Published by Maney Publishing (c) iom communications Ltd review welding residual stresses in ferritic power plant steels J. A. Francis* 1, H. K. D. H




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НазваниеPublished by Maney Publishing (c) iom communications Ltd review welding residual stresses in ferritic power plant steels J. A. Francis* 1, H. K. D. H
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Published by Maney Publishing (c) IOM Communications Ltd REVIEW Welding residual stresses in ferritic power plant steels J. A. Francis* 1 , H. K. D. H. Bhadeshia 2 and P. J. Withers 1 Many of the degradation mechanisms relevant to power plant components can be exacerbated by stresses that reside within the material. Good design or structural integrity assessments require therefore, an accounting of residual stresses, which often are introduced during welding. To do this it is necessary to characterise the stresses, but this may not be possible in thick components using non-destructive methods. These difficulties, and a paucity of relevant engineering data, have led to an increasing emphasis on the development and validation of suitablemodellingtools.Advancesareprominentintheestimationofweldingresidualstressesin austenitic stainless steels. The progress has been less convincing in the case of ferritic alloys, largelyduetothecomplexitiesassociatedwiththesolidstatephasetransformationsthatoccurin multipass welding. We review here the metallurgical issues that arise in ferritic steel welds, relate these to the difficulties in calculating residual stresses, and highlight some stimulating areas for future research. Keywords: Phase transformation, Power plant, Residual stress, Steel, Structural integrity, Weld Introduction Residual stresses are those which are not required for a engineering structure to maintain equilibrium with its environment. 1 Although they can have many different origins, residual stresses are always the result of some form of mis?t; either between different parts, different regions within the same part, or even different phases within a microstructure. 2 Welding residual stresses arise as a consequence of the heterogeneous application of energy and localised fusion. When the fused region solidi?es, theaccompanying contraction exerts a pull on the surrounding material which may be prevented from complying by constraint. The contraction of the weld metal may be too large to sustain elastically, so plastic deformation is induced. All this means that in the absence of transformation effects, signi?cant tensile stresses reside in the near weld region after the component has reached thermal equilibrium. 3 Many of the degradation mechanisms relevant to power plant components can be accelerated by the presence of residual stresses. Tensile welding residual stresses in particular can contribute to fatigue crack development in a structure even under compressive cyclic loading. 4,5 Similarly, stresscorrosion crackingcan occur in austenitic weldments if the sum of the applied and residual stress exceeds a threshold. 6 Residual stresses are also known to affect fracture processes, 7,8 and have been shown to accelerate the onset of creep damage. 9,10 Itisnotsurprisingtherefore,thatsigni?cant resourcesaredevotedtotheinclusionofresidualstresses in engineering integrity assessments. 11–3 Many plant components are subjected to externally applied loads at elevated temperatures over design lives thatspandecades.Reactorpressurevessels,headersand the main steam pipe in fossil ?red boilers are all thick walled components designed to withstand harsh operat- ingenvironments.Unfortunately,itisextremelydif?cult to measure bulk residual stresses non-destructively in such thick components, and this has contributed to a paucity of engineering data. 14 Instead, the focus is often placed on the validation of numerical modelling techniques so that stresses can be estimated. While a number of challenges remain, there have been examples of the successful implementation of numerical models for welding residual stress development in austenitic stainless steels. 15,16 By comparison, modelling activities focussing on ferritic steels are less advanced, largely due to thecomplexities that areintroduced by the solid state phase transformations that take place during multipass welding. Thepurposeofthisarticleis toreview recentprogress in understanding the development of welding residual stresses in ferritic steels. We begin with a description of the metallurgy, before addressing the consequences of solid state phase transformations on stresses induced by welding. Attention is then given to published stress measurements. Finally, an assessment is made of the status of weld modelling and here we highlight some exciting challenges for future work. It is hoped that this review will provide a useful summary of the issues relating to ferritic welds, and serve as a stimulus for 1 School of Materials, University of Manchester, Grosvenor Street, Manchester M1 7HS, UK 2 Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK *Corresponding author, email John.Francis@manchester.ac.uk 2007 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 20 April 2007; accepted 22 May 2007 DOI 10.1179/174328407X213116 Materials Science and Technology 2007 VOL23 NO9 1009 Published by Maney Publishing (c) IOM Communications Ltd advances that ultimately translate into engineering practice. Weld metallurgy Fusionweldinginvolvesthelocalisedinjectionofintense heat and its dissipation by conduction into the parent material. The weld microstructure at each location is therefore closely related to the thermal history. 