Prediction of Creep Rupture Time Using Constitutive Lawsand Damage Rules in 9Cr­1Mo­V­Nb Steel Welds

Kozo Koiwa+, Masaaki Tabuchi, Masahiko Demura, Masayoshi Yamazaki and Makoto Watanabe

Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science,Tsukuba 305-0047, Japan

Long-term creep tests for the parent metal, a simulated heat-affected zone (HAZ) and a weld joint were conducted based on 9Cr­1Mo­V­Nb steel. The creep rupture time, tr, for the weld joint was predicted by computationally simulating creep damage based on Norton’s lawcombined with the time exhaustion rule (TER), where the equivalent stress (·eq), maximum principal stress (·1), or Huddleston stress (·hud) wasused to evaluate the rupture time. Creep damage analysis was also conducted based on the Hayhurst-type damage mechanics rule (HDR), inwhich creep rupture time was evaluated in relation to the rupture stress, ·r. The computed creep rupture times and damage distributions werecompared with the experimentally obtained rupture time and void distribution of the actual weld joint, respectively. Furthermore, the effect of thebevel angle of the HAZ was examined. The key findings from this study were as follows: (1) cautious predictions could be obtained for a loadingstress of 80MPa and higher; (2) the computed fracture initiation positions were on the HAZ boundaries, consistent with the type IV fractureobserved at the stress of 80MPa; (3) the magnitudes of the predicted rupture times were tr (·1) < tr (·hud) µ tr (·r) < tr (·eq); (4) the bevel angledependence previously reported was reasonably reproduced with the TER models that used ·eq and ·hud and with the HDR model.[doi:10.2320/matertrans.ME201703]

(Received October 23, 2017; Accepted May 9, 2018; Published November 9, 2018)

Keywords: 9% chromium 1% molybdenum vanadium niobium (9Cr­1Mo­V­N) steel, welds, creep damage analysis, finite element model,Norton’s law, time exhaustion technique, Hayhurst-type damage mechanics rule

1. Introduction

To ensure the mechanical reliability of structural materialsused in high-temperature environments, such as those foundin boilers or heat exchangers, assessment of their time-dependent performance is of crucial importance. The creepproperty is among the most critical mechanical propertiesimpacting performance. Creep failure often occurs at welds,and therefore various creep tests on welds have beenconducted. However, because such creep tests are time-consuming and expensive, they have hindered materialdevelopment and the optimization of structural design.

Computational approaches are widely expected to resolvesuch problems, thereby potentially reducing the numberand duration of creep tests necessary to ensure that safetystandards are met. In order to evaluate creep damage tostructural components, several creep damage accumulationmodels have been proposed in previous studies, such as thetime exhaustion rule, strain exhaustion rule, and damagemechanics.1­4) In creep damage analyses, it is consideredimportant to evaluate the effect of the multiaxial stress stateon the creep damage distribution and evolution.

For the high-Cr ferritic heat-resisting steels used in ultra-supercritical (USC) thermal power plants, type IV failuresin the heat-affected zone (HAZ)5) become a critical issue.Damage distributions and the creep life of type IV failureshave been studied using creep damage accumulationmodels.6­9) These studies confirmed that creep voiddistributions of structures that have a complicated shapesuch as weld joints can be well predicted using damageanalysis, but have scarcely examined the prediction of thelong-term creep rupture time at welds.8) Furthermore, thecontribution of different types of creep damage rules in creepdamage analysis has not been investigated.

In this study, we conducted long-term creep tests on theparent metal, a simulated HAZ, and a weld joint using 9Cr­1Mo­V­Nb steel (ASME Gr. 91). We also conducted a creepdamage analysis using a finite element model (FEM) basedon two creep damage models: the time exhaustion rule (TER)model and the Hayhurst-type damage mechanics rule (HDR)model. We analyzed the characteristics and accuracy of eachmodel by comparing the computed and experimental resultsunder several stress conditions.

