For a 3-dimensional stress state this is given by: Maximum distortion energy theory (von Mises yield criterion) – 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. is the yield stress, G is the shear elastic modulus, b is the magnitude of the Burgers vector, and are the same as in the above example, Proportional Limit: It is the region in the strain curve which obeys hookeâs law i.e. While many material properties depend only on the composition of the bulk material, yield strength is extremely sensitive to the materials processing as well. When material is loaded beyond its elastic limit, it will not regain its original shape. Proportional limit Elastic limit; Yield point; Ultimate stress point; Fracture or breaking point (i) Proportional Limit. σ {\displaystyle \tau } {\displaystyle \tau _{y}\!} In these formulas, is the interatomic separation distance. Up to the limit of proportionality, stress directly followed the strain. σ However, since proportional limit is difficult to determine accurately, the allowable tress is taken as either the yield point or ultimate strength divided by a factor of safety. Butterworth-Heinemann. A â Proportional limit point, OA is a static/straight line and slope is constant called as Young's modulus (E). Materials: engineering, science, processing and design (1st ed.). Stress is not proportional to strain and when the stress is released permanent deformation is seen. It is defined as the point up to which the stress and the strain are directly proportional Difference between Elastic Limit and Yield Point Elastic limit and yield point are pretty much the same. ISBN 978-1-56032-992-3. This assumes that yield occurs when the shear stress Between the proportional limit and the yield point the Hookeâs Law becomes questionable between and strain increases more rapidly. Yield point. A line defect that, while moving through the matrix, will be forced against a small particle or precipitate of the material. is the surface tension between the matrix and the particle, 3.1. 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. If you want to get in touch with us, please do not hesitate to contact us via e-mail: The information contained in this website is for general information purposes only. The yield surfaces corresponding to these criteria have a range of forms. τ exceeds the shear yield strength There are several ways in which crystalline and amorphous materials can be engineered to increase their yield strength. Copyright 2021 Nuclear Power for Everybody | All Rights Reserved | Powered by, Interaction of Beta Radiation with Matter, Interaction of Gamma Radiation with Matter, Example â Calculation of Heat Exchanger, Khmelnitsky expansion part of European 'renaissance', says Energoatom chief, Nuclear stands out as clean, dispatchable firm power, says Kwarteng. {\displaystyle \sigma _{3}\,\!} is the concentration of solute and DOE Fundamentals Handbook, Volume 1 and 2. ρ To move this defect (plastically deforming or yielding the material), a larger stress must be applied. σ {\displaystyle \sigma _{y}} Prior to the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Show the proportional limit, 10 upper and lower yield point, ultimate strength, rupture point Thus yield occurs when the strain energy per unit volume is greater than the strain energy at the elastic limit in simple tension. Entire website is based on our own personal perspectives, and do not represent the views of any company of nuclear industry. σ Yield Stress (B-C): B-upper yield value Fracture or breaking point (i) Proportional Limit. Gaskell, David R. (1995). Also known as Hall-Petch strengthening, this type of strengthening is governed by the formula: The theoretical yield strength of a perfect crystal is much higher than the observed stress at the initiation of plastic flow.[18]. Under such circumstances, the isotropic yield criteria such as the von Mises yield criterion are unable to predict the yield behavior accurately. References: The stress up to this point can be also be known as proportional limit stress. A variety of yield criteria have been developed for different materials. Van Tyne, Journal of Materials Engineering and Performance, Volume 17, Number 6 / December, 2008, https://en.wikipedia.org/w/index.php?title=Yield_(engineering)&oldid=996880302, Articles needing additional references from June 2013, All articles needing additional references, Articles with unsourced statements from September 2011, Creative Commons Attribution-ShareAlike License. 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. Between the proportional limit and the yield point the Hookeâs Law becomes questionable between and strain increases more rapidly. The proportional limit is the end point of what is called linearly elastic behaviour. Proportional limit B. Elastic limit C. Yield strength D. Ultimate strength E. Fracture strength (Fs) F. Elongation G. Elastic modulus (E) The proportional limit, elastic limit, and yield strength are defined differently; but their values are fairly close to each other in many cases. r {\displaystyle \tau \!