Talk:Stress (physics)

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1 Brittle and ductile
2 This is an article about stress
3 Mohr's circle
4 Microscopic Interpretation of Stress Force
5 Cauchy v. Piola–Kirchhoff
6 Title
7 Stress as a vector
8 formatting
9 force on cube face
10 Extending side menu: Continuum mechanics
11 Poisson's Ratio
12 Residual Stresses
13 Tensor notation
14 Stresses in Equilibrium
15 Thermal Stress
16 Intro cleanup
17 Re arrenging the whole article
18 Premature FAC withdrawn
19 Consistency of invariants

[edit] Brittle and ductile

I am skeptical about "By definition, brittle materials fail under normal stress, and plastic or ductile materials fail under shear stress." Don't ductile materials undergo plastic yield before failing whereas brittle materials simply break? (I am in the midst of a stress class; if nobody touches this, I'll come back to it later.)

I added this statement, and agree that it is simplified and can be improved. Please do.

However, I don’t believe the statement is false. Its not only that brittle materials simply break; they break in an orientation where the greatest normal stress is seen. And ductile materials do yield before breaking, but in the orientation of maximum shear stress, and plastic flow is a result of shear stress.

By the way, you can sign and date stamp your talk entries with four tildas (~~~~).

Duk 21:30, 16 Oct 2004 (UTC)

I disagree with the anonymous poster. The article is correct, as is. The above statement by Duk is indeed accurate, and very well written. --Simian, 2005-10-03, 06:44 Z

[edit] This is an article about stress

This is an article about stress. Stress can occure in solids, liquids and gases so it is unhelpful to turn this into an article about stress in solids. I think that it would be systematic to confine discussions about brittle and ductile fracture to the article fracture which really could do with turning into a decent article. Cutler 12:10, Oct 17, 2004 (UTC)

sounds good. Duk 02:48, 19 Oct 2004 (UTC)

I think the article is excellent, as is. It briefly mentions these terms in one or two sentences, as it should. Then if the reader wants further information, (s)he simply clicks on the links. The stress article should briefly mention this as it does now, and is very well written. --Simian, 2005-10-03, 06:44 Z

[edit] Mohr's circle

Rankine the pioneer of Mohr's stress circle? See Talk:Christian_Otto_Mohr#Rankine —DIV (128.250.204.118 06:42, 14 May 2007 (UTC))

Should this be a short summary of Mohr's circle and a link to the Mohr's circle page? Bradisbest 20:38, 25 October 2007 (UTC)

Sure. At least remove the steps and figures. -Fnlayson 20:46, 25 October 2007 (UTC)
Done. -Fnlayson 21:24, 25 October 2007 (UTC)

[edit] Microscopic Interpretation of Stress Force

I am missing any reference to the microscopic interpretation of the stress force in the article, and in particular to the fact that the stress/strain curve is only linear (i.e. obeys Hooke's law) over a much smaller region than one should expect if molecular forces are responsible. I have discussed this issue on my page http://www.physicsmyths.org.uk/hooke.htm and suggested there that in fact plasma polarization fields due to free electrons in the material might actually be responsible for the linear stress/strain curve in the Hooke-region.

Thomas

[edit] Cauchy v. Piola–Kirchhoff

There should be some discussion here about the distinction between the Cauchy and the Piola–Kirchoff stress tensors (corresponding, I believe, to true and engineering stress respectively.) —BenFrantzDale 15:59, 11 October 2005 (UTC)

I feel that we should resist the temptation to make this article too complicated and off-putting. Most people who come here will simply want to know the difference between stress and strain without any math. Technical points like this should go to stress tensor. Cutler 18:45, 11 October 2005 (UTC)

~~If BenFrantzDale is in agreement, this sounds like a good suggestion by Cutler. This does seem to be a perfect fit for the stress tensor article. --Simian, 2005-10-14, 04:22 Z~~

I agree, except that stress tensor has something to do with relativity. Perhaps there should be a new page for the nitty-gritty details of stress tensors in engineering? —BenFrantzDale 04:48, 14 October 2005 (UTC)

Good point. That page states up front it's devoted to relativity. So I currently retract my previous comment, and my two posts here can be deleted by the next editor. --Simian, 2005-10-14, 13:05 Z

Gonz - I agree.

