Estimating LongEndurance Fatigue Strength of GirthWelded Pipes using Local Stress Approach
Yanhui Zhang and Steve J Maddox
TWI Ltd, Granta Park, Great Abington, Cambridge CB21 6AL, UK
Paper presented at Proceedings 33rd International Conference on Ocean, Offshore and Arctic Engineering (OMAE 2014) June 813, 2014, San Francisco, USA
Abstract
Nominal and hot spot stresses are conventionally used for fatigue design of welded joints. In this paper, use of local stress approaches was attempted to estimate the long endurance fatigue strength of girth welded pipes. Finite element modelling was carried out to determine the dependence of the stress concentration and throughwall stress distribution on weld root bead profile, with hilo values ranging from 0.25 up to 1.0mm. Two local stress approaches, critical distance and reference radius, were used to estimate the fatigue strength of girth welds at 5x10^{6} and 10^{7} cycles, which were then compared with available fullscale fatigue test results. To use the critical distance approach, the relevant material properties, such as threshold stress intensity factor range and fatigue limit for flush ground welds, were determined experimentally. This paper presents the results of the fatigue strength estimates and draws conclusions about the applicability of the local stress approaches to girth welds.
Introduction
Fatigue design of welded joints is generally based on SN curves expressed in terms of either the nominal or structural hotspot stress range [eg, 1,2]. Neither of these stresses includes any allowance for the notch effect of the stress concentration at the fatigue crack initiation site. Instead, this is built into the SN curve by basing it on the results of fatigue tests on actual welded specimens. That stress concentration depends on the local weld geometry which in turn depends on such factors as the welding process, the welding position and the type and extent of any welding flaws. Variations in these factors lead to scatter in fatigue test data, scatter that is particularly wide in the longendurance regime. Thus, although the above design approach is convenient for designers, weaknesses are that the longendurance fatigue life and the constant amplitude fatigue limit (CAFL) are not well defined and that it is not possible for the designer to make allowance for known characteristics related to the factors that influence the local stress concentration and hence fatigue life. To overcome these inadequacies, there is increasing interest in the development of local stress approaches that include allowance for the notcheffect of the weld itself, for the fatigue design of welded joints.
Local stressbased fatigue assessment approaches involve use of the stress range at the point of potential fatigue crack initiation under consideration in conjunction with a suitable SN curve. This might be an SN curve for the same material without a stressconcentrating feature, typically that for smooth specimens when assessing machined notches. In this context, one way to determine the local stress range is to multiply the applied nominal stress range by the maximum stress concentration factor (SCF), K_{t}. This is a simple task if the assessment concerns a welldefined geometry for which a published SCF is available. However, even then the approach can prove to be too conservative, with the actual life being significantly higher than that determined by this method. In other words, the SCF is higher than the fatigue strength reduction factor, K_{f} [3]. A simple example is a plate with a hole in it, where K_{t} = 3.0. For a very small hole (for example, in μm), K_{f} is found to be 1.0. However, for a hole with a sufficient size (for example, in mm), K_{f} approaches K_{t}. A number of researchers have attempted to produce methods of calculating a local stress that takes account of this behaviour by assuming that the apparent increase in strength for small notches is due to the fact that the stress concentration occurs over only a small volume of material. The underlying assumption is that, in order for fatigue failure to occur, the average stress must exceed the fatigue limit of the material without stress concentration, ΔS_{o}, over some critical volume surrounding the notch, rather than the maximum stress range. Neuber [4] proposed a microstructural support concept which considers the effect of a stress gradient on fatigue behaviour. The effect can be taken into account by different hypotheses in the elastic stress analysis of a notch. For simplicity of calculation, this approach is often reduced to a consideration of the stress at a single point [3,57], the stress averaged over a given distance [4,68] or the stress averaged over an area [7,9]. The resulting local stress might still be suitable for comparison with the notchfree SN curve for the material or, and certainly in the case of welded joints, a better comparison might be with an SN curve derived from fatigue test results obtained from notched samples that are expressed in terms of the same local stress.
Steel catenary risers (SCRs) are increasingly used for deepwater oil and gas developments. Pipes are joined by girth welds commonly made from one side. The fatigue performance of the welds, especially in the long endurance regime, is a major design consideration since SCRs can experience cyclic loading from a variety of sources, including very high numbers of low stress cycles due to vortex induced vibration (VIV). Thus, a local approach that improves the accuracy of longendurance fatigue life or CAFL estimations could be highly relevant. A recent TWI project involving fatigue tests of girth welded pipes included comprehensive posttest examination of the welds with particular attention to the geometry in the weld root region where fatigue cracking initiated [10]. This provides a good opportunity to examine the suitability of local stress approaches for girth welds. Thus, two widely recognised approaches, critical distance and reference radius, were used to estimate the longendurance fatigue strengths of girth welds.
