Modeling of Precipitate Formation in Continuous Steel Casting

Transcription

1 ANNUAL REPORT 27 UIU, June 12, 27 Modelng of Precptate Formaton n ontnuous Steel astng Kun Xu (PHD Student) & Bran G. Thomas Department of Mechancal Scence and Engneerng Unversty of Illnos at Urbana-hampagn Introducton: Transverse cracks Wdespread crazng and fne transverse cracks at oscllaton marks on the as-cast surface of a lne ppe steel slab (top sde). astng drecton Reference:E. S. Szekeres, A Revew of Strand astng Factors Affectng Transverse rackng, Proceedngs of the 6 th Internatonal onference on lean Steel, Balatonfüred, Hungary, 1-12 June 22. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 2

2 Effect of oscllaton marks on gran sze mold gap Steel shell Molten steel pool Larger grans beneath depressons & oscllaton marks Due to: * more heat flow resstance across gap * hgher shell temperature * faster gran growth auses: * Tensle stran concentraton area * Make hot grans actually algn Secondary recrystallzaton blown grans * Embrttled wth large numbers of fne precptates at the weak gran boundares cracks open up along boundares transverse cracks Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 3 The formaton of surface cracks & ntrde embrttlement STAGE I - Normal soldfcaton on mold wall. Surface grans are small but hghly orented. STAGE II - Surface grans blow locally due to hgh temperature (>135 o ) and stran, especally at the base of deeper oscllaton marks. γ γ γ γ γ γ STAGE III - Ntrde precptates begn to form along the blown gran boundares. Mcrocracks ntate at weak boundares. STAGE IV - Ferrte transformaton begns and new precptates form at boundares. Exstng mcrocracks grow & new ones form. STAGE V - At the straghtener, mcrocracks propagate and become larger cracks, prmarly on top surface of the strand. Reference:E. S. Szekeres, 6 th Internat. onf. on lean Steel, Balatonfüred, Hungary, June 22. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 4

3 Project Overvew Temperature & Phase fracton --- ON1D Amount of precptates --- Equlbrum precptaton model Sze dstrbuton and volume fracton of precptates --- Knetc model for precptate growth Gran sze of steel matrx --- Gran growth model evolvng wth tme, temperature hstory and precptates constrant Stress and stran analyss concernng effects of gran sze and precptates accumulatng on the gran boundares --- stress analyss Fnal goal: Predct ductlty problem and transverse cracks Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 5 Equlbrum precptaton model Two common methods for precptate calculaton: Free energy and solublty product. We choose solublty product: more accurate from drect measurements x[ M] + y[ N] MxNy eg. [ Nb] + [ N] NbN x y [ am] [ an] Defne solublty product KMxN = y amxny The actvty of pure M x N y s unty. For low alloy steels, actvty~concentraton. Solublty product Expermental measurements The crteron for precptaton formaton x KM [ % (, )] [ % (, )] xn = wt M x t wt N x t y A log KMxN = + B y T x y [ wt% M ( x, t)] [ wt% N( x, t)] > K M N x y y Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 6

4 Precptates ncluded n the model (oxdes and sulfdes) Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 7 Precptates ncluded n the model (ntrdes and carbdes) Dfferent phases have dfferent crystal structures and thus dfferent solublty lmts. Generally, solublty product n lqud s 1 tmes that n austente and 1 tmes that n ferrte. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 8

5 Mutual solublty of precptates If two precptates have the same crystal structures and close lattce parameters, they wll mutually dssolve and form mxture precptates of unform composton For example, NbN and AlN are mutually exclusve [ wt% Nb][ wt% N]/ xnbn = KNbN [ wt% Al][ wt% N]/ xaln = K AlN x = 1, x = 1 NbN and TN are mutually dssolved [ wt% Nb][ wt% N]/ xnbn = KNbN [ wt% T][ wt% N]/ xtn = KTN x NbN NbN + x = 1 TN AlN Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 9 Groups of precptates TN, T, NbN, Nb, VN, V (f.c.c structure) Expermental valdaton (lattce msmatch ~7.92%) Al 2 O 3, T 2 O 3 (hexagonal structure) lattce msmatch ~8.6% MgO, MnO (f.c.c structure) lattce msmatch ~5.54% MnS, MgS(f.c.c structure) lattce msmatch ~.38% TS(trgonal structure) T 4 2 S 2 (hexagonal structure) AlN(hexagonal structure) BN (hexagonal structure) r 2 N (hexagonal structure) More data about solublty products of precptates n dfferent phases are stll needed Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 1

