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This article is about the science of material yield. For predicting yield, see Material failure theory.

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Stress–strain curve showing typical yield behavior for nonferrous alloys. (Stress, , shown as a function of strain, .)

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 tát 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 tát the yield point at which the material begins to tát deform plastically. The yield strength is often used to tát determine the maximum allowable load in a mechanical component, since it represents the upper limit to tát forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, and no precise yield point. 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 can be specified in terms of the three-dimensional principal stresses () with a yield surface or a yield criterion. A variety of yield criteria have been developed for different materials.


Material Yield strength
Ultimate strength
ASTM A36 steel 250 400
Steel, API 5L X65[1] 448 531
Steel, high strength alloy ASTM A514 690 760
Steel, prestressing strands 1650 1860
Piano wire   1740–3300[2]
Carbon fiber (CF, CFK) 5650[3]
High-density polyethylene (HDPE) 26–33 37
Polypropylene 12–43 19.7–80
Stainless steel AISI 302 – cold-rolled 520 860
Cast iron 4.5% C, ASTM A-48[4] 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
Brass 200+ ~ 550
Spider silk 1150 (??) 1400
Silkworm silk 500  
Aramid (Kevlar or Twaron) 3620 3757
UHMWPE[5][6] 20 35[7]
Bone (limb) 104–121 130
Nylon, type 6/6 45 75
Aluminium (annealed) 15–20 40–50[8]
Copper (annealed) 33 210
Iron (annealed) 80–100 350
Nickel (annealed) 14–35 140–195
Silicon (annealed) 5000–9000  
Tantalum (annealed) 180 200
Tin (annealed) 9–14 15–200
Titanium (annealed) 100–225 240–370
Tungsten (annealed) 550 550–620

It is often difficult to tát precisely define yielding due to tát the wide variety of stress–strain curves exhibited by real materials. In addition, there are several possible ways to tát define yielding:[9]

True elastic limit
The lowest stress at which dislocations move. This definition is rarely used since dislocations move at very low stresses, and detecting such movement is very difficult.
Proportionality limit
Up to tát this amount of stress, stress is proportional to tát strain (Hooke's law), sánh the stress-strain graph is a straight line, and the gradient will be equal to tát the elastic modulus of the material.
Elastic limit (yield strength)
Beyond the elastic limit, permanent deformation will occur. The elastic limit is, therefore, the lowest stress point at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on the equipment used and operator skill. For elastomers, such as rubber, the elastic limit is much larger than vãn the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses.[10][11]
Yield point
The point in the stress-strain curve at which the curve levels off and plastic deformation begins to tát occur.[12]
Offset yield point (proof stress)
When a yield point is not easily defined on the basis of the shape of the stress-strain curve an offset yield point is arbitrarily defined. The value for this is commonly phối at 0.1% or 0.2% plastic strain.[13] The offset value is given as a subscript, e.g., MPa or MPa.[14] For most practical engineering uses, is multiplied by a factor of safety to tát obtain a lower value of the offset yield point. High strength steel and aluminum alloys vì thế not exhibit a yield point, sánh this offset yield point is used on these materials.[13]
Upper and lower yield points
Some metals, such as mild steel, reach an upper yield point before dropping rapidly to tát a lower yield point. The material response is linear up until the upper yield point, but the lower yield point is used in structural engineering as a conservative value. If a metal is only stressed to tát the upper yield point, and beyond, Lüders bands can develop.[15]

Usage in structural engineering[edit]

Yielded structures have a lower stiffness, leading to tát 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. 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 material cannot be used as a scale to tát measure strengths on another.[16] Hardness testing can therefore be an economical substitute for tensile testing, as well as providing local variations in yield strength due to tát, e.g., welding or forming operations. For critical situations, tension testing is often done to tát eliminate ambiguity. However, it is possible to tát obtain stress-strain curves from indentation-based procedures, provided certain conditions are met. These procedures are grouped under the term Indentation plastometry.

Strengthening mechanisms[edit]

There are several ways in which crystalline materials can be engineered to tát increase their yield strength. By altering dislocation mật độ trùng lặp từ khóa, 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 tát the materials processing as well.

These mechanisms for crystalline materials include

  • Work hardening
  • Solid solution strengthening
  • Precipitation strengthening
  • Grain boundary strengthening

Work hardening[edit]

Where deforming the material will introduce dislocations, which increases their mật độ trùng lặp từ khóa in the material. This increases the yield strength of the material since now more stress must be applied to tát move these dislocations through a crystal lattice. Dislocations can also 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 mật độ trùng lặp từ khóa.

Solid solution strengthening[edit]

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.

The relationship of this mechanism goes as:

Xem thêm: truyện con đường bá chủ truyenfull

where is the shear stress, related to tát 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 tát adding the impurity.

Particle/precipitate strengthening[edit]

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.

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.

Grain boundary strengthening[edit]

Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain size decreases, the surface area to tát volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Since it requires a lot of energy to tát move dislocations to tát 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:


is the stress required to tát move dislocations,
is a material constant, and
is the grain size.

