yield (engineering)pdf

Materials failure modes

Buckling Corrosion Creep Fatigue Fouling Fracture Hydrogen

embrittlement Impact Mechanical overload

Stress corrosion cracking Thermalshock Wear Yielding

From Wikipedia, the free encyclopedia

The yield strength or yield point of a material is defined inengineering and materials science as the stress at which a materialbegins to deform plastically. Prior to the yield point the material willdeform elastically and will return to its original shape when the appliedstress is removed. Once the yield point is passed, some fraction of thedeformation will be permanent and non-reversible.In the three-dimensional space of the principal stresses (1,2,3), aninfinite number of yield points form together a yield surface.

Knowledge of the yield point is vital when designing a componentsince it generally represents an upper limit to the load that can be applied. It is also important for the control ofmany materials production techniques such as forging, rolling, or pressing. In structural engineering, this is a softfailure mode which does not normally cause catastrophic failure or ultimate failure unless it acceleratesbuckling.

1 Definition2 Yield criterion

2.1 Isotropic yield criteria2.2 Anisotropic yield criteria

3 Factors influencing yield stress3.1 Strengthening mechanisms

3.1.1 Work Hardening3.1.2 Solid Solution Strengthening3.1.3 Particle/Precipitate Strengthening3.1.4 Grain boundary strengthening

4 Testing5 Implications for structural engineering6 Typical yield and ultimate strengths7 See also8 References

8.1 Notes8.2 Bibliography

It is often difficult to precisely define yielding due to the wide variety of stressstrain curves exhibited by realmaterials. In addition, there are several possible ways to define yielding:[1]

True elastic limitThe lowest stress at which dislocations move. This definition is rarely used, since dislocations move at verylow stresses, and detecting such movement is very difficult.

Yield (engineering) - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Yield_(engineering)

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Typical yield behavior for non-ferrous alloys.1: True elastic limit2: Proportionality limit3: Elastic limit4: Offset yield strength

Proportionality limitUp to this amount of stress, stress is proportional tostrain (Hooke's law), so the stress-strain graph is astraight line, and the gradient will be equal to the elasticmodulus of the material.

Elastic limit (yield strength)Beyond the elastic limit, permanent deformation willoccur. The lowest stress at which permanentdeformation can be measured. This requires a manualload-unload procedure, and the accuracy is criticallydependent on equipment and operator skill. Forelastomers, such as rubber, the elastic limit is muchlarger than the proportionality limit. Also, precise strainmeasurements have shown that plastic strain begins atlow stresses.[2][3]

Yield point The point in the stress-strain curve at which the curvelevels off and plastic deformation begins to occur.[4]

Offset yield point (proof stress) When a yield point is not easily defined based on the shape of the stress-strain curve an offset yield point isarbitrarily defined. The value for this is commonly set at 0.1 or 0.2% of the strain.[5] The offset value isgiven as a subscript, e.g., Rp0.2=310 MPa.[citation needed] High strength steel and aluminum alloys do notexhibit a yield point, so this offset yield point is used on these materials.[5]

Upper yield point and lower yield pointSome metals, such as mild steel, reach an upper yield point before dropping rapidly to a lower yield point.The material response is linear up until the upper yield point, but the lower yield point is used in structuralengineering as a conservative value. If a metal is only stressed to the upper yield point, and beyond, Ldersbands can develop.[6]

A yield criterion, often expressed as yield surface, or yield locus, is a hypothesis concerning the limit ofelasticity under any combination of stresses. There are two interpretations of yield criterion: one is purelymathematical in taking a statistical approach while other models attempt to provide a justification based onestablished physical principles. Since stress and strain are tensor qualities they can be described on the basis ofthree 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 propertiesin all directions). Other equations have been proposed or are used in specialist situations.

Isotropic yield criteria

Maximum Principal Stress Theory - Yield occurs when the largest principal stress exceeds the uniaxial tensileyield strength. Although this criterion allows for a quick and easy comparison with experimental data it is rarelysuitable for design purposes.

Maximum Principal Strain Theory - Yield occurs when the maximum principal strain reaches the strain


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corresponding to the yield point during a simple tensile test. In terms of the principal stresses this is determinedby the equation:

Maximum Shear Stress Theory - Also known as the Tresca yield criterion, after the French scientist HenriTresca. This assumes that yield occurs when the shear stress exceeds the shear yield strength :

Total Strain Energy Theory - This theory assumes that the stored energy associated with elastic deformation atthe point of yield is independent of the specific stress tensor. Thus yield occurs when the strain energy per unitvolume is greater than the strain energy at the elastic limit in simple tension. For a 3-dimensional stress state thisis given by:

Distortion Energy Theory - This theory proposes that the total strain energy can be separated into twocomponents: the volumetric (hydrostatic) strain energy and the shape (distortion or shear) strain energy. It isproposed that yield occurs when the distortion component exceeds that at the yield point for a simple tensiletest. This is generally referred to as the Von Mises yield criterion and is expressed as:

Based on a different theoretical underpinning this expression is also referred to as octahedral shear stresstheory.[citation needed]

Other commonly used isotropic yield criteria are the

Mohr-Coulomb yield criterionDrucker-Prager yield criterionBresler-Pister yield criterionWillam-Warnke yield criterion

The yield surfaces corresponding to these criteria have a range of forms. However, most isotropic yield criteriacorrespond to convex yield surfaces.

