The prediction of grain size of the heat affected zone of welded s304h steel tubes using a mathematical model

75 THE PREDICTION OF GRAIN SIZE OF THE HEAT AFFECTED ZONE OF WELDED S304H STEEL TUBES USING A MATHEMATICAL MODEL Ja omí Mo a ec * Jose B adáč ** I a No áko á *** Heinz Neumann Technical Uni e si y o Libe ec Facul y o Mechanical Enginee ing Depa men o Enginee ing Technology S uden ská 2, 461 17, Libe ec 1, Czech Republic [email p o ec ed] ** [email p o ec ed] *** [email p o ec ed] * ŠkodaAu o Uni e si y Au omobile Technology Depa men Tř. V. Klemen a 869, 293 60, Mladá Bolesla , Czech Republic * [email p o ec ed] Abs ac Supe 304H is an aus eni ic s eel, which is mainly used o boile s in he mal powe plan s and he ene gy sec o . S eng h a high empe a u es has become one o he mos impo an a ibu es in he design o boile ubes. The di e ences in ma e ial p ope ies, especially in i s c eep esis ance compa ed o o he aus eni ic s eels o simila composi ion, a e mainly achie ed by he addi ion o abou 3 w .-% o coppe . The o ma ion o ine Cu- ich p ecipi a es du ing manu ac u e leads o an inc eased c eep s eng h du ing he p ocess o p ecipi a ion ha dening. The impac o he welding cycle on he g ain coa seness in he hea - a ec ed zone (HAZ) o S304H s eel will be demons a ed in his pape . The op ions and p ocedu es o p edic ing g ain size by ma hema ical modeling o welding and hea ea men will also be shown he e. The me hod o acqui ing he inpu da a o he ma hema ical models, which p edic he g ain size, will also be desc ibed. In oduc ion The con inuous end o ope a ional pa ame e s o inc ease hei ene gy and chemical condi ions also equi es he de elopmen o new ma e ials, which a e able o ope a e unde such condi ions. Hea - esis an s eels can undoub edly be classed as one o hese ma e ials. They ha e o ul ill many equi emen s, which a e o en con adic o y. The main equi emen lies in i s enhanced esis ance agains long e m loading unde high empe a u es. No less impo an is su icien esis ance agains co osion, which o ms an oxide laye on he s eel su ace. [1] Applica ions o such new ma e ials and he inclusion o he echnological p ocesses o joining hem oge he a e o en accompanied by he use o welding simula ions and hea ea men compu a ions. These compu a ions can la gely elimina e he isks, which a e connec ed wi h he occu ence o unaccep able de ec s, o hey can lead o he elimina ion o inne s esses caused by he p ocess. The Sysweld p og am is one o he mos commonly used p og ams o his ype o compu a ion. 76 When p edic ing he s uc u e and esul ing p ope ies o he welded join s a ea, i is impo an o know no only he g ain size in he ini ial s a e, bu also du ing he welding p ocess. Fo his eason, his pape desc ibes he me hodical p ocedu es and he expe imen al esul s, which lead o he de ini ion o a compu a ional model. This model hen enables he p edic ion o he aus eni ic g ain size o he weldmen s made by S304H s eel, especially in he hea - a ec ed zone, bu no in he weld a ea. 1 The Cha ac e is ics and Uses o S304H S eel Gene ally speaking, aus eni ic s eels ha e good mechanical p ope ies and excellen co osion esis ance e en a high empe a u es, a ying om 650-700°C. Howe e , his ad an age is coun e ed by hei un a ou able he mal-physical p ope ies such as low he mal conduc i i y and high he mal expansi i y. Ano he majo d awback is he possible damage o he ma e ial h ough he mal a igue, especially when hese s eels a e used in powe s a ions whe e hey a e wo king in cyclic he mal modes. The cos o hese s eels p ohibi s hei use on a la ge scale. [6] Cu en ly aus eni ic hea esis an s eels g ade 304, a e used in Eu ope, USA and Japan. Recen ly, S304H, which is a new ype o aus eni ic s ainless s eel con aining 3% coppe , is being adop ed o he p oduc ion o supe -hea e / e-hea e ubes o 600°C USC powe plan boile s. [2] The s eng h o his ma e ial a high empe a u es is ele a ed and pa icula ly i s c eep p ope ies a e imp o ed by adding abou 3 w .