Dear Michael William

I think that the problem of the measurement accuracy of the initial dimensions of the sample is related to other experimental errors when using the extensometer at elevated temperatures. Usually, the extensometer is calibrated at room temperature, but this is not assurance that the strain measurement during the elevated-temperature test will have equal accuracy. That’s why ASTM E 21-09 not recommend to determine proportional limit and offset yield strength of 0.02% or less, for elevated temperature tension. According to ASTM E 139-00, during creep the strain should be calculated by dividing the extension by the extensometer gage length measured at room temperature (section 10.2.1).

I like your post. I agree that the temperature of the measurement should be unambiguously given.

Your,

Mirek

Very good post.... i follow

Dear Mirek

Thank you for your answer, which is sufficient to answer my question.

For my part I have also checked the ISO standards:

For Tensile testing at elevated temperature ISO 6892-2:2011 it states:

" original gauge length L0 gauge length measured at room temperature before heating of the test piece and before application of force"

and with respect to original cross sectional area the standard states "All stresses referred to in this part of ISO 6892 are engineering stresses, calculated using the cross-sectional area of the test piece derived from dimensions measured at room temperature."

For Creep testing ISO 204:2009 states:

" original gauge length L0 length between gauge marks on the test piece measured at ambient temperature before the test"

and

"cross-sectional area of the parallel length as determined at ambient temperature prior to testing"

Therefore, with respect to testing standards the answer seems clear, engineering stress and engineering strain are defined by the original room/ambient temperature measurements on test pieces prior to testing.

I will add some text on my suggestions regarding true stress and true strain (uniform deformation) later once I have edited the text.

Till now my understanding was Lo/Ao are gauge length and area before application of load and after heating the specimen :)

Do we subtract the elongation due to heating before generating stress-strain curve at elevated temperature?

Dear Naveen

I think it would be a good idea to take thermal expansion into account but how is it best to do so? Nevertheless, the testing standards are clear that L0 and S0 should be "measured at ambient/room temperature".

I am just using these posts to point out this fact and to open a discussion on the topic.

In my opinion, I like to be clear that engineering stress and strain use L0 and S0 "measured at ambient/room temperature before application of load" as this make to it easy to understand the calculations that experimentalists have done. In this way engineering strain is extension divided by L0 and engineering stress is load divided by S0. It is then a simple matter for the experimentalists to report their measurements of L0 and original Diameter, D0. Then so long as the experimentalists report engineering strain, stress and or extension, load it is very easy to perform any other calculations we like based on their data. If however, we mess around with the definition of L0, S0 and D0 there will be a lot of confusion regarding how people have calculated stress and strain.

With regards to true stress and true strain, this then is the more interesting part and is in my opinion where we should be doing things like taking thermal expansion into account. As an example, how can we formulate equations to calculate true stress and true strain unless we know exactly how the experimentalists have defined the engineering approximations?

I will post more on true stress and true strain once RG get their file attachment utility working.

You have answered your question by way of Engineering Stress/True Stress and Engineering Strain/True Strain. If someone is just writing Stress, it is implied that it is Engineering Stress. For true stress values, one has to write True Stress and not just the stress. For Creep studies; since the phenomenon relates to increasing strain at constant load and at a particular elevated temperature; one studies changes in strain values with time or even simpler, deformation vs. time. Here there is no confusion with true stress or true strain.

Dear Ravi

I do very much agree (although your post is not really related to my question). Nevertheless, I would very much prefer it if test laboratories and experimentalists would present their creep test data electronically as:

Time (hh,mm,ss), Date (dd/mm/yy), Temperature (units), Extension (units) and Load (units)

Here extension means the change of the gauge length measured by an extensometer in the units for which the extensometer was calibrated.

Load also means the force applied to the specimen, in the units for which the force was calibrated. Of course I also need to know the dimensions of the specimen as measured at room temperature and the calibration certificates for all measurement devices (including for each of the thermocouples).

I am a pedant, I know. Nevertheless, I can calculate Elapsed Time, Engineering Strain and Engineering Stress myself and I don't need to guess how somebody else did it before sending me the data.

