Hi Konstantin

What happens if you re-plot this as true stress vs true strain?  Is it perfectly plastic or does it still soften?  If it still softens can this be explained by creep?  

Dear Dr Naumenko,

My reply follow the same observation of Dr Spindler, and it is based on my experience on cyclic loading. I known that hold periods within a cycle, with associated stress relaxation, increase the coarsening of the sub-grains. I will look in my archive to find out something, it is an interesting question!

I may be wrong but I would not say that the softening (coarsening process of subgrain structure) localizes before necking starts.

I remember having seen the same kind of behaviour on simple C-steel subjected to Constant Strain Rate (0.00111 s-1) Tensile Test (CSRTT) at very high temperature (1473 K) : see enclosed figure A.11. extracted from Appendix A (p. 285) of the book «Quantitative General Adaptation». Though the abscissa is time in this figure, the main shape of the curve should be similar when the strain is put in abscissa. I also remember CSRTT having been performed by Dr Mark Steen at the University of Gent in the years 1980 on low-alloy Cr-Mo steels at 770 – 870 K : these tests showed the same general shape of curves.

According to me, this kind of curve is analogous to what occurs in creep : three stages are observed. The difference of curve shape between creep and CSRTT lies in the difference between the tests : imposed constant stress (or load) and « strain rate allowed to vary » in creep versus imposed constant strain rate and « stress (or load) allowed to vary » in CSRTT. Therefore as in the case of creep necking would start from a local weak point at a moment during the third stage, but this does not mean that there is local weakening before : the descending branch is the « third stage » as resulting from the testing conditions.

However, I must admit that I didn’t check this in those times (by metallography, ….).    

Thank you Mike and Daniele for your comments. Yes, we calculated the actual cross-section area  by I) volume constancy assumption and II)  measurements of cross.section diameter from interrupted tests. Both the measurements lead to the same result. The true stress vs strain curve shows a descending branch. For  slightly lower temperature it looks perfectly plastic (viscous). It can certainly be related to (higher stress regime) creep.

Thank you Dr. Crevecoeur  for your answer and examples for low-alloy steels. I agree with your comments: these results show clear analogy to creep. In many recently published papers on  advanced 9-12%Cr steels  it is shown by TEM observations, that tertiary creep is primarily controlled by coarsening of initially fine subgrain structure: I am not metallurgist, but I believe these  results indicate that the material becomes softer as the high dislocation density decreases. This is in contrast to the tertiary creep caused by grain boundary cavitation, usually observed in low alloy steels and called creep damage. We know that such kind of creep damage may localize in the last stage befoere creep rupture, (even) in a uni-axial specimen. Therefore my question was, is there anything similar, which can be related to softening ?

Dear Dr Naumenko,

Ø  This is in contrast to the tertiary creep caused by grain boundary cavitation, usually observed in low alloy steels and called creep damage.

Yes, grain boundary cavitation is commonly observed in low alloy steels during the tertiary stage (but also sometimes in the secondary stage, although very sparsely and with smaller dimension, say less than 0.5 µm diameter) : however this occurs only for long creep lifetimes. Typically, for 1Cr-0.5Mo or 2.25Cr-1Mo-steels, as frequently used in thermal power plants, you would find isolated cavities (e.g. 1 to 3.5 µm) at grain boundaries and triple points only after several 10 000 hours of operation. Not to speak of arrays of cavities which would be expected after 150 000 hours and much more ….

Beginning the years 1980, I had the opportunity to perform creep tests on 2.25Cr-1Mo-steels at the University of Louvain. Temperature was 923 K (650°C) and stress 10 kg/mm2(units of that time). The tests were stopped after successive times. One of the aims of the tests was to detect the start and increase of grain boundary cavitation (using SEM). Not any one cavity was found, even close to rupture. But coarsening of the subgrain structure and slight changes in dislocation density (dislocation creep is rule at these temperatures) could be observed. Also micro-hardness measurements showed softening in the final stage. So, « creep damaging » can be several things, not only grain boundary cavitation, but also softening occurrences as described by you for advanced 9-12 %Cr steels. It depends on the subjacent governing phenomenon : dislocation density, dislocation sliding/climbing, diffusion, subgrain structure, grain boundary sliding, carbide distribution, dynamical recrystallisation (at higher temperatures), ….     

What is actually noteworthy is that the creep curve always shows the same shape with 3 stages, be it for lifetimes of 200 000 hours at 813 K (540°C), 6 hours at 923 K (650°C) or 1 minute at 1473 K (1200°C). And this despite the completely different subjacent phenomena at work to allow for the imposed stress and given temperature !      