-% o coppe , inc easing he ca bon con en and adding ce ain amoun s o niobium and ni ogen. The addi ion o ni ogen leads o a solid solu ion hea s eng hening o he ma e ial. This inc eases he ensile s ess esis ance. The s ess esis ance unde c eep condi ions is mainly inc eased by he p ecipi a ion o a Cu- ich phase in he ma ix. [4]The Cu- ich phase is mainly composed o Cu and also a pa o Fe, C and Ni. The con en o Cu in he Cu- ich phase is lowe han 20 a pc a ea ly s age o p ecipi a ion a e 1 hou aging, and hen i is inc easing con inually wi h aging ime and eaches almos 90 a pc a cen e when aging o 500 hou s. These esul s ep esen ha Cu a oms g adually concen a e o Cu- ich pa icles and he o he elemen s (such as Fe, C , Ni e c.) di use away om Cu- ich pa icles o ma ix wi h he inc easing o aging ime a ± 650°C. I is easonable o sugges ha Cu will be he only main composi ion in Cu- ich phase when aging o e y long ime. [11] Du ing manu ac u e, his Cu- ich phase and a niobium ca boni ide phase p ecipi a e simul aneously. S304H is cha ac e ized by an excellen p ecipi a ion ha dening e ec . I eaches peak ha dness (246 HV) a 1000 h and main ains almos he same le el ill 8000 h a 650°C. [3] The di usion o ch omium o he su ace is accele a ed and he o ma ion o an adhe en and dense ch omium oxide (C 2O3) laye is enhanced. This p o ec i e laye educes u he oxida ion o a minimum. Tubes o he ma e ial (ø 38 mm, wall hickness 6.3 mm) we e used o g ain size p edic ion. I s chemical composi ion analysis is shown in Table 1. Figu e 1 shows he ini ial s a e mic os uc u e o he es ed ma e ial. Tab. 1: Chemical composi ion o es ed ma e ial C Mn Si P S C Ni Nb Cu N w . % 0.090 0.873 0.243 0.005 0.015 18.8 8.449 0.508 3.515 0.091 Sou ce: Own 77 Sou ce: Own Fig. 1: Ini ial s a e mic os uc u e o S304H s eel (80 ml HCl; 13 ml HF; 7 ml HNO3) 2 The compu a ion o g ain size using he Sysweld p og am The educ ion o Gibbs su ace ee ene gy ac s as he he modynamic d i ing mechanism o g ain g ow h. The g ain g owing p ocess esul s in he educ ion o he g ain su ace bounda y and hus o a dec ease in ee ene gy. G ain size is impo an in wo espec s. I is impo an wi h ega d o he mechanical p ope ies o he ma e ial (e.g. b i leness), bu also wi h espec o he in luence on he ans o ma ion p ocesses. The i s models, which we e buil on he physical basis, we e de eloped a he beginning o 1950s. In 1980, a new app oach based on ma hema ical modelling was in oduced. On he basis o compu ed simula ions i was also possible o moni o he p ocesses, which we e p e iously di icul o obse e, o example he olume change a e o he indi idual g ains. Cu en ly, he mos commonly used simula ion me hod is he “Mon e Ca lo Po s Model” me hod. A desc ip ion o his me hod is gi en as an example in [5, 7]. An ideal ule o g ain g ow h is gi en by equa ion (1). [8] eCDD TR Q aa    0 (1) D – g ain diame e (mm), D0 – ini ial g ain size (mm), C – ma e ial cons an (mma·s-1), Q – ac i a ion ene gy (J·mol-1), R – gas cons an (J·K-1·mol-1), T – empe a u e (K), – ime (s) a – coe icien (-). I was es ablished by expe imen s ha coe icien alues a y be ween 2 and 5. Value a=2 applies i he g owing p ocess is solely con olled by di usion. Value a=4 is de e mined in he case whe e he e is p ecipi a ion and di usion along he g ain bounda y. G ain g owing is, howe e , in luenced by o he ac o s, o example, hea ing a e and g ain g ow h ba ie s. The compu a ion o g ain size p oceeds in he Sysweld simula ion p og am based on equa ion (2) which exp esses he g owing a e o he g ain size.         