17 The different zones and their characteristics have been described for a single pass weld by Mannan and Laha, 18 and are shown in Fig. 1. 19,20 Regardless of the primary solidi?cation structure, the fusion zone in low alloy steels transforms to austenite at a temperature not far from the solidi?cation point, 21 and then undergoes a solidstatetransformationtoastructurethatwilldepend on both the hardenability of the alloy and the cooling rate. Adjacent to the fusion zone is a heat affected zone (HAZ); a region that is not heated suf?ciently to cause melting, but nevertheless is altered by the welding thermal cycle. As indicated in Fig. 1, the HAZ can be subdivided according to the extent to which grain growth and austenitisation occur; into a coarse grained zone (CGHAZ), a ?ne grained zone (FGHAZ), an intercritical zone (ICHAZ) and over tempered base metal. Fusion welding of thick walled components necessa- rily involves many weld passes to ?ll up the joint. Weld beads covered by other passes then experience multiple heat pulses and a further subdivision of metallurgical zones. Some of the possible combinations of thermal cycles are illustrated in Fig. 2. 22,23 With regard to the sequence shaded dark grey in Fig. 2, the initial inter- critical heating cycle may not have a signi?cant effect on the ?nal microstructure, since the subsequent cycle introduces a much higher peak temperature at that location. However, other sequences can have signi?cant and detrimental effects. For example, the intercritically reheated CGHAZ is the zone of the CGHAZ which is only partly reaustenitised during a subsequent thermal cycle and is shaded black in Fig. 2. In some steels a concentration of austenite stabilisers, such as carbon, 1 Metallurgical zones in single pass weld, categorised according to maximum local temperature: 19 micrographs, after Ref. 20, correspond to weld in 2?25Cr–Mo steel 2 Examples of thermal cycles in multipass weld, adapted from Refs. 22 and 23 3 Variation in dilution of ?ller metal in power plant weld Francis et al. Welding residual stresses in ferritic power plant steels 1010 Materials Science and Technology 2007 VOL23 NO9 Published by Maney Publishing (c) IOM Communications Ltd can occur in the regions that are reaustenitised and, upon cooling, these locations transform into hard microstructures associated with poor toughness, the so called local brittle zones. Given that the austenite in the CGHAZ would have originally been coarse, the decline in toughness in the intercritically reheated CGHAZ can be marked. 24,25 Filler metals for ferritic steels are generally selected to achieve an appropriate balance between strength and toughness, or to mitigate against toughness related problems such as cold cracking. 26 Other factors may also be relevant, such as with 9–2Cr creep resistant steels, where it is important to avoid the formation of d- ferrite at high temperatures yet still achieve a complete transformation to martensite at ambient temperature. 27 The design requirements for weld ?ller metals generally necessitate a chemical composition that differs from the parent material. Thus, in a multipass weld, the com- position of one weld bead can vary from the next as a consequence of changes in dilution levels. A schematic representation of how dilution might vary in a typical power plant steel weld is given in Fig. 3. The extent to which dilution might in?uence microstructure will depend on the mismatch between the compositions of the ?ller metal and parent material. However, in micro- alloyed steels, even a relatively small change in com- position due to dilution has been shown to signi?cantly affect weld toughness. 28 Austenite that forms in the fusion zone after solidi?cation, and in the HAZ as a consequence of material being heated above the Ac 1 temperature, will generally transform upon cooling to some combination of ferrite, pearlite, Widmansta ¨tten ferrite, bainite or martensite. If the residual stresses in ferritic welds are to be predicted then it is necessary to understand which transformations are likely to occur, and the tempera- tures at which they will occur 29 because each of these phasechangesisassociatedwithatransformationstrain. In the context of welding thermal cycles, the most convenient presentation of the kinetics of these trans- formations is a continuous cooling transformation (CCT) diagram. The CCT diagrams and chemical compositions for two different classes of a (grade 3 SA508) reactor pressure vessel steel are shown in Fig. 4. 30 Even though there are only minor differences in chemical composition between the two steels, there are noticeable differences between the transformation curves, as well as the respective Ac 1 and Ac 3 tempera- tures.Indeedthetwomostsigni?cantin?uencesonCCT diagrams are the steel composition and the prior austenite grain size. 31 The sensitivity to composition, as is illustrated in Fig. 4, suggests that models for residual stresses in multipass welds would need to account for the effects of dilution. The effects of austenite grain size are signi?cant in the context of welds because of the spatial variation of peak tempera- turewithintheHAZleadingtocorrespondingvariations in grain or precipitate size. The experimental determination of CCT diagrams using techniques such as dilatometry or differential scanning calorimetry can be tedious. One way of esti- mating these is a semi-empirical model for hardenable steels developed by Kirkaldy and Venugopalan, 32 and laterre?nedbyLietal. 