materials science
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries.
The intellectual origins of materials sci ...
, hardness (antonym: softness) is a measure of the resistance to plastic deformation, such as an indentation (over an area) or a scratch (linear), induced mechanically either by pressing or abrasion. In general, different materials differ in their hardness; for example hard metals such as
titanium
Titanium is a chemical element; it has symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion in ...
and
beryllium
Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with ...
are harder than soft metals such as
sodium
Sodium is a chemical element; it has Symbol (chemistry), symbol Na (from Neo-Latin ) and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 element, group 1 of the peri ...
wood
Wood is a structural tissue/material found as xylem in the stems and roots of trees and other woody plants. It is an organic materiala natural composite of cellulosic fibers that are strong in tension and embedded in a matrix of lignin t ...
and common
plastic
Plastics are a wide range of synthetic polymers, synthetic or Semisynthesis, semisynthetic materials composed primarily of Polymer, polymers. Their defining characteristic, Plasticity (physics), plasticity, allows them to be Injection moulding ...
s. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, hardness can be measured in different ways, such as
scratch hardness
Scratch hardness refers to the hardness of a material in terms of resistance to scratches and abrasion by a harder material forcefully drawn over its surface. Scratch hardness test or scratch test refers to any of a number of methods of measuring s ...
ductility
Ductility refers to the ability of a material to sustain significant plastic Deformation (engineering), deformation before fracture. Plastic deformation is the permanent distortion of a material under applied stress, as opposed to elastic def ...
,
elastic
Elastic is a word often used to describe or identify certain types of elastomer, Elastic (notion), elastic used in garments or stretch fabric, stretchable fabrics.
Elastic may also refer to:
Alternative name
* Rubber band, ring-shaped band of rub ...
stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Calculations
The stiffness, k, of a ...
toughness
In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing.viscoelasticity
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist both shear flow and strain lin ...
, and
viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
. Common examples of hard matter are
ceramic
A ceramic is any of the various hard, brittle, heat-resistant, and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcela ...
s,
concrete
Concrete is a composite material composed of aggregate bound together with a fluid cement that cures to a solid over time. It is the second-most-used substance (after water), the most–widely used building material, and the most-manufactur ...
, certain
metal
A metal () is a material that, when polished or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, electricity and thermal conductivity, heat relatively well. These properties are all associated wit ...
s, and
superhard material
A superhard material is a material with a hardness value exceeding 40 gigapascals (GPa) when measured by the Vickers hardness test. They are virtually incompressible solids with high electron density and high Covalent bond, bond covalency. As a res ...
s, which can be contrasted with
soft matter
Soft matter or soft condensed matter is a type of matter that can be deformed or structurally altered by thermal or mechanical stress which is of similar magnitude to thermal fluctuations.
The science of soft matter is a subfield of condensed ...
.
Measures
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.
Scratch hardness
''Scratch hardness'' is the measure of how resistant a sample is to
fracture
Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress (mechanics), stress. The fracture of a solid usually occurs due to the development of certain displacemen ...
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
The Mohs scale ( ) of mineral hardness is a qualitative ordinal scale, from 1 to 10, characterizing scratch resistance of minerals through the ability of harder material to scratch softer material.
The scale was introduced in 1812 by the Ger ...
, which is used in
mineralogy
Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical mineralogy, optical) properties of minerals and mineralized artifact (archaeology), artifacts. Specific s ...
. One tool to make this measurement is the sclerometer.
Another tool used to make these tests is the pocket hardness tester. This tool consists of a scale arm with graduated markings attached to a four-wheeled carriage. A scratch tool with a sharp rim is mounted at a predetermined angle to the testing surface. In order to use it a weight of known mass is added to the scale arm at one of the graduated markings, the tool is then drawn across the test surface. The use of the weight and markings allows a known pressure to be applied without the need for complicated machinery.
Indentation 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
Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...
and
metallurgy
Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys.
Metallurgy encompasses both the ...
. The tests work on the basic premise of measuring the critical dimensions of an indentation left by a specifically dimensioned and loaded indenter. Common indentation hardness scales are Rockwell,
Vickers
Vickers was a British engineering company that existed from 1828 until 1999. It was formed in Sheffield as a steel foundry by Edward Vickers and his father-in-law, and soon became famous for casting church bells. The company went public in 18 ...
,
Shore
A coast (coastline, shoreline, seashore) is the land next to the sea or the line that forms the boundary between the land and the ocean or a lake. Coasts are influenced by the topography of the surrounding landscape and by aquatic erosion, su ...
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. Two scales that measures rebound hardness are the Leeb rebound hardness test and Bennett hardness scale. Ultrasonic Contact Impedance (UCI) method determines hardness by measuring the frequency of an oscillating rod. The rod consists of a metal shaft with vibrating element and a pyramid-shaped diamond mounted on one end.
work hardening
Work hardening, also known as strain hardening, is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation. This characteristic is what sets ductile materials apart from brittle materi ...
martensitic transformation
A diffusionless transformation, commonly known as displacive transformation, denotes solid-state alterations in crystal structures that do not hinge on the diffusion of atoms across extensive distances. Rather, these transformations manifest a ...
.
In solid mechanics
In
solid mechanics
Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature chang ...
, solids generally have three responses to
force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
, 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
Stiffness is the extent to which an object resists deformation in response to an applied force.
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Calculations
The stiffness, k, of a ...
in the case of a given object, or a high
elastic modulus
An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it.
Definition
The elastic modu ...
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
In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and w ...
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
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
when undergoing plastic deformation; this is called
viscoelasticity
In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist both shear flow and strain lin ...
.