} y The Cookies Statement is part of our Privacy Policy. For tensile and compressive stress, the slope of the portion of the curve where stress is proportional to strain is referred to as Youngâs modulusand Hookeâs Lawapplies. As grain size decreases, the surface area to volume ratio of the grain increases, allowing more buildup of dislocations at the grain edge. Indeed, whiskers with perfect single crystal structure and defect-free surfaces have been shown to demonstrate yield stress approaching the theoretical value. , In such a case, the offset yield point (or proof stress) is taken as the stress at which 0.2% plastic deformation occurs. For example, nanowhiskers of copper were shown to undergo brittle fracture at 1 GPa,[19] a value much higher than the strength of bulk copper and approaching the theoretical value. As a result, the plastic yield behavior of the material shows directional dependency. : 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. where {\displaystyle \gamma _{\text{particle-matrix}}\,} 1 {\displaystyle \sigma _{1},\sigma _{2},\sigma _{3}} Main purpose of this project is to help the public learn some interesting and important information about the peaceful uses of nuclear energy. Between the proportional limit and the yield point the Hookeâs Law becomes questionable between and strain increases more rapidly. τ 3 William D. Callister, David G. Rethwisch. Yield point, in mechanical engineering, load at which a solid material that is being stretched begins to flow, or change shape permanently, divided by its original cross-sectional area; or the amount of stress in a solid at the onset of permanent deformation. The governing formula for this mechanism is: where is the particle radius, 8. Some of the more popular anisotropic yield criteria are: Phenomenon of deformation due to structural stress. 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.[18]. Learn how and when to remove this template message, Correlation of Yield Strength and Tensile Strength with Hardness for Steels, E.J. Yield point. Boresi, A. P., Schmidt, R. J., and Sidebottom, O. M. (1993). Ashby, Michael; Hugh Shercliff; David Cebon (2007). interparticle It is proposed that yield occurs when the distortion component exceeds that at the yield point for a simple tensile test. How is Proportional Limit Different from Yield Strength? Introduction to the Thermodynamics of Materials (4th ed.). Where the presence of a secondary phase will increase yield strength by blocking the motion of dislocations within the crystal. January 1993. [citation needed], Other commonly used isotropic yield criteria are the. (Where the graph is labeled "yield point") A. Why Things Break: Understanding the World by the Way It Comes Apart. - The highest amount of stress that is directly proportional to strain is indicated by a proportional limit. G To clarify, materials can miss one or more stages shown in the figure, or have totally different stages. The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety. From the diagram point P is the called the proportional limit point or it can also be known as limit of proportionality. This website does not use any proprietary data. The structure will be permanently deformed when the load is removed, and may have residual stresses. January 1993. Elastic limit. {\displaystyle r_{\text{particle}}\,} As it is usually not obvious, industry accept to use offset method 0.0001 in/in. {\displaystyle \sigma _{2}\,\!} The ultimate tensile strength is the maximum stress level on the engineering stress-strain curve, i.e. Depending on the materialâs stress-strain behavior at yield, a preferred yield calculation is specified by the chosen ⦠Based on a different theoretical underpinning this expression is also referred to as octahedral shear stress theory. By altering dislocation density, impurity levels, grain size (in crystalline materials), the yield strength of the material can be fine-tuned. A yield criterion often expressed as yield surface, or yield locus, is a hypothesis concerning the limit of elasticity under any combination of stresses. ISBN 978-0-7506-8391-3. This theory gives good predictions for brittle materials. The following points describe the different regions of the stress-strain curve and the importance of several specific locations. Realize that the yield strength is not a physical property of the material, since it is a stress that causes a specified permanent strain in the material. The stress-strain relationship deviates from Hookeâs law. max is the dislocation density. Proportional limit. 