**Liwu Wei, Weijing He and Simon Smith**

TWI Ltd

Paper presented at the ASME 2011 Pressure Vessels & Piping Division Conference, Baltimore, Maryland, USA, July 17-21, 2011, PVP2011-57518

## Abstract

The level of welding residual stress is an important consideration in the ECA of a structure or component such as a pipeline girth weld. Such a consideration is further complicated by their variation under load and the complexity involved in the proper assessment of fracture mechanics parameters in a welding residual stress field.

In this work, 2D axi-symmetric FEA models for simulation of welding residual stresses in pipe girth welds were first developed. The modelling method was validated using experimental measurements from a 19-pass girth weld. The modeling method was used on a 3-pass pipe girth weld to predict the residual stresses and variation under various static and fatigue loadings. The predicted relaxation in welding residual stress is compared to the solutions recommended in the defect assessment procedure BS 7910. Fully circumferential internal cracks of different sizes were introduced into the FE model of the three-pass girth weld. Two methods were used to introduce a crack. In one method the crack was introduced instantaneously and the other method introduced the crack progressively. Physically, the instantaneously introduced crack represents a crack originated from manufacturing or fabrication processes, while the progressively growing crack simulates a fatigue crack induced during service. The J-integral values for the various cracks in the welding residual stress field were assessed and compared. This analysis was conducted for a welding residual stress field as a result of a welding simulation rather than for a residual stress field due to a prescribed temperature distribution as considered by the majority of previous investigations.

The validation with the 19-pass welded pipe demonstrated that the welding residual stress in a pipe girth weld can be predicted reasonably well. The relaxation and redistribution of welding residual stresses in the three-pass weld were found to be significantly affected by the magnitude of applied loads and the strain hardening models. The number of cycles in fatigue loading was shown to have little effect on relaxation of residual stresses, but the range and maximum load together governed the relaxation effect. A significant reduction in residual stresses was induced after first cycle but subsequent cycles had no marked effect. The method of introducing a crack in a FE model, progressively or instantaneously, has a significant effect on J-integral, with a lower value of J obtained for a progressively growing crack. The path-dependence of the J-integral in a welding residual stress field is discussed.

## Nomenclature

BRSL | Block removal splitting and layering |

CTOD | Crack tip opening displacement |

CMOD | Crack mouth opening displacement |

E | Elasticity modulus |

ECA | Engineering critical assessment |

FAD | Failure assessment diagram |

FE | Finite element |

FEA | Finite element analysis |

f(L_{r}) |
function of the assessment line in FAD |

IH | Isotropic hardening |

J | J integral |

K | Stress intensity factor |

KH | Kinematic hardening |

K_{I} ^{P} |
Stress intensity factor due to primary stress |

K_{I} ^{S} |
Stress intensity factor due to secondary stress |

K_{J} |
J converted stress intensity factor |

L_{r} |
Load ratio |

N | Number of cycles |

RSP | Residual stress profile |

S_{max} |
Maximum stress in cyclic load |

S_{min} |
Minimum stress in cyclic load |

WCL | Weld centre line |

Poisson's ratio | |

ρ | Plasticity correction factor |

σ_{a} |
Applied stress |

σ_{ref} |
Reference stress |

σ_{f} ^{,} |
Flow strength at proof test temperature |

σ_{Y} ^{,} |
Yield strength at proof test temperature |

## Introduction

The level of welding residual stress is an important consideration in the ECA of a structure or component such as a pipeline girth weld. A realistic evaluation of the residual stress distribution in the area of interest should be made to avoid the excessive conservatism associated with assuming a residual stress of yield strength for an ECA.

Apart from the determination of residual stresses by various experimental techniques such as centre-hole drilling, sectioning and neutron diffraction, a large amount of work has been undertaken for over many years in FEA of welding residual stresses [*eg* ^{[1-2]}]. Much progress has been made with respect to the development of heat source models and in the investigation of the effects of various material hardening models on residual stresses. However, the data of welding residual stress documented in publications are subject to a large amount of scatter.^{[3]} This implies that effort is still required for development in numerical procedures for determining welding residual stress more consistently and reliably, and of validation through experimental data.

