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Procedía Engineering 130 (2015) 531 - 543

Procedía Engineering

www.elsevier.com/locate/procedia

14th International Conference on Pressure Vessel Technology

Three Dimensional Weld Residual Stresses Simulations of Start/Stop and Weld Repair Effects

E. Bonnauda'*, J. Gunnarsa

aInspecta Technology AB, Box 30100, 104 25 Stockholm, Sweden

Abstract

Weld Residual Stresses are a major concern as they markedly reduce reliability. Accurate prediction is therefore essential and is usually carried out by mean of Finite Element Analysis. In many cases, two dimensional axisymmetric modelling is sufficient but comparison with measurement has shown limitations. Full 3D simulations are therefore now preferred in several applications and especially when it comes to studying start/stop and (partial) repair effects. These two events have here been simulated in 3D and comparison with 2D results indicate a significant increase in Weld Residual Stresses. As an illustration, the reduction on critical crack size is assessed by a Fracture Mechanics analysis.

© 2015 The Authors.PublishedbyElsevierLtd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

Keywords: weldresidual stresses; finite element analysis; three dimensional simulations; start/stop effects; repair effects.

1. Introduction

When manufacturing and connecting pressure vessels to pipes, welding is always part of the process, see Fig. 1. Unfortunately, because of the non-uniform plastic deformations due to rapid local heating and cooling cycles and solidification, residual stresses appear locally in the weld and in the surrounding Heat Affected Zone. Weld Residual Stresses play a significant role for failure mechanisms such as fracture, Stress Corrosion Cracking and fatigue: tensile residual stresses (especially at the surface) generally decrease the reliability of a component whereas compressive residual stresses are often beneficial.

* Corresponding author. Tel.: +46 8 50113065; fax: +46 8 50113001. E-mail address: etienne.bonnaud@inspecta.com

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICPVT-14

doi:10.1016/j.proeng.2015.12.260

Fig. 1. Partial root pipe weld. Oxidation reveals the shape of the temperature distribution during welding.

Finite Element Analyses are a very convenient way to predict weld residual stresses before or after manufacturing. The results are often used as raw data in subsequent fracture mechanics analyses to assess -among others- critical crack size. The procedure simulates the successive addition of molten metal that cools and consists of two distinct steps: a transient thermal analysis followed by an elastic-plastic mechanical analysis. For practical reasons and despite the three dimensional nature of the problem, these simulations have, up to very recently, been carried out in two dimensions only, see for example [1,2]. The benefits are obvious: easier modelling procedure and smaller models leading to lower requirement on computer memory and processor speed. Unfortunately this approximation has also drawbacks. Firstly, in two dimensions, heat can only propagate perpendicular to the weld direction whereas in reality it can propagate in all directions. This calls for a Heat Source Calibration which aims at reducing the amount of energy transferred to the simulation model. This procedure is not straight-forward and is still the focus of active research, meaning that no unique calibration method prevails. Secondly, as a weld bead in a two dimensional simulation reduces to a surface, adding a new bead occurs necessarily instantly whereas, in reality, the bead is laid down over a certain duration during which the bead front location constantly moves forwards. A detailed review of issues related to 2D and 3D simulations is presented in [3].

Finally, some effects can only be caught in three dimensional simulations. Among those, start/stop and weld repair are particularly interesting. When closing a circular weld or when changing a welding electrode after partially welding a bead, a portion of the weld is reheated, which markedly alters the residual stresses in this specific region. When it comes to weld repair and especially partial weld repair in the eventuality of having found a crack of limited extension, grinding a portion of one of several beads and re-welding the removed part also markedly alters the residual stresses in the region. Different attempts to study weld repairs can be found in [4] where changes in microstructure are in focus and in [5,6] where simulations results are compared with measurements. Such comparisons have shown better and better agreement see [7,8] as both measurement techniques (incremental Deep Hole Drilling, Contour method...) and simulations capabilities have rapidly improved during the past few years.

Here a three dimensional model of a cylindrical structure is presented. The weld consists of five beads of Alloy 182 and connects dissimilar metals, namely Alloy 600 and stainless steel SS316L. Heat input is taken directly from the Weld Procedure Specification corresponding to the geometry. Results of the three dimensional simulations are first extracted in different cross-sections at different angles and compared to a two dimensional simulation.

