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Yield (engineering)From Wikipedia, the free encyclopedia

[hide]

V

T

E

Mechanical failure modes

Buckling

Corrosion

Corrosion fatigue

Creep

Fatigue

Fouling

Fracture

Hydrogen embrittlement

Impact

Mechanical overload

Stress corrosion cracking

Thermal shock

Wear

Yielding

A yield strengthor yield pointof a material is defined inengineeringandmaterials scienceasthestressat which a material begins todeform plastically.Prior to the yield point the material willdeformelasticallyand will return to its original shape when the applied stress is removed. Once theyield point is passed, some fraction of the deformation will be permanent and non-reversible.

In the three-dimensional space of the principal stresses ( ), an infinite number of yieldpoints form together ayield surface.

Knowledge of the yield point is vital when designing a component since it generally represents anupper limit to the load that can be applied. It is also important for the control of many materialsproduction techniques such asforging,rolling,orpressing.In structural engineering, this is a softfailure mode which does not normally causecatastrophic failureorultimate failureunless itacceleratesbuckling.

Contents

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1 Definition

2 Yield criterion

o 2.1 Isotropic yield criteria

o 2.2 Anisotropic yield criteria 3 Factors influencing yield strength

o 3.1 Strengthening mechanisms

3.1.1 Work hardening

3.1.2 Solid solution strengthening

3.1.3 Particle/Precipitate strengthening

3.1.4 Grain boundary strengthening

4 Testing

5 Implications for structural engineering

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6 Typical yield and ultimate strengths

7 See also

8 References

o 8.1 Notes

o 8.2 Bibliography

Definition[edit]

Typical yield behavior for non-ferrous alloys.

1: True elastic limit

2: Proportionality limit

3: Elastic limit

4: Offset yield strength

It is often difficult to precisely define yielding due to the wide variety ofstressstrain curvesexhibitedby real materials. In addition, there are several possible ways to define yielding :

[1]

True elastic limit

The lowest stress at whichdislocationsmove. This definition is rarely used, sincedislocations move at very low stresses, and detecting such movement is very difficult.

Proportionality limit

Up to this amount of stress, stress is proportional to strain (Hooke's law), so the stress-straingraph is a straight line, and the gradient will be equal to theelastic modulusof the material.

Elastic limit (yield strength)

Beyond the elastic limit, permanent deformation will occur. The lowest stress at whichpermanent deformation can be measured. This requires a manual load-unload procedure,and the accuracy is critically dependent on equipment and operator skill. Forelastomers,

such asrubber,the elastic limit is much larger than the proportionality limit. Also, precisestrain measurements have shown that plastic strain begins at low stresses.

[2][3]

Yield point

The point in the stress-strain curve at which the curve levels off and plastic deformationbegins to occur.

[4]

Offset yield point (proof stress)

When a yield point is not easily defined based on the shape of the stress-strain curvean offset yield pointis arbitrarily defined. The value for this is commonly set at 0.1 or 0.2%

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strain.[5]

The offset value is given as a subscript, e.g., Rp0.2=310 MPa.[citation needed]

Highstrength steel and aluminum alloys do not exhibit a yield point, so this offset yield point isused on these materials.

[5]

Upper yield point and lower yield point

Some metals, such asmild steel,reach an upper yield point before dropping rapidly to alower 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 onlystressed to the upper yield point, and beyond,Lders bandscan develop.[6]

Yield criterion[edit]

This section does notciteanyreferences or sources.Please

help improve this section byadding citations to reliable sources.

Unsourced material may be challenged andremoved.(June 2013)

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. Since stress and strain aretensorqualities

they can be described on the basis of three principal directions, in the case of stress these are

denoted by , , and .

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.

Isotropic yield criteria[edit]

Maximum Principal Stress Theoryby W.J.M Rankine(1850). 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 Theoryby St.Venant. Yield occurs when the maximum

principalstrainreaches 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 TheoryAlso known as theTresca yield criterion,after the

French scientistHenri Tresca.This assumes that yield occurs when the shear

stress exceeds the shear yield strength :

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Total Strain Energy TheoryThis 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 strainenergy at the elastic limit in simple tension. For a 3-dimensional stress state this is given

by:

Distortion Energy TheoryThis theory proposes that the total strain energy can

be separated into two components: the volumetric(hydrostatic)strain energy and

the shape(distortion orshear)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 thevon Mises yield criterion.

