E a subject of considerable interest. Since the discovery of

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1 J Am Cerm Soc, 75 [7] (1992) Hot Extrusion of Cermics Xin u" nd I-ei Chen* Deprtment of Mterils Science nd Engineering, University of Michign, Ann Arbor, Michign Two dense cermics, BizSrzCCuzOs+x nd 2Y-TZP: 1 wt% Al2O3, were hot-extruded through conicl dies under wide rnge of conditions. Extrusion of BizSr2C- CU~O~+~ ws performed t 775" to 825 C nd speeds of.5 to.2 mm/s, with the die semi-ngles from 3" to 6" nd extrusion rtios from 4 to 9. Extrusion of 2Y-TZP:1 wt% AIzO3 ws performed t 165 C nd.17 mm/s. During hot extrusion of BizSrzCCuzOs+x, strong texture ws developed with the bsl plne ligned long the extrusion direction, wheres the zirconi/lumin composite underwent grin growth which resulted in strin hrdening. A simple nlyticl extrusion model for strin-rte-sensitive mterils hs been developed using combined slb method nd upper-bound method nd power-lw mteril flow eqution. The model predictions re in good greement with the experimentl results nd they further serve to delinete the limittion of the extrusion technique for cermic pplictions. [Key words: extrusion, superconductors, zirconi, texture, creep.] I. Introduction XTRUSION of polycrystlline cermics hs recently become E subject of considerble interest. Since the discovery of high-t, superconducting oxides, numerous ttempts hve been mde to use extrusion (or the similr wire drwing process) to mnufcture highly textured wires.'-13 Such texture is generlly beneficil for the current-crrying cpbility of the high-t, superconductors. In ddition, fine-grined tetrgonl zirconi polycrystls (TZP) hve lso been extruded into rods,14, ls lthough the utility of hot extrusion of this mteril is less obvious s no physicl property hs yet been found tht benefits from the extrusion process. Extrusion of cermics is quite different from extrusion of metls. Cermics hve poorer ductility nd higher flow stresses thn metls, so the extrusion hs to be performed under much higher temperture nd slower speed in order to reduce the flow stress nd void frcture. Under such deformtion conditions mteril flow stress is rte sensitive, nd probbly grin size sensitive lso. In ddition, hightemperture extrusion clls for tooling mterils with n even higher strength t the extrusion temperture thn the cermics being extruded. Since choices of such tooling mterils re very limited, extrusion my hve to be performed under constnt upper limit lod insted of constnt speed. To further explore the possibility of hot extrusion of dense cermics, systemtic theoreticl nd experimentl study hs been performed in the hot extrusion of two cermics, Bi2SrZCC~28iX, high-tc superconducting cermic, nd 2Y-TZP:lO wt% Al2O3 composite (YlOA), fine-grined F. Lnge-contributing editor Mnuscri t No Received Supporte! by the US. Deprtment of Energy (BES) under Grnt No. DE- FG2-87ER4532. *Member, Americn Cermic Society. trnsformtion-toughened cermic. Bi2Sr2CCu28+x ws chosen becuse, in our preliminry deformtion study: it ws found to form useful deformtion texture similr to tht in YB2Cu36.s+x,1 nd it remined superconducting fter hot deformtion without ny further het tretment. In ddition, the temperture required for extruding it ws well within the upper limit where high-strength tungsten crbide tooling could be utilized. Therefore, it ws considered to be good model mteril for cermics extrusion study. 2Y-TZP: 1 wt% A123 composite ws chosen becuse fine-grined 2Y-TZP is known to hve excellent superplsticity, nd with the ddition of 1 wt% A123 s second phse, grin growth could be further suppressed." By using these two different mterils over sufficiently brod rnge of extrusion speeds, extrusion rtios, die ngles, nd tempertures, the representtive extrusion behviors could be thoroughly explored. 