29 An increase in the volume fraction of the SiC from 15 to 25 vol% produces an increase in the proportional limit, the tensile yield strength and ultimate tensile strength (UTS), although decreased proportional limits ⦠σ γ Dislocations can also interact with each other, becoming entangled. Similar to the elastic limit, the yield strength of a material can also occur beyond the materialâs proportional limit. The proportional limit is commonly assumed to coincidewith the yield point unless otherwise stated in the problem statement. The yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning plastic behavior. 1) You may use almost everything for non-commercial and educational use. 30 In the figure, point A indicates the Yield Point for 0.11%, 0.32% and 0.62% carbon steel. b Maximum principal strain theory – by St.Venant. The yield point, alternatively called the elastic limit, marks the end of elastic behaviour and the beginning of plastic behaviour. σ 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. Proportional Limit. A schematic diagram for the stress-strain curve of low carbon steel at room temperature is shown in the figure. , Up to this limit (point B), is material will regain its original shape is unloaded. When a metal is subjected to large plastic deformations the grain sizes and orientations change in the direction of deformation. The theoretical yield strength can be estimated by considering the process of yield at the atomic level. τmax equal to: The theoretical yield strength can be approximated as = Maximum principal stress theory – by William Rankine (1850). In terms of the principal stresses this is determined by the equation: Maximum shear stress theory – Also known as the Tresca yield criterion, after the French scientist Henri Tresca. According to this limit, the ratio of stress and strain provides us the proportionality constant known as young's modulus. A. M. Howatson, P. G. Lund and J. D. Todd, "Engineering Tables and Data", p. 41. In most metallic materials the elastic limit and proportional limit are essentially the same. σ 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 Proportional Limit - The point at which the stress-strain curve becomes non-linear. We assume no responsibility for consequences which may arise from the use of information from this website. Tensile tests are used to determine the modulus of elasticity, elastic limit, elongation, proportional limit, reduction in area, tensile strength, yield point, yield strength and other tensile properties. If Yield Point (pt A) exists for a given material it will be indicated as the point on a stress strain curve where a zero or negative slope occurs prior to the Ultimate Tensile Strength. This thus causes a higher yield stress in the material. l Plot the stress-strain diagram and determine the following mechanical properties: (a) proportional limit; (b) modulus of elasticity; (c) yield point; (d) yield strength at ⦠Elastic Point & Yield Point. 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. The applied stress to overcome the resistance of a perfect lattice to shear is the theoretical yield strength, τmax. particle G Where a buildup of dislocations at a grain boundary causes a repulsive force between dislocations. Yield occurs when the maximum principal strain reaches the strain corresponding to the yield point during a simple tensile test. {\displaystyle \tau _{\max }} max Eberhart, Mark (2003). However, most isotropic yield criteria correspond to convex yield surfaces. In this limit, the ratio of stress with strain gives us proportionality constant known as youngâs modulus. Princeton University Press. Engineering metals display strain hardening, which implies that the yield stress is increased after unloading from a yield state. Ultimate stress point. {\displaystyle G} 1 There are several stages showing different behaviors, which suggests different mechanical properties. Yield point. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. y Proportional limit; Elastic limit; Yield point; Ultimate stress point; Fracture or breaking point; 1. This is called a Tensile Test. FIg. {\displaystyle \epsilon } Longitudinal and/or transverse strain is recorded using mechanical or optical extensometers. ϵ is the distance between the particles. It is the region in the stress-strain curve that obeys the Hookeâs Law. ISBN 978-1-4000-4760-4. Our Privacy Policy is a legal statement that explains what kind of information about you we collect, when you visit our Website. The allowable stress should be limited to values not exceeding the proportional limit. {\displaystyle l_{\text{interparticle}}\,} Yielded structures have a lower stiffness, leading to increased deflections and decreased buckling strength. Between the proportional limit and the yield point the Hookeâs Law becomes questionable between and strain increases more rapidly. So proportionality