**Yan-Hui Zhang and Stephen J Maddox,**

TWI Limited, Cambridge, UK

Paper presented at OMAE 2012 31st Annual Conference on Ocean, Offshore and Arctic Engineering, 1-6 July 2012, Rio de Janeiro, Brazil. Paper No.83054

## Abstract

In the fatigue design of steel catenary risers there are concerns regarding the fatigue damage to girth welds from low stresses, below the constant amplitude fatigue limit, in the loading spectrum and the validity of Miner's cumulative damage rule. In both cases there is increasing evidence that current design methods can be non-conservative. These fundamental issues were addressed in a recent JIP. A key feature was development of the resonance fatigue testing rigs to enable them to test full-scale pipes under variable amplitude loading. Such tests were performed under a loading spectrum representative of that experienced by some risers, with many tests lasting over 100 million cycles to investigate the fatigue damage due to small stresses as well as the validity of Miner's rule. However, the resonance rigs are only capable of producing spectrum loading by gradually increasing or decreasing the applied load, whereas more 'spiky' random load sequences may be relevant in practice. Therefore the programme also included fatigue tests in conventional testing machines on strip specimens cut from pipes to compare the two types of loading sequence. This paper presents the results of these tests, conclusions drawn and recommendations for changes to current fatigue design guidance for girth welded pipes regarding the definition of the fatigue limit, allowance for the damaging effect of low stresses and the validity of Miner's rule.

## 1 Introduction

The majority of structures and components are subjected to variable amplitude (VA) loading in service. Fatigue design of welded joints in such structures is normally based on data obtained under constant amplitude (CA) loading, usually in the form of a design S-N curve, used in conjunction with Miner's rule to estimate the damage introduced by the different magnitudes of stress cycles in the service stress history. For a VA stress spectrum consisting of n_{i} cycles at stress range S_{i} and an S-N curve from which the CA life expected at S_{i} is N_{i}, where i = 1,2,3, etc, Miner's rule states that Σ (n_{i}/N_{i})=1 at failure.

An implicit assumption in Miner's rule is that the fatigue damage due to the application of a particular stress cycle in a VA loading sequence is exactly the same as that due to the same stress cycle under CA loading. However, there is extensive evidence ^{[Tilly, 1985; Gurney, 2006; Berger et al, 2002; Zhang and Maddox, 2009]} to suggest that it can be higher, with the result that under certain circumstances Miner's rule is unsafe (ie the Miner's sum Σ (n/N) <1.0 at failure). There is also some disagreement in design codes about how to allow for the damaging effect of stresses below the CA fatigue limit (CAFL). The common approach is to extend the S-N curve beyond the CAFL but there are various options regarding the definition of the CAFL and the slope of the extrapolated curve. This issue is particularly important in the fatigue design of deepwater steel catenary risers (SCRs). These can experience very high numbers of low stress cycles due to vortex induced vibration (VIV) with the result that the choice of method for accounting for them can be highly significant in terms of the estimated fatigue life.

This situation raises a number of fundamental questions regarding the current fatigue design approach for girth welds:

- Is Miner's linear cumulative damage rule correct?
- How should the constant amplitude fatigue limit (CAFL) be defined?
- What fatigue damage is induced by stress ranges below the CAFL?
- What is the most appropriate fatigue design method for girth welds in which most fatigue damage is due to low stresses?

These issues were addressed in a recent Joint-Industrial Project (JIP) managed by TWI. This paper describes the results obtained and the fatigue design guidance proposed for girth welded pipes.

## 2 Outline of project

The fatigue damage due to low stresses in a VA loading spectrum representative of those experienced by risers was investigated by fatigue testing full-scale girth welded pipes under spectrum loading. The testing was carried out using resonance testing rigs, specially modified to allow VA loading ^{[Zhang and Maddox, 2011]}. The high loading frequency achievable in such rigs enabled very long endurance testing (up to 2x10^{8} cycles) to be performed in a reasonable timescale, thus facilitating investigation of the damaging effect of small stresses in the spectrum.

A feature of the resonance rigs is that VA loading can only be applied by gradually increasing or decreasing the applied load, whereas more 'spiky' random load sequences may be relevant in practice. In order to investigate the effect of loading sequence, comparative fatigue tests were also performed in conventional computer-controlled fatigue testing machines on strip specimens cut from girth welded pipes under both the sequential spectrum used for the resonance tests on full-scale pipes and a random version of the same spectrum.

A spectrum representative of that experienced by SCRs and with fatigue damage predominantly from small stresses was derived to investigate the effect of small stresses. Several sub-spectra were produced from this spectrum. These had the same peak/maximum stress histograms but different minimum stresses. Using the same approach as ^{[Gurney, 2006]}, it was anticipated that by successively adding progressively smaller stress ranges, Miner's sum would increase significantly as non-damaging stress ranges were approached. On the other hand, if the lowest stress in a spectrum produced fatigue damage consistent with the CA S N curve extrapolated beyond the CAFL without a slope change, Miner's sum would be expected to be almost constant.

## 3 Experimental details

### 3.1 Specimen designs

The full-scale specimens consisted of lengths of steel pipe joined together with either one or two girth welds located in the middle. For the latter, the welds were about one diameter apart. 406mm (16 inch) outside diameter (OD) by 19.1mm wall thickness (WT) seamless steel pipe to API 5L-X70 specification was used. The yield and tensile strengths of the parent and weld metals, both determined from tensile tests, are given in *Table 1*.

**Table 1 Tensile properties of the base and weld metals**

Metal | Yield strength, MPa | Tensile strength, MPa | Elongation, % | Reduction area, % | Loading direction |
---|---|---|---|---|---|

Base | 519.0 | 601.0 | 24.0 | 79.0 | Parallel to pipe |

Weld | 728.0 | 782.1 | 18.1 | 64.5 | Parallel to weld |

The specimens were manufactured by Heerema Marine Contractors (HMC). The girth welds were made from the outside in the 5G position by PGMAW/GMAW onto copper backing. The weld cap at each start/stop position was ground flush with the pipe surface. All welds were shown to be acceptable to a typical SCR specification on the basis of 'Rotoscan' and magnetic particle inspection carried out in compliance with API 1104.