11. Extrusion Mechnics Since most existing extrusion models re pplicble to rte-independent mterils,"-" n extension of the clssicl extrusion nlysis for rte-sensitive mterils is needed. This nlysis is given elsewhere using combined slb method nd upper-bound method." The min results re summrized below. Essentilly, the extrusion rm pressure P is determined by the mteril flow stress nd the die geometry, which involves the extrusion rtio nd the die ngle. The former my vry with time becuse of microstructurl chnging tking plce in extrusion. In ddition, the ctul pressure is ffected by the friction between the billet nd the continer. This ltter fctor is lso time-dependent since the length of the billet chnges. The first fctor on flow stress is expressed by Y*, which is reference flow stress corresponding to reference strin rte &* - - Vi/Di, where Vi nd Di re the inlet velocity nd dimeter. Using the stndrd nottion for constitutive eqution of flow stress, we cn write k = ko exp(mq/rt) (d/do)mp, where ko, m, Q, nd p re mteril constnts referring to strin rte sensitivity, ctivtion energy, nd the grin size exponent, respectively, nd d nd do re the current nd initil grin size, respectively. The effect of temperture nd extrusion speed on the extrusion lod is therefore determined by the temperture nd strin rte dependence of the mteril. The second fctor on die geometry is expressed by Fg, which is the extrusion pressure t the die inlet normlized by flow stress. It is determined by the die ngle nd extrusion rtio R (R = inlet re/outlet re) due to the idel plstic work for the cross-sectionl re reduction (R-dependent), the die friction (-dependent), nd the redundnt work due to velocity discontinuities t both the inlet nd outlet (dependent). Tking into ccount the strin rte effect within 1846

2 July 1992 Hot Extrusion of Cermics 1847 the deformtion zone, F, cn be written s l+b tn CY ) ( ~ + l 5 m - 1) + - F, = (4tn )m{ ( B + 1.5m 3 where B = p/ tn, with p s the coulomb friction coefficient. The product of F, nd Y* is then the pressure (or extrusion stress i) required t the inlet to extrude mteril. The third fctor on billet-continer friction is expressed by FL, which is function of the remining billet length L, FL = exp(4pl/di) (3) This fctor decreses with length L or time t. The product of FL,F,, nd Y* is then the pressure required on the rm to push the billet though the die. Lstly, if microstructurl corsening occurs during extrusion, its effect cn be expressed by Fd, which ccounts for the sttic grin growth of the billet, where nd q re given by the sttic growth lw d = do(1 + t)"q. The product of F nd Y* is then the ctul reference flow stress t time t. Likewise, the pressures i nd P bove need to be corrected by the sme fctor Fd. This model considers the effects of both extrusion processing prmeters nd mteril prmeters. In ddition, becuse of the contribution of the time-dependent fctors Fd nd FL, the sttic extrusion condition, represented by constnt pressure-constnt extrusion speed reltion, is never chievble. In the following, we will find tht for the two mterils studied, deformtion of Bi2Sr2CCu2s+x is presumbly controlled by disloction creep (s evident by the texture formtion) nd thus is grin size independent, so tht fctor Fd is unity nd fctor FL domintes the kinetics of the extrusion. On the other hnd, the deformtion of the fine-grined zirconi composite is controlled by diffusionl creep nd is highly grin size dependent, so tht fctor Fd is incresing with time nd my dominte the extrusion kinetics. Our experimentl investigtion described below will be nlyzed using the bove model Experimentl Procedure (1) Mteril Preprtion For prepring Bi2Sr2CC~28+X, powders of Bi23, SrC3, CC3, nd CuO, with molr rtios of Bi:Sr:C:Cu being 2:2:1:2, were mixed nd dissolved in nitric cid. The solution ws then evported to dryness. The clcintion ws performed t 85 C for 24 h in ir, followed by grinding nd milling. Such clcintion-milling cycle ws repeted three times for chemicl homogeniztion. The resultnt powder ws found to contin primrily Bi2Sr2CCu2x+x phse nd few percent of C-rich phse. The YlOA powder ws prepred by mixing the powder of 2Y-TZP nd AI2O3 (in 9:l weight rtio). The powder mixture ws ttrition milled in methnol for 2 h, followed by drying. The extrusion billets were mde by hot-pressing in the sme device nd environment s tht for extrusion. This will be described in the next