Talk:Young's modulus/Archive 1

Archive 1

Error in Table

The table units should read GPa, not MPa. — Preceding unsigned comment added by 163.1.243.243 (talk) 12:44, 6 December 2005 (UTC)

GPa

The units should be GPa, not MPa. I have compared the value for steel to a text book and the german wikipedia, which both state that steel has a young modulus of E = 210 000 N/mm2 (= 210 GPa). —Preceding unsigned comment added by 146.140.3.210 (talk • contribs)

Was changed by a recent edit, either clueless or vandalism. Reverted. Femto 11:14, 3 March 2006 (UTC)

Table section should be checked thoroughly

I think the table is inaccurate to say the least. For some of the materials the unit is GPa and some it is MPa according to my textbook. On some materials it isn't even the correct table column the data is from. Let's take aluminum as the example. According to this wikipedia article, young's modulus is 69 GPa, but this is a wrong lookup. My textbook says that its space-expanding-coefficient is 69 * 10^(-6) K^(-1), and the correct value in Pa is in another column(!). The correct value being 13 * 10^(-12) Pa^(-1) (That's 13 MPa). My point is that the table should be removed until it has been thoroughly checked and corrected, and the data should come from a place where we can be sure that there are no legal issues. Last but not least, this discussion is very messy and should be organized a bit. I have a report due in 4 hours, so i might come back and fix it later.—The preceding unsigned comment was added by 80.62.69.154 (talk • contribs) 02:19, 3 May 2006.

Um... what's a space-expanding-coefficient, and what's it got to do with this article? The Young's modulus of Aluminium is generally agreed to be about 69-70 GPa (see, for example, Aluminium or this course slide from a Cornell university course, or numerous other places) Note also the title "approximate values" and the comment "the value for [...] metals can vary by 5% or more[...]" preceding the table). If you can spot any specific errors (and come up with a decent source for a better value) then, by all means, raise it here. However, most of these values are easily checked in engineering or materials science textbooks; all the metals listed look about right to me, from my recollection of my studies; the other materials don't appear outrageous, either. Finally, the young's modulus of any given material is a physical property, which as far as I know, can't be copyrighted. If this table was copied wholesale from another source, then there would be copyright issues. That did happen at some point in the history of this article, but it's been extensively edited and expanded since then, so I'm pretty sure it's no longer a problemBlufive 19:16, 3 May 2006 (UTC)

---

The table appears to be a direct copy from

http://phyastweb.la.asu.edu/classes/phs581-culbertson/students/youngsmodulus/Youngs_Modulus.html

Does HFastedge have permission to use this material?

I found the same table at http://www.answers.com/topic/young-s-modulus. However, the heading for E on that table states the units as GPa, rather than MPa - anyone know which is correct? (the la.asu.edu url 404ed on me, so I can't compare) Bewildebeast 23:08, 4 December 2005 (UTC)

Well you would find the same table in answers.com, since they have become mostly a wikipedia clone site, but I don't think anyone can copyright actual facts. Like, if I found a site that gave the melting points of certain materials (at a certain pressure), I could use it here because facts are facts.--User:Rayc 18:16, 20 December 2005 (UTC)

---

There seems to be an inconsistency in the dimensions in this article (or I don't understand it): Young's modulus (or modulus of elasticity) has units Pa (N/m2), it says in the table. But in the equation below, energy (N m) is equal to modulus of elasticity times length. So modulus of elasticity has units N.

Modulus times length. (N/M^2) times M = N/M modulus times length = energy. no inconsistency just be careful when you parse the english to get which is supposed to be multiplied by what to equal what.

Furthermore, Young's modulus is the slope of the stress-straincurve, hence has units of [stress]/[strain]. But in the article Stress, I read that the unit of stress is Pa. So strain is dimensionless? Mtcv 14:39, 28 Jun 2004 (UTC)

In Wikibooks Solid Mechanics they say that in fact strain is dimensionless. That leaves open my first question. Maybe x (bottom of page) is dimensionless? Mtcv 14:48, 28 Jun 2004 (UTC)

Strain is dimensionless, it is easiest to understand engineering strain which is roughly current length / initial length in the case of 1-D tensile loading (for small displacements). So yes Young's Modulus has the same units as stress. It's a weird way of looking at it, I agree, but it is self consistent. As strain has to be the same when the material is feeling the same deformation. If the bar is 1 inch long or 15 feet long they should ideally have the same values of strain when they are equivalently deformed, which should be a much larger length for the 15 foot bar vs the 1 inch bar.