2. Experimental and Computational SimulationProcedures

2.1 Material and creep testsThe material used in this study was 9Cr­1Mo­V­Nb steel

(ASME Gr. 91), and its chemical composition is shown inTable 1. A tube of this material was normalized at 1050°C for60min and then tempered at 760°C for 60min. This materialwas labeled as MGB in the NIMS Creep Data Sheet 43A.10)

Using this material, a weld joint with a single “V” groovewas made by gas tungsten arc welding (GTAW) usingwelding wire (TGS-9Cb). The weld was located in the centerof the specimen, and the bevel angle of the weld joint was30°. After welding, the welded joint was subjected to post-weld heat treatment for 4 h at 740°C. Creep tests on the weldjoint were conducted at 600°C using a round bar specimencut from the welded tube with a gage length, L, of 30mm anda diameter, D, of 6mm.

To conduct creep damage analysis of the weld joint usingthe finite element method, the creep parameters were requiredfor each material: the parent material (PM), the weld metal(WM), and the simulated HAZ. The creep properties of thePM were published in the NIMS Creep Data Sheet 43A.10)

We assumed that the WM had the same properties as the PM.To evaluate the material and creep properties of the HAZ,

a fine-grained HAZ specimen was simulated. HAZ heat+Corresponding author, E-mail: KOIWA.Kozo@nims.go.jp

Materials Transactions, Vol. 60, No. 2 (2019) pp. 213 to 221Special Issue on Development of Materials Integration in Structural Materials for Innovation©2018 The Japan Institute of Metals and Materials

treatment was simulated on the PM using the Gleeble testingmachine as a welding simulator, which applied rapid heating(60°C/s) to a peak temperature of 900°C, followed by gascooling (40°C/s). The simulated HAZ specimen was around bar with a length of 15mm and diameter of 4mm. Thecreep properties of the simulated HAZ were obtained byexperimental creep tests on an actual HAZ specimen.

Table 2 shows the tensile properties of the PM and HAZ.8)

Tables 3, 4, and 5 show the creep parameters of the PM andHAZ. The creep constitutive law and damage rules related tothese parameters are discussed in the following section.

2.2 Creep constitutive law and damage rule2.2.1 Time exhaustion rule

For the creep damage analysis, we used two types ofdamage mechanics models: the time exhaustion rule (TER),1)

and the constitutive equation of the Hayhurst-type damagemechanics rule (HDR).2)

The former is a well-known technique for evaluatingcreep life time.1) The formulations of the TER model are asfollows:

Dc ¼Z t

0

1

trdt; ð1Þ

where Dc is the creep damage. As the damage accumulates,Dc increases, with creep rupture at Dc = 1.0. The creeprupture time tr can be written as a function of the localstress ·

tr ¼ a2·a1 ; ð2Þ

where a1 and a2 are the creep parameters of the material,which can be obtained by fitting to the experimentallydetermined relationship between the creep rupture time trand the applied stress ·a for each material, PM and HAZ.Table 4 shows these parameters obtained from creep tests onthe PM and HAZ of the present Gr. 91 steel.

The creep parameters of the PM and HAZ were obtainedfrom uniaxial creep tests. However, multiaxial stress occursin complicated structures like weld joints and affects thecreep behavior.11) For the TER model, the effect of themultiaxiality appears in the creep damage, Dc, througheq. (2); that is, Dc depends on what type of scalar stress isused. Here, we use three types: (i) equivalent stress, ·eq, (ii)

Table 1 Chemical composition of 9Cr­1Mo­V­Nb steel tube (mass percent).10)

Table 2 Tensile properties of 9Cr­1Mo­V­Nb steel at 600°C.8)

Table 3 Parameters for secondary creep in eqs. (4) and (5)* at 600°C.

Table 4 Parameters for creep rupture time in eq. (2)* of 9Cr­1Mo­V­Nbsteel at 600°C.

Table 5 Creep parameters of Hayhurst-type damage rule for 9Cr­1Mo­V­Nb steel at 600°C.

