Prevention of the overestimation of long-term creep rupture life by multiregion analysis in strength enhanced high Cr ferritic steels

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Prevention of the overestimation of long-term creep rupture life by multiregion analysis in strength enhanced high Cr ferritic steels
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  Materials Science and Engineering A 490 (2008) 66–71 Prevention of the overestimation of long-term creep rupture life bymultiregion analysis in strength enhanced high Cr ferritic steels Hassan Ghassemi Armaki a , ∗ , Kouichi Maruyama b ,Mitsuru Yoshizawa c , Masaaki Igarashi c a Graduate School of Engineering, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan b Graduate School of Environmental Studies, Tohoku University, 6-6-02 Aobayama, Sendai 980-8579, Japan c Corporate Research and Development Laboratories, Sumitomo Metal Industries Ltd., 1-8 Fuso-Cho, Amagazaki 660-0891, Japan Received 10 September 2007; received in revised form 21 December 2007; accepted 25 January 2008 Abstract Long-term creep rupture life is often evaluated from short-term data by a time–temperature parameter (TTP) method. However the conventionalTTP methods sometimes fail in understanding creep rupture behavior of strength enhanced high Cr ferritic steels and overestimate creep rupturelife in long-term creep. In the present paper, creep rupture data of seven kinds of heat resistant steels with different W and Cr concentrations havebeen analyzed. The conventional TTP method like Orr–Sherby–Dorn analysis evaluates long-term creep rupture life assuming a unique value of activation energy for all the creep rupture data. This analysis is called single region analysis in this paper. The single region analysis can representwell the creep rupture data of steels containing less than 8% Cr. The creep rupture analyses of steels containing more than 8% Cr exhibit thatapparent activation energy changes from a high value in short-term creep region to a low value in long-term creep region. In each case a creep datawas divided into several data sets, and then the conventional single region analysis was applied to each divided data set. This analysis is referredto as multiregion analysis. The multiregion analysis describes very well all the data points, whereas regression curves of the single region analysisdeviate from the data points, resulting in overestimation of long-term rupture life. The difference between the two activation energies of short-termand long-term creep increases with increasing Cr concentration. Therefore, the overestimation due to singles region analysis is expected to be moreserious at higher Cr concentration.© 2008 Elsevier B.V. All rights reserved. Keywords:  Heat resistant steel; High Cr ferritic steel; Time–temperature parameter analysis; Overestimation of rupture life; Effect of Cr concentration 1. Introduction The research and development of heat resistant steels forhigh-efficient low-emission ultra-supercritical (USC) powerplants are being now promoted [1]. Information on long-term creep rupture strength of advanced high Cr ferritic steels is nec-essary to use them in such high temperature plants. However,creep experiments longer than 10 4 h are not easily performed.Hence the long-term creep properties are often evaluated fromshort-term creep rupture data by time–temperature parameter(TTP) methods, such as Larson–Miller [2], Orr–Sherby–Dorn [3] and Manson–Haferd [4] methods. The evaluation has not made any serious mistake in conventional low Cr ferritic heat ∗ Corresponding author. Tel.: +81 22 795 7326; fax: +81 22 795 7325.  E-mail address:  hasan gm2003@yahoo.com (H. Ghassemi Armaki). resistantsteels.Butresults[5–8]showthattheconventionalTTP methods overestimate rupture life for several advanced high Crferritic steels with higher creep strength.Orr–Sherby–Dorn (OSD) method [3] is representative increep rupture life prediction. In the OSD method, the long-termcreep lives are predicted by a linear extrapolation of a log t  r  ver-sus 1/  T   line as shown in Fig. 1(a), where  t  r  is the rupture life,and T  isthetestingtemperature.Inotherwords,thelog t  r  − log σ  curve measured at  T  1  is simply shifted to longer life accordingto the activation energy  Q  (dotted line in Fig. 1(b)). The linear extrapolation is based on a crucial assumption that the activa-tionenergydeterminedbytheshort-termdatadoesnotchangeinlong-termcreep.However,thisisnotalwaystrue.Theactivationenergyforrupturelifesometimesdecreasesinlong-termcreepasshownbythedashedlineinFig.1(c),andthelinearextrapolation (open circles) overestimates the true rupture life (solid circles).This is called “premature failure” [5,9,10]. Therefore, it could 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2008.01.072   H. Ghassemi Armaki et al. / Materials Science and Engineering A 490 (2008) 66–71  67Fig. 1. Evaluation procedure of long-term creep rupture life, and explanationsof premature failure [6]. be derived that the change in  Q =d(ln( t  r ))/d(1/  T  ) is the causeof the overestimation and premature failure. In order to preventthe overestimation the multiregion analysis has been proposedby Maruyama et al. [11] as a suitable analysis method of creep rupture data. This method has been applied to austenitic stain-less steels [12,13] and ferritic steels [14]. The results show that thismethodpreventstheoverestimationverywell[12,14,15].In presentpaper,thedecreaseofactivationenergyisproposedtoberesultedinoverestimationoflong-termcreeprupturelifeinhighCr ferritic steels and the multiregion is subjected for preventionof overestimation. 2. Experimental procedure The chemical composition of the steels studied is listed inTable 1. All the chemical compositions given in the presentpaper are expressed in mass%. The steels marked by “A” have1.8–2% W and their Cr concentration increases from 5% (A5)to 12% (A12). The steels marked by “B” have 3% W andtheir concentrations of Cu, Ni and Mo are less than 0.01%. Allof the alloys were vacuum-induction-melted (VIM) and thenhot-forged to 25mm thickness. In the next stage, they were nor-malized at 1050 ◦ C for 0.5h and were cooled in air, followedby tempering at 770 ◦ C for 2h. These heat treatments make atempered martensitic lath structure with precipitates of M 23 C 6 MX. Creep specimens of 6mm in diameter and 30mm in gagelength were tested at 600, 650 and 700 ◦ C under constant loadin air. Fig. 2. Creep stress vs. creep rupture life curves of alloy A7 with 7%Cr. 3. Results and discussion 3.1. Single region analysis Fig. 2 represents stress dependence of creep rupture lifefor alloy A7 with 7% Cr. As evident on the curves testedat 650 and 700 ◦ C, the stress exponent of creep rupture life n = − d(ln t  r )/d(ln σ  )changesfrom n =10athighstressandshort-term creep to  n =4 at low stress and long-term creep. The OSDmethod is based on the following equation of rupture life  t  r : t  r  =  t  0 σ  − n exp   QRT    (1)where t  0  isaconstant, Q theactivationenergy,  R thegasconstantand  T   is the absolute temperature. The OSD method assumes aunique value of   Q  for all the data points. If this is the case,then all the data points can be presented by a single curve whenthey are normalized to a temperature for example 873K, by thefollowing equation: t  r(873)  =  t  r( T  )  exp  QR   1873   −   1 T    (2)where  t  r (873)  and  t  r (T)  are the rupture lives tested at 873K and T  , respectively. Fig. 3 shows the normalized curve based on Eq. (2) f or alloy A7. It is found that all the data points are fitted witha unique value of activation energy ( Q =555kJ/mol), although Table 1Chemical composition of the steels studied (mass%)Name C Si Mn P S Cu Ni Cr Mo V W Nb NA5 0.098 0.26 0.53 0.012 0.001 0.88 0.31 5 0.39 0.24 2.02 0.049 0.037A7 0.095 0.25 0.51 0.012 0.001 0.86 0.31 7 0.39 0.22 1.96 0.048 0.038A9 0.097 0.25 0.52 0.010 0.001 0.87 0.31 9 0.39 0.20 1.87 0.052 0.054A10 0.098 0.26 0.49 0.010 0.001 0.87 0.33 10.5 0.37 0.20 1.87 0.053 0.058A12 0.093 0.25 0.49 0.006 0.001 0.86 0.31 12 0.39 0.20 1.86 0.049 0.066B9 0.099 0.26 0.51 0.010 0.001 <0.01 <0.01 9 <0.01 0.19 2.96 0.065 0.053B10 0.096 0.25 0.51 0.011 0.001 <0.01 <0.01 10.5 <0.01 0.20 2.95 0.064 0.057  68  H. Ghassemi Armaki et al. / Materials Science and Engineering A 490 (2008) 66–71 Fig. 3. Creep stress vs. creep rupture life curve of alloy A7 normalized to T  =873K with  Q H  =555kJ/mol. stress exponent changes at around 100MPa. Consequently, thesingle region analysis established upon the unique activationenergy assumption can estimate long-term creep strength of thesteel adequately.All the creep rupture data of alloy A5 with 5%Cr can also berepresented by a unique value of activation energy. This find-ing suggests that the conventional OSD method is enough todescribe creep rupture strength of the steels with Cr concentra-tion ( C  Cr ) less than 8%. In these steels (containing  C  Cr  <8%)there is two regions H 1  and H 2  with different stress exponent( n ), but activation energy of rupture life ( Q ) is same in bothregions. So, the multiregion analysis of creep rupture data is notnecessary. 