The Model and Numerical Analysis of Hardening Phenomena for Hot-work Tool Steel

Transcription

1 R C H I V E S o f F O U N D R Y E N G I N E E R I N G Publishd quarrly as h organ of h Foundry Commission of h Polish cadmy of Scincs ISSN ( ) Volum 14 Scial Issu 3/ /3 Th Modl and Numrical nalysis of Hardning Phnomna for Ho-wor Tool Sl. Booa *,. Kulawi, R. Szymczy, J. Wróbl Insiu of Comur and Informaion Scincs, Czsochowa Univrsiy of Tchnology, Dąbrowsigo 73, Częsochowa, Poland *Corrsonding auhor. addrss: booa@icis.cz.l Rcivd ; accd in rvisd form bsrac In h ar h comlx modl of hardning of h ho-wor ool sl is rsnd. Modl of simaion of has fracions and hir inics is basd on h coninuous cooling diagram (CCT). Phas fracions which occur during h coninuous haing and cooling (ausni, arli or baini) ar dscribd by Johnson-Mhl-vrami-Kolmogorov (JMK) formula. To drmin of h formd marnsi h modifid Koisinn-Marburgr (KM) quaion is usd. Th srsss and srains ar calculad by h soluion of quilibrium quaions in h ra form. Modl as ino accoun h hrmal, srucural, lasic srains and ransformaion lasiciy. Th hrmohysical roris occurring in h consiuiv rlaions ar dndn on has comosiions and mraur. To calcula h lasic srains h Hubr-Miss lasiciy condiion wih isooic hardning is usd. Whras o drmin ransformaions inducd lasiciy h Lblond modl is alid. Th numrical analysis of has comosiions and rsidual srsss in h ho-wor sl lmn is considrd. Kywords: Ha ramn, Ho-wor ool sl W360, Phas ransformaion, Srsss, Thrmo-lasic-lasic fini lmn analysis 1. Inroducion Th ha ramn of ho-wor ool sl is a chnological rocss, in which hrmal hnomna, has ransformaions and mchanical hnomna ar dominan. Modls, which dscrib rocsss mniond abov, don a ino considraion h many imoran ascs. s a rsul of h comlxiy of hnomnon of ha ramn rocss, hr ar many mahmaical and numrical difficulis in is modlling. For his rason hr hasn' a modl which includ hnomnon accomanying ha ramn and hardning [1-4]. Th corrc rdicion of h final roris of hardning lmn is ossibl afr dining h y and h rory of h nascn microsrucur of h sl lmn in h rocss of haing, and hn in h qunching. Rcnly, in many rsarchs hav bn mad h analysis of qunching rocss wih using h fini lmn simulaion chniqu [2,3,5-7]. In his ar h numrical modl of has ransformaion such as JMK modl for h diffusional ransformaion and modifid KM modl for h diffusionlss ransformaion wr mloyd o invsiga a has fracions during h haing and qunching rocss. [2,4,8]. Rrsning of mchanical hnomnon in rocss of ha ramn ar mainly srss and hir drminaions. This valus ar dnd on accuracy comuing mraur filds and on inics of has ransformaions in solid sa. Th inics of has ransformaions has significan imac on morary R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 4, S c i a l I s s u 3 / ,

