Evolution of artificial defects during shape rolling

Transcription

1 Evoluton of artfcal defects durng shape rollng Mrjana Flpovć Lcentate Thess Royal Insttute of Technology Industral Engneerng and Management Department of Materal Scence and Engneerng Dvson of Mechancal Metallurgy Stockholm 2007

2 Akademsk avhandlng som med tllstånd av Kungl Teknska Högskolan framlägges tll offentlg gransknng för avläggande av teknsk lcentatexamen tsdagen den 24 aprl 2007 kl vd Insttutonen för Materalvetenskap, Kungl Teknska Högskolan, konferensrummet K408, 4:e vånngen, Brnellvägen 23, Stockholm. Fakultetsopponent är Jan-Olov Perä, MEFOS, Box 812, Luleå. ISBN ISRN KTH/MSE--07/12--SE+MEK/AVH Mrjana Flpovć, Mars 2007

3 Abstract Very often defects are present n rolled products. For wre rods, defects are very deleterous snce the wre rods are generally used drectly n varous applcatons. For ths reason, the market nowadays requres wre rods to be completely defect-free. Any wre wth defects must be rejected as scrap whch s very costly for the producton mll. Thus, t s very mportant to study the formaton and evoluton of defects durng wre rod rollng n order to better understand and mnmze the problem, at the same tme mprovng qualty of the wre rods and reducng producton costs. The present work s focused on the evoluton of artfcal defects durng rollng. Longtudnal surface defects are studed durng shape rollng of an AISI M2 hgh speed steel and a longtudnal central nner defect s studed n an AISI 304L austentc stanless steel durng ultra-hgh-speed wre rod rollng. Expermental studes are carred out by rollng short rods prepared wth artefcal defects. The evoluton of the defects s charactersed and compared to numercal analyses. The comparson shows that surface defects generally reduce qucker n the experments than predcted by the smulatons whereas a good agreement s generally obtaned for the central defect. Keywords: shape rollng, wre rod rollng, artfcal defects, defect evoluton, surface cracks, porosty, FEM, hgh speed steel, stanless steel

4 Preface Durng my work wth ths thess, I have receved a lot of help from dfferent people and organsatons, n the form of gudance, fnancng, dscussons and general support. I would lke to express my deepest grattude to all of them: The Swedsh Knowledge Foundaton (KK-Stftelsen), the Swedsh Steel Producers Assocaton (Jernkontoret) and Fagersta Stanless AB for fnancal support. Professor Stefan Jonsson, for supervsng me throughout ths work wth dscussons, comments and help wth wrtng of the thess and the second artcle. My colleagues, both at Dalarna Unversty and Fagersta Stanless AB, for ther contrbuton to a nce workng envronment. I am especally grateful to Dr. Conny Erksson, who has been my supervsor at Fagersta Stanless AB, for all dscussons and nce frendshp. Professor Sven-Erk Lundberg and Dr. Henrk Överstam from Örebro Unversty, for frendly cooperaton durng the work on the frst artcle. Dalarna Unversty and Fagersta Stanless AB, for support wth equpment and personnel durng the experments. My parents and my brother and hs famly for ther endless support and love. My companon n lfe, Nedjo for fllng my lfe wth extraordnary joy. Mrjana Flpovć Borlänge, March 2007 v

5 Contents 1. Introducton Roll pass desgn Am of the work Rollng Heatng Roughng mll, reversng mll and ntermedate tran Wre rod block Fnal treatment Defects Classfcaton Metallurgcal defects Defects from mproper mll practce Cracks and scratches Fns and laps Corner cracks Porosty Defects from mproper roll pass desgn Materals Theoretcal consderatons Evoluton of surface defects Evoluton of nner defects Expermental technques Evaluaton of surface cracks Evaluaton of nner defects Numercal smulatons Materal models Hgh speed steel AISI M Austentc stanless steel AISI 304L FE-smulatons Summary of results Evoluton of surface defects Evoluton of nner defects Conclusons Surface defects Inner defects Suggeston of future work v