6 Precptate conservaton equatons to solve P precptates need P equatons for solublty product lmt M alloyng elements need M-1 equatons for chemcal reacton between any two elements Q groups of mutually soluble precptates need Q equatons for constrant of the mutually soluble coeffcents 1 fnal equaton s requred for dstrbuton of weght rato among all groups of precptates P+M+Q = total equatons to solve at each step For current system, P=17, M=12, Q=4 33 equatons totally Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 11 Equatons for solublty product lmt (P) g For each mutually soluble precptate group, such as TNbV(N) TNbVN [ T][ N] [ T][ ] [ Nb][ N] [ Nb][ ] [ V][ N] [ V][ N] = K K K K K K gtnbvn If [ T][ N] KTN [ T][ ] K T N f TN f T If g TNbVN < 1 w TNbVN = ftn N ft fnbn N fnb fvn N fv TN T NbN Nb VN V 1 x = TN x = T [ Nb][ N] K NbN [ Nb][ ] K Nb N f NbN f Nb xtn + xnbn + xvn + xt + xnb + xv 1= x = NbN x = Nb [ V][ N] K VN [ V][ ] K xtn = xnbn = xvn = xt = xnb = xv = 1/6 V N f VN f V x = VN x = V Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 12

7 Equatons for chemcal reacton (M-1) To judge whch element really forms precptates and can be used to calbrate the reacted amounts of other elements Judge domnant group of precptates (from the maxmum values of all g ) g g TNbVN rn ftn N ft fnbn N fnb fvn N fv [ T][ N] [ T][ ] [ Nb][ N] [ Nb][ ] [ V][ N] [ V][ N] = K K K K K K frn [ r][ N] N = K rn TN T NbN Nb VN V If max(g )=g TNbVN, g AlN, g BN or g rn and N hoose N as the standard to calbrate the amounts of other elements If max(g )=g TNbVN and N =, If max(g )=g MnMgS, g TS or g TS and S S If max(g )=g AlTO or g mnmgo and O O Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 13 Remanng precptaton model equatons onstrants for mutually soluble coeffcents (Q) xtn + xnbn + xvn + xt + xnb + xv 1= xalo + xto 1= xmno + xmgo 1= x + x 1= MnS MgS Dstrbuton of weght ratos among all groups of precptates (1) wtnbvn + walto + wmnmgo + wmnmgs + wts + wts + waln + wbn + wrn 1= Sde constrants for all parameters [ M] M x MX 1 1 w for all alloyng element concentratons for all coeffcents of mutually soluble groups of precptates for weght ratos of each group of precptates Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 14

8 Precptate model calculaton procedure Put the ntal concentraton of elements to calculate g If all g 1, then there s no precptaton formng If any one of the g >1, the ntal guess s needed If there s the frst place when precptates form, use some method to gve the approxmate values as the ntal guess For the below temperature, the ntal guess for the current temperature s the fnal results of the last step at hgher temperature Loop untl all equatons converge to zero ompute all g and fnd ther maxmum ompute the values of functons F and ts gradent A 1 alculate the Newton step s = A F and update values of all parameters Add sde constrant and check f the value of norm(f,nf) decreases If yes, contnue next teraton; f not, dvde Newton step by two and repeat untl norm(f,nf) decreases Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 15 Valdaton: a sngle precptate NbN n γ phase Mnmum temperature of complete dssoluton Only Nb and N n Fe Effect of Nb on solublty of.2% N n austente Analytcal soluton exsts At hgh temperature when Nb N K NbN no precptate At low temperature when Nb N > KNbN 2 ( MNbN MN Nb) + ( MNbN MN Nb) + 4MNbMN KNbN [ N] = 2M Nb 2 ( M N M Nb) + ( M N M Nb) + 4M M K [ Nb] = 2M Nb N Nb N Nb N NbN N Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 16

9 Sze dstrbuton and mcrograph of ntrde precptates n steel Small AlN partcles Precptates nucleate and grow n the lqud, durng soldfcaton, on the gran boundares and nsde the grans. The sze dstrbuton and composton of precptates can evolve wth temperature and tme. Reference: J. A. Garrson, Alumnum ntrde precptaton behavor n thn slab materal, AIST 25 proceedng, Volume II, June 22. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 17 Precptates form n dfferent stages Dfferent sze peaks shows that precptates form n dfferent stages 1). Formng n the lqud (most possbly float nto the top slag to be removed) 2). Formng between the dendrte arms (durng soldfcaton) 3). Formng n the sold (remanng precptates) 1. If there are precptates formng n the lqud, calculate amounts of precptates and choose dssolved concentraton at the lqudus temperature T lq as the ntal concentraton for the next calculaton durng soldfcaton 2. alculate the amounts of precptates formng durng soldfcaton whch depends on the segregaton model chosen. At soldus temperature T sol, subtract the alloys mass ncluded n the precptates form from the ntal concentraton at T lq to get the new ntal concentraton for the next calculaton n the sold 3. Use the new ntal concentraton to calculate the precptates n the sold, the solublty product s the combnaton of those n ferrte and austente Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 18

