Study of surface crackng durng extruson of alumnum alloy AA 2014 Z. Peng and T. Sheppard Surface crackng s generally recognsed as one of the man defects occurrng durng the process of alumnum extruson, especally n the case of the so called hard alumnum alloys. Prevous experments suggest that ths type of defect s caused by the rse n temperature as the process proceeds. Some experments ndcate that the surface qualty s good even though the temperature may be hgh durng extruson. It s also well known that crack crtera have been adopted to explan the crackng that occurs n extruson, blankng and rollng, etc. In ths study, a fnte element method (FEM) s used n dfferent ways to predct surface crackng durng hot extruson. The crack crtera are ntegrated nto the FEM code FORGE 1 2.0. The effectveness of these crtera n predctng surface crackng n the case of hot extruson s dscussed. The FEM smulaton also provdes some other quanttatve data, such as the temperature rse durng extruson from dfferent ntal temperatures. In addton, the prncpal stresses at the de land area at dfferent extruson stages are also shown. MST/5986 Keywords: Alumnum alloys, Extruson, Defects, Surface crackng The authors are at DEC, Bournemouth Unversty, 12 Chrstchurch Road, Bournemouth, UK, BH1 3NE (tsheppar@bournemouth. ac.uk). Manuscrpt receved 22 September 2003; accepted 5 February 2004. # 2004 IoM Communcatons Ltd. Publshed by Maney for the Insttute of Materals, Mnerals and Mnng. Introducton Al Cu Mg alloy systems have been n use snce ther dscovery over half a century ago. The development of AA 2014 alloy utlsed the effect of slcon to produce an Al Cu Mg alloy that s more susceptble to artfcal agng than 2017, and provdes a hgh level of strength unobtanable n naturally aged 2017. Ths alloy has wdespread applcatons n the arcraft ndustry. The chemcal composton lmts for 2014 are shown n Table 1. Copper s one of the most mportant alloyng consttuents for alumnum because of ts apprecable solublty and strengthenng effect, the strength ncreasng wth ncreasng copper content up to a maxmum of approxmately 6%. Magnesum s used n combnaton wth copper to accelerate and ncrease age hardenng at room temperature. The equlbrum compounds for ths system are CuAl 2 (h phase) and CuMgAl 2 (S phase). 1,2 These are soluble n the matrx durng soluton heat treatment. Durng extruson, mperfectons n the qualty of the extrudate may arse, rangng from a rough or uneven surface to complete dsntegraton of the extrudate. The surface fnsh of the product s as mportant as the mechancal propertes, and the control of defects s often the decdng factor n determnng the extruson condtons. Defects that may occur vary from vsble blemshes such as cracks, blsters, and de lnes, to nvsble ones that show up after anodsng. Whle n hgh strength alumnum alloys where de lnes and surface scorng have only secondary mportance to the mechancal property requrements (because the surface often has to be machned to remove recrystallsed layers) the defect s tolerated provded the de lnes are not so coarse that stress concentratons arse. 3 For 4%Cu alloys, surface crackng (or speed crackng) s a major problem, especally at hgh temperatures and stran rates. Snce the product must be scrapped due to poor surface qualty and nferor mechancal propertes, t s of prmary mportance to study the occurrence of surface crackng n the extruson of hard alloys. In order to evaluate surface crackng, extrusons have been placed nto one of three categores: 3 () A no evdence of crackng () B crackng commences at some dstance along the extrudate () C Crackng occurs along the entre length of the extrudate ncreasng n severty as extruson proceeds Typcal examples of these three categores are shown n Fg. 1, all taken from the same poston half way along the extruded length at 0. 