In content 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 contentwill 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 contentproperty and is the stress corresponding to the yield point at which the contentlaunch to deform plastically. The yield strength is often utilize to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that shouldbe applied without producing permanent deformation. In some content, 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 0.2% plastic deformation occurs. Yielding is a gradual failure mode which is normally not catastrophic, unlike ultimate failure.
In solid mechanics, the yield point shouldbe specified in rulesof the three-dimensional principal stresses () with a yield surface or a yield criterion. A variety of yield criteria have been developed for different content.
|ASTM A36 steel||250||400|
|Steel, API 5L X65||448||531|
|Steel, high strength alloy ASTM A514||690||760|
|Steel, prestressing strands||1650||1860|
|Carbon fiber (CF, CFK)||5650|
|High-density polyethylene (HDPE)||26–33||37|
|Stainless steel AISI 302 – cold-rolled||520||860|
|Cast iron 4.5% C, ASTM A-48||172|
|Titanium alloy (6% Al, 4% V)||830||900|
|Aluminium alloy 2014-T6||400||455|
|Copper 99.9% Cu||70||220|
|Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu||130||350|
|Spider silk||1150 (??)||1400|
|Aramid (Kevlar or Twaron)||3620||3757|
It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real content. In addition, there are several possible method 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 tinysample with a fixed cross-section locationand then pulling it with a controlled, gradually increasing force until the sample modify shape or breaks. This is called a Tensile Test. Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers.
Indentation hardness correlates roughly linearly with tensile strength for most steels, but measurements on one contentcannot be utilize as a scale to measure strengths on another. Hardness testing shouldtherefore be an economical substitute for tensile testing, as well as providing local variations in yield strength due to, e.g., welding or forming operations. However, for critical situations, tension testing is done to eliminate ambiguity.
There are several method in which crystalline content shouldbe engineered to increase their yield strength. By altering dislocation density, impurity levels, grain size (in crystalline content), the yield strength of the contentshouldbe 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 huge stress must be applied. This thus causes a higher yield stress in the material. While many contentproperties depend only on the composition of the bulk material, yield strength is extremely sensitive to the content processing as well.
These mechanisms for crystalline content include
Where deforming the contentwill introduce dislocations, which increases their density in the material. This increases the yield strength of the contentsince now more stress must be applied to move these dislocations through a crystal lattice. Dislocations shouldalso interact with each other, becoming entangled.
The governing formula for this mechanism is:
where is the yield stress, G is the shear elastic modulus, b is the magnitude of the Burgers vector, and is the dislocation density.
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 zonewith the impurity atom.
The relationship of this mechanism goes as:
where is the shear stress, associatedto the yield stress, and are the same as in the above example, is the concentration of solute and is the strain induced in the lattice due to adding the impurity.
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 versusa tinyparticle or precipitate of the material. Dislocations shouldmove through this particle either by shearing the particle or by a process known as bowing or ringing, in which a freshring of dislocations is madearound the particle.
The shearing formula goes as:
and the bowing/ringing formula:
In these formulas, is the particle radius, is the surface tension between the matrix and the particle, is the distance between the particles.
Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface locationto 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 kindof strengthening is governed by the formula:
|Material||Theoretical shear strength (GPa)||Experimental shear strength (GPa)|
The theoretical yield strength of a excellentcrystal 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 shouldbe explained by the presence of dislocations and defects in the content. Indeed, whiskers with excellentsingle crystal structure and defect-free surfaces have been present to demonstrate yield stress approaching the theoretical value. For example, nanowhiskers of copper were present 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 shouldbe estimated by considering the process of yield at the atomic level. In a excellentcrystal, shearing effect 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 freshlattice site. The applied stress to overcome the resistance of a excellentlattice to shear is the theoretical yield strength, τmax.
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.
where is the interatomic separation distance. Since τ = G γ and dτ/dγ = G at tinystrains (i.e. Single atomic distance displacements), this equation becomes:
For tinydisplacement of γ=x/a, where a is the spacing of atoms on the slip plane, this shouldbe rewritten as:
Giving a value of τmax equal to:
The theoretical yield strength shouldbe approximated as .
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