Anisotropic yield criteria

When a metal is subjected to large plastic deformations the grain sizes and orientations change in the directionof deformation. As a result the plastic yield behavior of the material shows directional dependency. Under suchcircumstances, the isotropic yield criteria such as the von Mises yield criterion are unable to predict the yieldbehavior accurately. Several anisotropic yield criteria have been developed to deal with such situations. Some ofthe more popular anisotropic yield criteria are:

Hill's quadratic yield criterion.Generalized Hill yield criterion.Hosford yield criterion.


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The stress at which yield occurs is dependent on both the rate of deformation (strain rate) and, moresignificantly, the temperature at which the deformation occurs. Early work by Alder and Philips in 1954 foundthat the relationship between yield stress and strain rate (at constant temperature) was best described by apower law relationship of the form

where C is a constant and m is the strain rate sensitivity. The latter generally increases with temperature, andmaterials where m reaches a value greater than ~0.5 tend to exhibit super plastic behaviour.

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-rate - often described by the Zener-Hollomon parameter:

where QHW is the activation energy for hot deformation and T is the absolute temperature.

Strengthening mechanisms

There are several ways in which crystalline and amorphous materials can be engineered to increase their yieldstrength. By altering dislocation density, impurity levels, grain size (in crystalline materials), the yield strength ofthe material can be fine tuned. This occurs typically by introducing defects such as impurities dislocations in thematerial. 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 thecomposition of the bulk material, yield strength is extremely sensitive to the materials processing as well for thisreason.

These mechanisms for crystalline materials include

Work HardeningSolid Solution StrengtheningParticle/Precipitate StrengtheningGrain boundary strengthening

Work Hardening

Where deforming the material will introduce dislocations, which increases their density in the material. Thisincreases the yield strength of the material, since now more stress must be applied to move these dislocationsthrough a crystal lattice. Dislocations can also interact with each other, becoming entangled.

The governing formula for this mechanism is:


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where y is the yield stress, G is the shear elastic modulus, b is the magnitude of the Burgers vector, and is thedislocation density.

Solid Solution Strengthening

By alloying the material, impurity atoms in low concentrations will occupy a lattice position directly below adislocation, such as directly below an extra half plane defect. This relieves a tensile strain directly below thedislocation by filling that empty lattice space with the impurity atom.

The relationship of this mechanism goes as:

where is the shear stress, related to the yield stress, G and b are the same as in the above example, C_s is theconcentration of solute and is the strain induced in the lattice due to adding the impurity.

Particle/Precipitate Strengthening

Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocationswithin the crystal. A line defect that, while moving through the matrix, will be forced against a small particle orprecipitate of the material. Dislocations can move through this particle either by shearing the particle, or by aprocess 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 andthe particle, is the distance between the particles.

Grain boundary strengthening

Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. As grain sizedecreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at thegrain edge. Since it requires a lot of energy to move dislocations to another grain, these dislocations build upalong the boundary, and increase the yield stress of the material. Also known as Hall-Petch strengthening, thistype of strengthening is governed by the formula:

where


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0 is the stress required to move dislocations,k is a material constant, andd is the grain size.

Yield strength testing involves taking a small sample with a fixed cross-section area, and then pulling it with acontrolled, gradually increasing force until the sample changes shape or breaks. Longitudinal and/or transversestrain is recorded using mechanical or optical extensometers.

Indentation hardness correlates linearly with tensile strength for most steels.[7] Hardness testing can therefore bean economical substitute for tensile testing, as well as providing local variations in yield strength due to e.g.welding or forming operations.

Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. Thestructure will be permanently deformed when the load is removed, and may have residual stresses. Engineeringmetals display strain hardening, which implies that the yield stress is increased after unloading from a yield state.Highly optimized structures, 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 normaloperation) to yield criteria.[citation needed]

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

MaterialYield

strength(MPa)

Ultimatestrength(MPa)

Density(g/cm)

free breakinglength(km)

ASTM A36 steel 250 400 7.8 3.2

Steel, API 5L X65[8] 448 531 7.8 5.8

Steel, high strength alloy ASTMA514 690 760 7.8 9.0

Steel, prestressing strands 1650 1860 7.8 21.6

Piano wire 22002482 [9] 7.8 28.7

Carbon Fiber (CF, CFK) 5650 [10] 1.75

High density polyethylene (HDPE) 26-33 37 0.95 2.8Polypropylene 12-43 19.7-80 0.91 1.3Stainless steel AISI 302 -Cold-rolled 520 860


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MaterialYield

strength(MPa)

Ultimatestrength(MPa)

Density(g/cm)

free breakinglength(km)

Cast iron 4.5% C, ASTM A-48[11] * 172 7.20 2.4

Titanium alloy (6% Al, 4% V) 830 900 4.51 18.8Aluminium alloy 2014-T6 400 455 2.7 15.1Copper 99.9% Cu 70 220 8.92 0.8Cupronickel 10% Ni, 1.6% Fe, 1%Mn, balance Cu 130 350 8.94 1.4