Further, the evaluation of welding residual stresses requires an understanding of the effects of a number of parameters such as static loading, cyclic loading and crack growth. Only a few studies^{[4-8]} have been carried out to investigate such effects. Clearly a better understanding of this aspect is needed if a more realistic ECA of welded structures is to be carried out.

This paper reports the work undertaken on pipeline girth welds to validate the FEA simulation of welding residual stresses with measured data, to assess the effects of static and cyclic loading on residual stresses, and to evaluate fracture mechanics parameters (K and J) in a welding residual stress field.

## FEA prediction of welding residual stresses and their variations

### Geometry and FE meshes

Two girth welded pipes were modeled. The first one, used for validation, was a 910mm OD x 32mm WT X52 grade steel pipe containing a 19-pass girth weld. Details of the experimental work for this validation case were reported in [9], including mechanical tests, the production of macrographs for each weld pass, temperature measurement, transient strain measurement and measurement of residual stresses. The second pipe was a 418mm OD x 19mm WT 316L stainless steel pipe containing a 3-pass girth weld. The 3-pass welded pipe was modeled for investigating the effects of static and cyclic loads on residual stress relaxation and for the assessment of fracture mechanics parameters in welding residual stress fields.

FE meshes of the two pipes were constructed in ABAQUS/CAE 6.7 with quadratic axi-symmetric elements. The whole pipe with a 19-pass girth weld was modeled due to the asymmetrical placement of weld passes. Only one half of the 3-pass girth welded pipe was modeled because of the symmetrical layout of the weld beads.

### FEA procedures

The welding simulation included two sequential analyses, a thermal analysis followed by a mechanical analysis. The thermal analysis provided temperature histories corresponding to weld passes, which were used as input for the mechanical analysis (elastic-plastic) for the determination of welding residual stresses.

### Heat source model

The heat source model was assumed to have a triangular time history of heat flux, with the peak heat flux occurring at a quarter of the heating time. This represented the stages in which a welding heat source approaches, passes through and departs from a specific location along the welding path. The heat flux (with units of W/mm^{3}), was determined as equivalent to an actual moving heat source and the heating time was estimated to be equal to the time that the weld pool (8mm long) took to pass a location.

The thermal properties (conductivity, specific heat and coefficient of expansion) used in the analysis are shown in *Figure 1*. As no thermal properties were found for X52 steel, those for a similar steel (X60)^{[10]} were used in the analysis.

**Figure 1. Physical properties used in analysis: (a) conductivity and specific heat;** **(b) elasticity modulus and coefficient of expansion**

### Strain hardening models

Various material hardening models including isotropic hardening, linear kinematic hardening, perfectly plastic deformation (*ie* no hardening) and annealing, were considered to demonstrate the effects of material hardening on welding residual stresses. Other more complex hardening rules such as the non-linear combined isotropic/kinematic hardening were not considered in this work as no sufficient experimental data were available to define those hardening models.

The elasticity modulus and stress-strain curves at various temperatures used in the analysis are shown in *Figures 1-3*. The properties for the parent metal (X52 steel) and the weld metal used in modeling the 19-pass welded pipe were measured, as reported in ^{[9]}. The properties of 316L stainless steel used for the 3-pass welded pipe were referred to an IIW round robin project. ^{[3]}

**Figure 2. Stress-strain data used in modeling the 19-pass welded pipe**

### Effects of external loading

The effects of static and cyclic loading on residual stresses were investigated using the axi-symmetric model of the three-pass welded pipe. Various cases of static and cyclic loading were studied, as shown in the *Table*.