TR Q CDaexp  (2) 78 Cons an C is usually 0.4948·1014 mma.s-1. This compu a ional equa ion is designed o cases when he amoun o aus eni e is cons an o is dec easing. I he amoun o aus eni e inc eases, wo de elopmen s a e obse ed:  Exis ing g ains inc ease in size.  New g ains a e gene a ed wi h ze o ini ial g ain size. By gene alizing he con en ional equa ion in o de o de e mine he g ain size, we a i e a he ollowing equa ion (3). aa D TR Q CD             exp (3) In his equa ion, he λ alue exp esses he aus eni e p opo ion while he alue   shows he ans o ma ion a e o his phase. Fo   >0 he aus eni e is c ea ed. I he aus eni e is no c ea ed, i.e.    0 hen is he g ain size exp essed by he equa ion (2). 3 Expe imen al de e mina ion o g ain size Fo nume ical analysis in Sysweld, i is impo an o know he inpu condi ions de ining he g ain size changes, which depend on ime and he mal exposu e o he ma e ial. The es samples we e 12 mm long ings cu om he gi en ube (ø 38 mm, wall hickness 6,3 mm). Since i conce ned he moulding p oduc , he specimens we e measu ed longi udinally and ans e sely, because o he ac ha he g ains could by de o med du ing he moulding p ocess. The specimens we e he mally exposed in an o en a 1000°C, 1100°C o 4 and 8 hou s and we e subsequen ly cooled in wa e . While hea ing up o he es empe a u e he hea ing a e o all specimens was 420°C/hou . Specimens o alida ing he s uc u e we e p epa ed acco ding o a s anda d me allog aphic p ocedu e. To accen ua e he g ain bounda ies he specimens we e cau e ized in solu ion (80 ml HCl; 13 ml HF; 7 ml HNO3). This solu ion had o be used because cau e iza ion agen s like Villela Bain o Vogel, which a e commonly used o alloy ma e ials, do no wo k wi h he used ma e ial. The g ain size was e alua ed acco ding o CSN EN ISO 643 s anda d. The e alua ion o he g ain size was exp essed by he in e sec ion me hod and by he planime ic me hod. Based on hese measu emen s, he a e age numbe o sec ions o one millime e o measu ed line NL was de e mined using he in e sec ion me hod. Then, da a such as he a e age leng h o linea sec o l, he g ain size numbe G1 and he numbe o g ains in one mm2 ma ked m we e also de e mined. Fo he planime ic me hod i is impo an o de e mine he g ain size numbe , G2 (based on his da a i is possible o de e mine he a e age g ain diame e d and he a e age g ain su ace a ea a ). F om his, he eal a e age g ain su ace a ea s a , he eal a e age g ain diame e d and he numbe o g ains in one mm2 can also be compu ed. [9] The de e mined alues o he g ain size o each se o expe imen al condi ions o he in e sec ion and planime ic me hod a e shown in able 2. 79 Tab. 2: De e mined alues o g ain size The da a de e mined by help o in e sec ional me hod The da a de e mined by help o planime ic me hod Specimens S 304H NL l G1 Numbe o g ains in 1mm2 G2 Numbe o g ains in 1mm2 Middle g ain su ace [mm2] Middle g ain diame e [mm] Ini ial s a e LD 52.326 0.01911 8 2048.0 8 2131.3 0.0004691 0.02166 TD 47.007 0.02127 8 2048.0 8 2325.7 0.0004301 0.02074 1000 °C 4 hou s LD 40.716 0.02456 7-8 1536.0 8 2045.5 0.0004888 0.02211 TD 53.353 0.01874 8 2048.0 8 1949.6 0.0005129 0.02265 1000 °C 8 hou s LD 45.857 0.02181 8 2048.0 8 1917.6 0.0005214 0.02284 TD 67.634 0.01479 9 4096.0 8 2365.1 0.0004228 0.02056 1100 °C 4 hou s LD 41.222 0.02426 7-8 1536.0 7 847.8 0.0011794 0.03434 LD 35.911 0.02785 7 1024.0 7 949.0 0.0010537 0.03246 TD 45.880 0.02180 8 2048.0 7 1011.2 0.0009888 0.03145 TD 51.672 0.01935 8 2048.0 7 1337.9 0.0097474 0.02734 1100 °C 8 hou s LD 21.842 0.04578 6 512.0 6 591.2 0.0016915 0.04113 TD 36.882 0.02711 7 1024.0 6 544.5 0.0018365 0.04286 NL – a e age numbe o g ains g ipped o he line uni leng h, l – a e age leng h o linea sec o , G1 – g ain size numbe e alua ed wi h in e sec ional me hod, G2 – g ain size numbe e alua ed wi h planime ic me hod, LD – longi udinal di ec ion, TD – ans e sal di ec ion Sou ce: [9] 4 Ma hema