Upper And Lower Yield Point PdfBy Matthew P. In and pdf 31.03.2021 at 14:33 5 min read
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- Yield Point Phenomena and their Theoretical Background
- Yield Point Phenomena and their Theoretical Background
- A Theory of Sharp Yield Point in Low-Dislocation Crystals.pptx
Yield Point Phenomena and their Theoretical Background
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. The yield strength or yield stress is a 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 load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium , there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine.
In such a case, the offset yield point or proof stress is taken as the stress at which 0. Yielding is a gradual failure mode which is normally not catastrophic , unlike ultimate failure. A variety of yield criteria have been developed for different materials. It is often difficult to precisely define yielding due to the wide variety of stress—strain curves exhibited by real materials.
In addition, there are several possible ways to define yielding: . Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength.
The structure will be permanently deformed when the load is removed, and may have residual stresses. Engineering metals display strain hardening, which implies that the yield stress is increased after unloading from a yield state.
Yield strength testing involves taking a small sample with a fixed cross-section area and then pulling it with a controlled, gradually increasing force until the sample changes shape or breaks. This is called a Tensile Test. Indentation hardness correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another.
However, for critical situations, tension testing is done to eliminate ambiguity. There are several ways in which crystalline materials can be engineered to increase their yield strength.
By altering dislocation density, impurity levels, grain size in crystalline materials , the yield strength of the material can be fine-tuned.
This occurs typically by introducing defects such as impurities dislocations in the material. To move this defect plastically deforming or yielding the material , a larger stress must be applied. This thus causes a higher yield stress in the material. While many material properties depend only on the composition of the bulk material, yield strength is extremely sensitive to the materials processing as well.
Where deforming the material will introduce dislocations , which increases their density in the material. This increases the yield strength of the material since now more stress must be applied to move these dislocations through a crystal lattice. Dislocations can also interact with each other, becoming entangled.
By alloying the material, impurity atoms in low concentrations will occupy a lattice position directly below a dislocation, such as directly below an extra half plane defect. This relieves a tensile strain directly below the dislocation by filling that empty lattice space with the impurity atom. Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocations within the crystal.
A line defect that, while moving through the matrix, will be forced against a small particle or precipitate of the material. Dislocations can move through this particle either by shearing the particle or by a process known as bowing or ringing, in which a new ring of dislocations is created around the particle.
Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Since it requires a lot of energy to move dislocations to another grain, these dislocations build up along the boundary, and increase the yield stress of the material.
Also known as Hall-Petch strengthening, this type of strengthening is governed by the formula:. The theoretical yield strength of a perfect crystal is much higher than the observed stress at the initiation of plastic flow. That experimentally measured yield strength is significantly lower than the expected theoretical value can be explained by the presence of dislocations and defects in the materials. Indeed, whiskers with perfect single crystal structure and defect-free surfaces have been shown to demonstrate yield stress approaching the theoretical value.
For example, nanowhiskers of copper were shown to undergo brittle fracture at 1 GPa,  a value much higher than the strength of bulk copper and approaching the theoretical value. The theoretical yield strength can be estimated by considering the process of yield at the atomic level. In a perfect crystal, shearing results in the displacement of an entire plane of atoms by one interatomic separation distance, b, relative to the plane below. In order for the atoms to move, considerable force must be applied to overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site.
The stress displacement curve of a plane of atoms varies sinusoidally as stress peaks when an atom is forced over the atom below and then falls as the atom slides into the next lattice point. Single atomic distance displacements , this equation becomes:.
A yield criterion often expressed as yield surface, or yield locus, is a hypothesis concerning the limit of elasticity under any combination of stresses. There are two interpretations of yield criterion: one is purely mathematical in taking a statistical approach while other models attempt to provide a justification based on established physical principles.
The following represent the most common yield criterion as applied to an isotropic material uniform properties in all directions. Other equations have been proposed or are used in specialist situations. Maximum principal stress theory — by William Rankine Yield occurs when the largest principal stress exceeds the uniaxial tensile yield strength. Although this criterion allows for a quick and easy comparison with experimental data it is rarely suitable for design purposes.
This theory gives good predictions for brittle materials. Maximum principal strain theory — by St. Yield occurs when the maximum principal strain reaches the strain corresponding to the yield point during a simple tensile test.
In terms of the principal stresses this is determined by the equation:. Maximum shear stress theory — Also known as the Tresca yield criterion , after the French scientist Henri Tresca. Total strain energy theory — This theory assumes that the stored energy associated with elastic deformation at the point of yield is independent of the specific stress tensor.
Thus yield occurs when the strain energy per unit volume is greater than the strain energy at the elastic limit in simple tension. For a 3-dimensional stress state this is given by:.
Maximum distortion energy theory von Mises yield criterion — This theory proposes that the total strain energy can be separated into two components: the volumetric hydrostatic strain energy and the shape distortion or shear strain energy. It is proposed that yield occurs when the distortion component exceeds that at the yield point for a simple tensile test.
This theory is also known as the von Mises yield criterion. Based on a different theoretical underpinning this expression is also referred to as octahedral shear stress theory. The yield surfaces corresponding to these criteria have a range of forms. However, most isotropic yield criteria correspond to convex yield surfaces.
When a metal is subjected to large plastic deformations the grain sizes and orientations change in the direction of deformation.
As a result, the plastic yield behavior of the material shows directional dependency. Under such circumstances, the isotropic yield criteria such as the von Mises yield criterion are unable to predict the yield behavior accurately. Several anisotropic yield criteria have been developed to deal with such situations. Some of the more popular anisotropic yield criteria are:. From Wikipedia, the free encyclopedia. Phenomenon of deformation due to structural stress. True elastic limit Proportionality limit Elastic limit Offset yield strength.
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Yield Point Phenomena and their Theoretical Background
The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning plastic behavior. Prior to the yield point, the 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. The yield point determines the limits of performance for mechanical components since it represents the upper limit to forces that can be applied without permanent deformation. In structural engineering, this is a soft failure mode which does not normally cause catastrophic failure or ultimate failure unless it accelerates buckling. Advances in measurement techniques allow higher precision mapping of the yield point which, as Marcus Reiner stated, showed "there was no yield point". Yield strength is the critical material property exploited by many fundamental techniques of material-working: to reshape material with pressure such as forging, rolling, pressing, bending, extruding, or hydroforming , to separate material by cutting such as machining or shearing, and to join components rigidly with fasteners.
These two points are termed as upper and lower yield points respectively. From figure you can easily understand that, When ductile material is stretched.
A Theory of Sharp Yield Point in Low-Dislocation Crystals.pptx
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. The yield strength or yield stress is a 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 load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation.
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