33 Theformofthemodelisbased on formulae for isothermal transformations described by Zener 34 and Hillert, 35 which can be expressed as t X,T ðÞ ~ FC ,Mn,Si,Ni,Cr,Mo,G ðÞ DT n exp{ Q RT null SX ðÞ (1) where tisthetimedelayrequiredforthetransformation to proceed to a fraction of completion X, at constant temperature T; F is a function of steel composition and ASTM number for grain size G;DT is the undercooling; Q is the activation energy for the steel, R is the gas constant, T the absolute temperature and S(X) is a reactionratetermthatapproximatesthesigmoidaleffect ofphasetransformations. 33 Liandco-workersexamined the TTT diagrams for many steels and developed empirical expressions for the function F, for ferritic, pearlitic and bainitic transformations. As with the Kirkaldymodel,thedegreeofundercoolingiscalculated with respect to the Ae 3 and Ae 1 temperatures for the ferritic and pearlitic transformations respectively, and with respect to the bainite start temperature B S , for bainitic transformations. Li and co-workers estimated the martensite start temperature M S , with an empirical expression due to Andrews. 36 Once expressions were 4 Curves of CCT for class 1 (solid lines) and class 2 (broken lines) of grade 3 SA508 reactor pressure ves- sel steel 30 5 Calculated CCT curves for different locations in HAZ of SA508 grade 3, class 1 reactor pressure vessel steel as consequence of differing prior austenite grain size: cooling curves corresponding to these locations are also shown 37 Francis et al. Welding residual stresses in ferritic power plant steels Materials Science and Technology 2007 VOL23 NO9 1011 Published by Maney Publishing (c) IOM Communications Ltd obtained for each transformation, Li et al. suggested that critical cooling rates for the formation of marten- site, for example, could be determined by the larger of the rates for the formation of 1% ferrite or 1% bainite, with equations of the form CCR 1%F ~ ð Bs Ae 3 dT t 1%F T ðÞ (2) Inequation (2),CCR 1% F istheconstantcoolingratefor the formation of 1% ferrite, and t 1% F (T)i st h e isothermal time delay required to form 1% ferrite as a function of temperature. A similar equation can be written for the bainitic reaction. Kim et al. 37 calculated CCT curves for different locations in the HAZ of an SA508 reactor pressure vesselsteelweldusingthemodeldescribedbyLiandco- workers, and their results are shown in Fig. 5. The Ae 3 and Ae 1 temperatures were calculated using commer- cially available thermodynamic software, and they estimated the austenite grain sizes for their steel according to a generalised equation for grain growth proposed by Leblond and Devaux, 38 namely d dt zD a ðÞ ~zCexp { Q RT null , dz dt ¢0 d dt zD a ðÞ ~Cexp { Q RT null , dz dt v0 (3) where t is time, z is the volume fraction of austenite, D a is average grain size, and Q is the activation energy for the steel. The signi?cance of grain size variations within the HAZ is evident in Fig. 5 –the predicted proportions of product phases would differ signi?cantly between the two locations under consideration. Note also that transformations within the HAZ of a welded joint are predicted to occur more rapidly than when the same steel has been austenitised at 890uCf o r 15 min (Fig. 4). Thus, it is evident that if a CCT diagram for the parent plate material is to be used to predict weld microstructures, it is necessary to know the corresponding austenite grain size and account for the different grain sizes that will arise in the HAZ of a welded joint. Transformation effects The mechanism by which austenite transforms upon cooling can be described as being either reconstruc- tive or displacive. 31 The former mechanism involves the diffusion of all elements, including iron. Allotriomorphic (grain boundary) ferrite, idiomorphic ferrite and pearlite are all products of reconstructive transformations. The only strain that cannot then be cancelled by diffusion is the volume change due to the differenceindensitiesoftheparentandproductphases–thestrain due to reconstructivetransformations in steels is therefore an isotropic volume change. In contrast, displacive transformations typically involve an invariant plane strain shape deformation with a large shear parallel to the invariant plane and a dilatation normal to the plane (the invariant plane is oftenreferredtoasthehabitplane).Theydonotinvolve the diffusion of iron atoms or substitutional solutes. Widmansta ¨tten ferrite, acicular ferrite, bainite and martensite are all products of displacive transforma- tions. 31 Here the movement of iron and substitutional solutesoccursinacoordinatedmanner,leadingtoawell de?ned and reproducible crystallographic relationship betweentheparentandproductphases.Itisemphasised that while displacive transformations in steels are associated with a volume change, this change is not isotropic but occurs as a dilatation normal to the habit plane which remains macroscopically undistorted. Furthermore, the volume strain is typically 0?03, which is much smaller than the shear strain which is typically 0?26 (Ref. 39). The different features of reconstructive and displacive transformations are illustrated in Fig. 6. The volume changes that occur in steels as they are heated and cooled can be inferred from dilatometry, where the change in length of an unloaded specimen is measured as a function of temperature. Figure 7 illustrates such an experiment 40 –the upper straight line representstheexpansionofthebodycentredcubicphase (ferrite, bainite, martensite) and the lower line that of austenite (c). Data at locations between the upper and lower lines correspond to the co-existence of the parent and product phases. The transformations occurred at 6 Nature of reconstructive transformations (left) and dis- placive transformations (right) from austenite on cool- ing: for bainite