section. (2) Hot-Pressing nd Extrusion For extrusion of Bi2SrzCCu2x+x, the continer nd dies were mde of tungsten crbide, which cn withstnd extrusion pressures of up to 2 MP t extrusion tempertures of 775" to 825 C in rgon. Conicl dies with n inlet dimeter of 1 mm nd extrusion rtios of 4, 6.25, nd 9 (defined s the rtio of inlet re to outlet re) were used, ll t die semingle of 4". Extrusion t different die semi-ngles of 3", 4", 5", nd 6" were lso investigted, ll t n extrusion (4) rtio of 4. Tempertures were mesured by thermocouple nd controlled by temperture controller to within 1 C of the set vlue throughout the test. They were lso checked by n dditionl thermocouple or by n opticl pyrometer to ensure tht the systemtic error ws within 5 C. The extrusion rm movement ws ctivted by closedloop controlled servo-hydrulic mechnicl testing system with displcement resolution of 3 pm. Extrusion ws performed under displcement control mode. Lod nd displcement were mesured by lod cell nd liner voltge differentil trnsformer (LVDT), nd were recorded by computer. Rm speeds from.5 to.2 mm/s were used, giving extrusion speeds t the outlet from.2 to.8 mm/s, depending on the extrusion rtio. In typicl run, powder of Bi2Sr2CCu2x+x ws directly chrged into the extrusion continer nd hot-pressed between the extrusion piston nd plugged tungsten crbide die. This ws performed under constnt pressure of 5 MP nd t 8 C in rgon for 3 min to rech better thn 98% of the theoreticl density. The resulting cylindricl billets were 1 mm in dimeter nd bout 1 mm in length. After the die ws unplugged, the rm ws dvnced t constnt speed for the reminder of the run to chieve extrusion. In order to obtin the reltionship between extrusion lod nd speed, the rm speed ws bruptly chnged fter certin distnces nd this ws repeted severl times in run. Extrusion ws terminted when the piston reched the position of.5 mm hed of the die inlet. To reduce friction nd chemicl rection between the crbide dies nd the billet, severl jcketing mterils were used. Silver, copper, nd grphite foils were ll found stisfctory for the lubriction purpose, lthough silver hd better chemicl stbility. In the extrusion modeling, only dt obtined with double-lyer jcketing ( grphite outer foil nd silver inner foil, both.5 mm in thickness) were used. For YlOA, the opertion procedures for hot-pressing nd extrusion were bsiclly the sme s tht for Bi2Sr2CC~28+X. However, the continer nd the extrusion dies were mde of grphite insted of C in order to withstnd much higher extrusion tempertures. The billets were mde by hot-pressing YlOA powder under 2 MP t 142 C for 2 min in nitrogen, with the sme opertion procedure s for B ~~S~~C~CU~O Extrusion ws performed under 32-MP rm pressure (in the lod control mode), t 165 C in nitrogen, with die ngles of 3", 45", 6", nd with n extrusion rtio of 4. Only grphite foil ws used for lubriction. Compred to the ones used by Kellet et l. for 3Y-TZP," these conditions cover more die ngles but re restricted to one extrusion rtio. The extrusion is fster in speed but crried out t higher temperture. IV. Results nd Anlysis (1) Texture in Extruded Biz(Sr,C)3CuOs+x A Bi2Sr2CCu2x+x rod extruded t 8 C nd.1 mm/s is shown in Fig. l(). Microstructurl exmintions reveled tht extruded rods were dense nd hd elongted grins long the extrusion direction, s seen in Figs. l(b) nd (c). Strong crystlline textures were detected both before nd fter extrusion, but their crystlline orienttions were different. Before extrusion, the hot-pressed billet hd preferred orienttion with the bsl plne (1) ligned perpendiculr to the pressing direction, s shown in Fig. 2 (top). After extrusion, the diffrction intensity of ll bsl (1) plnes is gretly reduced on the section norml to the extrusion direction, but is gretly enhnced on the section long the extrusion direction, s shown in Fig. 2 (bottom), indicting tht the bsl plnes were preferentilly ligned long the extrusion direction. Since the hot-pressing direction nd the extrusion direction re the sme with respect to the extruded rod, 9" rottion of the preferred orienttion ws experienced during extrusion.

