rather than the inverse. Nevertheless, from a practical viewpoint it does not matter how the resistance of a DLC material is developed, it can be harder than natural diamond in usage. One method of testing the coating hardness is by means of the Persoz pendulum.
Hard water
Seawater is considered to be very hard due to various dissolved salts. Typically seawater's hardness is in the range of 6630 ppm. In contrast, freshwater has hardness in the range of 15 - 375 ppm.
Acid strength
The usual measure of the strength of an acid is its acid dissociation constant ("K"), which can be determined experimentally by titration methods. Stronger acids have a larger "K" and a smaller logarithmic constant (p"K"=−log"K") than weaker acids. The stronger an acid is, the more easily it loses a proton, H. Two key factors that contribute to the ease of deprotonation are the polarity of the H—A bond and the size of atom A, which determine the strength of the H—A bond. Acid strengths also depend on the stability of the conjugate base.
Stiffness
In the International System of Units, stiffness is typically measured in newtons per meter. 
In Imperial units, stiffness is typically measured in pounds(lbs) per inch.
International Roughness Index
In the early 1980s the highway engineering community identified road roughness as the primary indicator of the utility of a highway network to road users. However, existing methods used to characterize roughness were not reproducible by different agencies using different measuring equipment and methods. Even within a given agency, the methods were not necessarily repeatable. Nor were they stable with time.
Stiffness matrix
By defining the vector "F" with components "F" = formula_5, the coefficients "u" are determined by the linear system "AU" = "F". The stiffness matrix is symmetric, i.e. "A" = "A", so all its eigenvalues are real. Moreover, it is a strictly positive-definite matrix, so that the system "AU" = "F" always has a unique solution. (For other problems, these nice properties will be lost.)
Surface roughness
Roughness plays an important role in determining how a real object will interact with its environment. In tribology, rough surfaces usually wear more quickly and have higher friction coefficients than smooth surfaces. Roughness is often a good predictor of the performance of a mechanical component, since irregularities on the surface may form nucleation sites for cracks or corrosion. On the other hand, roughness may promote adhesion. Generally speaking, rather than scale specific descriptors, cross-scale descriptors such as surface fractality provide more meaningful predictions of mechanical interactions at surfaces including contact stiffness and static friction.
Vickers hardness test
If HV is expressed in kgf/mm then the tensile strength (in MPa) of the material can be approximated as ≈ HV× ≈ HV/0.3, where is a constant determined by yield strength, Poisson's ratio, work-hardening exponent and geometrical factors - usually ranging between 2 and 4.. In other words, if HV is expressed in N/mm (i.e. in MPa) then the tensile strength (in MPa) ≈ HV/3. However it should be noted this empirical law depends variably on the work-hardening behavior of the material.
Toughness
Another definition is the ability to absorb mechanical energy up to the point of failure. The area under the stress-strain curve is called toughness.
Hardness
Rebound hardness, also known as "dynamic hardness", measures the height of the "bounce" of a diamond-tipped hammer dropped from a fixed height onto a material. This type of hardness is related to elasticity. The device used to take this measurement is known as a scleroscope.
Knot thickness
The thickness is defined using the simpler concept of the local thickness τ("x"). The local thickness at a point "x" on the link is defined as
where "x", "y", and "z" are points on the link, all distinct, and "r"("x", "y", "z") is the radius of the circle that passes through all three points ("x", "y", "z"). From this definition we can deduce that the local thickness is at most equal to the local radius of curvature.
Specific strength
The specific strength is a material's strength (force per unit area at failure) divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio or strength-to-mass ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pa m/kg, or N·m/kg, which is dimensionally equivalent to m/s, though the latter form is rarely used.
International Roughness Index
The International Roughness Index (IRI) is the roughness index most commonly obtained from measured longitudinal road profiles. It is calculated using a quarter-car vehicle math model, whose response is accumulated to yield a roughness index with units of slope (in/mi, m/km, etc.). Since its introduction in 1986, IRI has become the road roughness index most commonly used worldwide for evaluating and managing road systems.
Vickers hardness test
To convert the Vickers hardness number to SI units the hardness number in kilograms-force per square millimeter (kgf/mm²) has to be multiplied with the standard gravity (9.806 65) to get the hardness in MPa (N/mm²) and furthermore divided by 1000 to get the hardness in GPa.
Rockwell scale
The Rockwell scale is a hardness scale based on indentation hardness of a material. The 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 preload. There are different scales, denoted by a single letter, that use different loads or indenters. The result is a dimensionless number noted as HRA, HRB, HRC, etc., where the last letter is the respective Rockwell scale (see below).