Each girth weld was instrumented with eight foil resistance strain gauges, 45° apart, to allow measurement of axial strain and its variation around the circumference on the outside surface of pipe. The gauge centres were approximately 60mm from the weld cap toe. The nominal strains on the inside surface were calculated by simply considering a linear stress distribution across the pipe wall thickness under the applied bending.

Strip specimens were extracted from 0.8m long ring samples containing identical girth welds to those in the full-scale pipe fatigue test specimens. *Figure 1* shows the design for the strip specimens.

**Figure 1. Resonance fatigue testing of the full-scale pipes**

### 3.2 Fatigue tests under constant amplitude loading

**3.2.1 Full-scale girth welded pipes**

Full-scale girth welded pipes were fatigue tested in resonance rigs, as shown in *Figure 2*, in order to establish the CA S-N curve. An axial tensile mean stress of 150MPa was applied by pressurising the pipes internally with tap water at a pressure of 34.1MPa (4,950psi). All the tests were conducted in air at ambient temperature and loading frequencies between 25 and 30Hz. During each test, the motor speed, which controls the stress amplitude, was kept constant until the test pipe failed or ran out.

**Figure 2. Strip specimen dimensions and strain gauge locations**

The nominal strains measured by the strain gauges were used in conjunction with measurements of axial misalignment of the joint, made after testing, to calculate the local stress range in the region of fatigue crack initiation. Since, as expected, this was the weld root, the local stress was defined as the nominal stress range on the inside of the pipe multiplied by the stress concentration factor (SCF), K_{m}, due to joint misalignment adjacent to the failure position. K_{m} was calculated using the analytical solution given in ^{[BS 7910 (2005)]}.

For those pipes containing two test welds, the first to fail was repaired by welding in order to allow testing of the second weld to continue. However, if the repair weld then failed, no further repair was attempted and, as long as there was no evidence of fatigue cracking, the second of the two original girth welds was declared a run-out.

**3.2.2 Strip specimens**

CA fatigue tests were also performed on strip specimens to establish their S-N curve. The specimens were tested under axial loading in fatigue testing machines. Two pairs of curved packers, with the same radius as the pipe, were used in gripping the ends of the specimen in wedge jaws. Specimen edges were dressed round and smoothed to prevent premature fatigue failure from an edge. As for the full-scale specimens, the initial strip specimens were tested at a constant tensile mean stress of 150MPa. However, higher mean stresses between 230 and 380 MPa were also tried as the strip specimens exhibited a higher CAFL than the full-scale pipes, as discussed later.

The local stress range near the failure site, allowing for any misalignment-induced secondary bending, was determined for each specimen using the measured strains. By assuming that stress is proportional to strain, the SCF at the weld root due to misalignment was calculated by the following equation:

_{r}is the strain measured at the weld root of interest and ε

_{t}is the strain at the opposite weld cap toe. The stress range at the weld toe is the product of K

_{m}and the nominal stress range, which was defined as the applied load divided by the cross-sectional area of specimen adjacent to the weld.

### 3.3 Fatigue tests under variable amplitude loading

**3.3.1 Loading spectrum**

A literature review and discussions with offshore operators was first carried out to determine the loading spectra representative of those experienced by SCRs. With the additional requirement to produce conservative design data, a spectrum with the following characteristics was proposed ^{[Zhang and Maddox, 2011]}:

- Narrow-band loading, with gradual increase and decrease of the stress range for the full-scale fatigue tests.
- High tensile mean stress, around 150MPa. This would be conservative when the test results are applied to the touch-down position (TDP) of risers.
- Maximum stress range of around 180MPa.
- An approximately linear stress distribution, as a compromise between the concave-up distribution for the top of risers and a convex-up distribution for the TDP of risers.
- A long block length (i.e. the number of cycles applied before the sequence is repeated).

The proposed stress distribution was checked against a 'generic' West Africa case and showed good agreement.

Several sub-spectra with the same maximum stress histograms but different minimum stresses were produced from this spectrum. The characteristics of the five initial sub-spectra, VT-1 to VT-5, as well as their stress distributions are shown in *Figure 3*. Subsequently, an intermediate sub-spectrum VT-4/5, with a minimum stress range of 45MPa, was introduced. In each case, the exceedence at the minimum stress is the block length for that sub-spectrum.

**Figure 3. Stress distribution and definition for each sub-spectrum**

_{i}against the total fatigue damage in the spectrum,

^{3}n) increased with decreasing minimum stress range in the sub-spectrum, so that it increased progressively from VT-1 to VT-5

^{[Zhang and Maddox, 2011]}.

**3.3.2 VA tests for full-scale pipes**

Details of the development of the full-scale fatigue test under VA loading have been reported ^{[Zhang and Maddox, 2011]}. In summary, the implementation of a VA test involved several procedures including establishing a polynomial relation between the motor speed in RPM (revolutions per minute) and strain range, dividing each block (a whole sub-spectrum) into a number of sub-blocks to simulate the sea states, establishing the relation between RPM and time for each sub-block, data recording and processing. In each sub-block, the stress range increased from the minimum value to a peak value and then decreased to the minimum value. The minimum value was the same for each sub-block, but four different peak values were used, namely 140, 180, 110 and 80MPa for sub-blocks A to D respectively. An example of the resulting sequence of sub-blocks, for sub-spectrum VT-3 (minimum stress range of 60MPa), is shown in *Figure 4*. Sub-spectra VT-2 to VT-5 were all divided into six sub-blocks in this way. In these, the upper parts (minimum stress range=80MPa) of the sub-blocks A - C were identical to those in sub-spectrum VT-1 as described below. The three sub-blocks D in each sub-spectrum were identical and the upper parts of sub-block D were identical in all sub-spectra. For sub-spectrum VT-1, there were only three sub-blocks and they were identical to the A-C sub-blocks in other sub-spectra.