Based on a different theoretical underpinning this expression is also referred to

as octahedral shear stress theory.[citation needed]

Other commonly used isotropic yield criteria are the

Mohr-Coulomb yield criterion

Drucker-Prager yield criterion

Bresler-Pister yield criterion

Willam-Warnke yield criterion

Theyield surfacescorresponding to these criteria have a range of forms. However,

most isotropic yield criteria correspond toconvexyield surfaces.

Anisotropic yield criteria[edit]

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:

Hill's quadratic yield criterion.

Generalized Hill yield criterion.

Hosford yield criterion.

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Factors influencing yield strength[edit]

This section does notciteanyreferences or

sources.Please help improve this section

byadding citations to reliable sources.

Unsourced material may be challenged

andremoved.(June 2013)

The stress at which yield occurs is dependent on both the rate of deformation (strain

rate) and, more significantly, the temperature at which the deformation occurs. In

general, the yield strength increases with strain rate and decreases with

temperature. When the latter is not the case, the material is said to exhibityield

strength anomaly,which is typical forsuperalloysand leads to their use in

applications requiring high strength at high temperatures.

Early work by Alder and Philips in 1954 found that the relationship between yield

stress and strain rate (at constant temperature) was best described by a power law

relationship of the form

where C is a constant and m is the strain rate sensitivity. The latter generally

increases with temperature, and materials where m reaches a value greater

than ~0.5 tend to exhibitsuper plastic behaviour.m can be found from a log-log

plot of yield stress at a fixed plastic strain versus the strain rate.[7]

Later, more complex equations were proposed that simultaneously dealt

with both temperature and strain rate:

where and A are constants and Z is the temperature-compensated

strain-rateoften described by theZener-Hollomon parameter:

where QHWis the activation energy for hot deformation and T is the

absolute temperature.

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Strengthening mechanisms[edit]

There are several ways in which crystalline and amorphous

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 for this reason.

These mechanisms for crystalline materials include

Work hardening

Solid solution strengthening

Precipitation strengthening

Grain boundary strengthening

Work hardening[edit]

Where deforming the material will introducedislocations,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.

The governing formula for this mechanism is:

where is the yield stress, G is the shear elastic modulus, b

is the magnitude of theBurgers vector,and is the dislocation

density.

Sol id solut ion strengthening[edit]

Byalloyingthe 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.

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The relationship of this mechanism goes as:

where is theshear stress,related to the yield stress, G

and b are the same as in the above example, C_s is the

concentration of solute and is the strain induced in the

lattice due to adding the impurity.

Particle/Precipitate streng thening[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 particleeither 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 bou ndary 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 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

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material. Also known as Hall-Petch strengthening, this type

of strengthening is governed by the formula:

whereis the stress required to move dislocations,

k is a material constant, and

d is the grain size.

Testing[edit]

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. Longitudinal

and/or transverse strain is recorded using

mechanical or optical extensometers.

Indentation hardnesscorrelates linearly

with tensile strength for most

steels.[8]

Hardness testing can therefore

be an economical substitute for tensile

testing, as well as providing local

variations in yield strength due to e.g.

welding or forming operations.

Implications forstructuralengineering[edit]

Yielded structures have a lower stiffness,

leading to increased deflections and

decreased buckling strength. The structurewill 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. Highly optimized structures,

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such as airplane beams and components,

rely on yielding as a fail-safe failure mode.

No safety factor is therefore needed when

comparing limit loads (the highest loads

expected during normal operation) to yieldcriteria.

[citation needed]

Typical yield and ultimate strengths[edit]

Note: many of the values depend on manufacturing process and purity/composition.

