As per theory: damage, in its mechanical sense is the creation and growth of voids inside material. But what is the physical interpretation of the sentence 'creep damage or fatigue damage is this much (some number)'.
For example in the following figure what does the point (0.3, 0.3) indicates. If this point represent the current status of the material of a structure and a straight line between (0,1) and (1,0) is the envelop, what physically has happened to the material?
I have found this discussion late and it is difficult for me to grasp all of the threads. I will therefore make things easy for myself by starting at a suitable beginning.
In order to make engineering calculations simple we try to limit our problems to two failure mechanisms in a single procedure. In design calculations we try to be conservative and simple in a single procedure. This discussion, seems to me to be about the life of a structure that experiences a thermal cycle which results in a mechanical strain cycle (strain controlled fatigue) with a period of steady operation at elevated temperature (strain controlled creep). The appropriate Design Procedure is intended to avoid the initiation of a creep-fatigue crack within a certain life/endurance.
What we mean by the initiation of a creep-fatigue crack is a crack which is small with respect to it's structural significance. In R5 (the UK life assessment procedure see Pub. 1) we usually consider 10% of the section thickness to be "initiation of a structurally significant crack" the reason for choosing 10% is so that the calculations can use the stress analysis from an un-cracked body (we are keeping things simple, as I mentioned earlier, here by avoiding crack body analyses, although R5 allows the user to do crack growth calculations also. )
Nevertheless, this means that a critical level of damage equates to the development of a sizable creep-fatigue crack. For example in a 50mm thick section, initiation is a 5mm deep crack.
To make the calculations simple it is usual to calculate the effect of creep and the effect of fatigue separately. This is where the concept of creep and fatigue damage comes from. The engineer calculates these separately, so they have separate names and are based on common summation rules or life fraction rules such as Miner's rule for fatigue and Robinson's rule for creep. Therefore, fatigue damage, df, cycles over cycles to failure, creep damage which comes in two main versions; (i) life fraction time over time to failure, dc, and (ii) ductility exhaustion (strain fraction) strain over strain at failure can both be calculated separately for each cycle (damage per cycle). Each can be summed for the total number of cycles over the design life to get total Creep damage, Dc and Fatigue damage Df.
The engineer now has two different numbers (Dc and Df) representing the two failure mechanisms but no real way to deal with these two values. The simple thing is to assume a linear summation, initiation is conceded if Dc+Df>=1. Also with two values it is simple to plot these on a 2D graph or "interaction diagram".
For the structural engineer all they have to do is calculate Dc and Df plot them on the "interaction diagram" and if the data lie on the inside then they have demonstrated that the structure will not initiate a creep-fatigue crack. Of course I have oversimplified things greatly. There is great skill and knowledge needed to estimate the total strain range of each cycle, which is needed to calculate Df and to estimate the stress at the start of the creep dwell, which is needed to calculate Dc. Not to mention the material engineer, who is needed to define the material properties for all of the possible steels and Ni-alloys, at every operating condition such as temperature. These are big areas of work and can introduce many uncertainties and conservatisms into the final Design Procedure.
But I want to get back to my narrative: There is also the testing engineer who is the villain of this piece (I am a testing engineer so sorry for being the villain). They perform some creep-fatigue tests on uniaxial test specimens and calculate and plot Dc and Df on the "interaction diagram". Then the bad thing happens, rather too many of the points (Dc, Df) lie inside of the interaction diagram (which is often the original linear interaction or a straight line between (1,0) to (0.1) ). There is a simple solution for the testing engineer they just change the interaction diagram to bound all the data and now everything is conservative again. The new interaction diagram with say a locus at (0.3,0.3) is now put into the design code and all the structural engineers have to use it. Some years later another testing engineer tests another material and points lie inside (0.3,0.3) so they empirically adjust the interaction diagram again to say (0.1, 0.01).
However, lets be clear THERE IS NO PHYSICAL BASIS TO THE INTERACTION DIAGRAM it is purely empirical.
My personal opinion is that the linear interaction is the only correct creep-fatigue damage interaction and all other interactions are proof that the creep damage has not been calculated using the most realistic method. (Why not the fatigue damage? Well Df is easier to calculate, cycles over cycles to failure, so is more likely to be realistic, over-simplistic again sometimes it is worth reexamining the fatigue damage calculation too, for example the effect of oxidation and compression dwell).
Well done to anybody who has read this far. Now I shall get complex. Remember I defined initiation as as crack 10% of the section, so the crack might actually be a few mms long. Therefore, what we are really doing with creep and fatigue damage is a simplified calculation of crack nucleation followed by a limited amount of crack growth. (You really need to look at R5). Nevertheless, the issue is simple in a laboratory fatigue test the endurance is the number of cycles to grow a fatigue crack to a size where the specimen suffers rapid fracture (which will be a crack a big proportion of the section). Or if the test engineer defines a certain load drop then the specimen has a certain size crack in it. A creep-fatigue test is the same. Nevertheless, It is useful to use the same concept for a structure as for the test specimen, which means that we can scale the test specimen fatigue life to cover both thin sections (less crack growth and endurance than a test specimen) and thick structures (more crack growth and endurance than a test specimen). Only now that I have defined everything can we get to the physical meaning of fatigue and creep damage.
In fatigue the Calculated Endurance(in cycles) = 1/df (fatigue damage per cycle). Now this endurance starts with an completely uncracked structure. So first of all the structure will cycle for many cycles in this uncracked state before any cracks nucleate (20micron crack as defined by R5). But please note fatigue cracks are transgranular. So a total fatigue damage Df of say 0.1 means no crack but some of the available fatigue life has been consumed. For the creep-fatigue case: Calculated Endurance(in cycles) = 1/(df+dc) , this is for the linear interaction. Therefore, it is assumed that the physical basis of the creep-fatigue interaction is that the presence of creep damage, dc (inter-granular creep cavities) enhances the nucleation and growth of the (transgranular) fatigue crack (df+dc).
This is the basis of the creep-fatigue design and life assessment calculation. But you might have spotted some logic flaws.
Structural engineers need nice clear simple procedures and codes such as ASME III NH and RCC-MRx and R5 do provide simple. But this does not mean that it has any physical meaning. There are lots of logic flaws. For example, these are actually crack growth calculations with little thought to cracks. Creep damage is intergranular but fatigue damage is transgranular. Do these really interact as (df+dc) or is it more complex? Initiation is made up from nucleation of a 20micron crack in a previously uncracked structure, the crack then grows a few mms. Is (df+dc) equally applicable to both nucleation and growth of a 1mm crack? What if nucleation is not a transgranular fatigue crack, what if intergranular cracks nucleate..............What about other high temperature mechanisms such as oxidation. How do these interact...........
