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It may be more accurate to delete or change
"because the stress tensor has six independent components"
The stress tensor must be positive-definite, so the components are related and only five can be independent.
Tibbits ( talk) 17:19, 2 December 2013 (UTC)
Currently the links take you to the stress page; however, the deviatoric stress invariants aren't defined their. They're defined on the Cauchy stress tensor page. Should they be included on the stress page, or should we simply redirect that link to the Cauchy stress tensor subsection? Jdc2179 ( talk) 12:11, 7 June 2013 (UTC)
I think that two important details should be mentioned in the article: Firstly the fact that we are looking at a /projection/ here from an (at least) 6-dimensional space to a 3-dimensional space. Obviously, during this projection, some information of the Cauchy stress tensor gets lost... And secondly the fact that the /position/ of the stress point inside the yield surface does not have any physical meaning - except that it shows the proximity to possible yielding by its shortest distance to the surface (which in fact could more easily be shown in a one-dimensional plot). Any comments on that? Kassbohm ( talk) 04:56, 18 February 2010 (UTC)
I believe your sentence, "It is most applicable to ductile materials where the ratio of the yield and ultimate strengths is near 0.577." should better read " It is most applicable to ductile materials where the ratio of the shear yield to tensile yield strengths is appx. 0.577, or 1 over the square root of 3.
You are right, this was my mistake.
-samba6566
Since the third term is squared, it does not matter whether the sigma(x) or the sigma(z) come first (mathematically). The mathematical convention, however, is that the terms are presented in order, x then y then z with there complimentary terms following each. —The preceding unsigned comment was added by Samba6566 ( talk • contribs) 23:17, 2 March 2007 (UTC).
Was this supposed to say sigma_v over square root of 3? Readertonight 01:23, 17 August 2007 (UTC)
I started improving the section on the Yield Criterion, and then realized that both sections within this article are redundant. Which made me think that this article needs to be re-organized and include the following: 1- what the von Mises yield criterion states (definition and assumptions) 2- equations and figures for the yield function and yield surface 3- equations for the different stress conditions (triaxial, biaxial, uniaxial, and pure shear) 4- The Flow Rule Associated with the von Mises Yield Function I will try to re-organize this article according to these suggestions. Please comment Sanpaz 00:39, 1 December 2007 (UTC)
I just posted the new version of the article. I know it is a huge change, but I saw necessary to add more content and re-organize the article. There is still more to be added. I apologize for the big change. Please comment
Sanpaz
02:39, 4 December 2007 (UTC)
These changes deviate the intent of the article. The article is about the overall yield criterion, not solely about the interpretation of, or the use of it(von vises stress). However, the concept of von mises stress needs to be included. Sanpaz ( talk) 18:36, 19 January 2008 (UTC)
I reintroduced the concept of Equivalent stress or von Mises stress into the article, but into its correct spot within the context of the article (i.e. in the uniaxial stress condition section ). Sanpaz ( talk) 20:06, 19 January 2008 (UTC)
I found a much more succinct and usefully answer on yahoo answers.
"What is Von Mises Stress in layman terms?
Good question. Von Mises Stress is actually a misnomer. It refers to a theory called the "Von Mises - Hencky criterion for ductile failure".
In an elastic body that is subject to a system of loads in 3 dimensions, a complex 3 dimensional system of stresses is developed (as you might imagine). That is, at any point within the body there are stresses acting in different directions, and the direction and magnitude of stresses changes from point to point. The Von Mises criterion is a formula for calculating whether the stress combination at a given point will cause failure.
There are three "Principal Stresses" that can be calculated at any point, acting in the x, y, and z directions. (The x,y, and z directions are the "principal axes" for the point and their orientation changes from point to point, but that is a technical issue.)
Von Mises found that, even though none of the principal stresses exceeds the yield stress of the material, it is possible for yielding to result from the combination of stresses. The Von Mises criteria is a formula for combining these 3 stresses into an equivalent stress, which is then compared to the yield stress of the material. (The yield stress is a known property of the material, and is usually considered to be the failure stress.)
The equivalent stress is often called the "Von Mises Stress" as a shorthand description. It is not really a stress, but a number that is used as an index. If the "Von Mises Stress" exceeds the yield stress, then the material is considered to be at the failure condition.
