Paper presented at IMechE seminar, 'Which Code for Pressure Vessels - ASME, BS or CEN?', 1 October 2003, London, UK
Revision of the fatigue design rules in BS 5500 (now PD 5500  ), to bring them more into line with those in British Standard specifications for other structures, was one of the most radical changes in recent years.  Subsequently, similar rules for welded vessels, but allied more closely with those in Eurocode 3  and the IIW fatigue design recommendations,  were included in the new CEN pressure vessel rules, EN 13445.  Meanwhile, ASME VIII,  which also contains fatigue design rules, continues to be used. This paper compares the fatigue design rules in these three codes, identifies the main differences and considers them in the light of experimental evidence. It is known that the rules in ASME VIII are currently under review and that major changes are likely to be made in the near future. In view of this situation, rather less attention is paid to ASME than the other two codes.
2. Fatigue design methods
All three codes base fatigue design on S-N curves used in conjunction with Miner's rule to assess variable amplitude loading. However, the basis of the design curves, their final forms and the ways in which they are used differ significantly. This partly reflects differences in emphasis but also in design philosophy.
The ASME rules date back to the early 1960s  . They are based on the concept that the fatigue life of any component or structure can be estimated from the S-N curve for the material concerned, as obtained from fatigue tests on small polished specimens, by applying appropriate fatigue strength reduction factors (Kf). Initially, the design curves were obtained from low-cycle fatigue tests conducted under strain control and they covered lives up to only 106 cycles. Later, they were extended to very long lives 1011 cycles, presumably to enable potential fatigue damage from vibration to be assessed. Even so, the overall design approach is clearly directed mainly at high-strain low-cycle fatigue conditions. Furthermore, little attention is paid to weld details as sources of fatigue, implying that non-welded features, such as crotch corners in nozzles, are expected to be the most critical locations.
In contrast, both BS and CEN place particular emphasis on the fatigue assessment of weld details. Furthermore, they recognise the fact that the original ASME concept, that the plain material S-N curve can be simply factored to produce a design curve for a structural detail, is not applicable to weld details. [2,8] Consequently, they provide completely different design data for assessing plain material and weld details, with the latter based on those developed for designing other welded structures (notably bridges and offshore structures). The data used to derive the design curves for weld details relate more to high-cycle than low-cycle fatigue, but it has proved possible to adapt them to cover the full range of endurances relevant to pressure vessels.
2.2 Design procedures
All three design codes provide 'screening tests' to enable further fatigue analysis to be avoided, generally based on a limit to the number of stress cycles expected during the design life of the vessel. In addition, they all provide simplified fatigue analysis procedures based on assumptions about the loading and fatigue resistance. Finally, they all provide a detailed fatigue analysis procedure. These approaches are compared later.
Only ASME provides guidance on the use of special fatigue testing to prove a particular vessel or part, as a substitute for design. Plans are in hand to provide a similar route in the CEN rules. Meanwhile, guidance in the CEN and BS codes is confined to the use of special fatigue tests to validate or change a design curve for a particular detail. In all cases, the results of the testing are analysed in such a way that they embody the same level of safety as the official design curves.
2.3 Design curves
The methods for deriving the design curves from fatigue test data differ between the codes. In the case of ASME and the curves for assessing plain steel in the CEN rules, selected safety factors were applied to the mean curve fitted to the data. These factors were 2 on stress or 20 on life in the case of ASME compared with 1.5 on stress and 10 on life in the CEN rules. One consequence is that the design curves are non-linear even when plotted on a log-log basis.
The design curves for weld details in the BS and CEN rules are statistical lower bounds to test data. Therefore, in contrast to the curves for assessing plain materials, they embody known probabilities of survival. This is more in keeping with the design data in most modern fatigue design rules than the use of arbitrary safety factors. The probability of survival is higher in the CEN rules than in the BS. A further difference compared with the curves for plain materials is that they are linear on a log-log basis, extending down to a fatigue limit for constant amplitude loading at which point they become horizontal. For the usual practical case of variable amplitude loading, discussed later, this fatigue limit is ignored and the curves are extrapolated linearly at a shallower slope. In the case of CEN, the curves then terminate with an absolute fatigue limit at N = 108 cycles.
The fatigue design rules in all cases cover all the materials specified in the relevant code. ASME is the most comprehensive in this respect, including steels, nickel and copper alloys, but not aluminium alloys. The British Standard covers steel and aluminium alloys, but the CEN rules are confined to steels. However, there is no doubt that the main background information in all cases comes from fatigue testing of steels, mainly ferritic. The author is not aware on any experimental evidence obtained specifically from pressure vessels to validate the design rules for any material other than steels.