Remember, ASME III NH and RCC-MRx and R5 provide simple methods. They are not necessary physically accurate but we do try to make them easy to use and conservative.
Article R5 procedures for assessing structural integrity of componen...
As the material properties and loading conditions are not given it is difficult to say what will happen. Yielding and Fracture are two different phenomenon. Yielding is the mechanical measure of elasticity limit after which the material starts behaving like nonlinear material(Nonlinear stress strain path) (Which is also a kind of failure in certain conditions) But the separation of surface hasn't happened. i.e. Fracture is the measure of separation of surfaces and the energy supplied to material in form of body or surface forces is used to create additional crack surfaces. The problem described above can be easily solved using Abaqus or Ansys if the material properties, loading condition and boundary conditions are know.
This diagram may be of little help for physical interpretation of damage. It is a pratical two criteria for engineering damage assessment. The "straight line" is replaced by a bi-linear creep-fatigue interaction envelope. The different envelopes given in the current design codes limit the application for different materials to a low and usually unpractical intersection point, see ASME Section III, NH 2004.
Dear sirs first of all thanks for sharing your thoughts……
Dear Mr. Manfred Staat.
I completely agree with you that this diagram do not help in understanding the physical interpretation and used in design codes. That’s why I want to understand if the current state of a component is represented by a point on this diagram, what actually is happening in the material. For example factor of safety tells linearly how far the component is from failure (say plastic collapse if FOS is given as ratio of yield strength to applied stress), does this diagram give any such information about crack initiation or rupture or any other metallurgical phenomenon (any micro, meso or macro information) There must be some physical meaning of that. If yes, what is that?
Also if i consider it a conservative design curve......from what it will positively prevent....crack initiation, rupture, crack reaching to critical size or...?
Maybe this paper may answer some of your questions:
P. Agatonovic: DAMAGING PROCESS IN CREEP-FATIGUE-OXIDATION ENVIRONMENT AND ITS CONSIDERATION IN LIFE PREDICTION
http://www.agatonovic.de/DamageHTO.pdf
Hello everyone….I tried to find out the answer of this question and I feel there is a delta improvement in my understanding……I m sharing my opinion…..please feel free to reject/correct/improve it….
Damage process is having two stages initiation and propagation and different approaches are used to define cumulative damage in these two stages. During propagation crack is in meso / macro level and hence damage can be related to a measurable phenomenon like crack length extension. As damage is at micro level during initiation so can not measured in a structure in operation. Hence during initiation phase damage in a structure, which is subjected to complex loading, is related to small laboratory specimen test. Laboratory tests and actual component are related by equally stressed volume of material which means rupture of specimen is equal to formation of a visible crack in structure.
Now if we go to ASTM E2714-13 section 1.4 it tells “Data that may be determined from creep fatigue tests include (d) cycles to formation of a single crack or multiple cracks in test specimens” so this damage diagram is lower bound of the test data corresponding to visible crack formation (as per my understanding).
In the light of above it is how I interpret the damage diagram (Assumption: the whole phenomenon is happening at a constant temperature). If during its lifetime a component is subjected to t hours of continuous loading (with stress magnitude σ) and N number of times it is subjected to strain range Δε. Same thing can be represented by N cycles of strain range Δε with hold time of t/N hours each cycle (at stress level of σ). If a laboratory specimen of same material is subjected to such hold cycles it fails after Nf cycles. Also as all the parameters are same in every cycle it will follow a linear path on damage diagram. Hence if component is at point A in damage diagram and we draw a straight line, which intersect the damage curve at B, OA/OB is giving margin in terms of hold cycles to a visible crack to appear in the structure.
All your views are most welcome.....
Regards
Please go through the book "Damage Mechanisms and Life Assessment of High Temperature Components", Ramaswamy Viswanathan, ASM International, 1989, 497 pages. It is a good book and also deals the subject from engineers view point.
@ Phaniraj C
Thanks for the suggestion sir....will you please also comment on my previous reply to this question...am i understanding this phenomenon correct.
Also please see: i) Ashby, M.F. and Dyson, B.F. (1984): "Creep Damage Mechanics and Micro-mechanisms", In: ICF- Advances in Fracture Research, pp. 3-30, Pergamon Press; ii) Book: "Design for Creep", R.K. Penny and D.L. Marriott, Springer Science & Business Media, 2nd Edition,1995 (ISBN-13: 978-0412590405), and (iii) “A Study of Creep Damage Rules” by M.M. Abo El Ata and I. Finnie 1972, ASME J. Basic Eng., 94, pp. 533–541.
Explanation in brief: (please see the work or papers of 1) Kachanov, 2) Robotnov, 3) Lemaitre, 4) Chaboche and 5) D.R. Hayhurst).
1) Creep damage (in broad sense) can be defined as that which leads to the progressive reduction in the materials ability to resist stress and this leads to an increasing creep strain rate regime (i.e., tertiary creep). This can happen by various micro-mechanisms. Note that the fracture mechanics deals with subject of crack propagation and the criterion that addresses when does the crack propagate (say K or J-integral approaches) since finally the propagation of crack(s) can lead to failure. Essentially, fracture mechanics deals with: Linear elastic fracture mechanics (LEFM), Small Scale Yielding (SSY) and Elastic-plastic fracture mechanics (EPFM).
Whereas, damage mechanics models has much broader scope and deals the subject on a micro scale state up to a creation of crack on a meso-scale. And the evolution of various micro-mechanisms (that cause damage) are generally expressed by the set of equations. The approach expresses damage in terms of internal state variable(s) [say one for cavities evolution, the other for loss of cross section, the other for coarsening of precipitates, etc]. The internal state variable can be a scalar, vector or tensor. Say, it deals with the coupled equations (expressing the evolution of damage) and for e.g. creep strain rate is expressed in terms of damage state variable, and solving the equations, one can get functional form of strain in terms of time.
Please see link if you have access: http://www.tf.uni-kiel.de/matwis/instmat/departments/brocks/milano_lectures.pdf
2) What you are asking is the creep or creep-fatigue damage rule diagram, say cumulative damage rule as represented for design (Robinson's time fraction rule or Miner's rule), say either in terms of summation of t/tf or N/Nfs equal to unity. This will tell you whether the rule is conservative or not. Further, Robinson's life fraction (creep damage) rule is applicable for temperature changes (or excursions) and it fails for stress excursions. This is the reason why creep life extrapolation is preferred under iso-stress conditions [plots of time to failure (i.e., creep rupture life) vs. temperature at constant stress].