Afterwards, effects of start/stop and partial weld repairs are simulated and results are presented in the relevant cross sections. Finally, to illustrate the effect on acceptable crack size, fracture mechanics analyses are carried at the Center Line location.

2. Simulation models

The purpose of this study is to simulate the welding process between two cylinders. Both cylinders have the same inner radius (R = 25.7 mm) and the same thickness (t = 4.5 mm). Each cylinder has a height slightly larger than 10\fm , this is to say 107 mm, so that the boundary conditions at the ends of the cylinder do not influence the weld region. Two models were built: a two dimensional axisymmetric model and a three dimensional model. In order to limit the simulation time, only a half of the 3D geometry was modelled, see Fig. 2. As it will be shown in section 4, half a model is sufficient to capture the transient and the steady-state regimes. The two dimensional axisymmetric model is locked in the vertical direction to avoid rigid body motion. The lower half cylinder of the three dimensional model is locked in all three directions whereas the top of the upper cylinder is totally unconstrained.

(a) (b)

Fig. 2. Whole geometry of(a) the 2D model and (b) the 3D model.

Stainless Steel

Alloy 182

Alloy 600

Fig. 3. Detail of(a) the material distribution and (b) the bead sequence (before capping removal).

The weld in focus here is a Dissimilar Metal Weld connecting together Stainless Steel (316L) to a nickel based alloy (Alloy 600), see Fig. 3.a. The weld material is also a nickel based alloy (Alloy 182). In the simulations, both Alloy 600 and Alloy 182 are assigned the same thermal and mechanical properties. The weld consist of 5 beads laid symmetrically with respect to the Center Line, see Fig. 3.b. Parts of beads 4 and 5 lay outside the weld preparation area; this extra material, usually called capping is removed in the last step ofthe simulation.

The mesh ofthe 3D model (visible in several pictures in the next sections) is revolved from the mesh from the 2D model. The number of elements in the hoop direction is 70. Similar meshes allow easier comparison and eliminate possible discrepancies due to different mesh densities. The 2D mesh consists of 1261 nodes and of 1368 four-nodes elements whereas the 3D mesh consists of89531 nodes and of78540 eight-nodes elements.

The mechanical material behaviors of Alloy 600 and 316L follow a nonlinear isotropic hardening model and a nonlinear mixed hardening model respectively, see [9,10] for details. The welding simulation consists oftwo distinct steps: a thermal analysis followed by a mechanical analysis. The Finite Element procedure simulates the successive addition of molten metal that cools in a sequence of transient thermal analyses and elastic-plastic analyses. All simulations are carried out using the Finite Element program Abaqus, [11].

3. Thermal simulations

3.1. Two dimensional simulations

As the actual 3D welding process is modelled by 2D analyses, a central issue is to evaluate the amount of heat transferred to the model for every added bead. The liquid weld pool is modeled by an equivalent heat conduction model corresponding to the welding method. Heat Source Calibration is conducted using the travelling heat source method based on actual Welding Procedure Specifications, see [10] for details. For this specific weld, the temperature is ramped up between 20°C to 1500°C during 2.9 s and hold at 1500 °C during 1.5 s. The inter-pass temperature is set to 20°C. Fig. 4 shows the temperature distribution in the model after laying the first bead and after laying the fifth bead.

i- 1.5E+03

- 1.4E+03

- 1.3E+03

- 1.2E+03

- 1.0E+03

\- 912.5E+00

k 785.0E+00

- 657.5E+00

- 530.0E+00

- 402.5E+00

- 275.0E+00

- 147.5E+00

L 20.0E+00

Fig. 4. 2D model; temperature distribution during the welding of (a) the first bead and (b) the last bead. Values are in °C degrees. 3.2. Three dimensional simulations

As previously mentioned, when dealing with 3D simulation, the need for Heat Source Calibration vanishes. Instead, data from Welding Procedure Specifications can be used directly. Knowledge of the weld length and of the

travel speed gives the simulation running time; knowledge of the net line energy and of the bead cross section gives the heat flow see Table 1 for values used in the 3D simulation.

Table 1. Heat flow values.