5L. Hstorcally a tral and error method has been used to form extruson products of suffcent qualty, a costly, uncertan, and tme consumng practce. The ablty to dentfy and predct these defects s crtcal to modern practce and s challengng fundamentally. Recently, the development and applcaton of numercal technques, such as the fnte element method (FEM), to contnuum mechancs problems has provded a powerful faclty to solve ths problem. A typcal smulaton procedure carred out by FEM, can consder the effect of: () the geometry of the de and workpece; () operatng varables such as temperature and the rate of deformaton, the bulk consttutve response of the materal, and the nteracton wth sold boundares. () Stresses and strans are then calculated as functons of tme, from whch predctons regardng the occurrence of fractures are obtaned. Crackng crtera There exst a number of crtera for assessng rupture n metal formng process, 4,5 whch are based on expermental work that utlses a deformaton process related to actual ndustral applcatons. The ntaton of ductle fracture n Table 1 Chemcal composton of AA 2014 (balance Al) S Fe Cu Mn Mg Cr Zn T 0. 50 1. 2 0. 7 3. 9 5. 0 0. 40 1. 2 0. 20 0. 8 0. 10 0. 25 0. 15 DOI 10.1179/026708304225022016 1179
1180 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1 Three categores of surface crackng metals depends strongly on the stress and stran hstores. Many ductle fracture crtera have the form that fracture occurs when the value of a damage parameter, whch s gven as an ntegral form of stress and stran, reaches a partcular value. In ths study, several of the crtera were combned nto the FEM subroutne to see f there was a crtcal value to ndcate the ntaton of surface crackng n hot extruson. The detals of the selected crtera are: (1) Oyane ð er 0 1zA s H s eq de eq C1 : : : : : : : : (1) where A and C1 are constants, s H s the hydrostatc stress, s eq s the equvalent stress, e eq s the equvalent stran. The process by whch fractures occur n metal formng has been wdely modelled as vod ntaton and growth, followed by coalescence to form a crack. Based on ths hypothess, crtera for ductle fracture have been suggested by McClntock et al. 6 and Oyane et al. 7 (2) Cockroft and Latham (C L1) ð er 0 s de eq C2 : : : : : : : : : : : : (2) s ~Max(s 1,s 2,s 3 ) : : : : : : : : : : : (3) where C2 s a constant, s* s the maxmum prncple stress. Cockcroft and Latham 8 consdered the effects of the maxmum prncpal tensle stress over the plastc stran path to fracture. (3) Cockroft and Latham normalsed (C L2) ð er s de eq C3 : : : : : : : : : : : : (4) 0 s eq where C3 s a constant. Ths crteron has a dependence on hydrostatc stress. (4) Ayada ð er s H s eq 0 de eq C4 : : : : : : : : : : : (5) where C4 s a constant. (5) Generalsed work crteron (GW) or Freudenthal crteron ð er 0 or ðer 0 s eq de eq C5 : : : : : : : : : : : : (6) (s 1 _e 1 zs 2 _e 2 zs 3 _e 3 ) C5 : : : : : : : : (7) where C5 and C59 are constants.s 1, s 2, and s 3 are the prncple stresses and ė 1, ė 2, and ė 3 are the correspondng prncple stran rates. Freudenthal 9 proposed that energy s the crtcal parameter at fracture. Wth ths crteron, fracture occurs n a materal element when the rate of plastc energy dsspaton reaches a crtcal value when ntegrated wth respect to tme, followng the element as t travels through the de. Ths s the only crteron that accurately predcted the ste of fracture ntaton for all three metal formng processes consdered: upsettng, extruson (brass), and strp deformaton n the work of Clft et al. 5 (6) Temperature T C6 : : : : : : : : : : : : : : : (8) where C6 s a constant. If the heat generaton near the de land area ncreases the local temperature such that the appled stresses exceed the resstance to deformaton then severe crackng at the surface may be expected. Ths temperature generaton s a functon of the alloy chemstry, extruson speed, extruson rato, aspect rato, contaner temperature, and ntal bllet temperature. 3 Much of the heat generated at the surface occurs through the dead metal zone and the deformaton zone shear band, whch termnates on the face of the de mmedately ahead of the de land area. Ths results n a steep rse n the temperature as the materal approaches the de land. 10 Heat generaton s comparatvely less n the ndrect mode of extruson compared to the drect mode. Accordng to the sx crtera descrbed above, when the constants C1 C6 reach a crtcal value, the crack occurs. By ntegratng the crack crtera nto FEM programs, research has been carred out to study varous crtera adopted n metal formng processes. Hambl and Reszka 4 checked fracture crtera valdty usng an FEM model of the