6 1. Introducton Hot rollng, usng grooved rolls, s an mportant ndustral method of producng bars and wre rods of round cross sectons. The deformaton process does not only reduce the cross secton and lengthens the rolled bar, t also mproves the propertes, such as strength and toughness, of the prmary cast metal by refnng the gran sze and mprovng homogenety. The stran dstrbuton durng rollng s charactersed by the area-reducton rato, the stran rate and temperature hstory, as well as the chemcal composton of the rolled steel. All of these varables together wth the roll pass desgn have a strong nfluence on the shape and qualty of the fnal product. In many commercal wre rod rollng mlls, the prme concern s to produce an approprate cross-sectonal shape and area rollng as quckly as possble and usng as few passes as possble n order to ncrease market satsfacton and productvty. Dmensonal accuracy and qualty of the wre rod are very mportant, snce these wre rods are normally used drectly n many applcatons. It s thus mpossble to accept products wth any marks, scratches, shells, cracks, overflls or oxde partcles on the surface. Nowadays n the steel ndustry, demands on qualty, dmensonal tolerances and mechancal propertes of the rolled products are ncreasngly becomng more rgorous. In addton, many hgh-alloyed steels have a narrow temperature nterval for rollng. At low temperatures, the flow stress becomes too hgh and the process s lmted by the maxmum rollng force of the mll. At hgh temperatures, on the other hand, there s a rsk of partal meltng n gran boundares because of the ntense deformaton heatng durng rollng. In such cases the bar collapses durng rollng. Thus, n order to control the rollng process, many rollng mlls of today have on-lne gauge measurement systems and on-lne gap adjustng procedures [1]. The mproved process controls of the rollng mlls guarantee that the requred product propertes are met wth a mnmum of scrap producton. In hot rollng of wre rods, the deformaton behavour of the rolled bllets s very complex and because of ths, roll pass desgn s, at present, essentally a traland-error procedure. The pass desgn sequences usually used n mlls are square-oval and false round (round)-oval, but t s also common to use damond-square and damond-damond sequences. As the market demands for hgh qualty wre rod ncreases, t s of great mportance to better understand how defects behave durng rollng and how the roll pass desgn affects the evoluton of defects. As a result, ths thess ncludes an expermental and a numercal analyss of the behavour of surface and nner defects durng hgh speed rollng. 1

7 1.1. Roll pass desgn Roll pass desgn s an mportant feld of rollng mll technology. In bar and wre rod rollng usng grooved rolls, the cross-sectonal area s reduced and the bar s elongated wth large lateral spread. The functon of roll pass desgn s to ensure the producton of the desred shape, good surface wthout any defects and at the lowest possble cost [2]. A good seres of grooves must guarantee stable rollng. The most common pass desgn sequences used n ntermedate mll are squareoval and false round (round)-oval. It s also common to use damondsquare and damond-damond sequences upstream n the rollng mll. In the roughng mll, also box grooves are common. The characterstcs of the squareoval and false round-oval sequences are shown n Fg. 1. False round-oval seres are very popular n contnuous mlls. The reason s that the seres are gentle to the bar and have hgh flexblty. The reducton capacty s lower than for square-oval seres and s usually about 17% per pass, but can be consderably hgher when usng flat ovals [3]. Twstng of the bars s elmnated n ths seres by arrangng the stands n alternatng horzontal and vertcal poston. It could be mentoned that roller gudes are needed for gudng the oval bar nto the false round grooves, see Fg. 1a, b. Fg. 1 Common sequences n wre rod rollng: a) oval-false round, b) false roundoval, c) square-oval and d) oval-square [4]. The square-oval seres are stable and have a relatvely hgh reducton capacty. Average reducton s about 25% per pass. The square s twsted 45 before enterng the oval groove. After reducton, the ovals are turned 90 before enterng the square groove. Ths seres s not recommended for rollng of heavy 2

8 sectons. When a square s twsted 45 before enterng the oval groove, they can become dstorted. In addton, the corner of the square s too sharp to ft n the oval groove, and because of that, the oval grooves are worn out very fast causng hgh cost and extra downtme for roll replacement. Normally, roller gudes are used to stablse the oval bars before enterng the square grooves, see Fg. 1c, d. A specal sequence s round-oval, whch compared to false round-oval gves lower flexblty. Ths pass desgn s commonly used n fnshng rollng sectons such as wre rod blocks. Damond-square, or damond-damond, sequences have lower reducton capacty than the square-oval seres, about 20%. The seres are stable and commonly used n roughng mlls where the bte angle s large [5]. Damondsquare seres are seldom used n rollng because of the hgh rollng force and rsk for bte problems. Even problems wth uneven bar temperature dstrbuton can arse. The corners of the bar are coolng down much faster than the bar sdes and centre causng a rsk for corner cracks due to hgh tensle stresses Am of the work Ths work analyses the wre rod rollng process n order to better understand the behavour of defects durng rollng. Two types of defects are consdered. Longtudnal surface defects and a central longtudnal cavty, the former representng longtudnal surface cracks and the latter a strng of pores. The employed methods nclude both expermental and numercal work n order to allow a comparson between the two methods. In recent years, numercal smulatons tend to replace costly and tme consumng experments. In addton, the numercal analyses present a method of studyng the deformaton behavour n detal, whch s very trcky expermentally. Thus, there s a strong need to valdate the predcted results from calculatons wth expermental nvestgatons. When a numercal method s reproducng the expermental data satsfactorly t s, n prncple, possble to examne the effect of varous process parameters on the qualty of the rolled product. In ths respect the fnal step n wre rod rollng s the man focus snce the largest deformaton rates appear there resultng n the most severe deformaton condtons. The am of ths thess s to nvestgate the evoluton of defects usng 3D FE smulatons of wre rod rollng n a wre rod block usng a FE program MSC.Marc. The most mportant detals and results wll be presented n the thess whereas more precse and detaled nformaton s presented n the appended papers. 3