ical compu a ion o g ain size using Sysweld The expe imen ally de e mined alues o g ain size (see able 2) we e used as inpu da a o he g ain size calcula ion in he Sysweld simula ion p og am. The compu a ions o his p og am a e based on equa ions (2) and (3). The alue o he ac i a ion ene gy, Q, can be se in he de ini ion o he compu a ion model by using a posi i e powe cons an , a, and he cons an , C. In he i s phase, he inpu da a leads o a compu ed g ain size, which co esponds o he expe imen ally de e mined g ain size. Based on expe ience, i can be said ha he main pa ame e o p edic ing g ain size by ma hema ical simula ion is he ac i a ion ene gy, Q. Cons an C emain unchanged, C=0,4948·1014 mm4.s-1 and he powe cons an , a, usually ma ches a=4 ( he case o p ecipi a ion and di usion along he g ain bounda y). Based on hese esul s, he ac i a ion ene gy Q o he a io Q/R is hen de e mined. In he case o S304H s eel i is op imal o keep he a io Q/R=73400 o a empe a u e o 1000°C and Q/R=74800 o a empe a u e o 1100°C. [10] 80 This alida ed model is consequen ly used o he calcula ion o he g ain size based on non- s a iona y empe a u e ields appea ing du ing welding. Figu e 2 depic s a 3D simula ion model o a weld made up o h ee weld beads as well as he weld´s basic geome y. All he weld beads on he simula ion model a e only c ea ed by using an addi ional ma e ial. Howe e , he simula ion model he o hea sou ce co espond wi h mel ing bounda ies o he eal weld geome y o indi idual weld beads. Sou ce: [10] Fig. 2: 3D simula ion model o he weld wi h h ee weld beads and he weld geome y Figu e 3 shows he esul s o compu ing he g ain size in HAZ o he weld made on S304H s eel ube ø 38, wall hickness 6.3 mm. The weld was made by an au oma ed machine using GTAW me hod. Th ee weld beads we e made wi h a p ehea ing empe a u e o 180°C, an in e pass empe a u e o 290 °C and using addi ional ma e ial The mani MTS 616. The edges o he indi idual weld beads we e ecip ocally shi ed by 120° while he welding di ec ions o he successi e beads we e e e sed. None o he weld beads was inished immedia ely a e 360°, hey all o e lapped hei edges a leas by 10 mm. Expe imen al welds we e made in Ví ko ice S eel company and he welding pa ame e s a e hei know-how. The asyme ici y o he aus eni e g ain dis ibu ion in HAZ in o a y symme ical model ( ig.3) occu s in he a eas whe e he ends o o iginal beads we e ewelded by abou 10 mm. Figu e 4 displays he de ails o g ain coa seness in HAZ on he bounda y o he second and hi d weld bead. 81 Sou ce: [10] Fig. 3: The esul s o compu ing g ain size in HAZ a e welding (S304H) Sou ce: Own Fig. 4: De ail De ails o g ain coa seness in HAZ a e welding on he bounda y o he second and hi d weld bead (S304H) Following he eal-li e welding expe imen , he compu ed da a o he g ain size and he eal- li e g ain size o med in HAZ we e compa ed. Speci ically poin s 0.5; 1; 1.5; 2; 2.,5; 3 and 5 mm om he mel ing bounda y (MB) we e compa ed. Table 3 shows he compa ison o he g ain size esul s compu ed nume ically and o med expe imen ally. 82 Tab. 3: Compa ison o he g ain size esul s compu ed nume ically and o med expe imen ally Dis ance om he MB [mm] 0.5 1.0 1.5 2.0 2.5 3.0 5.0 Middle g ain size [mm], expe imen 0.0880 0.0845 0.0272 0.0239 0.0209 0.0190 0,0207 Numbe o g ains in 1 mm2, expe . 