K. Koiwa, M. Tabuchi, M. Demura, M. Yamazaki and M. Watanabe214

maximum principal stress, ·1, and (iii) Huddleston stress,·hud. ·hud is given by

·hud ¼ ·eq exp b·1 þ ·2 þ ·3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi·21 þ ·2

2 þ ·23

p � 1:0

!" #; ð3Þ

where ·1, ·2, and ·3 are the principal stresses, and b is thematerial constant relating to the multiaxial stress state.3) FromRef. 3, b = 0.24 gives significantly better life predictionsbased on available biaxial creep data for types 304 and 316stainless steel and Ni base alloy. These stress values werecalculated by the FEM using the TER with Norton’sconstitutive law:

_¾eq ¼ A·neq; ð4Þ

where _¾eq is the equivalent creep strain rate, and ·eq is theequivalent stress; A and n are material constants. Theseconstants of Norton’s law were obtained from creep tests onthe PM and HAZ as shown in Table 3.2.2.2 Hayhurst-type damage rule

The Hayhurst-type damage rule (HDR) has often beenused since its development in 1983.2) This rule considers theeffect of the accelerating creep deformation that occurs justbefore the fracture in such a way that the creep strain rate _¾

and damage rate _½ are accelerated by the damage variable ½

and the multiaxiality of the stress. Such a positive feedbackrelationship between the strain rate and the damage valuescharacterizes the HDR model. The damage value ½ can becalculated by applying eqs. (5), (6), and (7) to the FEM.

_¾ij ¼3

2A

·eq

1� ½

h in Sij·eq

tm ð5Þ

_½ ¼ M·»r

ð1þ ºÞð1� ½Þº tm ð6Þ

·r ¼ ¡·1 þ ð1� ¡Þ·eq ð7ÞHere, as with Dc, when the ½ value reaches 1, creep fractureoccurs; ·r is the rupture stress, ·1 is the maximum principalstress, and ·eq is the equivalent stress; Sij is the deviatoricstress; and A, n, m, M, º, and » are material constantsobtained from experimental creep data. A and n have thesame values as when used in Norton’s law, as shown inTable 3; m, M, º, and » are shown in Table 5. ¡ is aparameter that represents the multiaxial stress state. Here,we used ¡ = 0.3, from Ref. 8.

2.3 FEM analysisFigure 1 shows the FEM of the weld joint creep test

specimen, the dimensions of which were measured from theactual weld joint. The size of the fine-grained HAZ wasapproximately 1.3mm in width. The FEM mesh consistedof 22578 nodes and 20230 primary elements. In this study,an in-house finite element analysis code was used for thecreep damage analysis. The creep damage calculations wereconducted under tensile stresses of 50, 80, 100, and 120MPa,and the calculated creep rupture time and the damagedistribution were compared with the experimentally obtainedrupture time and the creep void distribution. Because it hasbeen reported that the bevel angle of the HAZ region affectsthe creep rupture time,9,12­14) a sensitivity analysis of thebevel angle was conducted. The bevel angle, ª, was changedfrom 0° to 45°, in increments of 5°.

3. Results and Discussion

3.1 Creep test resultsFigure 2 shows the experimental results of the relationship

between the applied stress and the creep rupture time fromthe uniaxial creep tests on the PM, the simulated fine-grainedHAZ (HAZ), and the weld joint (WJ) at 600°C. The creeprupture times of the HAZ were more than one order ofmagnitude shorter than those of the PM. The creep rupturetime of the WJ was between that of the PM and that of theHAZ at 120, 100, and 80MPa.

Figure 3 shows the relationship between the applied stressand the minimum creep rate in the uniaxial creep test on thePM and HAZ at 600°C. The minimum creep rate of the HAZwas more than one order of magnitude faster than that of thePM. The material constants A and n (Table 3) of the PM andHAZ were obtained from this figure.

Figure 4 shows the fracture morphology of the actual weldjoints in the case of 80 and 50MPa. As shown by the arrowin Fig. 4(a), fracture occurred at the boundary between theHAZ and the PM at 80MPa, the fracture mode of which isdenoted as type IV.5,15) We confirmed that the fracture modeswere also type IV for stresses of 100 and 120MPa. Whensubjected to low stress (<50MPa) for a long duration(64,650 h), however, fracture occurred inside the WM inareas of localized creep deformation. This fracture mode is

Fig. 1 Finite element model of the weld joint.