**Table - Cases of static and cyclic loading**

Cases | Loading | Strain hardening model |
---|---|---|

1 | Axial loading = 0.5σ_{y} |
IH |

2 | Axial loading = 1σ_{y} |
IH |

3 | Axial loading = 1.5σ_{y} |
IH |

4 | Axial loading = 0.5σ_{y} |
KH |

5 | Axial loading = 1σ_{y} |
KH |

6 | Axial loading = 1.5σ_{y} |
KH |

7 | Pi* = 12.5MPa | KH |

8 | Pi* = 25MPa | KH |

9 | Pi* = 25MPa + axial loading = 1σ_{y} |
KH |

10 | S_{min}/S_{max} = 1, S_{max} = 0.5σ_{y}, N = 1, 5,10 |
IH |

11 | S_{min}/S_{max} = 0, S_{max} = 0.5σ_{y}, N = 1, 5,10 |
IH |

12 | S_{min}/S_{max} = 0, S_{max} = 1σ_{y}, N = 1, 5,10 |
IH |

13 | S_{min}/S_{max} = 0, S_{max} = 1σ_{y}, N = 1, 5,10 |
KH |

Note: * The internal pressure Pi only produced a hoop stress in these cases (*ie* the pressure was applied to an open-ended pipe)

## Crack growth and assessing fracture mechanics parameters in welding residual stress fields

A fully circumferential internal crack was simulated using the 3-pass girth weld model (*Figure 4*). The cracks of various crack depths (2.5, 5.07 and 10mm) were postulated to be situated at the WCL (*ie* the symmetric plane). The cracks were introduced into the model with an initial welding residual stress field, followed by application of an axial load at the ends of the pipe. Two methods of introducing a crack were employed to illustrate the effects of introducing a crack numerically. One method was the introduction of a crack instantaneously, while the other introduced a crack progressively. In the case of instantaneous crack growth, all the crack flank restraints were made free simultaneously, while progressive crack growth allowed the crack flank restraints to be released in sequence from node to node in an FE model. Note, however, that for the cases of 5.07 and 10mm long cracks (*Figure 12*), only part of the crack face was released progressively to save simulation steps. This should not affect the results obtained as the progressive crack growth started sufficiently far from the crack tip.

## Results and discussion

### Validation

Validation of the thermal analysis was undertaken by comparing the simulated cross-sectional profile of each weld pass and the macro-section of each weld pass. It is found that the simulated weld cross-sections for each weld pass match the actual ones reasonably well. As an example, *Figure 5* shows the comparison between the simulated last weld pass with the actual one.

Validation of the mechanical analysis was made by comparing the through-wall distributions of axial and hoop residual stresses at the WCL predicted from various material hardening models with those from measurements using the BRSL technique, as shown in *Figure 6*. The BRSL method is classified as a destructive method and commonly used to measure the residual stress distributions through the thickness of a structure or component. Three steps are included in this method:

- Block removal: removal of a block where the residual stresses are required;
- Splitting: the block is split into two pieces at the mid-plane parallel to the inner and outer surfaces;
- Layering: layers parallel to the splitting plane are removed from each of the block halves.

**Figure 6. Comparison of the through-thickness distributions of residual stress at the WCL predicted from various FE material hardening models and measurements. (a) axial stress;** **(b) hoop stress**

The BRSL technique has been demonstrated to produce the measurements with an overall accuracy within ±50MPa.^{[11]} As illustrated in *Figure 6*, the predicted through-thickness distributions of residual stresses from various material hardening models demonstrate a similar trend to the one from the measurements, although there are some discrepancies in magnitude. The discrepancies were considered to be caused mainly by the limitations of all the material hardening models in describing the complicated mechanical behaviour present in the thermal cycles of multi-pass welding. Among the different hardening models, the linear kinematic hardening model predicted the lowest residual stress level, while the isotropic hardening model predicted the highest value. In this study, the variation of residual stresses in the pipe wall, as predicted from the linear kinematic hardening model, was in best agreement with those from the measurements. This may reflect on the fact that the linear hardening model was more representative of the mechanical behaviour in welding than other models considered in this work. As mentioned before, the non-linear combined isotropic/kinematic hardening model was not tested in this work due to the insufficiency of data in definition of such a complicated model. In theory, the combined hardening model should be the most favorable one in describing the thermal mechanical behaviour occurring in welding. However, this can be valid only on the premise of generating accurate parameters required to define a combined hardening model, which usually requires a substantial effort.

