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Encyclopedia > Yield (engineering)
Mechanical failure modes
Thermal shock
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The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. 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. In the three-dimensional space of the principal stresses (σ123), an infinite number of yield points form together a yield surface. This article is about engineering. ... For the hazard, see corrosive. ... Creep is the term used to describe the tendency of a material to move or to deform permanently to relieve stresses. ... In materials science, fatigue is the progressive, localised, and permanent structural damage that occurs when a material is subjected to cyclic or fluctuating strains at nominal stresses that have maximum values less than (often much less than) the static yield strength of the material. ... For other uses, see Fracture (disambiguation). ... In physics, melting is the process of heating a solid substance to a point (called the melting point) where it turns into a liquid. ... Rupture, or ductile rupture describes the ultimate failure of tough ductile materials loaded in tension. ... Thermal shock and thermal loading refer to the disfuntion (and perhaps, crack) of a material due to the heating, especially non-stationary and non-uniform. ... For other uses, see Wear (disambiguation). ... Look up material in Wiktionary, the free dictionary. ... Engineering is the discipline of acquiring and applying knowledge of design, analysis, and/or construction of works for practical purposes. ... The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... Stress is a measure of force per unit area within a body. ... For other uses, see Plasticity. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... Yield surface is described in three dimensional space of principal stresses (), and encompasses the elastic region of material behavior. ...

Knowledge of the yield point is vital when designing a component since it generally represents an upper limit to the load that can be applied. It is also important for the control of many materials production techniques such as forging, rolling, or pressing. In structural engineering, this is a soft failure mode which does not normally cause catastrophic failure or ultimate failure unless it accelerates buckling. This article is about smithing. ... profile rolling (to manufacture a cone) Rolling is a fabricating process in which the metal, plastic, paper, glass, etc. ... Power press with a fixed barrier guard A press, or a machine press is a tool used to work metal (typically steel) by changing its shape and internal structure. ... Catastrophic failure is a sudden and total failure of some system from which recovery is impossible. ... This article is about engineering. ...



Typical yield behavior for non-ferrous alloys. 1: True elastic limit 2: Proportionality limit 3: Elastic limit 4: Offset yield strength
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 of stress–strain curves exhibited by real materials. In addition, there are several possible ways to define yielding[1]: A stress–strain curve is a graph derived from measuring load (stress – σ) versus extension (strain – ε) for a sample of a material. ...

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 this amount of stress, stress is proportional to strain (Hooke's Law), so the Stress Strain Graph is a straight line, and the gradient will be equal to the Young's modulus of the material.
Elastic limit 
Beyond the elastic limit, permanent deformation will occur. The lowest stress at which permanent deformation can be measured. This requires a manual load-unload procedure, and the accuracy is critically dependent on equipment and operator skill. For elastomers, such as rubber, the elastic limit is much larger than the proportionality limit.
Offset yield point (yield strength or proof stress) 
This is the most widely used strength measure of metals, and is found from the stress-strain curve as shown in the figure to the right. A plastic strain of 0.2% is usually used to define the offset yield stress, although other values may be used depending on the material and the application. The offset value is given as a subscript, e.g. Rp0.2=310 MPa. In some materials there is essentially no linear region and so a certain value of strain is defined instead. Although somewhat arbitrary, this method does allow for a consistent comparison of materials.
Upper yield point and lower yield point
Some 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 structural engineering as a conservative value.

In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. ... In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ... The term elastomer is often used interchangeably with the term rubber, and is preferred when referring to vulcanisates. ... This does not cite any references or sources. ...

Yield criterion

A yield criterion, often expressed as yield surface, or yield locus, is an 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 are tensor qualities they can be described on the basis of three principal directions, in the case of stress these are denoted by  sigma_1 ,!,  sigma_2 ,! and  sigma_3 ,!. Yield surface is described in three dimensional space of principal stresses (), and encompasses the elastic region of material behavior. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...

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 - 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.

 sigma_1 le sigma_y ,!

Maximum Principal Strain Theory - 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: This article is about the deformation of materials. ...

 sigma_1 - nu(sigma_2 + sigma_3) le sigma_y. ,!

Maximum Shear Stress Theory - Also known as the Tresca criterion, after the French scientist Henri Tresca. This assumes that yield occurs when the shear stress tau! exceeds the shear yield strength tau_y!: Henri Tresca (1814–1884) was French Mechanical Engineer, professor of Conservatoire National des Arts et Métiers in Paris. ...

 tau = frac{sigma_1-sigma_3}{2} le tau_{ys}. ,!