9 2. Rollng Normally cast bllets of near quadratc cross secton are used as raw materal when a wre s beng produced. At Fagersta Stanless AB, beng studed n the present thess, quadratc bllets of 150 mm 2 cross secton, 6200 mm length and 1050 kg of weght are used. Supplers of stanless steels are generally Outokumpu SMACC, Sheffeld, UK, or AB Sandvk Materals Technology, Sweden. A layout of the rollng mll s gven n Fg. 2. Next, the detals wll be dscussed. Bllets Walkng-beam furnace Contnuous caster Two-hgh stand Loop layng head Wre rod block - 8 roll pars Intermedate tran - 12 stands Fg. 2 Quenchng zone Quenchng zone Layout of the wre rod mll at Fagersta Stanless AB. Hgh frequency furnace Two-hgh stand 2.1. Heatng The wre makng process starts by placng the bllets n a so-called walkng beam furnace. The name reflects that the bllets are lyng on parallel beams n the furnace movng up, forward, down and back n order to move the bllets through the furnace. The furnace tself has three zones wth varable temperatures dependng on the materal beng rolled. The fnal temperature may vary from 1050 and 1300 C n ths respect. The cycle tme for the bllets n the walkng beam furnace s about 3 h but can be much longer under down-tme n the rollng mll. Normally, the processng n the rollng mll s very quck. Typcally a bllet s rolled down to a wre of dameter 5.6 to 13.5 mm n only 10 mnutes Roughng mll, reversng mll and ntermedate tran Frst, the bllet enters a reversng roughng mll (schematcally llustrated n Fg. 3) where t s rolled n two box grooves down to 125 mm 2 cross secton n three 4

10 passes. Then, t enters a reversng duo mll wth seven passes (damonddamond-damond-square-boxoval-boxoval-round) where t s rolled down to a round cross secton of dameter 60 mm. Durng rollng n the duo mll, the temperature of the bllet has dropped from about 1050 C to about 950 C at the head end and to about 880 C at the tal end. The temperature of the bar s then rased to 1000 C by passng a hgh frequency furnace before enterng an ntermedate tran (llustrated n Fg. 4) wth 12 passes (oval-round-oval-roundoval-square-oval-square-oval-square-oval-round) at a speed of approxmately 0.65 m/s. As the bar exts the ntermedate tran t has a round cross secton wth dameter mm and an extng speed of about m/s. Then, the bar passes a short quenchng zone lowerng the temperature to about C before enterng a wre rod block. Fg. 3 An llustraton of an old roughng mll [6]. 5

11 Fg. 4 Vew of the ntermedate lne (tran) n Fagersta Wre rod block The wre rod block conssts of eght pars of rolls drven by one motor through a fxed gearbox producng an oval-round-oval-round-oval-round-oval-round profle, see Fg. 5. The stands n the wre block are tlted ±45 from the vertcal lne and are evenly dstrbuted along the rollng lne. Three man seres 5.6 mm, 6.0 mm and 6.5 mm are used to produce fnshed dmensons of the same dameter. The average reducton s 17.2% n the round sequences and 18.6% to 19.7% n the oval sequences. The fnshed rollng speed for the three seres s 60, 52 or 40 m/s dependng on the steel grades. Due to the hgh rollng speed t takes only about 90 s for a whole heat to pass a stand n the mll. 6

12 Fg. 5 The wre-rod block at Fagersta Stanless AB, wth open hood. The rollng drecton s from left to rght n the fgure Fnal treatment The wre rod produced n the wre-rod block runs out n a quenchng zone where t s lad n a spral (Fg. 6) and quckly quenched n cold water. The sprals are then collected and packed as cols. The cols may be delvered n the hot rolled condton or after beng soft annealed n bell furnaces at a peak temperature of 1070 C for 15 mn wth a total cycle tme of about 3 h. Fg. 6 Layng of fnshed wre n a spral. 7