**Figure 4. An actual cyclic loading sequence (peak stresses in each loading and unloading cycle) that illustrates the good repeatability of the loading block in the VA testing**

**3.3.3 VA tests for strip specimens**

As noted previously, the significance of the practical limitation that resonance rigs can only apply VA loading spectra in a sequential order, with gradual changes in applied stress range (*Figure 4*), was checked by performing comparative tests on strip specimens in testing machines capable of applying both sequential and random VA loading.

Sub-spectra VT-2 (with a minimum nominal stress range of 70MPa) and VT-3 (with a minimum nominal stress range of 60MPa) were chosen for this investigation. However, to compensate for the higher CAFL associated with the strip specimens (described later), all stress ranges in these spectra were doubled. Thus, the maximum and minimum nominal stress ranges were increased to 360 and 140MPa for sub-spectrum VT-2 and 360 and 120MPa for sub spectrum VT-3, respectively. The applied mean stress in all tests was 230MPa, the same as that used for most CA tests.

The tests were performed in a computer-controlled testing machine that was programmed to apply the stress cycles in each block from the same basic loading spectrum in either a sequential or a random order. For the former, the loading sequence was the same as that used in the full-scale tests. For the latter, it was achieved by selecting the relative stress ranges, P_{i} (ΔS_{i}/ΔSΔ_{max}), using a random number generator. When the whole of the first block had been applied the process started again and subsequent blocks were applied in the same sequence. This process was repeated until the specimen failed or achieved run-out. A segment of the loading pattern from both sequential and random loading is shown in *Figure 5*. It should be emphasised that this was an exploratory investigation simply comparing 'sequential' and 'random' loading. Precise details of the random loading sequences seen by SCRs are not available and the present one may not be truly representative.

**Figure 5. Loading patterns of the sub-spectrum VT-2, used for VA testing of the strip specimens: (a) Sequential loading (same sequence as that used for the full-scale pipes);**

**(b) Random loading.**

### 3.4 Post-test examinations

Comprehensive post-test examinations were carried out for all full-scale girth welds tested. For full-scale pipes, the examination included measurements of wall thickness, weld root hi-lo, weld root bead height (WRBH) relative to the neighbouring pipe surface at each gauge location, as well as dye penetrant inspections of the test welds. When a test weld ran out, a macro-section was taken at a location where the weld root bead profile was considered to be the most unfavourable (ie highest stress concentration, generally where the hi-lo and WRBH were largest) along the circumference of that weld.

## 4 Test results

### 4.1 Fatigue tests under CA loading

**4.1.1 Full-scale pipes**

Six pipes, with a total of eleven girth welds, were tested to establish the CA S-N curve. The test results are plotted in *Figure 6* where they are seen to be generally better than the ^{[BS 7608 (1993)]} Class D mean S-N curve. Examination of the failed girth welds confirmed that fatigue cracking always initiated at the weld root. Noting that the lowest stress that produced failure, with an endurance of 4.4x10^{7} cycles, was 55.4MPa, it appears that the CAFL for these girth welds may correspond to an endurance between 5x10^{7} and 10^{8} cycles, which considering the two unbroken welds that survived for 10^{8} cycles, would be between 45 and 55MPa. The same was found in relation to CA tests on girth-welded 20 inch pipe ^{[Maddox and Zhang, 2008]}. It is apparent that the Class D mean fatigue limit of 74MPa, corresponding to 10^{7} cycles, over-estimates the value suggested by the present tests. This argument was further supported by the results of the post-test examination on two unbroken welds which had both been tested under relatively low stresses. One was tested under a local stress range of 54.4MPa and declared a run-out after 5.16x10^{7} cycles while the other was tested under a local stress range of 45.2MPa and declared a run-out after 10^{8} cycles. The post-test examination revealed fatigue cracking from the weld root for both welds, 0.26mm deep in the first and 0.14mm deep in the other.

**Figure 6. Comparison of the constant amplitude fatigue performance of the full-scale and strip specimens with the Class D mean curve.**

Assuming that all the results from failed welds lie on the same S-N curve, regression analysis produced the mean S-N curve ΔS^{3.25}N = 2.02 x 10^{13}, slightly shallower than the Class D curve, for which m = 3. However, the value of m = 3 is within the 95% confidence estimates of the slope and therefore it would be legitimate to assume this value when fitting the S-N curve. For convenience this assumption was made and the resulting S-N curve became ΔS^{3}N=6.174 x 10^{12}. This curve was used to calculate N values for the application of Miner's rule in the analyses of the VA test results from the full scale pipes. Furthermore, since there were no failures beyond 5x10^{7} cycles, it was assumed that the CAFL corresponded to this endurance, giving a value mean of 49.8MPa, 42% lower than the stress corresponding to N=10^{7} cycles, the conventional CAFL.

**4.1.2 Strip specimens**

As for the full-scale specimens, initially the strip specimens were tested at a constant tensile mean stress of 150MPa. However, although the two results obtained at relatively high stress ranges were in agreement with those obtained from the full-scale pipes, the test at a stress range of 120MPa was a run-out at 2.67x10^{7} cycles, which was significantly greater than the fatigue endurance of the full-scale pipe tested at this stress level. It was thought that this difference might be due to relaxation of welding-induced residual tensile stresses during extraction of strip specimens. Therefore, the mean stress was increased for the additional tests at this and lower stress levels. However, these specimens, tested under mean stresses of 250 and 380MPa, still ran out, indicating a CAFL more than double that for the full-scale pipes.

Subsequently, further CA tests were carried out at higher stress ranges and a mean stress of 230MPa. Furthermore, as post-test examinations of the tested welds suggested that the fatigue performance of girth welds strongly depended on weld root bead profile, one strip specimen with a hi-lo of 0.48mm (resulting in a very poor profile) was tested at a nominal stress range of 110MPa. This specimen failed in a life close to the lower bound of the data scatter for the strip specimens. Recalling that some tests ran out at higher stress ranges and higher mean stresses, it appears that the higher fatigue limit associated with the strip specimens, as compared with the full-scale, can be at least partly attributed to their favourable weld root profiles.