The formula is actually pretty simple, if you want to know it: (S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2Se^2 Where S1, S2 and S3 are the principal stresses and Se is the equivalent stress, or "Von Mises Stress". Finding the principal stresses at any point in the body is the tricky part."
I find this a lot with engineering articles, they are all written at graduate student level. But if you think about it, someone of that level, wouldn't need to look this up. Try to write these kinds of articles in such a way that someone can be like "wait, what is von mises stress anyways", and then they can come here and figure it out. Not many people ask "wait, what was the mathematical approximation you used to find this von mises stress" —Preceding unsigned comment added by 75.162.56.142 ( talk) 23:43, 9 March 2008 (UTC)
I have shad more light on the meaning of the yield strength with respect to the yield criterion. IMHO, it makes best sense to describe the yield condition such that it is met when the von Mises stress reaches the yield strength. The previous version, though formally a correct alternative, did not show this. It used a critical stress k that was related but not equal to the yield strength. This is neither instructive nor common practice, at least not in my surrounding.
Unfortunately, my changes induce many consistency changes, namely the factor 3, when the squared alternative of the yield criterion was used. I am afraid, I might have missed some instances, when screening the text. I will check more often the consistency of this article in the coming days and try to eliminate all errors that I might have introduced. However, I would deeply appreciate your assistance with that.
I hope everyone agrees that the yield criterion: influence - resistance = 0 is better stated with the yield strength being the resistance. I am sorry for the amount of work this conceptual change induces. Tomeasy ( talk) 09:03, 23 April 2008 (UTC)
I understand what you are suggesting now. Pretty much, we are talking about different ways of showing or expressing the Von Mises Criterion. You are suggesting to express the criterion as a function of . However, the original formulation by Von mises,(see [1], says that yielding occurs when reaches a critical value . However, the Von mises stress is a concept derived or obtained from this formulation. It is an interpretation of the formulation. This interpretation is that to obtain the yield strength of material loaded triaxially (3-D) one needs only the yield strength of the material obtained from uniaxial tests. This uniaxial strength is the Von Mises Stress . So, my suggestion is to be general in the formulation, and later talk about the interpretations given to the formulation, which is what the article had before. Sanpaz ( talk) 19:40, 23 April 2008 (UTC)
I am unable to comprehend what is said about the maximum octahedral shear stress. Especially I have a problem with the second part of this equation
The first part simply states the shear stress acting on the octahedron, but where does the second part come from. It is important to mention that the equation stated above is still based on a formulation of the yield criterion that compares the square root of to a critical value, which is equal to the shear stress at the onset of yielding in a pure shear experiment. Please note, that at present the remainder of the article is based on a yield formulation that compares the von Mises stress to the yield strength, which is equal to the tensile stress at at the onset of yielding in a uniaxial tensile experiment.
While trying to adjust this section to the latter formulation, I am in trouble, because I do not understand the second part of the equation in the first place. According to my naive thinking the shear stress on the octahedron at at the onset of yielding should (with the first formulation of the yield criterion in mind) simply equal the critical value k, and not . I probably miss a point here, perhaps some geometric reason. Can anyone help me out so that a consistent version can finally be established?
Independent from this, I acknowledge that it is not yet decided which formulation should stand in the end. However, my question to the above formula exist even if the yield criterion is stated as in the earlier version. Moreover, I am trying to establish a consistent version of the yield strength based formulation, so that in the end we can simply choose between the two, both being formally OK. This section is the last piece that lacks this consistency. Tomeasy ( talk) 08:34, 25 April 2008 (UTC)
I have set up a new article for the von Mises stress. I think can take a little bit the pressure away as to how formulate things on this page. Actually, one could delete now the equations stated in the subsection arbitrary loading conditions as they are double now on the new page. I will leave this deletion to other users, since I am not disturbed by this redundancy. Tomeasy ( talk) 06:01, 27 April 2008 (UTC)
I have substituted the value k by the fracture strength, as can be done if the yield criterion is stated the way it currently is. This simplifies the whole article enormously. That's why I chose to do so. However, should we decide in the future to step back to the generic critical value (the one that equals the square root of J2) than we will also revert these edits. Please, comment on what you prefer. Tomeasy ( talk) 06:05, 27 April 2008 (UTC)
I appreciate this description of Von Mises yield criterion as a graduate-level discussion of the concept. However, when I imagined that my undergraduate students might look up "von Mises stress" on wikipedia, I felt that they would be confused by this article.