3.2. Multiregion analysis Creep ruptures life of alloy A10 containing 10.5% Cr is plot-ted in Fig. 4 as a function of creep stress. The stress exponent Fig. 4. Creep stress vs. creep rupture life plot for alloy A10 containing 10.5Cr–1.87W–0.4Mo–VNb.Fig. 5. Creep stress vs. creep rupture life curves of alloy A10 normalized to T  =873K in (a) high stress region;  Q H  =800kJ/mol and (b) low stress region; Q L  =451kJ/mol. ( n ) decreases twice, first time from region H 1  to H 2  and secondfrom region H 2  to L. The lengths of the arrows drawn in thefigure indicate the different values of activation energy betweenregions H and L, although the length of the arrows in H 1  andH 2  regions is same. Fig. 5(a) and (b) shows stress dependence of creep rupture life normalized to  T  =873K according to Eq.(2).  Q H  =800kJ/mol characterizes the high stress data, while Q L  =451kJ/mol is the activation energy of the low stress data.A good fit of the data of regions H 1  and H 2  (solid symbols) isattainedwith Q H  athighstressinFig.5(a),butlargedeviationof  data points (open symbols) is evident at low stress. On the otherhand, in Fig. 5(b), the small activation energy ( Q L ) can char-acterize well the data points (open symbols) at low stress andlong-term creep. But there is a large deviation of data points athigh stress and short-term creep. So the activation energy deter-mined in short-term and high stress regions (H 1  and H 2 ) is notapplicable to the creep rupture data in long-term and low stressregion (L). The creep rupture data set of A10 was divided intotwo data sets on the basis of  Fig. 5: region H with  Q H  (solidsymbols) and region L with  Q L  (open symbols). Each divided   H. Ghassemi Armaki et al. / Materials Science and Engineering A 490 (2008) 66–71  69Fig. 6. Creep stress vs. creep rupture life plot for 9Cr–2.96W–0.01Mo–VNbsteel (B9). data set was analyzed with the conventional OSD method basedon Eq. (1) and the regression curves are drawn in Fig. 4. All the data points are very well represented by the regression curves.Infact,thestressexponentdecreasesfromregionH 1  toregionH 2  but the activation energy is the same. The decrease in  n  hasnothing to do with the overestimation of rupture life withoutthe change in  Q  value. On the other hand both stress exponentand activation energy decreases from region H 2  to region L. Inthis case, the decrease in stress exponent is accompanied by thedecrease of   Q  value results in the overestimation of long-termrupturelife.SimilarchangesinactivationenergyappearinalloysA9, A10 and A12 containing 1.8% W.It is important to check whether the multiregion analysis isnecessaryinsteelsB9andB10containing3%W.Asanexampleof the two alloys, the data points of alloy B9 is plotted againstrupture life in Fig. 6. As shown in this figure, the same trend as alloy A10 is evident in these alloys, too. There are two regionsH 1  and H 2  with different stress exponents but having the sameactivationenergy.Ontheotherhandthedecreaseofstressexpo-nent from region H 2  to region L is accompanied by the decreaseof activation energy from  Q H  =824kJ/mol to  Q L  =494kJ/mol.Therefore, the estimation of creep rupture life in the long-termcreeponthebasisoftheactivationenergyoftheshort-termcreepruptureinregionsH 1  andH 2  resultsintheoverestimationofrup-ture life. Consequently, the multiregion analysis is necessary toavoid the overestimation in the steels containing higher than 8%Cr regardless of the W concentration. 3.3. Effect of Cr concentration on the activation energy and stress exponent  In Fig. 7 the activation energy values of all the alloys areplotted as a function of Cr concentration ( C  Cr ). The activationenergyvaluesofthehighstressregion( Q H )aredenotedbysolidsymbols, while those of the low stress region are remarked byopen marks. As derived in the proceeding section, regions H 1 and H 2  with the same activation energy ( Q H ) are present in allthe alloys. Fig. 7 shows that the activation energy values of the Fig. 7. Variations of activation energy values as a function of Cr concentrationin high stress and low stress regions. high stress region ( Q H ) increase with increasing Cr concentra-tion up to 9%. But it does not change sensitively above 9% Crconcentration.On the other hand, the region L with the lower activa-tion energy ( Q L ) appears when Cr concentration exceeds 8%.The activation energy values of this region ( Q L ) decrease withincreasing chromium concentration. The same trend is evidentfor both alloys containing 1.8% W and 3% W. Fig. 7 indi-cates that activation energy value of the low stress region ( Q L )decreases with increasing tungsten concentration at  C  Cr  >9%.The values of stress exponent are plotted against Cr concen-tration in Fig. 8. High stress region consists of two subregions (H 1  and H 2 ) with different stress exponent. The stress exponentdecreases from H 1  to H 2  in all the alloys, but the decrease of stress exponent does not accompanied by the change in acti-vation energy. It should be noted that the variation of stressexponent value is not always accompanied by the change inactivation energy value [16]. Fig. 8. Variations of stress exponent as a function of Cr concentration in highstress and low stress regions.  