What is Fatigue? If you ask this question, all engineers working in Pressure Equipment design will certainly give the correct answer: Fatigue is that phenomenon, for which in metallic structures subject to cyclic loading, in some particular location, after a certain number of load cycles, a fatigue crack will be generated. Well, we could possibly make a slight correction to this general definition: the particular location in which the start of a fatigue crack is possible is not the same for welded structures and for unwelded structures: for unwelded structures the crack can start at the locations where a sharp corner or a sharp variation of shape is causing what we generally call a stress concentration, that is, a significant increase of the local stress caused by the loads; while for welded structures the defects certainly contained in the weld (to a greater or lesser extent, depending on the type of weld) constitute themselves a singularity of shape capable of locally generating a stress concentration.
But are we sure that the word “stress concentration” is really applicable to all the possible situations? Of course, the simple formulae contained in the pressure vessel calculation standards are not always able to detect these stress concentrations, so the only means at our disposal is the stress analysis performed with numerical methods: the so-called finite element calculations. Well, although a significant progress has been made on the computer programs capable of making such calculations, the great majority of them are actually still performed using the classic linear elastic model: that is, an approach where the elastic behaviour of the material (stresses always proportional to strains) is supposed to exist also beyond the physical limit given by the yield point of the material. But what happens in the locations where they are above this limit, or better, when the computer tells you that they are above this limit?
It is clear that, in ductile materials such as carbon and low-alloy steels, stresses greater than the yield point cannot exist: because when the material is arrived at the yield point, with a further increase of the external loads, permanent deformations will take place, so that we should not get stress concentrations, but, more exactly, strain concentrations, that cannot be detected by the classic finite element programs based on the elastic analysis. In any case all the standards dealing with fatigue calculations contain “fatigue curves” (that is, curves that give the allowable number of cycles possible with a certain value of the “stress range”, where for stress range – in some standards it is called the “deltasigma”, in other standards the “alternating stress” – we mean the difference between the maximum and minimum stress in a cycle). The problem is that such curves have always been determined using the full elastic approach; and only in some more recent standards a clear distinction has been made among curves for unwelded components, and curves for different classes of welded components.
Another question is the following: what is the meaning of the number of cycles that we should find at the end of our stress analysis? Is this the number of cycles expected for just the start of a crack, or the number of cycles expected for the propagation of the crack through the entire thickness of our component? In this case there is a remarkable difference between unwelded structures and welded structures, particularly for those welds that are likely to contain a greater number of defects. Everybody knows that the best welds are those made with a back pass, because the back pass will cause the fusion of the root of the weld made on the opposite side, and therefore the disappearance of all the defects that are generally contained in the root pass of the first weld. Therefore, a longitudinal butt weld in a cylindrical shell, possibly also ground flush on both sides, is certainly less susceptible to fatigue than the partial penetration weld of a nozzle: in this latter case you can suppose that each one of the weld defects contained in the root pass is already a possible start of a crack, thus greatly reducing the amount of load cycles needed for the propagation of the crack through the entire thickness of the component.
However, the distinction among different weld classes is not the only difference among the different standards dealing with pressure equipment. Other differences are due to the type of stress to be taken into consideration for the calculation of the stress range: some standards use the “structural stress”, that is the overall membrane plus bending stress on the entire thickness, thus excluding the peaks: other standards use the total stress, including the “peak stress”, or the so-called “hot-spot stress”. But the meaning of these definitions is not the same in the different standards, so that, even starting from the same finite element analysis, made with the same methods (full linear elastic or limit analysis), you will get different results using different pressure equipment standards.
Pressure vessel designers are accustomed to evaluate the correctness of their calculations on the basis of the safety factor, that is, on the basis of the ratio between the allowable stress (if you prefer the European definition, the nominal design stress) and the stress actually calculated with the formulae. But when you get a number of cycles from a fatigue curve, what is the safety factor? Looking a little bit in the literature, you will find that, depending on the standard, the theoretical safety factor on the stress range is variable between 1,5 and 2, while the safety factor on the number of cycles is variable between 10 and 20: which means that, if your calculation tells you that your structure is capable to withstand 1000 cycles, you will probably get a failure when you will reach 10000 or 20000 cycles. But the standards generally do not specify the type of failure: is it a safety factor on the start of a crack, or a safety factor on the final stage of the crack, that is, on the number of cycles that will cause the propagation of the crack through the full thickness of the component?
