a method for calculating weld-induced residual stresses

Nuclear Engineering and Design 206 (2001) 139–150

Numerical weld modeling — a method for calculatingweld-induced residual stresses�

S. Fricke, E. Keim, J. Schmidt *Siemens AG, KWU NT1, Postfach 32 20, 91050 Erlagen, Germany

Received 29 March 2000; received in revised form 19 September 2000; accepted 24 November 2000

Abstract

In the past, weld-induced residual stresses caused damage to numerous (power) plant parts, components andsystems (Erve, M., Wesseling, U., Kilian, R., Hardt, R., Brummer, G., Maier, V., Ilg, U., 1994. Cracking in StabilizedAustenitic Stainless Steel Piping of German Boiling Water Reactors — Characteristic Features and Root Causes. 20.MPA-Seminar 1994, vol. 2, paper 29, pp.29.1–29.21). In the case of BWR nuclear power plants, this damage can becaused by the mechanism of intergranular stress corrosion cracking in austenitic piping or the core shroud in thereactor pressure vessel and is triggered chiefly by weld-induced residual stresses. One solution of this problem that hasbeen used in the past involves experimental measurements of residual stresses in conjunction with weld optimizationtesting. However, the experimental analysis of all relevant parameters is an extremely tedious process. Numericalsimulation using the finite element method (FEM) not only supplements this method but, in view of modern computercapacities, is also an equally valid alternative in its own right. This paper will demonstrate that the techniquedeveloped for numerical simulation of the welding process has not only been properly verified and validated onaustenitic pipe welds, but that it also permits making selective statements on improvements to the welding process.For instance, numerical simulation can provide information on the starting point of welding for every weld bead, theeffect of interpass cooling as far as a possible sensitization of the heat affected zone (HAZ) is concerned, the effectof gap width on the resultant weld residual stresses, or the effect of the ‘last pass heat sink welding’ (welding of thefinal passes while simultaneously cooling the inner surface with water) producing compressive stresses in the root areaof a circumferential weld in an austenitic pipe. The computer program FERESA (finite element residual stress analysis)was based on a commercially available ABAQUS code (Hibbitt, Karlsson, Sorensen, Inc, 1997. ABAQUS user’s manual,version 5.6), and can be used as a 2-D or 3-D FEM analysis; depending on task definition it can provide a startingpoint for a fracture mechanics safety analysis with acceptable computing times. © 2001 Elsevier Science B.V. Allrights reserved.

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� 25th MPA Seminar Safety and Reliability Integrity Verification, Component Qualification, Damage Prevention-Stuttgart, 7 and8 October, 1999.

* Corresponding author. Tel.:+49-9131-182530; fax:+49-9131-182911.E-mail address: [email protected] (J. Schmidt).

0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.

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S. Fricke et al. / Nuclear Engineering and Design 206 (2001) 139–150140

1. Background

Residual stresses are a crucial factor in service-induced crack formation in nuclear power plants.Component integrity is considerably influenced bycrack formation, depth and distribution, particu-larly if corrosion mechanisms play a role in crackinitiation and at least initial crack propagation(e.g. intergranular stress corrosion cracking inaustenitic pipes, or the core shroud in the reactorpressure vessel, or strain-induced corrosion crack-ing in ferritic pipes in BWR plants). Weld residualstresses are initially caused by the heat used tocreate a fusion zone and, thereafter, by coolingprocesses, which produce areas of local deforma-tion in the weld region.

Established test techniques are available formeasuring weld-induced residual stresses. Theseinclude X-ray examination or strain gauge mea-surements. Analytical or simpler numerical tech-niques (2-D FEM) are also used to confirm testresults. However, the fact remains that measure-ments always contain geometrical singularities,crack initiation is always a local phenomenon,and the residual stress condition is by no meansrotationally symmetrical. In this respect, great

importance is attached to a method of represent-ing relationships, which realistically simulates theboundary conditions in the actual component, i.e.3-D modeling.

The computer program FERESA is a company-internal adaptation and application of the com-mercially available ABAQUS code, as no toolearlier in the market could meet sufficiently all ofthe requirements described above. The followingdiscussion reports on applications to date andtheir results.

2. Description of the technique

The objective was to perform realistic weldsimulations which would provide additional infor-mation not-affected by tolerances with respect tothe welding process, pipe dimension, residualstress measurements and methods, and allow ver-ification of that information.

The welding of a circumferential weld in aDN100×6.3 mm (austenitic) pipe was, therefore,simulated under the most realistic conditions pos-sible using the 3-D finite element method. Themesh configuration is shown in Fig. 1.

