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Materials Science and Engineering A 476 (2008) 178185 Equal channel angular extrusion of flat products V.M. Segal Engineered Performance Materials, 11228 Lemen Received 19 February 2007; received in revised form Abstract A of It adv 2007 Elsevier B.V. All rights reserved. K 1. tion An ment in Such fe between attracti SPD mation optimization of processing characteristics. Irrespective of pro- cessing goal, material and temperaturestrain rate conditions, the mechanics of SPD should provide intensive and uniform strains, simple shear deformation mode and low stresses. Among a (ECAE) trial imperfecti majority w impose follo products ization. first plates, cal practical well are publications details 2. Lets consider ECAE of a rectangular billet (Fig. 1) with thick- ness T, width W and length L through sharp corner channels with tool angle 90 . Original 1 and final 2 billet positions are shown in Fig. 1 by long chain and solid lines, correspondingly. As the 0921-5093/$ doi: few known methods of SPD, equal channel angular extrusion is presently considered as the most promising for indus- applications. However, realization of ECAE still remains ve. Despite of extensive activity in the field, absolute of the published works dealt with elongated billets as as originally described in 1. These bars or rods like billets restrictions on materials, characteristics of ECAE and wing processing. They are difficult to use as semi finished Tel.: +1 517 548 3417. E-mail address: . billet width W remains the same and the billet is moved inside the channels as a rigid body, the flow is near plane and the plas- tic zone is localized around a crossing plane of channels. It is known 6 that the stressstrain state and extension of the plas- tic zone strongly depend on boundary conditions imposed by an inlet channel 1 and an outlet channel 2. Thus, corresponding conditions should be analyzed first. 2.1. Inlet channel At the beginning of ECAE, the well lubricated billet is placed into the inlet channel. An actual friction force depends on real see front matter 2007 Elsevier B.V. All rights reserved. 10.1016/j.msea.2007.04.092 The paper considers equal channel angular extrusion (ECAE) of sufficiently stress analysis is performed inside plastic zone and inlet and outlet channels the processing mechanics and strategy to design tools are formulated. antages for processing of massive slab-like billets and technology commercialization eywords: ECAE; Optimization of processing; Flat products; Large scale commercialization Introduction The 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 a w microns to 0.2 micron, provide a reasonable compromise high strength and satisfactory ductility that is especially ve for structural applications. For commercialization of substantial progress should be made in the related defor- techniques. The key factors are deformation method and Rd-Suite A, Whitmore Lake, MI 48198, USA 20 April 2007; accepted 24 April 2007 long rectangular billets with different width-to-thickness ratios W/T. depending on contact friction and the billet geometry. Optimization is shown that flat billets with W/T greatermuch 1 provide important technical on 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 as sheets, strips and foils. Together with other technologi- advantages, this processing concept of ECAE presents great perspectives. While ECAE of elongated billets is now investigated, special features of the ECAE of flat billets not understood and were not disclosed in just a few related 35. The present paper addresses some important of the ECAE technology in the case of flat billets. Processing mechanics V.M. Segal / Materials Science and Engineering A 476 (2008) 178185 179 Fig. 1. ECAE of rectangular billets. plastic nel similar on where p plastic local pressure contact lubricant ment pressure p where sho linear suppose and Delta1p Here f is a full contact area between billet and walls. When 1 is known for specific conditions, the maximum increment of the extrusion pressure in the stationary rectangular channel with four friction walls (Fig. 2a) is: Delta1p Y = (2n 1)(1 + m)( 1 /Y) m (2) Here parameters n = L/T and m = W/T define relative billet length and width. In particular, m = 1 corresponds to the ordi- nary case of long bar- or rod-like billets, m greatermuch 1 corresponds to flat 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 p e may be significantly bigger than the material flow stress Y even for low friction 1 . The effective way to reduce contact friction, increase tool life and punch stability is via movable channel walls 7.In one possible case (Fig. 2b, for detail see 7), the inlet channel is formed by one stationary die wall