Best wishes.
Naveen, Dr. Phaniraj has given an elaborate explanation.
I just want to add one thing. Do not get confused between crack initiation and damage. Damage is a precursor to the crack initiation stage. When the damage level reaches a critical value, crack initiation starts. Once the crack has initiated, you may not able to apply the damage mechanics (as the governing principles are derived from continuum mechanics) and you have to switch over to fracture mechanics based approach to comment on whether the component is safe or not.
The diagram that you have posted (from a creep-fatigue interaction situation), tells that at point "A", the material has equal probability of getting damaged by both creep and fatigue process. Should it be straight line or is it the conservative estimate?... is an entirely different topic open to debate. As a matter of fact, modelling damage/life prediction during creep-fatigue interaction is still evolving.
The answer to your opening question "what physically has happened to the material at the given point?" is explained in bold letters above without getting into the debate of whether the construction of the diagram is correct or not.
Continuation of earlier comment....
works of Lemaitre is a good starting point to understand the "damage" and "damage mechanics"
I presume, you understand the "damage mechanisms" during creep or fatigue.
Hello everyone Happy new year to all of you............
@ Dr. S. Shivaprasad - thanks for sharing the information sir...and also for suggesting the book...
A few clarifications sirs....but before that i would like to clarify that I am a mechanical designer and not a material expert....so please reply that fit in the small domain of my understanding.
1. Is damage a precursor of crack initiation (micro crack) or it is precursor of initiation of an engineering crack (0.1 inch)...
2. Please elaborate the sentence "at point A, the material has equal probability of getting damaged by both creep and fatigue process" written in the previous reply..for time being we can assume the diagram is correct...and hopefully that 'equal' is coming as point A is at (0.3,0.3)...so we can take a general point (x,y) below the line for onward discussion.
Appreciate all the help and time.
Naveen
ah...ha...I expected these questions. Let me try my best to explain. Irrespective of whether you are a design engineer or materials engineer, damage is a "material condition" and I have to explain it in terms of material...bear with me.
1.Before coming to whether damage is a precursor to small crack initiation or a sufficiently large crack as defined in engineering design, let us first try to understand damage level in various length scales. At the smallest length scale (micro level), the material damage is often confined to sub-atomic level and is due to generation of point defects/vacancies. Experimentally measuring the damage at this level is difficult and is mostly done through molecular dynamics (MD) simulations. But, to have a meaningful simulation, the number of molecules considered in the simulation process have to be sufficiently large that poses a huge challenge to the power of computing. Let us accept/assume that you have obtained a quantitative measure of defects formed at this level. When this quantity exceeds "a certain level" (let me come to this term later), the damage level reaches a "meso" scale in which you start noticing significant changes in dislocation density/substructure, micro-void nucleation (micro void is still treated under continuum since it is viewed as micro-pores and not exactly as a discontinuity in the material), effective elastic modulus or even new phase evolution. All these factors contribute to a change in the original property of the material and a combined influence of all these factors, measured as a quantity will signify the damage at this level. You can experimentally measure the damage due to various components described above both directly (using SEM/TEM/XRD/neutron scattering) and indirectly (non-destructive evaluation tools like linear/non-linear ultrasonic, magnetic Barkhausen, Eddy current and many more). There are continuum models (eg., GTN) that can account for the influence of various factors to predict the damage level. Remember the damage is still in a pre-conditioning stage and no crack (whatsoever be its size) has nucleated yet. When this damage reaches a "critical level" the material enters into a "macro" level damage wherein actually the crack nucleate and grow. The cracks we consider here are beyond the engineering definition and there are small crack growth based models that predict their growth rate. Once the crack reach a "measurable" size as defined in engineering codes, fracture mechanics based calculation is applied. The small and large crack situation can be put together under the macro damage basket.
We have a better understanding and tools to measure the damage in a material at individual levels to a reasonable estimate. What we do not know is how to define the transition & "the certain critical level" mentioned earlier at each stage. Also what we do not know (or at least to perfect our understanding) is how to effectively implement this scale hopping. After all the "damage quantity" that we measure must have an engineering meaning. Damage mechanics based engineering design is fast picking up and apparently GE has developed a first proto type engine completely based on damage mechanics (a fact yet to be verified) very recently. The point that I would like to convey (with respect to your question) is that the damage as per our current understanding is a pre-cursor to the small crack initiation and were yet to evolve with an engineering definition of damage. The challenges are described above.
2. The fact that point in your plot represent (0.3, 0.3) indicate that under the combined influence of creep and fatigue, the material in question will see equal magnitudes of damage due to creep and fatigue. The prevailing creep damage mechanisms and fatigue damage mechanisms will both influence the material behaviour equally and you cannot preferentially ignore the influence of one of them. On the contrary, if the point has shifted to the top LHS or bottom RHS, it means that major contribution of damage to the material is by creep (in the former) and that due to fatigue (in the latter). It all depends upon how much dwell time is available so that a particular damaging mechanism supersedes the other.
Hope that clear your doubts/confusions.
...addendum to my earlier explanation to #1:
whether it is the nucleation of the fresh crack or extension of the pre-existing flaw, the same damage principles and its accumulation leading to nucleation/crack extension (as the case may be) are applicable. After all, the crack extension from a pre-existing crack involves crack tip deformation process and eventually the material ahead of the crack tip has to go through the damage process as explained earlier. The major difference, however, in case of pre-existing flaw is that the enhanced state of stress (due to stress concentration) can lead to an enhanced damage level. So your question on whether the damage is a precursor to crack initiation or crack extension, depends upon what presumptions you have made while designing a component. Do you design a component with the presumption that the material is defect free or go by a pre-meditative approach that every material will have some defect and consider a defect size in your design? Hope that answers your question.
For all practical purposes, damage evaluation is being used for condition/health monitoring of components as of now (though we are not far off from designing components completely on damage mechanics based). It therefore really does not matter whether you have a nucleation of a fresh crack or extension of the existing flaw. Damage assessments will tell you how far the material has been degraded (eg 60% change in elastic modulus, high dislocation density, 10% cavity formation etc). This is just a warning bell. You can then use on-line NDE methods and fracture mechanics based calculation/stress analysis to detect and comment on the critically of the crack.
@ S. Sivaprasad - Thank you sir. I truly appreciate your time and effort for giving such detail explanation.
Hello everyone....