10 Precptaton model durng soldfcaton Precptaton model needs: Segregaton model Precptate accumulaton method omparson of segregaton models Schel equaton (no dffuson n sold) Lever rule (complete dffuson n sold) Smple segregaton model (part backward dffuson n sold) Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 19 Dfferental segregaton models and valdaton Dfferental Level rule + 1 L = [1 + ( k 1) f ] + S + 1 [1 ( k 1) fs ] L k=.3 Dfferental Schel model + 1 L 2 (2 k) fs kf = 2 kf (2 k) f s + 1 s + 1 s If no precptaton, dfferental form must gve the same result as the ntal equatons L L, =, /[1 + ( k 1) fs] (1 ) L, =, fs k 1 Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 2

11 Incremental model to accumulate precptates formng durng soldfcaton m n total Lpre, = ΔmLpre, = 1 For each step, for sold fracton: Knowng 1 Lds, for each alloy get segregated concentraton for current step Lseg, from dfferental segregaton model get dssolved concentraton Lds, from equlbrum precptaton model (use Lseg, us ntal concentraton for current step) calculate the amount of each precptate formng n ths step, 1 Δ mlpre, = ( Lseg, Lds, )[1 fs+ 1/2( fs f S )] Sum up contrbutons from all steps to get total amount of each precptate Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 21 Valdaton of precptaton model durng soldfcaton Smple case: Dssolved concentraton decreases from at lqudus temperature to /2 at soldus temperature Lds, = and fs = ( = 1, 2,..., n) 2 n n Dfferental Lever rule 1 [1 + ( k 1) fs ] 1 Lseg, = Lds, [1 + ( k 1) fs ] Dfferental Schel model 2 (2 k) f kf 1 = s s 1 Lseg, 1 Lds, 2 kf s (2 k) fs Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 22

12 onvergence study Lever rule Schel model Decreasng k ncreases the numercal error for fxed number of steps n Generally, for typcal values of k~.1, n=1 gves enough accuracy Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 23 Valdaton of precptaton model durng soldfcaton (AlN case) 55%.11 wt% Al,.9 wt% N k Al =.6, k N =.27 45% T lq = o, T sol =151.5 o Dfferental Schel model No AlN formng n the lqud Weght of AlN formng durng soldfcaton s AlN begn to form at around 153 o Maxmum possble amount of AlN s.167, and the percent of AlN durng soldfcaton s 4.1%. Possble reasons (knetc consderaton): The remanng AlN should stay dssolved untl 16 o n the sold. At ths low temperature, the nucleaton and growth of new AlN partcles n the sold s slow. However, the AlN partcles already present (from soldfcaton) can grow quckly. Fnally, the new nucle form n the sold at lower temperature, grow slowly from the small fracton of Al and N remanng. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 24

13 Valdaton of precptaton model n all three stages For an ndustral steel 16 Name % %Mn %S %T %Nb %V %B %N Partton coeffcent ~ Precptates TN, T, NbN, Nb, VN, V, BN wll form Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 25 Temperature hstory from ON1D (Shell surface) Mold length:.95m Temperature ( o ) 12 astng velocty V=3.7m/mn Start of frst spray zone:.85m 1 End of last spray zone: 11.25m Dstance from menscus (m) Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 26

14 Phase fractons from ON1D 1..8 T lq =1524. o Phase fracton.6.4 Lqud Delta ferrte Austente Alpha ferrte T sol = o No precptates form n the lqud due to the hgh solublty lmt Temperature ( o ) Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 27 Precptates formaton durng soldfcaton Dfferental Schel model % N =.1;% =.6;% T =.15;% Nb =.15;% V =.4;% B =.6 Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 28

15 Solublty products n the sold α α + γ γ δ γ + δ K( T) = f ( T) K ( T) + f ( T) K ( T) + f ( T) K ( T) δ δ γ γ α α Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 29 Precptates formaton n the sold The remanng element concentratons n the sold after soldfcaton % N = ;% = ;% T = ;% Nb = ;% V = ;% B = Startng from soldus temperature o Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 3