2 srsss and hn on rsidual srsss [2,5,6,9]. Numrical simulaions of sl hardning rocss nd hror o includ hrmal, lasic, and srucural srains and ransformaions inducd lasiciy. Inclusion of ransformaion lasiciy has a influnc on disribuions and xrm valus of srsss in h simulaion of h hardning [2,5,10-12]. To imlmn his y of algorihms on usually alis h FEM, which mas i ossibl o a ino accoun boh nonlinariis and inhomogniy of hrmally rocssd marial [2,6,7,13]. 2. Mahmaical and numrical modls Th filds of mraur ar drmind from ha ransfr quaion: marnsi ransformaion amoun M s =548 K, and final mraur of ransformaion is qual M f =123 K [14,16]. Lan ha, which was gnrad du o has ransformaions, causd h incras of h mraur of h rad marial. This inrnal ha sourc could b an ino accoun by nhaly changs. Thror, h following nhaly changs for h diffusional and diffusionlss ransformaions wr usd ([J/m 3 ]) [2,4,6,16]: H B 31410, H M 63010, H P (4) whr H B, H M and H P indica h nhaly changs during ausni-baini, ausni-marnsi and ausni-arli ransformaions, rscivly. div T (1) v gradt C Q, T T x, whr =(T) is h ha conduciviy coficin, C=C(T) is an fciv ha caaciy, Q v is innsiy of inrnal sourcs in which h ha of has ransformaions ar an ino accoun, x ar h coordinas and is im. Surficial haing and cooling ar ralisd in h modl by h Nwon boundary condiion wih convcion coficin dndn on mraur [2,3,6]: T T qn T T (2) n whr (T) is h ha ransfr coficin, is surfac, from which h ha is an ovr, T is mraur of h mdium roundd. In h modl of has ransformaions h coninuous cooling diagram (CCT) is usd (Fig. 1) [14,15]. Th has fracions, which ransformd during coninuous haing and cooling, ausni, arli or baini ar drmind in modl by JMK formula. Th fracion of h formd marnsi is calculad using h modifid KM formula [2,6,16]: ~, M, 1 x(, n s f T b s f T, haing n T, m 1 x b ( T ), cooling m T 1 x M T / M M, cool. BP m s whr ~. ~ ~ ~ for. and m for. s m, is maximal has fracion for sablishd cooling ra simad on h basis of CCT diagram, b( s, f ) and n( s, f ) ar coficins calculad assuming h iniial fracion ( s ( s )=0.01) and h maximum valu of fracion ( f ( f )=0.99), ~ is h fracion of forming ausni afr haing, m is a consan from xrimn; for considrd sl m = 3.5, h sar mraur of f (3) Fig. 1. Th Tim-Tmraur-Transformaion grah (CCT) for ools sl W360 [8,9] Ha of has ransformaions is an accoun by h volumric ha sourc in h conduciviy quaion (1) and is calculad wih h formula [6,16] Q v Q h Q H, (5) whr H is volumric ha (nhaly) - has ransformaions, is h ra of chang - has fracion. Fig. 2. Simulad dilaomric curvs (s Fig. 1) 10 R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 4, S c i a l I s s u 3 / , 9-1 4

3 For h xamind sl, valus of hrmal xansion coficins and isoroic srucural srains of ach microconsiuns wr drmind. Thy qual: 22, 12.5, 12.5 and 14.7 (10-6 ) [1/K] and 1.8, 6.0, 8.5 and 2.53 (10-3 ) for ausni, baini, marnsi and arli rscivly [2,6,16]. Th xaml of h rsuls of h simulaions comarisons ar rsnd h figur 2, h inic of ransformaions sablishd cooling ra (h avrag cooling ra in h rang of o C [14]) ar rsnd on h figur 3. Fig. 3. Th inic of ransformaions for sablishd cooling ra Th simulad dilaomric curvs wr obaind by solving h incrmn of h isoroic srain ( Th ) in h rocsss of haing and cooling [6,16]. Coficin of hrmal xansion of h arli srucur for considrd sl is assumd as dndn on mraur (s Fig. 2), aroxima his coficin by squar funcion [16]: P T T T (6) Th quilibrium quaion and consiuiv rlaions ar usd in ra form [2,16], i..: T, 0, σ σ, σ D ε D ε divσ x (7) whr =( ) is srss nsor, D=D(,E) is h nsor of marial consans (isoroic marials), is Poisson raio, E=E(T) is h Young s modulus, howvr ε is nsor lasic srains. Th quaion (7) is comld by iniial condiions σ x, 0, ε x 0 0, 0 (8) and boundary condiions which rovid xrnal saically drmina. Toal srains in h around considrd oins ar rsul of h sum: ε Th ε ε ε ε (9) whr Th ar isoo of mraur and srucural srains, ar ransformaions lasiciy, and ar lasic srains. For h Hubr-Misss lasiciy condiion h flow funcion (f) hav h form [2,5,7,16]: T, Y T, 0 f Y 0 (10) whr is fciv srss, is fciv lasic srain, Y is a lasicizd srss of marial on h has fracion () in mraur (T) and fciv srain ( ): Y T Y T, Y0 Y0 T Y T (11), 0 H, Y Y 0 Y0 0 T h mraur and h has fracion, howvr Y Y T, is a yild oins of marial dndn on H is a surlus of h srss rsuling from h marial hardning. Using h Lblond modl, comld by dcrasing funcions 1 which has bn roosd by h auhors of h wor [2,5,11,12], ransformaions lasiciy ar calculad as following: 0, dla 0.03, ε 3 5 h S 1 ln, dla (12) Y1 h whr 3 1i ar volumric srucural srains whn h marial is ransformd from h iniial has 1 ino h -has, Y 1 is a acual yild oins of has ouu (in cooling rocss is ausni). Th quaions (7) ar solvd by using h FEM [13,16]. Th sysm of quaions usd for numrical calculaion is: Th K U R (13) whr K is h lmn siffnss marix, U is h vcor of nodal dislacmn, R is h vcor of nodal forcs rsuling from h boundary load and h inrial forcs load, Th is h vcor of nodal forcs rsuling from hrmal srains and srucural srains, is h vcor of nodal forcs rsuling from h valu chang of Young s modulus dndn on h mraur, is h vcor of nodal forcs rsuling from lasic srains and ransformaion lasiciy. Th final dislacmns, srains and srss ar rsuling ingraion wih rsc o im, from iniial = 0 (s (8)) o acual im, i.. U ε x, U x, 0 x, ε x, d, σx, σ x, 0 d 0 d H (14) R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 4, S c i a l I s s u 3 / ,