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:

 sigma_{1}^2 + sigma_{2}^2 + sigma_{3}^2 - 2 nu (sigma_1 sigma_2 + sigma_2 sigma_3 + sigma_1 sigma_3) le sigma_y^2. ,!

Distortion Energy Theory - 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 is generally referred to as the Von Mises criterion and is expressed as: Fluid pressure is the pressure on an object submerged in a fluid, such as water. ... Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. ...

frac{1}{2} Big[ (sigma_1 - sigma_2)^2 + (sigma_2 - sigma_3)^2 + (sigma_3 - sigma_1)^2 Big] le  sigma_y^2. ,!

Based on a different theoretical underpinning this expression is also referred to as octahedral shear stress theory.

Factors influencing yield stress

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. 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

 sigma_y = C (dot{epsilon})^m ,!

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 exhibit super plastic behaviour.

Later, more complex equations were proposed that simultaneously dealt with both temperature and strain rate:

 sigma_y = frac{1}{alpha} sinh^{-1} left [ frac{Z}{A} right ]^{(1/n)} ,!

where α and A are constants and Z is the temperature-compensated strain-rate - often described by the Zener-Hollomon parameter:

 Z = (dot{epsilon}) exp left ( frac{Q_{HW}}{RT} right ) ,!

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 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:

1. Work Hardening - Where machining 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. Work hardening, or strain hardening, is an increase in mechanical strength due to plastic deformation. ... In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. ...

The governing formula for this mechanism is:

 Deltasigma_y = Gb sqrt{rho}

where σy is the yield stress, G is the shear elastic modulus, b is the magnitude of the Burgers vector, and ρ is the dislocation density. In materials science, a dislocation is a linear crystallographic defect, or irregularity, within a crystal structure. ...

2. Solid Solution Strengthening - 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. Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. ... An alloy is a homogeneous hybrid of two or more elements, at least one of which is a metal, and where the resulting material has metallic properties. ...

The relationship of this mechanism goes as:

 Deltatau = Gbsqrt{C_s}epsilon^{3/2}

where τ is the shear 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 ε is the strain induced in the lattice due to adding the impurity. Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...

3. Particle/Precipitate Strengthening - 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. Precipitation hardening, also called age hardening or dispersion hardening, are heat treatment techniques used to strengthen malleable materials, especially non-ferrous alloys including most structural alloys of aluminium, magnesium and titanium. ...

The shearing formula goes as:

 Deltatau = cfrac{r_{particle}}{l_{interparticle}} gamma_{particle-matrix}

and the bowing/ringing formula:

 Deltatau = cfrac{Gb}{l_{interparticle}-2r_{particle}}

In these formulas, rparticle is the particle radius, γparticlematrix is the surface tension between the matrix and the particle, linterparticle is the distance between the particles.

4. Grain boundary strengthening - 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 strenghthening, this type of strengthening is governed by the formula: Figure 1: Hall-Petch Strengthening is limited by the size of dislocations. ...

 sigma_y = sigma_0 + kd^{-1/2} ,


σ0 is the stress required to move dislocations,
k is a material constant, and
d is the grain size.

Implications for structural engineering

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. 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 normal operation) to yield criteria.[citation needed]