The test results are shown in comparison with those for the full scale pipes in *Figure 6*. It will be seen that failed strip specimens tested under applied mean stresses of both 150 and 230MPa gave results in agreement with one another and with those of the full-scale pipes. The best-fit curve to the strip specimen results had a slope of 2.47. By fixing the slope at m = 3.0, it became ΔS^{3}N=6.275 x 10^{12}, very close to the S-N curve for the full-scale pipes. This S-N curve was used to calculate N values for the application of Miner's rule in the analyses of the VA test results from the strip specimens.

### 4.2 Fatigue tests under VA loading

### 4.3 Full-scale pipes

The VA test results obtained from full-scale pipes were analysed in terms of both Miner's sums and, for graphical presentation, the equivalent constant amplitude stress range, ΔS_{eq}. For a particular endurance, ΔS_{eq} is the constant amplitude stress range which, according to Miner's linear cumulative damage rule, is equivalent in terms of fatigue damage to the VA stress spectrum. It relates to the constant amplitude S-N curve for the detail under consideration, ΔS^{m}N = A (a constant), as follows:

_{i}is the stress range that is applied n

_{i}times in a spectrum. Note that (Σn

_{i}) is the spectrum block length N

_{b}. It may be noted that ΔS

_{eq}values below, on or above the CA S-N curve correspond to Σ(n

_{i}/N

_{i}) values <1, =1 or >1, respectively.

An implicit assumption in Eq. [2] is that stresses below the CAFL are as damaging as implied by the S-N curve extrapolated beyond the CAFL at the same slope. However, it is common practice to assume that they are less damaging by adopting a bi-linear S-N curve with a slope change from m to m+2 at the CAFL. As noted above, BS7608 assumes that the CAFL is the stress range corresponding to N=10^{7} cycles, but the present full-scale pipes suggest a lower value, corresponding to N=5x10^{7} cycles. To allow for this, ΔS_{eq} was also calculated using the bi-linear S-N curve for which the slope changed from m=3 to m=5 at 5x10^{7}, on the basis of the equivalent fatigue damage concept expressed below:

_{1}= 3 and m

_{2}= 5. Selection of m and A on the right hand side depends on whether Seq is above or below the slope transition point in the S-N curve. The left hand side of the equation is the sum of the fatigue damage ratios due to stresses above (subscript 1) and below the fatigue limit (subscript 2), respectively. Parameters A1 and A2 correspond to the S-N curve above and below the fatigue limit, respectively.

The VA results obtained from full-scale pipes are summarised in *Table 2*. This includes the sub-spectrum used, its block length, the fatigue endurance, in terms of number of cycles and number of blocks, and the calculated Miner's sum Σ(n/N). The mean S-N curve for the full-scale pipes, ΔS^{3}N=6.174x10^{12}, was used to calculate N. However, two values of Σ(n/N) are given, one based on N values derived from the S-N curve extrapolated beyond the CAFL without a slope change and the other for N derived from the bi-linear S-N curve that changed slope from m=3 to 5 at N=5x10^{7} cycles, for stress ranges below 49.8MPa. The results are also presented in *Figure 7* in comparison with the CA results, with ΔS_{eq} calculated using Eq.[3].

**Figure 7. Comparison of variable amplitude test results for the full-scale pipes with bi-linear versions of constant amplitude S-N curves, with VA data presented in terms of equivalent stress range calculated using a bi-linear S-N curve with slope change from 3.0 to 5.0 at 5x10 ^{7} cycles.**

**Table 2 Summary of the VA test results for the full-scale pipes**

Pipe ID | Sub-spectrum | Min nominal stress range, MPa | Block length, cycles | Endurance | Average Miner's sum, Σ(n/N) | ||
---|---|---|---|---|---|---|---|

Number of cycles | Number of blocks | No slope change | Bi-linear^{1} | ||||

S23 | VT-1 | 80 | 28,237 | 9.76x10^{6} |
345.2 | 1.59 | 1.59 |

S24 | VT-1 | 80 | 28,196 | 7.30x10^{6} |
260.4 | 0.90 | 0.90 |

S28 | VT-2 | 70 | 85,073 | 3.15x10^{7} |
>370.2 | >2.90 | >2.90 |

S25 | VT-3 | 60 | 215,400 | 3.50x10^{7} |
162.5 | 1.55 | 1.55 |

S26 | VT-3 | 60 | 216,100 | >1.95x10^{8} |
>900.9 | >10.33 | >10.33 |

S27 | VT-3 | 60 | 217,100 | >1.52x10^{8} |
>700.0 | >7.23 | >7.23 |

S14-W1 | VT-4 | 50 | 601,600 | >6.06x10^{7} |
>101.4 | >1.90 | >1.87 |

S14-W2 | 4.22x10^{7} |
70.3 | 1.15 | 1.11 | |||

S17-W1 | VT-4 | 50 | 603,330 | 1.89x10^{7} |
31.3 | 0.78 | 0.78 |

S17-W2 | >2.85x10^{7} |
>47.3 | >1.03 | >1.02 | |||

S22-W1 | VT-4 | 50 | 602,220 | 2.30x10^{7} |
38.2 | 1.05 | 1.05 |

S22-W2 | >1.30x10^{8} |
>216.2 | >4.72 | >4.70 | |||

S29 | VT-4 | 50 | 600,850 | >1.59x10^{8} |
>263.8 | >4.30 | >4.14 |

S20-W1 | VT-4/5 | 45 | 1,106,950 | >1.71x10^{8} |
>155.4 | >3.26 | >2.89 |

S20-W2 | >3.36 | >2.99 | |||||

S31-W1 | VT-4/5 | 45 | 1,110,000 | >1.32x10^{8} |
>120.0 | >4.12 | >4.04 |

S31-W2 | >4.32 | >4.26 | |||||

S15-W1 | VT-5 | 40 | 1,671,000 | >1.96x10^{8} |
>115.3 | >3.61 | >3.16 |

S15-W2 | >3.29 | >2.81 | |||||

S16-W1 | VT-5 | 40 | 1,672,300 | >1.43x10^{8} |
>85.7 | >2.77 | >2.44 |

S16-W2 | >3.27 | >2.98 | |||||

S30 | VT-5 | 40 | 1,677,500 | 8.27x10^{7} |
49.3 | 1.18 | 0.96 |

Notes:

1. Slope change from 3.0 to 5.0 at the assumed slope transition point which corresponds to 5x10^{7} cycles with a stress range of 49.8MPa. Symbol '>' indicates that the weld was unbroken.