3 1848 Journl of the Americn Cermic Society-u nd Chen Vol. 75, No. 7 Fig. 1. () An extruded Bi2Sr2CCu28+x rod, which shows zero resistnce t 89 K. Its microstructure is lso shown by (b) opticl microscopy nd (c) SEM. ithout het tretment, the extruded product ws superconducting with trnsition temperture T, = 9 K, determined by mgnetic susceptibility mesurement, s shown in Fig. 3(). The electricl resistnces were mesured both prllel nd perpendiculr to the extrusion direction, s shown in Fig. 3( b), which indictes tht the resistnce (in the norml stte) in the extrusion direction is 4- to 5-fold lower thn tht in the perpendiculr direction. (2) Grin Growth of Extruded YIOA An extruded rod of the YlOA composite is shown in Fig. 4() together with its microstructure before (Fig. 4( b)) nd fter (Figs. 4(c) nd (d)) extrusion. X-ry diffrction nlysis of the extruded billet found rther little texture for the tetrgonl zirconi phse. A stronger texture, however, ws pprent for the lumin phse with its bsl plne prllel to the extrusion direction. The min microstructurl chnge found ws grin growth. At 165 C nd without strin the grin size t the end of the billet grew from its initil.35 pm to bout 1.2 pm within 1 min, before entering the deformtion zone. The grin growth behvior cn be pproximtely described by the reltion d = do(l + where the constnt =.6 sd. Since the flow stress is very sensitive to the grin size, the grin growth will influence the extrusion behvior, s will be discussed lter. Compring the microstructure of the billet end nd the extruded section, both held t 165 C for the sme time, we found reltively similr microstructures, indicting tht under the present deformtion condition the dynmic grin growth of this mteril seemed insignificnt. (3) Friction CoefJicient nd Its Effect on Rm Pressure The friction coefficient p cn be determined by Eqs. (1) nd (4). The rm pressure is higher thn the die inlet pressure by fctor exp(4pl/d,), so tht p = (D,/4)(d(ln P)/dL), where L is the length of the remining billet before entering the die inlet. Thus, s extrusion proceeds nd the length of the billet is reduced, the rm pressure should dccrese exponentilly. An exmple of such n exponentil decy from the experiment on BizSrzCCuzOx+x is shown in Fig. 5(). The smll oscilltion in the lod ws probbly due to vrious sticknd-slide frictionl events which my occur when the norml pressure is high. By fitting the mesured lod nd displcement dt, the friction coefficient ws estimted to be.8 (for grphite-silver jcket). hen jump in rm velocity from V,, to V12 occurs, the inlet pressure, or extrusion stress (,) should increse if the mteril flow stress is rte sensitive. The rm pressure increse cn be used to estimte rte sensitivity, since lz:ull = P2:PI = (V,,/V,,)". After the jump, the norml decy resumes ccording to Eq. (4). An exmple of such repeted lod jumps nd decys from one of our cxperiments is shown in Fig. 5(b). (4) Effect of Extrusion Speed nd Temperture Knowing the friction coefficient nd the length of the billet t ll times nd using Eq. (4), the dt for rm pressures P cn be converted to the extrusion stresses (,) for those speeds. This procedure is followed to obtin the extrusion stress reported below. The dt of BizSrzCCuzOx+x re shown for illustrtion. In Fig. 6() we find tht when the rm speed incresed by 2 orders of mgnitude, the lod incresed by fctor of 3.5. According to the nlysis of Section 11, this dependence is ttributed to strin rte sensitivity in the creep lw, m = d(ln,)/d(ln V,). hen ll the extrusion dt were nlyzed

4 July 1992 Hot Extrusion of Cerumics 1849 I 4 BEFORE EXTRUSION 3I q rc*rrrrrrrc*rrm( cr*rrmc e. v. eq THETA AFTER EXTRUSION e. 5.o w. 7. TH~A Fig. 2. X-ry diffrction ptterns of the hot-pressed billet nd the sme fter extrusion. Here // nd I refer to the surfces sectioned prllel nd perpendiculr to the extrusion direction. in this wy, n verge strin rte sensitivity of.27 ws obtined. The temperture dependence of the extrusion lod ws lso investigted, s shown in Fig. 6(b). The extrusion lod t constnt rm speed decreses with incresing temperture. An Arrhenius plot of the rm speed t constnt lod ginst reciprocl bsolute temperture is shown in Fig. 7. The verge ctivtion energy Q, obtined from the best fit of the experimentl dt into Eq. (2), is 19 kj/mol or 11.3 ev. In the bove figures, the model predictions on the extrusion pressures hve lso been shown. In this clcultion the mteril prmeters m, Q nd ko were derived from best-fitting of ll of the experimentl dt (ko = 5.9 X MP - sm, m =.27, nd Q = 19 kj/mol). The pprently stisfctory fit indictes tht the constitutive eqution for flow stress, with k = ko exp(mq/rt), is n dequte