I think that the discussion of Cauchy stress vs. Piola-Kirchhoff stress does have a place here. If this article is meant to represent the Continuum Theory of stress it is important to make the distinction between the two stress. They are theoretically and physically easy to understand as to not be "off-putting" yet at the same time important to the development of constitutive laws (where Cauchy is most often used) as compared to actual physical measurement (where the 1st P-K is most often used). A statement as to the conditions where these stresses are equal would be helpful as well.71.199.128.182

[edit] Title

This title is inaccurate. It should read either Stress (Mechanical Engineering) or Stress (Applied Physics).

'Stress (mechanics)' would be better, keeping both physicists and engineers happy. I've changed the first sentence to reflect this and link to mechanics. RDT2 09:49, 15 August 2006 (UTC)

Agree with 'Stress (mechanics)'. And I moved the 'Continuum mechanics' box to the top. --Duk 18:33, 14 January 2007 (UTC)

Agree with 'Stress (mechanics)'. Proposed merger with tensile stress. Katanada (talk) 23:47, 16 December 2007 (UTC)

[edit] Stress as a vector

In Voigt notation, stress is written formally as a column 'vector' simply to allow the fourth-order elasticity tensor to be written as a square matrix on a flat sheet of paper. However stress is a tensor and calling it a vector has misled generations of students. The sentence 'Simplifying assumptions are often used to represent stress as a vector' could simply be deleted. RDT2 10:03, 15 August 2006 (UTC)

I was bold and went ahead and made the change. —Ben FrantzDale 11:54, 15 August 2006 (UTC)

I think the reason people sometimes mistakenly believe that stress is a vector is because it's so often used that way in everyday calculations. Understanding how and why this comes about should be mentioned in the article. Maybe not in the intro though. --Duk 18:13, 14 January 2007 (UTC)

[edit] formatting

why are so many phrases in boldface? this is distracting and makes the article more difficult to read. i suggest that boldface be removed from everything that doesn't need special emphasis (such as the examples of what constitutes a one-dimensional system and every single appearance of the word stress).

[edit] force on cube face

The force on the cube face is stress*dA, not dV. I've reverted to the previous version.RDT2 10:25, 19 October 2006 (UTC)

[edit] Extending side menu: Continuum mechanics

Hi, I have updated the article about Strain and I think that it should be in this side menu Continuum mechanics, but I don't know how to add it. How do you customise side menus?

Janek Kozicki 13:31, 21 November 2006 (UTC)

I added it to the menu. In the future, you can edit by entering "Template:Continuum mechanics" in the search bar. PAR 17:29, 1 December 2006 (UTC)

great, thanks! Janek Kozicki 21:14, 3 December 2006 (UTC)

[edit] Poisson's Ratio

In the section dealing with nominal and engineering stress, it said "its cross-sectional area reduces by an amount that depends on the Poisson's ratio" I changes this to "may change" to reflect a more general condition where the material my have a negative or zero Poisson's ratio. 71.199.128.182

[edit] Residual Stresses

"Press fits are the most common intentional use of residual stress." I think this statement needs to be modified if not removed completely. It is unclear what is meant by "most common" and intentional. Many biologic tissues exhibit residual stresses. This is intentional as it helps the tissue function and is more common in the fact that many animals have tissues with residual stresses. I would propose "In material manufacturing, press fits are the most common intentional use of residual stress."71.199.128.182

[edit] Tensor notation

We have three different tensor notations in this article; $σ j i$ , $σ i j$ , and $σ$ & $τ$ . Should try to be more consistent here ? --Duk

[edit] Stresses in Equilibrium

70.51.153.89 made a good point in his/her edit.

The 3-d Cauchy stress tensor shown is only valid in equilibrium, unlike the corrected:

$\sigma_{ij}= \left[{\begin{matrix} {\sigma _x } & {\tau _{xy}} & {\tau _{xz}} \\ {\tau _{yx}} & {\sigma _y } & {\tau _{yz}} \\ {\tau _{zx}} & {\tau _{zy}} & {\sigma _z } \\ \end{matrix}}\right]$

In equilibrium, $τ y x = τ x y$ , $τ z x = τ x z$ , and $τ z y = τ y z$ , so the filled matrix becomes symmetric. The article is about Stress, however, not Stress in Equilibrium.