13 3. Defects 3.1. Classfcaton Dfferent defects can occur n rolled bars and wre rods. Verlag Stahlesen n Germany has publshed an atlas of dfferent wre-rod defects [7] dvdng them nto three groups accordng to: defects developed from metallurgcal practce or from the chemcal composton of the rolled steel defects developed from mproper mll practce defects developed from mproper roll pass desgn 3.2. Metallurgcal defects Localzed mpurtes n bllets, shrnkage cavtes and segregaton may gve cracks n the bllets. Incorrect dmensons, bent, twsted or rhombc bllets can cause serous defects such as cobbles,.e. dsntegraton of the bar, durng rollng. Thus, n order to mprove the surface qualty of the fnal products t s often necessary to grnd the bllets before rollng. Longtudnal surface cracks are often found on contnuously cast slabs and are located n regons close to the centre lne of the slab surface. They are very dffcult to elmnate durng subsequent hot rollng and wll reman as defects n the rolled product [8] Defects from mproper mll practce Cracks and scratches By experence, the most common defects n wre rods are cracks and scratches. Cracks, see Fg. 7, can be caused by mproper roll pass desgn, damaged roll surfaces, worn out grooves and coarse scale rolled nto the surface of the rolled product. Cracks can be found at any pont n the producton lne from steelmakng to fnshed product. Because of the elongaton durng rollng, cracks formed n the early stage of processng wll elongate durng the later. Cracks can be detected wth the naked eye or at a low magnfcaton after the surface of the wre rod has been chemcally or mechancally descaled. Often, eddy-current equpments are used n-lne to detect surface cracks. 8

14 Fg. 7 A surface crack. Scratches are depressons, always runnng longtudnally along the bar or wre. They are caused by physcal contact wth a sharp object such as poorly machned, worn or broken gudes. Scratches can be detected by the naked eye or at a low magnfcaton, even n the scaled condton Fns and laps Due to mproper roll adjustment, overfllng may occur n one pass. Then n the next pass, the overflled regon passes a roll-groove bottom, folds and s rolled nto the surface trappng a double oxde layer just beneath the rod surface. The folded materal s recognsed as fns or laps and the appearance s shown n Fg. 8. In a contnuous mll, laps cannot be avoded at the ends of the cols whch then have to be cut and recycled. The reason for formng laps s that the wre s smultaneously grpped by many rolls and normally stretched. At the ends, the stretchng dsappears and the bar becomes thcker overfllng the roll gap wth the formaton of laps. However, laps can also be formed when the roll pass s not adequately flled or when the gudes are badly algned. Poorly flled parts of the cross secton can then develop nto laps n the next roll pass. Often, t s dffcult to dstngush laps from defects of smlar appearance lke shells, scratches or scorng. 9

15 Fg. 8 Fns or laps on the surface of a rolled bar Corner cracks Some forms of surface crackng are caused by a combnaton of lmted ductlty and hgh stress concentratons [9]. These cracks are transversely orented, usually appearng on the corners of a bllet but may extend apprecably along the sdes as n Fg. 9. Many hgh-alloy steels have an nherent low ductlty and are partcularly prone to such corner cracks. Strct control of stock composton and reheatng condtons can reduce the severty of corner crackng [10]. Fg. 9 Extended corner cracks Porosty The fnshng rollng-speed for rollng wre rod has successvely ncreased up to m/s [11, 12]. Such a hgh rollng speed generates a hgh temperature rse and hgh stran rate n the wre rod n a short tme. Ths causes a rsk of partal meltng at gran boundares n the materal leadng to defect problems such as porosty, for nstance. See Fg

16 Fg. 10 Example of central porosty n a wre rod Defects from mproper roll pass desgn Durng rollng strans and heat are accumulated whch may result n the development of defects. Just as an mproper roll pass desgn may ntate and ncrease the defect sze durng rollng, a proper desgn may reduce the defects, and n the best case, even elmnate them. A study of a damond-square and a square-oval pass has shown, that the most effcent method for elmnatng an artfcal surface crack, s to desgn the roll pass for a materal flow n the radal drecton openng up the crack n the angular drecton [13]. 11

17 4. Materals In the present thess a common hgh speed steel, SS2722 (AISI/SAE M2) and an austentc stanless steel, AISI 304L have been studed. The compostons are lsted n Table 1. Admttedly, the exact composton of M2 was not known. As a result, a nomnal composton s lsted n the table for ths materal. Table 1 Chemcal composton of nvestgated steels n wt%. M2 from reference [14,15] Steel C S Mn P S Cr N Mo Co Cu N Nb W V 304L M