Bead cross TT _

Net line.- ^eat il°w

L nne section

energy [kJ/m] [TJ/m3]

Bead 1 640 4 160

Bead 2-3 880 5.8 152

Bead 4-5 880 8.9 99

The amount of heat transferred to the model is obviously proportional to the volume in which heat flow actually occurs. Therefore as well as the travel speed and the heat flow values, the size of this volume needs to be adjusted. Calibration can be made simply by setting the circumferential length ofthe weld pool equal to the height ofthe bead, which is consistent with experimental observations. A snapshot ofthe 3D thermal simulation ofthe first bead can be seen in Fig. 5. Comparison between this picture and the photography in Fig. 1 shows that the shapes of the temperature distributions are very similar.

A common 3D simulation technique is to add material in a discrete manner by repeatedly activating small portions ofthe weld, see [12] for example. Here instead, by sweeping through the whole bead length, heat input and material deposition occur continuously.

Note that in 2D, the heat input parameters are the melting temperature, the ramping time and the hold time whereas in 3D simulations, input parameters are the heat flow and the weld pool circumferential length.

- r 2.8E+03 - 1.5E+03 - 1.4E+03

- 1.3E+03

- 1.2E+03

- 1.0E+03

- 912.5E+00

- 785.0E+00

- 657.5E+00

- 530.0E+00

- 402.5E+00

- 275.0E+00

- 147.5E+00

- 20.0E+00

L 14.6E+00

Fig. 5. Temperature distribution during first bead welding: 3D model. Values are in °C degrees.

4. 3D results and comparison with 2D

Fig. 6 shows 3D weld residual stresses on the inside in the axial direction (033 in a cylindrical coordinate system) and Fig. 7 shows 3D weld residual stresses on the inside in the hoop direction (022 in a cylindrical coordinate system). Subsequent 3D plots are oriented in the same way, with the weld being laid from left to right. The left and the right locations are in the following referred to as the 0° and the 180° location respectively and act as reference for all locations in between.

The main result is that stress distributions in different cross sections change along the weld. This is due to the fact that the steady state regime is preceded by a transient regime. For this particular geometry, steady state is reached

after approximately 130°. Thereafter, the influence of the surface at 180° alter the results. This observation is consistent with earlier work, see [3] for example.

Weld start

S, S33 (CSYS-1)

(Avg: 75%)

r 479E+06

_ - 418E+06

— - 352E+06

- 285E+06

- 219E+06

- 152E+06

- 86E+06

- 20E+06

- -47E+06

- -113E+06

- -180E+06

H - -246E+06

_ \- -313E+06

\- -379E+06

■ L -476E+06

Weld stop

Fig. 6. 3D model - axial stress on the inside. Weld direction is indicated by the black arrow and cross section atl30° is materialized by a dotted line. Values are in Pa.

Weld start

S, S22 (CSYS-1)

(Avg: 75%)

r 470E+06

— - 406E+06

■ - 350E+06

- 293E+06

- 237E+06

- 181E+06

- 124E+06

- 68E+06

- 12E+06

- -45E+06

- -101E+06

- -157E+06

\- -214E+06

\- -270E+06

L -380E+06

Weld stop

Fig. 7. 3D model - hoop stress on the inside. Weld direction is indicated by the black arrow and cross section at 130° is materialized by a dotted line. Values are in Pa.

Stress distributions in cross sections at 130° were extracted from the 3D model and plotted in Figs. 8-9 beside corresponding 2D cases. Axial stress distributions are very similar both in the weld and at a distance, see Fig.8. Hoop stress distributions are very similar at a distance whereas the high stress areas in the weld is somewhat shifted towards the nickel based alloy side, see Fig. 9.

Stresses are obviously not symmetrical with respect to the weld: axial stresses have higher magnitudes in the nickel based material and hoop stresses below the weld are more compressive than in the region over the weld. The explanation is as follows.

Fig. 8. Axial stress comparison: (a) 3D model at 130° and (b) 2D model. Values are in Pa.

S, S22 (CSYS-1) (Avg: 75%) 470E+06 406E+06 350E+06 293E+06 237E+06 181E+06 124E+06 68E+06 12E+06 -45E+06 -101E+06 -157E+06 -214E+06 -270E+06 -380E+06

X JL Z

Fig. 9. Hoop stress comparison: (a) 3D model at 130° and (b) 2D model. Values are in Pa.

As described in section 2, the cylinder considered here has an inner radius of R = 25.7 mm and a thickness of t = 4.5 mm. The ratio "R/t" is therefore approximately 5.7. The bead size characteristic length can be set to b = 2 mm, which gives a "b/t" ratio of0.4.