2. Pipe S28 failed from corrosion pitting on the inside of the pipe remote from the weld. The weld profile was comparatively good.

3. Pipe S30 failed from an undetected 0.65mm deep lack of fusion defect at the w

Referring to *Table 2*, it will be seen that Σ(n_{i}/N_{i}) depends on the sub spectrum. It varied from 0.78 to 1.59 for pipes that failed under the spectra with a minimum stress range ≥50MPa (VT-1 to VT-4),. However, as seen in *Figure 7*, these values correspond to fatigue strengths that are within the range expected considering the scatter in the CA data. Thus, Miner's rule can be considered to be accurate for these sub-spectra. However, it may be noted that this would not be true if the slope change in the CA S-N curve was assumed to correspond to N=10^{7} cycles, as indicated in *Figure 7*, thus further confirming that the current design approach of locating the slope change at 10^{7} cycles is non-conservative. Miner's rule proved to be conservative for spectra with the minimum stress range <50MPa (VT-4/5 and VT-5), with eight out of nine welds being unbroken after endurances considerably more than predicted by Miner's rule (Σ(n_{i}/N_{i}) > 1).

Attention is drawn to two tests that gave results that were not consistent with the others. Pipe S28 failed from a corrosion pit on the inside of the pipe with no evidence of fatigue cracking from the weld root. Although the weld root bead profile was good it was no better than that in other welds that did fail from the root. Thus, its exceptionally long life could not be explained. In contrast, it was clear that the single pipe failure under VT-5 (pipe S30) occurred because the fatigue crack initiated at a 0.65mm deep lack of fusion defect at the weld root.

Since two full-scale pipes tested under CA loading ran-out at 10^{8} cycles, another possibility is to introduce a slope change at this endurance. Although not shown here, the ΔS_{eq} values corresponding to this bi-linear S-N curve were also calculated. Similar to *Figure 7*, the ΔS_{eq} values were also compared with the CA S-N curve with a slope change at 10^{8} cycles. It was found that all the VA data for endurances greater than 2x10^{7} cycles were above the mean curve, while those for endurances greater than 10^{8} cycles were above the upper bound S-N curve. In view of this, it is considered that the case for adopting the slope change at 10^{8} cycles, rather than 5x10^{7} cycles, is not strong and is unduly conservative. Meanwhile, using the slope change at 10^{8} cycles is clearly the more conservative of the two approaches and so it might be considered preferable for particularly critical cases.

### 4.4 Strip specimens

Fourteen strip specimens were tested under sub-spectrum VT-2 and four under spectrum VT-3, half under the sequential version of the spectrum and half under random loading. The results are presented in *Figure 8* in terms of ΔS_{eq}, calculated using Eq.[2]. No attempt was made to use Eq.[3], with a bi-linear S-N curve, because although the CAFL was not well defined it appeared as if all stress ranges in VT-2 and VT-3 were above it. *Figure 8* also shows the results obtained under sequential loading from the full-scale pipes and the S-N curves based on the combined CA data from full-scale pipes and strips. Although not conclusive, it appears that the random loading was the more damaging, with most of the results lying below the mean CA S-N curve while most sequential loading results were above it. Although there is no overlap of the results from failed specimens it will be evident that the VA data from both the strips and full-scale pipes follow the CA S-N curve. It will also be evident that apart from one of the results for failure under the sequential loading and three run-outs, which were all beyond the upper bound of the CA scatter-band, all the VA data from strip specimens are within the CA scatter-band. This suggests that Miner's cumulative damage rule was reasonably accurate for calculating the fatigue lives of the strip specimens under VA loading, as was found for the full-scale pipes tested under sub-spectra with all stress ranges above the CAFL.

The relatively large scatter in the strip specimen results in *Figure 8* probably reflects variations in the weld root bead profiles. However, it was observed that two strip specimens extracted from the same original girth weld had very similar relatively poor profiles, with both a hi-lo and WRBH of about 0.45mm. One was tested under the sequential version of VT-2 and the other under random loading. This provided a good opportunity to investigate the effect of loading sequence independently of a possible effect of a difference in weld root bead profile. The life obtained under sequential loading was ~1.3 times greater than that obtained under random loading.

**Figure 8. Variable amplitude fatigue data obtained from full-scale pipes and strip specimens illustrating effect of loading sequence ('sequential' or 'random') on fatigue performance.**

It was also apparent that weld root bead profile was significant in the welds tested under VT-3. Only two of the four failed, the unbroken welds surviving for lives more than 5 times those predicted by Miner's rule. Both had exceptionally good profiles, as indeed did the single unbroken weld tested under VT-2, with both the hi-lo and WRBH being less than 0.1mm. However, it is probably also significant in the case of VT-3 that stresses below 140MPa are unlikely to be as damaging as implied by the CA S-N curve in the region close to the CAFL.

## 5 Post test examination

### 5.1 Failure location for the full-scale pipes

Of the 33 welds tested major fatigue cracks occurred in 17 of them. All but three failed from the weld root bead toe, with two cap failures and one failure from a corrosion pit. All root failures originated within 10° of the weld start position or 4° of the weld stop position. The failure locations were often characterised by relatively poor weld root bead profiles, with the hi-lo and WRBH ≥0.5mm.

### 5.2 Fracture surfaces and macro-sections

All the girth welds tested were examined in detail, either from macro-sections or directly on the fracture surfaces of failed welds. Cracking was revealed in many run-out welds. Results from the examinations of four weld macro-sections are described below.

Pipe S12, which contained two welds and was tested under CA loading, was unbroken after 10^{8} cycles. No fatigue cracking was found at the weld start position in weld W1, but a 0.14mm deep weld root crack was found at the weld stop position, where the WRBH was 0.25mm, *Figure 9(a)*. Two sections from weld W2 of pipe S12 did not reveal any indication of fatigue cracking. One of these sections was made at the position with the poorest weld root bead profile (WRBH and hi-lo of 0.47mm), *Figure 9(b)*.