The context in which the average person would be searching wikipedia for "von Mises" is its connection to the maximum distortion energy failure theory. I was surprised to discover that there is no article describing the maximum distortion energy failure theory as referenced by this article.
I admit that precedence may be an issue. One undergraduate text, Shigley's Mechanical Design, gives precedence to von Mises, but a similar text, Juvinal and Marshek, attributes several others as potential originators of the max distortion theory concept.
In any case, would it be a good idea for someone to create a distortion energy entry for the benefit of people who require a pedestrian understanding of this topic?
Thanks, Deltapapamike ( talk) 04:53, 8 June 2009 (UTC)
In the equation → (sigma1)^2-sigma1*sigma2+(sigma2)^2=3k^2=sigmaY^2 ...sigmaY above refers to the yield strength. This equation does not equal yield strength. This equation should equal Sigma_e (Von Mises stress in my mech. design book) or Sigma_v as denoted in this article. Someone take a look at this and fix if this is indeed incorrect. It could be confusing to someone if it is equaling the yield strength instead of the Von Mises stress. I realize that for the Von Mises failure criterion sigma_e=Sy÷n where n is the safety factor and if it is 1, Sy can = Sigma_e but this is not always the case pbviously. So this formula should be changed. 192.91.173.36 ( talk) 21:20, 17 December 2009 (UTC)
I believe tau13 should be tau12 in the conditions column. I'm not involved in this article. Someone please change it, it's really bugging me. Thanks.-- 67.59.60.122 ( talk) 12:37, 14 December 2011 (UTC)
I like to use (tau) for shear stress, to help make it obviously different from normal stress. All my engineering books use tau for shear. I realize that some/older books use sigma for both kinds of stress. I know of one asme code that uses it both ways. Is there and advantage to using sigma for shear stress? Is tau typically used for something else? -- Zojj t c 19:20, 25 February 2012 (UTC)
I don't understand the formula for the deviatoric stress matrix as specified in the article,
shouldn't it be something like
cheers / Baxtrom ( talk) 12:41, 29 February 2012 (UTC)
sanpaz ( talk) 17:23, 29 February 2012 (UTC)
Why is there no hint about the physical reasoning that lead to the development of the von Mises yield criterion in the first place? It was well known that shear stress is what drives ductile yielding. This is the reason the Tresca (max shear) criterion was developed. But in multi-axial loading (more than just pure shear and simple tension/compression), it was noted that Tresca led to incorrect (conservative) predictions of yield, and that indeed there was need for terms in the failure criterion that coupled stresses in different directions. So, von Mises proposed that the stress components be decomposed into a hydrostatic (average normal stress) component, and whatever was left over to get the original stress state back (the deviatoric component). He then proposed that the hydrostatic component (because it involves no shear) be ignored, and worked only with the deviatoric component. Using the generalized Hooke's law, he calculated the strain energy density of only the deviatoric component for general 3-D loading.
He then proposed calculating the deviatoric strain energy density for any specific loading under consideration, and comparing it to the deviatoric strain energy density of a specimen in simple tension or compression at yield. When the two are equal, the specimen will yield. This leads to the conclusion that when the von Mises stress reaches the tensile yield strength of the material, yield occurs.
So, the statement at the end of the section "This implies that the yield condition is independent of hydrostatic stresses" is misleading. That the yield condition is independent of hydrostatic loading is not implied by the von Mises criterion. It was explicitly assumed from the start. — Preceding unsigned comment added by 157.201.95.254 ( talk) 22:11, 21 October 2013 (UTC)
The lede is
"The von Mises yield criterion [1] suggests that the yielding of materials begins when the second deviatoric stress invariant J_2 reaches a critical value.