Based on the the suggestions of Dr Phaniraj and Dr Sivaprasad I tried to go through some of the literature....A lot is available there…but in my opinion the initial work of Lemaitre and Chaboche is a good point to start…“A Course on Damage Mechanics” by Jean Lemaitre will be a nice book for this purpose. I did not read the complete book but the first chapter of this book explains the ‘Damage’ in a physical way. I will recommend this book for all the beginners…
I would like to thank everyone who contributed in this thread....
Regards
Naveen
Dear All,
I discover this discussion only now, so sorry for the late reaction. I hope that even 1 year later, it might still be of some help.
Very useful and relevant technical elements have been put forward by the various answerers, and also good literature, but I'm not sure that everybody reading this exchange of information will actually understand what the presented diagram means.
Therefore this answer.
This kind of diagrams was of "practical use" for discussions on exhaustion level and residual life assessment of fossil-fired power plants components in the years 1980's in several countries : those countries (among which European countries, USA, Japan) where fossil-fired power plants had been designed to safely operate (at least) 100,000 hours (in creep conditions). The problem was to check what was the exhaustion level reached, and thus the expected residual life of components subject to creep and low-cycle fatigue after 50,000, 75,000, 100,000 (and beyond) hours of operation (actual service life taking account that the 100,000 hours of design life were obtained using safety factors as imposed by the design codes). Concerned components were : superheaters, reheaters, high temperature (HT) headers, turbine parts, HT piping etc.
Creep comes from the high temperatures attained by the steam in fossil-fired power plants and fatigue from the use of these plants for electricity peak demand (and also because of changes in operating conditions) .
So, considerations ad thinking on te kind of diagrams as shown by Naveen Bhatt were useful to assess what should be done at the periodical shutdowns for maintenance (usually every 2 years) and where : visual inspection, non-destructive testing, destructive testing on samples, repair, replacement.
In the diagram, the ordinate is for the pure creep exhaustion : supposed to linearly cumulate from 0% to 100 % (0 to 1) following Robinson's rule :
Dc (creep exhaustion) = Sumi (ti/tri), with ti duration of operation under conditions "i" (of temperature and stress) and tri the time to rupture under conditions "i" (as given by standards). Dc=1 means full (100%) exhaustion in creep.
The abscissa is for the pure fatigue exhaustion : supposed to linearly cumulate from 0% to 100 % (0 to 1) following Miner's rule :
Df (creep exhaustion) = Sumj (nj/nrj), with nj number of cycles of operation under conditions "j" (of temperature and stress) and nrj the maximum number of cycles to rupture under conditions "j"(as given by Wöhler's curves). Df=1 means full exhaustion in fatigue.
The inclined line on the right corresponds to 100 % exhaustion in a mix of creep and fatigue.
So the point (0.3 / 0.3) corresponds to a component with 30% exhaustion in creep and 30% exhaustion in fatigue. This component has 50% residual life in pure creep, or 50% residual life in pure fatigue, or 30% residual life in an equal mix of creep and fatigue.
Kind regards
@ Guibert Crevecoeur...
Dear sir...greeting....thank you very much for a detail reply and making this discussion alive again...As you have pointed out...we in our organization also use same diagram for residual life assessment (RLA) of steam turbines....you have even explained the methodology in detail...
Hello everyone...
I have some additional questions now....I will be very happy if get some response on this thread.....
My first question is creep fatigue interaction diagram is used for design of nuclear components in ASME (section III subsection NH)....why it is not used for the design of non nuclear components in section VIII div2?.....is it only because of the failure consequences of nuclear component ?
My second doubt came because of the attached diagram (Reference: Hyeong-Yeon Lee, "Comparison of RCC-MRx and ASME Subsection NH as Elevated Temperature Design Codes" Korea Atomic Energy Research Institute, Nov 2015) why for the some materials (Alloy 800 and 9Cr1Mo) there are different CFI diagrams in different codes?
Regards
Naveen
Hi Naveen,
On your first question, this is to ask to the developers of the ASME code parts ! Probably not so easy ...! On base of my past experience in the field, I'd say that the developers of ASME III (NH) thought it useful to insist on the creep-fatigue interaction diagram, a.o. because there is no unique straight line on the right and there are differences from steel to steel, ...., and designers should be fully aware of it. Developers of ASME VIII (who are not necessarily the same) could think it less important for non-nuclear components, probably indeed because the risks are not the same. However, those engineers responsible for the periodical residual life assessment of operating plants are free to use the diagram of ASME III even for non-nuclear components. It's anyway an useful base for judgment and make a decision on "what has to be done".
Concerning your second question, same thing : the developers of the codes best know how the approach / philosophy they have adopted to build up their codes allow to handle the safety problems related to creep-fatigue interaction. For instance, in American ASME-NH, the creep damage is assessed through the section, while it is at a point in French RCC-MRx. The set of adopted rules is a whole.
Regards
Dr. Bhatt, I am seeing this discussion live again and like to add on to Prof. Guibert Crevecoeur.
As a designer, you know that the creep - fatigue damage (interaction) diagram is highly conservative (for nuclear components) and a number of safety factors are included. Say Nd term (from continuous cycling fatigue design curves) carries a safety factor 2 on stress and 20 on cycles. Further tD values (creep) are from the minimum (or statistically lower bound) curves and stress relaxation response under creep-fatigue is from isochronus stress-strain curves and so on. Whereas for non-nuclear components, I think the stress-rupture curves for creep:- it is the average (on which factor of safety) which is used rather than the minimum and design is not that conservative. Further, for nuclear components, the criterion of stress (with a factor of safety) for time to onset of tertiary creep in say 100,000 h is considered in addition to specific strain criterion (i.e., 1% strain) and rupture criterion.; the former takes care of damage as defined by excessive strain/dimensional tolerance limitation and the latter is to avoid failure.
(1) Please see the attached file: ANL report.
(2) you may also see:- (i) J Nuclear Materials 1992, vol. 199, page 43 and the references in this paper (particularly the paper in J. Basic Eng 94(3), 533-541 by Finnie) ; (ii) JNM, 1993, vol. 203, page 186; (iii) JNM 1993, vol. 203, page 187; (iv) JNM 1994, vol. 208, page 111
(3) Book "Design for Creep" by R. K. Penny, D. L. Marriott, and (4) Book "Damage Mechanisms and Life Assessment of High Temperature Components" by R. Viswanathan, ASM 1989.
Best wishes.