---

There are problems with article: e.g. locusts are not viviparous, so the first entry is invalid. This appears to be a "cartographer's error" to keep track of where this information is copied. (And it appears to be extensively copied.)

The lambda variable (λ) is in units of force - it is the product of the modulus of elasticity (force/length²) and the cross sectional area (length²) of the object. (The area of a slice taken perpendicular to the direction of "l".) That is the reason for the discrepancies noted above. Yes, strain is expressed in terms of length/length.

---

Oh boy, where to start. I've just done one small change, but I want to do more in the near future. Just so I don't surprise anyone too much, here's what I want to go at:

• Add notes about directional materials (wood, fibre-reinforced plastic composites)
• Add notes about variety of values for metals; (most metals come in a variety of alloys (especially steel, which is a term defining a whole group of alloys) and individual alloys can vary by at least as much as 5% from a nominal "pure" metal)
• Overhaul the table:
  • Remove the column giving values in GPa; it's pretty much redundant - values will just be the MPa values divided by 1000.
  • Amend values for metals to 3 significant figures; Quoting values for metals to five/six significant figures is pointless (see alloys above)
  • What materials should be included? I reckon we should have:
    • Common engineering materials
    • A few "ordinary" things that readers will encounter in day-to-day life
    • Some extremes
  • Remove the "pregnant locust" item; I agree with the anonymous user above, it's probably a deliberate error to catch copyright violations.
  • Remove plywood unless I can get a better value; Wood is a directional material (as already noted); plywood, being an assembled composite based on wood, will have a lower (but less blatantly directional) value. I reckon the plywood value should just be removed unless we can get a much more tightly-defined (and correct) value for it.
  • Remove Beryllium; AFAIK, it's not a significant engineering material (being toxic and difficult to work, amongst other reasons)
  • Add some common composites (GFRP, CFRP, maybe even Boron fibre composites)

Plus anything else I think of  :) Blufive 13:26, 16 Jan 2005 (UTC)

http://en.wikipedia.org/wiki/Beryllium Beryllium is a very useful material, higher modulus than steel, resists corrosion, good X-ray transparancy, light weight. It's a little exotic due to processing difficulities (i.e. toxicity of related compounds) but it's a very useful material, albiet a little expensive.

---

Maybee add some more common plastics to this list? I noted Polystyrene on one of the tables, but maybee a material with a much lower modulus like Polyethylene or polypropylene for reference. CoolMike 20:53, 27 Feb 2005 (UTC)

Done. --203.206.18.96 12:05, 21 August 2005 (UTC)

Isn't Young's modulus basically the modulus of tensile stress? On the other hand, the modulus of elasticity is a very generalized term, referring to the relation between stress and strain in general, as part of the Hooke's Law; whereas Young's modulus is associated with tensile stress only. It seems that defining the Young's modulus as the modulus of elasticity would be inaccurate, as is mentioned in the first line of the article- ....Young's modulus (also known as the modulus of elasticity or elastic modulus).... — Preceding unsigned comment added by 210.211.165.78 (talk) 15:40, 9 November 2005 (UTC)

F/A0 + 0?

why is there a + 0? should there be a note explaining this? Bungalowbill 15:17, 16 May 2006 (UTC)

"The Young Modulus"

As I mentioned above, every reference I've ever encountered to this property (which is a quite few, given that I studied engineering at university) including the dead-tree edition of Britannica downstairs, is as "Young's Modulus". Since there have now been a couple of editors suggesting "The Young Modulus", I've amended the "also known as" to include that form, but that's as far as I'm willing to go unless someone can come up with several substantive cites for "The Young Modulus" (fx: kicks self for fact that all my relevant textbooks are inaccessible right now) Blufive 18:54, 16 May 2006 (UTC)

Water?