18 5. Theoretcal consderatons Durng rollng, the bars are elongated n the rollng drecton and deformed n the cross secton keepng the total volume constant. Naturally, cracks may be postoned n regons where the materal s ether straned or compressed n the cross secton resultng n dfferent evoluton of the cracks. It s thus necessary to analyse the evoluton of defects wth respect to the geometrcal shape change of the cross secton durng rollng. The analyses wll be descrbed n the present secton. The frst paragraph wll cover surface defects whereas the second one wll cover a central, longtudnal cavty wth a round cross secton Evoluton of surface defects In order to scale the evoluton of the crack depth wth the correspondng eq evoluton of the cross secton an equvalent crack depth, c, was defned as: c eq = d d 0 Crack depth after pass = Orgnal crack depth (1) In order to scale ths quantty wth the cross secton evaluaton, the evoluton of a round bar rolled n round grooves was consdered. In such a case, the radus, r, scales accordng to: r A = (2) r 0 A 0 where A represents the cross secton area of the bars. The subscrpts ndcate the passes, 0 for the entry bar and after pass, respectvely. The scaled quantty, called relatve crack depth was thus defned as: c rel eq c eq A0 = = c (3) r / r A 0 Admttedly, ths relaton s only perfectly vald for round bars, but the devaton for the ovals s not so large, as dscussed by Nordén and Jonsson [16]. An llustraton from ther work s gven n Fg. 11, where the dashed lne ndcates the result of Eq. (2) whereas the sold lne ndcates the angular dependence of r / r 0 as measured on an oval. In ths case Eq. (2) scales the defects wth 1.6 whereas the scalng should vary from 1.5 to 1.9,.e. a devaton of maxmum ( )/1.6 = 19% s encountered. 13

19 Reducton of cross-secton (A 0 /A 4 ) r 0 /r Fg ϕ around the cross-secton of the bllet Illustraton of the devaton from Eq. (2) after pass 4, for an oval as functon of angle, φ, from the vertcal axs Evoluton of nner defects In the present thess an equvalent defect wdenng s defned for the central cavty as: w w eq = w 0 (4).e. the wdth after pass dvded by the orgnal wdth. Naturally, a smlar eq defnton can be used for an equvalent bar wdenng, W. By takng ther relaton, the relatve defect wdenng s defned as: w rel w = W eq eq w / w 0 = W / W 0 w = W W w 0 0 (5) If ths quantty s equal to one, the central cavty s reduced at the same rate as the bar,.e. the geometry s purely scaled by a factor. The character of the defect rel s unchanged. However, f w > 1, the defect s becomng more severe and f rel w < 1, the defect s becomng less severe. Thus, the relatve defect wdenng can be used to judge the evoluton of the defect harm. Naturally, smlar relatons can be defned for the heght changes, but ther analyses wll be less mportant snce the heght s severely reduced already n the frst pass. 14

20 Another aspect to analyse s the velocty ncrease of the bar as t passes the rolls n the block. The block s desgned for a sold bar but was now used to roll a hollow bar havng an addtonal freedom of deformaton. It can reduce the cross sectonal area of the central cavty alterng the ext velocty compared to a sold bar. Ths alteraton s a potental rsk for the stablty of the rollng process as the wre rod block s ncapable of adjustng to t. The contnuty relaton gves: ( ) = ( a v A + 1 a + 1) v + 1 A (6) whch can be rearranged to: v v A - a = + 1 (7) A a+ 1 where A and a denote the cross sectonal area of the bar and the cavty, respectvely, and v denotes the velocty. However, snce no velocty s measured t s not possble to recalculate the ndvdual veloctes between the dfferent rolls. On the other hand, t s possble to calculate the relatve velocty change n each pass usng: v v A - a = 1 (8) v A - a Wth the result of ths formula, t s possble to dscuss the change n nterstand stresses, for nstance, as a result of the artfcal defect. 15

21 6. Expermental technques 6.1. Evaluaton of surface cracks The M2 hgh speed steel was used for nvestgatng the evoluton of artfcal V- shaped, longtudnal surface cracks postoned at 0, 45 and 90 from the vertcal axs. See Fg. 12. A total of 9 bars were prepared wth artfcal cracks and rolled n sx passes n a false round-oval seres. The bars were rotated between the passes as ndcated n Fg. 12. Samples were cut from the rolled bars measurng the crack depth whch was related to the deformaton of the cross secton accordng to Eq. (3). The results wll be dscussed n secton 8. Pass Enterng cross secton Extng cross secton 1,3,5 2,4,6 Fg. 12 Illustraton of orentaton of bars and poston of cracks. Note that the bar s rotated between the passes Evaluaton of nner defects The AISI 304L steel was rolled down n 22 passes nto a bar of 12.5 mm n dameter at Fagersta Stanless AB, Fagersta, Sweden. The expermental bar was collected just before t should have entered the wre rod block and was later cut nto test bars of length 1200 mm. The bars were then prepared wth a central and longtudnal, artfcal cavty by cuttng them 400 mm from one end and drllng a 4 mm n dameter and 50 mm long hole nto both cut ends. Fnally the peces were welded together and ground to produce a correct geometry of the welds. One by one, the prepared bars were heated by resstance to 930±70ºC and fed manually nto the wre rod block, Fg. 5, set to produce a fnal extng speed of 60 m/s n pass 8. By enterng a gude after the frst roll par, the frst bar was led out from the block and drectly nto a water-flled tube for rapd quenchng. Then, the gude and tube were moved and postoned after the second roll par n 16

