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Critical Resolved Shear Stress
In materials science, critical resolved shear stress (CRSS) is the shear stress that is necessary to initiate Slip (materials science), slip on a particular slip system in a Crystallite, grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved in the slip direction on a slip plane that is neither perpendicular nor parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, , typically called the Schmid Factor, Schmid factor: :\tau_\text = \sigma_\text m = \sigma_\text (\cos \phi \cos \lambda) where \sigma_\mathrm is the magnitude of the applied tensile stress, \phi is the angle between the normal of the slip plane and the direction of the applied force, and \lambda is the angle between the slip direction and the direction of the applied force. The Schmid factor is most applicable to Face centered cubic, FCC single-crystal metals, but for polycrystal metals the G. I. Taylor, Taylor factor has b ...
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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 science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study. Materials scientists emphasize understanding how the history of a material (''processing'') influences its struc ...
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Grain Boundary Compatibility
A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legumes. After being harvested, dry grains are more durable than other staple foods, such as starchy fruits ( plantains, breadfruit, etc.) and tubers (sweet potatoes, cassava, and more). This durability has made grains well suited to industrial agriculture, since they can be mechanically harvested, transported by rail or ship, stored for long periods in silos, and milled for flour or pressed for oil. Thus, the grain market is a major global commodity market that includes crops such as maize, rice, soybeans, wheat and other grains. Cereal and non-cereal grains In the grass family, a grain (narrowly defined) is a caryopsis, a fruit with its wall fused on to the single seed inside, belonging to a cereal such as wheat, maize, or rice. More bro ...
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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 science and the technology of metals, including the production of metals and the engineering of metal components used in products for both consumers and manufacturers. Metallurgy is distinct from the craft of metalworking. Metalworking relies on metallurgy in a similar manner to how medicine relies on medical science for technical advancement. A specialist practitioner of metallurgy is known as a metallurgist. The science of metallurgy is further subdivided into two broad categories: chemical metallurgy and physical metallurgy. Chemical metallurgy is chiefly concerned with the reduction and oxidation of metals, and the chemical performance of metals. Subjects of study in chemical metallurgy include mineral processing, the extraction ...
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Dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as ''glide'' or Slip (materials science), slip. The crystalline order is restored on either side of a ''glide dislocation'' but the atoms on one side have moved by one position. The crystalline order is not fully restored with a ''partial dislocation''. A dislocation defines the boundary between ''slipped'' and ''unslipped'' regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plasticity (physics), Plastic deformation of a material occurs by the creation and ...
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Solid Solution Strengthening
In metallurgy, solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element (the alloying element) to the crystalline lattice of another element (the base metal), forming a solid solution. The local nonuniformity in the lattice due to the alloying element makes plastic deformation more difficult by impeding dislocation motion through stress fields. In contrast, alloying beyond the solubility limit can form a second phase, leading to strengthening via other mechanisms (e.g. the precipitation of intermetallic compounds). Types Depending on the size of the alloying element, a substitutional solid solution or an interstitial solid solution can form. In both cases, atoms are visualised as rigid spheres where the overall crystal structure is essentially unchanged. The rationale of crystal geometry to atom solubility prediction is summarized in the Hume-Rothery rules and Pauling's rul ...
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Homologous Temperature
Homologous temperature expresses the thermodynamic temperature of a material as a fraction of the thermodynamic temperature of its melting point (i.e. using the Kelvin scale): T_H = \frac For example, the homologous temperature of lead at room temperature (25 °C) is approximately 0.50 (TH = T/Tmp = 298 K/601 K = 0.50). Significance of the homologous temperature The homologous temperature of a substance is useful for determining the rate of steady state creep (diffusion-dependent deformation). A higher homologous temperature results in an exponentially higher rate of diffusion dependent deformation. Additionally, for a given fixed homologous temperature, two materials with different melting points would have similar diffusion-dependent deformation behaviour. For example, solder (Tmp = 456 K) at 115 °C would have comparable mechanical properties to copper (Tmp = 1358 K) at 881 °C, because they would both be at 0.85Tmp despite being at diff ...
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Critical Resolved Shear Stress With Temperature
Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in mission and business critical information systems *Critical theory, a school of thought that critiques society and culture by applying knowledge from the social sciences and the humanities *Critically endangered, a risk status for wild species *Criticality (status), the condition of sustaining a nuclear chain reaction Art, entertainment, and media * ''Critical'' (novel), a medical thriller written by Robin Cook * ''Critical'' (TV series), a Sky 1 TV series * "Critical" (''Person of Interest''), an episode of the American television drama series ''Person of Interest'' *"Critical", a song by Abhi the Nomad from the album ''Abhi vs the Universe'', 2021 *"Critical", a 1999 single by Zion I from the album ''Mind over Matter'' People *Cr1TiKaL ...
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Ductile-brittle Transition
Ductility refers to the ability of a material to sustain significant plastic deformation before fracture. Plastic deformation is the permanent distortion of a material under applied stress, as opposed to elastic deformation, which is reversible upon removing the stress. Ductility is a critical mechanical performance indicator, particularly in applications that require materials to bend, stretch, or deform in other ways without breaking. The extent of ductility can be quantitatively assessed using the percent elongation at break, given by the equation: \% \mathrm= \left ( \frac \right )\times100 where l_ is the length of the material after fracture and l_0 is the original length before testing. This formula helps in quantifying how much a material can stretch under tensile stress before failure, providing key insights into its ductile behavior. Ductility is an important consideration in engineering and manufacturing. It defines a material's suitability for certain manufactur ...
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Compatibility (mechanics)
In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that ''unique'' tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field. Compatibility is the study of the conditions under which such a displacement field can be guaranteed. Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886.C Amrouche, PG Ciarlet, L Gratie, S Kesavan, On Saint Venant's compatibility conditions and Poincaré's lemma, C. R. Acad. Sci. Paris, Ser. I, 342 (2006), 887-891. In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points. Each volume is assumed to be connected to its neighbors without any gaps or overlaps. Certain mathematical conditions have to be satisfied to ensure that gaps/overlaps do n ...
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Geometrically Necessary Dislocations
Geometrically necessary dislocations are like-signed dislocations needed to accommodate for plastic bending in a crystalline material. They are present when a material's plastic deformation is accompanied by internal plastic strain gradients. They are in contrast to statistically stored dislocations, with statistics of equal positive and negative signs, which arise during plastic flow from multiplication processes like the Frank-Read source. Dislocations in crystalline materials Statistically stored dislocations As straining progresses, the dislocation density increases and the dislocation mobility decreases during plastic flow. There are different ways through which dislocations can accumulate. Many of the dislocations are accumulated by multiplication, where dislocations encounters each other by chance. Dislocations stored in such progresses are called statistically stored dislocations, with corresponding density \rho_. In other words, they are dislocations evolved from rand ...
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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, a material will deformation (engineering)#elastic deformation, deform elastically and will return to its original shape when the applied stress (mechanics), stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as Deformation (engineering)#plastic deformation, plastic deformation. The yield strength or yield stress is a List of materials properties, material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable Structural load, load in a mechanical component, since it represents the upper limit to forces that can be applied without pro ...
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Dot Product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a Scalar (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. Not to be confused with scalar multiplication. is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two Euclidean vector, vectors is widely used. It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see ''Inner product space'' for more). It should not be confused with the cross product. Algebraically, the dot product is the sum of the Product (mathematics), products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euc ...
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