I agree. However, I remember that, for non-nuclear components, the design rule for creep was : minimum stress-rupture curve (uniaxial creep) to produce creep rupture in 100,000 hours divided by 1.25 (thus 80 % of minimum curve). Thus very conservative. But this was in the years 1970-1980 following the design codes (ASME, TRD, BSI, ....) in force in those times ! It might have changed meanwhile. See also p. 70 of the book "Damage Mechanisms and Life Assessment of High-Temperature Components" by Ramaswamy Viswanathan of EPRI (Ed. ASM International - 1989 - 1993 -1995) already quoted before in this discussion by C. Phaniraj.
Dr. Bhatt, please see whether the references below are helpful to you.
(1) "Pressure Vessels: Design and Practice", Somnath Chattopadhyay, CRC Press, 2004:- please see the link if you have access: http://www.fh-kl.de/~bernhard.platzer/downloads/APPBAU/Asme_Press_Pressure_Vessels_Design_And_Practice.pdf ; (2) "An Overview of Nuclear vs. Non-Nuclear Design Code Requirements for a Candidate Steam Supply System for Commercial Applications", Robert Jetter, April 2011:- please see the link if you have access: https://inldigitallibrary.inl.gov/sti/5094590.pdf ; (3) "Creep and Fracture in High Temperature Components: Design and Life assessment issues", ECCC Creep Conference, Sept. 2005 London, Eds. Shibli ET AL.. and (4) D.A. Woodford, Materials selection and design, ASM Handbook, vol. 20. ASM International; 1997. p. 573. Best wishes.
Dear Dr Phaniraj and Prof. Guibert
Thank you very much for sharing your views.....I will go through the references provided by you...
Regards
Prof. Guibert Crevecoeur, you are correct, one of the condition used is the minimum stress/1.25 (80%). I checked it up and for non-nuclear applications and for creep, the allowable stress (St ) is the lowest of:- (i) the stress required to cause a creep rate of 1%/100,000 hours (i.e., 1% strain in 100,000 h), (ii) (the average stress to cause rupture at 100,000 hours)/1.5 (i.e., 67% of the average curve on stress) and (iii) (the minimum stress to cause rupture at 100,000 hours)/1.25 (80% of minimum curve); in addition to Sm (time independent) values of (room-temperature tensile strength)/3.5 and room-temperature yield strength/1.5.
Thanks and best wishes, Phani
Thank you for the confirmation, Dr Phaniraj. So, I understand that the rules for the allowable stress in creep are still unchanged (non-nuclear design) !
Let me attend and continue this interesting discussion.
Dr. Phaniraj touched 9-12%Cr steels. I would like to add a comment regarding these materials. As pointed out by Dr. Phaniraj there are some safety factors to be included. For me it is not clear how to use in the linear/bilinear damage (life fractions) diagram, in general. Indeed, compare two tests with two loading profiles: 1. LCF with tensile holds and 2. LCF with compressive holds. The strain amplitude and the hold time are the same in both tests. Based on the damage interaction diagram I would assume that the specimen tested with the first profile would have much shorter life. This is because under compression, creep damage is not significant and can usually be ignored. So, the diagram says: in the first case we have "creep-fatigue interaction" while in the second one we have pure fatigue. The experimental data for a martensite steel show, that compressive holds lead to much shorter life (factor 2), see, for example
http://bibliothek.fzk.de/zb/berichte/FZKA6931.pdf
This is also partly touched in a parallel discussion,
https://www.researchgate.net/post/Why_is_the_creep-fatigue_interaction_diagram_for_modified_9Cr-1Mo_steel_different_in_RCC-MR_and_ASME_Sec-III
see references, given by Michael Spindler.
This effect can only be explained by (cyclic) softening, so we have possibly to put a third axis on the diagram, or introduce a lot of empirical safety factors ?
There are many other puzzles observed for cyclic loading with holds under multi-axial stress state.
I have found this discussion late and it is difficult for me to grasp all of the threads. I will therefore make things easy for myself by starting at a suitable beginning.
In order to make engineering calculations simple we try to limit our problems to two failure mechanisms in a single procedure. In design calculations we try to be conservative and simple in a single procedure. This discussion, seems to me to be about the life of a structure that experiences a thermal cycle which results in a mechanical strain cycle (strain controlled fatigue) with a period of steady operation at elevated temperature (strain controlled creep). The appropriate Design Procedure is intended to avoid the initiation of a creep-fatigue crack within a certain life/endurance.
What we mean by the initiation of a creep-fatigue crack is a crack which is small with respect to it's structural significance. In R5 (the UK life assessment procedure see Pub. 1) we usually consider 10% of the section thickness to be "initiation of a structurally significant crack" the reason for choosing 10% is so that the calculations can use the stress analysis from an un-cracked body (we are keeping things simple, as I mentioned earlier, here by avoiding crack body analyses, although R5 allows the user to do crack growth calculations also. )
Nevertheless, this means that a critical level of damage equates to the development of a sizable creep-fatigue crack. For example in a 50mm thick section, initiation is a 5mm deep crack.
To make the calculations simple it is usual to calculate the effect of creep and the effect of fatigue separately. This is where the concept of creep and fatigue damage comes from. The engineer calculates these separately, so they have separate names and are based on common summation rules or life fraction rules such as Miner's rule for fatigue and Robinson's rule for creep. Therefore, fatigue damage, df, cycles over cycles to failure, creep damage which comes in two main versions; (i) life fraction time over time to failure, dc, and (ii) ductility exhaustion (strain fraction) strain over strain at failure can both be calculated separately for each cycle (damage per cycle). Each can be summed for the total number of cycles over the design life to get total Creep damage, Dc and Fatigue damage Df.
The engineer now has two different numbers (Dc and Df) representing the two failure mechanisms but no real way to deal with these two values. The simple thing is to assume a linear summation, initiation is conceded if Dc+Df>=1. Also with two values it is simple to plot these on a 2D graph or "interaction diagram".
For the structural engineer all they have to do is calculate Dc and Df plot them on the "interaction diagram" and if the data lie on the inside then they have demonstrated that the structure will not initiate a creep-fatigue crack. Of course I have oversimplified things greatly. There is great skill and knowledge needed to estimate the total strain range of each cycle, which is needed to calculate Df and to estimate the stress at the start of the creep dwell, which is needed to calculate Dc. Not to mention the material engineer, who is needed to define the material properties for all of the possible steels and Ni-alloys, at every operating condition such as temperature. These are big areas of work and can introduce many uncertainties and conservatisms into the final Design Procedure.