All the rules require correction of the design curves for operation at elevated temperature, with rather similar values on the upper limit temperatures to which they apply (all below the creep regime). However, this is achieved simply on the basis of the reduction in elastic modulus in the ASME and BS rules. Higher factors, resulting in larger reductions in the design curves, are required by the CEN rules.
Although all the codes draw attention to the deleterious effect of a corrosive environment, none of them provides specific design data. Practical guidance in the BS on the operation of vessels in corrosive conditions has been included in the CEN code. That code also refers to the need to maintain the magnetite layer in water conducting parts in non-austenitic materials at elevated temperature.
2.6 Section thickness
Both the British Standard and the CEN rules recognise that fatigue strength tends to decrease with increasing section thickness, especially in the case of weld details. Thus, correction factors are applied to the design curves when the section thickness exceeds a specified reference value (25mm in CEN, 22mm in the BS). No such correction is required by ASME.
2.7 Complex loading
All three codes contain essentially the same guidance on the derivation of the required stress amplitude or range for multi-axial or combined loading. However, recent research has shown that the method for considering non-proportional loading, where the principal stress direction changes during a cycle, can be unsafe.  Alternative design methods are being developed and revision to the codes is likely in future.
2.8 Elastic-plastic conditions
All three codes introduce corrections to the estimated stress, that effectively lower the design curve, if the range exceeds twice yield. The correction procedure is the same in the CEN and British Standard rules, but a different procedure is given in ASME. There are doubts about the validity of both procedures and they are likely to be reviewed in future.
3. Fatigue assessment of plain material
3.1 Design rules
Both ASME and CEN provide S-N curves for steels related to their tensile strengths (UTS), the assumption being that fatigue resistance increases with increase in tensile strength. In the case of Cu-Ni alloys in ASME, the distinction is based on yield strength. The CEN design curves for steels come from the German AD-Merkblatt code.  They are higher than the corresponding curves in ASME, but in practice would usually be lowered to allow for surface finish and for mean stress if this is not zero, whereas the ASME curves would not. The CEN rules also provide a single lower design curve for steels, for use with the simplified assessment method. This is used independently of UTS, surface finish and mean stress. All the design curves were derived from fatigue test results generated from small-scale polished specimens, under stain control in the case of low-cycle fatigue data.
The ASME and CEN curves are used in conjunction with equivalent stresses, the stress amplitude in ASME and the stress range (twice the amplitude) in CEN. Both codes refer specifically to that based on the Tresca yield criterion (i.ethe maximum shear stress, although twice its value, referred to as the 'stress intensity', is actually used in ASME). However, any equivalent stress that 'produces the same fatigue damage as the applied multi-axial stress' is allowed by CEN. However, an implicit assumption is that this is not the maximum principal stress and therefore that the direction in which it acts is not known.
The BS provides a single design curve for assessing plain material, independent of UTS, surface finish and mean stress. In contrast to the other codes, it is used in conjunction with the maximum principal stress range. This curve was originally derived from fatigue test results obtained from welded specimens and it is used in other British Standards to assess longitudinal welds as well as plain steel.
The various design curves are compared in Figure 1. In practice, the CEN curves will usually be lowered as a result of the application of correction factors, but still there are large differences between the curves, chiefly due to the influence of the UTS. A recent review of experimental data obtained from fatigue tests on actual pressure vessels that failed in plain steel revealed not only that this variation was not justified, but also that some of the design curves were too high  . The relevant data are shown in Figure 2. Whilst the lower design curves are consistent with this database, the ASME curve for high strength steels and all the CEN curves for use in the detailed assessment procedure are not. There is a clear need for review of the CEN design procedure for assessing plain steel.
4. Fatigue assessment of weld details
4.1 Design rules
ASME provides very little guidance on the assessment of welds, recommending just one value of the fatigue strength reduction factor, namely 4 for fillet welds.