(following)

To be fully clear, the tests at 923 K (650°C) and 10 kg/mm2 on 2.25Cr-1Mo steels lasted 6 hours (to rupture).

The detection of cavities on this steel after several 10 000 hours in plant service conditions (at say 813 K) and the non-detection of cavities after 6 hours (rupture time) at 923 K in laboratory conditions can then be ascribed to the diffusion parameters of vacancies.

Vacancies (of atomic size, thus of order of 1 angström) migrate towards grain boundaries where they merge to form cavities (also called micro-voids). This takes time and strongly depends a.o. on the temperature as there is a factor 10 000 between the vacancy and micro-void sizes : angström (Å) for the former compared to micro-meter (µm) for the latter. A test dur              ation of 6 hours at 923 K would not be sufficient to allow for the migration of many thousands of vacancies towards grain boundaries to merge there into a few grain boundary cavities.

Hi Konstantin 

I am afraid that I work mostly on austenitic stainless steels rather than 9-12Cr Martensitic steels so I don't have my hand on the evidence that you asked for.  I will nevertheless, keep an eye out and if I spot any I will send it on to you.  

However, I am very interested in necking and plastic instability.  So your questions remains of interest to me.  Clearly, the softening occurring during the slow strain rate test is very similar to the softening that would occur during creep, which is time dependent and accelerated by stress, both factors are present in the slow strain rate tensile test.  It seems clear that a well formed constitutive model would predict both the constant strain rate and constant load creep tests.  Nevertheless, the necking and strain localisation needs some additional understanding and a continuum model would not predict that behaviour.  

From a practical point of view inhomogeneities in steel properties are normal.  There is a statistical distribution of properties in a poly-crystal and some clustering of weakness will certainly occur.  Somewhere in a specimen.  Furthermore, there is an additional experimental difficulties of; are the specimen dimensions perfect, is the temperature distribution perfect, is there some constraint from the extensometer ridges.     After all necks never occur perfectly in the centre of a specimen and always occur towards one end and never next to a ridge.  So my point is strain localisation and necking is inevitable in a ductile material.  

Indeed, I have often seen two necks in creep specimens.  

Of course necking is that interesting balance between work-hardening rate and the rate of increase in the true stress.  So the usual path is a specimen in which a small strain localisation are always occurring all over the specimen (because localisations are common and the norm) followed by a stress increase but the increased work hardening strengthens the local region and instead of a neck forming the strain extends into the surrounding gauge length and the specimen extends uniformly.    However, in your case of a perfectly plastic material which is also creeping there is no work hardening, so the stress goes up in the strain localisation, the material can not sustain that stress and the neck develops to failure.  

The other factor is the test machine stiffness and control.  For example in a strain rate controlled test once necking occurs the load drops, once the load drops it also drops in the loading bars in which the elastic strain falls and the loading bars themselves shrink elastically.  Therefore, the specimen receives extra extension (elastic follow-up).  In a stiff machine this is minimised, but if the machine is not stiff then specimens can fail quickly with necking.  

Interestingly in a constant load creep test as the load does not fall the specimen does not experience this elastic follow-up and the necking will actually be different!

I know none of this has answered your question but I have enjoyed writing it down.  .  

>> Michael,

Interesting thinking : as if made by an observer inside the metal …. :=)

>> Konstantin,

Do you have full experimental curves corresponding to the constant (low) strain rate tensile tests on the 12 % Cr steel shown ?

If there is a knee after a while in the descending branch with a second steeper fall of stress afterwards, this could be an indication of start of necking. There is chance that it was the case for Specimen 4 (but, as showed by the testpiece photograph, the test was not conducted to rupture).

Dear Dr Naumenko,

This sentence made me thinking " It can certainly be related to (higher stress regime) creep." If we start to think in terms of creep ductility it would be possible to justify the necking (elevated reduction of area) and the presence of creep damage ( but not its position, but I totally agree with Dr Spindler). As I know ( and correct me if I am wrong), depending on the creep strain rate the creep strain to failure of a material can exhibit three different stages. 1) Visco-plastic cavity growth at high strain rates,  2) diffusion controlled cavity growth for intermediate strain rates, and 3) constrained diffusion for very low strain rates. Normally to identify the upper-bound of this plot high temperature tensile tests and high stress creep test are adopted. If the failure is located in this region, a great reduction of area is expected. In literature I found that for the dissimilar metal weld research program (ORNL) was a common practice to perform high stress creep test to obtain results in reduced time. However, recently (INL) it has been discovered that the failure mechanism associated to these test was not reflecting the proper low ductile failure observed on field experience. The component tested at high stress exhibited strong ductile failure, with RA near to 90%. This can be reasonable if the applied load is high enough to cause the rupture in short time.