Does the Wikipedia community wish to limit its audience to those who understand all of that introductory sentence? So for example, does Wikipedia want to exclude every reader who doesn't understand the term "second deviatoric stress"? — Preceding unsigned comment added by Mcamp@cinci.rr.com ( talk • contribs) 00:20, 15 May 2015 (UTC)
NearlyMad, you reinstated an edit I reverted. Putting aside the "minor" incorrect marking issue, and the possibility of scientific inaccuracy, there are at least concerns:
I know the article is not in great shape and I have done little if any to correct that, but that is not a reason to deteriorate it further. Tigraan Click here to contact me 18:18, 18 October 2016 (UTC)
Trigaan I am trying to make this article a little more useful. I have been providing edits to this page for over ten years (under various usernames). The applicability of any engineering/scientific information must be listed before the information is presented. If you can't see this value within the article I'd have to assume you are not well versed in it and question why you are editing it. As for inline citations, I was not aware of them and as a courtesy you could have added them then told me it should be done.
I have been dealing with von Mises criterion for over thirty years, it's a fascination with me. It is obvious Wikipedia does not need any help from someone with sufficient and adequate knowledge and experience. Good luck, I'll quit watching this page.
Joseph L. Moore Senior Aerospace Engineer NASA
@ NearlyMad, provide a more specific citation on this comment:
"Although the given criterion is based on a yield phenomenon, extensive testing has shown that use of a "von Mises" stress is applicable at ultimate loading "
I have read through the Timoshenko text and I cannot find information that agrees with your statement.
Timoshenko makes reference to R. v. Mises in a footnote on p478 in a discussion about the development of the maximum strain energy theory. He goes on to mention “recent experiments” that showed correlation between maximum strain energy theory and maximum shear theory, and notes that “in most cases the difference between these two theories is not so large as to make it of practical importance”. However, these discussions are focused on defining the yield point for ductile materials, not ultimate failure, so I do not believe it is relevant.
Later, on p482, there is a reference to “very extensive experiments” and a footnote regarding applying the theory to ultimate stresses, but this is explicitly noted in reference to brittle materials.
I should point out that all of my references above are in “Part II” of the text. Your citation notes “Part I”, but I have not been able to locate a reference to von Mises in that portion of the text. 216.243.30.3 ( talk) 22:13, 5 January 2024 (UTC)
This article is rated Start-class on Wikipedia's
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It may be more accurate to delete or change
"because the stress tensor has six independent components"
The stress tensor must be positive-definite, so the components are related and only five can be independent.
Tibbits ( talk) 17:19, 2 December 2013 (UTC)
Currently the links take you to the stress page; however, the deviatoric stress invariants aren't defined their. They're defined on the Cauchy stress tensor page. Should they be included on the stress page, or should we simply redirect that link to the Cauchy stress tensor subsection? Jdc2179 ( talk) 12:11, 7 June 2013 (UTC)
I think that two important details should be mentioned in the article: Firstly the fact that we are looking at a /projection/ here from an (at least) 6-dimensional space to a 3-dimensional space. Obviously, during this projection, some information of the Cauchy stress tensor gets lost... And secondly the fact that the /position/ of the stress point inside the yield surface does not have any physical meaning - except that it shows the proximity to possible yielding by its shortest distance to the surface (which in fact could more easily be shown in a one-dimensional plot). Any comments on that? Kassbohm ( talk) 04:56, 18 February 2010 (UTC)
I believe your sentence, "It is most applicable to ductile materials where the ratio of the yield and ultimate strengths is near 0.577." should better read " It is most applicable to ductile materials where the ratio of the shear yield to tensile yield strengths is appx. 0.577, or 1 over the square root of 3.
You are right, this was my mistake.
-samba6566
Since the third term is squared, it does not matter whether the sigma(x) or the sigma(z) come first (mathematically). The mathematical convention, however, is that the terms are presented in order, x then y then z with there complimentary terms following each. —The preceding unsigned comment was added by Samba6566 ( talk • contribs) 23:17, 2 March 2007 (UTC).