Typical yield strength

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

Material Yield strength
Ultimate strength
Structural steel ASTM A36 steel 250 400 7.8
Steel, API 5L X65 (Fikret Mert Veral) 448 531 7.8
Steel, high strength alloy ASTM A514 690 760 7.8
Steel, prestressing strands 1650 1860 7.8
Steel Wire     7.8
Steel (AISI 1060 0.6% carbon) Piano wire 2200-2482 MPa[2]   7.8
High density polyethylene (HDPE) 26-33 37 0.95
Polypropylene 12-43 19.7-80 0.91
Stainless steel AISI 302 - Cold-rolled 520 860  
Cast iron 4.5% C, ASTM A-48 276 (??) 200  
Titanium alloy (6% Al, 4% V) 830 900 4.51
Aluminium alloy 2014-T6 400 455 2.7
Copper 99.9% Cu 70 220 8.92
Cupronickel 10% Ni, 1.6% Fe, 1% Mn, balance Cu 130 350 8.94
Brass approx. 200+ 550 5.3
Tungsten   1510 19.25
Glass   50 (in compression) 2.53
E-Glass N/A 3450 2.57
S-Glass N/A 4710 2.48
Basalt fiber N/A 4840 2.7
Marble N/A 15  
Concrete N/A 3  
Carbon Fiber N/A 5650 1.75
Spider silk 1150 (??) 1200  
Silkworm silk 500    
Aramid (Kevlar or Twaron) 3620   1.44
UHMWPE 23 46 0.97
UHMWPE fibers[3][4] (Dyneema or Spectra) 2300-3500 0.97
Vectran   2850-3340  
Pine Wood (parallel to grain)   40  
Bone (limb) 104-121 130  
Nylon, type 6/6 45 75  
Rubber - 15  
Boron N/A 3100 2.46
Silicon, monocrystalline (m-Si) N/A 7000 2.33
Silicon carbide (SiC) N/A 3440  
Sapphire (Al2O3) N/A 1900 3.9-4.1
Carbon nanotube (see note above) N/A 62000 1.34
Elements in the annealed state Young's Modulus
Proof or yield stress
Ultimate strength
Aluminium 70 15-20 40-50
Copper 130 33 210
Gold 79   100
Iron 211 80-100 350
Lead 16   12
Nickel 170 14-35 140-195
Silicon 107 5000-9000  
Silver 83   170
Tantalum 186 180 200
Tin 47 9-14 15-200
Titanium 120 100-225 240-370
Tungsten 411 550 550-620
Zinc (wrought) 105   110-200

(Source: A.M. Howatson, P.G. Lund and J.D. Todd, "Engineering Tables and Data" p41) mega- (symbol M) is an SI prefix in the SI system of units denoting a factor of 106, i. ... For other uses, see Pascal. ... For other uses, see Steel (disambiguation). ... A36 steel is a standard steel alloy which is the most common structural steel used in the United States. ... A514 is a particular type of high strength steel, which is quenched and tempered alloy steel, with basic strength of 100,000 psi (100 ksi, where 1 ksi = 1,000 psi) (700 MPa). ... Piano wire is a specialized type of wire made for use in piano and other musical instrument strings, as well as many other purposes. ... HDPE has SPI resin ID code 2 High-density polyethylene (HDPE) is a polyethylene thermoplastic made from petroleum. ... Polypropylene lid of a Tic Tacs box, with a living hinge and the resin identification code under its flap Micrograph of polypropylene Polypropylene or polypropene (PP) is a thermoplastic polymer, made by the chemical industry and used in a wide variety of applications, including food packaging, ropes, textiles, stationery, plastic... The 630 foot (192 m) high, stainless-clad (type 304) Gateway Arch defines St. ... Cast iron usually refers to grey cast iron, but can mean any of a group of iron-based alloys containing more than 2% carbon (alloys with less carbon are carbon steel by definition). ... Titanium alloys are metallic materials which contain a mixture of titanium and other chemical elements. ... Aluminium alloys or aluminum alloys are alloys of aluminium, often with copper, zinc, manganese, silicon, or magnesium. ... For other uses, see Copper (disambiguation). ... Cupronickel is an alloy of copper, nickel and strengthening impurities, such as iron and manganese. ... Brazen redirects here. ... For other uses, see Tungsten (disambiguation). ... This article is about the material. ... There is a disputed proposal to merge this article with glass-reinforced plastic. ... There is a disputed proposal to merge this article with glass-reinforced plastic. ... Basalt fiber or fibre is a material made from extremely fine fibers of basalt, which is composed of the minerals plagioclase, pyroxene, and olivine. ... For other uses, see Marble (disambiguation). ... This article is about the construction material. ... Carbon fiber composite is a strong, light and very expensive material. ... Spider silk is a fibre secreted by spiders. ... Binomial name Bombyx mori Linnaeus, 1758 For other senses of this word, see silkworm (disambiguation). ... Aramid fiber (1961) is a fire-resistant and strong synthetic fiber. ... Kevlars molecular structure; BOLD: monomer unit; DASHED: hydrogen bonds. ... Chemical structure of Kevlar. ... Ultra high molecular weight polyethylene (UHMWPE), also known as high modulus polyethylene (HMPE) or high performance polyethylene (HPPE), is a thermoplastic. ... Ultra high molecular weight polyethylene (UHMWPE), also known as high modulus polyethylene (HMPE) or high performance polyethylene (HPPE), is a thermoplastic. ... Vectran is a manufactured fibre, spun from a liquid crystal polymer created by Celanese Acetate LLC. These fibres are noted for thermal stability at high temperatures, high strength, and good chemical stability. ... Subgenera Subgenus Strobus Subgenus Ducampopinus Subgenus Pinus See Pinus classification for complete taxonomy to species level. ... For other uses, see Wood (disambiguation). ... This article is about the skeletal organs. ... For other uses of this word, see nylon (disambiguation). ... This does not cite any references or sources. ... For other uses, see Boron (disambiguation). ... Not to be confused with Silicone. ... Except where noted otherwise, data are given for materials in their standard state (at 25 Â°C, 100 kPa) Infobox disclaimer and references Silicon carbide (SiC) is a ceramic compound of silicon and carbon that is manufactured on a large scale for use mainly as an abrasive but also occurs in... For other uses, see Sapphire (disambiguation). ... 3D model of three types of single-walled carbon nanotubes. ... For other uses, see Annealing. ... In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ... Yield strength, or the yield point, is defined in engineering as the amount of strain that a material can undergo before moving from elastic deformation into plastic deformation. ... Aluminum redirects here. ... For other uses, see Copper (disambiguation). ... GOLD refers to one of the following: GOLD (IEEE) is an IEEE program designed to garner more student members at the university level (Graduates of the Last Decade). ... General Name, symbol, number iron, Fe, 26 Chemical series transition metals Group, period, block 8, 4, d Appearance lustrous metallic with a grayish tinge Standard atomic weight 55. ... General Name, Symbol, Number lead, Pb, 82 Chemical series Post-transition metals or poor metals Group, Period, Block 14, 6, p Appearance bluish gray Standard atomic weight 207. ... For other uses, see Nickel (disambiguation). ... Not to be confused with Silicone. ... This article is about the chemical element. ... General Name, Symbol, Number tantalum, Ta, 73 Chemical series transition metals Group, Period, Block 5, 6, d Appearance gray blue Standard atomic weight 180. ... This article is about the metallic chemical element. ... General Name, symbol, number titanium, Ti, 22 Chemical series transition metals Group, period, block 4, 4, d Appearance silvery metallic Standard atomic weight 47. ... For other uses, see Tungsten (disambiguation). ... General Name, symbol, number zinc, Zn, 30 Chemical series transition metals Group, period, block 12, 4, d Appearance bluish pale gray Standard atomic weight 65. ...