A more deep investigation on this topic has been done by Dr Holdsworth in the past on 1CrMoV, and I found it really interesting.

thanks for any correction, is always nice to share ideas and opinion.

Regards

To continue the discussion, please have a look on attached files. Here the "true" stress (it is only true in the range of homogeneous deformation) is given as the function of the true (logarithmic or Hencky) plastic strain. At 500°C the material exhibits "perfectly viscoplastic" behaviour up to the start of necking. For 650°C the softening regime is clearly observed.

@Mike, is there any analogy to austenitic steels? One interesting point is: we analyzed surface roughness of specimens 1, 2 and 3 (see interrupted_tests2.pdf). The start of necking is observed for specimen 3 at two positions. Interestingly one of these two necks propagates leading to final fracture. We did a series of tests at different strain rates and temperatures, in most cases the necking was observed at the same position, as shown in interrupted_tests2.pdf.

Regarding the mechanism of necking, we may run the FEA for a specimen with an imperfection placed at different positions along the gauge length. In my view there are concurrent mechanisms: stress increase in the zone of stress concentration, and stress relaxation and redistribution due to inelastic flow, so the deformation would be more or less homogeneous over a range of plastic strain, up to a certain level of cross-section shrinkage.

@Dr. Crevecoeur, in the attached stress-strain diagrams the change in slope indicates the progressive necking.

@Daniele, for this stress and strain rate regimes grain boundary cavities do not cause fracture (there is not enough time for cavity growth), see the discussion by Dr. Crevecoeur. We may define the ductility (approximately) as the plastic strain at which the necking starts?

I knew you had this totally under control all the time!  I am sure your work will be fruitful, good luck.   

Nevertheless, I remain very interested in necking.  This is because I use ductility exhaustion models to calculate creep damage and my observations suggest that the true local inelastic strain a failure as calculated from the reduction of area (Z), which is given by true local inelastic strain at failure=ln(1/(1-Z/100) is the most realistic measure of ductility for creep damage calculations.  All of the other definitions of ductility, uniform strain, elongation etc..... Appear to be too pessimistic.  

However, there are problems with using the  reduction of area (Z) in this way; firstly experimental, Z is calculated from a small change in a small dimension in a region of a specimen where area is changing rapidly and the specimen is no longer round.....etc..  Secondly, elongation and reduction of area are both affected by specimen geometry and testing practice.  And even elongation is affected by necking, the geometry and number of necks.  Not to mention the microstructural inhomogeneities that you have asked about.  

Furthermore,  and by no means least when we do tensile and creep tests we can keep the temperature approximately constant but the other explanatory variables stress (in a tensile test) and strain rate (in a creep test) vary greatly.  This makes defining the creep damage model as functions of stress and/or strain rate rather complicated.  

There is a strong idealogical case for "uniform elongation".  However, my experience is that "uniform elongation" is always too pessimistic.  

Hence, my interest in necking.

I look forward to your findings avidly.  

Excuse me, how much was the specimen deformed before testing? Was it cold-worked? What amount of reduction?

Best regards

Jiri Zyka

Konstantin

I forgot, you asked about  "any analogy to austenitic steels".  The creep rate is much slower for austentics than 9-12Cr tempered Martensite and the work hardening rate is much greater.  So no softening at engineering relevant temperatures (500-650°C).  I have attached some data at 550°C, which I have to hand.  Of course at much higher temperatures things are different more like the 9-12Cr tempered Martensite.  May be later I will plot the data for you.  

Hi All

I thought of some more interesting things, while we are on the case of true stress, true strain and creep and tensile and necking.  Have a look at these papers.  

Does anybody know of anything similar?  

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

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

Dear Dr Naumenko,

Thank you for these full curves : they are what I expected from true stress – true strain diagrams. I am nearly sure that Michael would observe the same kind of behaviour on austenitic steels. I write « nearly » because you never know if anybody won’t discover a new interesting unexpected phenomenon …. with the exciting challenge to find an interpretation to it !

