# More Definitive Point of Onset of Plastic Deformation

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Theoretical Problem:

Many definitions to define the on-set of plastic deformation exist based on the offset yield (i.e 0.2 % , 0.02%, Johnson's Apparent limit etc.) strengthand all of these depend on a non-robust methodology namely: find the Elastic Modulus, construct an off-set line, and were is crosses the load extension curve there is the on-set of (practical) plastic deformation.

I have often wondered why (say by the use of a biaxial extentensometer) the use the change in Possion ratio as a more robust definition for the on-set of plastic deformation was never utilized. In the elasticity realm roughly =B5 =3D 0.20 - 0.35 (material dependant) but at the onset of true plastic deformation =B5 =3D 0.5 due to the constancy of volume (for all metals - at least up to a second order approximation - i.e. density decreases with workhardening so 0.5 will decrease during increasing deformation).

Does anyone know or remember if this was ever considered or see reason why it will not work?

Ed Vojcak

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Just do the measurement and look!

Michael Dahms

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Dear Ed. I am currently working on a problem (for Al) to study the variation of yield surface and elastic modulus with plastic deformation. The method which you of propose is good but the use of extensometers are not very accurate as compare to strain gages. So, here i suggest you one of the method which is easy as compared to what you have discussed and yet precise.

1) use strain gages rather than extensometer. 2) check the onset of plastic deformation use the defnition of deviation of linearity and use 5 or 10 or 20 microstrain definition which is much more precise that what you have described.

here are few references--

Pandey A., Kazmi R. and Khan A.S., 2006, An Experimental Study on Subsequent Yield Surfaces with Finite Deformation in Aluminum, 12th International Symposium on Plasticity, Halifax, Canada, July 17- 22,

140- 143.

Khan A.S. and Wang X., 1993, "Experimental Study on Subsequent Yield Surface After Finite Shear," Int. Jou. of Plasticity, vol. 9, 889-905.

Stout, M.G. and Martin P.L., 1985, "Multiaxial Behavior of 1100 Aluminum following Various Magnitudes of Prestrian", Int. Jou. of Plasticity, 1, 163- 174.

Phillips A. & Das P., 1985, "Yield Surfaces and Loading Surfaces of Aluminum & Brass", Int. Jou. of Plasticity, 1, 89-109.

I hope this will solve your problem

Let me know about the results

Amit Pandey PhD Student Univ of Maryland, USA

Ed wrote:

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Of course, Ready-FIRE-Aim. Measurements must be understood and their limitations observed before they are considered useful.

Ed

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Amit,

Thanks for the advice. Several points I must clear up:

ASTM E251-03 (Appendix X2-X3) the typical Gage Factor uncertainty for a strain gage is =B10.5% neglecting the additional added uncertainty of the rest of the measurement system this is equal to a "Class B1" extensometer (ASTM E83-02) having an overall uncertainty of =B10.5%.

The digital "resolution" of the strain gage electronics may imply greater "precision" (repeatable number for assumed strain input) but the accuracy of the result (measured strain per length) is limited by uncertainty in the Gage Factor. Equal length strain gages (circumferential to longitudinal) mounted on a round tensile sample would be the only way utilize the strain gage's greater resolution (neglecting offset errors see below).

Using strain gages (or class B1 extensometers) for determination of the Poisson ratio within the ELASTIC LIMIT is covered method by ASTM E132-04 "Standard Test Method for Poisson's Ratio at Room Temperature" Figure 2 shows the basic difficulty i.e. plotted experimental lines of longitudinal and transverse strains don't necessarily pass through the zero coordinates - indicative of an offset error -compensation for offset is problematic.

Theoretical plot of Poisson's ratio into plastic realm (0.3 hyperbolic to 0.5) presented in A. Nadai "Theory of Flow and Fracture of Solids" volume 1, 1950 page 387 figure 24-3 never seen any experimental verification or practical utilization of this phenomena.

Ed

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There is one argument that in a real sense, the stress-strain curve is never (or rarely) precisely linear at least for common FCC materials. There was a flurry of microplasticity work in the late 1950's and early

1070's. Then it seemed to die, at least for a while.

If you get enough measuring sensitivity, the stress strain relationship is a gradual curve, not a "straight line which then goes non-linear". So said some of the believers in importance of microplasticity.