Can anyone come up with a cite for the figure for water that just got added? I assume the value is under compression, while confined, as any other situation seems seems kinda bizarre with respect to a liquid. Unless the value is for solid water (which is to say, ice). The value given, however, does seem to match the value included for water under bulk modulus - in which case it can't be the correct value for the Young's Modulus, surely? (see elastic modulus for the relationships between values) Blufive 19:15, 26 May 2006 (UTC)

OK, I've removed water from the table. Per the bulk modulus article, Bulk modulus is the only elastic modulus which is meaningful for non-solids. The value quoted appeared to be the bulk modulus, in any case. Blufive 18:46, 27 May 2006 (UTC)

Conseqence of Pauli principle

"Young's modulus (as well as a bulk modulus of liquids and solids) is a mathematical consequence of the Pauli exclusion principle for fermions (electrons in the outer shell of an atom)."

Isn't it formally true only for compression and not for stretching? When atoms get closer, the electon wave function indeed has increased repulsion due to Pauli repulsion but when they get farther away, the overlap is lowered. When the chemical bond is stretched, it is the lower potential energy due to weaker interaction of the electrons with the nuclei that create this force and not Pauli repulsion. Poszwa 03:52, 9 June 2006 (UTC)

Table:Virus

Why is there a virus in the table? Maybe I don't understand...please enlighten me.Civil Engineer III 13:13, 22 June 2006 (UTC)

Virus shells are squishy too? This needs some cite and an explanation of its relevance, or it should be removed. Femto 16:45, 22 June 2006 (UTC)

No citation banner

I put up the no citation banner. I will try to remember to do some work on that myself. Notthe9 16:13, 10 November 2006 (UTC)

Symbol

Do people find Y the symbol used for the modulus in literature? It's used here as well as E (in the table).

This should be standardized. All texts I've referred to use E. --Eat411 08:58, 23 March 2006 (UTC)

Indeed, I have always seen E used to represent Young's Modulus. I am changing the article now. It can be reverted if there is good reason to use Y. Going through a few books here really quick, the following use E for the modulus of elasticity:

• Mechanics of Materials be Beer et. al.
• Theory of Elasticity by Timoshenko and Godbeer
• Advanced Mechanics of Materials by Boresi and Schmidt
• The AISC Steel Construction Manual
• The ACI committee 318 Building Code

I could name quite a few more if necessary. I've never seen Y. --Notthe9 15:30, 10 November 2006 (UTC)

Y is used quite regularly in journal articles (e.g. Physical Review Letters 95 195501), it should at least be mentioned in the article, though Ashby, "Engineering Materials 1" uses E 129.78.64.106 08:14, 23 November 2006 (UTC)

Units

How about make conversions to the International System? 87.16.128.181 (talk) 17:57, 22 February 2008 (UTC)

Definition

"It is defined as the ratio, for small strains, of the rate of change of stress with strain."

This sentence mixes up two things. Usually the Young's modulus is a property of materials which obey Hooke's Law. In the range of strains over which Hooke's law is obeyed the rate of change of stress with strain will be a constant and is called the Young's modulus. As per the definition of strain the intercept (of a stress strain plot) is zero so the ratio of stress with strain in the linear region is sufficient to calculate the rate of change.

Some fields extend the definition to be the rate of change of stress with strain for any material at any strain. This will give the same result for the range of strains over which Hooke's law is obeyed in those materials but makes the Young's modulus a function of material and strain instead of a material property. Under this definition it would be incorrect to state the Young's modulus of a material as is done in the table (You'd have to call it the Young's modulus at zero strain) and the integrals couldn't be simplified in the "Elastic potential energy" section so apparently there is some disagreement on this extension.

To say there is a disagreement on definition on the page as done here would be overstating it but the current sentence is just plain wrong. Any suggestions? 137.205.78.240 (talk) 12:47, 18 April 2008 (UTC)

Did the minimum to make this correct by removing "rate of change" feel free to improve. Additionally replaced for small strains with the more precise "in the region in which Hooke's Law is obeyed". 137.205.78.240 (talk) 12:09, 21 April 2008 (UTC)

Confusion of two topics?

quote from Young's modulus:

"In solid mechanics, Young's modulus (E) is a measure of stiffness. It is also known as the Young modulus, modulus of elasticity, elastic modulus or tensile modulus..."

this says that Young's modulus and the elastic modulus are the same thing, but there are different pages on each one. These pages need to be merged if they are the same thing or if not it has to be clarified what is going on. --LeakeyJee (talk) 02:09, 18 April 2008 (UTC)