The outcome from the validation case demonstrates that an axi-symmetric model can be used to simulate the multiple weld passes for a pipe girth weld for determination of welding residual stresses. In practice, the use of axi-symmetric model may be the only practical option for a multiple-pass pipe girth weld as the effort in creating a 3D model, the computer run-time and memory requirements may be prohibitively huge.

### Static loading effects on 3 pass weld

*Figure 7* shows the variation of residual stresses with thickness at the WCL due to the three static axial loads only. The three load levels were 0.5, 1 and 1.5 times the yield strength (250MPa) as applied to cases 1 to 6 of the *Table*. *Figure 8* demonstrates the effect of internal pressure (12.5 and 25MPa) and the combination of internal pressure (25MPa) and axial loading (equal to the yield) for cases 7-9 in the *Table*. Internal pressures of 12.5 and 25MPa produced hoop stresses in the pipe of 125 and 250MPa respectively (*ie* 0.5 and 1 times the yield).

**Figure 7. Static loading effects on (a) axial residual stresses;**

**Figure 7. Static loading effects on (a) axial residual stresses;** **(b) on hoop stress**

As shown in *Figure 7*, regardless of which strain hardening model (isotropic or kinematic) was used, small beneficial effects were gained when a static load was below 50% of the yield strength, whereas a substantial decrease in peak tensile stress was attained when the static load was above the yield strength.

From the isotropic hardening model, the peak tensile axial stress was decreased by about 75% (from 92 to 23% of the yield strength) after the application of an axial load equal to the yield strength. More profound reduction in the peak tensile stress (from 92 to -27% of the yield strength) was induced as a result of applying an axial load equal to 1.5 times the yield strength. From the kinematic hardening model, however, nearly the same level of decrease in the peak tensile stress (from 65% to minus 3% of the yield strength) was found for the cases with the axial load equal to the yield strength or 1.5 times the yield strength. Similarly, substantial reduction was also found in hoop stresses when the applied axial load was above the yield.

The results shown in *Figure 8* demonstrates that an internal pressure of 12.5MPa caused a marked relaxation of the peak axial stress (from 65% to 23% of the yield strength), compared with a much smaller decrease due to an axial load equal to 50% the yield.

The different strain hardening models had a profound implication on the amount of relaxation in residual stress due to mechanical loading. In theory, the kinematic hardening model should be more representative of the material deformation behavior due to loading and unloading because it represents more accurately the BAUSCHINGER effect. However, further work with experimental validation is needed to demonstrate which strain hardening model is more appropriate.

### Implication in ECA

Consideration of residual stress relaxation due to proof or overload testing is recommended in BS7910:2005^{[12]} for ECA. In Annex O of BS 7910:2005, the relaxation of a yield magnitude membrane residual stress due to proof or overload testing is given by the following equations.

**(****Equation** **1)**

**(****Equation** **2)**

Equation (1) is applicable to the assessment of a cracked component that has been proof tested, while Equation (2) applicable to the case where a crack was initiated in service after the proof loading. The limits for the relaxed residual stress are between 0.4σ_{Y} ^{,} and σ_{Y} ^{,} from Equation (1) and between 0.3σ_{Y} ^{,} and σ_{Y} ^{,} from Equation (2). In this work, σ_{Y} ^{,} was taken to be 250MPa for the 3-pass weld model.

It was found in this work that the peak tensile axial stress was decreased by 75% (from 230 to 57.5MPa) from the isotropic hardening model, and by 106% (from 162.5 to -10.75MPa) from the kinematic hardening model after an axial static loading (*ie* σ_{ref} for a non-cracked structure) equal to the yield strength (0.72 times the flow strength, 350MPa). A decrease of 32% (from 250 to 170MPa) in residual stress would be calculated using Equation (1), and 70% (from 250 to 75MPa) using Equation (2).

For an axial static loading of 1.5 times the yield, the peak tensile axial stress was decreased by about 130% (from 230 to -72.5MPa) from the isotropic hardening model, and by 106% (from 162.5 to -10.75MPa) from the kinematic hardening model. For this loading condition, Equation (1) and (2) reached the limits, 0.4σ_{Y} ^{,} and 0.3σ_{Y} ^{,}, which suggests a reduction in residual stress by 60% (from 250 to 100MPa) and 70% (from 75MPa), respectively.