Material

Yield

strength

(MPa)

Ultimate

strength

(MPa)

Density

(g/cm)

free breaking

length

(km)

ASTMA36 steel 250 400 7.85 3.2

Steel, API 5L X65[9]

448 531 7.85 5.8

Steel, high strength alloy ASTMA514 690 760 7.85 9.0

Steel, prestressing strands 1650 1860 7.85 21.6

Piano wire 22002482[10]

7.8 28.7

Carbon Fiber(CF, CFK) 5650[11]

1.75

High density polyethylene(HDPE) 2633 37 0.95 2.8

Polypropylene 1243 19.780 0.91 1.3

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Material

Yield

strength

(MPa)

Ultimate

strength

(MPa)

Density

(g/cm)

free breaking

length

(km)

Stainless steelAISI 302Cold-rolled 520 860

Cast iron4.5% C, ASTM A-48[12]

* 172 7.20 2.4

Titanium alloy(6% Al, 4% V) 830 900 4.51 18.8

Aluminium alloy2014-T6 400 455 2.7 15.1

Copper99.9% Cu 70 220 8.92 0.8

Cupronickel10% Ni, 1.6% Fe, 1%

Mn, balance Cu130 350 8.94 1.4

Brass approx. 200+ 550 5.3 3.8

Spider silk 1150 (??) 1400 1.31 109

Silkwormsilk 500 25

Aramid(KevlarorTwaron) 3620 1.44 256.3

UHMWPE[13][14] 20 35[15] 0.97 400

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Material

Yield

strength

(MPa)

Ultimate

strength

(MPa)

Density

(g/cm)

free breaking

length

(km)

Bone(limb) 104121 130 3

Nylon,type 6/6 45 75 2

*Grey cast iron does not have a well defined yield strength because the stress-strain relationship is

atypical. The yield strength can vary from 65 to 80% of the tensile strength.[16]

Elements in the annealed state[17]

Young's modulus

(GPa)

Proof or yield stress

(MPa)

Ultimate Tensile Strength

(MPa)

Aluminium 70 1520 4050

Copper 130 33 210

Iron 211 80100 350

Nickel 170 1435 140195

Silicon 107 50009000

Tantalum 186 180 200

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Tin 47 914 15200

Titanium 120 100225 240370

Tungsten 411 550 550620

References[edit]Notes[edit]

1. Jump up^G. Dieter, Mechanical Metallurgy, McGraw-Hill, 19862. Jump up^Flinn, Richard A.; Trojan, Paul K. (1975). Engineering Materials and their

Applications. Boston: Houghton Mifflin Company. p. 61.ISBN0-395-18916-0.

3. Jump up^Kumagai, Naoichi; Sadao Sasajima, Hidebumi Ito (15 February 1978)."Long-termCreep of Rocks: Results with Large Specimens Obtained in about 20 Years and Those withSmall Specimens in about 3 Years".Journal of the Society of Materials Science (Japan)(JapanEnergy Society) 27(293): 157161. Retrieved 2008-06-16.

4. Jump up^Ross 1999,p. 56.

5. ^Jump up to:abRoss 1999,p. 59.

6. Jump up^Degarmo, p. 377.

7. Jump up^Dynamic Behavior of a Rare-Earth-Containing Mg Alloy, WE43B-T5, Plate withComparison to Conventional Alloy, AM30-F , Sean Agnew, Wilburn Whittington, AndrewOppedal, Haitham El Kadiri, Matthew Shaeffer, K. T. Ramesh, Jishnu Bhattacharyya, Rick

Delorme, Bruce Davis , Volume 66, Issue 2 / February, 20148. Jump up^Correlation of Yield Strength and Tensile Strength with Hardness for Steels , E.J.

Pavlina and C.J. Van Tyne, Journal of Materials Engineering and Performance, Volume 17,Number 6 / December, 2008

9. Jump up^ussteel.com

10. Jump up^Don Stackhouse @ DJ Aerotech

11. Jump up^complore.com

12. Jump up^Beer, Johnston & Dewolf 2001,p. 746.

13. Jump up^Technical Product Data Sheets UHMWPE

14. Jump up^unitex-deutschland.eu

15. Jump up^matweb.com

16. Jump up^Avallone et al. 2006,p. 635.

17. Jump up^A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data", p. 41.18. http://en.wikipedia.org/wiki/Yield_(engineering)

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