If you look at the elastic modulus page you'll see that the Young's modulus is one of several elastic moduli but since it is the most widely used it's sometimes referred to as 'the' elastic modulus. You're correct that this could be clarified with something like "(though the Young's modulus is actually one of several elastic moduli such as the bulk modulus and the shear modulus)" after elastic modulus instead of "(the bulk modulus and shear modulus are different types of elastic modulus)". 137.205.78.240 (talk) 12:47, 18 April 2008 (UTC)

well perhaps you or someone else with more knowledge on the subject than me could remedy this? --LeakeyJee (talk) 15:24, 19 April 2008 (UTC)

Done.137.205.78.240 (talk) 11:54, 21 April 2008 (UTC)

cheers! --LeakeyJee (talk) 14:09, 23 April 2008 (UTC)

Please add relations to longitudinal/shear wave speeds

. . . which are very important for anyone dealing with waves in solid media.

Vs=sqrt(G/rho)=sqrt(E/(2rho*(1+PR)); shear wave speed where E - Young Modulus; rho - density; PR - poission Ratio; Vl=sqrt((K+(4/3)*G)/rho)) - logngitudal wave speed

and so on . . . —Preceding unsigned comment added by 130.159.254.2 (talk) 11:53, 5 May 2008 (UTC)

Mtcv is right

Y is in newtons, extension/linear-strain is dimensionless .. i am working on an elastic-space model of elementary particles with cores of temporal curvature. a summary page of this idea can be found at msu.edu/~micheal/physics/ i am also interested in creating a new wiki page about Young's modulus of space or adding that concept to this page. Y₀ = h-bar/2l_Pt_P appr.eq. 10⁴⁴ N. i'm also working on a layperson's version of Gravitation and Elementary Particles called N and Omega. let me know if you're interested in a copy, sam micheal, &Delta (talk) 22:29, 4 November 2008 (UTC)

Soils or coils?

QUESTION: Soils? should that be coils??? —Preceding unsigned comment added by 221.249.82.13 (talk) 01:35, 27 February 2009 (UTC)

As far as I can tell it should be soils, because Young's modulus is a material property. Wizard191 (talk) 18:21, 27 February 2009 (UTC)

Just a suggestion

To quote from the article, This can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. Perhaps we ought to mention that this data can be obtained by compressive testing, too.--Nick 18:54, 15 January 2006 (UTC)

To keep it simple, perhaps we ought also to mention that Young's modulus is the stress required to halve, or to double, the length of the specimen under test (depending on whether the test is compressive or tensile). Mind, my physics is pretty rusty, so this might be downright wrong. --Nick 19:02, 15 January 2006 (UTC)

Sorta-kinda. (Disclaimer: it's late in the day, my engineering is seriously rusty, and I've been consuming some of the west country's finest so I'm slightly addled). If memory serves, the definition of YM assumes, and hence the formulae given here are only correct for, small deformations. Basically, strain is somewhat non-linear, so when the deformation starts to get to be the same order of magnitude as the initial size of the sample, the numbers get messy (I think that's due to complications like Poisson's ratio and hence shear stress starting to kick in as the deformation starts to get more than one-dimensional). A strain of 0.05 is pretty huge, as far as something like a bridge or a wing is concerned, and few engineering materials can withstand that much deformation without plastically deforming anyway. However, if a material were to stay elastic, and maintain a constant YM, the YM does correspond to the force required to double the length of a sample under tension. Not so sure about compression, though (if nothing else, double length = strain 1, half length = strain -0.5; at which point the formulae given on this page don't work any more) Given all those caveats, it may be better to leave it out, to avoid confusing people, or at least putting it down the bottom in some sort of "vaguely interesting but complicated stuff" section, well away from the main definitons. Blufive 21:25, 5 February 2006 (UTC)

Oh, and one last thing, I'm not sure that Young's modulus is a measure of stiffness. Elasticity, surely?--Nick 19:10, 15 January 2006 (UTC)

Well, formally, it's the "modulus of elasticity". In plain English, it's a measure of how stiff things are. The higher the number, the stiffer something is. So, technically, you're correct - but the meaning of "stiffness" is clearer to the lay reader, IMO. Blufive 21:25, 5 February 2006 (UTC)

