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55-601: [REDACTED] Look up hardiness in Wiktionary, the free dictionary. Not to be confused with hardness . Hardiness may refer to: Hardiness (plants) , the ability of plants to survive adverse growing conditions Hardiness zone , area in which a category of plants is capable of growing, as defined by the minimum temperature of that area Psychological resilience or mental resilience, positive capacity of people to cope with stress and catastrophe Hardiness (psychology) ,

110-468: A 90-degree rotation; both these deformations have the same spatial strain tensors yet must produce different values of the Cauchy stress tensor. Even though the stress in a Cauchy-elastic material depends only on the state of deformation, the work done by stresses might depend on the path of deformation. Therefore, Cauchy elasticity includes non-conservative "non-hyperelastic" models (in which work of deformation

165-493: A conceptual framework for psychological resilience Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Hardiness . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Hardiness&oldid=1135422516 " Category : Disambiguation pages Hidden categories: Short description

220-484: 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

275-424: 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

330-501: A function of the deformation gradient ( F {\displaystyle {\boldsymbol {F}}} ). By also requiring satisfaction of material objectivity , the energy potential may be alternatively regarded as a function of the Cauchy-Green deformation tensor ( C := F T F {\displaystyle {\boldsymbol {C}}:={\boldsymbol {F}}^{\textsf {T}}{\boldsymbol {F}}} ), in which case

385-468: A given isotropic solid , with known theoretical elasticity for the bulk material in terms of Young's modulus,the effective elasticity will be governed by porosity . Generally a more porous material will exhibit lower stiffness. More specifically, the fraction of pores, their distribution at different sizes and the nature of the fluid with which they are filled give rise to different elastic behaviours in solids. For isotropic materials containing cracks,

440-411: A one-dimensional rod, can often be reduced to applications of Hooke's law. The elastic behavior of objects that undergo finite deformations has been described using a number of models, such as Cauchy elastic material models, Hypoelastic material models, and Hyperelastic material models. The deformation gradient ( F ) is the primary deformation measure used in finite strain theory . A material

495-413: 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

550-435: A resistance to deformation under an applied load. The various moduli apply to different kinds of deformation. For instance, Young's modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear . Young's modulus and shear modulus are only for solids, whereas the bulk modulus is for solids, liquids, and gases. The elasticity of materials is described by a stress–strain curve , which shows

605-455: A special case, which prompts some constitutive modelers to append a third criterion that specifically requires a hypoelastic model to not be hyperelastic (i.e., hypoelasticity implies that stress is not derivable from an energy potential). If this third criterion is adopted, it follows that a hypoelastic material might admit nonconservative adiabatic loading paths that start and end with the same deformation gradient but do not start and end at

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660-464: 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 (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

715-527: Is a constant known as the rate or spring constant . It can also be stated as a relationship between stress σ {\displaystyle \sigma } and strain ε {\displaystyle \varepsilon } : where E is known as the Young's modulus . Although the general proportionality constant between stress and strain in three dimensions is a 4th-order tensor called stiffness , systems that exhibit symmetry , such as

770-405: Is different from Wikidata All article disambiguation pages All disambiguation pages 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. Scratch hardness

825-421: Is known as perfect elasticity , in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs. In engineering , the elasticity of a material is quantified by the elastic modulus such as

880-665: 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. There are five hardening processes: Hall-Petch strengthening , work hardening , solid solution strengthening , precipitation hardening , and martensitic transformation . In solid mechanics , solids generally have three responses to force , depending on

935-459: 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 any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus . Stiffness

990-407: Is often confused for hardness. Some materials are stiffer than diamond (e.g. osmium) but are not harder, and are prone to spalling and flaking in squamose or acicular habits. 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

1045-444: Is often presumed to apply up to the elastic limit for most metals or crystalline materials whereas nonlinear elasticity is generally required to model large deformations of rubbery materials even in the elastic range. For even higher stresses, materials exhibit plastic behavior , that is, they deform irreversibly and do not return to their original shape after stress is no longer applied. For rubber-like materials such as elastomers ,

1100-416: Is path dependent) as well as conservative " hyperelastic material " models (for which stress can be derived from a scalar "elastic potential" function). A hypoelastic material can be rigorously defined as one that is modeled using a constitutive equation satisfying the following two criteria: If only these two original criteria are used to define hypoelasticity, then hyperelasticity would be included as

1155-506: Is said to be Cauchy-elastic if the Cauchy stress tensor σ is a function of the deformation gradient F alone: It is generally incorrect to state that Cauchy stress is a function of merely a strain tensor , as such a model lacks crucial information about material rotation needed to produce correct results for an anisotropic medium subjected to vertical extension in comparison to the same extension applied horizontally and then subjected to

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1210-413: 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

1265-453: 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

1320-436: 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

1375-699: The Deborah number . In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow like a viscous liquid. Because the elasticity of a material is described in terms of a stress–strain relation, it is essential that the terms stress and strain be defined without ambiguity. Typically, two types of relation are considered. The first type deals with materials that are elastic only for small strains. The second deals with materials that are not limited to small strains. Clearly,

1430-400: The Young's modulus , bulk modulus or shear modulus which measure the amount of stress needed to achieve a unit of strain ; a higher modulus indicates that the material is harder to deform. The SI unit of this modulus is the pascal (Pa). The material's elastic limit or yield strength is the maximum stress that can arise before the onset of plastic deformation. Its SI unit is also