These results demonstrate generally a substantial underestimation of the relaxation effect by BS7910. It should be noted, however, that the relaxation in residual stress assessed numerically was based on the peak stress in a distribution profile rather than a membrane stress of the yield level as prescribed analytically in Equation (1) and (2). Some change may occur in the level of relaxation in residual stress obtained numerically if a membrane residual stress of yield level was prescribed in a model.

### Cyclic loading effects

The through-wall axial stress distributions affected by various cyclic loadings as specified for cases 10-13 in the *Table* are shown in *Figures 9-10*. *Figure 9* presents the results obtained for the three sets of cyclic loading for the IH model. *Figure 10* compares the results from the IH and KH models.

For each level of the fatigue loading, the effect was seen immediately after the first cycle, and no marked difference in the effect on residual stresses was found between one, five and ten cycles. Because of this, the profiles affected by cyclic loading are similar to those affected by static loading discussed above. With their numerical investigation, Dattoma et al^{[4]} also demonstrated a significant reduction in the initial residual stresses after the first load cycle, and subsequent cycles did not show any effect on the redistribution of welding residual stresses.

However, in contrast to the cases of static loading in which the effect was governed only by the magnitude of a static load, the effects on residual stresses due to a cyclic load were shown to be due to the combined action of the maximum load and the minimum reversed load leading to yielding in reversed compression. This was demonstrated from a more pronounced effect of stress relaxation from case 10 (S_{min}/S_{max} = -1 and S_{max} = 0.5 times the yield) than from case 11 (S_{min}/S_{max} = 0 and S_{max} = 0.5 times the yield).

Finally, it is worthwhile noting that the underlying mechanism for relaxation of residual stresses due to either static loading or cyclic loading is the occurrence of yielding of the materials under the combined action of residual stresses and the stresses due to external loading. Obviously, no relaxation of residual stresses would occur if no yielding was induced, as usually in cases of high cycle fatigue (*ie* low external stresses).

### Crack growth and assessment of fracture mechanics parameters

The J-integrals corresponding to the various crack heights (2.5, 5.07 and 10mm) were evaluated from the elastic-plastic FEA models. Different combinations of the residual stress distribution and primary membrane loads were investigated. The primary membrane loads were applied at the ends of the girth welded pipe, perpendicular to the postulated crack plane. Based on the J values from FEA, the effective crack driving force (K_{J}) was evaluated by the following relation:

**(****Equation** **3)**

The effective driving force K_{J} in terms of the assessment procedure in R6^{[13]} was also evaluated using the following equation.

**(Equation 4)**

All the parameters in Equation (4) were calculated using R-code (an assessment program based on the R6 procedure). Two methods given in R-code, the simplified and the inelastic, were used to calculate the factor. The inelastic method is generally less conservative than the simplified method.

The effective driving forces K_{J} from FEA and R-code are presented in *Figure 11* for the crack heights (5.07 and 10mm) in the girth weld. The average value of the J-integrals evaluated by FEA over the domain close to the crack tip was used to calculate the FEA K_{J}. The values of load ratio Lr were evaluated from the R-code program, rather than from FEA.

Firstly, a thorough examination of the FEA evaluations of J-integral was made with respect to the path-independence of J-integral in a welding residual stress field. When the J-integral domain included only the region close to the crack tip (approximately within one fifth of the crack size), it was found that the path-independence feature of a J-integral was largely maintained in the two crack heights (5.07 and 10mm) for the fully internal crack, regardless of which method of introducing a crack (instantaneously or progressively) was used. This path-independence was found to be improved as the primary load was increased. These observations were consistent with those by Bouchard et al^{[5]} and Smith and Goldthorpe^{[6]}, although the whole welding residual stress and strain fields in this work were significantly more complex than the one investigated by Smith and Goldthorpe and Bouchard et al.

