喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== 喜歡就充值下載吧。。資源目錄里展示的文件全都有，，請(qǐng)放心下載，，有疑問咨詢QQ:414951605或者1304139763 ======================== Materials Science and Engineering A 476 (2008) 178185Equal channel angular extrusion of flat productsV.M. SegalEngineered Performance Materials, 11228 Lemen Rd-Suite A, Whitmore Lake, MI 48198, USAReceived 19 February 2007; received in revised form 20 April 2007; accepted 24 April 2007AbstractThepaperconsidersequalchannelangularextrusion(ECAE)ofsufficientlylongrectangularbilletswithdifferentwidth-to-thicknessratios W/T.A stress analysis is performed inside plastic zone and inlet and outlet channels depending on contact friction and the billet geometry. Optimizationof the processing mechanics and strategy to design tools are formulated. It is shown that flat billets with W/T?1 provide important technicaladvantages for processing of massive slab-like billets and technology commercialization on the large metallurgical scale. 2007 Elsevier B.V. All rights reserved.Keywords: ECAE; Optimization of processing; Flat products; Large scale commercialization1. IntroductionThe control of material structures by severe plastic deforma-tion (SPD) presents significant scientific and practical interest.An important advantage of this approach is structure refine-ment to the sub-micron scale that can be attained in bulk billets,in a cost effective manner and for different metals and alloys.Such ultra-fine grained structures, usually in the range from afew microns to 0.2 micron, provide a reasonable compromisebetweenhighstrengthandsatisfactoryductilitythatisespeciallyattractive for structural applications. For commercialization ofSPD substantial progress should be made in the related defor-mation techniques. The key factors are deformation method andoptimization of processing characteristics. Irrespective of pro-cessing goal, material and temperaturestrain rate conditions,the mechanics of SPD should provide intensive and uniformstrains,simplesheardeformationmodeandlowstresses.Amonga few known methods of SPD, equal channel angular extrusion(ECAE)ispresentlyconsideredasthemostpromisingforindus-trial applications. However, realization of ECAE still remainsimperfective. Despite of extensive activity in the field, absolutemajority of the published works dealt with elongated billets aswas originally described in 1. These bars or rods like billetsimpose restrictions on materials, characteristics of ECAE andfollowing processing. They are difficult to use as semi finishedTel.: +1 517 548 3417.E-mail address: .products and still there are no reports on process commercial-ization. In contrast, ECAE of flat billets followed by rolling,first introduced in 2, corresponds to universal products such asplates, sheets, strips and foils. Together with other technologi-cal advantages, this processing concept of ECAE presents greatpractical perspectives. While ECAE of elongated billets is nowwell investigated, special features of the ECAE of flat billetsare not understood and were not disclosed in just a few relatedpublications35.Thepresentpaperaddressessomeimportantdetails of the ECAE technology in the case of flat billets.2. Processing mechanicsLetsconsiderECAEofarectangularbillet(Fig.1)withthick-nessT,widthWandlengthLthroughsharpcornerchannelswithtool angle 90. Original 1 and final 2 billet positions are shownin Fig. 1 by long chain and solid lines, correspondingly. As thebillet width W remains the same and the billet is moved insidethe channels as a rigid body, the flow is near plane and the plas-tic zone is localized around a crossing plane of channels. It isknown 6 that the stressstrain state and extension of the plas-tic zone strongly depend on boundary conditions imposed byan inlet channel 1 and an outlet channel 2. Thus, correspondingconditions should be analyzed first.2.1. Inlet channelAtthebeginningofECAE,thewelllubricatedbilletisplacedinto the inlet channel. An actual friction force depends on real0921-5093/$ see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2007.04.092V.M. Segal / Materials Science and Engineering A 476 (2008) 178185179Fig. 1. ECAE of rectangular billets.plastic contact and normal pressure between material and chan-nel walls. Assuming that a stress state inside the channel issimilar to linear plastic compression, the normal pressure non channel walls is (Fig. 2a)n (p Y)where p is the axial pressure and Y is the material flow stress. IfpY, the pressure n0, and for long billets with L/T?1 theplastic contact is formed by transverse buckling. Such irregular,local contact provides low friction force. If p2Y, the normalpressure nY, and the plastic contact approximates to the fullcontact area between billet and channel. In this case, the samelubricant will result in large friction force and significant incre-mentofpressure?palongachannellength.Then,theextrusionpressure peis:pe= p1+ ?p(1)where p1is the axial pressure at the channel entry. Experimentsshowthatinallcasestheincrementofpressure?pchangesinthelinear