* They
fracture
Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress (mechanics), stress. The fracture of a solid usually occurs due to the development of certain displacemen ...
—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
In mechanics, compressive strength (or compression strength) is the capacity of a material or Structural system, structure to withstand Structural load, loads tending to reduce size (Compression (physics), compression). It is opposed to ''tensil ...
tensile strength
Ultimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or F_\text in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials, the ultimate ...
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
A material is brittle if, when subjected to stress (physics), stress, it fractures with little elastic deformation and without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of h ...
, in technical usage, is the tendency of a material to fracture with very little or no detectable plastic 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 perfectly brittle materials, yield strength and ultimate strength are the same, because they do not experience detectable plastic deformation. The opposite of brittleness is
ductility
Ductility refers to the ability of a material to sustain significant plastic Deformation (engineering), deformation before fracture. Plastic deformation is the permanent distortion of a material under applied stress, as opposed to elastic def ...
.
The
toughness
In materials science and metallurgy, toughness is the ability of a material to absorb energy and plastically deform without fracturing.energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
it can absorb before fracturing, which is different from the amount of
force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
that can be applied. Toughness tends to be small for brittle materials, because elastic and plastic deformations allow materials to absorb large amounts of energy.
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.
Hardness of a material to deformation is dependent on its microdurability or small-scale
shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the Elasticity (physics), elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear s ...
stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force.
The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Calculations
The stiffness, k, of a ...
properties such as its
bulk modulus
The bulk modulus (K or B or k) of a substance is a measure of the resistance of a substance to bulk compression. It is defined as the ratio of the infinitesimal pressure increase to the resulting ''relative'' decrease of the volume.
Other mo ...
or
Young's modulus
Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Youn ...
. Stiffness is often confused for hardness. Some materials are stiffer than diamond (e.g. osmium) but are not harder, and are prone to
spall
Spall are fragments of a material that are broken off a larger solid body. It can be produced by a variety of mechanisms, including as a result of projectile impact, corrosion, weathering, cavitation, or excessive rolling pressure (as in a ba ...
ing and flaking in squamose or acicular habits.
Mechanisms and theory
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, P. (1978). Physical metallurgy. Cambridge ng. New York: Cambridge University Press. At the atomic level, the atoms in a metal are arranged in an orderly three-dimensional array called a
crystal lattice
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystal, crystalline material. Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that ...
. 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
In materials science, an interstitial defect is a type of point crystallographic defect where an atom of the same or of a different type, occupies an interstitial site in the crystal structure. When the atom is of the same type as those already p ...
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.
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.
Dislocations provide a mechanism for planes of atoms to slip and thus a method for plastic or permanent deformation. 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 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.
Relation between hardness number and stress-strain curve
Careful note should be taken of the relationship between a hardness number and the stress-strain curve exhibited by the material. The latter, which is conventionally obtained via tensile testing, captures the full plasticity response of the material (which is in most cases a metal). It is in fact a dependence of the (true von Mises plastic strain on the (true) von Mises stress, but this is readily obtained from a nominal stress – nominal strain curve (in the pre- necking regime), which is the immediate outcome of a tensile test. This relationship can be used to describe how the material will respond to almost any loading situation, often by using the
Finite Element Method
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...
(FEM). This applies to the outcome of an indentation test (with a given size and shape of indenter, and a given applied load).
However, while a hardness number thus depends on the stress-strain relationship, inferring the latter from the former is far from simple and is not attempted in any rigorous way during conventional hardness testing. (In fact, the Indentation Plastometry technique, which involves iterative FEM modelling of an indentation test, does allow a stress-strain curve to be obtained via indentation, but this is outside the scope of conventional hardness testing.) A hardness number is just a semi-quantitative indicator of the resistance to plastic deformation. Although hardness is defined in a similar way for most types of test – usually as the load divided by the contact area – the numbers obtained for a particular material are different for different types of test, and even for the same test with different applied loads. Attempts are sometimes made to identify simple analytical expressions that allow features of the stress-strain curve, particularly the
yield stress
In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elasticity (physics), elastic behavior and the beginning of plasticity (physics), plastic behavior. Below the yield point ...
and Ultimate Tensile Stress (UTS), to be obtained from a particular type of hardness number. However, these are all based on empirical correlations, often specific to particular types of alloy: even with such a limitation, the values obtained are often quite unreliable. The underlying problem is that metals with a range of combinations of yield stress and
work hardening
Work hardening, also known as strain hardening, is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation. This characteristic is what sets ductile materials apart from brittle materi ...
characteristics can exhibit the same hardness number. The use of hardness numbers for any quantitative purpose should, at best, be approached with considerable caution.
Hardness comparison
A variety of hardness-testing methods are available, including the Vickers, Brinell, Rockwell, Meyer and Leeb tests. Although it is impossible in many cases to give an exact conversion, it is possible to give an approximate material-specific co ...
Work hardening
Work hardening, also known as strain hardening, is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation. This characteristic is what sets ductile materials apart from brittle materi ...
Janka hardness test
The Janka hardness test (; ), created by Austrian-born American researcher Gabriel Janka (1864–1932), measures the resistance of a sample of wood to denting and wear. It measures the force required to embed an steel ball halfway into a sample ...
*
*Davis, J. R. (Ed.). (2002). ''Surface hardening of steels: Understanding the basics.'' Materials Park, OH: ASM International.
*Dieter, George E. (1989). ''Mechanical Metallurgy.'' SI Metric Adaptation. Maidenhead, UK: McGraw-Hill Education.
*
*Revankar, G. (2003). "Introduction to hardness testing." ''Mechanical testing and evaluation'', ASM Online Vol. 8.