129 140 1348 1749 2289 2752 2325 G ain size numbe G, expe . G4 G4 G7 G8 G8 G8 G8 Middle g ain size [mm], compu a ion 0.0539 0.0512 0.0296 0.0243 0.0204 0.0204 0.0204 Numbe o g ains in 1 mm2, comp. 344 381 1141 1693 2403 2403 2403 G ain size numbe G, comp. G5 G5 G7 G8 G8 G8 G8 Sou ce: Own Conclusion The compu a ional p og am module o he de e mina ion o g ain size using he Sysweld p og am was de eloped as a ma ginal module, mainly mean o public pu poses. Howe e , we can now see an inc easing demand o his ype o simula ion compu a ion. Tha is why one o he aims o he TA02010992 p ojec is he alida ion and, i necessa y, he modi ica ion o his p og am module, hus he p edic ed alues o aus eni ic g ain size a e welding o hea ea men co espond o he eal si ua ion. The mos impo an aspec is he op imiza ion o he HAZ esul s, because he p ocesses a e e y dynamic he e and hus we can expec in ensi e g ain g ow h in ha a ea. F om Table 3 i is e iden ha he p edic ion o aus eni ic g ain size using ma hema ical models e lec s he eali y e y well. This close ag eemen is especially e iden a 1.5 mm om he mel ing bounda y. In he a ea wi h he highes he mal g adien s o he a ea 1.5 mm om he mel ing bounda y, he g ains p edic ed by simula ions (G5) a e smalle han hose de e mined expe imen ally (G4). This disc epancy is p obably caused by he compu a ional p og am module design, which, a p esen , makes i impossible o inse he inpu da a in he o m o empe a u e dependency. This pa icula inaccu acy could also be caused by he g ain size de e mina ion me hod acco ding o CSN EN ISO 643 s anda d. Acco ding o his no m, he g ain size is de e mined a he de ined su ace. The e is i egula empe a u e dis ibu ion in he HAZ o he weld and he g ain size dec eases as he dis ance o he mel ing bounda y inc eases. Howe e , he e a e no s anda d ins uc ions o p edic ing g ain size in he HAZ and hus he selec ed me hod p o ides he mos ele an esul s. Acknowledgemen s The a icle was p epa ed wi hin he scope o he TA02010992 g an p ojec . Li e a u e [1] SHINGLEDECKER, J.P.; MAZIASZ, P.J.; EVANS, N.D.; POLLARD, M.J.: Alloy addi ions o imp o ed c eep- up u e p ope ies o a cas aus eni ic alloy. P oceedings o he Con e ence o C eep De o ma ion and F ac u e, Design, and Li e Ex ension, The Ma e ials Socie y, Wa endale, PA, 2005, pp. 129-138. 83 [2] PRABHA, B.; SUNDARAMOORTHY, P.; SURESH, S.; MANIMOZHI, S.; RAVISHANKAR, B.: S udies on S ess Co osion C acking o Supe 304H Aus eni ic S ainless S eel. Jou nal o Ma e ials Enginee ing and Pe o mance. Decembe 2009, Volume 18, Issue 9, pp 1294–1299. [3] TOHYAMA, A.; HAYAKAWA, H.; MINAMI, Y.: De elopmen o high s eng h s eel boile ube (TEMPALOY AA-1). NKK Technical e iew, No. 84, 2001, p. 30-35. [4] SAWARAGI, Y.; OGAWA, K.; KATO, S.; NATORI, A.; HIRANO, S.: De elopmen o he economical 18-8 s ainless s eel (SUPER 304H) ha ing high ele a ed empe a u e s eng h o ossil i ed boile s. The Sumi omo sea ch, No. 48, 1992, pp. 50-58. [5] ZÖLLNER, D.; STREITENBERGER, P.: Th ee-dimensional no mal g ain g ow h: Mon e Ca lo Po s model simula ion and analy ical mean field heo y. Sc ip a Ma e ialica 54. 2006, pp 1697–1702. [6] CABRILLAT, M.T.; ALLEGRE, P.; PLUYETTE, E.; MICHEL, B.: In e g anula ehea c acking in S 304H componen s. Expe imen s and damage e alua ion. T ansac ions, SMiRT 16, 2001. [7] ZÖLLNER, D.; STREITENBERGER, P.: Mon e Ca lo Po s Model Simula ion and Mean-Field Theo y o No mal G ain G ow h. Shake Ve lag GmbH, Ge many, 2006, 170 p. [8] KHZOUZ, E.: G ain G ow h Kine ics in S eels. A Majo Quali ying P ojec Repo . Wo ces e poly echnic ins i u e, Ap il 2011, 144 p. [9] MORAVEC, J.; NOVÁKOVÁ, I.: Measu emen o aus eni ic g ain size by S304H s eel.Technical epo TUL-Z-12-VZ-03. 2012, 8 p. [10] SLOVÁČEK, M.; TEJC, J.; KOVAŘÍK, J.; BEJVL, J.; RICHTER, T.; VANĚK, M.: De elopmen and alida ion o ma e ial models, cu en s a e cha ac e iza ion. Technical epo Mecas ESI M_Z_12_024_R01. 2012. 44 p. [11] CENGYU, CH.; HONGYAO, Y.; JIANXIN, D.; XISHAN, X.; ZHENGGIANG, C.; XIAOFANG, CH.; FUSHENG, L.: S eng hening e ec o Cu- ich phase p ecipi a ion in 8C 9Ni3CuNbN aus eni ic hea - esis ing s eel. Ac a Me allu gica Sinica (Engl. Le .) Vol. 24, Ap il 2011, pp 141–147. Ing. Ja omí Mo a ec, Ph.D.; Ing. Jose B adáč, Ph.D.; Ing. I a No áko á, Ph.D.; doc. Ing. Heinz Neumann, CSc.