Hardness: Wikis


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From Wikipedia, the free encyclopedia

Hardness refers to various properties of matter in the solid phase that give it high resistance to various kinds of shape change when force is applied. Hard matter is contrasted with soft matter.

Macroscopic hardness is generally characterized by strong intermolecular bonds. However, the behavior of solid materials under force is complex, resulting in several different scientific definitions of what might be called "hardness" in everyday usage.

In materials science, there are three principal operational definitions of hardness:

  • Scratch hardness: Resistance to fracture or plastic (permanent) deformation due to friction from a sharp object
  • Indentation hardness: Resistance to plastic (permanent) deformation due to a constant load from a sharp object
  • Rebound hardness: Height of the bounce of an object dropped on the material, related to elasticity.

In physics, hardness encompasses:

The equation based definition of hardness is the pressure applied over the projected 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.


Materials science

A Vickers hardness tester

Hardness is a characteristic of a solid material expressing its resistance to permanent deformation. Hardness can be measured on the Mohs scale or various other scales. Some of the other scales used for indentation hardness in engineering—Rockwell, Vickers, and Brinell—can be compared using practical conversion tables.

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. [1]

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.

It is important to note that hardness of a material to deformation is dependent on its microdurability or small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus. Scientists and journalists often confuse stiffness for hardness,[2][3] and spuriously report materials that are not actually harder than diamond because the anisotropy of their solid cells compromise hardness in other dimensions, resulting in a material prone to spalling and flaking in squamose or acicular habits in that dimension (e.g., osmium is stiffer than diamond but only as hard as quartz). In other words, a claimed hard material should have similar hardness characteristics at any location on its surface.


Scratch hardness

In mineralogy, hardness commonly refers to a material's ability to penetrate softer materials. An object made of a hard material will scratch an object made of a softer material. Scratch hardness is usually measured on the Mohs scale of mineral hardness. One tool to make this measurement is the sclerometer.

Pure diamond is the hardest readily-available natural mineral substance and will scratch any other natural material. Diamond is therefore used to cut other diamonds; in particular, higher-grade diamonds are used to cut lower-grade diamonds.

The hardest substance known today is aggregated diamond nanorods - a nanocrystalline form of diamond. Estimates from proposed molecular structure indicate the hardness of beta carbon nitride should also be greater than diamond (but less than aggregated diamond nanorods). This material has not yet been successfully synthesized.

For a list of materials harder than diamond, see Harder than diamond materials.

Indentation hardness

Indentation hardness tests 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.

Rebound hardness

Also known as dynamic hardness, rebound hardness measures the height of the "bounce" of a diamond-tipped hammer dropped from a fixed height onto a material. The device used to take this measurement is known as a scleroscope.[4]

Two scales that measures rebound hardness are the Leeb rebound hardness test and Bennett hardness scale.


Diagram of a stress-strain curve, showing the relationship between stress (force applied per unit area) and strain or deformation of a ductile metal.

In solid mechanics, solids generally have three responses to force, depending on the amount of force and the type of material:

  • They exhibit elasticity—the ability to temporarily change shape, but return to the original shape when the pressure is removed. "Hardness" in the elastic range—a small temporary change in shape for a given force—is known as stiffness in the case of a given object, or a high elastic modulus in the case of a material.
  • They exhibit plasticity—the ability to permanently change shape in response to the force, but remain in one piece. The yield strength is the point at which elastic deformation gives way to plastic deformation. Deformation in the plastic range is non-linear, and is described by the stress-strain curve. This response produces the observed properties of scratch and indentation hardness, as described and measured in materials science. Some materials exhibit both elasticity and viscosity when undergoing plastic deformation; this is called viscoelasticity.
  • They fracture—split into two or more pieces.

Strength is a measure of the extent of a material's elastic range, or elastic and plastic ranges together. This is quantified as compressive strength, shear strength, tensile strength depending on the direction of the forces involved. Ultimate strength is an engineering measure of the maximum load a part of a specific material and geometry can withstand.

Brittleness, in technical usage, is the tendency of a material to fracture with very little or no detectable deformation beforehand. Thus in technical terms, a material can be both brittle and strong. In everyday usage "brittleness" usually refers to the tendency to fracture under a small amount of force, which exhibits both brittleness and a lack of strength (in the technical sense). For perfectally brittle materials, yield strength and ultimate strength are the same, because they do not experience detectable plastic deformation. The opposite of brittleness is ductility.