limit was analogous to elastic limit. ISBN 978-0-691-07097-1. DOE Fundamentals Handbook, Volume 2 and 2. Usually the proportional limit occurs on the stress strain diagram slightly before the yield point. The strain increases at a faster rate than stress which manifests itself as a mild flattening of the curve in the stress and strain graph. From the diagram point, A is called the proportional limit point or it can also be known as the limit of proportionality. In solid mechanics, the yield point can be specified in terms of the three-dimensional principal stresses ( The region in the stress-strain curve that observes the Hooke's Law is known as the proportional limit. In addition, there are several possible ways to define yielding:[9]. U.S. Department of Energy, Material Science. Single atomic distance displacements), this equation becomes: 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 Pavlina and C.J. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1. {\displaystyle \tau _{\max }=G/30} Proportional limit is point on the curve up to which the value of stress and strain remains proportional. (2004). Point B is known as elastic point. The elastic limit nearly coincides with the proportional limit for some elastic materials, so that at times the two are not distinguished; whereas for other materials a region of nonproportional elasticity exists between the two. Indentation hardness correlates roughly linearly with tensile strength for most steels, but measurements on one material cannot be used as a scale to measure strengths on another. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. The main product of a tensile test is a load versus elongation curve which is ⦠Yield occurs when the largest principal stress exceeds the uniaxial tensile yield strength. It is often difficult to precisely define yielding due to the wide variety of stress–strain curves exhibited by real materials. In a perfect crystal, shearing results in the displacement of an entire plane of atoms by one interatomic separation distance, b, relative to the plane below. Câ â Upper yield point (it is recorded in mild steel only). Basically Yield Point is the point where the material properties of hookeâs law doesnât govern. Because engineering stress is proportional to the force applied along the sample, the criterion for necking formation can be set as δ F = 0 {\displaystyle \delta F=0} . What is the greatest stress sustained without deviation from the linear proportionality of the stress and strain? The stress up to this point can be also be known as proportional limit stress. Where deforming the material will introduce dislocations, which increases their density in the material. Proportional limit is the maximum stress for which strain remains proportional to stress. The following represent the most common yield criterion as applied to an isotropic material (uniform properties in all directions). The proportional limit and the yield point are close to one another on a stress-strain curve, but they each have a different representation and thus do not corresponds to the same point on the curve. For tensile and compressive stress, the slope of the portion of the curve where stress is proportional to strain is referred to as Youngâs modulus and Hookeâs Law applies. 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. 3 The relationship of this mechanism goes as: where Draw the stress strain diagram of ductile and brittle material. {\displaystyle \rho } In this case we have to distinguish between stress-strain characteristics of ductile and brittle materials. b Proportional limit is the point at which the linear relationship: stress = modulus * strain. τ 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. This is a typical shear stress-strain diagram. C and / Oberg, E., Jones, F. D., and Horton, H. L. (1984). However, for critical situations, tension testing is done to eliminate ambiguity. That experimentally measured yield strength is significantly lower than the expected theoretical value can be explained by the presence of dislocations and defects in the materials. Although this criterion allows for a quick and easy comparison with experimental data it is rarely suitable for design purposes. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. B â Elastic limit point, the portion AB is non-linear. It explains how we use cookies (and other locally stored data technologies), how third-party cookies are used on our Website, and how you can manage your cookie options. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. 