Furthermore, the data file should start at ambient temperature, include all of the time during heating-up, every increment of load applied to the specimen and not finish until the specimen is unloaded and the temperature has returned to ambient! The interval of logging should be appropriate to how rapidly the applied force or the measured temperature, and extension are changing. The file should further be annotated with comments, such as any testing difficulties, or interventions by the experimentalists. For example, if the beam is levelled or the extensometer is reset.

(This time publicly...)

The use of the room temperature measurements makes sense if the coefficient of thermal expansion remains constant or linear over the temperatures tested. When the coefficient of thermal expansion is not constant/linear, comparing stress and strain derived from room temperature measurements doesn't seem appropriate as the results are not all under one regime, uniform thermal expansion.

As for the extensometer, it is zeroed at temperature before loading but also as the test progresses moves out of the furnace and heated area with extension. This leads to the idea that choosing the material they are made from needs to have a constant/linear known thermal coefficient of expansion which is then interpreted into the strain measurement.

To answer your question, I would expect it to be measured at room temperature given the inability until recently to measure at temperature whilst concurrently testing (a capability most of us do not have still).

Maybe the solution is to list the coefficient of thermal expansion for the test temperature. Thus allowing 'true' stress and strain to be calculated and for it to be comparable to specimens at higher stresses and temperature where the thermal expansion coefficient may be different. Alas, this means accurate measurement of the coefficient of thermal expansion which is more testing and of course more costly.

Also just to annoy, in creep would the thermal expansion coefficient/rate change with changing microstructure given the material is now in a different state therefore impacting the ability and rate of expansion?

Hi Veronica

Thank you for your answer. Like all threads this one is beginning to wander and tangle up. So I will resist the temptation to straighten it and I will instead add to the confusion:

What we (experimentalists) do to derive mechanical properties should be driven by two things:

I am sorry if I have just upset all of the academics and scientists who read this but I value your work and place it in item 2.

Engineering calculations fall into largely three groups (i) hand calculations, (ii) simple elastic finite element analyses and (iii) rather complex non-linear finite element analysis.

In my opinion engineering stress and engineering strain are perfectly adequate for (i) and (ii) but when it comes to (iii) I think we should really be providing mechanical property data using true stress and true strain.

In addition, over the years I have observed a number of research projects which have reached to wrong conclusions simply because engineering stress and strain were used. For example based on engineering stress and strain you might conclude that the work hardening rate of two materials was different when in actual fact they are exactly the same in true stress true strain.

Now don't get me wrong I am not advocating true stress and strain for absolutely everything. I can still appreciate the usefulness of (i) hand calculations and (ii) simple elastic finite element analyses. In these cases mechanical properties such as Tensile Strength and Stress Rupture are defined in terms of engineering stress. Thereby it is only possible to use engineering stress in conjunction with such mechanical properties. Design codes which use such criteria have no choice they must use engineering stress and engineering strain exactly because Tensile Strength and Stress Rupture are defined in terms of the engineering approximations.

The key is (iii) rather complex non-linear finite element analysis. Really really need true stress and true strain and at elevated temperature complex non-linear finite element analysis can make full use of the physical properties to predict thermal expansion etc. It is therefore important that we "Materials Engineers" provide complex deformation data in true stress and true strain and take full account of the effects of thermal expansion on the test specimen dimensions.

I promise I will upload some files on true stress,strain as soon as RG allows me. !It worked!