Outline of the local stress approaches used in the analysis
Critical Distance Approach
This approach was first proposed by Tanaka [6] and further developed by Taylor [7] after analysing the stress distribution ahead of a crack and relating the average stress to a material constant a_{o}, originally proposed by Haddad et al [11]. For a component containing a crack, the fatigue limit, ΔS_{oc}, can be estimated using linear elastic fracture mechanics (LEFM) by the following equation:
where ΔK_{th} is the threshold stress intensity factor range, F is a parameter dependent on geometry, crack size and shape which is equal to 1.12 for an edge crack [12], and α is crack length. However, when the crack size is very small, less than about 1mm, the above relation becomes invalid, due to the socalled crack size effect [13]. LEFM predicts an almost infinite fatigue limit as the crack size approaches zero. However, in reality, it is known that, when a crack is small, the fatigue limit will not be as sensitive to the change of crack size as predicted by Eq.1 and there will be a definite fatigue limit of ΔS_{o} for a smooth, uncracked body. To calculate the fatigue limit for components containing small cracks, Haddad et al [11] proposed the following empirical equation by introducing the material constant a_{o}:
where ΔS is the stress range and ΔK is stress intensity factor range. When ΔK is equal to ΔK_{th}, ΔS is equal to ΔS_{oc}. By noting that, when crack size a approaches zero, ΔS_{oc}= ΔS_{o}. α_{o} can be estimated from:
The introduction of the parameter α_{o} was to overcome the difficulty of applying LEFM in the small crack regime. The above equations have been used to calculate fatigue limits for cracked components [78].
Taylor [7] found that a_{o} is an important material parameter which can also be used to estimate the fatigue limit for notched, but uncracked, components. He observed that the stress at a distance of a_{o}/2 from the maximum stress location, the average stress over a line distance of 2a_{o} and the average stress over an area within a radius of a_{o} from the surface with the maximum stress were almost identical to the fatigue limit of the uncracked material (ΔS_{o}). He termed the three stresses point, line and area respectively. Thus, the stress distribution approaching a notch (as seen later, in Figure 6) could be used to determine the fatigue limit of the notched component as the applied stress needed to produce the material’s ΔS_{o} value at these three locations. Indeed, he found that the same method produced reasonable estimates of the longendurance fatigue strength, endurances less than, but approaching, the fatigue endurance limit. In such an application, ΔS_{o} would be the fatigue strength of the plain material at the endurance of interest. The cases concerned were a wide plate containing a circular hole [7], a Tshaped fillet welded joint and a butt weld [14].
It will be evident that the fatigue strengths estimated by the above methods depend on α_{o}, which in turn depends on the parameters in Eq.3. The effect of changes is not clear cut. A decrease in F would increase ao and hence increase the fatigue strength estimate. However, the value of ΔS_{o} influences both a_{o} and the stress to be compared with that obtained from the stress distribution curve such that the estimated fatigue strength of the detail under consideration may be increased or decreased. This is considered later when the method is applied to girth welds.
The apparent success of the approach for estimating the fatigue strength of welded joints is surprising. A key parameter in the definition of the critical distance a_{o} is the fatigue limit for the unnotched material. This implies a connection between the fatigue performance of a welded joint and that of the parent metal, whereas none exists. This is particularly the case when highstrength materials are considered. In general, the fatigue strength and fatigue limit of the plain material increase with increase in tensile strength whereas those for welded joints are independent of tensile strength. Nevertheless, in spite of these misgivings it was decided to investigate the application of the approach to girth welded joints in steel pipes.
Reference Radius Approach
This is also an average stress approach that represents a sharp notch by a reference round notch. The basic idea is that the stress reduction due to averaging the stress over a certain distance from the notch tip can alternatively be achieved by introducing a fictitious, enlarged notch radius. Neuber [15] proposed the following equation for the fictitious radius, ρf :
where ρ is actual notch radius, s is a factor based on a stress multiaxiality and strength criterion and ρ* is a dimension analogous to Haddad’s material constant ao that would need to be established experimentally. For welded joints, Radaj et al [16] assumed s to be 2.5 for plane strain conditions, which was based on the stress analysis under different loading conditions [17], and ρ* to be 0.4 for lowstrength steel. This results in an increase of the actual radius by 1mm. For the most severe stress concentration, ρ can be assumed to be zero, resulting in a reference radius of 1mm. Applying this method to welded joints, the actual sharp notch (e.g. weld toe or root) is replaced by a reference radius of 1mm in the FE model and the maximum stress on the radius taken to be the local stress. Based on fatigue test results obtained from a variety of welded joints expressed in terms of this local stress range, the IIW FAT225 SN curve (the fatigue strength at N = 2 x 106 cycles being 225 MPa) has been proposed for design [18]. This approach has also been included in a DNV code [2]. Although less widely used, a reference radius of 0.05mm has also been proposed [19,20], for assessing very thin (sheet) specimens, related to the much higher FAT630 design curve. The current IIW recommendation is that it should only be needed for thicknesses up to 5mm. Although the 0.05mm radius would not be considered suitable for assessing the girth welds, this approach was explored here for comparison.