These ratios are of interest when dealing with axisymmetric geometries as they give an indication on the global deformation shape that in turn determines the stresses in the weld. Small R/t and b/t ratios render weld residual profiles going from tension to compression to tension in a characteristic sinus-like shape whereas high R/t and b/t ratios render more linear stress profiles going from tension on the inside to compression on the outside. This latter profile is therefore the one to be expected here, which is consistent with Fig. 8 and with the 2D plot (as welded) in Fig. 16. Some distance above and below the weld though, to comply with the global deformation shape, the stress distribution is reversed and stresses go from compressive on the inside to tensile on the outside. Discrepancies

between the regions above and below the weld are due to material properties. Stainless steel has lower Young's modulus and lower yield stress than Nickel based alloy. Stress magnitudes are therefore lower in the stainless steel cylinder.

When it comes to hoop stress, the large compressive region below the weld has to do again with material properties. The thermal expansion coefficient for stainless steel is higher than the thermal expansion coefficient for nickel based alloy. Consequently for the same temperature decrease, the part in stainless steel contracts more than the part in nickel based alloy: the stainless steel is therefore in tension when the nickel based alloy is in compression.

5. Start/Stop Effects

Circumferential welds need to be closed and it is sometimes necessary to change electrodes. The regions where these events occur are ofparticular interest as they experience another thermal and mechanical loading history.

Figure 10 shows 3D weld residual stresses on the inside in the axial direction and Fig. 11 shows 3D weld residual stresses on the inside in the hoop direction.

The plane where the weld closure event occurs is the 90° plane. The right part of the model (between 90° and 180°) is welded first, followed by the left part of the model (between 0° and 90°). Comparison of axial stress distributions (Fig. 10 and Fig. 6) and of hoop stress distributions (Fig. 11 and Fig. 7) reveals noticeable differences. Stress magnitudes are higher (both tensile and compressive) and regions with high stress magnitudes are larger. Fig. 12 shows axial and hoop stresses in the start/stop plane. Comparison with Fig. 8 and Fig. 9 confirms the higher level in stress magnitudes throughout the thickness.

The plane where the weld closure event occurs is the 90° plane. The right part of the model (between 90° and 180°) is welded first, followed by the left part of the model (between 0° and 90°). Comparison of axial stress distributions (Fig. 10 and Fig. 6) and of hoop stress distributions (Fig. 11 and Fig. 7) reveals noticeable differences. Stress magnitudes are higher (both tensile and compressive) and regions with high stress magnitudes are larger. Fig. 12 shows axial and hoop stresses in the start/stop plane. Comparison with Fig. 8 and Fig. 9 confirms the higher level in stress magnitudes throughout the thickness.

Axial stress data extracted from the steady state regime at 130° (Fig. 8) and from the start/stop plane at 90° (Fig. 12) will be used in section 7 for a reliability analysis.

Note that the weld closure results presented here should be seen as a conservative upper bound as all start/stop events occur in the same plane (the 90° plane). In reality, it is likely that operators choose to start beads at different locations in order to minimize the detrimental effect ofstart/stop events.

Fig. 10. 3D model - axial stress on the inside. The start/stop plane, in the middle, is materialized by a dotted line. Values are in Pa.

S, S22 (CSYS-1)

(Avg: 75%)

r 518E+06

- 406E+06

- 350E+06

- 293E+06

- 237E+06

- 181E+06

I 124E+06

\- 68E+06

I 12E+06

\- -45E+06

I -101E+06

I -157E+06

\- -214E+06

I -270E+06

L -396E+06

Fig. 11.3D model - hoop stress on the inside. The start/stop plane, in the middle, is materialized by a dotted line. Values are in Pa.

S, S33 (CSYS-1)

(Avg: 75%)

r 533E+06

- 418E+06

- 352E+06

- 285E+06

- 219E+06

— - 152E+06

- 86E+06

- 20E+06

- -47E+06

- -113E+06

- -180E+06

- -246E+06

■ - -313E+06 \- -379E+06 L -464E+06

S, S22 (CSYS-1)

(Avg: 75%)

r 518E+06

- 406E+06

- 350E+06

- 293E+06

- 237E+06

- 181E+06

- 124E+06

- 68E+06

- 12E+06

- -45E+06

- -101E+06

- -157E+06

5 - -214E+06 \- -270E+06 L -396E+06

(a) (b)

Fig. 12. 3D model - (a) axial and (b) hoop stress in the start/stop plane. Values are in Pa.