Was this supposed to say sigma_v over square root of 3? Readertonight 01:23, 17 August 2007 (UTC)
I started improving the section on the Yield Criterion, and then realized that both sections within this article are redundant. Which made me think that this article needs to be re-organized and include the following: 1- what the von Mises yield criterion states (definition and assumptions) 2- equations and figures for the yield function and yield surface 3- equations for the different stress conditions (triaxial, biaxial, uniaxial, and pure shear) 4- The Flow Rule Associated with the von Mises Yield Function I will try to re-organize this article according to these suggestions. Please comment Sanpaz 00:39, 1 December 2007 (UTC)
I just posted the new version of the article. I know it is a huge change, but I saw necessary to add more content and re-organize the article. There is still more to be added. I apologize for the big change. Please comment
Sanpaz
02:39, 4 December 2007 (UTC)
These changes deviate the intent of the article. The article is about the overall yield criterion, not solely about the interpretation of, or the use of it(von vises stress). However, the concept of von mises stress needs to be included. Sanpaz ( talk) 18:36, 19 January 2008 (UTC)
I reintroduced the concept of Equivalent stress or von Mises stress into the article, but into its correct spot within the context of the article (i.e. in the uniaxial stress condition section ). Sanpaz ( talk) 20:06, 19 January 2008 (UTC)
I found a much more succinct and usefully answer on yahoo answers.
"What is Von Mises Stress in layman terms?
Good question. Von Mises Stress is actually a misnomer. It refers to a theory called the "Von Mises - Hencky criterion for ductile failure".
In an elastic body that is subject to a system of loads in 3 dimensions, a complex 3 dimensional system of stresses is developed (as you might imagine). That is, at any point within the body there are stresses acting in different directions, and the direction and magnitude of stresses changes from point to point. The Von Mises criterion is a formula for calculating whether the stress combination at a given point will cause failure.
There are three "Principal Stresses" that can be calculated at any point, acting in the x, y, and z directions. (The x,y, and z directions are the "principal axes" for the point and their orientation changes from point to point, but that is a technical issue.)
Von Mises found that, even though none of the principal stresses exceeds the yield stress of the material, it is possible for yielding to result from the combination of stresses. The Von Mises criteria is a formula for combining these 3 stresses into an equivalent stress, which is then compared to the yield stress of the material. (The yield stress is a known property of the material, and is usually considered to be the failure stress.)
The equivalent stress is often called the "Von Mises Stress" as a shorthand description. It is not really a stress, but a number that is used as an index. If the "Von Mises Stress" exceeds the yield stress, then the material is considered to be at the failure condition.
The formula is actually pretty simple, if you want to know it: (S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2Se^2 Where S1, S2 and S3 are the principal stresses and Se is the equivalent stress, or "Von Mises Stress". Finding the principal stresses at any point in the body is the tricky part."
I find this a lot with engineering articles, they are all written at graduate student level. But if you think about it, someone of that level, wouldn't need to look this up. Try to write these kinds of articles in such a way that someone can be like "wait, what is von mises stress anyways", and then they can come here and figure it out. Not many people ask "wait, what was the mathematical approximation you used to find this von mises stress" —Preceding unsigned comment added by 75.162.56.142 ( talk) 23:43, 9 March 2008 (UTC)
I have shad more light on the meaning of the yield strength with respect to the yield criterion. IMHO, it makes best sense to describe the yield condition such that it is met when the von Mises stress reaches the yield strength. The previous version, though formally a correct alternative, did not show this. It used a critical stress k that was related but not equal to the yield strength. This is neither instructive nor common practice, at least not in my surrounding.
Unfortunately, my changes induce many consistency changes, namely the factor 3, when the squared alternative of the yield criterion was used. I am afraid, I might have missed some instances, when screening the text. I will check more often the consistency of this article in the coming days and try to eliminate all errors that I might have introduced. However, I would deeply appreciate your assistance with that.