A grammatical point: i was lead to believe that the correct term is specifically "The Young Modulus":- not "Young's Modulus". However, i suppose that when in general reference "Young's Modulus" may be correct but when refering to a specific material the correct reference would be "The Young Modulus of (eg) Iron" I can't seem to find anything supporting me on this but wondered if anyone had any furthur knowledge of this. [The previous comment added by Silvarbullet1 Blufive 21:25, 5 February 2006 (UTC)]

When I studied engineering, everyone, and I mean everyone, teaching the course referred to it as "Young's modulus". Regardless of how correct that is grammatically, that's what everyone calls it. Personally, I think that's grammtically good, too. Blufive 21:25, 5 February 2006 (UTC)

One suggestion for consideration - report Young's modulus in psi/ppm. First - it cuts back on counting the 0's. Aluminum is around 10psi/ppm; Steels are about 30psi/ppm; plastics about .25 psi/ppm. Second, thermal coefficient in deg F/ppm is around 6 deg F/ppm. Divide one by the other and you easily get psi/deg F or deg F/psi Third - the values are more tangible - a 10 pound weight on a 1 inch square aluminum support 1 inch high compresses it by 1 millionth of an inch. Warm it by six degrees F and it's almost back to where it began. —Preceding unsigned comment added by 70.238.137.66 (talk) 04:15, 18 December 2010 (UTC)

Young's modulus is named for Thomas Young. See http://en.wikipedia.org/wiki/Thomas_Young_%28scientist%29 Also, in the Usage section "The Young's modulus calculates the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads." seems awkward. Maybe - Young's modulus is used to calculate the change in the length of an isotropic elastic material under tensile or compressive loads. —Preceding unsigned comment added by 70.238.137.66 (talk) 04:25, 18 December 2010 (UTC)

Table Glitch

Does anyone know why the table is glitching? It has odd ASCII caracters instead of hyphens and superscripts. Specifically: – and  I see this sort of thing a lot in Wikipedia; I don't know if it is a browswer issue. (I'm using IE 7.0) If I try editing it, it shows up correct in the preview, so it looks like there is something wrong with going from there to the actual page. 65.200.157.177 (talk) 14:30, 9 May 2011 (UTC)

Must be your browser or language settings on your computer because it looks fine to me and you say its not just this article. Wizard191 (talk) 21:24, 9 May 2011 (UTC)

Young Modulus or Young's Modulus?

It would appear that the CIE examination board terms Young's Modulus as the Young Modulus. Is this a widespread thing, just a British thing, or is it just a weird thing about the A level curriculum? I could find no mention of it being termed Young Modulus in the article, and outside of exams, I have never heard it called Young Modulus, even my teacher calls it Young's Modulus.

Of particular note, even the Cambridge University website calls it Young's Modulus, which would contradict their examination board.

Maybe the article should make mention of it being called Young Modulus?

Beaver225 (talk) 00:59, 23 November 2011 (UTC)

The way more common form is Young's modulus. There are a few occurences without the 's, but these seem to be mistakes or something local to Cambridge. So change I will things back. --Ulrich67 (talk) 21:50, 12 January 2012 (UTC)

Images

What are the best illustrative images to show? the current image of 'searle's apparatus' is not helpful, of poor quality an not even discussed in the text. it should be removed. — Preceding unsigned comment added by 128.36.206.78 (talk) 12:39, 20 April 2012 (UTC)

Agreed and removed, thanks for pointing that out. Mikenorton (talk) 13:04, 20 April 2012 (UTC)

This article desperately needs a diagram pointing out the key variables and their direction (F, L0, delL and A0) - similar to the one in the article for the Shear modulus.128.187.97.26 (talk) 15:23, 29 May 2013 (UTC)

Young's modulus and Hooke's Law

The relationship between E and Hooke's k is not clearly spelled out in the article, i think this needs addressing by someone with a bit of expertise in this area. Furthurmore it is not made clear that E is only a (very useful) linear approximation to what is essentially a non-linear property, instead the article state "for small strains", which is not *strictly* true, it is actually valid for strains small enough to give a linear stress-strain response, which to some degree is up to the engineer.