Fig. 2 Rupture time of parent metal (PM), simulated HAZ, and weld joint(WJ) of 9Cr­1Mo­V­Nb steel at 600°C.

Prediction of Creep Rupture Time Using Constitutive Laws and Damage Rules in 9Cr­1Mo­V­Nb Steel Welds 215

denoted as type I15) in Fig. 4(b). The creep strength andhardness of the WM were previously reported to decreaseafter 30,000 h of creep at 600°C due to the recovery of themicrostructures.16) The softening of the WM was expected toyield a premature fracture at the weld metal prior to crackingin the HAZ, resulting in the type I fracture.

3.2 Comparison of experimental and simulated creeprupture times

Figure 5 compares the creep rupture times for theexperimental and computational simulations of the weldjoints. With the TER model, the predicted rupture timedepended significantly on which stress was used for theevaluation. This significant dependence indicated thedevelopment of multiaxiality during creep deformation,which, in turn, led to differences among the scalar values ofthe stress tensor. Interestingly, despite changes in the appliedstress values, the relationships between the magnitudes of therupture times evaluated by each stress component remainedthe same: tr (·1) < tr (·hud) µ tr (·r) < tr (·eq). The HDRmodel, representing the damage mechanics, also yieldedappropriate predictions of the weld joint’s creep rupture time.

Moreover, the calculations provided cautious predictionsfor all conditions except for the stress condition at 50MPa;that is, the predicted values were less than the actual onesfor each condition. Given that conservative predictions arepreferable in actual applications, the present prediction

method would likely be useful at least for a relativelyshort-term rupture at an applied stress of 80MPa or higher.Regarding the fracture mode, we confirmed that for thisrelatively short-term rupture, a type IV fracture occurred(Fig. 4(a)). As shown later, the type IV fracture wasreasonably predicted by the present simulation, in which itwas possible to specify the position at which the accumulateddamage reached the rupture value of 1. The consistency ofthe type IV fracture also supports the appropriateness of thecreep damage models for relatively short-term ruptures.

However, for the long-term rupture of 64,650 h at 50MPa,all the predicted values were longer than the actual values,as shown in Fig. 5, representing a shift from the cautiouspredictions for short-term ruptures. In contrast to theexperimental results, we confirmed neither localized creepdeformation nor significant damage accumulation inside theWM in the computational simulation. The type I fractureoccurring with the localized creep deformation (Fig. 4(b))indicated that the creep strength decreased in the WM duringthe long-term creep test, and the creep strength of the WMshould be significantly lower than that of the HAZ and thePM. A similar decrease in creep strength was previouslyreported by Hongo et al. for a long-term creep test over10,000 h in the same Gr. 91 steel.16) However, the presentsimulation could not take into account this decreased creepstrength, which is expected to be the cause of the longer andthus unsafe rupture time predictions, where there was no signof damage accumulation corresponding to the type I fracture.

Figure 6 shows damage contour maps just before fracture(t/tr > 0.9), with the failure initiation positions for theapplied stress of 100MPa superimposed; here, the failureinitiation position refers to the element at which the value ofthe damage, Dc or ½, reached 1 first among all the elements ofthe FEM. As shown in Fig. 6(a) and (c), for the TER using·eq and ·hud, two failure initiation positions were identifiedthat were symmetrically located at the top end of the HAZ/PM boundary and at the bottom end of the HAZ/WMboundary; the damage accumulation was significantlyconcentrated along the line between these positions.Similarly, for the HDR model, the failure initiation positionswere located at the top and bottom ends of the HAZ

Fig. 3 Minimum creep rate of PM and HAZ of 9Cr­1Mo­V­Nb steel at600°C.

Fig. 4 Fracture type of WJ for different stresses. (a) Type IV failure under80MPa for 11,490 h and (b) Type I failure under 50MPa for 64,650 h.