I hope everyone agrees that the yield criterion: influence - resistance = 0 is better stated with the yield strength being the resistance. I am sorry for the amount of work this conceptual change induces. Tomeasy ( talk) 09:03, 23 April 2008 (UTC)
I understand what you are suggesting now. Pretty much, we are talking about different ways of showing or expressing the Von Mises Criterion. You are suggesting to express the criterion as a function of . However, the original formulation by Von mises,(see [1], says that yielding occurs when reaches a critical value . However, the Von mises stress is a concept derived or obtained from this formulation. It is an interpretation of the formulation. This interpretation is that to obtain the yield strength of material loaded triaxially (3-D) one needs only the yield strength of the material obtained from uniaxial tests. This uniaxial strength is the Von Mises Stress . So, my suggestion is to be general in the formulation, and later talk about the interpretations given to the formulation, which is what the article had before. Sanpaz ( talk) 19:40, 23 April 2008 (UTC)
I am unable to comprehend what is said about the maximum octahedral shear stress. Especially I have a problem with the second part of this equation
The first part simply states the shear stress acting on the octahedron, but where does the second part come from. It is important to mention that the equation stated above is still based on a formulation of the yield criterion that compares the square root of to a critical value, which is equal to the shear stress at the onset of yielding in a pure shear experiment. Please note, that at present the remainder of the article is based on a yield formulation that compares the von Mises stress to the yield strength, which is equal to the tensile stress at at the onset of yielding in a uniaxial tensile experiment.
While trying to adjust this section to the latter formulation, I am in trouble, because I do not understand the second part of the equation in the first place. According to my naive thinking the shear stress on the octahedron at at the onset of yielding should (with the first formulation of the yield criterion in mind) simply equal the critical value k, and not . I probably miss a point here, perhaps some geometric reason. Can anyone help me out so that a consistent version can finally be established?
Independent from this, I acknowledge that it is not yet decided which formulation should stand in the end. However, my question to the above formula exist even if the yield criterion is stated as in the earlier version. Moreover, I am trying to establish a consistent version of the yield strength based formulation, so that in the end we can simply choose between the two, both being formally OK. This section is the last piece that lacks this consistency. Tomeasy ( talk) 08:34, 25 April 2008 (UTC)
I have set up a new article for the von Mises stress. I think can take a little bit the pressure away as to how formulate things on this page. Actually, one could delete now the equations stated in the subsection arbitrary loading conditions as they are double now on the new page. I will leave this deletion to other users, since I am not disturbed by this redundancy. Tomeasy ( talk) 06:01, 27 April 2008 (UTC)
I have substituted the value k by the fracture strength, as can be done if the yield criterion is stated the way it currently is. This simplifies the whole article enormously. That's why I chose to do so. However, should we decide in the future to step back to the generic critical value (the one that equals the square root of J2) than we will also revert these edits. Please, comment on what you prefer. Tomeasy ( talk) 06:05, 27 April 2008 (UTC)
I appreciate this description of Von Mises yield criterion as a graduate-level discussion of the concept. However, when I imagined that my undergraduate students might look up "von Mises stress" on wikipedia, I felt that they would be confused by this article.
The context in which the average person would be searching wikipedia for "von Mises" is its connection to the maximum distortion energy failure theory. I was surprised to discover that there is no article describing the maximum distortion energy failure theory as referenced by this article.
I admit that precedence may be an issue. One undergraduate text, Shigley's Mechanical Design, gives precedence to von Mises, but a similar text, Juvinal and Marshek, attributes several others as potential originators of the max distortion theory concept.
In any case, would it be a good idea for someone to create a distortion energy entry for the benefit of people who require a pedestrian understanding of this topic?
Thanks, Deltapapamike ( talk) 04:53, 8 June 2009 (UTC)
In the equation → (sigma1)^2-sigma1*sigma2+(sigma2)^2=3k^2=sigmaY^2 ...sigmaY above refers to the yield strength. This equation does not equal yield strength. This equation should equal Sigma_e (Von Mises stress in my mech. design book) or Sigma_v as denoted in this article. Someone take a look at this and fix if this is indeed incorrect. It could be confusing to someone if it is equaling the yield strength instead of the Von Mises stress. I realize that for the Von Mises failure criterion sigma_e=Sy÷n where n is the safety factor and if it is 1, Sy can = Sigma_e but this is not always the case pbviously. So this formula should be changed. 192.91.173.36 ( talk) 21:20, 17 December 2009 (UTC)
I believe tau13 should be tau12 in the conditions column. I'm not involved in this article. Someone please change it, it's really bugging me. Thanks.-- 67.59.60.122 ( talk) 12:37, 14 December 2011 (UTC)
I like to use (tau) for shear stress, to help make it obviously different from normal stress. All my engineering books use tau for shear. I realize that some/older books use sigma for both kinds of stress. I know of one asme code that uses it both ways. Is there and advantage to using sigma for shear stress? Is tau typically used for something else? -- Zojj t c 19:20, 25 February 2012 (UTC)
I don't understand the formula for the deviatoric stress matrix as specified in the article,
shouldn't it be something like
cheers / Baxtrom ( talk) 12:41, 29 February 2012 (UTC)
sanpaz ( talk) 17:23, 29 February 2012 (UTC)
Why is there no hint about the physical reasoning that lead to the development of the von Mises yield criterion in the first place? It was well known that shear stress is what drives ductile yielding. This is the reason the Tresca (max shear) criterion was developed. But in multi-axial loading (more than just pure shear and simple tension/compression), it was noted that Tresca led to incorrect (conservative) predictions of yield, and that indeed there was need for terms in the failure criterion that coupled stresses in different directions. So, von Mises proposed that the stress components be decomposed into a hydrostatic (average normal stress) component, and whatever was left over to get the original stress state back (the deviatoric component). He then proposed that the hydrostatic component (because it involves no shear) be ignored, and worked only with the deviatoric component. Using the generalized Hooke's law, he calculated the strain energy density of only the deviatoric component for general 3-D loading.