To evaluate the accuracy of the present fatigue strength estimates, the corresponding mean SN curves should be used. According to Sonsino [21], the mean curves for both FAT 225 and FAT 630 can be estimated by multiply the FAT number by 1.37. This results in fatigue strengths at 2 x 106 cycles of 308MP for the 1mm reference radius and 863MPa for the 0.05mm. The estimated fatigue strength was equivalent to the nominal stress when the local stress was equal to the fatigue strength corresponding to the designated mean SN curve.
Girthweld data used to apply local stress approaches
Fatigue Performance of FullScale Girth Welded Pipes
Details of the material, testing conditions and fatigue performance of the girth welds are contained in [10]. In brief, 406mm outside diameter by 19.1mm wall thickness seamless steel pipes to API 5LX70 specification were tested. The girth welds were made from one side using PGMAW/GMAW processes, in the 5G position. The weld cap at each start/stop position was ground flush with the pipe surface. All welds were acceptable to a typical SCR weld quality specification. Each weld was instrumented with strain gauges to allow measurement of axial strain and its variation around the circumference on the outside surface of the pipe. The nominal strains were used in conjunction with axial misalignment measurements to calculate the stress range in the region of fatigue crack initiation. The tests were performed in resonance fatigue testing machines at around 30 Hz with an axial tensile mean stress of 150MPa, achieved by pressurising the pipes internally with tap water.
A total of eleven girth welds were tested to establish the constant amplitude (CA) SN curve. Fatigue cracking always initiated at the weld root and propagated through the pipe wall to the outside. Regression analysis produced a mean SN curve of the familiar form ΔS^{m}.N = C, where m and C are material constants, with m = 3.25 and C = 2.02 x 10^{13}, slightly shallower than the design SN curves for weld toe or root failure, for which m = 3. However, the value of m = 3 is within 95% confidence estimates of the slope and therefore it would be legitimate, because of the small number of tests, to assume this value when fitting the SN curve, giving ΔS^{3}.N = 6.174 x 10^{12}. The test results and the mean, lower (mean minus 2 standard deviations of log N) and upper bound (mean plus 2 standard deviations) curves are plotted in Figure 1 where they are seen to be generally better than the BS 760^{8} [1] Class D mean SN curve. The lowest stress range that produced failure, with an endurance of 4.4x10^{7} cycles, was 55.4MPa. Thus, it appears that the CAFL for these girth welds may correspond to an endurance between 5x10^{7} and 108 cycles which, considering also the two unbroken welds that survived for 108 cycles, would be between 45 and 55MPa. It is apparent that the Class D mean fatigue limit of 74MPa, corresponding to 10^{7} cycles, overestimates the value suggested by the present test results.
Extensive posttest examination of failure locations and macrosectioning of unbroken welds were carried out. The fatigue performance of the girth welds strongly depended on the profile of the weld root bead toe where the fatigue cracks always initiated. Poor weld root profile, which was indicated by a large step between the surfaces of the weld root bead and the adjacent pipe, created a high stress concentration.
In the present girth welds the step was equivalent to the hilo, the step between the pipe surfaces either side of the weld, because of the very flat weld root bead, as indicated in Figure 2. For each girth weld, the majority of the weld along the pipe
Figure 1 Fatigue test results obtained from fullscale girthwelded pipes
circumference exhibited a relatively good weld root profile, with hilo values less than 0.2mm. However, regions with poor weld root bead profile were always found along the weld and crack initiation often occurred at a location with the poorest weld root bead profile. Figure 2 shows two examples. In the first (Fig.2(a) and (b)), a small crack, 0.32mm deep, had developed at a location with a hilo of 0.5mm after the weld had endured 4.0x10^{6} cycles at 116MPa. In the second example
Figure 2 Macrosections of two girth welds
a) Low magnification view of weld W2 in pipe S13 which was unbroken after 4.0x10^{6} cycles at a stress range of 116MPa;
b) Higher magnification view of weld W2 in pipe S13. The crack and the hilo were respectively 0.32mm and 0.5mm at the section.
c) Macrosection of weld W2 in pipe S10 which was unbroken after 2.97x10^{7} cycles at a stress range of 72MPa. The crack and the hilo were respectively 0.24mm and 0.5mm at the section.
(Fig.2(c)), where the hilo was also 0.5mm, a 0.24mm deep had developed after 2.97x10^{7} cycles at 72MPa. Both welds were declared to be runouts since failure occurred in other welds in the specimens.
The worst hilo values from a total of 33 girth welds were measured (the project involved further tests under variable amplitude loading). They represented either the largest present in an unbroken weld or the value at the failure location. The average hilo value was 0.47mm. The measured hilo values of these girth welds are shown in Figure 3. Statistical analysis showed that 80% of them fall between 0.25 and 0.68mm