and martensite s<0?22–?26 and d<0?02–?03 (Ref. 39) 7 Dilatometric diagram of A508 class 3 reactor pressure vessel steel heated at 30 K s 21 a n dc o o l e da t2Ks 21 (Ref. 40) Francis et al. Welding residual stresses in ferritic power plant steels 1012 Materials Science and Technology 2007 VOL23 NO9 Published by Maney Publishing (c) IOM Communications Ltd different temperatures upon heating and cooling. The transformation temperature is a function of the cooling rate, steel composition and austenite grain size. The measured coef?cient of thermal expansion is larger for austenite (,23610 26 K 21 ) than for ferrite (,156 10 26 K 21 ). As a consequence, the volume change due to transformation is greater during cooling than during heating. The volume expansion due to the transforma- tion of austenite can partly compensate for thermal contraction strains arising as a welded joint cools. 41,42 Each grain of austenite can in general transform into 24 crystallographic variants of bainite or martensite. Whenalloftheseform,theeffectonamacroscopicscale is that the shear strains due to the totality of plates average to zero. The volume strain cannot be cancelled in this way since it is always positive with respect to the sample frame, but because of the large number of variants that form, the dilatation observed macroscopi- callyappearsisotropic,eventhoughthatassociatedwith an individual plate is not (Fig. 6). The situation changes when a displacive transforma- tion is in?uenced by external stress because those crystallographic variants whose transformation strain complies with the stress are favoured, 43 as illustrated in Fig. 8. The shear components of the shape deformation then become prominent, 44 all dimensional changes become anisotropic, 45–7 and the material acquires a transformation texture. 48,49 Because the shear strain component is relatively large, there is a much greater potentialtoexploitthephasechangeinordertomitigate the residual stresses that develop during the cooling of welds. 50 Variant selection has been reported in simulated weld specimens by Bhadeshia et al., 45 who showed that the presence of stresses well below the yield stress led to the preferential selection of crystallographic variants in a bainitic pressure vessel steel. These workers also observed that a non-random austenite texture aids the development of a transformation texture and hence anisotropic strains. As emphasised previously, the large shear component of the invariant plane strain deforma- tion, as illustrated in Fig. 6, would also suggest that large reductions in stress can be achieved through the variant selection mechanism, until the point is reached where the transformation is exhausted. Jones and Alberry conducted experiments that illus- trate the effects of phase transformations on residual stress development in steels. 51,52 They measured the stresses that were developed in tensile specimens whose ends were rigidly ?xed at a high temperature in the austenite phase ?eld, and then allowed to cool, for three cases: non-transforming austenitic, bainitic and marten- sitic steels. A schematic representation of the develop- ment of residual stresses in experiments of this type is giveninFig. 9forthreedifferenttransformationevents. 53 Before the commencement of a transformation, all of the constrained samples would develop stresses compar- able to the yield strength of austenite. This is to be expected because, for an austenite thermal expansion coef?cient of 23610 26 K 21 and a modulus of 200 GPa, contraction stresses in excess of 400 MPa would develop for every 100uC of cooling. 39 These are too large to be accommodatedelastically,causingthesampletorelaxby plasticdeformationdowntotheyieldstrength.However, thestressesineachsamplestarttodiminishtowardszero at the beginning of the respective transformations to ferritepearlite(,700uC)bainite(,400uC)andmartensite (,250uC). During this stage the transformation strains overwhelm the effect of thermal contraction as the temperature decreases. However, once the austenite is exhausted, continued thermal contraction causes once again the accumulation of stress. There are two further features which are noteworthy. First, because the martensite transformation occurs at a lower temperature than the bainite and ferrite pearlite transformations, the residual stress left at ambient temperature is much smaller. This is because there is a smaller range between themartensite ?nish and ambient temperatures, thus minimising the regime over which thermal contraction alone is active once the transforma- tion is completed. It clearly is an advantage to engineer the transformation ?nish temperature to be close to the ambient temperature. 8 Polycrystalline specimen of austenite a may transform by displacive mechanism in absence of macroscopic stress to b randomly orientated sets of plates or, in presence of macroscopic stress, to c sets of plates with orientations that favour compliance with stress 9 Schematic representation of axial stress development in uniaxially constrained samples during cooling for a ferritic pearlitic, b bainitic and c martensitic steels: 53 parameter s is fraction of cross-section that has transformed Francis et al. Welding residual stresses in ferritic power plant steels Materials Science and Technology 2007 VOL23 NO9 1013 Published by Maney Publishing (c) IOM Communications Ltd A second observation is that because the martensite transformation commences at a lower temperature than is the case for bainite, the stress experienced by the martensite at its initiation is greater. This will lead to a greater degree of variant selection, i.e., to favour those variantswhichcomplywiththestress.Itfollowsthatthe shear component of the shape deformation for displa- cive transformations becomes much more prominent as the transformation temperature decreases, leading to a greater reduction in stress and the possibility of over- shooting into compression. In summary, a second advantage of promoting transformation to lower tem- peratures is that it then occurs under the in?uence of a larger accumulated stress, thus permitting greater variant selection and exploitation of the transformation strain.Withidealvariantselectionitispossibletoobtain an elongation due to transformation alone of some 15%. 