Fig. 5 Comparison of WJ creep rupture time by experiment andsimulation.

K. Koiwa, M. Tabuchi, M. Demura, M. Yamazaki and M. Watanabe216

boundaries, although the damage concentration was not soevident along the line between them (see Fig. 6(d)). For theTER model using ·1, however, the failure initiation positionswere shifted from the ends to the center of the HAZboundaries, and the damage concentration appeared over amuch broader region around the line between the failureinitiation positions (see Fig. 6(b)).

Figure 7 shows the contour maps for each stress valuetogether with that of the equivalent strain for the TER justbefore fracture initiation: ¾eq (a), ·eq (b), ·1 (c), and ·hud (d).In the TER models, the equivalent strain was common for allthe cases; (a) was the same time as (b). The value of eachstress was heterogeneously distributed in the HAZ regionbecause of the constraints exerted by the PM and WMregions, where the extent of the equivalent strain was lessthan one-fourth of that in the HAZ region. The distributionshape of each stress value agreed with that of the

corresponding damage value (see Fig. 6) which wascomputed from that stress value according to eq. (1).Therefore, the fracture initiation position can be understoodfrom the distribution of the corresponding stress value fromthe TER model.

Regarding the equivalent stress and Huddleston stress,their magnitudes were diminished as the multiaxial stressstate became evident; then, the multiaxial stress state becamemore evident under increased constraint from the surroundingelements. As shown in Fig. 7(a), the equivalent strainexhibited its highest peaks at the top end of the PM/HAZboundary and at the bottom end of the WM/HAZ boundary.That is, the elements located at these ends were able todeform at the highest creep strain rate, probably becausethey were on free surfaces. We can thus conclude that theequivalent and Huddleston stresses exhibited their highestpeaks at these edge locations (Fig. 7(b, d)). The peaks ofthe maximum principal stress were found at relatively interiorpositions in relation to the HAZ boundaries, as shown inFig. 7(c).

For the HDR model, the relationship between the stressand the damage was more complicated. Figure 8 showscontour maps of ¾eq (a), ·eq (b), ·1 (c), and rupture stress ·r(d) (eq. (7)) at the time just before fracture initiation.Although the ¾eq peak was found at the free-surface edgesof the HAZ boundaries, as was observed with the TERmodels, ·eq is relatively low on the HAZ boundaries, even atthe free-surface edges. From contour maps drawn at an earlystage of the creep rupture test, however, we confirmed that

Fig. 6 Damage contour map just before creep fracture, and failure initiationposition in HAZ region under the condition of ·a = 100MPa. (a) TERmodel using equivalent stress, ·eq; (b) TER model using maximumprincipal stress, ·1; (c) TER model using Huddleston stress, ·hud; (d) HDRmodel; and (e) HDR model at rupture time.

Fig. 7 Contour maps of the equivalent strain and each stress value for theTER model just before the creep fracture in HAZ under the conditionof ·a = 100MPa. (a) equivalent strain, ¾eq; (b) equivalent stress, ·eq;(c) maximum principal stress, ·1; and (d) Huddleston stress, ·hud.

Prediction of Creep Rupture Time Using Constitutive Laws and Damage Rules in 9Cr­1Mo­V­Nb Steel Welds 217

both ·eq and ¾eq exhibited their highest peaks at the free-surface edges of the HAZ boundaries until half of the rupturetime, showing that the constraint was the weakest there, aswe concluded from the TER model. Regarding ·1, the peakswere found to be located at positions relatively interior tothe HAZ boundaries, as was the case with the TER model.Regarding ·r, we confirmed that the peaks were located at thefree-surface edge of the HAZ boundaries until two-fifths ofthe rupture time; that is, the distribution of the rupture stresswas close to that of the equivalent stress. This result isdescribed by eq. (7), where the rupture stress is affected bythe equivalent stress rather than by the maximum principalstress, using ¡ of 0.3 (see Table 3). Hence, the damageaccumulation rate, which is proportional to the power of therupture stress (eq. (6)), is expected to be fastest at the free-surface edge of the HAZ boundaries during the early stages,at least up to almost half of the total rupture time.