6. Weld repair

Evenly spaced inspections allow sometimes to detect cracks. In this eventuality, it is often preferable to dig a cavity to remove the entire crack plane. Thereafter, the cavity is filled with new solder material. Cracks, being often detected early, have not usually propagated all along the weld and are of limited extension. The repair is therefore also of limited extension. Fig. 13 shows the geometry of the repair studied here. The removed part was assumed to be the first bead and to cover a45° arc, symmetrically placed with respect to the 90° plane.

Results from the 3D simulations are shown in Fig. 14.a (axial stress) and Fig. 15.b (hoop stress). As for start/stop events, it appears clearly that repairs increase stress magnitudes and sizes of regions with high stress magnitudes, see Fig. 8.a and Fig. 8.b for comparison with 2D as welded simulations.

Even more relevant would be to compare 3D repair simulations with axisymmetric 2D repair simulations. Results, which obviously correspond to a 360° repair, are shown in Fig. 14.b and Fig. 15.b. An interesting feature is that both axial and hoop stress distributions reveal a large region with high compressive stresses on the outer part of the weld. In a fracture mechanics analysis, such high compressive stresses would cause powerful crack arrest and give the erroneous impression that the repaired weld is much more reliable than it actually is. In this case 2D simulations are not conservative.

Fig. 13. Repair geometry: (a) front and top views, (b) cross section ofthe repair region.

S, S33 (CSYS-1)

(Avg: 75%)

r 738E+06

- 418E+06

- 352E+06

- 285E+06

- 219E+06

- 152E+06

- 86E+06

- 20E+06

- -47E+06

- -113E+06

- -180E+06

- -246E+06

[■ -313E+06

\- -379E+06

L -460E+06

S, S22

(Avg: 75%)

r 422E+06

- 418E+06

- 352E+06

- 285E+06

- 219E+06

- 152E+06

- 86E+06

- 20E+06

- -47E+06

- -113E+06

- -180E+06

- -246E+06

\- -313E+06

\- -379E+06

L -522E+06

Fig. 14. Axial stress comparison: (a) 3D model at 90° and (b) 2D model. Values are in Pa.

S, S22 (CSYS-1)

(Avg: 75%)

r 786E+06

y L 406E+06

k 350E+06

- 293E+06

- 237E+06

- 181E+06

- 124E+06

- 68E+06

- 12E+06

- -45E+06

- -101E+06

H 1- -157E+06

■ L -214E+06

L -270E+06

L -447E+06

S, S33

(Avg: 75%)

r 505E+06

y - 406E+06

L 350E+06

- 293E+06

- 237E+06

- 181E+06

- 124E+06

- 68E+06

- 12E+06

- -45E+06

- - -101E+06

H 1- -157E+06

y L -214E+06

y \- -270E+06

L -672E+06

Fig. 15. Hoop stress comparison: (a) 3D model at 90° and (b) 2D model. Values are in Pa.

7. Reliability study

As commonly known, cracks are likely to initiate and grow in a weld or at the vicinity of a weld (in the Heat Affected Zone). Both axial cracks (driven by circumferential tensile stresses) and circumferential cracks (driven by axial stresses) may grow in connection to circumferential welds. However only circumferential cracks are likely to grow long enough to cause total failure of a cylindrical structure. Axial cracks are limited by the length of the weld residual stresses zone and can therefore at most lead to leakage.

To illustrate how start/stop effects influence reliability, two fracture mechanical assessments were carried out: one on results from the 2D simulation (Fig. 8.b) and the other on results from the 3D start/stop simulation (Fig. 12.a). Axial stresses were extracted in the midplane along the Center Line and plotted on Fig. 16 for comparison.

Fig. 16. 2D and 3D start/stop model - axial stress in the midplane along Center Line.

The damage tolerance analysis is based on the R6 method and was conducted using an Inspecta in-house developed software ProSACC (Professional tool for Safety Assessment of Cracked Components) [13]. A complete

circumferential internal surface crack loaded with a pressure load giving a 100 MPa tensile stress is considered, (see Fig. 17). Material parameters are listed in Table 2.

Table 2: Material parameters.