In contrast, both CEN and BS offer very detailed rules, reflecting the view that most vessels will be welded and the weld details will tend to be the most critical locations for potential fatigue cracking. A major difference between the American and European codes is the method of assessment. It has been known for decades that the fatigue performance of a weld detail is not related to the S-N curve for the parent metal obtained from tests on small polished specimens by a simple fatigue strength reduction factor, as assumed by ASME. Indeed, such an assumption can be very misleading and result in unsafe fatigue life estimates for weld details, notably because it infers a beneficial effect of increased tensile strength when in fact no such benefit actually exists.  The fundamental problem is that the fatigue life of the polished specimen is dominated by fatigue crack initiation process, whereas that in most weld details is dominated by fatigue crack growth from some pre-existing discontinuity. Thus, in common with most other design rules for welded structures, the CEN and BS rules are based on fatigue test results obtained from actual welded specimens. One consequence is that there are several design curves provided to cover the full range of weld details relevant to pressure vessels. A difference between the CEN and British Standard design curve is that the former are at least 3 standard deviations of log N below the mean S-N curve, while the latter are approximately 2 standard deviations of log N below the mean. Thus, the CEN curves embody a higher probability of survival than the BS curves and, therefore, for a given weld detail they are usually lower. Since the test data used to derive the design curves included the local stress concentration effect of the weld itself, the design curves are used in conjunction with the structural stress in the vicinity of the weld detail, neglecting the local stress concentration effect of the weld itself.
Each design curve refers to particular weld details, modes of fatigue failure and directions of loading. Tables are provided with sketches linking these features and the appropriate design curve or Class. However, an important difference is that the CEN rules favour use of the equivalent structural stress range, whereas the relevant principal stress range (i.e. that acting normal to the plane of potential fatigue cracking) is used in the BS. The CEN rules offer this as an option with the corresponding classification table in a separate annex. The advantage of the use of the principal stress is that account can be taken of the weld orientation. This is important because the fatigue strength of a weld detail usually varies with the direction of loading. Thus, more precise fatigue design is possible using the principal stress. However, it seems that industries in some European countries still prefer use of the equivalent stress range since this is the stress used for static design of the vessel.
Another difference between the CEN and BS rules concerns the form of the design curve in the high-cycle regime. The CEN design curves are based on those on Eurocode 3 and they embody the same assumption that the constant amplitude fatigue limit corresponds to an endurance of 5x106 cycles. In contrast, the BS adopts the fatigue limit used in other British Standards, which corresponds to an endurance of 107 cycles and is therefore lower. There is plenty of experimental evidence to show that some weld details will fail at stresses below that corresponding to 5x106 cycles on the S-N curves.  Thus, the BS design curves are considered to be more realistic than CEN in the high-cycle regime.
Two other features of the European rules that contrast with ASME are:
- The inclusion of recommendations for improving the fatigue strength of some weld details, by weld toe grinding;
- Recognition of misalignment as a major source of stress concentration due to the introduction of local secondary bending when the misaligned joint is loaded.
With regard to the latter, the manufacturing rules in all the codes limit the allowable extent of misalignment. However, both the BS and CEN rules note that even allowable misalignment can reduce the fatigue performance of a weld detail to a level below the design curve. Guidance is given on the calculation of the secondary bending stress due to the various types of misalignment relevant to pressure vessels. In contrast, an implicit assumption in the ASME rules is that allowable misalignment will not reduce the fatigue performance of a weld detail below that estimated using the rules.
The guidance on misalignment is essentially an application of the so-called fitness-for-purpose philosophy, whereby an imperfection in the structure can be considered to be acceptable as long as it does not reduce the strength of the structure below that required. The BS encourages use of this same philosophy for assessing the significance of welding flaws in general, making direct reference to BS7910,  that provides guidance on the application of the approach.
Validation of the design method for assessing welds on the basis of fatigue data obtained from actual pressure vessels was an important step in the adoption of the method in the British Standard. [2,8] The original validation exercise was repeated recently and was extended to consider the CEN rules. [11,14] Again, the BS rules were validated, but limited evidence suggested that some small changes should be made to the CEN rules.
5. Fatigue assessment of bolts
5.1 Design rules
ASME and BS provide essentially the same rules for assessing bolts. The corresponding design curves are expressed in terms of the nominal axial stress on the minimum bolt cross-section due to applied tension and bending. They are based on fatigue data obtained from polished specimens and therefore they must be used in conjunction with a fatigue strength reduction factor, 4 unless a lower value can be justified, to allow for the stress concentration effect ofthe thread root. In contrast, the design curve in BS7608,  lowered to correspond to mean - 3 standard deviations of log N, was adopted for CEN. This was based directly on fatigue data obtained from actual (steel) bolts. Thus, in this case, the design curve already incorporates the stress concentration effect of the thread root. Therefore, it is used in conjunction with the nominal stress. In all cases, it is assumed that the fatigue strength of a bolt increases with increase in material UTS, up to specified limits.
Recent fatigue test data obtained from steel bolts show that the fatigue lives of bolt threads are in fact independent of the tensile strength of the steel.  Therefore, there is no justification for assuming a higher design curve for higher strength bolts. However, the new data also suggest that all the present design curves are over-conservative, as seen in Figure 3. A preliminary analysis indicates that a single design curve, independent of steel strength, could be provided. 