16 Precptates for 16 steel (3.7m/mn) Temperature TN Nb BN NbN % N =.1;% =.6;% T =.15;% Nb =.15;% V =.4;% B =.6 Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 31 onclusons 1) The hgher temperature and lack of precptate formaton are lkely the controllng factors n susceptblty to cracks especally at oscllaton mark roots 2) The precptates can form n the three stages (n the lqud, durng soldfcaton and n the sold). Ths causes dfferent appearng locatons (removed from lqud, between dendrtes, on the gran boundary or nsde the gran) and dfferent number and sze dstrbutons. These dfferences have mportant nfluences on the qualty of fnal products. 3) A system of nonlnear equatons s establshed to calculate equlbrum dssolved concentraton and precptates amount for a gven ntal concentraton and set of solublty products. 4) A method s suggested to calculate the amounts of precptates n the dfferent stages, especally these formng due to segregaton durng soldfcaton. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 32

17 onclusons 5) onsder and separate precptates n dfferent stages (n the lqud, durng soldfcaton and n the sold) can explan mostly observed multple peak sze dstrbuton of the precptates n experments. Knetcs model should be ntroduced to valdate these sze measurements. 6) Among ntrdes and carbdes, TN s the most stable precptate due to ts lowest solublty lmt. BN s another mportant ntrde f there are enough remanng free ntrogen avalable n the steel. After ntrogen s combned wth other more stable ntrdes and there s always plenty of free carbon, Nb wll become more mportant because of the low rato of solublty products of carbde to ntrde of Nb and ts mutual solublty wth the more stable TN and NbN partcles. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 33 urrent work for precptates knetcs Add actvty coeffcents nfluence nto consderaton K MxNy x [ am] [ an] = a MxNy y Where [% ] j a and = f log f e[% ] e [% j] Generally, nteracton coeffcents of as affected by the alloyng element j e are functons of concentraton and temperature, so we need update the values of these coeffcents durng each teraton n calculaton = + Partcle coarsenng knetcs (Wagner equaton) ' 3 3 8γ DV m m m r r = t 9RT Assumpton: Volume fracton s almost constant. Equaton s only appled when peak temperature s well below the equlbrum solvus of the precptates. Partcles sze groupng model: supersaturaton effect ncluded and no assumpton of constant volume fracton Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 34 j

18 Knetc model for gran growth Drvng force for gran growth Zener retardaton pressure Gran growth model P Z 2 γ P G = 3 D 3 f = γ 4 r W: secondary coolng ntensty Q app dd * 1 1 f = M exp dt RT D k r (1/ n 1) The change of depth of oscllaton marks nfluences the temperature hstory at these locatons. Larger depth causes hgher temperature and thus larger gran sze beneath oscllaton marks. Reference:. Bernhard, J. Reter, Smulaton of austente gran growth n contnuous castng, AISTech 27. Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 35 The nfluence of growng precptates on the gran growth Gran growth model n the presence of growng precptates Q app dd * 1 1 f = M exp dt RT D k r (1/ n 1) t 2 * exp Qapp I1 = M dt t1 RT t 2 1 Q 2 1 exp( s I = c ) dt t1 T RT D r = k f Lm k I m = f I 2 1 Update the f / r value for the growng precptates for each step Some parameters to ft gran sze for manly T-mcroalloyed or Nbmcroalloyed steels are gven, but the nfluence of combned effect of many alloyng elements stll needs more work onstant volume fracton f for precptate Reference: I. Anderson, O. Grong, Acta Metall. mater. Vol. 43, No. 7, pp , Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 36

19 Future work 1) onsder knetc model to analyze the volume fracton and sze dstrbuton of the precptates formng n dfferent stages 2) Wth the knowledge of the temperature and precptaton hstory, use the gran growth model to smulate the gran sze evolvng wth tme, especally larger grans beneath oscllaton marks 3) onsder the relaton between the tensle stress (or stran) and the gran sze, and the nfluence of precptates on the ntergranular fracture ( transverse cracks) Ductlty problem Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 37 Acknowledgement ontnuous astng onsortum Members (Nucor, Postech, LWB Refractores, Algoma, orus, Laben, Mttal Rverdale, Baosteel, Steel Dynamcs) Prof B. G. Thomas Other graduate students n the lab Thank you for attendance! Unversty of Illnos at Urbana-hampagn Metals Processng Smulaton Lab Kun Xu 38