When testing metals, indentation hardness correlates linearly with tensile strength. This important relation permits economically important nondestructive testing of bulk metal deliveries with lightweight, even portable equipment, such as hand-held Rockwell hardness testers.
Hardness
There are three main types of hardness measurements: "scratch", "indentation", and "rebound". Within each of these classes of measurement there are individual measurement scales. For practical reasons conversion tables are used to convert between one scale and another.
Cupules
Typically cupules were created by direct percussion, i.e. using hand-held hammer-stones. Replication studies have shown that the time required for their production varies greatly, depending on the rock type. It can take one minute to create a 12 mm deep cupule on weathered sandstone, but 45,000 and 60,000 hammer-stone strokes on unweathered quartzite. The resistance of a rock to kinetic impact is determined by its hardness, toughness and strength. Hardness, in this context, is a complex articulation of several factors, essentially a measure of how resistant rock is to various kinds of permanent shape change when a compressive force is applied to it. These factors include scratch or abrasion resistance (Rosiwal scale), toughness, strength, ductility, indentation hardness (measured by the Brinell scale and expressed in BHN, or measured by the Vickers test and expressed in kg/mm²) and brittleness factor. Abrasion hardness, indentation hardness and brittleness factor (ratio of the uniaxial compressive strength and the uniaxial tensile strength) combine to determine the “composite hardness index” "θ", which governs the production coefficient "ρ":
Mohs scale of mineral hardness
The Mohs scale of mineral hardness is based on the ability of one natural sample of mineral to scratch another mineral visibly. The samples of matter used by Mohs are all different minerals. Minerals are chemically pure solids found in nature. Rocks are made up of one or more minerals. As the hardest known naturally occurring substance when the scale was designed, diamonds are at the top of the scale. The hardness of a material is measured against the scale by finding the hardest material that the given material can scratch, or the softest material that can scratch the given material. For example, if some material is scratched by apatite but not by fluorite, its hardness on the Mohs scale would fall between 4 and 5. "Scratching" a material for the purposes of the Mohs scale means creating non-elastic dislocations visible to the naked eye. Frequently, materials that are lower on the Mohs scale can create microscopic, non-elastic dislocations on materials that have a higher Mohs number. While these microscopic dislocations are permanent and sometimes detrimental to the harder material's structural integrity, they are not considered "scratches" for the determination of a Mohs scale number.
Roughness (psychophysics)
Roughness is studied by examining how textures are perceived and encoded by an individual's somatosensory system. In an experiment to measure and compare the roughness of different sounds, listeners are presented with different sounds and asked to rate their roughness, for example on a rating scale. Recent research has displayed that there are two different codes, at least, for roughness: a vibrotactile code used for fine surfaces, and a spatial code used for coarse to medium surfaces.
Nanoindentation
The hardness is given by the equation above, relating the maximum load to the indentation area. The area can be measured after the indentation by in-situ atomic force microscopy, or by 'after-the event' optical (or electron) microscopy. An example indentation image, from which the area may be determined, is shown at right.
Equivalent carbon content
In welding, equivalent carbon content (C.E) is used to understand how the different alloying elements affect hardness of the steel being welded. This is then directly related to hydrogen-induced cold cracking, which is the most common weld defect for steel, thus it is most commonly used to determine weldability. Higher concentrations of carbon and other alloying elements such as manganese, chromium, silicon, molybdenum, vanadium, copper, and nickel tend to increase hardness and decrease weldability. Each of these elements tends to influence the hardness and weldability of the steel to different magnitudes, however, making a method of comparison necessary to judge the difference in hardness between two alloys made of different alloying elements. There are two commonly used formulas for calculating the equivalent carbon content. One is from the American Welding Society (AWS) and recommended for structural steels and the other is the formula based on the International Institute of Welding (IIW).
Hardness
Indentation hardness measures the resistance of a sample to material deformation due to a constant compression load from a sharp object. Tests for indentation hardness are primarily used in engineering and metallurgy fields. The tests work on the basic premise of measuring the critical dimensions of an indentation left by a specifically dimensioned and loaded indenter.
Hard tissue
The large amount of mineral in enamel accounts not only for its strength but also for its brittleness. Tooth enamel ranks 5 on Mohs hardness scale and has a Young's modulus of 83 GPa. Dentin, less mineralized and less brittle, 3–4 in hardness, compensates for enamel and is necessary as a support. On radiographs, the differences in the mineralization of different portions of the tooth and surrounding periodontium can be noted; enamel appears lighter than dentin or pulp since it is denser than both and more radiopaque.