However, a strong path-dependence was found in the small crack height (2.5mm) for the fully internal circumferential crack, even with the increase in primary loading. This means that in this case, the J-integral is not a valid parameter for governing the crack-tip field of elastic-plastic deformation. A modified definition of the J-integral which accounts for the initial strain due to residual stress, *ie* JEDI^{[8]} may be able to address the issue of path-dependence. However, it should be noted that the path dependence of J-integral in a welding residual stress field is due to the complex cycles of loading and unloading experienced in welding and the crack extension leading to additional unloading. In the case of deeper cracks (5.05 and 10mm in this work), path-independence was demonstrated to be largely retained. This was mainly because the near-crack tip stresses for a deeper crack can be intensified sufficiently for overcoming the effect of residual stresses in comparison with a shallower crack. To avoid the issue of path dependence, CTOD may be considered as an alternative parameter for use in a welding residual stress field. However, it should be aware of the constraint effect (*ie* specimen dependence) on fracture mechanics parameters including CTOD and J integral.

The effect of the method of introducing a crack is clearly shown in *Figure 11*, which show that a lower value of KJ was obtained from a progressively growing crack. This effect occurred because the progressively growing crack front left a plastic wake along its flanks than the instantaneously growing crack. The comparison of crack opening profiles from the two methods is presented in *Figure 12*, clearly demonstrating the formation of a larger plastic wake for a progressively growing crack. As a result of this, a reduced crack opening displacement was attained by progressively growing a crack, making the progressively growing crack in a residual stress field more benign. Similar results were made by Bouchard et al^{[5]} who considered a repair weld in a pump casing, and by Charles et al ^{[7]} who considered a fully circumferential external crack in a pipe girth weld. However, it should be noted that the extent of reduction in K_{J} varied. This work and the work of Charles et al ^{[7]} showed smaller reductions in K_{J} than those of Bouchard et al.^{[5]}

**Figure 11. Comparison of the effective K factors due to the combination of RSPs and primary me****mbrane loads from FEA and R-code. The RSP in this example was referred to Initial RSP, IH in Figure 7. (a) for the 5.07mm long circumferential crack; (b) for the 10mm long circumferential crack.**

A few interesting points can be further revealed by examining the results shown in *Figure 11* for the fully internal circumferential crack with two heights of 5.07 and 10mm.

Firstly, the R-code evaluations of K_{J} were closer to the FE calculated K_{J} when the load ratio L_{r} was below about 0.7. After this value of L_{r}, the divergence in the K_{J} evaluated from the R-code methods and FEA tended to be substantial, with over-estimation of K_{J} from the R-code methods.

Secondly, while the simplified ρ method in R-code gave K_{J} values closer to the values from the FEA which simulated a instantaneously growing crack, the K_{J} values evaluated from the inelastic ρ method were more comparable with those from the FEA simulating a progressively growing crack.

Thirdly, when L_{r} was below about 0.7, the R-code evaluations could be non-conservative, particularly when the inelastic ρ method was adopted. Similar findings with respect to the non-conservatism of the R6 assessment procedure were also reported by Smith and Goldthorpe.^{[6]} However, it should be pointed out that to reach a general statement with regard to the observed non-conservatism would require investigating a wider range of cases.

## Conclusions

The conclusions are below:

- The predicted through-thickness distributions of welding residual stresses in a 19-pass girth weld from a 2D axi-symmetric model using kinematic hardening compared reasonably well with the measurements.
- Static loading was found to give substantial reductions in both axial and hoop stresses when at or above the yield strength, but had a small effect when the static load was lower than 50% of the yield strength.
- Compared with the simulation results, the level of residual stress relaxation due to a proof or overload testing given in Annex O of BS 7910:2005 is generally conservative.
- Cyclic loading was found to cause a relaxation of residual stresses after the first cycle and subsequent cycles did not show any effect.
- Material hardening models were found to have a significant effect on both the relaxation and initial residual stresses.
- Two methods of introducing a crack in a FE model, progressively or instantaneously, were shown to have significant effects on J-integral, with a lower value of J obtained for a progressively growing crack.
- Due to the complexity of the loading and unloading histories related to multiple-pass welding, the J-integral may be invalid because of path-dependence. CTOD may be considered as an alternative parameter for crack driving force in such cases.

## Acknowledgments

This work was funded by Industrial Members of TWI, as part of the Core Research Program.

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