When interpreting creep test results (or any other test results), you need to choose a specific configuration, which is used as a reference, to define stress and strain quantities. Common approaches consist of using either the initial (i.e. undeformed) configuration or the actual (i.e. deformed) configuration. In a general manner, when working with the initial configuration, the nominal (or 1st Piola-Kirchoff) stress tensor is often used as a stress measure while the infinitesimal strain tensor is used as a strain measure. For a uniaxial test, such quantities are calculated based on the initial area and initial gauge length: R=F/A0 and e=(L-L)/L0. When working with the actual configuration, the Cauchy (i.e. true) stress tensor is the preferred stress measure while the corresponding strain measure is given by the logarithmic strain tensor. For a uniaxial test, such quantities are defined based on the actual area and actual gauge length: sigma=F/A and epsilon=ln(L/L0). It should be noticed that the nominal stress tensor is not a "false" stress... It is just a different definition based on a different point of view. Also, from an experimental point of view, the determination of the Cauchy stress is often not easy as it requires measuring the evolution of the specimen area A. To circumvent this difficulty, one often makes some constitutive assumption to facilitate the determination of the Cauchy stress (e.g. incompressible material).

Dear Charles

I agree from a Mechanics point of view.

My point of view comes from that of an experimentalist, who provides mechanical property data to engineers:

Therefore, I very much prefer True stress and True strain. I consider Engineering Stress and Engineering Strain to be "approximations". Which are good enough for some applications but not good enough for all applications.

I also agree that engineering is full of assumptions (e.g. incompressible material). However, we all have computers on our desks these days and I bet everybody calculates engineering stress and engineering strain using computer code or a spreadsheet. If so why not just code True stress and True strain (it is a very similar effort)?

Michael,

I'm in FEM calculations, but make some material measurements for my material models as well.

Small correction:

" I can still appreciate the usefulness of (i) hand calculations and (ii) simple elastic finite element analyses. In these cases mechanical properties such as Tensile Strength and Stress Rupture are defined in terms of engineering stress. "

The simple FEM analysis cannot use Tensile Strength and Stress Rupture at all, because linear approach is valid only in linear range, below yield stress. In linear range only elastic modulus (and Poisson ratio) is used so there is no problem. Modulus can be temperature dependent.

In case (iii) - nonlinear calculations:

In my opinion experimentalist should provide only true stress/strain curve, engineering values are not interesting at all, because in general the FEM

codes requires true stress/strain.

For calculations in low/elevated temperatures it is required to define:

1. thermal expansion curve/coefficients

2. stress/strain curves at various temperatures,

The thermal expansion HAS to be excluded from measured curves. In calculations it is compensated with the use of the thermal expansion curve.

The question is, WHO will do it all. In my opinion it is much safer to do it by experimentalist, because he know all about the conditions of measurement. In such case no engineering curves are used at all and there is no problem.

The problem in your question exist only if you left all the calculations of the material characteristics to the FEM people. In such case a lot of additional data has to be provided, and it is just dangerous (a risk of misunderstanding).

To complicate it a little more :)

There is not only strain/stress/temperature. In some application there is a next variable - strain rate. I don't mean creep but high speed deformation. It makes things even more difficult to describe. Definitely, even for static tests always the strain rate should attached to the curves. In practice I have seen horrible misunderstandings in the material definitions.

Thank you Artur

I think you have exactly caught my point. Sorry for the small error. Especially I agree:

" In my opinion it is much safer to do it by experimentalist, because he know all about the conditions of measurement. In such case no engineering curves are used at all and there is no problem. "

Dear sirs,

I agree with both of you that " it is much safer to do it by experimentalists, because he/she knows all about the conditions of measurement". The end user should only use the data, he/she should not be bothered how it was generated/calculated/interpreted.

Regards

Naveen

I think you should use experimentation and add the statistical constant when using elevated temperature. I still think the ASTM standard will carry some error in the calculation

Dear Michael! Dear colleagues!

In my opinion standards proclaim that So and Lo are measured at room temperature because it is technically complicated to measure these values at high temperatures (in chambers for high-temp testing). But nowadays this problem can be solved by using optical methods. In my recent project i was studying creep of low-carbon steel in hydrogen at temperature 300°C. I used digital image correlation for local strain increase measurement. The initial "zero" image was captured before the engaging of heating system of testing chamber, the next images was captured after the temperature reach the needed value and after the specimen was loaded. Using these images I was able to measure the initial diameter of specimen at room temperature and at 300°C, but I used the value at 300°C for initial area calculation, assuming that would be more correct). So now we can easily measure the initial area in both cases, and I think the standards should be more specific on this point. Even though the influence of heat expansion on the cross-section area for most materials can be neglected, but if it can be measured, why can’t we consider it? I guess your pedanticism on this point make sense)

To the topic of true stress and strain.