Superhard material
Owing to the anisotropic nature of this material, the hardness depends on the crystal orientation. The (002) plane contains the most covalent character and exhibits a maximum Vickers hardness value of 40.5 GPa, while the perpendicular planes were 6% lower at 38.1 GPa. These values decrease with increased load, settling at around 28 GPa each. The nanoindentation values were found to be 36.4 GPa and 34.0 GPa for the (002) and perpendicular planes respectively. The hardness values depend on the material purity and composition – the more boron the harder the boride – and the above values are for a Re:B ratio of approximately 1.00:1.85. Rhenium diboride also has a reported bulk modulus of 383 GPa and a shear modulus of 273 GPa. The hardness of rhenium diboride, and most other materials also depends on the load during the test. The above values of about 40 GPa were all measured with an effective load of 0.5–1 N. At such low load, the hardness values are also overestimated for other materials, for example it exceeds 100 GPa for c-BN. Other researchers, while having reproduced the high ReB hardness at low load, reported much lower values of 19–17 GPa at a more conventional load of 3–49 N, that makes ReB a hard, but not a superhard material.
Grit (personality trait)
Salvatore Maddi (2006) defined "hardiness" as a combination of attitudes that provide the courage and motivation to do the hard, strategic work of turning stressful circumstances from potential disasters into growth opportunities. While grit is primarily a measure of an individual's ability to persist in obtaining a specific goal over an extended time period (Duckworth et al., 2007), hardiness refers to an individual's ability to persist through difficult circumstances and does not address the individual's long term persistence toward a specific goal. Maddi (2006) developed a theoretical model of hardiness as a tool for developing resilience.
Hard water
Hardness can be quantified by instrumental analysis. The total water hardness is the sum of the molar concentrations of Ca and Mg, in mol/L or mmol/L units. Although water hardness usually measures only the total concentrations of calcium and magnesium (the two most prevalent divalent metal ions), iron, aluminium, and manganese can also be present at elevated levels in some locations. The presence of iron characteristically confers a brownish (rust-like) colour to the calcification, instead of white (the color of most of the other compounds).
Glossary of phytopathology
hardiness
Hardiness (psychological)
There are several instrument developed to measure hardiness, the most frequently used being the Personal Views Survey, the Dispositional Resilience Scale, and the Cognitive Hardiness Scale. In addition to these, other scales based on hardiness theory have been designed to measure the construct in specific contexts and in special populations, such as for example parental grief and among the chronically ill.
Vickers hardness test
Vickers hardness numbers are reported as xxxHVyy, e.g. 440HV30, or xxxHVyy/zz if duration of force differs from 10 s to 15 s, e.g. 440HV30/20, where:Vickers values are generally independent of the test force: they will come out the same for 500 gf and 50 kgf, as long as the force is at least 200 gf.
Postage stamp paper
Another comparative set of terms refers to the paper's hardness. "Hard", "stout hard", and "soft" have been used to describe the paper. Experts have described the "snap" of the stamp when "flicked" as a means to determine if the stamp was printed on hard or soft paper. A sharper snap implied hard paper because the hardness is a characteristic of the amount or kind of sizing used when making the paper.
Indentation hardness
The equation based definition of hardness is the pressure applied over the contact area between the indenter and the material being tested. As a result hardness values are typically reported in units of pressure, although this is only a "true" pressure if the indenter and surface interface is perfectly flat.
Hard water
Water hardness is often not expressed as a molar concentration, but rather in various units, such as degrees of general hardness (dGH), German degrees (°dH), parts per million (ppm, mg/L, or American degrees), grains per gallon (gpg), English degrees (°e, e, or °Clark), or French degrees (°fH, °F or °HF; lowercase "f" is used to prevent confusion with degrees Fahrenheit). The table below shows conversion factors between the various units.
Janka hardness test
The results are stated in various ways, which can lead to confusion, especially when the actual units employed are often not attached. Overall, the resulting measure is always one of force. In the United States, the measurement is in pounds-force (lbf). In Sweden it is in kilograms-force (kgf), and in Australia, either in newtons (N) or kilonewtons (kN). This confusion is greatest when the results are treated as units, for example "660 Janka".