Threshold Stress Intensity Factor Range
In order to calculate the material constant a_{o} using Eq. 3, the threshold stress intensity factor range, ΔK_{th}, is required. This was determined in the girth weld project using singleedge notch bend specimens, notched in the welds which were at the centre. The tests were carried out under decreasing ΔK in accordance with BS 12108 [22] at a stress ratio R=0.7 and a loading frequency of 10Hz. ΔK_{th} corresponding to a crack growth rate of 10^{7}mm/cycle, in accordance with ASTM E647, was determined to be 134N/mm^{3/2}.
Fatigue limit of flush ground welds
In order to consider a welded joint, ΔS_{o} in Eq.3 should be the fatigue limit for flush ground girth welds. Relevant experimental data from flush ground girth welds in strip specimens cut from pipes [23] are presented in Figure 4.
Figure 3 The worst hilo values measured from a total of 33 girth welds.
Figure 4 Experimental results of flush ground girth welds [22] and the SN curve derived from these data.
Regression analysis of the data produces a mean SN curve with a slope of m = 4.2, compared with the value of 4 for the relevant BS 7608 design curve (Class B). Reanalysis of the data assuming m = 4 gives the mean curve shown in Figure 4, ΔS^{4}N=5.88 x10^{15}. It will be evident that the fatigue limit is not obvious from the available data. Therefore, for the benefit of the analysis of the girth welds values corresponding to the fatigue strengths at 5x10^{6} and 10^{7} cycles were used to define ΔS_{o}. From the fitted mean SN curve these are 185.2 and 155.7MPa, respectively. With the above ΔK_{th} value, the material constant ao was calculated to be 0.133mm for the fatigue strength at 5x10^{6} cycles and 0.188mm for the fatigue strength at 10^{7} cycles.
It was noted that most of the above fatigue data for flush ground girth welds were obtained at R = 0.1, lower than those used in the tests on aswelded girth welded pipes where a constant mean stress of 150MPa was applied. The impact of this on the fatigue strength estimates is considered later.
Estimation of longcycle fatigue strength of girth welds
Finite Element Analysis
A 2D axisymmetric FE model, incorporating a girth weld in a fullscale pipe, was generated using Abaqus software. Eightnoded quadratic elements were used in a static, elastic analysis. A nominal axial stress of 50MPa was applied to the pipe. In all models, the outer pipe wall surfaces were assumed to be aligned (no hilo at weld cap) and one side of the weld root bead was flush with the inner pipe surface, while a hilo was included on the other side of the bead, as found in most of the girth welds.
Figure 5 The FE model and the stress contour calculated for the weld root bead profile
a) FE Model
b) Meshing and the stress contour predicted
A fine mesh was adopted in the vicinity of the notch created by the corner between the weld root bead and the pipe inner surface.
Estimation by the Critical Distance Approach
Four FE models were produced, with hilo values of 0.25, 0.5, 0.75 and 1.0mm. Figure 5 shows that for a hilo of 1mm. Throughthickness stress distributions, starting from the weld root on the inside, were determined at locations where the stress along the pipe axis was at a maximum. Stress/distance curves were recorded along lines perpendicular to the local maximum principal stress, which corresponds to the direction normal to the surface. Two examples of the stress distributions are shown in Figure 6. It can be seen that the local stress, and hence SCF, increases with increase in hilo and decreases sharply within 0.1mm from the notch.
Only the first two of the three stress calculation methods described before were used. The third, the area method, was not used because of the difficulty of obtaining an average stress at the hilo. To obtain an average stress over a certain line distance for the line method, either a fourthorder polynomial equation or a power function was first derived for each model to characterise the stress distribution as a function of the distance from the inside surface. In all cases, the correlation coefficient (R^{2}) for each curve was better than 0.95. By integrating the equation from zero to 2a_{o}, the average stress corresponding to the line method was obtained. For the point method, the stress at the distance a_{o}/2 from the inside surface was read from the stress distribution for each model. The estimated fatigue strength was then equivalent to the nominal stress when the stress at a_{o}/2 was equal to the fatigue strength of the flush ground welds for the particular number of cycles (ΔS_{o}). Similarly, for the line method, the estimated fatigue strength was equivalent to the applied nominal stress when the average stress over the line distance of 2ao from the notch surface was equal to ΔS_{o}.
Attention was focused on the longendurance regime, in particular the estimated fatigue strengths at endurances of 5x 10^{6} and 10^{7} cycles. The former was selected because it is the assumed fatigue endurance limit (N corresponding to the CAFL) in some design codes [e.g. 24] while the latter is the more commonly accepted endurance limit, e.g. BS 7608 [1] and IIW [25]. The estimated results for different hilo values are given in Table 1 and plotted in Figure 7. It will be seen that the calculated fatigue strengths decreased with increasing hilo. For example, for a fatigue endurance of 10^{7}, the estimated fatigue strength using the point method was about 85MPa for a girth weld with a hilo of 1mm. Although the point and line methods
Table 1 Fatigue strengths for different weld root bead profiles calculated using critical distance approaches at two different endurances (10^{7} and 5x10^{6} cycles).
Hilo, mm