Brass approx. 200+ 550 5.3 3.8Spider silk 1150 (??) 1400 1.31 109Silkworm silk 500 25Aramid (Kevlar or Twaron) 3620 1.44 256.3

UHMWPE[12][13] 2400 0.97 400

Bone (limb) 104-121 130 3Nylon, 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.[14]

Elements in the annealed state[15]

Young's modulus(GPa)

Proof or yield stress(MPa)

Ultimate Tensile Strength(MPa)

Aluminium 70 15-20 40-50Copper 130 33 210Iron 211 80-100 350Nickel 170 14-35 140-195Silicon 107 5000-9000 Tantalum 186 180 200Tin 47 9-14 15-200Titanium 120 100-225 240-370Tungsten 411 550 550-620

Piola-Kirchhoff stress tensorStrain tensorStress concentrationLinear elasticity


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Yield curve (physics)Tensile strengthElastic modulusVirial stressYield surface

Notes

^ G. Dieter, Mechanical Metallurgy, McGraw-Hill, 19861.^ Flinn, Richard A.; Trojan, Paul K. (1975). Engineering Materials and their Applications. Boston: HoughtonMifflin Company. p. 61. ISBN 0-395-18916-0.

2.

^ Kumagai, Naoichi; Sadao Sasajima, Hidebumi Ito (15 February 1978). "Long-term Creep of Rocks: Results withLarge Specimens Obtained in about 20 Years and Those with Small Specimens in about 3 Years"(http://translate.google.com/translate?hl=en&sl=ja&u=http://ci.nii.ac.jp/naid/110002299397/&sa=X&oi=translate&resnum=4&ct=result&prev=/search%3Fq%3DIto%2BHidebumi%26hl%3Den) . Journal of the Society of MaterialsScience (Japan) (Japan Energy Society) 27 (293): 157161. http://translate.google.com/translate?hl=en&sl=ja&u=http://ci.nii.ac.jp/naid/110002299397/&sa=X&oi=translate&resnum=4&ct=result&prev=/search%3Fq%3DIto%2BHidebumi%26hl%3Den. Retrieved 2008-06-16.

3.

^ Ross 1999, p. 56.4.^ a b Ross 1999, p. 59.5.^ Degarmo, p. 377.6.^ 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(http://www.springerlink.com/content/q86642448t84g267/)

7.

^ http://www.ussteel.com/corp/tubular/linepipe-seamless.asp8.^ Don Stackhouse @ DJ Aerotech (http://www.djaerotech.com/dj_askjd/dj_questions/musicwire.html)9.^ [1] (http://www.complore.com/properties-materials-tensile-strength)10.^ Beer, Johnston & Dewolf 2001, p. 746.11.^ Technical Product Data Sheets UHMWPE (http://www.plastic-products.com/spec11.htm)12.^ [2] (http://www.unitex-deutschland.eu/pdf/download/Dyneema-Version-web-db.pdf)13.^ Avallone et al. 2006, p. 6-35.14.^ A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data", p. 41.15.

Bibliography

Avallone, Eugene A.; & Baumeister III, Theodore (1996). Mark's Standard Handbook forMechanical Engineers (8th ed.). New York: McGraw-Hill. ISBN 0-07-004997-1.Avallone, Eugene A.; Baumeister, Theodore; Sadegh, Ali; Marks, Lionel Simeon (2006). Mark'sStandard Handbook for Mechanical Engineers (http://books.google.com/?id=oOKqwp3CIt8C) (11th,Illustrated ed.). McGraw-Hill Professional. ISBN 9780071428675. http://books.google.com/?id=oOKqwp3CIt8C.Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John T. (2001). Mechanics of Materials(http://books.google.com/?id=TSDcA2-N2_sC) (3rd ed.). McGraw-Hill. ISBN 9780073659350.http://books.google.com/?id=TSDcA2-N2_sC.Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M. (1993). Advanced Mechanics of Materials, 5thedition John Wiley & Sons. ISBN 0-471-55157-0Degarmo, E. Paul; Black, J T.; Kohser, Ronald A. (2003). Materials and Processes in Manufacturing(9th ed.). Wiley. ISBN 0-471-65653-4.Oberg, E., Jones, F. D., and Horton, H. L. (1984). Machinery's Handbook, 22nd edition. Industrial


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Press. ISBN 0-8311-1155-0Ross, C. (1999). Mechanics of Solids (http://books.google.com/books?id=H_5zV2twBtwC) . City:Albion/Horwood Pub. ISBN 9781898563679. http://books.google.com/books?id=H_5zV2twBtwC.Shigley, J. E., and Mischke, C. R. (1989). Mechanical Engineering Design, 5th edition. McGraw Hill.ISBN 0-07-056899-5Young, Warren C.; & Budynas, Richard G. (2002). Roark's Formulas for Stress and Strain, 7thedition. New York: McGraw-Hill. ISBN 0-07-072542-X.Engineer's Handbook (http://www.engineershandbook.com/Materials/mechanical.htm)

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