As the damage accumulates, its effect becomes moreevident. First, the accumulated damage accelerates the creepstrain rate according to eq. (5) and leads to a straindistribution that is more concentrated at the free-surfaceedges of the HAZ boundaries. As a result of the excessivestrain concentration, the multiaxial stress state should becomemore evident, resulting in lower equivalent stress at the free-surface edges of the HAZ boundaries than at the otherelements, as shown in Fig. 8(b). From these analyses, we canconclude that for the HDR model, the fracture initiationpositions are strongly determined by the stress distribution

during the early stages of the simulation, which does notnecessarily correspond with the stress state at the final stage,immediately prior to the fracture initiation.

3.3 Comparison of calculated damage distribution andactual void distribution

Figure 9 shows the SEM image of the polished and etchedcross-section around the non-fracture side of the weld jointafter 11,490 h of the creep test at 600°C and 80MPa (dashed-line box shown in Fig. 4(a)). The SEM image exhibits thetype IV creep fracture. The width of the HAZ with fine grainswas approximately 1.3mm, and a large shear deformationcan be recognized along the boundary of the WM and HAZ.The black dots in the figure are the voids formed during creepdeformation. Extensive void growth was observed approx-imately 1­2mm below the upper surface of the specimenin the figure, and it was distributed along the WM/HAZboundary. The void distribution agrees well with the damagedistribution from the TER model using ·1 (see Fig. 6(b))despite the deflection of the void distribution in the PMdirection. The damage deflection in the PM direction wasconsidered to occur because of the different creep behaviorsof the PM and WM in the actual specimen, where a type IVfracture occurred at the HAZ/PM boundary (see Fig. 4(a)).

Figure 10 shows the distributions of creep damage at theHAZ/PM boundary through the central axis of the weld jointat a loading of 80MPa. The values at the time, t/tr = 0, 0.5,0.8, and 0.9 are plotted, where tr is the final rupture time.Except for the TER model using ·1, the highest damagevalue was found at the upper surface of the model. However,as can be seen in Fig. 9, void formation was observed atapproximately 1.5mm below the upper surface of the HAZ/PM boundary, and voids were not found at the surface. Onlyin the case of the TER model using ·1 was failure initiatedat the region approximately 1.5mm below the upper surface,and this trend is similar to the stress distribution and theactual void distribution observed in the experiment. Basedon this result, the TER model using ·1 is considered tooffer the most appropriate criterion to predict the creepdamage distribution in the weld joint. With the HDR model,the failure initiation position was affected by the stress

Fig. 8 Contour maps of the HDR model just before the creep fracturein HAZ under the condition of ·a = 100MPa. (a) equivalent strain, ¾eq;(b) equivalent stress, ·eq; (c) maximum principal stress, ·1; and (d) rupturestress, ·r.

Fig. 9 SEM image around the non-fracture side of the creep fracture ofthe weld joint after creep at 600°C and ·a = 80MPa for 11,490 h.

K. Koiwa, M. Tabuchi, M. Demura, M. Yamazaki and M. Watanabe218

distribution up to approximately t/tr = 0.5 of the analysisbecause in this model, the effect of damage acceleration islarger than the effect of decreasing stress.