For endurance of 107 cycles (a_{o}=0.236mm)

ΔS_{o}, fullscale girth weld, MPa

Point method

Line method

Calculated ΔS_{o}, MPa

Difference from experiment

Calculated ΔS_{o}, MPa

Difference from experiment

0.25

85.2

119.8

41%

121.7

43%

0.50

101.9

20%

105.9

24%

0.75

91.0

7%

95.4

12%

1.0

84.8

0%

87.7

3%


For endurance of 5x10^{6} cycles (a_{o}=0.167mm)

0.25

107.3

131.2

22%

137.2

28%

0.50

109.6

2%

117.4

9%

0.75

97.0

10%

104.0

3%

1.0

90.4

16%

95.6

11%

Figure 6 Examples of the stress distributions determined by FEA (the applied nominal stress was 50MPa).
Figure 7 Dependence on hilo of the fatigue strength of the girth welds calculated by the critical distance approaches.
gave similar results, the line method often gave slightly higher strengths than those obtained by the point method. A good estimate was made of the fatigue strength of the fullscale pipes at 10^{7} cycles, but only by assuming a hilo value of 1.0mm. The estimate based on the actual average hilo was reasonable only at the lower endurance of 5x10^{6} cycles
Estimation by the Reference Radius Approach
Since the wall thickness of the girth welded pipes considered in the present analysis was greater than 5mm, the relevant reference radius to be used when calculating the local stress is 1mm. However, for comparison the value normally confined to assessments of welded joints in plates ≤ 5mm was also considered. Two FE models were established for the 1mm reference radius, one with a hilo of 0.5mm and the other 1mm. In addition, four FE models were established for the 0.05mm reference radius , with a hilo values of 0.25, 0.5, 0.75 and 1mm. Figure 8 shows two FE models with the same hilo of 1mm, one with a radius of 1mm and the other 0.05mm.
Table 2 Fatigue strengths at 10^{7} and 5x10^{6} cycles calculated using the reference radius approach [9,25]
Radius