Knitting
The thickness or weight of the yarn is a significant factor in determining the gauge/tension, i.e., how many stitches and rows are required to cover a given area for a given stitch pattern. Thicker yarns generally require thicker knitting needles, whereas thinner yarns may be knit with thick or thin needles. Hence, thicker yarns generally require fewer stitches, and therefore less time, to knit up a given garment. Patterns and motifs are coarser with thicker yarns; thicker yarns produce bold visual effects, whereas thinner yarns are best for refined patterns. Yarns are grouped by thickness into six categories: superfine, fine, light, medium, bulky and superbulky; quantitatively, thickness is measured by the number of wraps per inch (WPI). In the British Commonwealth (outside North America) yarns are measured as 1ply, 2ply, 3ply, 4ply, 5ply, 8ply (or double knit),10ply and 12ply (triple knit). The related "weight per unit length" is usually measured in tex or denier.
Before knitting, the knitter will typically transform a hank/skein into a ball where the yarn emerges from the center of the ball; this making the knitting easier by preventing the yarn from becoming easily tangled. This transformation may be done by hand, or with a device known as a ballwinder. When knitting, some knitters enclose their balls in jars to keep them clean and untangled with other yarns; the free yarn passes through a small hole in the jar-lid.
Stiffness
Further measures of stiffness are derived on a similar basis, including:The elastic modulus of a material is not the same as the stiffness of a component made from that material. Elastic modulus is a property of the constituent material; stiffness is a property of a structure or component of a structure, and hence it is dependent upon various physical dimensions that describe that component. That is, the modulus is an intensive property of the material; stiffness, on the other hand, is an extensive property of the solid body that is dependent on the material "and" its shape and boundary conditions. For example, for an element in tension or compression, the axial stiffness is
Structural engineering theory
See also:
Stiffness depends upon material properties and geometry. The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law.
Vicat softening point
Vicat softening temperature or Vicat hardness is the determination of the softening point for materials that have no definite melting point, such as plastics. It is taken as the temperature at which the specimen is penetrated to a depth of 1 mm by a flat-ended needle with a 1 mm circular or square cross-section. For the Vicat A test, a load of 10 N is used. For the Vicat B test, the load is 50 N.
Leeb rebound hardness test
According to the dynamic Leeb principle, hardness value is derived from the energy loss of a defined impact body after impacting on a metal sample, similar to the Shore scleroscope. The Leeb quotient ("v","v") is taken as a measure of the energy loss by plastic deformation: the impact body rebounds faster from harder test samples than it does from softer ones, resulting in a greater value 1000×"v/v". A magnetic impact body permits the velocity to be deduced from the voltage induced by the body as it moves through the measuring coil. The quotient 1000×v/v is quoted in the Leeb rebound hardness unit HL.
Hardness
Common examples of hard matter are ceramics, concrete, certain metals, and superhard materials, which can be contrasted with soft matter.
Mental toughness
Mental toughness has been equated with better understood constructs from psychology such as resilience and hardiness. The term resilience is often incorrectly used interchangeably with mental toughness, and researchers have found the two constructs are positively associated with one another. However, psychologists define resilience as a positive adaptive "process" of coping with stress and adversity, as opposed to a collection of psychological attributes or personality traits. Hardiness has been suggested as a similar construct to mental toughness. Hardiness has typically been constructed as a personality trait, which is generally seen as stable throughout the lifetime. This differs from the conceptions of mental toughness offered by both Jones et al. and Gucciardi et al. These authors both conceive of mental toughness as unstable, arising in development, fluctuating over time, and varying for an individual performer between different sport and life scenarios. This definitional dilemma plagues the use of the term mental toughness and if mental toughness exists as a valid construct it may on occasion be maladaptive. Evidence to support this contention is derived from a study of overtraining behaviors and mental toughness by Tibbert (2013). She reported that "the MT attributes of mental self-concept and task familiarity displayed moderate curvilinear correlations with sport-specific recovery scales of the RESTQ-Sport. The curvilinear correlations reflect decreasing recovery at the highest levels of MT. The results suggest that some attributes of MT may relate to increased ability to recover whereas other attributes are associated with lower recovery (p.2-3). Arguably mental toughness is more closely linked with goal fixedness rather than adaptability and a flexible mindset, attributes which are central to resilience.