70  H. Ghassemi Armaki et al. / Materials Science and Engineering A 490 (2008) 66–71 Stress exponent of the first region H 1  increases with increas-ing Cr concentration up to 9% Cr and then remains almostconstant. The stress exponent of the second region H 2  is almostconstant at  C  Cr  >9%, too, but at  C  Cr  <9% the concentrationdependence of stress exponent is not clear and further studiesare needed in the range between 7 and 9% Cr.As shown in Figs. 4 and 6, stress exponent exhibits the sec- ond decreases from the higher stress region (H 2 ) to the lowerstress region (L) in the long-term creep. This reduction of stressexponent is accompanied by the decrease of activation energyvaluefromhighstressregion( Q H )tolowstressregion( Q L ).Thecreep rupture data in the low stress region of  Figs. 2, 4 and 6 are characterized by one stress exponent. In this region, the stressexponent decreases with increasing Cr concentration. 3.4. Effect of Cr concentration on overestimation Rupture lives of A9 and A12 at 98MPa are plotted againstreciprocal temperature in Fig. 9. The creep rupture life of alloy A12 is longer than that of A9 in the short-term creep. However,this is not the case in long-term creep at 650 ◦ C. Suppose long-termrupturelifeisevaluatedbylinearextrapolation(dottedline)basedontheactivationenergiesoftheshort-termdata( Q H ).Thisextrapolation predicts the open symbols at 650 ◦ C that is longerthan the actual value (solid symbols).The rupture life evaluated by the linear extrapolation is givenby the following equation: t  r(estimated)  =  t  0(H) σ  − n H exp  Q H RT    =  t  H  exp  Q H RT    (3)where  t  0(H)  and  n H  characterize rupture life at high stress regionand  t  H  =  t  0(H) σ  − n H . On the other hand, the actual rupture life t  r(actual)  in the long-term region  L  is defined by following equa-tion: t  r (actual)  =  t  0(L) σ  − n L exp  Q L RT    =  t  L  exp  Q L RT    (4) Fig. 9. Effect of Cr concentration on extend of the overestimation of creeprupture life in the log term creep region.Fig. 10. Correlation between ( Q H  − Q L ) and the extent of overestimation of creep rupture life. Creep rupture lives at 650 ◦ C and 98MPa were evaluatedfrom short-term creep data in region H. where  t  0(L)  and  n L  characterize rupture life at low stress regionand  t  L  =  t  0(L) σ  − n L . The two lines in Fig. 9 intersect at  T  *, andthe following relation holds:ln  t  H t  L   =  Q L  −  Q H RT  ∗  .  (5)Let us define the extent of overestimation as  t  r(estimated)  /  t  r(actual) ,that is expressed as follows:ln  t  r(estimated) t  r(actual)   = ( Q H  −  Q L ) R   1 T  − 1 T  ∗  .  (6)Eq. (6) suggests that the overestimation is more significant withincreaseinthedifferencesbetween Q H  and Q L  andbetween T   and  T  *. In Fig. 10 ln( t  r(estimated)  /  t  r(Actual) ) is plotted against( Q H  − Q L ) for rupture lives at 650 ◦ C and stress of 98MPa.This figure confirms the prediction from Eq. (6). As indicated in Fig. 7,  Q H  − Q L  increases with increasing Cr and W concentra-tion. The overestimation is more serious in the 12Cr steel thanthe 9Cr steel. It is also to be noted that the overestimation ismore serious in alloy B10 (3% W) than alloy A10 (1.8% W)under the same Cr concentration.If the same story is applicable to engineering steels, theoverestimation can be less serious in Gr. 91 (9Cr–1Mo–VNb)steel and Gr. 92 (9Cr–1.8W–0.4Mo–VNb) steel than Gr.122(12Cr–2W–0.4Mo–1Cu–VNb) steel. 4. Summary 1. Multiregionanalysisisnecessarytounderstandcreeprupturebehavior of advanced high Cr ferritic heat resistance steelscontaining Cr more than 8mass% since activation energy forrupture life is different between short-term and long-termregions.2. Change in stress exponent for rupture life is not alwaysaccompanied by change in activation energy.3. Activation energy value for rupture life in high stress region( Q H )increaseswithincreasingchromiumconcentrationupto
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