22 order for the second bar to be lead out and water quenched after beng rolled n pars 1 and 2. Then, the gude and tubes were postoned after par 3 allowng the thrd bar to pass pars 1, 2 and 3 before water quenchng, and so on. The process was repeated untl bar number eght was quenched after passng the whole wre rod block. By the rapd water quenchng, the gran structure was supposed to be preserved allowng t to be analysed after each pass n the block. In order to be able to characterse the orgnal structure, an extra bar was heated and then drectly water quenched wthout rollng. After rollng, samples were cut from the quenched bars, ground and polshed. For optcal examnaton, the samples were etched n a mxture of 50 ml HCl, 5 ml HNO 3 and 50 ml H 2 O at 55 C. Ths revealed the gran sze of the samples after each pass. The wdth and heght of the hole and the bar were measured drectly n an optcal mcroscope. The results wll be dscussed n secton 8. 17

23 7. Numercal smulatons 7.1. Materal models Hgh speed steel AISI M2 M2 was modelled as an elastc-plastc sotropc hardenng materal obeyng von Mses yeld crteron. The yeld stress was modelled accordng to Hensel and Spttel [17] wth the followng formulaton: σ & m1t m2 m3 = σ 0A1e A2ε A3ε (9) where σ, ε, ε& and T represent stress, stran, stran rate and temperature, respectvely. The other symbols represent parameters lsted n paper A Austentc stanless steel AISI 304L The materal behavour of the AISI 304L stanless steel s descrbed by a smple materal model based on dslocaton densty [18]. The effects of deformaton hardenng and dynamc recovery were ncluded n the model whlst statc recovery and recrystallzaton were not ncluded. The flow stress, (σ), s related to the dslocaton densty, (ρ), stran rate, ( ε& ), and absolute temperature, (T k ), by the followng equatons: σ = σ 0 + αgb ρ (10) d ρ m & ε 2 = Ωρ dt bl (11) Ω = Ω n Q Ω 0ε& exp (12) RTK where G, b and m are the shear modulus, the magntude of the Burgers vector and the average Taylor factor, respectvely. The parameters, σ 0, α, L, Ω 0, n and Q Ω are adjustable coeffcents whch can be evaluated from expermental flow curves for the current materal. The values were drectly taken from the same reference where the model was also used for an AISI 304L stanless steel. In ths reference the model s also descrbed n more detal FE-smulatons All FE-calculatons were performed wth MSC.Marc. The bars were modelled wth eght node soparametrc brck elements wth eght ntegraton ponts. Due to symmetry, one quarter of the cross secton was modelled to shorten computatonal tme. The materals were modelled as elastc-plastc sotropc hardenng materals and von Mses yeld crteron was used. The rolls were 18

24 consdered as rgd and where therefore modelled wth surface elements of constant angular velocty and temperature. Frcton was modelled usng a shear stress factor of 0.6 n Paper A whereas a coulomb frcton of 0.3 was used n Paper B. For the surface cracks, two seres of calculatons were performed. In one seres, real cracks were smulated whereas n the other seres only node ponts under the surface were montored durng the rollng smulatons. Thus, no cracks were present n the latter model. For the wre rod block (paper B) four models were bult, from one to four roll pars. The behavour of the metal durng wre rod rollng was smulated n a thermo-mechancally coupled analyss. Because of computatonal dffcultes, the numercal study was lmted to the frst four passes. 19

25 8. Summary of results In ths secton, the most mportant results wll be dscussed brefly. More nformaton s gven n the appended papers Evoluton of surface defects In order to llustrate the angular dependence of the defect evaluaton, the relatve crack depth s plotted n a crcular dagram where the radus represents c rel and the angle gves the orentaton durng rollng. See Fg. 13 and Fg. 14. For clarty, a crcle of radus 1 s plotted n the same dagrams. It represents a pure geometrcal scalng of the defects due to rollng. As seen, the calculated results show much less defect reducton than found expermentally whereas the dfference s small between calculatons wth and wthout cracks Wthout cracks Wth cracks Experment n out Fg. 13 Relatve crack depth after pass 1 at dfferent orentatons, 0, 45 and 90 from the vertcal axs Wthout cracks Wth cracks Experment n out Fg. 14 Relatve crack depth after pass 2 at dfferent orentatons, -90, -45 and 0 from the vertcal axs. 20

26 The evoluton of surface defects of dfferent orentaton durng rollng s gven n Fg. 15 to Fg. 17. As seen from Fg. 15, the FEM calculatons wthout cracks show the same tendency as the expermental results, except for the last oval. The reason for the dscrepancy s probably due to nstablty when rollng a false round bar. The FEM calculatons wth cracks show the same tendency as the other seres, but wth lower reducton of the defects. 1.4 Relatve crack depth Round bar G Oval S False round G Oval S Experment FEM wth cracks FEM wthout cracks False round S Oval G False round Fg. 15 Relatve crack depth evoluton for an ntal orentaton of 0 to the vertcal axs. G and S ndcate whether the crack s located n the groove or at the free sde. The nsert to the rght llustrates the orentaton of the crack. Also n Fg. 16, the calculated results show smaller reducton than found expermentally. The dfference between calculatons and experments are larger for ths crack orentaton, but the dfference between the calculatons s small. As before, nstablty occurs durng rollng. In Fg. 16, t appears n the second oval. 21