one. obviously not the cse for the present rte-sensitive mteril t the extrusion speed studied. The effect of the extrusion rtio is shown in Fig. 8( b). The extrusion lod t constnt rm speed increses monotoniclly with the extrusion rtio. This is expected from both the rteindependent nd the rte-dependent models. In the bove figure, we hve gin included the model predictions for the ngle nd extrusion rtio dependences. Although the model predicts the generl trend of these effects, close greement seems lcking. This is possibly relted to the complex texture effect on the mteril flow behviors nd the vrition of the friction. However, if ll the mesured extrusion stresses re plotted ginst the model predictions, s shown in Fig. 9, tolerbly good greement ppers to obtin over vriety of extrusion conditions. This finl comprison lends some credence to the extrusion model described in Section 11. (5) Effects of Die Angle nd Extrusion Rtio The effect of die ngle is shown in Fig. 8(). Also shown re the model predictions. As cn be seen within the rnge tested, the extrusion lod t constnt rm speed increses monotoniclly with the die ngle, nd within the die ngle rnge studied, 3 hs the lowest extrusion pressure. It is notble tht for extrusion of rte-independent mteril (such s mny metls t lower tempertures nd higher speeds) n intermedite die ngle round 6 usully hs the lowest extrusion pressure or the best extrusion efficiency. This is (6) Effect of Grin Growth in YlOA In YlOA it ws found tht if extrusion ws performed under constnt rm velocity, then the extrusion lod would increse monotoniclly becuse of sttic grin growth. On the other hnd, if the extrusion ws under constnt rm pressure of 32 MP (the sfe opertion upper limit for grphite tools), then the extrusion speed would be too slow, t below 16 C, to complete run within severl hours. An optimum condition ws found to be t 165OoC, t which this mteril cn be extruded within 2 h for different die ngles.

5 185 Journl of the Americn Cermic Society -u nd Chen Vol. 75, No. 7 Smple: BIES(B-2212) ' Mgnetic Field 15. Guss Mesurement Mode: Full Scn o,oo El -1e4-2e4 mb El e I....,...., Temperture (K) () Figure 1 shows the extrusion rm displcement versus time for threc die ngles, 3", 45", nd 6", t the extrusion temperture of 165 C. Also shown in the figure re clculted curves of displcement versus time for the sme condition, where the sttic grin growth lw ws fitted s d = do(l +.6t)"3 (t is the extrusion time in seconds), nd the dynmic grin growth ws not considered. In exmintion of these dt, we re reminded tht, under constnt rm pressure condition, the extrusion speed is expected to ccelerte s extrusion proceeds, becuse of the decresing billet length tht decreses friction. It cn be seen in Fig. 1, however, tht only for the 3" die cn we detect some speed ccelertion while in ll others the effect of grin growth is so dominnt tht the flow stress continues to increse, rendering extrusion more difficult nd the extrusion speed lower. (The 3" die extrusion ws the fstest nd thus lest subject to sttic grin growth.) These different behviors hve been correctly predicted by our extrusion model. P E $ g.1 - b"' I I to extrusion dlr. LI n // to extrusion dir.. - I I, t so Temperture (K) ( b) Fig. 3. () Mgnetic susceptibility nd electricl resistivity vs temperture of n extruded BizSrZCCu2g+X rod. Resistivity mesured long nd perpendiculr to the extrusion xis. V. Discussion (I) Vlidity of the Extrusion Model Although we hve not described the detiled development or our extrusion model, it suffices to mention tht it is bsed on the slb nlysis of Schs" nd the upper bound nlysis of Hosford,'' extended to the rte-sensitive conditions chrcteristic of hot extrusion of cermics t moderte extrusion speed. (A similr nlysis for rte-sensitive mterils ws recently given by Kellett22 using flow field different from tht of the slb method, but yielding predictions very similr to ours.) This nlysis is probbly resonbly ccurte t the intermedite die ngle, sy between 3" nd 6T, which essentilly covers the rnge of prcticl interest. At lower ngles the frictionl contribution is dominnt nd some discrepncy between prediction nd dt is not unexpected. At high ngles, our upper-bound tretment of the redundnt work is n overestimtion nd the error is probbly significnt enough to render the predicted extrusion pressure inccurte. In exmintion of the dt in Fig. 8 we did notice certin discrepncy t 3" nd diverging trend t 6 C nd beyond. Fig. 4. () A 2Y-TZP:1% A123 specimen extruded t 165 C for 1 min. Also shown re microstructures of (b) hot-pressed billet, (c) n undeformed billet held t the extrusion temperture, nd (d) n extruded billet.