3.4 Numerical sensitivity analysis of bevel angleFigure 11 shows the results of the sensitivity analysis in

relation to the bevel angle of the HAZ boundaries toward theload axis at a stress condition of 100MPa. Here, the bevelangle, ª, was changed from 0° to 45° in increments of 5°, andthe width of the HAZ was kept the same. In all the casesexcept for the TER model using ·1, each rupture timesignificantly depended on the bevel angle. That is, the rupturetime showed its maximum value when ª = 0°, at which pointthe rupture time was more than three times that at ª = 30°.The rupture time then decreased with increasing bevel angles,at least up to ª = 30°; in particular, the decreasing rate wasclearly high from 10°­25°. For the TER model using ·hud andthe HDR model, the rupture time showed a minimum value atapproximately ª = 30° and increased slightly with increasingbevel angles. For the TER model using ·eq, the rupture timeremained steady until ª = 40° and decreased slightly atª = 45°. A similar trend in rupture time for a weld joint wasreported in previous studies involving experimental andnumerical simulations of tube weld joints.9,12) In addition, anexperimental result suggesting longer rupture times at thebevel angle of ª = 0° was reported.13) This consistency withpreviously reported trends is likely to support the validity ofthese three criteria. Regarding the bevel angle for theminimum rupture time, the weld joint of an experimentalplate-type specimen was reported to exhibit a minimum value

at a bevel angle of ª = 45°.14) That is, the specimen shapecan change the bevel angle associated with the minimumrupture time.

The TER model using ·1 yielded a completely differenttrend from the above-mentioned three criteria. Therefore, thiscriterion is considered inappropriate for evaluating the effectof the groove angle.

Figure 12 shows the failure initiation position for eachdamage criterion at ª = 0°, 15°, 30°, and 45°. The failureinitiation positions for the TER model using ·eq were locatedinside the HAZ region at ª = 0°; interestingly, the failureinitiation positions form elliptical shapes, as shown by theareas with hatched lines in Fig. 12(a). The failure initiationpositions moved to the top of the HAZ/PM boundary and tothe bottom edges of the HAZ/WM boundary at ª = 15°­30°,

Fig. 10 Creep damage distribution at the HAZ/PM interface following the vertical direction of the weld joint under the condition of·a = 80MPa. (a) TER model using equivalent stress, ·eq; (b) TER model using maximum principal stress, ·1; (c) TER model usingHuddleston stress, ·hud; and (d) HDR model.

Fig. 11 Plot of simulated rupture time against the bevel angle of the weldjoint under the condition of ·a = 100MPa.

Prediction of Creep Rupture Time Using Constitutive Laws and Damage Rules in 9Cr­1Mo­V­Nb Steel Welds 219

and then finally moved to a position on the outer surface ofthe HAZ boundary at ª = 45° (Fig. 12(d)). Similarly, thefailure initiation positions for the TER model using ·hudformed elliptical shapes with smaller radii than for the TERmodel using ·eq at ª = 0°. Although these failure initiationpositions move similarly on the HAZ boundaries at ª = 15°,they are located at inner positions rather than at the free-surface edges, unlike the TER model using ·eq, and weconfirmed that they remained at the slightly interior positionsat least up to 20°. These slightly interior positions were closeto the positions where significant voids were formed (Fig. 9).The failure initiation positions moved further to the free-surface edges of the HAZ boundaries at ª = 25°­30° andfinally reached positions on the outer surface of the HAZboundaries at ª = 45°. The failure initiation positions of theTER model using ·1 were located near the center of the HAZregion except at ª = 0°; they then became slightly scatteredalong an inclined line at ª = 15°, and moved onto the HAZboundaries at ª = 30°.

For the HDR model, there were two failure initiationpositions near the center of the HAZ region at ª = 0°, alignedalong the loading direction. Interestingly, they were found tobe located at positions interior to the HAZ boundaries atª = 15°­20° and then moved to the free-surface edges atª = 30°; these trends were very similar to the case of the TERmodel using ·hud.

3.5 Assessment of the computational predictions fromeach damage model

We assessed the capability of each model to predict thecreep damage behavior based on comparisons with theexperimentally obtained results. Here, we limit the assess-ment to the case of the high applied stress condition over80MPa, i.e., the case of a relatively short-term rupture time.