It seems as if it would follow that the lateral strain response would be similarly non-linear, as would be the strain ratios of axial to transverse strains.

Sometimes it seems as if we may wish to force a convenient behavior onto materials - convenient for our purposes.

There is sometimes a difference between the engineering definition of something (the onset of plastisity, for example) and the scientific basis of what is actually going on.

Maybe we just have to put up with the use of slightly sloppy terms such as "onset of yielding", which are really only convenient indicators of when linear behavior assumptions are beginning to show errors of whatever magnitude you use to define "onset of plasticity".

Circular significance? Possibly. Absolutely answerable? Less likely.

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The idea behind my theoretical inquire is that per the Round Robin results of ASTM E8 of 0.2% offset yield strength has COV (coefficient of variation) about twice that of the tensile strength (max load over orginal area - very definitive) and for 0.02% offset yield strength a COV of about three times!

Microplasticity has always been an issue in yield strength determination C.L. Zener- in "Elasticity an Anelasticity of Metals" (and others) addressed this issue extensively.

My idea is to find whether there is a plasticity based (rather than elasticity based) numerically large differential at the Poisson's ratio change to define the beginning of the plastic realm more definitively i.e. with less COV than the current offset yield method and adopt this into organizations as ASTM.

If we don't challege "accepted practice" improvement in the field of metallurgy (pursuit of happyness) will not occur in our times.

Ed Vojcak

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Yes, I understand.

Please accept my encouragement in pushing forward the hunt for better techniques.

Thanks for the background.

Jim

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In fact, you suggest to replace the measurement of /sigma vs. /epsilon_L by /sigma vs. (/epsilon_D /over /epsilon_L). You will see that in both cases, there is a continuous elastic-plastic transition, but the latter measurement is more difficult.

If we look to the deformation of real crystals, there is no distinct /point/ of onset of plastic deformation.

Michael Dahms

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All "detectors" are subject to POD (Probability of Detection) being poor. Sorry.

You state that "If we look to the deformation of real crystals..." and please forgive my stupid pun, but just what "crystal ball" are you using?

I'm getting back to the point that the onset of deformation is judged by an offset (established as 0.004" in 2" -ie.at the limits of normal human visual resolution using dividers) of an elastic line (E). Using the ratio of longitudinal and transverse strains should plot as a horizontal line (as per my ref. from A. Nadai - above) - making the determination of the onset of plastic strain a simple (and perhaps more robust) statistical test.

The present offset yield method is based on error compounded methods developed by mechnical engineers with their own (and not necessarly wrong) agenda and has been repeat by metallurgist until it becomes (unquestioned) fact.

Ed

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It is called "textbook", and then there are tools like microscopes and diffractometers.

Each individual crystal starts its plastic deformation at a different microscopic stress since the crystal is oriented differently (Taylor, Bishop and Hill). Thus, the stress-strain-field in a polycrystal is inhomogeneous. Hence, there must be a continuous transition from elastic to elastic-plastic deformation, and we need an arbitrarily defined point of onset.

Michael Dahms

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Mike,

You are right - current theory does state that "micro plasticity" exist and manifest itself mostly in FCC crystals (as Jim points out above) and an arbitrary point defined. Impure BCC crystals (esp. Fe) do have a definitive yields points- this inheritance alos leads to several other phenomena as hydrogen embrittlement susceptibly, a high cycle fatigue endurance limit, etc.

However, if Poisson's ratio =B5 =3D 0.5 for plasticity definition is correct then the deviation from elasticity is more robust (but yes, still arbitrary) since elastic hysteresis will not be an issue as it is in offset yield test and we should see the "erasure" of elasticity (=B5 =3D 0.25 to 0.30 changing to 0.5) more clearly during the bi-axial test.

This is why I originally ask the question whether it has even been closely looked at by anyone - apparently not for this small Google group audience. Like Peterson's rule (LCF 1000 cycles @ 1% strain all materials fracture) - it seem to be a phenomena we have passed by with just a quick look (AQL).

Besides if we don't question the "textbooks" why bother learning? These are smart men who wrote textbooks, and have shoulders we have to climb onto, not just admire.

Ed

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current experience

If you look carefully, there is non-linear behaviour before the yield point in bcc metals.

Then you really should try to measure /mu vs. /epsilon.

Michael Dahms

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