Elasticity Modulus E (GPa) Yield Strength ff, (MPa) Tensile Strength ffu (MPa) Fracture Toughness Kcr (MPa.m1'2)

200 200 500 150

The crack depth for initiation of failure based on the 2D analysis was found to be 1.5 mm whereas the crack depth for initiation of failure based on the start/stop 3D analysis was found to be 1.1 mm which is a relatively large degradation.

Fig. 17. Sketch of a complete circumferential internal surface crack in a cylinder. Ri is the inner radius; t, the thickness and a, the crack depth.

8. Conclusions

Three dimensional weld residual stresses simulations have been carried out on a Dissimilar Metal Weld. The geometry being axisymmetric, 3D results were compared with axisymmetric 2D results. The main conclusions are as follows.

Weld residual stresses depend on the cross section location as the steady state region is preceded by a transient region. The transition for this particular geometry takes place around 130° after the weld start location.

Start/stop events are detrimental to reliability. The extra thermal and therefore mechanical loading increases the stress level markedly, which influences the crack depth for initiation of failure.

Repair events are also detrimental to reliability. Moreover axisymmetric 2D stress simulations can give the false impression that part of the weld experience high compressive stresses, which would be beneficial. Partial stress repairs should therefore not be modelled in 2D as the results are not conservative.

Acknowledgments

The authors want to express their sincere gratitude to Hakan Lind and Jan Granlund at SIMULIA Nordics CSE for their effective and enthusiastic support on simulation related issues.

References

[1] E. Bonnaud, J. Gunnars, Effect of inPlane and out of Plane Bending on Weld Residual Stresses, Proc. ASME PVP Conference, PVP2014-28737, 2014.

[2] D. Bremberg, J. Gunnars, E. Bonnaud, L.O. Edling, E. Kingston, Residual Stresses in Alloy 182 PWHT Buttering and Attachment Weld -Validation by Modelling and Measurements ofa Full Scale Mockup, Proc. ASME PVP Conference, PVP2014-28965, 2014.

[3] F.W. Brust, D.L. Rudland, Three Dimensional Aspects of Computational Weld Modelling, Proc. ASME PVP Conference, PVP2008-61558, 2008.

[4] W. Jiang, Y. Luo, G. Zhang, W. Woo, S.T. Tu, Experimental to Study the Effect of Multiple Weld Repairs on Microstructure, Hardness and Residual Stress for a Stainless Steel Clad Plate, Materials and Design, 51, pp. 1052-1059, 2013.

[5] D. George, D.J. Smith, P.J. Bouchard, Evaluation of Through Wall Residual Stresses in Stainless Steel Weld Repairs, Materials Science Forum, 347-349, pp. 646-651, 2000.

[6] C.D. Elcoate, R.J. Dennis, P.J. Bouchard, M.C. Smith, Three Dimensional Multi-Pass Repair Weld Simulations, International Journal of Pressure Vessels and Piping, 82, pp. 244-257, 2005.

[7] S. Hossain, C.E. Truman, D.J. Smith, K. Ogawa, Residual Stress Measurement Simulation in a Type 316 Stainless Steel Girth-Butt Weld Joint, Proc. ASME PVP Conference, PVP2008-61347, 2008.

[8] F.W. Brust, E. Punch, E. Kurth-Twombly, Part Repair and Start/Stop Effects and Three Dimensional Residual Stress in Dissimilar Metal Welds, Proc. ASME PVP Conference, PVP2015-45785, 2015.

[9] L. Lindgren, K. Domkin, S. Hansson, Dislocations, vacancies and solute diffusion in physical based plasticity model for AISI 316L, Mechanics ofMaterials, 40, pp. 907-919, 2008.

[10] J. Mullins, J. Gunnars, Validation of Weld Residual Stress Modeling in the NRC International Round Robin Study, SSM Report 2013:01, 2013.

[11] Abaqus 6.10, Analysis User's Manual, Dassault Systèmes Simulia Corp., Providence, RI, USA, 2010.

[12] F.H. Ku, T.G. Hicks, W.R. Mabe, J.R. Miller, Evaluation of Residual Stresses in Small Diameter Stainless Steel Pipe Welds by Two-Dimensional and Three-Dimensional Finite Element Analyses, Proc. ASME PVP Conference, PVP2014-28776, 2014.

[13] ProSACC, A combined deterministic and probabilistic Procedure for Safety Assessment of Components with Cracks - Handbook, SSM Report 2008:01, 2008.