50 Residual stresses Residual stresses can be classi?ed according to the length scale over which they self-equilibrate in the plane normal to which they act. 1 Macrostresses (type I) occur on scales in which the material can be considered as a continuum, and span distances that approach (but are not greater than) a characteristic dimension of the structure. For example, Bouchard and Withers 54 describe the case of a welded thick walled pipe where, from a residual stress standpoint, one characteristic distance might be the length of the pipe, another might beitswall thicknessandathirdmight correspondtothe dimensions of individual beads within the welded joint. Type I stresses that act over one of these characteristic dimensions could be categorised as either long range, medium range or short range respectively. In addition, type II stresses are usually present in polycrystalline or multiphase materials as intergranular stresses, whereas type III stresses arise within individual grains and are associated with point defects and dislocations. 54 In integrity assessments on power plant welds, the focus must be (and usually is) on type I stresses. The role of the types II and III stresses becomes prominent primarily when designing materials –as a variation of stress on a microstructural scale is likely to lead to localised corrosion attack in appropriate circumstances. The choice of welding parameters can in?uence the distribution of residual stress in ferritic welds since, together with the joint thickness and con?gura- tion; they largely determine the cooling rates that are experienced across the joint. This was demonstrated by Nitschke-PagelandWohlfahrt, 53 whopresentedresidual stress distributions for two gas tungsten arc steel welds made with different heat inputs. The composition of their steel is given in Fig. 10a, which also shows recorded cooling curves for each weld plotted against the corresponding CCT diagram. The variation in longitudinalstresswithdistancefromtheweldcentreline is plotted for each weld in Fig. 10b. It can be seen that the selection of a lower heat input led to a lower transformation temperature, which would have reduced the scope for contraction stresses to generate after the transformation was exhausted. Consequently, for the lowheatinputweldthelongitudinalresidualstressesare slightly compressive near to the weld centreline, in contrast to the high tensile stresses that were generated in the high heat input weld. The pronounced effect of transformation temperature on welding residual stresses has stimulated efforts to design ?ller metals with optimised transformation temperatures.There isa philosophicaldifferencetonote in this approach. Rather than requiring tight control over welding parameters in order to achieve a low transformation temperature, the composition of the ?ller metal is carefully selected so that, in the fusion zone, the ferrite pearlite and bainite transformations are avoidedatcoolingrates thatarelikelytobeexperienced in a welded joint. Thus, while the CCT curve is further to the right (longer times) for the ferrite pearlite and bainite transformations, the martensite transformation also occurs over a desired temperature range. Ohta et al. 55,56 and Wang et al., 57 for example, have proposed welding electrodes that achieve martensite start tem- peratures at or just under 200uC and martensite ?nish temperatures close to room temperature, and they have achievednearzeroorcompressiveresidualstressesinthe fusion zones of their welds. The restraint on an assembly during welding must naturally in?uence the nature and extent of residual stresses.Priceetal. 58 studiedsingleweldbeadsdeposited using gas metal arc welding (GMAW) on to 12 mm thick low carbon steel plates. In one case the plate was 10 Effects of weld heat input on a transformation temperature and b longitudinal residual stresses: 53 steel composition is given in wt-% in a Francis et al. Welding residual stresses in ferritic power plant steels 1014 Materials Science and Technology 2007 VOL23 NO9 Published by Maney Publishing (c) IOM Communications Ltd notrestrainedduringweldingwhereasintheotheritwas made more rigid by tack welding to a very thick steel substrate. After removal from the restraining plate, stresses were measured 1?5 mm below the plate surface, atdifferentdistancesfromtheweldcentreline,byneutron diffraction–theresultsareillustratedinFig. 11.Forthe unrestrained plate, the longitudinal tensile weld stresses of approximately 350–60 MPa are y25% higher than the estimated yield strength of the material when measured in monotonic tension (285 MPa). The peak stresses in the restrained case are more tensile overall, beingcloserto500 MPaintheweldandlesscompressive in the parent plate, with a corresponding increase in the hydrostatic component of stress. At present there appears to be a dearth of data relating to bulk residual stresses in multipass ferritic steel welds. However, Smith et al. 14 have made measurements down the weld centreline in a ferritic steel pipe with a wall thickness of 84 mm using the deep holedrillingmethod.Thehoopandaxialcomponentsof stressareplottedasafunctionofdistancefromtheouter surfaceofthepipeinFig. 