Sometimes I have met manufacturers who are building vessels working normally under cycling loads, because they are turned on and off many times every day, such as sterilization autoclaves or other vessels subject to a batch service. Well, most of them were sincerely convinced that their vessels had never experienced a fatigue failure, although, just giving a quick look at the drawing, I realized that they had never taken a great care in avoiding sharp corners or partially penetrated welds: but probably for them a fatigue crack becomes a real crack only when it will cause a well identifiable leak from the vessel content to the atmosphere.
One more thing on which the Pressure Vessel standards give different prescriptions, are the rules to be used for the determination of the need for a fatigue analysis. For example, ASME Section VIII division 2 is using the so-called screening criteria, that is a series of information that the user must transfer to the manufacturer to establish whether a fatigue analysis is needed (having read these criteria, I think that it would take less time in performing the stress analysis than in finding the information needed for their application). On the contrary, at least for the cases where the cycling is due to pressure only (and therefore the stresses are directly proportional to pressure, so that the stress range is equal to the maximum stress), the European standards generally give simple formulae based on an equivalent number of cycles, where for equivalent number of cycles they mean a relatively low figure (500 or 1000) multiplied by the ratio between the maximum allowable working pressure and the pressure range, elevated to 3; more complicate formulae are generally given for the cases where the cycles are due also to temperature.
The European standards however generally offer an alternative to the design by analysis: that is, a simplified method to find the stress concentrations using a stress concentration factor to be multiplied by the structural stress given by the simple code formulae: there are tables giving these factors for all possible components, taking also into account the type of welded connections, and also the weld class to be considered. Such procedures are generally more conservative that the procedures based on a numerical stress analysis, but they are an important simplification for all cases where a great precision in the calculations of the allowable number of cycles is not necessary.
But then, supposing to have already solved the problem of determining the allowable number of load cycles for a given vessel, there is a further problem, this time not for the designer, but certainly for the user: how is it possible to register the number of load cycles applied to the vessel in order to determine the moment in which it should be put out of service? Because when we say that a vessel is subject to fatigue, it is clear that its life will be terminated when the number of load cycles specified in design will be reached. This of course means that the vessel must be monitored in service, exactly as the vessels operating in creep conditions: the problem is that this monitoring is certainly possible for the large vessels working in chemical, petrochemical or energy plants, where the users make regular registrations of pressure and temperature together with the relevant fluctuations; but I strongly doubt that small sterilization autoclaves operating in hospitals or in medical practices, that are turned on and off several times a day, are subject to a monitoring system capable of counting the number of load cycles during their service life.
If we want to add a further problem, we have to consider the origin of all the fatigue curves used in the most important pressure vessel standards. Of course, these curves are the result of some kind of test, maybe performed several years ago, on test specimens of various dimensions and shapes, where the stresses were calculated by means of simple formulae or by means of a fully elastic stress analysis, whose results are therefore given in terms of stresses, sometimes, as explained above, higher than the yield point of the material. Therefore, the fatigue curves given in the different standards, together with the different type of stress range to be input into the fatigue curves, might lead to different results in terms of allowable number of cycles. Which, of course, is not a problem if the safety factor on the number of load cycles is 10 or 20, as explained above.
Anything else? Sorry, I have forgotten something: the curves used in the pressure vessel standards are usually made supposing that we are not in a corrosive environment: because in this case it is the corrosion which can cause, or accelerate, the start of a fatigue crack.
As you have certainly understood, the treatment of fatigue is still an open subject, in which a certain amount of theoretical and experimental studies could be useful in order to arrive at a better treatment of this complex phenomenon. In the meantime, what can we recommend to the poor designers? One very simple recommendation is the following: do not try to mix up the different standards: just choose the one which has been imposed by your customer or by the local legislation, and follow carefully all its prescriptions: and when it requires a stress analysis, pay attention to find out all the possible sources of alternating stresses, taking into account that temperature fluctuations are more dangerous than pressure fluctuations. Never forget that in fatigue problems what is really dangerous is not the stress itself (either thermal or mechanical), but its fluctuation: very easy to be found when you have a pressure cycle (all stresses proportional to pressure, no change in their direction during the cycle), more difficult when you have a temperature cycle, because in this case the stresses change not only in intensity, but also in direction. And, when you have finally found a number of cycles, never forget to communicate this number to the user, and recommend that he should prepare a suitable monitoring system capable to advise him that, when this number has been reached, the life of the vessel is finished.
Fernando Lidonnici
Convenor of WG53/CEN TC54
Milano, November 16th, 2024
Azienda certificata ISO 9001
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