Peierls–Nabarro stress proportionality
Where:
- the dislocation width
- = shear modulus
- = Poisson's ratio
- = slip distance or Burgers vector
- = interplanar spacing
Peierls stress (also known as the lattice friction stress [1] ) is the force (first described by Rudolf Peierls and modified by Frank Nabarro) needed to move a dislocation within a plane of atoms in the unit cell. The magnitude varies periodically as the dislocation moves within the plane. Peierls stress depends on the size and width of a dislocation and the distance between planes. Because of this, Peierls stress decreases with increasing distance between atomic planes. Yet since the distance between planes increases with planar atomic density, slip of the dislocation is preferred on closely packed planes.
Where:
The Peierls stress also relates to the temperature sensitivity of the yield strength of material because it very much depends on both short-range atomic order and atomic bond strength. As temperature increases, the vibration of atoms increases, and thus both peierls stress and yield strength decrease as a result of weaker atomic bond strength at high temperatures.
In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.
In materials science, creep is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point.
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. 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. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.
Work hardening, also known as strain hardening, is the strengthening of a metal or polymer by plastic deformation. Work hardening may be desirable, undesirable, or inconsequential, depending on the context.
Precipitation hardening, also called age hardening or particle hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel, titanium, and some steels and stainless steels. In superalloys, it is known to cause yield strength anomaly providing excellent high-temperature strength.
A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are 2D defects in the crystal structure, and tend to decrease the electrical and thermal conductivity of the material. Most grain boundaries are preferred sites for the onset of corrosion and for the precipitation of new phases from the solid. They are also important to many of the mechanisms of creep. On the other hand, grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve mechanical strength, as described by the Hall–Petch relationship. The study of grain boundaries and their effects on the mechanical, electrical and other properties of materials forms an important topic in materials science.
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 will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation.
Hardness is a measure of the resistance to localized plastic deformation induced by either mechanical indentation or abrasion. In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin, or wood and common plastics. Macroscopic hardness is generally characterized by strong intermolecular bonds, but the behavior of solid materials under force is complex; therefore, there are different measurements of hardness: scratch hardness, indentation hardness, and rebound hardness.
Critical resolved shear stress (CRSS) is the component of shear stress, resolved in the direction of slip, necessary to initiate slip in a grain. Resolved shear stress (RSS) is the shear component of an applied tensile or compressive stress resolved along a slip plane that is other than perpendicular or parallel to the stress axis. The RSS is related to the applied stress by a geometrical factor, m, typically the Schmid factor:
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 to the crystalline lattice of another element, 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.
Strain engineering refers to a general strategy employed in semiconductor manufacturing to enhance device performance. Performance benefits are achieved by modulating strain in the transistor channel, which enhances electron mobility and thereby conductivity through the channel.
Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.
Grain-boundary strengthening is a method of strengthening materials by changing their average crystallite (grain) size. It is based on the observation that grain boundaries are insurmountable borders for dislocations and that the number of dislocations within a grain has an effect on how stress builds up in the adjacent grain, which will eventually activate dislocation sources and thus enabling deformation in the neighbouring grain, too. So, by changing grain size one can influence the number of dislocations piled up at the grain boundary and yield strength. For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size.
Surface diffusion is a general process involving the motion of adatoms, molecules, and atomic clusters (adparticles) at solid material surfaces. The process can generally be thought of in terms of particles jumping between adjacent adsorption sites on a surface, as in figure 1. Just as in bulk diffusion, this motion is typically a thermally promoted process with rates increasing with increasing temperature. Many systems display diffusion behavior that deviates from the conventional model of nearest-neighbor jumps. Tunneling diffusion is a particularly interesting example of an unconventional mechanism wherein hydrogen has been shown to diffuse on clean metal surfaces via the quantum tunneling effect.
Dislocation creep is a deformation mechanism in crystalline materials. Dislocation creep involves the movement of dislocations through the crystal lattice of the material, in contrast to diffusion creep, in which diffusion is the dominant creep mechanism. It causes plastic deformation of the individual crystals, and thus the material itself.
In materials science, the yield strength anomaly refers to materials wherein the yield strength increases with temperature. For the majority of materials, the yield strength decreases with increasing temperature. In metals, this decrease in yield strength is due to the thermal activation of dislocation motion, resulting in easier plastic deformation at higher temperatures.
An antiphase domain (APD) is a type of planar crystallographic defect in which the atoms within a region of a crystal are configured in the opposite order to those in the perfect lattice system. Throughout the entire APD, atoms sit on the sites typically occupied by atoms of a different species. For example, in an ordered AB alloy, if an A atom occupies the site usually occupied by a B atom, a type of crystallographic point defect called an antisite defect is formed. If an entire region of the crystal is translated such that every atom in a region of the plane of atoms sits on its antisite, an antiphase domain is formed. In other words, an APD is a region formed from antisite defects of a parent lattice. On either side of this domain, the lattice is still perfect, and the boundaries of the domain are referred to as antiphase boundaries. Crucially, crystals on either side of an antiphase boundary are related by a translation, rather than a reflection or an inversion.
Dynamic strain aging (DSA) is an instability in plastic flow of materials, associated with interaction between moving dislocations and diffusing solutes. Although sometimes dynamic strain aging is used interchangeably with the Portevin–Le Chatelier effect, dynamic strain aging refers specifically to the microscopic mechanism that induces the Portevin–Le Chatelier effect. This strengthening mechanism is related to solid-solution strengthening and has been observed in a variety of fcc and bcc substitutional and interstitial alloys, metalloids like silicon, and ordered intermetallics within specific ranges of temperature and strain rate.
The strength of metal oxide adhesion effectively determines the wetting of the metal-oxide interface. The strength of this adhesion is important, for instance, in production of light bulbs and fiber-matrix composites that depend on the optimization of wetting to create metal-ceramic interfaces. The strength of adhesion also determines the extent of dispersion on catalytically active metal. Metal oxide adhesion is important for applications such as complementary metal oxide semiconductor devices. These devices make possible the high packing densities of modern integrated circuits.
Nabarro–Herring creep is a mode of deformation of crystalline materials that occurs at low stresses and held at elevated temperatures in fine-grained materials. In Nabarro–Herring creep, atoms diffuse through the crystals, and the creep rate varies inversely with the square of the grain size so fine-grained materials creep faster than coarser-grained ones. NH creep is solely controlled by diffusional mass transport. This type of creep results from the diffusion of vacancies from regions of high chemical potential at grain boundaries subjected to normal tensile stresses to regions of lower chemical potential where the average tensile stresses across the grain boundaries are zero. Self-diffusion within the grains of a polycrystalline solid can cause the solid to yield to an applied shearing stress, the yielding being caused by a diffusional flow of matter within each crystal grain away from boundaries where there is a normal pressure and toward those where there is a normal tension. Atoms migrating in the opposite direction account for the creep strain. The creep strain rate is derived in the next section. NH creep is more important in ceramics than metals as dislocation motion is more difficult to effect in ceramics.