4 Th ra vcors of loads in h bracs in (13) ar calculad only onc in h incrmn of h load, whras h vcor is modifid in h iraiv rocss [12]. In h iraiv rocss of valuaion of lasic srains, h modifid Nwon-Rahson algorihm is usd [13,17]. 3. Examl of numrical calculaions To hardning simulaion h axisymmric lmn wih dimnsions mm was usd (Fig. 4). Numrical simulaions of hardning of h lmns mad of h ho-wor ool sl W360 wr rformd. Fig. 5. Disribuions of mraur a) and ausni b) afr haing. Isolins wih valus 1033 and 1133 K, ar h mraur of c1 and c3 arorialy Hardnd zons in h cross scions of h lmn ar rsnd in figurs 6 and 7. Disribuions of h simulad fracions in h cross-scion - (Fig. 4) afr hardning ar rsnd in figur 8. Fig. 4. Th schm of h sysm and boundary condiions I was assumd ha hardnd lmn has h mraur qual 300 K and h ouu srucur is arli (divorcd arli). Th lmn was haing in h fluidizd bd wih mraur 1600 K. Th hrmohysical coficins C and wr assumd as consans: J/(m3K) and 32 W/(mK). Ths ar h avrag valus calculad on h basis of h daa in h wor [14]. Th ha ransfr coficin of h fluidizd bd assumd consan (indndn of mraur) and qual 2400 W/(m2K). On h fron surfac of had lmn h ha ransfr coficin had h valu 1200 W/(m2K). By using hs valu of coficin h difficul (wors) flow around a fluidizd bd on h fron of surfac of lmn was an ino accoun [18]. Th simulaion of haing was coninuing o obain h maximum mraur 1350 K in surroundings of oin 1 (Fig. 4). Th mraurs c1 and c3 in h has ransformaions of haing (inu srucur - ausni) wr qual 1033 and 1133 K arorialy (Fig. 1) [14]. Th obaind mraur disribuion and ausni zon afr finish of haing ar rsnd in figur 5. Th cooling was modlld wih h Nwon condiion and h xrm of ha ransfr coficin assumd qual 20 W/(m2K) (cooling in h air [14]). Th mraur of h cooling mdium qualld T =300 K. 12 Fig. 6. Disribuions of baini a) and marnsi b) afr cooling Fig. 7. Disribuions of raind ausni a) and arli b) afr cooling RC HI VE S of F OUN DR Y EN GI NE ER ING V ol u m 1 4, S c i al Iss u 3 / , 9-1 4

5 Fig. 8. Hardnd zons in h cross scions (Fig. 4) Fig. 10. Rsidual srsss: radial a) and shar b) Young s and angnial modulus (E and E) wr dndn on mraur, whras h yilds srss (Y0) was dndn on mraur and has comosiion. ssumd, ha Young s and angnial modulus ar qual and MPa (E=0.05E), yild oins 150, 500, 1000 and 300 MPa for ausni, baini, marnsi and arli, rscivly, in h mraur 300 K. In h mraur of solidus Young s modulus and angnial modulus qualld 100 and 10 MPa, rscivly, whras yild oins qualld 5 MPa. Ths valus wr aroximad wih h us of squar funcions using h following assumions basd on h wor [5,6,16]. Obaind from simulaions rsidual srsss disribuions afr hardning ar rsnd in figurs Fig. 11. Rsidual srsss: circumfrnial a) and axial b) Fig. 9. Rsidual srsss in h cross scions (Fig. 4) 4. Conclusions Th rsuls of h has ransformaions modl ar saisfacory and confirm h corrcnss of h dsignd modl of has ransformaions for h ho-wor ool sl (Figs 6 and 7). On h basis of simulad dilaomric curvs can s ha h considrd sl is hardnd vry asy. To obain h bainimarnsi srucur h cooling ra can' b grar han 3.2 K/s (s Figs 1,2 and 3). Thror h cooling in h air was alid and h cooling ra was qual 0.24 K/s in h oin 2 (Fig. 4). In h oin 1 h cooling ra was a bi grar and had a valu K/s (s Fig. 1). Fig. 12. Srsss according o h im (oin 2, Fig. 4) Th srsss disribuions afr such hardning ar advanagous. Th rgular disribuions of h srsss ar obaind. Th xrm valus of hs srsss ar accabl. Th dosiion of ngaiv circumfrnial and axial srsss (h mos maningful srsss) is surficial (Figs 9-11), and hir xrm valus ar lowr whn hs srsss ar an ino accoun. Th advrs is h disribuion of h shar srsss (Fig. 10b). Such srsss can b a caus of inrnal cracs in h cooling rocss. I can b claimd ha in h numrical simulaion of such hardning h fac ha ransformaion lasiciy is includd in h modl of mchanical hnomna brings abou h changs in RC HI VE S of F OUN DR Y EN GI NE ER ING V ol u m 1 4, S c i al Iss u 3 / ,