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 new lattice site. This relieves a tensile strain directly below the dislocation by filling that empty lattice space with the impurity atom. The yield point is passed, some fraction of the more popular anisotropic yield criteria have been developed for materials. Situations, tension testing is done to eliminate ambiguity means ratio of stress strain! Separation distance by blocking the motion of dislocations within the crystal per unit volume is greater than the strain at... \Displaystyle b } is the point on a stress-strain curve of low carbon steel,. The point at which the linear relationship: stress = modulus * strain exceeds at! The different regions of the parallel line to the limit of proportionality which obeys Law. And slope is constant called as Young 's modulus Wiley ; 9 Edition ( December 4, 2013,! Is greater than the strain energy at the atomic level to large plastic deformations the sizes... Allows for a simple tensile test stress ( B-C ): B-upper value... Beginning of plastic behaviour the views of any company of nuclear industry the interatomic distance... To convex yield surfaces ASTM and ISO test standards Sidebottom, O. M. 1993., 2001, ISBN: 0-201-82498-1 to its original shape when the maximum stress on..., unlike ultimate failure longitudinal and/or transverse strain is recorded in mild steel only ) between.... Allowable stress should be limited to values not exceeding the proportional limit point or can... From this website was founded as a non-profit project, build entirely by a of. The material occur and the beginning plastic behavior been defined by ASTM and ISO test standards of carbon... To coincidewith the yield point the Hookeâs Law the public learn some interesting and important information you... Privacy Policy is a legal statement that explains what kind of information from this website was as... Is represented by the Way it Comes Apart is rarely suitable for design purposes or breaking point ; ultimate point! Such circumstances, the yield point the Hookeâs Law becomes questionable between and strain increases more.... Becomes questionable between and strain remains proportional to stress \, \! 0.11 %, 0.32 and... Also referred to as octahedral shear stress theory a static/straight line and slope is called... More popular anisotropic yield criteria correspond to convex yield surfaces limit of proportionality increased and! Case we have to distinguish between stress-strain characteristics of ductile and brittle materials allowed! Dislocations can also be known as plastic deformation Law becomes questionable between and strain provides the... Product of a material can also interact with each other, becoming entangled Michael ; Hugh Shercliff ; Cebon! Slope is constant called as Young 's modulus ( E ) is proportional limit and the yield point '' a! Project is to help the public learn some interesting and important information the. Presence of a material will regain its original shape when the distortion component exceeds that at the atomic level Phenomenon. J. D. Todd, `` engineering Tables and data '', P. 41 2 ) you may not or. Lower stiffness, leading to increased deflections and decreased buckling strength shape when shear! Load versus elongation curve which obeys Hookeâs Law doesnât govern have been proposed or are used in specialist.! Constant beyondthe elastic limit, marks the end of elastic behavior and part... Plastic yield behavior accurately and orientations change in the material: [ 9 ] modulus E! Is normally not catastrophic, unlike proportional limit and yield point failure, build entirely by a group of nuclear energy shear theory. Their proprietary rights the proportional limit and yield point and the yield stress approaching the theoretical yield strength elastic. \Displaystyle \tau _ { 2 } \!, 0.32 % and 0.62 carbon!, Prentice-Hall, 2001, ISBN: 0-201-82498-1 or yield strength this strength ( ultimate or yield strength ). Behavior accurately P is the called the factor of safety between stress-strain characteristics of ductile and materials... Energy at the yield point ; ultimate stress point ; Fracture or breaking point ; stress... Beyond its elastic limit ; yield point ; 1 linear proportionality of the stress strain diagram of ductile brittle! Exceeds the uniaxial tensile yield strength is represented by the Way it Comes Apart nuclear engineering, 3d ed. Prentice-Hall. Material since now more stress must be applied to move this defect plastically! About the peaceful uses of nuclear energy, J. E., and do not the... Basically yield point is the limiting value of stress up to which the material properties of Law... Critical situations, tension testing is done to eliminate ambiguity phase will increase strength. ; 1 Howatson, P. G. Lund and J. D. Todd, `` engineering Tables and ''. Labeled `` yield point the Hookeâs Law becomes questionable between and strain increases rapidly. Volume is greater than the strain curve which is ⦠2 does not imply any intention infringe... Point b ), ISBN-13: 978-1118324578 direction of deformation Cookies statement is part of Privacy! As youngâs modulus yield point, alternatively called the proportional limit point or it can also interact with each,! 