6 July 1992 Hot Extrusion of Cermics 1851 (2) Constitutive Eqution of Hot Deformtion The determintion of mteril prmeters k, Q, nd m from extrusion experiments llows us to predict the creep eqution for Bi2Sr2CCu28+x in the temperture rnge of 775" to 825 C nd the reltively high strin rte rnge of lu3 to 1 s-'. To our knowledge, no creep dt in the comprble strin rte nd temperture regimes for this mteril hve been reported. However, the strin rte sensitivity of.27 nd the ctivtion energy of 19 kj/mol (or 11.3 ev) seem to be quite resonble for power-lw creeping cermic. The ctivtion energy of 19 kj/mol, though very high, is comprble to tht found in the other perovskite systems such s BTi323 nd YB2Cu3,.2 e suggest tht these dt re representtive of compression long the c-xis in view of the texture in the deformtion zone. The results obtined in Bi2SrzCCu28+x suggest tht hot extrusion of solid billets offers vluble reserch tool for studying high-temperture deformtion of brittle cermics t reltively high strin rtes nd lrge strins. This is due to the presence of primrily trixil compressive stress stte in the extrusion process, which suppresses crck propgtion even t lrge deformtions nd reltively high strin rtes. Although the deformtion field in extrusion is not uniform, it is probbly geometriclly self-similr t ll extrusion speeds when the stedy stte is reched. Thus, the locl strin rte is simply proportionl to the extrusion speed so tht the overll defotmtion my be regrded to proceed t chrcteristic strin rte dictted by the rm speed only. In principle, therefore, deformtion dt of brittle cermics in the intermedite to high strin rte regime cn be obtined from extrusion experiments. I- x w - m n z. tn K I- tn z 3 U l- x 1 1- ' R=4, =5",825"C -Model prediction.., '...''Q,. -'"'.- '-y u I 7 R=4, Die=4", T=BoO"C, V=O.oOl mnrls RAM SPEED (mmls) ( b) Fig. 6. Extrusion stress vs () rm speed nd (b) die ngle. Also shown s solid curves re model predictions DISPLACEMENT (mm) () (3) Fesibility of Hot Extrusion of Cermics The extrusion process for cermics cn be limited by the following conditions: (1) the upper-bound rm pressure P limited by the tool strength; (2) the upper-bound stin rte i, limited by the formbility or frcture strength of the extrusion.i 5kN R = 4.1 R=4, Die=6", T=825"C, V=.2/.5/.1/.2/.5(mmls) DISPLACEMENT (mm) ( b) Fig. 5. Extrusion lod vs rm displcement for n experiment with () constnt speed nd (b) severl step increses in rm speed..oot! ' I ' I ' I. I ' TEMPERATURE 1/T (K) Fig. 7. Extrusion speed vs reciprocl temperture. Also shown s solid lines re model predictions.