Crochet
The thickness or weight of the yarn is a significant factor in determining how many stitches and rows are required to cover a given area for a given stitch pattern. This is also termed the gauge. Thicker yarns generally require large-diameter crochet hooks, whereas thinner yarns may be crocheted with thick or thin hooks. Hence, thicker yarns generally require fewer stitches, and therefore less time, to work up a given project. The recommended gauge for a given ball of yarn can be found on the label that surrounds the skein when buying in stores. Patterns and motifs are coarser with thicker yarns and produce bold visual effects, whereas thinner yarns are best for refined or delicate pattern-work. Yarns are standardly grouped by thickness into six categories: superfine, fine, light, medium, bulky and superbulky. Quantitatively, thickness is measured by the number of wraps per inch (WPI). The related "weight per unit length" is usually measured in tex or denier.
Carbonate hardness
In a solution where only CO affects the pH, carbonate hardness can be used to calculate the concentration of dissolved CO in the solution with the formula CO = 3 × KH × 10, where KH is degrees of carbonate hardness and CO is given in ppm.
Toughening
The toughness of a brittle material is typically twice the surface energy associated with the formation of the fracture surfaces.
Superhard material
The hardness of a material is directly related to its incompressibility, elasticity and resistance to change in shape. A superhard material has high shear modulus, high bulk modulus and does not deform plastically. Ideally superhard materials should have a defect-free, isotropic lattice. This greatly reduces structural deformations that can lower the strength of the material. However, defects can actually strengthen some covalent structures. Traditionally, high-pressure and high-temperature (HPHT) conditions have been used to synthesize superhard materials, but recent superhard material syntheses aim at using less energy and lower cost materials.
Hardness
Hardness increases with decreasing particle size. This is known as the Hall-Petch relationship. However, below a critical grain-size, hardness decreases with decreasing grain size. This is known as the inverse Hall-Petch effect.
Harshness
Classical timbre’ NLDs are roughness, spectral centroid, and spectral flux. While harmonicity and inharmonicity can also be considered NLDs, harshness differs from them, as well as from roughness, once it reckons for a distinguished perceptual audio feature expressed by the summary spectral periodicity. This feature is especially clear in single-pitch, single-note, musical audio, where the timbre of two different musical instruments can greatly differ in levels of harshness (e.g., the difference in harshness between a flute and a saxophone is evident). As it is supposed to be, harshness is independent of all others NLDs.
Stiffness matrix
The stiffness matrix is the n-element square matrix A defined by
Weighted correlation network analysis
Next, an adjacency matrix (network), formula_11, is used to quantify how strongly genes are connected to one another. formula_12 is defined by thresholding the co-expression similarity matrix formula_13 . 'Hard' thresholding (dichotomizing) the similarity measure formula_14 results in an unweighted gene co-expression network. Specifically an unweighted network adjacency is defined to be 1 if formula_15 and 0 otherwise.
Because hard thresholding encodes gene connections in a binary fashion, it can be sensitive to the choice of the threshold and result in the loss of co-expression information. The continuous nature of the co-expression information can be preserved by employing soft thresholding, which results in a weighted network. Specifically, WGCNA uses the following power function assess their connection strength:
Friedrich Mohs
As part of this task, he started classifying minerals by their physical characteristics, instead of their chemical composition, as had been done traditionally. This emphasis on physical characteristics was at odds with the prevailing chemical systematics. However, both Theophrastus and Pliny the Elder had compared the relative hardness of minerals known to them in the ancient world, including diamond and quartz. They knew that diamond could scratch quartz, so showing it to be harder. This became the basis of the hardness scale developed by Mohs. The hardest mineral, diamond was given a value of 10 and softer minerals such as talc were given the very low value of 1 (unity). Other minerals were given intermediate values, depending on their ability to scratch another mineral in the scale. Thus gypsum was given the value 2 because it will scratch talc crystals, and calcite the value 3 because it will scratch gypsum. Minerals are also now classified by chemical characteristics, but the physical properties are still useful in field examination.
Structural engineering theory
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion. The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
Stiffness
The inverse of stiffness is "flexibility" or "compliance", typically measured in units of metres per Newton. In rheology, it may be defined as the ratio of strain to stress, and so take the units of reciprocal stress, "e.g". 1/Pa.
Stiffness
The stiffness, "k", of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as
Surface roughness
Each of the roughness parameters are calculated using a formula for describing the surface. Standard references that describe each in detail are Surfaces and their Measurement.