**Figure 9. Macro-sections of the two welds in pipe S12 after being tested under CA loading for 10 ^{8} cycles: (a) Weld W1, showing a 0.14mm deep crack at the toe of the weld root bead;**

**(b) Weld W2, with no evidence of cracking in the region of poorest profile (WRBH= 0.47mm). The definitions for hi-lo and WRBH are shown in the figure**

Both weld W1 and 2 of pipe S15, tested under sub-spectrum VT-5, were unbroken after 1.96x10^{8} cycles but macro-sections revealed fatigue cracking from the weld root bead toe in both. Two cracks were found in W1, one just 67µm deep at the weld start position but the other 0.19mm deep at the weld stop position, *Figure 10*. A section of W2 at a location away from the weld start/stop positions but where the WRBH was 0.58mm revealed a 93µm deep crack, *Figure 11*. Therefore, the remaining endurances of the two welds were significant even though their Miner's sums were already respectively greater than 2.8 and 3.1 (assuming a bi-linear S-N curve with a slope change from 3 to 5 at 5x10^{7} cycles).

**Figure 10. Macro-sections of the two welds in pipe S15 after being tested under VA-5 loading (minimum stress range of 40MPa) for 1.96x10 ^{8} cycles, showing fatigue cracking at the toe of weld root bead: (a) W1 weld, 0.19mm deep crack;**

**(b) W2 weld, 93µm deep crack that initiated in a region of poor profile (WRBH = 0.58mm)**

**Figure 11. Dependence of the ratio of the calculated fatigue life based on a bi-linear S-N curve to that based on a single slope S-N curve on the minimum stress range in the applied loading spectrum**

## 6 Discussion

### 6.1 Failure locations

In the full-scale CA and VA tests, a total of seventeen major fatigue cracks, which either led to failure or were more than 1mm deep, were observed, most near the weld start position and a few near the weld stop position. No failures initiated at locations away from these two positions, although indications of small cracks were found. For those welds which ran out, macro-sections revealed that cracking often initiated at the toe of a weld root bead with a poor profile.

In the present context, it seems that the best indication of a poor weld root bead profile is the combined weld root hi-lo and WRBH, especially the former. Not only does this lead to a sharp corner, and hence more severe stress concentration than would arise from a smooth transition from pipe to weld surface, but any associated axial misalignment would increase the local stress by introducing secondary shell bending. From the practical viewpoint, this highlights the importance of achieving as near perfect inner pipe wall alignment as possible when making girth welds. If perfect alignment between pipe wall surfaces cannot be achieved due, for example, to a difference in the wall thicknesses of the pipes, it would be preferable to place the thickness transition on the outside where the weld toe stress concentration is less severe and can be reduced by flush grinding the weld cap to achieve a smooth transition. This approach is recommended in ^{[DNV 2010]}.

Although it is unquestionable that weld root bead profile has a significant influence on the fatigue performance of girth welds, other factors may also play a part. This was evident from the fact that in some girth welds the worst weld root profile was not always at the weld start or stop position. However, major cracking still occurred at the weld start/stop positions. Other possible key factors could be welding imperfections and residual stresses.

### 6.2 Constant amplitude fatigue limit

The fatigue limit is generally defined as the maximum stress range at which fatigue failure will never occur under CA loading. However, as suggested by ^{[Pyttel et al, 2011]}, a fatigue limit may not exist. They found that even smooth specimens in various metals can fail after more than 10^{8} cycles and concluded that a more useful property was the fatigue strength at a defined number of cycles. The present CA test results add some support to this view in that fatigue failure occurred after 4.4x10^{7} cycles and fatigue cracking was found in several welds tested up to 10^{8} cycles, all far greater than the 10^{7} cycles commonly specified by many international codes as the endurance corresponding to the CA fatigue limit. Therefore, in this paper, fatigue limit means fatigue strength at a particular endurance. On this basis, defining the CAFL as the fatigue strength at 10^{8} cycles, the value for the present girth welds is between 45 and 50MPa. The S-N curve started to change slope as this limit was approached at an endurance of ~5x10^{7} cycles, similar to that obtained previously from girth-welded 20 inch OD pipes with a fatigue performance close to Class E ^{[Maddox and Zhang, 2008]}, lower than that for the present 16 inch pipes.

In the present work the CAFL is significant only as a guide to the choice of location for the transition point at which the S-N curve used in conjunction with Miner's rule changes slope. As noted previously, for convenience the value finally adopted for the present welds was the fatigue strength at N=5x10^{7} cycles, namely 49.8MPa.

### 6.3 Comparison of the fatigue performance of full-scale pipes and strip specimens cut from pipes

The fatigue performance of the present strip specimens was comparable with that of the full-scale pipes at high applied stress ranges but superior at low (stress ranges ≤~120MPa), even when the strip specimens were tested under very high tensile mean stress conditions. This finding was in agreement with the results in previous work by the present authors ^{[Maddox and Zhang, 2008]} but at odds with the claim that fatigue data from strip specimens can be correlated well with those from full-scale pipes as long as the strip specimens are tested under high tensile mean stress conditions to compensate for the loss of tensile residual stresses (Salama, 1999). It is recalled that one strip specimen, with a poor weld root bead profile (WRBH=0.48mm), was deliberately chosen for the CA fatigue test at a nominal stress range of 110MPa. Although several strip specimens ran out at 120MPa under a high tensile mean stress, this specimen failed, with an endurance close to the lower bound to the combined strip specimens and full-scale pipe data, *Figure 6*. Clearly, the weld root bead profile of the strip specimens also has a very significant effect on the difference in fatigue performance between the strip specimens and full-scale pipes in the long-life regime.

At high applied stresses, crack initiation would be easier and the fatigue life would be dominated by fatigue crack growth. As a result, the fatigue endurance would not be so sensitive to the weld root bead profile and the fatigue performance of the strip specimens would be comparable with that of the pipes, as seen in the present project. Therefore, when strip specimens have to be used to characterise the fatigue performance of full-scale girth welded pipes and the weld root bead profile of these strip specimens is favourable when compared to the worst profile of a full-scale weld, they should be tested under fully tensile high applied stress ranges where fatigue life is dominated by fatigue crack growth.