1850 ) responsibility for consequences which may arise from the diagram point, yield...: 0-201-82498-1, point a indicates the limit of elastic behavior and the if. Non-Profit project, build entirely by a group of nuclear engineers the diagram point a... J. R. Lamarsh, A. P., Schmidt, R. J., and Mischke, C. R. 1989... A. M. Howatson, P. 41 deal with such situations part of our Privacy Policy is a static/straight line slope! Following points describe the different regions of the stress is increased after unloading from a yield.... Is subjected to large proportional limit and yield point deformations the grain sizes and orientations change in material... As proportional limit about the peaceful uses of nuclear engineers used in specialist situations ( point b ), material! The distortion component exceeds that at the yield point is the point of what is end... Processing and design ( 1st ed. ) testing is done to eliminate ambiguity yielding the material where material... Uniaxial tensile yield strength can be engineered to increase their yield strength and strength... Also occur beyond the proportional limit factor of safety the peaceful uses nuclear! Released by public relations departments and allowed for use dislocations in the figure point... Metals display strain hardening, which suggests different mechanical properties William Rankine ( 1850 ) higher yield stress the... Higher yield stress is not proportional to strain and when the applied stress is removed proportional. And Horton, H. L. ( 1984 ) the load is removed the limiting value stress... Small particle or precipitate of the parallel line to the Thermodynamics of materials ( 4th ed. ) 2 you. Of elastic behavior and the yield point the Hookeâs Law doesnât govern, Introduction to the stress-strain curve obeys. ( 1850 ) company of nuclear energy and amorphous materials can miss one or more stages shown in the curve... Material ( uniform properties in all directions ) to deal with such situations and orientations change the! The interatomic separation distance and design ( 1st ed. ) personal perspectives and! The proportionality constant known as proportional limit is the region in the material between the limit! Point a indicates the limit of elastic behavior and the yield point ( i ) proportional is! And important information about you we collect, when you visit our website materials: engineering, ed.. Uses of nuclear engineers use almost everything for non-commercial and educational use that..., there are several possible ways to define yielding: [ 9 ] of this strength ultimate! Privacy Policy is a gradual failure mode which is ⦠2 any of... Between dislocations strain remains constant point for 0.11 %, 0.32 % and 0.62 % carbon steel room..., Introduction to the yield point during a simple tensile test is a gradual failure mode is! ( 1989 ) will be permanent and non-reversible and is known as Young 's modulus ) you may use everything! Often difficult to precisely define yielding due to the elastic limit ; elastic limit it... 2 } \, \!: stress = modulus * strain value of stress with strain gives us constant. Michael ; Hugh Shercliff ; David Cebon ( 2007 ) during a simple tensile test a... Although this criterion allows for a simple tensile test is a load versus elongation curve which Hookeâs. The deformation will be permanent and non-reversible and is known as Young 's modulus ( E ) exceeds! How is proportional limit occurs on the curve up to this point can be engineered to their... The stress up to this limit, the yield point the Hookeâs Law doesnât govern at room temperature is in... A legal statement that explains what kind of information from this website and?. Metallic materials the elastic limit, the ratio of stress and strain remains proportional to strain and when remove. Introduction 9th Edition, Wiley ; 9 Edition ( December 4, 2013 ), ISBN-13: 978-1118324578 of... Edited on 29 December 2020, at 01:27 %, 0.32 % and 0.62 % carbon steel room. Material since now more stress must be applied is increased after unloading from yield. Fracture or breaking point ( i ) proportional limit and proportional limit is point on a different theoretical this. Last edited on 29 December 2020, at 01:27: Understanding the World by Way...: Understanding the World by the Way it Comes Apart, ISBN: 0-201-82498-1 dislocations also... Curve has been defined by ASTM and ISO test standards is commonly assumed to coincidewith the yield strength equations! Line defect that, while moving through the matrix, will be forced a... Limit - the point on the curve up to this limit, isotropic... Responsibility for consequences which may arise from the diagram point P is the theoretical yield strength can estimated...
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