See also

This article needs to be cleaned up to conform to a higher standard of quality. ... The strain tensor, ε, is a symmetric tensor used to quantify the strain of an object undergoing a small 3-dimensional deformation: the diagonal coefficients εii are the relative change in length in the direction of the i direction (along the xi-axis) ; the other terms εij = 1/2 γij (i... This article is in need of attention from an expert on the subject. ... A stress concentration is a phenomenon encounterered in mechanical engineering where an object under load has higher than average local stresses due to its shape. ... // Linear elasticity The linear theory of elasticity models the macroscopic mechanical properties of solids assuming small deformations. ... The proof stress (also called offset yield strength) is the stress in a material that causes a small, specified amount of (permanent) plastic deformation in a test piece. ... Tensile strength isthe measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ... An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substances tendency to be deformed when a force is applied to it. ...


  1. ^ G. Dieter, Mechanical Metallurgy, McGraw-Hill, 1986
  2. ^ Don Stackhouse @ DJ Aerotech
  3. ^ Tensile and creep properties of ultra high molecular weight PE fibres
  4. ^ Mechanical Properties Data
  • Avallone, Eugene A.; & Baumeister III, Theodore (1996). Mark's Standard Handbook for Mechanical Engineers. New York: McGraw-Hill. ISBN 0-07-004997-1. 
  • Young, Warren C.; & Budynas, Richard G. (2002). Roark's Formulas for Stress and Strain, 7th edition. New York: McGraw-Hill. ISBN 0-07-072542-X. 
  • Engineer's Handbook
  • Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M. (1993). Advanced Mechanics of Materials, 5th edition John Wiley & Sons. ISBN 0-471-55157-0
  • Oberg, E., Jones, F. D., and Horton, H. L. (1984). Machinery's Handbook, 22nd edition. Industrial Press. ISBN 0-8311-1155-0
  • Shigley, J. E., and Mischke, C. R. (1989). Mechnical Engineering Design, 5th edition. McGraw Hill. ISBN 0-07-056899-5



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