I'll correct this tomorrow unless someone objects.

MinstrelOfC 00:06, 24 February 2007 (UTC)

I've made the change, and added some explanation. If someone can add how one may make the matrix symmetric when not in equilibrium, please do. About all I know is that it involves a virtual force, and expressing

τ y x

(etc) as a function of

τ x y

. MinstrelOfC 19:20, 25 February 2007 (UTC)

[edit] Thermal Stress

There is no apparent mention/disussion about thermal stress specifically (the thermal stress page just redirects to the article for this talk page, hence why I'm here).
The reason I mention this is that it's an important factor for things like computers, or any precise mechanics/electronics. -- Lee Carré 03:09, 2 May 2007 (UTC)

I think thermal stress is just stress resulting from strain resulting from thermal expansion. It may deserve mention here, but I think there's nothing special about thermal stress other than that it is an important source of stress.—Ben FrantzDale 17:30, 12 July 2007 (UTC)

[edit] Intro cleanup

I was reading this page to look up the difference between stress and strain, since I can never remember which is which. After reading the first paragraph and getting zero understanding, I found the Strain link, and became enlightened by that page. This suggests we need a better layman's description of what stress is before jumping into tensors. Unfortunately, I don't have sufficient background to myself write something simultaneously accurate and legible. I suspect something like the second paragraph, cleaned up, would make a good intro. Given how interwoven the two concepts are, I'd also expect an early sentence about the relation between stress and strain, and particularly how they differ. Bhudson 17:11, 12 July 2007 (UTC)

I just added this sentence to the end of the first paragraph: "In short, stress is to force as strain is to elongation." Does that help? —Ben FrantzDale 17:28, 12 July 2007 (UTC)

Somewhat, but the entire article is somewhat hard to follow and not helpful in many respects. I have a degree in engineering and the leap to advanced stress concepts jumps the gun a little to fast.—Preceding unsigned comment added by Dj245 (talk • contribs)

I wouldn't call it perfect, but it's much better; thanks. Bhudson 19:51, 16 July 2007 (UTC)

[edit] Re arrenging the whole article

I see a lot of things that need to be improved about this article. The first one: the logical order of sections. The article should start, after the introduction, with the Cauchy stress principle section. Here, the principle is stated and derived and the concept of stress vector is obtained. Then the the article should talk about "state of stresses at a point" in a continuum, which will lead to the definition of the stress tensor. The second section has to be the relationship between stress vector and stress tensor and the transformation of the stress tensor into other coordinate system which in fact defines it as a tensor. The Third section will the symmetry of the stress tensor, with its demonstration. The Fourth section would deal with the Stress Invariants (Principle stresses). The Fifth section would deal with the Stress Deviator Tensor. Other sections: Octahedral stresses and stresses in 2D. I know these are a lot of changes, but I think they are very necessary for the improvement of this article. Am I in the correct path here? Please comment.Sanpaz (talk) 00:39, 16 January 2008 (UTC)

I re-wrote the whole Cauchy's stress section. The previous version was not cohesive, stated many things without an particular order, and lacked mathematical development. I tried to include all the main things that were included in the previous version. However, somethings were left as they do not belong in this section. I am trying to include them in other parts of the article so those statements are not lost. I know it is very radical change but I think it was necessary. Please comment. Sanpaz (talk) 01:07, 30 January 2008 (UTC)

I deleted the section named Stress in three dimensional bodies. The reason for this is that the concepts of hydrostatic and deviator stress are already included in their respective section. And the stresses for a viscous fluid are in fact a topic related to a constitutive equation that relates stress and strains (e.g. hooke's law). In other words, this concepts do not explain what stress is but rather explain the behavior of a body subjected to loads. Therefore, it should go somewhere else (any suggestions where it can go?) Sanpaz (talk) 23:10, 9 February 2008 (UTC)

Cauchy stress tensor for a viscous fluid

For viscous fluids the Cauchy stress tensor

σ

is defined as:

$\ \sigma_{ij}=-p\delta_{ij}+\lambda^*e_{kk}\delta_{ij}+2\eta e_{ij}$

If the fluid is incompressible it follows that:

$p = \frac{\mathrm{tr}(T)}{3} = \frac{\sigma_{11} + \sigma_{22} + \sigma_{33}}{3}$

If the fluid is compressible the assumption above is true, if the viscosity of compression $\ \mu_D$ vanishes:

$\mu_D = \lambda^*+\frac{2}{3}\eta$

I deleted two sections; 1D stresses and 2D stresses. All the conntent of the 1D section is included in the new section called stress conditions. However, the content of the 2D stresses was not all included. The reason for this is that most of that section was about principal stresses which is already explain it the section Principal stresses and stress invariants; and the paragraphs about the morh circle should go in the Mohr circle section. Sanpaz (talk) 23:38, 9 February 2008 (UTC)

Please, review all the changes made. All of them where made with the intent of improving the development of the topic. I tried to keep all which was written before about stress in the previous articles. If I missed something, please include it in the new article. Comments? Sanpaz (talk) 23:42, 9 February 2008 (UTC)

I remember this article sucking the last time I viewed it. Your changes are excellent, thank you so much! — Ben pcc (talk) 19:21, 21 March 2008 (UTC)

[edit] Premature FAC withdrawn

Wikipedia:Featured article candidates/Stress (physics)/archive1. SandyGeorgia (Talk) 19:58, 23 April 2008 (UTC)

[edit] Consistency of invariants

In the section derivation of principal stresses and stress invariants, $I 2$ is included in the characteristic equation with a positive sign. In Invariants of the stress deviator tensor, $J 2$ is included with a negative sign. This introduced an sign error in the expression for $I 2$ , which I corrected. For consistency, I feel that either the sign of $I 2$ or the sign of $J 2$ must be corrected. Yet, I feel reluctant to choose, since $I_2 = \sigma_1 \sigma_2 \ etc.$ seems better without a minus, and $\sigma_e = \sqrt(3J_2)$ too. Any input how this is in the textbooks? Martenjan (talk) 10:22, 10 June 2008 (UTC)

I see the mistake. Thanks for the correction. In the textbooks the characteristic equation appears with either

- I 2

+ I 2

. I don't have a reason to go one way or the other. Sanpaz (talk) 14:45, 10 June 2008 (UTC)

The signs of the equations were correct. The way the equations and the invariants are presented is a matter of choice. Some books present the characteristic equation as

$\ -\lambda^3 + I_1\lambda^2 - I_2\lambda + I_3=0$

$\ +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$

$\ +\lambda^3 - I_1\lambda^2 - I_2\lambda - I_3=0$

I could not tell you which one is "better" Sanpaz (talk) 20:36, 10 June 2008 (UTC)

Expanding the determinant $\ \left|\sigma_{ij}- \lambda\delta_{ij} \right| \$ always results in a minus sign before

λ 3

, making the first equal signs in the second and third equation false.

To find the eigenvalue

λ

, this determinant needs to be zero. Then, of course,

$\ -\lambda^3 + I_1\lambda^2 - I_2\lambda + I_3=0$

has the same solution as

$\ +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$

Would we have defined

I 2

with a different sign, as I presume is the case for books in favor of the third equation, then the third is correct too.

My solution to keep the plus sign in front of

λ 3

is to use the following equation

$\ -\left|\sigma_{ij} - \lambda\delta_{ij} \right| = +\lambda^3 - I_1\lambda^2 + I_2\lambda - I_3=0$ Martenjan (talk )(Dont' forget to sign your posts...)

The different equations (with different signs) are not "False". All of them are correct. The only difference between them is how you present the result of the different coefficients( $\ I_2=\sigma_1\sigma_2+\sigma_2\sigma_3+\sigma_1\sigma_3$ or $\ I_2=-(\sigma_1\sigma_2+\sigma_2\sigma_3+\sigma_1\sigma_3)$ ), or if you multiply the equation by -1 or not. ~~But I would suggest using the first equation with the sign (-) first as this is how you solve first the determinant~~ The (+) equation is fine by me.Sanpaz (talk) 13:28, 11 June 2008 (UTC)

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