Fig. 1. Mesh configuration for simulation of welding process (DN 200).

S. Fricke et al. / Nuclear Engineering and Design 206 (2001) 139–150 141

To ensure realistic results, 8 node elements withan integration order of 2*2*2 were used. Forreasons of computer capacity (the calculationswere performed on an HP-J210 UNIX workstationwith 1 GB of RAM), it is not currently possible(because of the long computing time required) touse the more suitable 20 node elements, whichcould supply even more accurate information onhighly localized phenomena such as root forma-tion. For the time being, however, the resultsobtained with the eight node 3-D elements serveas a good approximation of the welding process.

The problem was treated as an uncoupled ther-mal and mechanical problem; first the tempera-ture field was calculated (element type DC3D8 per(Hibbitt et al., 1997)), and stresses and displace-ments were then deduced from these results (ele-ment type C3D8). The austenitic material wasassumed to exhibit characteristic elastic-plastic be-havior. All requisite material characteristic data(for base and weld metal, based on tensile tests),including their temperature dependency, were en-tered in the FE model. While, this is essential foraccuracy, it substantially increases computingtime.

The model size can best be described by thenumber of nodes, elements, and degrees offreedom

Number of nodes 31082220Number of elements

Number of degrees 3108 (temperature fieldcalculation)of freedom9324 (stress displacementfields)

It was not possible to use a symmetrical model,because one of the problems faced was the calcu-lation of the dwelling time of ‘heat-affected zone’-elements in the temperature range between 500and 800°C and this time duration is depending onthe layer-sequence of weld build-up. These hold-ing times provide important information for de-termining weld-induced sensitization; everyindividual weld bead was modeled on the basis ofconventional weld geometry using realistic weld-ing parameters. The element density in the region

of the heat-affected zone was increased to a mini-mal element width of 0.2 mm, to obtain higheraccuracy in that area, which is critical for crackinitiation.

3. Simulation and results

3.1. Con6entional weld geometry in DN100 andDN200 pipes

In the initial applications, welds with conven-tional weld geometry and with narrow gap ge-ometry were simulated in DN100 pipes (and to alimited extent in DN200 pipes) as realistically aspossible and compared with test measurements. Itwas possible to verify the calculated shrinkage,the resultant residual stresses and the heat inputboth qualitatively and quantitatively by compari-son with the test results:

The calculated residual stresses are tensile at theweld root (Fig. 2), and compressive at the outersurface of the weld. The stress profile across thewall thickness is approximately linear (the sym-bols in Fig. 2 represent the results of the finiteelement analysis). This fact is confirmed bynumerous measurements on relatively thin-walled components, which exhibited also anearly linear distribution for axial residualstresses (NUREG-1061, vol. 1). The residualstress distribution (axial stress S33) in the weldregion at the ID surface forms a M-configura-tion with a local minimum in the middle of theweld, and local maxima in both heat affectedzones (Fig. 3). The maximum (calculated) resid-ual stress value is greater than the yield stress(205 MPa) determined in the (single-axis) ten-sile test. The increased residual stresses seemplausible given the actual restrained transverseexpansion; they also coincide quantitativelywith test values typically obtained for thismaterial.The results of calculations (Fig. 4, DN 100 pipeweld) confirmed by test measurements (Fig. 4,DN 450 pipe weld) show that residual stressdistribution (axial stress at the ID-surface) is byno means constant around the pipe circumfer-


Fig. 2. Axial stress through wall thickness (DN 100 — middle of weld).

ence. It exhibits considerable variation (whichmight be dependent on the pipe dimensions)but this appears essentially to be a function ofthe starting point of welding: peak residualstresses occur at the weld starting point but thiscould be avoided in practice by offsetting thestarting point for every subsequent weld bead(a numerical simulation of this scenario has yetto be performed). In the case of conventionalweld geometry, the maximum axial stress levelis located at the ID-surface and is diagonallyopposing to the last weld bead deposited (Fig.5); this means that the final pass also has aconsiderable impact on total residual stresses.In both qualitative and quantitative terms, theresults for axial (Fig. 6) and radial shrinkageobtained from the numerical simulation alsocompare well with measurements on actualcomponents. Weld shrinkage affects the leveland the distribution of residual stresses in theroot area; however, shrinkage ultimately alsodetermines the occurrence and geometry ofmash folds in the weld root (Fig. 7), Thegreater the axial shrinkage, the more likely theoccurrence of a mash fold, and the deeper thismash fold will be. This factor is important ifintergranular stress corrosion cracking is to bereliably prevented because the mash fold (in the

region of the fusion line) is a stress raiser (stressconcentration factor), and because elementswhich can promote the corrosive attack can beconcentrated in this fold. In addition, the mate-rial has undergone strain hardening in this area— as a result of shrinkage — and has alsobeen subjected to the greatest heat input. All ofthese factors contribute to the fact — demon-strated in comparative studies (Zimmer andKilian, 1998) — that the IGSCC attack ob-served in stabilized, austenitic piping almost

Fig. 3. Axial stress with distance from weld zone.