12,forboththeasweldedand post-weld heat treated (PWHT) conditions. Before PWHT, the maximum tensile stresses were measured in the hoop direction, midway through the wall thickness. Apartfromasmallregionofcompressionneartheinner surface of the pipe, the hoop stresses were entirely tensile. While the axial stresses were compressive near each surface, they were also tensile across the majority of the pipe wall. Post-weld heat treatment resulted in signi?cantrelaxationofboththetensileandcompressive residual stresses across the pipe wall. Interestingly, despite the fact that the radial stress was not measured here, it seems plausible that only the deviatoric component of stress, and not the hydrostatic compo- nent, was relieved by PWHT. (Hydrostatic residual stresses may have accumulated during welding once a suf?cient number of passes had been deposited to provide a high level of restraint for later passes, i.e. at a certain distance from the inner surface of the pipe.) It is possible that the deviatoric component of stress is relievedduringPWHTbydislocationcreep,whereasthe hydrostatic component of stress may only relieved by longer term mechanisms involving diffusion and grain boundary sliding, as has been suggested by Kimmins and Smith. 59 Indeed, there is a great need to understand how hydrostatic stresses evolve when subjected to thermal aging, either in the context of PWHT or creep during service. This has recently inspired efforts to design samples for material testing in which triaxial stresses can be generated across signi?cant volumes of the specimen. 60 Modelling challenges Within the community concerned with modelling of residual stresses, fusion welding is often considered to involve a combination of thermal, metallurgical and mechanical processes. It is common and computation- ally ef?cient to use a one way coupled approach, 61 i.e. accounting for thermal history in a mechanical analysis while ignoring the effect of mechanical work in a thermal analysis. Complex arc and weld pool phenom- ena are generally not considered and instead pragmatic models for the welding heat source are implemented. Gastungstenarcs,forexample,areoftenrepresentedby Gaussian heat distributions such as the double ellipsoid model proposed by Goldak et al., 62 or a combination of surface ?ux and body ?ux. 63 The characteristic para- meters required by such models are usually obtained usingacalibrationprocedurewhereby,forawellde?ned testcase,thebestagreementissoughtbetweeneitherthe predicted and measured location of the fusion surface, or the predicted and measured thermal excursion 11 Effect of restraint on residual stresses measured 1?5 mm below surface by neutron diffraction in a unrestrained and b restrained GMAW single bead welds deposited on 12 mm thick low carbon steel plates 58 12 Through wall axial and hoop residual stress measure- ments in ferritic steel pipe girth weld 14 Francis et al. Welding residual stresses in ferritic power plant steels Materials Science and Technology 2007 VOL23 NO9 1015 Published by Maney Publishing (c) IOM Communications Ltd recorded at one or more locations. Indeed, the complex nature of welding processes necessitates a signi?cant number of simplifying assumptions, and in many circumstances these need not be obstacles to the attainment of acceptable results. 64 In addition to thermal, metallurgical and mechanical processes, the arc and weld pool are host to complex electromagnetic processes, as well as ?uid and mass transport. Details of these physical processes can be obtained elsewhere, 65,66 and are only brie?y mentioned here. It is important to mention, however, that these processes do have implications for residual stress development. The divergence of current within the welding arc, for example, generates a plasma jet that places a downward pressure, referred to as arc pressure, on the weld pool. The weld pool has a free surface that may distort under the in?uence of arc pressure, and any changes in weld pool shape can lead to signi?cant changes in the pro?le of the fusion line. Furthermore, thetemperature gradients (andcompositional gradients) that arise within the weld pool give rise to associated surface tension gradients and buoyancy forces which, together with an electromagnetic force, drive convection withintheweldpool.Itiswellestablishedthatweldpool convection patterns can have dramatic effects on the pro?leofthefusionline. 65,66 Giventhattheshapeofthe fusion surface is in?uenced by such complex phenom- ena, it is not reasonable to expect approximate heat source models to accurately reproduce the shape of the fusion surface and near weld temperature ?elds for all test cases. As such, care needs to be taken when using the fusion surfaces as a basis for calibrating idealised heat source models. There are in fact hybrid models which are better at modelling realistic weld pool shapes by using neural networks which are constrained by the physics described above. 