Materials Science and Engineering A 476 (2008) 178185Equal channel angular extrusion of flat productsV.M. SegalEngineered Performance Materials, 11228 LemenReceived 19 February 2007; received in revised formAbstractAof Itadv 2007 Elsevier B.V. All rights reserved.K1.tionAnmentinSuchfebetweenattractiSPDmationoptimization of processing characteristics. Irrespective of pro-cessing goal, material and temperaturestrain rate conditions,the mechanics of SPD should provide intensive and uniformstrains, simple shear deformation mode and low stresses. Amonga(ECAE)trialimperfectimajoritywimposefolloproductsization.firstplates,calpracticalwellarepublicationsdetails2.Lets consider ECAE of a rectangular billet (Fig. 1) with thick-ness T, width W and length L through sharp corner channels withtool angle 90. Original 1 and final 2 billet positions are shownin Fig. 1 by long chain and solid lines, correspondingly. As the0921-5093/$doi:few known methods of SPD, equal channel angular extrusionis presently considered as the most promising for indus-applications. However, realization of ECAE still remainsve. Despite of extensive activity in the field, absoluteof the published works dealt with elongated billets asas originally described in 1. These bars or rods like billetsrestrictions on materials, characteristics of ECAE andwing processing. They are difficult to use as semi finishedTel.: +1 517 548 3417.E-mail address: .billet 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 channelAt the beginning of ECAE, the well lubricated billet is placedinto the inlet channel. An actual friction force depends on real see front matter 2007 Elsevier B.V. All rights reserved.10.1016/j.msea.2007.04.092The paper considers equal channel angular extrusion (ECAE) of sufficientlystress analysis is performed inside plastic zone and inlet and outlet channelsthe processing mechanics and strategy to design tools are formulated.antages for processing of massive slab-like billets and technology commercializationeywords: ECAE; Optimization of processing; Flat products; Large scale commercializationIntroductionThe control of material structures by severe plastic deforma-(SPD) presents significant scientific and practical interest.important advantage of this approach is structure refine-to the sub-micron scale that can be attained in bulk billets,a cost effective manner and for different metals and alloys.ultra-fine grained structures, usually in the range from aw microns to 0.2 micron, provide a reasonable compromisehigh strength and satisfactory ductility that is especiallyve for structural applications. For commercialization ofsubstantial progress should be made in the related defor-techniques. The key factors are deformation method andRd-Suite A, Whitmore Lake, MI 48198, USA20 April 2007; accepted 24 April 2007long rectangular billets with different width-to-thickness ratios W/T.depending on contact friction and the billet geometry. Optimizationis shown that flat billets with W/T greatermuch 1 provide important technicalon the large metallurgical scale.and still there are no reports on process commercial-In contrast, ECAE of flat billets followed by rolling,introduced in 2, corresponds to universal products such assheets, strips and foils. Together with other technologi-advantages, this processing concept of ECAE presents greatperspectives. While ECAE of elongated billets is nowinvestigated, special features of the ECAE of flat billetsnot understood and were not disclosed in just a few related35. The present paper addresses some importantof the ECAE technology in the case of flat billets.Processing mechanicsV.M. Segal / Materials Science and Engineering A 476 (2008) 178185 179Fig. 1. ECAE of rectangular billets.plasticnelsimilaronwherepplasticlocalpressurecontactlubricantmentpressurepwheresholinearsupposeandDelta1pHere 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:Delta1pY=(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 greatermuch 1 corresponds toflat plate-like billets and m lessmuch 1 corresponds to strip-like billets.Formulae (1) and (2) show that, depending on n and m, the extru-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 wayfrictionincrementarewpressureallto-thicknessbeTheforpressureratiosureforfunctionlongbilletscontact and normal pressure between material and chan-walls. Assuming that a stress state inside the channel isto linear plastic compression, the normal pressure nchannel walls is (Fig. 2a)n (p Y)p is the axial pressure and Y is the material flow stress. If Y, the pressure n 0, and for long billets with L/T greatermuch 1 thecontact is formed by transverse buckling. Such irregular,contact provides low friction force. If p 2Y, the normaln Y, and the plastic contact approximates to the fullarea between billet and channel. In this case, the samewill result in large friction force and significant incre-of pressure Delta1p along a channel length. Then, the extrusionpeis:e= p1+ Delta1p (1)p1is the axial pressure at the channel entry. Experimentsw that in all cases the increment of pressure Delta1p changes in theproportion with the channel length L. That allows one tothat effective plastic friction 1is uniformly distributedthe Delta1p may be calculated by the formula:= 1fFig. 2. Distribution of friction in inlet channels with: (a) stationaryis eliminated along three channel walls. The maximumof extrusion pressure is:Delta1pY= (n 1)parenleftBig1YparenrightBig(3)In another case (Fig. 2c), two side walls of the inlet channelformed by movable sliders 2, 3 whereas back and front diealls are stationary. Correspondingly, the increment of the punchis:Delta1pY= (2n 1)parenleftBig1YparenrightBig(4)It is informative to compare results of formulae (2)(4).Incases, the extrusion pressure increases with the billet length-ratio n. For effective processing, this ratio shouldsufficiently large. Practically, n is selected between 4 and 8.increment Delta1p/Y is almost twice as large for Fig. 2c thanFig. 