The TER model using ·eq provided the closest predictionof the rupture time within a factor of 2 (Fig. 5). Thedependence on the bevel angle at least up to 30° wasconsistent with previously reported results (Fig. 11). Thefailure initiation positions were on the HAZ boundaries, in

the vicinity of the experimentally observed voids (Fig. 9).However, the positions differed as follows: although theexperimentally observed location of significant void for-mation was slightly interior to the HAZ location, thepredicted location of the failure initiation positions was onthe free-surface edges. In addition to these summarizedassessments, a much more accurate prediction of the rupturetime could have been obtained by assuming a lower bevelangle than that assumed for the present simulation. Forexample, the predicted rupture time was almost comparableto the experimental one when the bevel angle was 20° (seeFig. 11). Nonetheless, this potential assumption did not yieldan appropriate prediction of the fracture initiation positions(Fig. 12).

The TER model using ·hud and the HDR model providedsimilar prediction results for the rupture time and position aswell as for the bevel angle dependency. The predicted rupturetimes were five times shorter than that observed in theexperiment, and the predicted rupture position was differentfrom that where the void formation was experimentallyobserved, as with the TER model using ·eq. As discussed inthe previous section, the bevel angle dependency agreed wellwith the previously reported results.9,10,12) If we assume thatthe bevel angle was smaller, for example 20°, the differencebetween the prediction and the experiment would be smallerand the rupture position would move toward the inside of thespecimen, resulting in better agreement with the actual voidformation position.

These three cases indicated the initiation of the rupture atthe HAZ boundary for a wide range of bevel angles(approximately 15°­30°), and the type IV failure predom-inantly occurred in that bevel angle range. In other words,these three models provided a sufficient guide as to thefracture type, although a more detailed examination of therupture position to determine its occurrence on the freesurface edges or a slightly inner location would be difficult.Under such constraints on the prediction of the ruptureposition, the TER model using ·eq provided the most exactprediction of the rupture time for the present case.

Fig. 12 Images of the transition of the computed failure initiation position for different bevel angles: (a) ª = 0°, (b) ª = 15°, (c) ª = 30°,and (d) ª = 45°.

K. Koiwa, M. Tabuchi, M. Demura, M. Yamazaki and M. Watanabe220

Lastly, although the TER model using ·1 has thepossibility of predicting the rupture initiation position, itcannot predict the effect of the bevel angle.

4. Conclusions

In this study, we conducted long-term creep tests onwelded joints in 9Cr­1Mo­V­Nb steel (ASME Gr. 91). Weinvestigated the characteristics of two types of creep damagemodels, the TER and the HDR models, in terms of theirpredictions of the creep rupture time and the fracture initiationposition for the weld joint. Our results are summarized asfollows.

The calculations produced cautious predictions for shortrupture times of up to 10,000 h in a high stress region of80MPa and above, and the fracture initiation position wasconsistent with the type IV fracture mode obtained exper-imentally. However, in the case of 50MPa, the type I fracturemode, which appeared in the experiment, was not reproducedin the present simulation.

At the bevel angle of 30°, the relationship between thestress magnitudes is described by ·1 > · hud µ ·r > ·eq at thefailure initiation position, and the magnitudes of the rupturetime show a relationship of tr (·1) < tr (·hud) µ tr (·r) < tr(·eq). These trends did not change under any of the tensilestress conditions.

The rupture time of the TER model using ·eq wasrelatively close to that of the actual weld joint, and itssensitivity to the bevel angle was also similar to that observedexperimentally. The detailed positions of the fractureinitiation were, however, different from the void distributionof the actual weld joint.

The TER model using ·hud and the HDR model providedvery similar predictions in terms of the rupture time and thefracture initiation position. In addition, their sensitivity tothe bevel angle was almost even, which was similar to thatobserved experimentally.

The damage distribution of the TER model using ·1 wassimilar to the void distribution of 100MPa and ª = 30°.However, this model cannot predict the effect of the bevelangle.

By comparison of these creep damage laws, it wasconsidered that the TER model using ·hud and the HDRmodel are good creep damage laws for predicting both creeprupture time and fracture initiation position.

Acknowledgement

This work was partly supported by the Council forScience, Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP),“Structural Materials for Innovation” (Funding agency: JST).

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Prediction of Creep Rupture Time Using Constitutive Laws and Damage Rules in 9Cr­1Mo­V­Nb Steel Welds 221