But I want to get back to my narrative: There is also the testing engineer who is the villain of this piece (I am a testing engineer so sorry for being the villain). They perform some creep-fatigue tests on uniaxial test specimens and calculate and plot Dc and Df on the "interaction diagram". Then the bad thing happens, rather too many of the points (Dc, Df) lie inside of the interaction diagram (which is often the original linear interaction or a straight line between (1,0) to (0.1) ). There is a simple solution for the testing engineer they just change the interaction diagram to bound all the data and now everything is conservative again. The new interaction diagram with say a locus at (0.3,0.3) is now put into the design code and all the structural engineers have to use it. Some years later another testing engineer tests another material and points lie inside (0.3,0.3) so they empirically adjust the interaction diagram again to say (0.1, 0.01).
However, lets be clear THERE IS NO PHYSICAL BASIS TO THE INTERACTION DIAGRAM it is purely empirical.
My personal opinion is that the linear interaction is the only correct creep-fatigue damage interaction and all other interactions are proof that the creep damage has not been calculated using the most realistic method. (Why not the fatigue damage? Well Df is easier to calculate, cycles over cycles to failure, so is more likely to be realistic, over-simplistic again sometimes it is worth reexamining the fatigue damage calculation too, for example the effect of oxidation and compression dwell).
Well done to anybody who has read this far. Now I shall get complex. Remember I defined initiation as as crack 10% of the section, so the crack might actually be a few mms long. Therefore, what we are really doing with creep and fatigue damage is a simplified calculation of crack nucleation followed by a limited amount of crack growth. (You really need to look at R5). Nevertheless, the issue is simple in a laboratory fatigue test the endurance is the number of cycles to grow a fatigue crack to a size where the specimen suffers rapid fracture (which will be a crack a big proportion of the section). Or if the test engineer defines a certain load drop then the specimen has a certain size crack in it. A creep-fatigue test is the same. Nevertheless, It is useful to use the same concept for a structure as for the test specimen, which means that we can scale the test specimen fatigue life to cover both thin sections (less crack growth and endurance than a test specimen) and thick structures (more crack growth and endurance than a test specimen). Only now that I have defined everything can we get to the physical meaning of fatigue and creep damage.
In fatigue the Calculated Endurance(in cycles) = 1/df (fatigue damage per cycle). Now this endurance starts with an completely uncracked structure. So first of all the structure will cycle for many cycles in this uncracked state before any cracks nucleate (20micron crack as defined by R5). But please note fatigue cracks are transgranular. So a total fatigue damage Df of say 0.1 means no crack but some of the available fatigue life has been consumed. For the creep-fatigue case: Calculated Endurance(in cycles) = 1/(df+dc) , this is for the linear interaction. Therefore, it is assumed that the physical basis of the creep-fatigue interaction is that the presence of creep damage, dc (inter-granular creep cavities) enhances the nucleation and growth of the (transgranular) fatigue crack (df+dc).
This is the basis of the creep-fatigue design and life assessment calculation. But you might have spotted some logic flaws.
Structural engineers need nice clear simple procedures and codes such as ASME III NH and RCC-MRx and R5 do provide simple. But this does not mean that it has any physical meaning. There are lots of logic flaws. For example, these are actually crack growth calculations with little thought to cracks. Creep damage is intergranular but fatigue damage is transgranular. Do these really interact as (df+dc) or is it more complex? Initiation is made up from nucleation of a 20micron crack in a previously uncracked structure, the crack then grows a few mms. Is (df+dc) equally applicable to both nucleation and growth of a 1mm crack? What if nucleation is not a transgranular fatigue crack, what if intergranular cracks nucleate..............What about other high temperature mechanisms such as oxidation. How do these interact...........
Remember, ASME III NH and RCC-MRx and R5 provide simple methods. They are not necessary physically accurate but we do try to make them easy to use and conservative.
Article R5 procedures for assessing structural integrity of componen...
@ C. Phaniraj, Guibert Crevecoeur and Konstantin Naumenko....thank you very much for sharing your views.
@ Michael William Spindler.....sir, thank you very much for such a detailed answer….Reading it was really a delight.
Will you please elaborate on “My personal opinion is that the linear interaction is the only correct creep-fatigue damage interaction and all other interactions are proof that the creep damage has not been calculated using the most realistic method”. Why so?
My sincere thanks to all you people who shared their views in this thread and educated me…Please keep the thread alive :)
Regards
Naveen
Dr. Bhatt, you may see the work/papers of Professor Alan Ponter (Prof. A.R.S. Ponter); the link in RG is:- https://www.researchgate.net/profile/Alan_Ponter
Naveen asked if I elaborate my opinion that "the linear interaction is the only correct creep-fatigue damage interaction and all other interactions are proof that the creep damage has not been calculated using the most realistic method”
I do like making controversial statements. Research papers are often not the best place to express opinions or challenge logic and conferences often do not allocate enough time. Therefore, this thread is the perfect place for this discussion.
I have published most of my existing work on creep-fatigue in the following publication, from which you can follow my working methods. However, the logic is not necessarily spelt out so I will do this here: Fatigue damage is calculated from the number of cycles to failure and creep damage is calculated from either creep rupture time to failure or creep strain at failure. All of these materials properties are usually plotted in logarithmic axes. This is clearly the right thing to do as the test data (both fatigue and creep) are approximately log normally distributed. The important thing about material properties that are log normally distributed is that the scatter is defined by a factor x or ÷ (and not ± as for data which are normally distributed).Next point is in both creep and fatigue failure data the factor describing scatter is relatively large (a factor of 2 for batch specific data and a factor of 5 to 10 for material grade specific data). Also remember in creep-fatigue we often use the factor of 2 for batch specific data as a bench make for a good prediction of creep-fatigue endurance.
So what does that mean? Well it means that creep-fatigue interaction diagrams should always be plotted with logarithmic x and y axes. Now if I was to plot my creep-fatigue test data and some candidate interaction diagrams on Log Dc and Log Df axes. I would be exceptionally pleased if the scatter in the the data was x or ÷ a factor of 2. Also I would plot the interaction line with x or ÷ a factor of 2 lines on either side.
Now that I have done this I can't discriminate any significant difference between a wide range of different interaction diagrams. The bi-linear interaction with a locus of (0.3,0.3) note 0.3+0.3=0.6, should have a scatter out to (0.15,0.15) and (0.6,0.6), where 0.15+0.15=0.3 and 0.6+0.6=1.2. So on any objective measure, you could conclude that the bi-linear interaction were appropriate (for the case where Dc=Df) if the total damage (Dc+Df) calculated for tests lies anywhere between 0.3 and 1.2.
However, of course the linear interaction goes through (0.5,0.5) , where 0.5+0.5=1 with scatter bands (0.25,0.25) and (1,1), where 0.25+0.25=0.5 and 1+1=2. Therefore for the linear interaction to be appropriate the test data should lie between 0.5 and 2.