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Fig. 5. Residual stresses due to pipe welding (convent/narrow gap) — experimental/numerical analysis.

invariably originates in mash folds. Calculatedweld shrinkage increases with the number ofpasses, confirming expectations: smaller pipedimensions, therefore, tend to be less at riskthan pipes with larger dimensions — assumingidentical weld geometry.Greater attention has recently been directed inwelding practice to maintaining/checking thepreheat temperature during welding ofaustenitic materials. The results of the com-puter simulation confirm the expediency of this.As can be seen in Fig. 8, the interpass tempera-ture would increase steadily to more than some400°C without intermediate cooling after everywelding pass. Total heat input consequentlyincreases drastically due to the slower rate ofcooling for every individual (temperature) cycle.Greater importance has, therefore, to be at-tached to interpass cooling, particularly withregard to possible material sensitization causedby the welding process.

The effect of heat input in terms of a possiblesensitization of the material has already beenmentioned. It is a fact that the potential sensi-tization of austenitic materials (to a certainextent undoubtedly a function of the particularchemical composition) occurs as a result of heatinput in the temperature range between 500 and800°C (Schmidt et al., 1986). The interestingtime period in this respect is when a solidelement in the bulk of the material is in thistemperature range. The total holding time inthis temperature range is calculated from thetemperature cycles for every individual weldbead. As shown in Fig. 9, the values from thecomputer simulation agree very well with thevalues obtained from test welds. The calculatedcumulative holding time serves as a measure forheat input and, therefore, in the case ofaustenitic materials, a measure of postulated,segregation-induced sensitization. This holding


time in the ‘critical’ temperature range is com-paratively longer in parts with larger wall thick-

ness because of the increased number of passes(number of weld beads).

Fig. 6. Axial shrinkage during pipe welding — experimental/numerical analysis.

Fig. 7. Importance of the contraction fold.


Fig. 8. Transient temperature 0.2 mm beside the fusion line in HAZ DN 100/DN 200 weld simulation.

Fig. 9. Total keeping time at sensitizing temperature due to welding experimental/numerical analysis.


Modeling of a circumferential weld in anaustenitic DN100×6.3 mm pipe on the worksta-tion used for these studies required a com-puting time of around 9 h for the temperaturefield calculation and a further 53 h for calculatingdeformations and stresses. Computing time in-creased to around 4 weeks for a circumferentialweld on a DN200×11 mm pipe with elements ofcomparable size. Soon to be available computersare likely to shorten these computation times by afactor of 20, so that tasks of this nature willassume acceptable dimensions.

3.2. Comparison of con6entional weld withnarrow-gap weld

The results (Fig. 5) confirm, for example, theadvantages of the narrow-gap weld in comparisonwith conventional weld geometry with regard toshrinkage, residual stresses and cumulative heatinput (Schmidt et al., 1986),

The mean residual stress level is significantlylower in comparison with conventional weldgeometry.Also, in the simulation process it is necessary,like in practical performance to overlap thestarting point of welding by a defined amountto exhibit the advantages of narrow-gapwelding.

3.3. The effect of last pass heat sink welding(LPHSW)

The results of residual stress measurements onaustenitic pipes, which had undergone post-weldtreatment for stress redistribution purposes arepresented in (Schmidt et al., 1995). The resultspublished here included measurements of weldson which, an additional overlay weld, and alsowelds which had been subjected to the LPHSWprocess, i.e. rewelding of the last pass (after firstmachining away weld bead material) or weldingof additional passes with a relatively high heatinput while simultaneously, cooling the weld rootwith water (Fig. 10). At that time, it was demon-strated that the process of LPHSW converts ten-sile stresses at the weld root to compressivestresses. Over the wall thickness stresses are grad-ually reversed, in other words, axial stresses at theouter surface of the weld are tensile.

A subsequent calculation using a 3-D finiteelement analysis fully confirms these measure-ments (Fig. 11, the axial stresses are the mostrelevant stress components, because possible flawsare assumed to originate in the HAZ of thiscircumferential weld, oriented in circumferentialdirection, therefore, the figure is focused on theaxial stresses). As mentioned above, distributionis quite irregular around the circumference. Since,

Fig. 10. Postweld heat treatment — last pass heat sink welding (LPHSW).