27 1.4 Relatve crack depth G G S G G G Experment FEM wth cracks FEM wthout cracks 0.0 Round bar Oval False round Oval False round Oval False round Fg. 16 As n Fg. 15, but for an ntal orentaton of 45 to the vertcal axs. In Fg. 17 there are also large devatons between calculatons and experments. As before, the expermental results show a qucker reducton of the defects. In fact, the defects could not be found at all n the two last, false round passes Relatve crack depth S G G Experment FEM wth cracks FEM wthout cracks S 0.0 Round bar Oval False round Oval False round Oval False round Fg. 17 As n Fg. 15, but for an ntal orentaton of 90 to the vertcal axs Evoluton of nner defects The cross sectons of the bars prepared wth a central cavty are shown n Fg. 18. Two dotted crcles are supermposed on the mcrographs to show the 22

28 geometrcal scalng of the orgnal artfcal defect. As seen, the defects reduce n sze qucker than predcted by a pure geometrcal scalng. a), Pass 1 b), Pass 2 c), Pass 3 d), Pass 4 e), Pass 5 f), Pass 6 g), Pass 7 h), Pass 8 Fg. 18 Cross sectons of hollow bars after each pass (a-h) n a round-oval seres. The dotted nserts llustrate unform shrnkage of the orgnal cavty by geometrcal scalng. 23

29 The relatve sze change of the defects, wth respect to wdth and heght, s shown n Fg. 19. As seen, the calculated and expermental results are n good agreement. The round passes appear to reduce the wdth of the cavty more effectvely than the ovals as they tend to show lower values. In pass 6 (round) a devaton from the prevous trend can be seen. Ths devaton s caused by the development of a Z-shape appearance of the cavty. See Fg. 18f. As also seen from Fg. 19, the heght of the defect s effectvely reduced n the frst pass and s much less than the wdth of the cavty n all succeedng passes. Relatve sze change of defect Wdth exp. Wdth calc. 1.2 Heght exp. Heght calc Ro Ov Ro Ov Ro Ov Ro Ov Ro Pass Fg. 19 Relatve sze change of defect wth respect to wdth and heght. Eq. (5) s used for calculatng the relatve defect wdenng. A smlar equaton s used for the heght changes. In Fg. 20, the calculated and expermental profles of the cross sectons are compared. As seen, the expermental ovals show clear asymmetry wth overfllng on the left. The rounds also show asymmetry wth slght overfllng at the top and bottom. The strong asymmetry for the expermental ovals s probably caused by nsuffcent gudng of the entry bar or dsturbances from the extra gude nserted after the roll gap to catch the rolled bar before enterng the 24

30 next roll gap. The calculated results, on the other hand, do not suffer from such problems. The round profles, Fg. 20b and Fg. 20d show excellent agreement between the calculated and expermental results. A slght overfllng s predcted, just as found expermentally. In Fg. 20b, the central cavty s well reproduced, whereas n Fg. 20d, t s too thn. a) Pass 1 b) Pass 2 c) Pass 3 d) Pass 4 Fg. 20 Expermental and predcted profles of bar and cavty after pass 1-4. Two longtudnal cross sectons are shown n Fg. 21. The left-hand seres shows a secton perpendcular to the frst roll gap whereas the rght-hand seres shows a secton parallel to the frst roll gap,.e. rotated 90 to the frst seres. Both sectons show compresson, wdenng and reopenng of the central defect as t s rolled through the dfferent passes on ts way from the top to the bottom of the page. As seen, the deformaton s concentrated along the sdes of the cavty. 25

31 RD RD Fg. 21 Length sectons though the rolled bar at pass 1-4 showng the effectve stran n colour. For optmum contrast, each secton has ts own colour scale. Lne drawngs next to the sectons llustrate the drecton of deformaton, ether n the plane of the paper or perpendcular to t. Rollng drecton, RD, s from top to bottom, as ndcated by the arrows. In Fg. 22, the relatve velocty change s calculated from Eq. (8) usng the expermental and calculated cross sectons. As seen, the largest splt between the curves for sold and hollow bars occurs n the frst pass and s then reduced quckly n the followng passes. Due to the alternatng closng and openng of the central cavty, the curve for the hollow bar crosses the curve for the sold bar 26