67 There has been signi?cant progress in recent years towards understanding and modelling complex arc and weld pool phenomena, 68,69 but this progress has generally not permeated through to calculations of residual stress development. If arc and weld pool phenomena were to be integrated into models for residual stress, the complex nature of the physical processes and their interactions might be represented schematically as in Fig. 13. As might be expected, many researchers and engineers who are concerned with residual stress development focus primarily on the metallurgical and mechanical processes that take place during welding (i.e. those in the bottom half of Fig. 13). It may be computationally prohibitive to attempt to account for all of the phenomena shown in Fig. 13 in engineering integrity assessments. However, within academic and research communities in particular, it may prove fruitful to explore integrated modelling approaches in order to establish domains in which simplifying assumptions can be made with minimal losses in accuracy and, simultaneously, identify the physical processes that do need to be incorporated in to residual stress models for engineering integrity assess- ments in the future. With respect to metallurgical processes, complexity is introduced by solid state phase transformations and the 13 Processes and interactions that arise in arc welding of ferritic steels: engineering integrity assessments currently focus on the lower half of the diagram Francis et al. Welding residual stresses in ferritic power plant steels 1016 Materials Science and Technology 2007 VOL23 NO9 Published by Maney Publishing (c) IOM Communications Ltd thermal cycling that takes place in multipass ferritic power plant welds. However, the modelling of micro- structural evolution was greatly assisted by a mathema- tical formalism due to Leblond and Devaux 38 who proposedevolutionequationsfortransformationsofthe following form dz dt ~ z eq (T){z t(T) (4) where z, for example, is the proportion of austenite, t is time, z eq is the equilibrium proportion of austenite, t is the time constant for the transformation and T is the temperature. The equation basically assumes that the rate of reaction is proportional to the deviation from equilibrium and therefore asymptotically achieves the equilibrium fraction as time increases. The model can cope with the case where the equilibrium fraction is not unity,i.e.situationsinwhichz eq ,1,andcanaccountfor hysteresis (Fig. 7) where the transformation on cooling occurs over a different temperature range than for the reverse transformation on heating. Sluggish reaction kinetics can also be accommodated by rede?ning the equilibrium proportion of a phase such as ferrite, for example, to be the proportion that is achieved under very slow cooling conditions. Finally, the effects of austenitegrain sizecanbeaccounted foriftheevolution equations are coupled with an equation for average austenite grain size, such as equation (3). 38 The Leblond and Devaux model requires experimen- tal data in the form of a CCT diagram for the steel of interest in order to derive the ?tting constants. The authors have seen though that Kirkaldy and Venugopalan 32 and later Li et al. 33 have proposed models that predict CCT diagrams for steels. Furthermore, the initial model proposed by Kirkaldy has been shown to make reasonable predictions for HAZ microstructures in welds. 70,71 Thus, a framework existsforthepredictionofphasetransformationsduring multipass welding. It is important, however, to bear in mind that these models do not account for any microstructural changes that might be associated with thetemperingeffectsofsubsequentweldpasses.Itmight also be useful, on a given steel, to conduct experiments that establish whether there are likely to be any signi?cant changes in the CCT diagram from one thermal cycle to the next. Thecomponentsofstraininmechanicalanalyseshave beendescribedbyLindgren, 72 andcanbesummarisedas follows e~e e ze p ze vp ze c ze th ze tp (5) where edenotesstrainandthesubscriptse,p,vp,c,th,tp denote elastic, plastic, viscoplastic, creep, thermal and transformation plasticity respectively. Among these, the only component that is somewhat unique to ferritic steels,atleastinthecontextofpowerplantcomponents, is the strain associated with transformation plasticity. This component arises due to the volume and shear strains associated with austenite to a9 transformations, as well as the extent to which variant selection takes place under the action of stress in the event of a bainitic or martensitic transformation. There is also a contribu- tion associated with hard product phases, such as martensite, inducing plasticity in the softer parent phase (austenite) as a transformation proceeds. To date, it appearsthatvariant selectionhas notbeenincorporated in to models for welding residual stresses. The fact that the shear component of the deformation during an austenite to bainite/martensite transformation is much greater than the dilatational component would suggest thatit is importantto incorporate variant selection in to residual stress models. However, in the ?rst instance there appears to be a need to characterise the extent to which variant selection occurs in welded joints. To perform this would also require additional information on the austenite grain structure –grain size data would not be suf?cient. A knowledge of the crystallographic textureoftheausteniteisalsoessentialsinceitin?uences thetransformationtextureandhencethetransformation strains. Effects of variant selection on the generation of compressive residual stresses in welds made with low transformation temperature ?ller metals would also appear to provide interesting avenues for investigation. The thermomechanical cycling that occurs during multipass welding presents challenges due to the simultaneous occurrence of deformation and annealing. Strain cycling and the Bauschinger effect are usually accounted for through the application of hardening models such as isotropic or kinematic hardening, 73,74 or a mixed hardening model. Simple methods of account- ing for annealing effects include the resetting of plastic strain to zero upon exceeding a certain