2b. For the stationary channel (Fig. 2a), the extrusionalso strongly depends on the billet width-to-thicknessm. However, this ratio does not affect the extrusion pres-in both cases of movable channel walls. Calculated resultstypical conditions n =6,1/Y = 0.15 are shown on Fig. 3 inof m. Three characteristic situations are outlined: (I)billets (m = 1); (II) plate-like billets (m greatermuch 1); (III) strip-like(m lessmuch 1). It is evident that ECAE of long and, especially,walls; (b) three movable walls; (c) two movable sidewalls.180 V.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 multifoldincreasestresshardchannelmoechannelsflat2.2.nelchangebottommaterialsticking7andusing7Fig. 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 billetcontactguidethesliderstablemaybilletCorrespondingnottioncoef2.3.of the extrusion pressure in comparison with the flowY. In these cases, ECAE of sufficiently large billets andmaterials can be performed only in dies with movablewalls at powerful presses. However, for flat billets, twovable channel walls provide insignificant reduction of thextrusion pressure. Therefore, simple dies with stationary inletand ordinary presses can be used in many cases of largebillets.Outlet channelIn contrast to the inlet channel, lubrication of the outlet chan-is a challenging problem (Fig. 4a). Because of the sharpin the extrusion direction, high normal pressure at thewall, intensive slip and uncovering of the atomic cleanalong a bottom contact surface O1B, heavy scratches,and galling can be observed even with the best lubricants. That leads to high extrusion pressure, poor billet surfaceintensive die wear. All these problems can be eliminated bya movable slider along the bottom channel wall (Fig. 4b). That way plastic friction between material and die is sub-Fig. 4. Stationary outlet channel (a) and outletsurface O1B to overcome friction between slider and aplate:2fO1B= p1WT (5)Here fO1Bis an area of the contact surface O1B and iscoefficient of Coulombs friction. At normal conditions, thespeed is close to the extrusion speed. As friction is not aphenomenon, certain deviations in the slider movementbe observed. If stresses 2exceed plastic friction betweenand slider, the flow becomes similar to the stationary die.boundary conditions in the outlet channel doprovide a localized plastic zone and simple shear deforma-mode necessary for effective processing 6. Therefore, theficient should be sufficiently low.Plastic deformation zoneInlet and outlet channels define friction boundary conditions1, 2for the plastic zone. A slip line solution is shown on Fig. 5channel with movable bottom wall (b).V.M. Segal / Materials Science and Engineering A 476 (2008) 178185 181for the case 1 21. 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=bracketleftbigg Arccos(1/k)2bracketrightbigg,2=bracketleftbigg Arccos(2/k)2bracketrightbigg,whereparticulartooutletlimitthefullhighLthatmaterialsnotplicityapplications.(ties.bewhenlineandorderandparametersinletpressurenel,or(withforsidefurthere3.3.1.tions,roducedmostdierotationserties.ofbeneficiallater3.2. of the plastic zone (Fig. 5) is small. In this case, materialstraining during crossing the plastic zone includes mainly twosimple shears along boundaries DO and AFO 6. Approxi-mately, such accumulated shear is equivalent to single shear = 2 along slip line O1O of the corresponding “zero solution”when =0.Fig. 6 shows transformation of the “unit” materialelement abcd into parallelogram a1b1c1d1caused by shear 3In the paper, we will use the same designation of routes like in 7 to underlinethat each basic route is independent from others. Similar routes but with differentdesignation were also used in 3.k = Y/3 is the material shear flow stress. Solutions forcases of 1, 2were considered in 6.Now we can gather results and outline the optimal strategydesign ECAE processing. First of all, note that the stationarychannel always induces the lubrication problem. In thesituation 2 k, 1 0, a slip line analysis 6,7 gives forentry pressure at the inlet channel p1/Y2.3. That results incontact between billet and channel walls and leads to theextrusion pressure pein all practical cases of long channels/T greatermuch 1 and finite friction 1 0. In fact, published data showthe extrusion pressure may be as high as p/Y7 9. For mostat low processing temperatures, so large pressures areadmissible for modern tool alloys. Therefore, despite sim-, stationary outlet channels are unpractical for industrialWith a proper movable bottom wall of the outlet channelFig. 4b), friction 1, 2and coefficient are small quanti-Under these conditions, the slip line field of Fig. 5 canconsidered as a small modification of the “zero solution”1= 2= = = 0 and the plastic zone is the single slipO1O. Then, using the perturbation method for slip lines 10omitting intermediate results, with accuracy to the secondof magnitude, formulae (5) and (6) give:2 Y, (1+ Y)kthe entry pressure inside the inlet channel is:p1Y23+1Y+ parenleftbigg1 +122parenrightbigg(7)In accordance with Eq. (7), there is a sufficient room for1and to form the local contact between billet andchannel with low friction, if the increment of the extrusionDelta1p also remains moderate. With movable outlet chan-the inlet channel may be performed as stationary (Fig. 2a)with two movable walls (Fig. 2c). As was previously shownFig. 3), the simple stationary channel is effective for flat billetsthe length-to-thickness ratio L/T more than four whereaslong billets (L/T = l) and strip-like billets (L/T lessmuch l) movablewalls are necessary. Therefore, only the first case will beconsidered.1An alternative solution for 14, the moderate extrusion pres-(Y 2Y)in full contact and the high friction. In all cases, a mov-bottom wall of the outlet channel is an effective technical4See .V.M. Segal / Materials Science and Engineering A 476 (2008) 178185 185solution to eliminate friction, material sticking and to reduce theextrusion 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 lessmuch 1). In these cases, the inlet channelswith two movable walls are necessary to reduce the extrusionpressure. For flat billets with W/T greatermuch 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 spe