### 6.4 VA results from full-scale pipes and validity of Miner's rule

The VA test results obtained from the full-scale pipes (*Table 2*) indicate that, for the basic spectrum used, Miner's rule is reasonably accurate if the minimum stress range ≥50MPa (sub-spectra VT-1, VT-2, VT-3 and VT-4). The results obtained under sub-spectra VT-3 and VT-4 were the most widely scattered, with many welds remaining unbroken. However, this is not surprising since the fatigue damage in these spectra came mainly from stress ranges that correspond to the transition regime as the CA data approach the fatigue limit, where the CA data are also widely scattered. It will be noted that the choice of S-N beyond the CAFL, extrapolation with or without a slope change, had little or no effect on the life calculated by Miner's rule. This is reasonable since all applied stress ranges were above the estimated CAFL. However, this is not the case using a bi-linear S-N curve with the slope change at 10^{7} cycles, as currently recommended in many design rules. The S-N curve would then be as shown in *Figure 7*. Although the ΔS_{eq} values corresponding to this S-N curve are not shown, they would be either the same (tested under higher minimum stresses) or lower (tested under lower minimum stresses) than those obtained for a S-N curve with a slope change at 5x10^{7} cycles. Since many of the data points already lie below the mean S-N curve with a slope change at 10^{7} cycles, the current design approach of locating the slope change at 10^{7} cycles would be non-conservative.

Sub-spectra VT-4/5 and VT-5 included stress ranges down to 45MPa. Consequently, shorter lives were estimated assuming the bi-linear rather than single-slope S-N curve. However, these were still considerably shorter than the actual endurances suggesting that stress ranges below the estimated CAFL are less damaging than implied by the bi-linear S-N curve with the slope change at 5x10^{7} cycles. Again referring to *Figure 7* the same may not be the case for a slope change at 10^{7} cycles; ideally more data, especially from welds that fail, are required to confirm this. Meanwhile, noting from *Figure 7* that the data obtained under sub-spectra VT-4/5 and VT-5 are clearly biased above the bi-linear S-N curve slope change at 5x10^{7} cycles, it seems reasonable to adopt bi-linear CA S-N curves with the slope change at 5x10^{7} cycles as a safe but not unduly conservative approach for cumulative damage calculations. The one factor that might be seen to contradict this conclusion is the test result obtained from pipe S30 under VT-5. This failed at a lower Seq value than the deduced CAFL as a result of a 0.65mm deep weld root defect. If inspection of girth welds for offshore pipelines cannot be relied upon to detect such small defects it would clearly be prudent to adopt a lower CAFL, corresponding to N closer to 10^{8} cycles.

### 6.5 Effect of loading sequence

The VA test results from the strip specimens appear to indicate that random loading was more damaging than the sequential loading used for testing the full-scale pipes. A comparison of the fatigue endurances between two specimens with similar weld root bead profiles suggested that the fatigue endurance under sequential loading was about 1.3 times longer than that obtained under random loading.

In terms of the impact of these findings on the fatigue design of SCRs, it should be born in mind that the random sequence was an artificial one. It was not based on actual observations of the sequence actually experienced by risers but simply randomisation of the stress spectrum. In practice, SCRs may not see such a sequence. Indeed, it could be argued that, although actual SCRs may experience random loads, the stress changes would be gradual as they are controlled by environmental loading. Then the random loading sequence used in the present tests may not be truly representative and the deduced life reduction factor may be too high. However, if actual SCRs do experience such random loading or when it is uncertain, it would be prudent to apply a life reduction factor of 1.3 to account for the possible loading sequence effect.

### 6.6 Implication of current results to fatigue design of girth welds

The fatigue test results obtained from the girth welds tested under sub-spectra with different minimum stress ranges were assessed by Miner's rule using two different CA S-N curves, one with no slope change and the other a bi-linear curve with a slope change from 3 to 5 at 5x10^{7} cycles (the assumed CAFL). From *Table 2*, it will be seen that the introduction of a slope change from 3 to 5 at 5x10^{7} cycles made little difference to the Miner's sums for sub-spectra VT-1 to VT-3. The effect was small for sub-spectrum VT-4 and increased for sub-spectra VT-4/5 and VT-5. The results indicated that it would be over-conservative to adopt a single-slope S-N curve in design for loading spectra with minimum stress ranges <50MPa. Assessments based on a bi-linear S-N curve were more accurate, although introduction of the slope change at 10^{7} cycles, as currently recommended in many design rules, would be potentially unsafe. A slope change in the S-N curve is also in compliance with the possibility that the proportion of life spent initiating a fatigue crack becomes more significant in the long endurance regime, hence producing a shallower S-N curve.

As an illustration of the benefit of adopting a bi-linear S-N curve, *Figure 11* shows the variation in ratio of fatigue life calculated using Miner's rule in conjunction with a bi-linear S-N curve, with the slope change at 5x10^{7} cycles, and that obtained using a single slope curve for each sub-spectrum. It will be seen that the relative fatigue endurances increase with decreasing minimum stress range in the spectrum. Thus, adoption of the bi-linear curve justifies a significant increase in estimated fatigue design life, or corresponding increase in allowable stress range, when compared with that estimated on the basis of a single-slope S-N curve. For example, for a loading spectrum with a linear stress distribution and a minimum nominal applied stress range of 10MPa, the calculated design fatigue life can be increased by a factor of 1.76 using the bi linear S-N curve.

Although the recommendation to retain the bi-linear S-N curve approach for cumulative damage calculations remains, the case of failure from an undetected 0.65mm deep weld root defect in pipe S30 mentioned earlier leaves a question mark over the choice of the point at which the slope change should be introduced. If inspection of girth welds for offshore pipelines cannot be relied upon to detect such small defects it would clearly be prudent to extend the S-N curve to perhaps 10^{8} cycles before the slope change.