Fig. 11. Contour plot of stress values in the welding region — 12:00 h position before and after LPHSW.

passes 1–6 are each welded in two steps, a singu-larity is obtained in 06:00 (starting point of weld-ing) and 12:00 h position (end of first half ofwelding). An interesting feature of the calculationresults is that peak residual stresses occur at thekey location (laterally approximately 0.2 mmaway from the fusion line (HAZ) on the innersurface of the pipe) while the root pass (bead 1 inFig. 12) is being welded. There is a ‘steady’ reduc-tion in residual stresses during welding of thesubsequent passes. Residual tensile stresses never-theless prevail at the weld root until the weld gaphas been filled. Compressive axial stresses do notoccur at the weld root until LPHSW is simulated;these compressive stresses persist over a consider-able distance from the weld and the entire area,which is potentially susceptible to weld sensitiza-tion is consequently affected favorably by com-pressive residual stresses.

3.4. Operational influences

The results of residual stress measurements oncircumferential welds in austenitic pipes whichhad been removed from a reactor plant aftermany years in service were also presented in(Schmidt et al., 1995). As was to be expected,these welds exhibited a lower residual stress levelon the average than similarly welded piping jointsin their as-welded condition. It can be postulatedthat this stress reduction is the result of settlingprocesses (precursor to relaxation).

For the numerical simulation, plant operationwas modeled so as to simulate start-up, and shut-down repeated several times with correspondingheating and cooling rates, and a short holdingtime at operating temperature (ten cycles in total).The simulation included thermal stratification;this stratification was achieved by inserting a plate


Fig. 12. Axial stress at the inner side (0.2 mm positive direction from fusionline) — after cooling to interpass temperature.

Fig. 13. Axial stress (inner surface, 0.2 mm from fusionline) — after welding sequence, aging 1st/10th cycle, and final stage.


into the pipe in such a way, that the two inletmass flows were separated into cold and hot waterregions.

The results of the computer simulation aregiven in Fig. 13 for a representative weld that hasbeen improved by LPHSW. Here too, peak resid-ual stresses near the starting point of welding areinitially symptomatic, a weld in the vertical upposition was simulated in this case, i.e. the heatsource did not move continuously around thecircumference of the pipe; instead the weldingprocess was performed in two steps, both stepsbeginning at 06:00 h, and ending at 12:00 h withone half moving through the 03:00 h position, andthe other through the 09:00 h position. The solidline indicates stresses in the as-welded condition(measured after welding). The dotted line (aftersimulation of one cycle), and the broken line(after simulation of ten cycles) indicate the weldcondition with allowance for heating and internalpressure. A comparison of the continuous line(after welding), and the dotted and dashed line(final stage), both plotted in a weld no longerunder service conditions, clearly indicates the ef-fect of operational stress reduction. In the finalstage (dotted and dashed line) peak stresses havebeen reduced in both the tensile and the compres-sive range.

4. Outlook

The technique presented here is a useful tool

which can be used not only to predict/recalculateweld-induced residual stresses in austenitic materi-als but also, with appropriate further develop-ment, to validate the calculations ofmanufacturing-related residual stresses (followingforming, heat treatment). Present computers havesufficient capacity to simulate individual manufac-turing conditions. The tool is above all useful as ameans of expanding investigations (parametervariation), and yields essential input for safetyanalyses on components which require rigorousdetermination of manufacturing-related residualstresses.

References

Hibbitt, Karlsson, Sorensen, Inc, 1997. ABAQUS user’s man-ual, version 5.6.

Schmidt, J., Weiß, E., Pellkofer, D., 1986. Avoiding IGSCC inAustenitic Piping System of BWR Nuclear Power Plantsfrom the Standpoint of Welding Technology, Proceedingsof the American Power Conference, Chicago.

Schmidt, J., Pellkofer, D., Weiß, E., 1995. Alternativen bei derNachbehandlung von austenitischen Rohrleitungsnahtenzur Erhohung der Betriebssicherheit von SWR-Anlagen,21. MPA-Seminar, Stuttgart, October 1995.

Zimmer, R., Kilian, R., 1998. Neuronale Netze zurBeurteilung von Einflußgroßen auf die interkristallineSpannungsrißkorrosion, VGB Konferenz, ‘‘Forschung furdie Kraftwerkstechnik 1998’’, Essen, February 1998, TB233.

NUREG-1061, vol. 1, Report of the US Nuclear RegulatoryCommission, Piping Review Committee Investigation andEvaluation of Stress Corrosion Cracking in Piping ofBoiling Water Reactor Plants.

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a method for calculating weld-induced residual stresses

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