proportion with the channel length L. That allows one tosuppose that effective plastic friction 1is uniformly distributedand the ?p may be calculated by the formula:?p = 1fHere f is a full contact area between billet and walls. When1is known for specific conditions, the maximum increment ofthe extrusion pressure in the stationary rectangular channel withfour friction walls (Fig. 2a) is:?pY=(2n 1)(1 + m)(1/Y)m(2)Here parameters n=L/T and m=W/T define relative billetlength and width. In particular, m=1 corresponds to the ordi-nary case of long bar- or rod-like billets, m?1 corresponds toflat plate-like billets and m?1 corresponds to strip-like billets.Formulae(1)and(2)showthat,dependingonnandm,theextru-sion pressure pemay be significantly bigger than the materialflow stress Y even for low friction 1.The effective way to reduce contact friction, increase toollife and punch stability is via movable channel walls 7. Inone possible case (Fig. 2b, for detail see 7), the inlet channelis formed by one stationary die wall and rectangular slot ofthe slider 2, which moves together with the billet 1. That wayfriction is eliminated along three channel walls. The maximumincrement of extrusion pressure is:?pY= (n 1)?1Y?(3)In another case (Fig. 2c), two side walls of the inlet channelare formed by movable sliders 2, 3 whereas back and front diewallsarestationary.Correspondingly,theincrementofthepunchpressure is:?pY= (2n 1)?1Y?(4)It is informative to compare results of formulae (2)(4). Inall cases, the extrusion pressure increases with the billet length-to-thickness ratio n. For effective processing, this ratio shouldbe sufficiently large. Practically, n is selected between 4 and 8.The increment ?p/Y is almost twice as large for Fig. 2c thanfor Fig. 2b. For the stationary channel (Fig. 2a), the extrusionpressure also strongly depends on the billet width-to-thicknessratio m. However, this ratio does not affect the extrusion pres-sure in both cases of movable channel walls. Calculated resultsfor typical conditions n=6, 1/Y=0.15 are shown on Fig. 3 infunction of m. Three characteristic situations are outlined: (I)long billets (m=1); (II) plate-like billets (m?1); (III) strip-likebillets (m?1). It is evident that ECAE of long and, especially,Fig. 2. Distribution of friction in inlet channels with: (a) stationary walls; (b) three movable walls; (c) two movable sidewalls.180V.M. Segal / Materials Science and Engineering A 476 (2008) 178185Fig. 3. Effect of billet ratio m on the increase of pressure along inlet channel(L/T=6, 1/Y=0.15) with: (1) stationary walls; (2) three movable walls; (3) twomovable walls.strip-like billets in stationary channels results in the multifoldincrease of the extrusion pressure in comparison with the flowstress Y. In these cases, ECAE of sufficiently large billets andhard materials can be performed only in dies with movablechannel walls at powerful presses. However, for flat billets, twomovable channel walls provide insignificant reduction of theextrusion pressure. Therefore, simple dies with stationary inletchannelsandordinarypressescanbeusedinmanycasesoflargeflat billets.2.2. Outlet channelIncontrasttotheinletchannel,lubricationoftheoutletchan-nel is a challenging problem (Fig. 4a). Because of the sharpchange in the extrusion direction, high normal pressure at thebottom wall, intensive slip and uncovering of the atomic cleanmaterial along a bottom contact surface O1B, heavy scratches,stickingandgallingcanbeobservedevenwiththebestlubricants7. That leads to high extrusion pressure, poor billet surfaceand intensive die wear. All these problems can be eliminated byusing a movable slider along the bottom channel wall (Fig. 4b)7. That way plastic friction between material and die is sub-Fig. 5. Slip line solution with different friction in channels.stituted by elastic friction between slider 1 and guide Plate2. During extrusion, the slider 1 usually remains free and someslip and shear stresses 2should be developed along the billetcontact surface O1B to overcome friction between slider and aguide plate:2fO1B= p1WT(5)Here fO1Bis an area of the contact surface O1B and isthe coefficient of Coulombs friction. At normal conditions, theslider speed is close to the extrusion speed. As friction is not astable phenomenon, certain deviations in the slider movementmay be observed. If stresses 2exceed plastic friction betweenbillet and slider, the flow becomes similar to the stationary die.Corresponding boundary conditions in the outlet channel donot provide a localized plastic zone and simple shear deforma-tion mode necessary for effective processing 6. Therefore, thecoefficient should be sufficiently low.2.3. Plastic deformation zoneInlet and outlet channels define friction boundary conditions1,2fortheplasticzone.AsliplinesolutionisshownonFig.5Fig. 4. Stationary outlet channel (a) and outlet channel with movable bottom wall (b).V.M. Segal / Materials Science and Engineering A 476 (2008) 178185181for the case 121. It is supposed that the material behavior issimilar to the ideal plastic body28. The slip line field includescentral fan FEDO, mixed boundary area CDE and dead metalarea O1CA. The central angle of the dead area is:1= 1+ 2 (6)Angles 1, 2are calculated by formulae 8:1=? Arccos(1/k)2?,2=? Arccos(2/k)2?,where k=Y/3 is the material shear flow stress. Solutions forparticular cases of 1, 2were considered in 6.Now we can gather results and outline the optimal strategyto design ECAE processing. First of all, note that the stationaryoutlet channel always induces the lubrication problem. In thelimitsituation2k,10,asliplineanalysis6,7givesforthe entry pressure at the inlet channel p1/Y2.3. That results infull contact between billet and channel walls and leads to thehigh extrusion pressure pein all practical cases of long channelsL/T?1 and finite friction 10. In fact, published data showthattheextrusionpressuremaybeashighasp/Y79.Formostmaterials at low processing temperatures, so large pressures arenot admissible for modern tool alloys. Therefore, despite sim-plicity, stationary outlet channels are unpractical for industrialapplications.With a proper movable bottom wall of the outlet channel(Fig. 4b), friction 1, 2and coefficient are small quanti-ties. Under these conditions, the slip line field of Fig. 5 canbe considered as a small modification of the “zero solution”when 1=2=0 and the plastic zone is the single sliplineO1O.Then,usingtheperturbationmethodforsliplines10and omitting intermediate results, with accuracy to the secondorder of magnitude, formulae (5) and (6) give:2 Y, (1+ Y)kand the entry pressure inside the inlet channel is:p1Y23+1Y+ ?1 +122?(7)In accordance with Eq. (7), there is a sufficient room forparameters1andtoformthelocalcontactbetweenbilletandinlet channel with low friction, if the increment of the extrusionpressure ?p also remains moderate. With movable outlet chan-nel, the inlet channel may be performed as stationary (Fig. 2a)or with two movable walls (Fig. 2c). As was previously shown(Fig. 3), the simple stationary channel is effective for flat billetswith the length-to-thickness ratio L/T more than four whereasfor long billets (L/T=l) and strip-like billets (L/T?l) movablesidewalls are necessary. Therefore, only the first case will befurther considered.1An alternative solution for 14, the moderate extrusion pres-sure (Ype2Y)results in full contact and the high friction. In all cases, a mov-able bottom wall of the outlet channel is an effective technical4See http:/www.epm-.V.M. Segal / Materials Science and Engineering A 476 (2008) 178185185solutiontoeliminatefriction,materialstickingandtoreducetheextrusion pressure.The billet width-to-thickness ratio W/T also has a notableeffect on the extrusion pressure for long square (W/Tl) andstrip-like billets (W/T?1). In these cases, the inlet channelswith two movable walls are necessary to reduce the extrusionpressure. For flat billets with W/T?1 this effect is insignificantand simple stationary inlet channels may be used.The basic processing routes for flat billets lead to similarmaterial distortions as in long square billets. However, routes Band D with spatial plastic flows provide different orientationsof shear bands/high angle boundaries and are less effective thanfor long billets. Other processing routes, similar to consideredroutes E and D, should be introduced in special cases.ECAE of bulk slab-like billets provides important technicaladvantagesinfabricationofdifferentflatproducts.Thisprocess-ing concept is cost effective, productive and preferable for largescale industrial commercialization.References1 V.M. Segal, Sc.D. Thesis, Physical-Technical Institute, Minsk, 1974.2 V.M. Segal, U.S. Patent No. 5,850,755 (1998).3 M.Kamachi,M.Furukawa,Z.Horita,T.G.Langdon,Mater.Sci.Eng.A361(2003) 258.4 S. Ferrasse, V.M. Segal, S.R. Kalidindi, F. Alford, Mater. Sci. Eng., A 368(2004) 28.5 S. Ferrasse, V.M. Segal, F. Alford, Mater. Sci. Eng., A 372 (2004) 235.6 V.M. Segal, Mater. Sci. Eng., A 345 (2003) 36.7 V.M. Segal, Mater. Sci. Eng., A 386 (2004) 269.8 R. Hill, The Mathematical Theory of Plasticity, Oxford, 1950.9 A. Mishra, V. Richard, F. Gregori, R.J. Asaro, M.A. Meyers, Mater. Sci.Eng., A 410411 (2005) 290.10 A.J.M. Spencer, J. Mech. Phys. Solids 9 (1961) 279.12 V.M. Segal, in: S.L. Semiatin (Ed.), ASM Handbook, Metalworking: BulkForming, 14A, ASM, 2006, p. 528.13 A.P. Zhilyaev, K. Oh-ishi, G.I. Raab, T.R. McNalley, Mater. Sci. Forum503504 (2006) 65.14 T.C. Lowe, Y.T. Zhu, in: M. Zehetbauer, R.Z. Valiev (Eds.), Nanomaterialsby Severe Plastic Deformation, NANOSPD2, Vienna, Wiley, 2004.15 L. Oleinik, A. Rosochowski, Bull. Pol. Acad. Sci., Tech. Sci. 53 (2005)413.16 S. Ferrasse, V. Segal, F. Alford, S. Strothers, J. Kardokus, S. Grab-meier, J. Evans, in: B.S. Altan (Ed.), Severe Plastic Deformation:Toward Bulk Production of Nanostructured Materials, Nova, New York,2006.17 H.J. Cui, R.E. Goforth, K.T. Hartwig, JOM-e 50 (1998) 1.