1485-406: The dimension L ⋅M⋅T . For most commonly used engineering materials, the elastic modulus is on the scale of gigapascals (GPa, 10 Pa). As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. This relationship is known as Hooke's law . A geometry-dependent version of the idea

1540-412: The actual (not objective) stress rate. Hyperelastic materials (also called Green elastic materials) are conservative models that are derived from a strain energy density function ( W ). A model is hyperelastic if and only if it is possible to express the Cauchy stress tensor as a function of the deformation gradient via a relationship of the form This formulation takes the energy potential ( W ) as

1595-451: The amount of force and the type of material: 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,

1650-475: 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

1705-461: The configuration which minimizes the free energy, subject to constraints derived from their structure, and, depending on whether the energy or the entropy term dominates the free energy, materials can broadly be classified as energy-elastic and entropy-elastic . As such, microscopic factors affecting the free energy, such as the equilibrium distance between molecules, can affect the elasticity of materials: for instance, in inorganic materials, as

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1760-458: The critical dimensions of an indentation left by a specifically dimensioned and loaded indenter. Common indentation hardness scales are Rockwell , Vickers , Shore , and Brinell , amongst others. 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

1815-433: 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. Careful note should be taken of the relationship between a hardness number and the stress-strain curve exhibited by

1870-478: 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

1925-400: 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

1980-445: The hyperelastic model may be written alternatively as Linear elasticity is used widely in the design and analysis of structures such as beams , plates and shells , and sandwich composites . This theory is also the basis of much of fracture mechanics . Hyperelasticity is primarily used to determine the response of elastomer -based objects such as gaskets and of biological materials such as soft tissues and cell membranes . In

2035-443: 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

2090-529: The manufacturing of today’s goods are determined by the microstructure of a material. 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

2145-402: The material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity , in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals , the atomic lattice changes size and shape when forces are applied (energy is added to

2200-412: 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

2255-403: The pascal (Pa). When an elastic material is deformed due to an external force, it experiences internal resistance to the deformation and restores it to its original state if the external force is no longer applied. There are various elastic moduli , such as Young's modulus , the shear modulus , and the bulk modulus , all of which are measures of the inherent elastic properties of a material as

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2310-415: The possibility of large rotations, large distortions, and intrinsic or induced anisotropy . For more general situations, any of a number of stress measures can be used, and it is generally desired (but not required) that the elastic stress–strain relation be phrased in terms of a finite strain measure that is work conjugate to the selected stress measure, i.e., the time integral of the inner product of

2365-537: The presence of fractures affects the Young and the shear moduli perpendicular to the planes of the cracks, which decrease (Young's modulus faster than the shear modulus) as the fracture density increases, indicating that the presence of cracks makes bodies brittler. Microscopically , the stress–strain relationship of materials is in general governed by the Helmholtz free energy , a thermodynamic quantity . Molecules settle in

2420-416: The relation between stress (the average restorative internal force per unit area) and strain (the relative deformation). The curve is generally nonlinear, but it can (by use of a Taylor series ) be approximated as linear for sufficiently small deformations (in which higher-order terms are negligible). If the material is isotropic , the linearized stress–strain relationship is called Hooke's law , which

2475-406: 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

2530-462: The same hardness number. The use of hardness numbers for any quantitative purpose should, at best, be approached with considerable caution. Elasticity (physics) In physics and materials science , elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if

2585-484: The same internal energy. Note that the second criterion requires only that the function G {\displaystyle G} exists . As detailed in the main hypoelastic material article, specific formulations of hypoelastic models typically employ so-called objective rates so that the G {\displaystyle G} function exists only implicitly and is typically needed explicitly only for numerical stress updates performed via direct integration of

2640-484: 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 from the amount of force 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

2695-518: The second type of relation is more general in the sense that it must include the first type as a special case. For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor ; the resulting (predicted) material behavior is termed linear elasticity , which (for isotropic media) is called the generalized Hooke's law . Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for

2750-420: The slope of the stress–strain curve increases with stress, meaning that rubbers progressively become more difficult to stretch, while for most metals, the gradient decreases at very high stresses, meaning that they progressively become easier to stretch. Elasticity is not exhibited only by solids; non-Newtonian fluids , such as viscoelastic fluids , will also exhibit elasticity in certain conditions quantified by

2805-413: The stress measure with the rate of the strain measure should be equal to the change in internal energy for any adiabatic process that remains below the elastic limit. The SI unit for elasticity and the elastic modulus is the pascal (Pa). This unit is defined as force per unit area, generally a measurement of pressure , which in mechanics corresponds to stress . The pascal and therefore elasticity have

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2860-464: The stress-strain curve, particularly the yield stress 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 characteristics can exhibit

2915-404: The system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers , elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of deformation, regardless of how large that distance becomes. This

2970-412: 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 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 . The tests work on the basic premise of measuring

3025-422: Was first formulated by Robert Hooke in 1675 as a Latin anagram , "ceiiinosssttuv". He published the answer in 1678: " Ut tensio, sic vis " meaning " As the extension, so the force ", a linear relationship commonly referred to as Hooke's law . This law can be stated as a relationship between tensile force F and corresponding extension displacement x {\displaystyle x} , where k

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