One outcome from the failure of pipe S30 from a defect that could be seen as positive is that it provides an indication of the acceptance level for weld root defects in girth welds. As seen in *Figure 7*, the test result agreed very closely with the mean S-N curve obtained from defect-free welds which itself was above the Class D mean curve. Clearly further confirmation is needed from fatigue tests over a wide range of applied stress levels but, at this stage, it appears possible that Class D, but even more certainly Class E, fatigue performance could be achieved from girth welds with root defects approaching 1mm in depth. At the same time it would have to be recognised that it may be necessary to assume a lower CAFL than that for defect-free welds.

### 6.7 Design considerations and recommendations for full-scale pipes under spectrum loading

The present work suggests that the fatigue performance of girth welded pipes under spectrum loading containing significant proportions of low stresses should be evaluated using Miner's rule in conjunction with a bi-linear S-N curve with the slope change at 5x10^{7} cycles. This is in agreement with the results obtained in a previous JIP ^{[Maddox and Zhang, 2008]} from lower design class girth welds.

**Equation.4.**

When facilities for full-scale testing under VA loading are not available, the following design approach is proposed:

- Establish the constant amplitude S-N curve using strip specimens extracted from representative girth welds in the pipe of interest.
- Conduct variable amplitude tests, using a loading spectrum representative of the actual service condition, to check the 'severity' of the spectrum by establishing the validity of Miner's rule on the basis of
*Equation.4.*values at failure. - Establish the constant amplitude S-N curve and CAFL for full-scale specimens. Experience from tests on girth welds suggests that the CAFL should be defined as the fatigue strength at which the CA data start to deviate from the linear logS-logN curve fitted to data obtained at higher stresses. This should not be assumed to correspond to an endurance <10
^{7}cycles. In fact, it may be necessary to continue testing to endurances approaching 10^{8}cycles to be sure of reaching the CAFL. - Calculate the fatigue life of the full-scale specimen using Miner's rule, in conjunction with the 'spectrum severity' (
*ie**Equation.4.*value at failure) obtained in step (b) and the S-N curve obtained in step (c). A slope change from m to m+2 at the STP of the full-scale specimen is recommended for use in the calculation of*Equation.4.*

With respect to the fatigue tests, the strip specimens should be selected to include the worst weld root bead profiles (highest hi-lo and WRBH) found in the actual girth welds, they should be conducted under fully tensile loading, preferably at a high tensile mean stress, and they should utilise spectra that contain only stress ranges that are well above the apparent CAFL.

With reference to the difference between sequential and random loading, the present endurance tests on strip specimens indicate there can be a difference in fatigue performance. Therefore, ideally step b) above should be conducted using the actual loading sequence anticipated in service. If this is not known the Miner's summation values obtained in the variable amplitude loading sequence used in the tests may need to be reduced; the present limited study suggested a reduction factor of 1.3. More study is required, including checks to determine if a 'spiky' random loading sequence of the type used here can ever actually arise in a SCR where factors such as inertia may limit the rate of change of stress, to establish the general applicability of such a factor.

## 7 Conclusions

The following conclusions refer to the results of fatigue tests on full-scale 16 inch OD steel pipes and strip specimens extracted from them, both containing girth welds with fatigue strengths better than UK Class D, carried out under constant and variable amplitude loading, the latter based on a load spectrum considered to be relevant to SCRs.

- Fatigue failures were obtained from full-scale girth welded pipes at stress levels up to 42% lower than the conventional fatigue limit (corresponding to N=10
^{7}cycles), such that the fitted S-N curve extended to 5x10^{7}cycles. Consequently, the CAFL was defined as the stress range corresponding to N = 5x10^{7}cycles on the fitted S-N curve. - The fatigue performance of the full-scale and strip specimens agreed for applied stresses above 110MPa but the CAFL for the strips was around double that for the full-scale pipes.
- Miner's rule proved to be reasonably accurate for the loading spectrum used.
- The VA results suggested that it would be non-conservative to adopt a bi-linear S-N curve with a slope change at 10
^{7}cycles as recommended in most fatigue design codes. However, introducing the slope change at 5x10^{7}cycles (the new CAFL) was conservative, but not unduly so. - Limited data from comparative VA fatigue tests on strip specimens indicated that a 'spiky' random loading sequence was more damaging than the 'sequential' loading conditions possible with a resonance test rig, with a reduction factor of about 1.3 on endurance. However, further work is needed to assess the relevance of the 'spiky' sequence to actual SCRs and, if necessary, perform further tests on more realistic sequences.
- The fatigue performance of the girth welds was strongly influenced by the weld root bead profile. The weld root bead height (WRBH) and hi-lo, sources of stress concentration and secondary bending, were identified as significant indicators of fatigue performance.
- Based on the present test results, as well as others from a previous JIP, a change to the current fatigue design guidance for girth welded pipes is proposed. In particular, Miner's rule should be used in conjunction with the appropriate constant amplitude S-N curve (
*eg.*a BS 7608 design curve or the lower bound curve established by special testing) with the slope change from 3 to 5 introduced at N= 5x10^{7}cycles. For greater accuracy, a procedure was proposed involving special VA fatigue tests on strip specimens under truly representative spectrum loading conditions, including a representative sequence of loading if known, to establish the appropriate Miner's rule sum for design, together with CA tests on full-scale pipes to establish the appropriate design S-N curve. - One reservation regarding the above recommendations was the case of a girth welded pipe failing from an undetected 0.65mm deep weld root defect to give a lower fatigue life than that expected from the S-N curve obtained from the defect-free welds. If defects of this size cannot be detected reliably or indeed for particularly critical cases, it would be prudent to perform cumulative damage calculations using S-N curves that extended to perhaps 10
^{8}cycles before introducing the slope change.

## 8 Acknowledgements

The authors are pleased to acknowledge financial and technical support of the sponsors for this work: BP Exploration and Production Ltd, Chevron Energy Technology Company, ExxonMobil Upstream Research Company, Heerema Marine Contractors, Petrobras, Saipem SpA, Tenaris Tamsa and the UK Health and Safety Executive. Help from Nick Zettlemoyer of ExxonMobil regarding the derivation of the effective stress range ΔS_{eq} for the bi-linear S-N curve is also acknowledged.

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