temperature. However, such an approach is not representative of reality. Annealing effects present challenges in weld modellingbecausetheychangetheeffectiveaccumulated plastic strain, as de?ned in equation (5), in addition to altering the microstructure and mechanical properties. At present there is a need for developmental work on annealing models in ferritic welds. A related issue is the occurrenceofstrainsaturationeffectsandthepossibility for ‘lock dumping’of weld beads. For example, in a multipass weld with more than 50 weld passes, it is extremely useful to know whether it is necessary to model the deposition of every pass individually, or whether the strain cycling and annealing effects saturate after a small number of passes. If it can be established that saturation occurs after only a few beads have been deposited, then substantial ef?ciencies in modelling can be achieved by introducing subsequent beads in blocks (or groups). The need to account for the shape of individual weld beads, together with the effects of annealing and variant selection in models for residual stress development in multipass ferritic welds was recently reported by Deng and Murakawa. 75 They considered four test cases when they modelled the effects of the martensite transforma- tion on welding residual stresses in a 9Cr–Mo steel pipe. The cases included: no change in volume or phase dependent yield stress; changes in volume only; changes in yield stress only; and changes in both volume and yield stress. They also compared their predictions with measured surface stresses. The predicted and measured hoop stresses on the outer surface of the pipe are shown for the four modelling cases in Fig. 14. It can be seen that compressive stresses are predicted in parts of the weldmetalforthecasesthatconsideredvolumechanges. However, the best agreement was observed when only volume changes were considered. They reasoned that in their models, the changes in yield stress upon transfor- mation were being over estimated due to the annealing Francis et al. Welding residual stresses in ferritic power plant steels Materials Science and Technology 2007 VOL23 NO9 1017 Published by Maney Publishing (c) IOM Communications Ltd that occurs upon deposition of subsequent weld passes. Although both models that considered the effects of volume changes achieved reasonable agreement with measurements, Deng and Murakawa suggested that further improvements could be achieved if the shapes of individual weld beads were accounted for accurately, andeffectssuchasthoseduetotransformationplasticity were also incorporated. Suggestions for future work In summary, progress continues to be made in our understanding of welding residual stresses in ferritic power plant steels. There remain exciting and challen- ging opportunities for future work. Some areas that deserve particular mention include the following parts. 1. Integrated modelling approaches: there is a need to integrate models for complex arc, weld pool and solidi?cation phenomena in to a modelling framework for residual stress development. This will require both interdisciplinary expertise and computational resources. The reward would be tangible in terms of the under- standing of the origin of residual stresses and in identifying the controlling aspects of the problem. 2. Variant selection: variant selection is not yet incorporated into models for welding residual stresses. This is anomalous since variant selection in bainitic and martensitic transformations may affect residual stress development to a greater extent than any volume changes, since the shear component of the associated deformation is signi?cantly larger than the dilatational component. A viable theory for the extent of variant selection must depend on the balance between the mechanical and chemical driving forces for transforma- tion. Variant selection is expected to be strong when the ratioofthemechanicaltochemicaldrivingforceislarge. Experimentalworkisalsorequiredtocon?rmtheextent to which austenite texture and variant selection during bainitic and martensitic transformations affect residual stresses in ferritic steel welds. 3. Thermomechanical cycling effects on transforma- tions: transformations in steels depend not only on the composition, austenite grain size and cooling rate but also on stress and thermal history. Welding gives rise to manypossiblecombinationsofthermomechanicalcycles and,assuch,itisconceivablethattheCCTdiagramand transformation behaviour may change from one weld passtothenext.Thus,thestudyoftheresponseofsteels tothermomechanicalcyclingappearstobeanimportant and exciting area in which to conduct research. 4. Annealing models: development is needed on models for the effects of annealing in multipass welds. Currentapproachestendtounderestimatetheannealing thattakesplaceduetothethermalcyclesassociatedwith subsequent weld passes. 5. Implications for weld design: it is hoped that advances in our understanding of residual stress devel- opment will ultimately translate to improvements in joining technology and weld design. Ongoing work is required to understand how the mechanical and trans- formation properties of ?ller metals, the selection of weldingparameters suchasthepreheattemperature,the pass sequence and the joint con?guration can all be optimised with respect to residual stresses and weld integrity. Acknowledgements The authors would like to acknowledge helpful discus- sions with Dr Hui Dai and Dr Mark Turski at the University of Manchester. JAF is also grateful for support from Roll-Royce Naval Marine. References 1. P. J. Withers and H. K. D. H. 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