32 between every pass. In the oval passes, the sold bar s ncreasng ts relatve speed more than the hollow one. In the round passes, the stuaton s reversed. Snce the hollow bar ncreases ts speed less than the sold bar, t wll enter the second pass too slowly. When the second par of rolls has grpped the bar, t wll be held back by the frst par of rolls. Hence, the nterstand stresses between pass 1 and 2 wll be hgher for the hollow bar than for the sold one. Between pass 2 and 3, on the other hand, the stuaton s reversed, as the velocty ncrease n pass 2 s hgher for the hollow bar than for the sold. It s satsfactory to se that there s good agreement between calculatons and experments. 0.4 Relatve velocty change Sold exp. Sold calc. Hollow exp. Hollow calc. Ro Ov Ro Ov Ro Ov Ro Ov Ro Pass Fg. 22 Relatve velocty change at pass 1-8 calculated from Eq. (8). 27

33 9. Conclusons The short, general conclusons drawn from the work n the present thess can be condensed to: 9.1. Surface defects Calculatons show less reducton than found expermentally. Calculatons wth and wthout cracks gve smlar results. Calculatons show both smlar and devatng trends compared to the experments Inner defects Calculatons show less reducton than found expermentally. Calculatons of relatve sze change show good agreement wth experments. Calculated profles are n good agreement wth expermental results for the rounds. The ovals have suffered from msalgnment durng rollng. Deformaton s concentrated near the cavty. Calculated relatve velocty change s n good agreement wth experments. The altered velocty gves altered nterstand stresses as the block cannot adjust tself to local velocty changes due to cavtes. 28

34 10. Suggeston of future work The present work has studed two materals, M2 and 304L. The results are stmulatng snce t shows good agreement n some cases, but s also devatng n some cases. There s thus a need to understand how the calculatons should be modfed n order to reproduce the expermental results better. It s also necessary to apply the methods to other materals, lke duplex stanless steels to see f smlar results can be obtaned as presented n the present thess. Some suggestons for future actvtes are: Materal models can be developed takng hgh stran rates nto account as well as recrystallsaton, gran sze and gran growth. Defect evoluton n other materals can be nvestgated. Effects of dfferent rollng temperature and rollng velocty on the defect evoluton. By calculatons, t may be possble to optmse the pass seres wth respect to defect reducton. 29

35 References [1] Orbs-The next generaton compact cost-compettve verson of globally establshed Orbs gauge system, Brochure from IPL Integrated Photomatrx Inc, Dorchester, Dorset DT3SY,UK. [2] Wusatowsk Z. Fundamentals of rollng. Pergamon Press, London, 1969, p501. [3] Erksson C, Bases for Desgn of Flexble Roll Pass Sequences for Wre Rod Rollng, Metallurgy and New Materals Researches 13 (2005) [4] Erksson C, Workng Range for Sequences and Seres of Two- Symmetrcal Grooves n Wre Rod Rollng, Journal of Materals Processng Technology 174 (2006) [5] Lundberg S-E, Stahl and Esen, The "revenge" of the three-hgh rougher 124 (2004) [6] RoughngMllPandyMllOlderMll.jpg.JPG [7] Walzdrahtfehler, Wre rod defects, Les defaults dans le fl-machne, Verlag Stahlesen GmbH, Düsseldorf, [8] Hawbolt E, Wenberg F, Brmacombe J, Influence of hot workng on nternal cracks n contnuously cast steel bllets, Metall. Trans. B 10B (1979) [9] Rollason, E.C. Metallurgy for engeneers, (4th edn), 61-63, 1961, London, Arnold. [10] Brmacombe J K, Sormach K, Crack Formaton n the Contnuous Castng of Steel, Metallurgcal Transactons B, 8B (1977) [11] Lestan M, New concepts n the producton of specalty steel n bars and cols, La Revue de Metallurge - CIT, 94 (1997) [12] Lundberg S-E, Development Trends n Hgh Productvty Hot Rollng of Hgh Qualty Carbon Steel Wre Rod, BHM 147 (2002) [13] Matsu T, Ogata S, Fujta M, Hasunuma M, Relatonshp between Surface Flaws and Calber Desgn on Bar and Rod Rollng, Annals of the CIRP, 23 (1974) [14] [15] [16] Nordén K, Jonsson S, A study of Surface Deformaton durng Wre-Rod Rollng of Hgh Speed Steels usng Expermental and Computatonal Technques, Accepted for publcaton n Steel Research Internatonal 30

36 [17] Hensel A, Spttel T, Kraft- und Arbetsbedarf bldsamer Formgebungsverfahren, VEB Deutscher Verlag für Grundstoffndustre, Lepzg [18] Rljak S, Expermental and Numercal Analyss of Hot Rollng n Wre Block, Conference Proceedngs of the 7 th Esaform Conference on Materal Formng, Trondhem, Norway

37 Appendx Papers A and B 32