As a second point heat treatment and composition are the only things listed in the small disclaimer at the start of the table, really there are many other properties of the microstructure (natural ageing) etc that can affect this, I would suggest that a better sentence state "Dependant on the exact nature of the microstructure of the material, which can be affected by processes such as heat treatment and minor compositional differences in the material" 129.78.64.106 08:37, 23 November 2006 (UTC)

I hope to have clarified in the "linear vs nonlinear" section the problem of Hooke's law as an approximation. It is a bit verbose now, but something had to be done IMO.Tigraan (talk) 17:11, 27 June 2013 (UTC)

Carbyne

The modulus for carbyne listed in the table was >10 times too large, and was based on a misreading of the cited paper (which was, admittedly, confusing). The authors focus on "specific modulus", not modulus per se, and they quote a modulus value for a single strand based on a peculiar notion of its radius (less than a standard atomic radius) and hence an unrealistic cross-sectional area for a strand in a solid.

The number I inserted has the virtue of not being wrong by an order of magnitude, but I urge someone to examine the paper more closely and extract a more accurate value from the numbers they give for specific strength. This requires a density for the hypothetical carbyne material. 86.149.137.103 (talk) 20:32, 7 June 2014 (UTC)

After 25 years..

after 25 years, i finally found a researcher who is investigating elementary particles as elastic deformations in space-time - paralleling my own developments but much more formally. he may claim to be doing otherwise, but his work is Foundational in this realm. his name is Markus Lazar and you can find his papers at arXiv by clicking on his name. we are not associated in any way - so please do not tarnish his image by linking him with me. (i encountered this issue with a french associate who objected to my use of the word 'associate'.) i have recommended developing decisive tests to him and await his reply.. if his ideas survive the test of time and come to be recognized as central to the unification issue in physics, my work here will be largely done (at least in the physics realm) .. you can find some of my work at: temporal curvature and N and Omega. my name is sam micheal and i sincerely wish you a happy thanksgiving and merry christmas.&Delta (talk) 05:42, 24 November 2008 (UTC)

"my work here" rich 84.227.254.106 (talk) 07:12, 18 August 2014 (UTC)

Examples for usage

It is a good idea to have some examples for usage of the Young's modulus. Currently the "examples" are are or less repeating the definition and are rather similar to the part describes under Calculation. The application from geology (oil and gas) is however a rather bad choice. Here the young's modulus is just one of maybe hundreds of parameters - likely one will even prefer using the bulk and shear modulus instead of Youngs's modulus and Poisson's ratio. The elastic properties enter somehow, but this is far from obvious how. Even it a reference for this example is given, I strongly suggest removing it, as it does not help the typical reader. There are many more examples that have much closer relation to day to day life. The important part to the young's modulus is, that it is made for applications with uniaxial stress, like tension on a wire or load an a column.--Ulrich67 (talk) 19:09, 16 September 2014 (UTC)

Actually, Young's modulus is considered to be one of five or six critical parameters in evaluating unconventional fields. Given the importance of tight oil and gas, this is as critical as other examples given. I think that its use in geophysics also demonstrates the broad applicability of the principle--Rpclod (talk) 01:58, 17 September 2014 (UTC)

How and why the Young's modulus enters in the geology example is far from obvious. Besides a good Reference, that is definitely needed for this part, one would also need an explanation why it's the youngs modulus and not other elastic parameters (shear and Bulk modulus) that are important. As I don't expect a uniaxial stress state - I would even have some well founded doubt that using the young's modulus for this application is a good idea. Even if the field is important, it does not mean it makes a good example. So far its unreferenced, hard to understand, not helpfull and even somewhat doubtful. So 3 good reasons to delete. --Ulrich67 (talk) 14:14, 19 September 2014 (UTC)

Considerable variation?

I changed the text that precedes the table of values from

Young's modulus can vary considerably depending on the exact composition of the material. For example, the value for most metals can vary by 5% or more, depending on the precise composition of the alloy and any heat treatment applied during manufacture. As such, many of the values here are approximate.

to

Young's modulus can vary somewhat due to differences in sample composition and test method. The values here are approximate.

A 5% variation is not a considerable change. A considerable change is more like 5:1 (eg. tensile strength of steel). See Talk:Alloy#Young's modulus for more discussion and some sources. —Ryan 15:15, 21 October 2007 (UTC)

Just a note, Young's Modulus often changes by ±10% or more for a given material from one specimen to the next - it is subject to a number of effects, such as anisotropy. For the way Young's Modulus is used in a number of engineering calculations, variation on this scale is indeed considerable.— Preceding unsigned comment added by 50.41.47.115 (talk) 02:39, 9 October 2014 (UTC)

References