Hilo, mm

For endurance of 10^{7} cycles

ΔS_{o}, fullscale girth weld, MPa

Calculated fatigue strength, MPa

Difference from experiment

1mm

0.5

85.2

99.6

17%

1.0

83.5

2%

0.05mm

0.25

146.4

72%

0.5

114.8

35%

0.75

98.7

16%

1.0

88.3

4%



For endurance of 5x10^{6} cycles

1mm

0.5

107.3

125.5

17%

1.0

105.1

2%

0.05mm

0.25

184.4

72%

0.5

144.7

35%

0.75

124.4

16%

1.0

111.3

4%

FIGURE 8 The FE model and the calculated stress contour for the weld root bead profile with a hilo of 1.0mm (in this case, hilo=weld root bead height, 18.5/19.5mm wall thickness, applied nominal stress=50MP a) Corner radius = 1mm
FIGURE 8 The FE model and the calculated stress contour for the weld root bead profile with a hilo of 1.0mm (in this case, hilo=weld root bead height, 18.5/19.5mm wall thickness, applied nominal stress=50MPa b) Corner radius = 0.05mm
The estimated fatigue strengths at 10^{7} and 5x10^{6} cycles for the two reference radii and different hilo values are compared with the experimental values in Table 2. As the reference SN curves have the same slope as that for the fullscale girth welds (m = 3), the differences between the actual and calculated fatigue strengths were the same for both endurances. It can be seen that, for both reference radii, the calculated fatigue strengths at both long endurances agreed well with the actual fatigue strengths for a hilo value of 1mm, with the differences being less than ±5%. However, for a hilo of 0.5mm, which was about the average of the worst hilo values of the 33 girth welds examined, both methods overestimated the actual fatigue strength, by 17% for the 1mm reference radius and 35% for the 0.05mm reference radius.
FIGURE 9 Dependence on hilo of the fatigue strength of the girth welds calculated by the critical distance approaches based on flushground weld CAFL corrected for mean stress
Discussion
The 1mm reference radius approach is considered first since, in view of its widespread use in some industries and even acceptance by some design standards, it is the least controversial of the two fatigue strength calculation methods investigated here. Referring to Table 2, good estimates of the actual fatigue strengths at 5x10^{6} and 10^{7} cycles, within 5%, were achieved. However, this was the largest hilo seen among the 33 welds examined. Assuming a hilo of 0.5mm, the case closest to the average actual hilo of 0.47mm, overestimated the fatigue strengths at the two endurances considered, by 17%. This might reflect a deficiency in the analysis method, but it might also be an indication that the IIW FAT 225 classification is too high. Although it was derived from experimental data [18] subsequent check fatigue tests on filletwelded joints have produced significantly lower lives than expected for this SN curve [26]. The specimens concerned were produced using industrial production welding conditions whereas the database used to derive the FAT 225 curve was produced using specimens made in laboratory conditions. Their lower fatigue strengths were attributed to poorer weld profiles and the presence of undercut or cold laps, although the welds met typical weld quality acceptance limits. It is certainly possible that the quality of the girth welds considered here was more comparable with the industrial specimens than the laboratory ones. The above fatigue strength estimate for 0.5mm hilo would suggest that FAT 192 is a better choice than FAT 225 for industrial welds, very close to the FAT 194 classification suggested on the basis of the results from the industrial fillet welds [26].
Turning to the results of the analysis assuming a 0.05mm reference radius, rather similar fatigue strengths were obtained as for 1mm reference radius for the 1mm hilo case (see Table 2). However, the error for 0.5mm hilo was even greater than for the 1mm reference radius. In view of this and bearing in mind the need for more detailed finite element modelling, it will be evident that there is no advantage to be gained from the use of the 0.05mm reference radius compared with the recommended 1mm radius for wall thicknesses greater than 5mm.