Now here is the problem; there is too big an overlap between the objective measure for the bi-linear interaction 0.3 to 1.2 and the objective measure for the linear interaction 0.5 to 2. Therefore, with a factor of 2 scatter even the best methods to calculate damage for my test results how can I ever conclude that one interaction diagram is better than another?
Add to this the problem that I can try different methods to calculate creep damage and fatigue damage such as life fraction, strain fraction, I can define failure in different ways use different materials models and soon end up not with a factor of 2 but a factor of 10 difference between different methods to calculate creep damage. So I conclude that small changes to interaction diagram are a complete waste of time (in which case just use the linear interaction as it is the easiest) and we should instead focus on finding the best ways to calculate firstly creep damage (and then secondly fatigue damage). Then and only then might it be worth asking the question "does the linear interaction still apply for this material"?
This is where I suggest that the "Stress Modified Ductility Exhaustion" is the answer to the calculation of creep damage, and direct you to read my papers on the topic.
Nevertheless, if you are feeling really ambitious then: With very careful experimentation split the test results into (i) cycles to nucleate a crack (
Dear sir…thank you very much for a detailed reply….
First let me explain what I got from your explanation…..there is a factor of 2 (multiplication or division) on scatter hence band is increasing as the locus point increases….also a factor not with ± and with ×÷ is increasing the band unevenly on both side…on multiplication side, it is offsetting by 100% while on division side offset is only by 50%....
In the figure (attached) the red hatched portion is showing band for bilinear locus of (0.3,0.3), while green hatched portion is showing band for linear interaction going through (0.5,0.5). From this figure we can see that MAXIMUM PORTION of bilinear interaction with (0.3,0.3) locus is subset of linear interaction (there is a big lap). I have plotted it on a normal scale the difference on logarithmic scale will be not even visible.
IF MY UNDERSTANDING OF WHAT YOU EXPLAINED IS CORRECT…..IT IS REALLY NOT POSSIBLE TO CONCLUDE THAT ONE INTERACTION DIAGRAM IS BETTER THAN OTHER….and linear interaction diagram can accommodate maximum test points…
But as a component designer what I want to understand is…linear interaction diagram seems good as most of the test data points will fall in the scatter band of 0.5 and 2…but either during a fresh design or during residual life assessment of a component could we always take linear interaction diagra...independent of what is provided in design codes for that particular material…I am not able to judge if the factor of 2, with which linear interaction diagram is accommodating a very large area is narrow/conservative enough.
Regards
Dear Naveen
Yes, you have understood perfectly. Having a discussion on "which interaction diagram is best"; is like arguing "How many angels can dance on the head of a pin?" (please see the link if the theological reference is unfamiliar).
You are a component designer and naturally you start with a design code, such as ASME III Div 1 - NH, to be absolutely correct to the design code you must follow their rules fully and use only their materials data (and in this case their interaction diagram). However, this is not very helpful to you as ASME NH only includes Gr22, Gr91, Type 316, Type 304 and Alloy 800H. Either ASME NH will give you too pessimistic a result, and predicts your designs will fail rather quickly, or you actually want to use a different material all together. Either way the published design code does not help you. There are four things you can do:
(i) Approach ASME and ask them to modify their design code for your requirements, which they will do but they will ask you to do much of the work and it could take some time before the code is changed.
(ii) Alternatively Bharat Heavy Electricals Limit..., Steam Turbine Engineering-R&D, can develop your own internal company design code, which is a very good idea but will take a lot of R&D in structural integrity engineering, materials data generation and validation experiments to check that your predictions are realistic. I don't know your company do you have enough people and time to do this?
(iii) Another idea is you could try using R5, although you would still need the materials data and you will still need to justify this to your company and your customers.
(iv) Finally, and I suspect this is the easiest route; you basically try to follow ASME III Div 1 - NH but you modify it with your own materials data and other changes such as to the interaction diagram. Although you would still need to justify this to your company and your customers.
However, you need to be careful as there are lots of reasons why a design code might be too pessimistic (not just the interaction diagram). To calculate creep damage the code must estimate the start of dwell stress depending on the stress analysis and the stress strain data the estimated start of dwell stress might be unrealistically high. For example elastic stress analysis will give a very high start of dwell stress. Simplified elastic-plastic analysis such as Neuber will also overestimate the start of dwell stress. Next the stress strain data needs to be realistic or otherwise again start of dwell stress could be un-realistic. For example for a cyclic softening material don't use the first cycle or monotonic stress strain data as this will over-estimate the start of dwell stress. There are a similar set but often opposite set of conditions to estimating the strain range for the fatigue data calculations. Then a very important consideration is that design calculations use lower bound failure data, such as fatigue endurance and creep rupture strength (or creep ductility). These can be a large factor below the best estimate. For example fatigue design curves can be a factor of 50 lower than the best estimate. Design creep rupture lives can be a factor 7 to 10 lower than the best estimate life. So even if you get the perfect estimate of start of dwell stress and strain range (and stress relaxation) and use best estimate failure data to get Dc=0.5 and Df=0.5 (for example), once you have used lower bounding data Dc=0.5*10 and Df=0.5*50 so your design damages could be Dc=5 and Df=25, which would be way outside of the interaction diagram (0.3,0.3) even way outside the linear interaction (0.5,0.5), hence we need not discuss "How many angels can dance on the head of a pin?" .
Therefore, we must:
(i) Improve our stress analysis predictions of the start of dwell stress, the strain range.
(ii) Improve our predictions of stress relaxation and
(ii) Reduce the scatter band in our bounding material data. Preferably to say a factor of 2. To do this we must understand the reasons for the scatter in LCF and creep relaxation and creep failure data.
At best we can expect to reach best estimate failure data to get Dc=0.5 and Df=0.5 and bounding predictions Dc=0.5*2 and Df=0.5*2, giving Dc=1 and Df=1 with an uncertainty of xor/ 2. Even this is a large uncertainty for a real steam turbine, if it is designed last 40years then in reality to ensure 40 years design the best estimate will be 80years and it might actually last 160years. Try telling your customers that their new steam turbine was designed for 40years but to achieve this you needed to reduce its operating temperature and ability to cycle, and hence it's efficiency, so that it might actually last 160years but at a very great cost. I think your customer might buy a different steam turbine. One that was designed to last 10years only (the designer will not admit this, they will pretend it will last longer), but with luck might actually last for 20 to 40years.