Concerning the wordings «start of necking » (used by you to describe the observed change in surface roughness at two positions for specimen 3, as shown in interrupted_tests2.pdf) and « neck forming » and « neck develops » (used by Michael), I would comment as follows : when necking starts at one or several positions like the two positions of specimen 3 (detected by change in surface roughness), one can say that softening becomes heterogeneous and localizes at these positions (and maybe at other positions not observed …) until the gross “neck forming” develops (as visually observed on specimen 4 compared to specimen 3 (*)) leading to rupture. To show that heterogeneous softening exists before the local changes in surface thoughness, i.e. for instance from the beginning of the descending branch needs further investigation. It would be nice to hold us informed …

(*) develops from one of these weak positions detected before by observation of changes in surface roughness as you comment it.

Please read "roughness" instead of "thoughness" in preceding post. Thus :

"To show that heterogeneous softening exists before the local changes in surface roughness, i.e. for instance from the beginning of the descending branch needs further investigation."

Dear Michael,

It seems that we sent posts simultaneously !

Concerning your true stress vs true strain curves of austenitic steel at 550°C, I think they are more like stress-strain curves at room temperature. While Dr Naumenko's curves, as corresponding to higher temperatures, they become to be more like stress vs time curves at those temperatures : indeed as mentioned in former posts they reflect some creep analogous behaviour.

About your other post (development of new measurement of TT), I haven't encountered this issue before : so I have to first study it !      

Konstantin, 

Have you conducted FEA of the effect of the extensometer collar or ridge on the stresses in the specimen.  Here is one we did.  This was loaded to a nominal stress of 300MPa with around 0.2% plastic strain (this was a creep test so the elastic plastic analysis was stopped once it reached 300MPa).   The nominal stress 300MPa is yellow in the pictures so most of the specimen is at the nominal stress however, the constraint of the ridge creates the orange zone of enhanced axial stress.  Can this be the reason for your localised softening?  

Mike,

many thanks for this comment. We are currently working on constitutive model for a 12%Cr steel in order to desctibe available experimentall data (tensile+creep) including hardening/recovery and softening effects. Then it should be implemented inside a FE-code to analyze specimens with non-uniform geometry. Certainly ridges may cause non-uniform deformation and softening. We have to check wether ridges may cause  localization and neckong in the future.

3D Digital Image Correlation (DIC) would be useful. This could track the yield front.  My guess is that yield starts somewhere in the middle 60% of the specimen then moves outwardly towards both ends of the specimen until it interacts with the stress field set up by the ridge (or grip end) the yield front will get stuck at that location and then the neck forms at that location.   The stress distribution at that location (the interaction between the ridge and the yield front) will be the cause of the softening.  

The FEA will probably show you this anyway.  An DIC experiment will just be experimental confirmation.  

My other thoughts on this matter relate to the role of the radial strain.  When looking at the results of multiaxial creep tests I noticed how stress states which give high absolute radial strains (because these are mostly negative) promote strain localisation.  The classic case is the torsion test in which radial strain = 0 and necking does not occur (so long as you avoid buckling).  

I would be very pleased if the FEA shows that the absolute radial strain is high at the location where necking starts.  Perhaps the FEA will find that at this location the axial stress and hoop stress are both enhanced, hence high absolute radial strains.

Strain localisation then is a mechanics problem and not a material inhomogeneity problem.   

Dear Konstantin Naumenko

I found this question very interesting, when it first came out and I know that Johanna Eisenträger has completed her thesis. So I can ask; which came first does (i) strain localisation cause softening or does (ii) softening cause strain localisation?

Hi Mike,

thank you for this question. Our experimental analysis suggests that in the first part of the descending branch of the true stress-strain diagram the softening is uniform over the gauge length. The necking starts much later (roughly after the grey point in the stress-strain curve, see interrupted_test2.pdf ).

So, my answer is: strain localisation is due to necking (bifurcation of uniform deformation). Softening (coarsening of subgrains in martensite steel) is not the cause of this localisation mode. However, softening may accelerate the onset of necking since it leads to an increase of inelastic strain rate.

Dear Konstantin Naumenko

Thank you for your explanation. The work that Johanna did has been very useful to helping me to explain the behaviour of uniaxial tests. Particularly, the creep test.

Mike

Dear Dr. Spindler,

Thank you very much for your valuable comments in this discussion! Concerning softening and necking/localisation, I agree with Konstantin Naumenko. This topic has also been discussed in my thesis, while presenting the experimental results.

Kind regards,

Johanna Eisenträger

The forward creep would be signficant during a tensile deformation with very low loading-up strain rate.