In my experience it is absolutely unacceptable to use engineering stress and strain in non-linear FEM calculations. In this study Article Analysis of the Stress-Strain State of the Process Zone of a...

But i should note that so called true stress is actually not true either (at least for metals). It is calculated by dividing the force to the actual area of the metal specimen in the process of loading, but it is known that at some point (which approximately correspond to engineering ultimate stress) the central crack initiates in the neck of specimen, so the area of the crack should be taken into account. This means that "actual true stress" at the fracture point is much higher than so called "true stress". Of course, for most engineering calculation this is not relevant because even plastic strain is considered as unacceptable, but in some cases it is important.

To expand the discussion slightly, and also with reference to the original question about standards, ASTM standards are quite clear that the gauge lengths are measured at room temperature, before any part of the test has started, which also means before heating. This is true for room temperature tension (ASTM E8), high temperature tension (ASTM E21), room temperature compression (ASTM E9) and high temperature compression (ASTM E209).

All four standards mention measurement of 'original length', and reference ASTM E6 (mechanical testing) for the same. ASTM E6 says '“original” refers to dimensions orshape of cross section of specimens at the beginning of testing.'

So, like the ISO, ASTM mandates that the measurement be done at room temperature. Coming to the point made by Veronica and Yuriy about the possibility of measuring the gauge length at high temperature, it is certaining becoming possible to do so, especially with DIC. However, though such a stress-strain curve may be more 'correct', it can't be directly compared to stress-strain curves generated through room temperature gauge length measurement. This can lead to difficulties which are not just pedantic; after all data generated will eventually go into literature/databooks and somewhere down the line it will be compared to other data. Therefore, I think that if such high temperature measurements are performed, the user should be furnished with the entire procedure. Else, if done according to the standard, simply the standard number can be given (which is also convenient while reporting).

As for converting engineering stress-strain to true stress-strain, I think there is no standard, so the formulation given by Michael could certainly be used, provided the formula is explicitly mentioned in the text/report.

This is what I said you should correlate for certain error using statistical cte since the measurement is correct at room temp,

Dear Gabi Nehme, Yuriy Molkov and Aashranth B.

Your answers have greatly contributed to this discussion.

I have added an Excel file to give two examples of the method I proposed, which in doing the implementation on the examples I have added a little to (I would appreciate any comments, suggestions etc).

With regards to testing standards (national and international) they tend to be aimed at providing mechanical property data as defined by Design Codes. Such as proof/yield strength, tensile strength and rupture strength. This is why these testing standards tend to be based on engineering stress and strain. Complex non-linear FEM are not (usually) required by Design Codes. This is the reason True Stress and Strain are not defined in the Testing Standards and it would worry me if they did. This is because Testing Standards tend to stifle innovation as people tend only to do what is required by the standard, whereas so much more is possible in the real world. For example the excellent work described by Yuriy Molkov.

To list some other efforts to improve the understanding of the effects on non-uniform deformations I would like to list:

https://www.researchgate.net/post/Localized_softening_in_9-12Cr_tempered_martensitic_steels_at_high_temperature?_ec=topicPostOverviewFollowedQuestions

Article Analysis of Temperature and Strain Rate Dependencies of Soft...

http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1618961

Article Creep Lifetime Under Constant Load and Constant Stress: Theo...

https://www.researchgate.net/publication/320127767_Analysis_of_the_Stress-Strain_State_of_the_Process_Zone_of_a_Plate_with_Central_Crack_Under_Biaxial_Loading

Can anybody add to this list?

I totally agree that testing standard do not provide the real answer sometimes. They put you in a mode that you can not innovate. In the real world we should think of them as restricted methods, but good enough to establish certain protocol and try to understand the whole concept of temperature and error in our case. Therefore true stress and strain depend on other variables. Thank you for a good and helpful discussion.