It is a very difficult job. Please keep this thread open as we need to discuss creep-fatigue life predictions.
https://en.wikipedia.org/wiki/How_many_angels_can_dance_on_the_head_of_a_pin%3F
I agree with Michael Spindler that discussion on "which interaction diagram is best" will hardly lead to final agreement. Designing components is one thing. Assessing their behaviour and exhaustion in actual operating conditions in power or (petro-) chemical plants is another thing. Damage level might appear to be very different than expected at design stage. I can only report on my own experience in the years 1980 - begin 1990 in Belgium. At the end of the years 1970, we launched a program for the follow-up of components in low-alloy Cr-Mo-steels (and a few others steels) as used in the Belgian fossil-fired thermal power plants (coal, fuel). This was because several power plants reached their 100,000 hours of design life. As mentioned before, the design calculations followed ASME code (80 % minimum creep stress causing rupture in 100,000 hours : i.e. the most conservative allowable stress as quoted by C. Phaniraj in a former answer).
That time, the current practice in Belgium (like in other countries) was to perform visual maintenance inspection every 2 years (at shut-down of the power production unit). The "100,000 hours" follow-up program was thus included as an additional part to the usual maintenance inspection program.
It was decided, first for the power plants reaching 100,000 hours, to start with exhaustion calculations Under operating conditions as actually lived by the components subject to creep (1st step). The exhaustion being calculated with "actual" stress times 1.25 (to compare to the minimum creep rupture curve) and using Robinson's law. Low-cycle fatigue exhaustion was similarly assessed using Miner's law. Let's call E(C) the calculated exhaustion in pure creep and E(C+F) the exhaustion in creep and fatigue. Then, if E(C)>=0.5 or E(C+F)>=0.6, one had to go to specific non-destructive testing (NDT) - dye penetrant, magnetic, ultrasonics, SEM on replica's - mainly in zones with stress concentration (2nd step). If E(C+F)>=0.8, one had to go to NDT in all zones and to specific destructive testing (DT) : mainly isostress accelerated creep tests on samples taken from the service aged components where feasible (3rd step).
The results showed (for a total of about 30 units) that :
- E(C+F) lay between 0.1 and 0.5 after 100,000 hours
- E(C+F) lay between 0.15 and 0.75 after 150,000 hours (with only seldom a few aligned microvoids : those were usually sparsed)
Some units could even be brought to operate beyond 200,000 hours.
To my knowledge, none of the units was stopped because a level of 100% calculated exhaustion had been reached, nor because of general damage due to creep or creep-fatigue interaction. They were finally stopped for economical and environmental reasons.
We also have similar experience...now a days many of the subcritical power plants installed by our organization in India are completing their design life (around 25 years)....we recommend our customers to go for inspections and residual life assessment (RLA) time to time...first inspection of plant is conducted after 10 years (called condition monitoring, where we do inspection - mainly visual and a very minimal NDT)...Detailed RLA is conducted after > 20 years generally....numbers may be different but procedure for RLA is almost similar as described by Prof Guibert Crevecoeur...and as per my knowledge we also did not reject any component till 20 years of service...in some cases if some surface cracks were found on some casings (even some times on rotors)...after detailed examination they were generally removed and component was placed again on unit...
Although our government is pushing for supercritical or USC units but still some of the customers wanted for modernization of their plant (especially turbine)...these plants are >25 years old now...till now only a very few such cases have been attempted by us ...during modernization some of the components are replaced as their technology is much advanced now (e.g. blading, governing systems etc)...we replaced some of the high temperature components (casings/rotors) also...but reason was never the complete consumption of life...it was always an envisaged higher efficiency due to replacement of the component.
But there are some cases were we rejected our components...lots of surface cracks were observed in some of our components...generally it happened due to improper handling of component or some accidental kind of condition...Like in one case due to failure of one non return valve (NRV) water spray that is used in HP bypass line came inside HP casing (which was at 537 deg C)...its a short of accident...such components are rejected based on NDT not based on RLA calculations.
Regards
In complement to my former answer and to be exhaustive, the calculations for the low-cycle fatigue exhaustion were performed following the German code TRD 301 (TRD = Technische Regeln für Dampfkessel - Technical Rules for Steam Boilers), using actual service data (as far as available). In TRD 301, the actual number of cycles is compared to the number of cycles to rupture following Wöhler's curves (bi-logarithmic). Safety factor was "2" in case of a mix of cool and warm start-ups and "5" in case of only cool start-ups. Concerning the rule of adding creep and fatigue exhaustions, it was given by TRD 508.
We also developed a software package including databanks (of metals, heat exchange data, ...) and calculations of creep and low-cycle fatigue exhaustions, using own-developed models for the fitting of the curves as given by the standards and taking account of thickness lowering due to oxidation (or erosion) in operating conditions. A short description of this software package is enclosed.
I should also briefly talk about the experience with Unit 2 of the Portuguese power plant of Carregado which was put into service in 1969. This will be done in a coming answer.
I had the opportunity to participate to the assessment of unit 2 of the Carregado power plant in Portugal (north of Lisbon). It was a fuel-fired unit (with possibility to switch to natural gas) put into service in 1969. In 1987, it had reached 102,878 hours of operation and so an evaluation of the creep-fatigue exhaustion was needed. A presentation of the results was made at a symposium in Vigo (Spain) in 1988. The results showed that E(C+F) lay between 17 % and 48 %, thus similar to our experience in Belgium.
The Carregado power plant was decommissioned in 2010 (for economical and probably also environmental reasons), i.e. after 41 years of operation for units 1 and 2, 36 years for units 3 and 4 and 34 years for units 5 and 6. All units worked satisfactorily up to their decommissioning, although nearly exclusively in peak conditions the last years. For none of these 6 units, it had been necessary to stop it for reasons of full creep-fatigue exhaustion.
A copy of the presentation at the Vigo symposium of 1988 is enclosed (in Portuguese, but it gives a detailed description of the followed procedure, and maybe Google Translate can help give an idea ! Sorry also for the poor quality of this document, but graphic means were not developed that time as they are today).
I must still react on the comment of Naveen that "....although our government is pushing for supercritical or USC units but still some of the customers wanted for modernization of their plant...". I forgot to mention that a brand new power plant, called Ribatejo power plant with all up to date technical improvements, was built up on a ground in close vicinity to Carregado.
Different manifestations of mechanical damage, including creep damage and (cycle) fatigue damage, can be found briefly but clearly presented at: Jean Lemaitre, "A Course on Damage Mechanics", Springer-Verlag, 1992, pp. 4-9.
Please participate in this thread also
https://www.researchgate.net/post/Why_not_Engineering_Damage_Mechanics
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