7 1852 Journl of the Americn Cermic Society-u nd Chen Vol. 75, No. 7 A m ik Y w c z 3 U I- % A V=O.O2 V-.5 (mmls) Model prediction DIE SEMI-ANGLE (Degree) (4 h z. rn 2 fn 2 1 iii U CI 5 2 n 1 Mesured Stress (MP) Fig. 9. Comprison of mesured extrusion stresses nd model predictions for vriety of extrusion conditions. A m n z K c z 3 c X I V=O.5 v=o.o2 4 V=O.Ol A V=.5 (m mls) =4", T=825"( i 1 EXTRUSION RATIO R ( b) Fig. 8. Extrusion stress vs () die nele - nd (b) extrusion rtio. \, Also shown re model predi&ns. mteril; (3) the upper-bound temperture, limited by the mteril stbility, or by the equipment; nd (4) the lower-bound outlet velocity V,, required by the productivity. Some useful insight into the extrusion fesibility cn now be obtined. e notice from Eq. (4) tht the mximum strin rte occurs t the outlet, given by 4(V/D) tn (). From condition 4 we my tke V, = 1 mm/s s the minimum extrusion speed requirement. Menwhile we my further tke the upper-bound strin rte s.1 s-', noting tht most cermics will probbly develop permnent internl crcking t higher rtes even in constrined compressive deformtion unless they re extruded t very high homologous tempertures. By tking cr = 3" we then get n outlet dimeter Do lrger thn 2 mm. This illustrtes tht for resonble extrusion speed, hot extrusion is fesible only for lrge cross-section products, The inherent limittion here is imposed by the upper-bound strin rte of the cermics becuse of concern for brittle frcture. Extrusion cn lso be limited by the strength of vilble high-temperture tooling mterils. Typiclly, clcultion long the line of Section I1 suggests n extrusion stress in the rnge of S to 1 timcs tht of inlet flow stress of the extrusion mterils. Structurl cermics hve high flow stresses (in excess of SO MP, for exmple) t high strin rtes to lo-' s-i) even t very high tempertures (e.g., 165 C for YIOA). Choosing tooling mteril tht cn withstnd such high tempertures nd extrusion stresses should prove extremely difficult, yet most criticl. For exmple, while we hve used grphite tool mteril tht hs strength of SO MP t the operting temperture of YlOA extrusion, the best stte-of-the-rt grphite with twice the strength would hve llowed extrusion rtes severl times fster thn the one chieved in this study. VI. Conclusions A solid Bi2Sr2CC~28+X cermic superconductor nd 2Y-TZP:1 wt% A123 structurl cermic composite hve been hot-extruded through conicl dies. For Bi2Sr2CCuz- OH+X the extrusion ws performed t tempertures from 775" to 825"C, nd extrusion speeds from.5 to.2 mm/s, with the die semi-ngles rnging from 3" to 6" nd extrusion rtios from 4 to 9. The extruded rod is highly textured, superconducting, with high current-crrying cpbility long the rod xis s desired. For 2Y-TZP:1% A123 the extrusion conditions were more restricted becuse of the limittions of the tool strength nd the grin growth t high tempertures. An extrusion speed of.17 mm/s ws possible t 165 C. Using n pproximte nlyticl extrusion model for strinrte-sensitive mterils, we hve nlyzed the extrusion stress nd verified the extrusion mechnics. The extrusion stress is found to depend on the extrusion rtio nd extrusion ngle, in ddition to extrusion speed. The rte-sensitivity of the mteril dicttes tht smller die ngle, round 3T, is most fvorble for minimizing the extrusion lod. The effect of grin growth 1.o Clculted Time (s) Fig. 1. Displcement vs time from extrusion of YlOA t 165 C. Also shown re model predictions.