There are many different roughness parameters in use, but formula_1 is by far the most common, though this is often for historical reasons and not for particular merit, as the early roughness meters could only measure formula_1. Other common parameters include formula_3, formula_4, and formula_5. Some parameters are used only in certain industries or within certain countries. For example, the formula_6 family of parameters is used mainly for cylinder bore linings, and the "Motif parameters" are used primarily in the French automotive industry. The MOTIF method provides a graphical evaluation of a surface profile without filtering waviness from roughness. A "motif" consists of the portion of a profile between two peaks and the final combinations of these motifs eliminate ″insignificant″ peaks and retains ″significant″ ones. Please note that formula_1 is a dimensional unit that can be micrometer or microinch.
Superhard material
The incompressibility of a material is quantified by the bulk modulus B, which measures the resistance of a solid to volume compression under hydrostatic stress as B = −Vdp/dV. Here V is the volume, p is pressure, and dp/dV is the partial derivative of pressure with respect to the volume. The bulk modulus test uses an indenter tool to form a permanent deformation in a material. The size of the deformation depends on the material’s resistance to the volume compression made by the tool. Elements with small molar volumes and strong interatomic forces usually have high bulk moduli. Bulk moduli was the first major test of hardness and originally shown to be correlated with the molar volume (V) and cohesive energy (E) as B ~ E/V Bulk modulus was believed to be a direct measure of a material’s hardness but this no longer remains the dominant school of thought. For example, some alkali and noble metals (Pd, Ag) have anomalously high ratio of the bulk modulus to the Vickers of Brinell hardness. In the early 2000s, a direct relationship between bulk modulus and valence electron density was found as the more electrons were present the greater the repulsions within the structure were. Bulk modulus is still used as a preliminary measure of a material as superhard but it is now known that other properties must be taken into account.
Barcol hardness test
Originally called the Barber-Colman Impressor, the Barcol impressor was developed by Walter Colman as a hand-held, portable means of assessing the hardness of a material during World War II. The United States Army Air Corps required a hand-held method of checking the hardness of rivets due to concerns that aircraft could be sabotaged by replacing normal rivets with soft lead or wooden ones which would fail during flight. The impressor operates when the tip is pressed against the material in question. The hardness of the material determines how far the tip indents and this is transferred by a tension spring and lever to be read on a dial.
Hard and soft science
The modern distinction between hard and soft science is often attributed to a 1964 article published in "Science" by John R. Platt. He explored why he considered some scientific fields to be more productive than others, though he did not actually use the terms themselves. In 1967, sociologist of science Norman W. Storer specifically distinguished between the natural sciences as hard and the social sciences as soft. He defined hardness in terms of the degree to which a field uses mathematics and described a trend of scientific fields increasing in hardness over time, identifying features of increased hardness as including better integration and organization of knowledge, an improved ability to detect errors, and an increase in the difficulty of learning the subject.
HSAB theory
and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum softness, where softness is defined as the reciprocal of hardness.
Flatness problem
Since the constant formula_7 is known and the expansion rate formula_2 can be measured by observing the speed at which distant galaxies are receding from us,
formula_9 can be determined. Its value is currently around . The ratio of the actual density to this critical value is called Ω, and its difference from 1 determines the geometry of the universe: corresponds to a greater than critical density, , and hence a closed universe. gives a low density open universe, and Ω equal to exactly 1 gives a flat universe.
Water
Water hardness is also a critical factor in food processing and may be altered or treated by using a chemical ion exchange system. It can dramatically affect the quality of a product, as well as playing a role in sanitation. Water hardness is classified based on concentration of calcium carbonate the water contains. Water is classified as soft if it contains less than 100 mg/l (UK) or less than 60 mg/l (US).
Hardness comparison
There are a large number of hardness testing methods available (e.g. Vickers, Brinell, Rockwell, Meyer and Leeb). Although it is impossible in many cases to give an exact conversion, it is possible to give an approximate material-specific comparison table e.g. for steels.
Heat treating
Case hardening is specified by hardness and "case depth". The case depth can be specified in two ways: "total case depth" or "effective case depth". The total case depth is the true depth of the case. For most alloys, the effective case depth is the depth of the case that has a hardness equivalent of HRC50; however, some alloys specify a different hardness (40-60 HRC) at effective case depth; this is checked on a Tukon microhardness tester. This value can be roughly approximated as 65% of the total case depth; however the chemical composition and hardenability can affect this approximation. If neither type of case depth is specified the total case depth is assumed.
Nanoindentation
The indentation hardness, formula_46 is defined slightly different.
Hard
Hard or hardness may refer to:
Mohs scale of mineral hardness
Comparison between hardness (Mohs) and hardness (Vickers):