and rectangular slot of the slider 2, which moves together with the billet 1. That way friction increment are w pressure all to-thickness be The for pressure ratio sure for function long billets contact and normal pressure between material and chan- walls. Assuming that a stress state inside the channel is to linear plastic compression, the normal pressure n channel 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 the contact is formed by transverse buckling. Such irregular, contact provides low friction force. If p 2Y, the normal n Y, and the plastic contact approximates to the full area between billet and channel. In this case, the same will result in large friction force and significant incre- of pressure Delta1p along a channel length. Then, the extrusion p e is: e = p 1 + Delta1p (1) p 1 is the axial pressure at the channel entry. Experiments w that in all cases the increment of pressure Delta1p changes in the proportion with the channel length L. That allows one to that effective plastic friction 1 is uniformly distributed the Delta1p may be calculated by the formula: = 1 f Fig. 2. Distribution of friction in inlet channels with: (a) stationary is eliminated along three channel walls. The maximum of extrusion pressure is: Delta1p Y = (n 1) parenleftBig 1 Y parenrightBig (3) In another case (Fig. 2c), two side walls of the inlet channel formed by movable sliders 2, 3 whereas back and front die alls are stationary. Correspondingly, the increment of the punch is: Delta1p Y = (2n 1) parenleftBig 1 Y parenrightBig (4) It is informative to compare results of formulae (2)(4).In cases, the extrusion pressure increases with the billet length- ratio n. For effective processing, this ratio should sufficiently large. Practically, n is selected between 4 and 8. increment Delta1p/Y is almost twice as large for Fig. 2c than Fig. 2b. For the stationary channel (Fig. 2a), the extrusion also strongly depends on the billet width-to-thickness m. However, this ratio does not affect the extrusion pres- in both cases of movable channel walls. Calculated results typical conditions n =6, 1 /Y = 0.15 are shown on Fig. 3 in of 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) 178185 Fig. 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) two movable walls. strip-like billets in stationary channels results in the multifold increase stress hard channel mo e channels flat 2.2. nel change bottom material sticking 7 and using 7 Fig. 5. Slip line solution with different friction in channels. stituted by elastic friction between slider 1 and guide Plate 2. During extrusion, the slider 1 usually remains free and some slip and shear stresses 2 should be developed along the billet contact guide the slider stable may billet Corresponding not tion coef 2.3. of the extrusion pressure in comparison with the flow Y. In these cases, ECAE of sufficiently large billets and materials can be performed only in dies with movable walls at powerful presses. However, for flat billets, two vable channel walls provide insignificant reduction of the xtrusion pressure. Therefore, simple dies with stationary inlet and ordinary presses can be used in many cases of large billets. Outlet channel In contrast to the inlet channel, lubrication of the outlet chan- is a challenging problem (Fig. 4a). Because of the sharp in the extrusion direction, high normal pressure at the wall, intensive slip and uncovering of the atomic clean along a bottom contact surface O 1 B, heavy scratches, and galling can be observed even with the best lubricants . That leads to high extrusion pressure, poor billet surface intensive die wear. All these problems can be eliminated by a 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 outlet surface O 1 B to overcome friction between slider and a plate: 2 f O1B = p 1 WT (5) Here f O1B is an area of the contact surface O 1 B and is coefficient of Coulombs friction. At normal conditions, the speed is close to the extrusion speed. As friction is not a phenomenon, certain deviations in the slider movement be observed. If stresses 2 exceed plastic friction between and slider, the flow becomes similar to the stationary die. boundary conditions in the outlet channel do provide a localized plastic zone and simple shear deforma- mode necessary for effective processing 6. Therefore, the ficient should be sufficiently low. Plastic deformation zone Inlet and outlet channels define friction boundary conditions 1 , 2 for the plastic zone. A slip line solution is shown on Fig. 5 channel with movable bottom wall (b). V.M. Segal / Materials Science and Engineering A 476 (2008) 178185 181 for the case 1 2 1 . It is supposed that the material behavior is similar to the ideal plastic body 2 8. The slip line field includes central fan FEDO, mixed boundary area CDE and dead metal area O 1 CA. The central angle of the dead area is: 1 = 1 + 2 (6) Angles 1 , 2 are calculated by formulae 8: 1 = bracketleftbigg Arccos( 1 /k) 2 bracketrightbigg , 2 = bracketleftbigg Arccos( 2 /k) 2 bracketrightbigg , where particular to outlet limit the full high L that materials not plicity applications. ( ties. be when line and order and parameters inlet pressure nel, or ( with for side further e 3. 