6. Practical application of the fatigue rules
6.1 Exemption from fatigue analysis
Both ASME and CEN include simple ' screening test' criteria for exemption from fatigue analysis, based on specified numbers of stress cycles (1000 in ASME, 500 in CEN), together with some restrictions on the type of vessel concerned. However, a difference is that ASME allows consideration of both pressure and thermal cycles, whereas CEN is restricted to vessels that only experience pressure cycling.
BS provides a more comprehensive approach that limits a combination of the number of cycles from any source of loading and the design stress to a value that would lie on a relatively low S-N curve. The designer has the option toreduce the allowable design stress for the design of the vessel as a whole to meet the criterion if required.
6.2 Simplified fatigue design method
All three codes provide simplified methods that can make use of conservative estimates of cyclic stresses. However, again the BS method is the most comprehensive. In ASME, the various sources of fatigue loading (pressure, temperature and mechanical) are identified and methods for estimating the resulting stress are given. However, it is acknowledged that some of these are non-conservative. The resulting stresses are then compared with the design curve. The corresponding number of cycles from the design curve at that stress must not exceed the number of cycles expected in service from the same load source. Clearly, a further non-conservative feature of this approach is that the possible combined effect of more than one load source, which is always more damaging than that due to the sum of the damage due to the separate load sources,  is neglected.
Neither of the non-conservative aspects of the ASME method is present in the BS and CEN approaches, which are similar. However, as in the case of the 'screening tests', the CEN method is restricted to vessels experiencing only pressure loading. The basic method is to make conservative estimates of the cyclic stresses due to the various load sources (only pressure in CEN), perform a simplified cycle counting procedure (which combines load sources in the case of BS), and apply Miner's rule in conjunction with the appropriate design curve, or a specified low curve if this is not known. The BS rules give conservative estimates of the stresses due to pressure and thermal loading, with the basic assumption that details will be located in regions of structural stress concentration with an SCF of 3. However, the user has the option to perform analysis to produce more accurate stresses if required. In this context, a valuable feature of the CEN rules is the inclusion of SCFs (called 'stress factors') for a wide range of structural details.
6.3 Cumulative damage calculations
As noted earlier, all the rules recommend the use of Miner's rule to assess the fatigue damage introduced under variable amplitude loading. However, only the CEN and BS rules provide guidance on the analysis of fatigue loading, both referring to the use of the Reservoir cycle counting methods for converting complex stress spectra into recognisable cycles. Furthermore, they both acknowledge the need to modify the design S-N curve in the high-cycle regime to allow for the fact that stresses below the original constant amplitude fatigue limit become damaging once a fatigue crack has initiated under higher stresses in the spectrum. They both adopt the commonly used approach of extrapolating the S-N curve beyond the fatigue limit at a shallower slope. The CEN design curves then introduce an absolute cut-off fatigue limit for any loading conditions at 108 cycles. Since the ASME curves do not include a sharp cut off at the fatigue limit, in a sense they are already suitable for cumulative damage calculations.
It should be mentioned that there is now an extensive body of experimental data that throw doubt on the validity of Miner's rule and the method of allowing for the damaging effect of stress ranges below the fatigue limit.  This is the subject of some research projects and revisions to the current cumulative damage approach may be introduced in future.
6.4 Stress analysis
Although all three codes provide details of the stresses used in pressure vessel design, a particular effort was made in the CEN rules to include clear descriptions of the stresses used specifically in fatigue assessments. Even so, there is still a growing need for clearer guidance on the extraction of the relevant stresses from finite element (FE) outputs.
In the context of detailed stress analysis by methods such as FE, an important development that is likely to influence all the pressure vessel design rules in future is use of the so-called structural hot-spot stress for designing weld details from the viewpoint of potential fatigue failure from the weld toe. Preliminary guidance on the use of hot spot stress is given in both the BS and CEN rules, the latter being particularly detailed. However, the method of deriving the hot-spot stress given in the BS needs revision in the light of more recent research.  Similarly, the guidance contained in the CEN document does not go far enough in applying the approach, in that the hot-spot stress could be used with higher design curves in some cases. It is understood that the approach is currently being developed to allow major revision of the ASME fatigue rules for weld details.  Meanwhile, of the three design codes considered here, at present the most advanced guidance on the use of the hot-spot stress is that contained in the CEN rules.
7. Future needs
- Review of rules for assessing plain materials
- Revision of rules for threads and bolts
- Development of hot-spot stress approach
- Review of treatment of complex loading and elastic-plastic fatigue
- Clearer link between FEA and fatigue design data
- Procedure for use of experimental methods in design
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