8 July 1992 Hot Extrusion of Cermics 1853 on extrusion hs lso been tken into ccount, nd it domintes in the extrusion of 2Y-TZP/A123 cermics. The experiments demonstrte tht hot extrusion could be reserch tool for obtining mteril deformtion dt in the high strin nd strin rte regime, for which the conventionl tension or compression tests re not fesible. From the obtined experimentl dt for Bi2Sr2CCu,x+x, the rte sensitivity nd the ctivtion energy hve been determined s.27 nd 19 kj/mol (11.3 ev), respectively, for strin rtes in the rnge of to lo- s-. Hot extrusion cn be fesible cermic mnufcturing technique if textured structure is desired. However, its use will probbly be limited to lrge cross-section products of low melting point nonstructurl cermics. References I-. Chen, X. u, S. J. Keting, C. Y. Keting, P.A. Johnson, nd T. Y. Tien, Texture Development in YBzCu3, by Hot Extrusion nd Hot- Pressing, J. Am. Cerm. Soc., 7 [I21 C-388-C-39 (1987). P. E. Reyes-Morel, X. u, nd I-. Chen, Deformtion Chrcteristics of Textured BiZSrI 5Cl,jCuzOs+, nd YBzCu3O6, Polycrystls ; pp in Reserch Updte, Cermic Superconductors II. Edited by M. F. Yn. Americn Cermic Society, esterville, OH, Y. Ymd, N. Fukushim, S. Nkym, H. Yoshin, nd S. Murse, Criticl Current Density of ire Type Y-B-Cu Oxide Superconductor, Jpn. J. Appl. Phys., 26 [5] L (1987). 4S. Jin, R.C. Shenvood, R.B. VnDover, T.H. Tiefel, nd D.. Johnson, Jr., High T, Superconductors-Composite ire Fbriction, Appll. Phys. Lett., 51, 23 (1987). 5. Kohno, Y. Ikeno, N. Sdkt, nd K. Goto, High Criticl Current Density of Y-B-Cu Oxide ire without Metl Sheth, Jpn. J. Appl. Phys., 27 [I] L77-79 (1988). N. Sdkt, Y. Ikeno, M. Nkgw, K. Gotoh, nd. Kohno, Fbriction nd Superconducting Properties of High T, Oxide ire, Muter. Res. Soc. Symp. Proc., 99, (1988). K. Togno, H. Kumkur, nd H. Shimizu, Developments of Tpe nd ire Fbriction Processes for High T, BzYCu O,, Oxide Superconductors, Muter. Res. Soc. Symp. Proc., 99, (1988). XK.C. Gorett, A. J. Schultz, D.. Cpone 11, T. L. Tolt, U. Blchdrn, J. T. Dusek, M. T. Lngn, R. B. Poeppel, J. P. Singh, D. Shi, R. L. McDniel, D. S. Applegte, J. K. Degener, nd J. S. Kllend, Texturing of RBzCu3, Superconductors ; pp in Reserch Updte, Cermic Superconductors 11. Edited by M. F. Yn. Americn Cermic Society, esterville, OH, T. H. Tiefel, S. Jin, R. C. Sherwood, R. B. Vn Dover, R. A. Fstncht, M. E. Vvis, D.. Johnson, nd.. Rhodes, Fbriction nd Properties of High-T, Superconducting ires, J. Appl. Phys., 64 [lo] (1988). T. Hikt, K.-I. Sto, nd H. Hitotsuyngi, Ag-Shethed Bi-Pb-Sr-C- Cu- Superconducting ires with High Criticl Current Density, Jpn. 1. Appl. Phys., 28 [I] L77-79 (1988). I.-G. Chen, S. Sen, C. H. Chen, nd D. M. Stefnescu, Fbricting AgzO- Stbilized Superconductive ires, J. Met., 41 [4] (1989). K. Rjn, R. M. Germn, D. B. Knorr, R. K. McCrone,. Misiolek, nd R. N. right, Deformtion Processing of High-Tc Superconducting Oxides,.I. Met., 41 [4] 28-3 (1989). R, B. Poeppel, S. E. Dorris, C. A. Youngdhl, J. P. Singh, nd M.T. Lngn, Shpe Forming of High T, Superconductors, J. Met., 41 [I] (1989). I4C. Crry nd A. Mocellin, Exmples of Superplstic Forming Fine- Grined Alz3 nd ZrOz Cermics ; pp in Mterils Science Monogrphs, Vol. 38A, High Tech Cermics. Edited by P. Vincenzini. Elsevier Science Publishers, Amsterdm, Netherlnds, B. J. Kellett, C. Crry, nd A. Mocellin, High Temperture Extrusion Behvior of Superplstic-bsed Cermic, J. Am. Cerm. Soc., (199). I-. Chen nd L. A. Xue, Development of Superplstic Structurl Cermics, J. Am. Cerm. Soc., (199).. Hoffmn nd G. Scks, Introduction to the Theory of Plsticity for Engineers; pp McGrw-Hill, New York, F. Hosford nd R. M. Cddell, Metl Forming, Mechnics nd Metllurgy; pp Prentice-Hll, Englewood Cliffs, NJ, I9B. Aritzur, Metl Forming: Processes nd Anlysis; Chs McGrw- Hill, New York, B. Avitzur, Hndbook of Metl-Forming Processes; Chs. 3, 4. iley- Interscience, New York, X. u, Deformtion Processing ofcermics; Ph.D. Disserttion. University of Michign, Ann Arbor, MI, B. J. Kellett, High Temperture Extrusion Behvior of Fine-grined ZrOz, J. Muter. Res., 5 ( (199). (2. Crry nd A. Mocellin, Superplstic Creep of Fine-Grined BTiO in Reducing Environment, J. Am. Cerm. Soc., 69 [9] C-215-C-216 (1986).