The results obtained using the critical distance approach are summarised in Table 1 and Figure 7. As with the reference radius method the best estimates of the fatigue strength at 10^{7} cycles were obtained by both the point and line method for a 1mm hilo. For the actual average hilo of around 0.5mm the fatigue strength was overestimated by 20 to 24%. At 5x10^{6} cycles, reasonable estimates were obtained for 0.5mm hilo while those for 1mm hilo were underestimated by 11 to 16%. These variations are consistent with the fact that the slope of the SN curve upon which the fatigue strength estimates were based, that for flushground butt welds, was shallower (higher m value) than that obtained from the fatigue tests of the girth welds. This will generally be the case when the method is applied to details incorporating relatively severe stress concentrations, like most welded joints. A further deficiency of the approach is that it proved to be less accurate at 10^{7} cycles than 5x10^{6} cycles for the relevant hilo, when the opposite would be expected since the method is primarily directed at estimates of fatigue limits. However, recalling the comments made earlier about the parameters that influence a_{o} , further analysis was carried out to assess the effect of making different assumptions. In particular, it was noted that the experimental data used to determine ΔS_{o} (Figure 4), and hence a_{o}, were obtained at R = 0.1 whereas values of 0.47 and 0.56 were used for the girth weld tests [10] at the two endurances investigated here. The fatigue strength of the flushground welds would be expected to be lower at such high stress ratios, resulting in higher values of ao. To investigate this, ao was recalculated using a value of the CAFL for the flushground welds modified by applying the Goodman mean stress correction [27]:
where S_{UTS} is the tensile strength of material (601MPa), ΔS_{R=1} is the fatigue limit at stress ratio R = 1 and ΔS_{R} is the fatigue limit to be estimated for constant amplitude cyclic loading with a mean stress of S_{m} . With two equations of the above form, one for R=0.1 and the other for R=0.47 (or 0.56), the item ΔS_{R=1} can be deleted and the ΔS_{o}, with the same stress ratios as those for the fullscale pipes, at 5 x106 and 107 cycles, were calculated to be 159.1 and 133.8MPa, respectively. Working as before, these values were used to calculate the fatigue strengths at the two endurances for a series of hilo values. The results are presented in Figure 9. Comparing these with those in Figure 7, it can be seen that the lower ΔSo values have improved the correlation between estimated and actual girth weld fatigue strengths by reducing the estimated values, but only slightly. The same was found by Taylor et al [7] in fatigue strength estimates for some butt and fillet welds. In the case of the parameter F, it would be justifiable to assume a lower value than 1.12 on the basis that fatigue cracks are generally semielliptical in shape or for finite plate. However, this will simply increase the estimated fatigue strengths for the girth welds making those estimates even more inaccurate. Assuming the lowest possible value of F = 1 overestimates the fatigue strengths for 0.5mm hilo by 28% (point method) to 29% (line method) at 10^{7} cycles and 914% at 5 x 10^{6} cycles. Thus, overall the deficiencies noted earlier still stand and this method does not seem to be well suited for application to welded joints.
Conclusions
FE modelling was carried out to determine the throughwall stress distribution and stress concentration at the weld root bead toe. Two local stress approaches, critical distance and reference radius, were used to estimate the longendurance fatigue strengths of girth welds. The following conclusions were drawn:
 FEA confirmed that the hilo in a girthwelded joint influenced the local stress, the SCF increasing with increase in hilo.
 Although both critical distance methods provided reasonable estimates of the fatigue strength of the girth welds at 5 x 106 cycles assuming the average measured hilo, it was overestimated considerably (20 to 24%) at 10^{7} cycles, the endurance regime where the method was expected to be best suited. It was necessary to assume the maximum measured hilo to achieve reasonable fatigue strength estimates.
 Legitimate modification of the input parameters used to define the critical distance had little effect on the fatigue strength estimates.
 In general the local distance approach does not seem to be well suited for application to severelynotched components like welded joints.
 The reference radius method also proved to be inaccurate when related to the average hilo but this could be explained on the basis of the assumed reference SN curve rather than any deficiency in the principle of the method. As has been found in the application of the method to other industrial welds, the currently accepted IIW reference SN curve FAT 225 should be reduced to around FAT 190 for general design.
 No advantage can be gained from the use of the 0.05mm reference radius currently recommended for assessing welded joints in thin material (<5mm) in the assessment of thicker sections when the 1mm radius is sufficient.
References
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