Theoretical yield strength[edit]

Material Theoretical shear strength (GPa) Experimental shear strength (GPa)
Ag 1.0 0.37
Al 0.9 0.78
Cu 1.4 0.49
Ni 2.6 3.2
α-Fe 2.6 27.5

The theoretical yield strength of a perfect crystal is much higher than vãn the observed stress at the initiation of plastic flow.[17]

That experimentally measured yield strength is significantly lower than vãn 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 tát demonstrate yield stress approaching the theoretical value. For example, nanowhiskers of copper were shown to tát undergo brittle fracture at 1 GPa,[18] a value much higher than vãn 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 tát the plane below. In order for the atoms to tát move, considerable force must be applied to tát overcome the lattice energy and move the atoms in the top plane over the lower atoms and into a new lattice site. The applied stress to tát overcome the resistance of a perfect lattice to tát 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.[17]

where is the interatomic separation distance. Since τ = G γ and dτ/dγ = G at small strains (i.e. Single atomic distance displacements), this equation becomes:

Xem thêm: mối tình đầu của siêu sao

For small displacement of γ=x/a, where a is the spacing of atoms on the slip plane, this can be rewritten as:

Giving a value of τmax equal to:

The theoretical yield strength can be approximated as .

See also[edit]

  • Specified minimum yield strength
  • Ultimate tensile strength
  • Yield curve (physics)
  • Yield surface


  1. ^ "ussteel.com". Archived from the original on 22 June 2012. Retrieved 15 June 2011.
  2. ^ ASTM A228-A228M-14
  3. ^ "complore.com". Archived from the original on 19 July 2011. Retrieved 10 September 2010.
  4. ^ Beer, Johnston & Dewolf 2001, p. 746.
  5. ^ "Technical Product Data Sheets UHMWPE". Archived from the original on 14 October 2011. Retrieved 18 August 2010.
  6. ^ "unitex-deutschland.eu" (PDF). Archived from the original (PDF) on 25 March 2012. Retrieved 15 June 2011.
  7. ^ matweb.com
  8. ^ A. M. Howatson, Phường. G. Lund and J. D. Todd, "Engineering Tables and Data", p. 41.
  9. ^ G. Dieter, Mechanical Metallurgy, McGraw-Hill, 1986
  10. ^ Flinn, Richard A.; Trojan, Paul K. (1975). Engineering Materials and their Applications. Boston: Houghton Mifflin Company. p. 61. ISBN 978-0-395-18916-0.
  11. ^ Barnes, Howard (1999). "The yield stress—a review or 'παντα ρει'—everything flows?". Journal of Non-Newtonian Fluid Mechanics. 81 (1–2): 133–178. doi:10.1016/S0377-0257(98)00094-9.
  12. ^ Ross 1999, p. 56.
  13. ^ a b Ross 1999, p. 59.
  14. ^ ISO 6892-1:2009
  15. ^ Degarmo, p. 377.
  16. ^ Pavlina, E.J.; Van Tyne, C.J. (2008). "Correlation of Yield Strength and Tensile Strength with Hardness for Steels". Journal of Materials Engineering and Performance. 17 (6): 888–893. Bibcode:2008JMEP...17..888P. doi:10.1007/s11665-008-9225-5. S2CID 135890256.
  17. ^ a b H., Courtney, Thomas (2005). Mechanical behavior of materials. Waveland Press. ISBN 978-1577664253. OCLC 894800884.{{cite book}}: CS1 maint: multiple names: authors list (link)
  18. ^ Richter, Gunther (2009). "Ultrahigh Strength Single-Crystalline Nanowhiskers Grown by Physical Vapor Deposition". Nano Letters. 9 (8): 3048–3052. Bibcode:2009NanoL...9.3048R. CiteSeerX doi:10.1021/nl9015107. PMID 19637912.


  • Avallone, Eugene A. & Baumeister III, Theodore (1996). Mark's Standard Handbook for Mechanical Engineers (8th ed.). New York: McGraw-Hill. ISBN 978-0-07-004997-0.
  • Avallone, Eugene A.; Baumeister, Theodore; Sadegh, Ali; Marks, Lionel Simeon (2006). Mark's Standard Handbook for Mechanical Engineers (11th, Illustrated ed.). McGraw-Hill Professional. ISBN 978-0-07-142867-5..
  • Beer, Ferdinand Phường.; Johnston, E. Russell; Dewolf, John T. (2001). Mechanics of Materials (3rd ed.). McGraw-Hill. ISBN 978-0-07-365935-0..
  • Boresi, A. Phường., Schmidt, R. J., and Sidebottom, O. M. (1993). Advanced Mechanics of Materials, 5th edition John Wiley & Sons. ISBN 0-471-55157-0
  • Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003). Materials and Processes in Manufacturing (9th ed.). Wiley. ISBN 978-0-471-65653-1..
  • Oberg, E., Jones, F. D., and Horton, H. L. (1984). Machinery's Handbook, 22nd edition. Industrial Press. ISBN 0-8311-1155-0
  • Ross, C. (1999). Mechanics of Solids. City: Albion/Horwood Pub. ISBN 978-1-898563-67-9.
  • Shigley, J. E., and Mischke, C. R. (1989). Mechanical Engineering Design, 5th edition. McGraw Hill. ISBN 0-07-056899-5
  • Young, Warren C. & Budynas, Richard G. (2002). Roark's Formulas for Stress and Strain, 7th edition. New York: McGraw-Hill. ISBN 978-0-07-072542-3.
  • Engineer's Handbook