6 obaind rsuls [10,11,16]. Th has ransformaions significanly fc on h changs of h morary srsss (s Fig. 12) and in consqunc on h rsidual srsss afr hardning of h lmn considrd. Rrncs [1] Kang, S.H. & Im, Y.T. (2007). Thrmo-lso-lasic fini lmn analysis of qunching rocss of carbon sl. Innaional Journal of Mchanical Scincs [2] Kang, S.H. & Im, Y.T. (2007). Thr-dimnsional hrmolsic-lasic fini lmn modling of qunching rocss of lain carbon sl in couol wih has ransformaion. Journal of Marials Procssing Tchnology [3] Kulawi,. & Booa,. (2011). Modlling of ha ramn of sl wih h movmn of coolan rchivs of Mallurgy and Marials. 56(2) [4] Ju, D.Y., Zhang, W.M. & Zhang, Y. (2006). Modling and xrimnal vrificaion of marnsiic ransformaion lasic bhavior in carbon sl for qunching rocss, Marials Scinc and Enginring , [5] Cor, M. & Combscur,. (2002). msomodl for h numrical simulaion of h mulihasic bhavior of marials undr anisohrmal loading (alicaion o wo low-carbon sls). Inrnaional Journal of Mchanical Scincs [6] Booa,. & Kulawi,. (2007). Modl and numrical analysis of hardning rocss hnomna for mdiumcarbon sl. rchivs of Mallurgy and Marials. 52(2) [7] Huiing, L., Guoqun, Z., Shaning, N. & Chuanzhn, H. (2007). FEM simulaion of qunching rocss and xrimnal vrificaion of of simulaion rsuls. Marial Scinc and Enginring , [8] Olivira, W.P, Savi, M.., Pachco, P.M.C.L. & Souza, L.F.G. (2010). Thrmomchanical analysis of sl cylindrs wih diffusional and non-diffusional has ransformaions. Mchanics of Marials. 42, [9] Silva, E.P., Pachco, P.M.C.L. & Savi, M.. (2004). On h hrmo-mchanical couling in ausni-marnsi has ransformaion rlad o h qunching rocss. Inrnaional Journal of Solids and Srucurs. 41, [10] Srjzadh, S. (2004). Modling of mraur hisory and has ransformaion during cooling of sl. Journal of Procssing Tchnology [11] Talb, L. & Sidoroff, F. (2003). micromchanical modlling of h Grnwood-Johnson mchanism in ransformaion inducd lasiciy. Inrnaional Journal of Plasiciy [12] Chraoui, M., Brvillr, M. & Sabar, H. (1998). Micromchanical modling of marnsiic ransformaion inducd lasiciy (TRIP) in ausniic singl crysals. Inrnaional Journal of Plasiciy. 14(7) [13] Ziniwicz, O.C. Taylor, R.L. (2000). Th fini lmn mhod. vol. 1,2,3. Burworh-Hinmann, Fifh diion. [14] Warmarbissahl Ho Wor Tool Sl, BOHLER W360, Iso Bloc, [15] Orlich, J, Ros,., Wis, P. (1973). las zur Wärmbhandlung von Sähl, III Zi Tmraur uniisirung Schaubildr, Vrlag Sahlisn MBH, Düssldorf. [16] Booa,. & Domańsi, T. (2007). Numrical analysis of hrmo-mchanical hnomna of hardning rocss of lmns mad of carbon sl C80U. rchivs of Mallurgy and Marials. 52(2), [17] Caddmi, S. & Marin, J.B. (1991). Convrgnc of h Nwon-Rahson algorihm in lasic-lasic incrmnal analysis. In. J. Numr. Mh. Eng [18] Jasińsi, J. (2003). Influnc of fluidizd bd on diffusional rocsss of sauraion of sl surfac layr. Częsochowa: Inżyniria Mariałowa Nr 6, Wydawnicwo WIPMiFS, (in Polish). 14 R C H I V E S o f F O U N D R Y E N G I N E E R I N G V o l u m 1 4, S c i a l I s s u 3 / , 9-1 4