The toughness of a material is the maximum amount of energy it can absorb before fracturing, which is different than the amount of force that can be applied. Toughness tends to be small for brittle materials, because it is elastic and plastic deformations that allow materials to absorb large amounts of energy.

Materials whose properties are different in different directions (because of an asymmetrical crystal structure) are referred to as anisotropic.

Mechanisms and theory

A representation of the crystal lattice showing the planes of atoms.

The key to understanding the mechanism behind hardness is understanding the metallic microstructure, or the structure and arrangement of the atoms at the atomic level. In fact, most important metallic properties critical to the manufacturing of today’s goods are determined by the microstructure of a material (Haasen, 1, 1978). At the atomic level, the atoms in a metal are arranged in an orderly three-dimensional array called a crystal lattice. In reality, however, a given specimen of a metal likely never contains a consistent single crystal lattice. A given sample of metal will contain many grains, with each grain having a fairly consistent array pattern. At an even smaller scale, each grain contains irregularities.

There are two types of irregularities at the grain level of the microstructure that are responsible for the hardness of the material. These irregularities are point defects and line defects. A point defect is an irregularity located at a single lattice site inside of the overall three-dimensional lattice of the grain. There are three main point defects. If there is an atom missing from the array, a vacancy defect is formed. If there is a different type of atom at the lattice site that should normally be occupied by a metal atom, a substitutional defect is formed. If there exists an atom in a site where there should normally not be, an interstitial defect is formed. This is possible because space exists between atoms in a crystal lattice. While point defects are irregularities at a single site in the crystal lattice, line defects are irregularities on a plane of atoms. Dislocations are a type of line defect involving the misalignment of these planes. In the case of an edge dislocation, a half plane of atoms is wedged between two planes of atoms. In the case of a screw dislocation two planes of atoms are offset with a helical array running between them (Samuel, 52, 2009).

Planes of atoms split by an edge dislocation.

Dislocations provide a mechanism for planes of atoms to slip and thus a method for plastic or permanent deformation (Haasen, 265, 1978). Planes of atoms can flip from one side of the dislocation to the other effectively allowing the dislocation to traverse through the material and the material to deform permanently. The movement allowed by these dislocations causes a decrease in the material's hardness.

The way to inhibit the movement of planes of atoms, and thus make them harder, involves the interaction of dislocations with each other and interstitial atoms. When a dislocation intersects with a second dislocation, it can no longer traverse through the crystal lattice. The intersection of dislocations creates an anchor point and does not allow the planes of atoms to continue to slip over one another (Leslie, 31, 1981). A dislocation can also be anchored by the interaction with interstitial atoms. If a dislocation comes in contact with two or more interstitial atoms, the slip of the planes will again be disrupted. The interstitial atoms create anchor points, or pinning points, in the same manner as intersecting dislocations.

By varying the presence of interstitial atoms and the density of dislocations, a particular metal's hardness can be controlled. Although seemingly counter-intuitive, as the density of dislocations increases, there are more intersections created and consequently more anchor points. Similarly, as more interstitial atoms are added, more pinning points that impede the movements of dislocations are formed. As a result, the more anchor points added, the harder the material will become.

See also

Other strengthening mechanisms

Hard materials



  • Dieter, George E. (1989). Mechanical Metallurgy (SI Metric Adaptation ed.). Maidenhead, UK: McGraw-Hill Education. ISBN ISBN 0-07-100406-8. 
  • Malzbender, J (2003). "Comment on hardness definitions". Journal of the European Ceramics Society 23: 1355. doi:10.1016/S0955-2219(02)00354-0. 
  • Chinn, R. L. (2009). Hardness, bearings, and the Rockwells. Advanced Materials & Processes, 167 (10), 29-31.
  • Davis, J. R. (Ed.). (2002). Surface hardening of steels: Understanding the basics. Materials Park, OH: ASM International.
  • Haasen, P. (1978). Physical metallurgy. Cambridge [Eng.] ; New York: Cambridge University Press.
  • Leslie, W. C. (1981). The physical metallurgy of steels. Washington: Hempisphere Pub. Corp ; New York: McGraw-Hill.
  • Revankar, G. (2003). Introduction to hardness testing. Mechanical testing and evaluation, ASM Online Vol. 8.
  • Samuel, J. (2009). Introduction to materials science course manual. Madison, Wisconsin: University of Wisconsin-Madison.

External links


Up to date as of January 23, 2010

From Wikibooks, the open-content textbooks collection


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.


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.


There 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:

1. Rockwell hardness test 2. Brinell hardness 3. Vickers 4. Knoop hardness 5. Shore


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