3.1. tions, rotations pass. introduced most die rotations erties. of beneficial later 3.2. of the plastic zone (Fig. 5) is small. In this case, material straining during crossing the plastic zone includes mainly two simple shears along boundaries DO and AFO 6. Approxi- mately, such accumulated shear is equivalent to single shear = 2 along slip line O 1 O of the corresponding “zero solution” when =0.Fig. 6 shows transformation of the “unit” material element abcd into parallelogram a 1 b 1 c 1 d 1 caused by shear 3 In the paper, we will use the same designation of routes like in 7 to underline that each basic route is independent from others. Similar routes but with different designation were also used in 3. k = Y/ 3 is the material shear flow stress. Solutions for cases of 1 , 2 were considered in 6. Now we can gather results and outline the optimal strategy design ECAE processing. First of all, note that the stationary channel always induces the lubrication problem. In the situation 2 k, 1 0, a slip line analysis 6,7 gives for entry pressure at the inlet channel p 1 /Y2.3. That results in contact between billet and channel walls and leads to the extrusion pressure p e in all practical cases of long channels /T greatermuch 1 and finite friction 1 0. In fact, published data show the extrusion pressure may be as high as p/Y7 9. For most at low processing temperatures, so large pressures are admissible for modern tool alloys. Therefore, despite sim- , stationary outlet channels are unpractical for industrial With a proper movable bottom wall of the outlet channel Fig. 4b), friction 1 , 2 and coefficient are small quanti- Under these conditions, the slip line field of Fig. 5 can considered as a small modification of the “zero solution” 1 = 2 = = = 0 and the plastic zone is the single slip O 1 O. Then, using the perturbation method for slip lines 10 omitting intermediate results, with accuracy to the second of magnitude, formulae (5) and (6) give: 2 Y, ( 1 + Y) k the entry pressure inside the inlet channel is: p 1 Y 2 3 + 1 Y + parenleftbigg 1 + 1 2 2 parenrightbigg (7) In accordance with Eq. (7), there is a sufficient room for 1 and to form the local contact between billet and channel with low friction, if the increment of the extrusion Delta1p 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 shown Fig. 3), the simple stationary channel is effective for flat billets the length-to-thickness ratio L/T more than four whereas long billets (L/T = l) and strip-like billets (L/T lessmuch l) movable walls are necessary. Therefore, only the first case will be considered. 1 An alternative solution for 1 4, the moderate extrusion pres- (Y p e 2Y) in full contact and the high friction. In all cases, a mov- bottom wall of the outlet channel is an effective technical 4 See http:/www.epm-. V.M. Segal / Materials Science and Engineering A 476 (2008) 178185 185 solution to eliminate friction, material sticking and to reduce the extrusion pressure. The billet width-to-thickness ratio W/T also has a notable effect on the extrusion pressure for long square (W/Tl) and strip-like billets (W/T lessmuch 1). In these cases, the inlet channels with two movable walls are necessary to reduce the extrusion pressure. For flat billets with W/T greatermuch 1 this effect is insignificant and simple stationary inlet channels may be used. The basic processing routes for flat billets lead to similar material distortions as in long square billets. However, routes B and D with spatial plastic flows provide different orientations of shear bands/high angle boundaries and are less effective than for long billets. Other processing routes, similar to considered routes E and D, should be introduced in special cases. ECAE of bulk slab-like billets provides important technical advantages in fabrication of different flat products. This process- ing concept is cost effective, productive and preferable for large scale industrial commercialization. References 1 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: Bulk Forming, 14A, ASM, 2006, p. 528. 13 A.P. Zhilyaev, K. Oh-ishi, G.I. Raab, T.R. McNalley, Mater. Sci. Forum 503504 (2006) 65. 14 T.C. Lowe, Y.T. Zhu, in: M. Zehetbauer, R.Z. Valiev (Eds.), Nanomaterials by 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.