He then proposed calculating the deviatoric strain energy density for any specific loading under consideration, and comparing it to the deviatoric strain energy density of a specimen in simple tension or compression at yield. When the two are equal, the specimen will yield. This leads to the conclusion that when the von Mises stress reaches the tensile yield strength of the material, yield occurs.
So, the statement at the end of the section "This implies that the yield condition is independent of hydrostatic stresses" is misleading. That the yield condition is independent of hydrostatic loading is not implied by the von Mises criterion. It was explicitly assumed from the start. — Preceding unsigned comment added by 157.201.95.254 ( talk) 22:11, 21 October 2013 (UTC)
The lede is
"The von Mises yield criterion [1] suggests that the yielding of materials begins when the second deviatoric stress invariant J_2 reaches a critical value.
Does the Wikipedia community wish to limit its audience to those who understand all of that introductory sentence? So for example, does Wikipedia want to exclude every reader who doesn't understand the term "second deviatoric stress"? — Preceding unsigned comment added by Mcamp@cinci.rr.com ( talk • contribs) 00:20, 15 May 2015 (UTC)
NearlyMad, you reinstated an edit I reverted. Putting aside the "minor" incorrect marking issue, and the possibility of scientific inaccuracy, there are at least concerns:
I know the article is not in great shape and I have done little if any to correct that, but that is not a reason to deteriorate it further. Tigraan Click here to contact me 18:18, 18 October 2016 (UTC)
Trigaan I am trying to make this article a little more useful. I have been providing edits to this page for over ten years (under various usernames). The applicability of any engineering/scientific information must be listed before the information is presented. If you can't see this value within the article I'd have to assume you are not well versed in it and question why you are editing it. As for inline citations, I was not aware of them and as a courtesy you could have added them then told me it should be done.
I have been dealing with von Mises criterion for over thirty years, it's a fascination with me. It is obvious Wikipedia does not need any help from someone with sufficient and adequate knowledge and experience. Good luck, I'll quit watching this page.
Joseph L. Moore Senior Aerospace Engineer NASA
@ NearlyMad, provide a more specific citation on this comment:
"Although the given criterion is based on a yield phenomenon, extensive testing has shown that use of a "von Mises" stress is applicable at ultimate loading "
I have read through the Timoshenko text and I cannot find information that agrees with your statement.
Timoshenko makes reference to R. v. Mises in a footnote on p478 in a discussion about the development of the maximum strain energy theory. He goes on to mention “recent experiments” that showed correlation between maximum strain energy theory and maximum shear theory, and notes that “in most cases the difference between these two theories is not so large as to make it of practical importance”. However, these discussions are focused on defining the yield point for ductile materials, not ultimate failure, so I do not believe it is relevant.
Later, on p482, there is a reference to “very extensive experiments” and a footnote regarding applying the theory to ultimate stresses, but this is explicitly noted in reference to brittle materials.
I should point out that all of my references above are in “Part II” of the text. Your citation notes “Part I”, but I have not been able to locate a reference to von Mises in that portion of the text. 216.243.30.3 ( talk) 22:13, 5 January 2024 (UTC)