blankng operaton by an nverse technque approach. Ther study showed that vald crtcal values for crack ntaton by shearng mechansms could be predcted by the followng fracture crtera: Rce, Freudenthal, Cockroft and Latham, Atkns, Oyane, Ayada, and plastc stran. Clft et al. 5,11 descrbed the use of the fnte element technque to predct fracture ntaton n a range of smple metal formng operatons, whch ncluded smple upsettng, axsymmetrc extruson, and strp compresson and tenson. In the case of axsymmetrc extruson, ther study showed that numercally predcted stes of fracture agreed wth experment when the Oyane, Freudenthal, and C L crtera were adopted. However, the extruson rato was very small n ther study and the nfluence of temperature rse, whch s a very mportant factor for crack ntaton durng extruson, was agan gnored. In the work of Ko et al., 12 The C L crteron was adopted for FEM smulaton and t was confrmed to be vald for predctng crack ntaton durng alumnum
Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1181 2 Extruson lmt extruson. However, the extruson rato used was also very small and the temperature rse was not studed. It s nterestng to see that some studes on paste extruson, whch can be assumed to be a real sothermal process, have been performed by Domant et al. 13 The C L crteron and the generalsed work crteron are dscussed n ther study, and these crtera are shown to be successful n predctng the ncrease n fracture wth ncreasng de entry angle. They are also proved to be at least qualtatvely correct n consderng the effect of extruson rato on surface fracture. Domant et al. s work s an deal example of an sothermal extruson, whch can be contrasted wth the present work, n whch the temperature evoluton has to be nvolved. Some nvestgatons 3,4,12 have shown that t s dffcult to choose a fracture crteron that s unversal enough n the sense that t gves consstent results for operatng condtons outsde the calbraton range. Applcatons of crtcal values of fracture crtera are only successful when they are both charactersed and appled under smlar loadng condtons. A materal mght crack at a relatvely small deformaton durng forgng, yet mght be satsfactorly deformed to a very large stran by extruson. The onset of crackng depends both on the detals of the workng process to whch the materal s subjected and on ts basc ductlty. In addton to the crtera mentoned above, there also exsts an emprcal method to predct surface crackng occurrng n hot extruson, proposed by Sheppard and Tutcher. 14 They nvestgated the ncdence of speed crackng n the rod form of AA 5456 alloy and showed that the Z parameter may be used to correlate results over wdely varyng temperature and speed condtons. For acceptable surface qualty 6: 35 10 20 ln Z A T 7 :06 : : : : : : : : : : (9) where Z s the Zener Holloman parameter usng the average stran rate and the ntal temperature Z ~_ee exp (Q=RT ) : : : : : : : : : : : (10) e6. s the average stran rate, defned by _ee~ 6D2 Bv(azb Ln R)(Czd Tan v) D 3 B {D3 E : : : : : (11) D B s the bllet dameter, D E s the extrudate dameter, v s the ram speed, R s the extruson rato, v s the deformaton zone cone sem-angle, 1 whch s defned by v~38 : 7{6 : 9LnR : : : : : : : : : : (12) a, b, c, and d are constants (a~0. 171, b~1. 86, c~38. 7, d~6. 9). 10 T s the ntal temperature. Ths type of analyss has also been appled to the observed surfaces of shaped extrusons n 2024 alloy, 1 and ntroducng the l 2 modfcaton for shaped extrusons, acceptable surfaces were acheved when 1 n ln Z 2: 113 10 9 l2 A T 2 :866 for drect extruson and 1 n ln 2: 113 10 9 l2 Z A T 2 :866 : : : : : : : : (13) : : : : : : : : (14) for ndrect extruson. l s the shape factor. These crtera are shown n Fg. 2 for a number of Al alloys. In the case of 2014 extruson, Patterson 15 and Verod 16,17 provded the followng emprcal crtera: For drect extruson, Patterson gave the followng equaton ln Z 6924: 2 T 0 :857 (correlaton: 0:9986) : : : : (15) and for ndrect extruson 15909 Ln Z : 5 T 0: 982 (Correlaton : 0:9991) : : : : (16) where T s the ntal bllet temperature n kelvn. Verod also reported that dfferent preheat approaches affected ths crteron such that for conventonal heatng (CH, ndcatng heatng contnuously to the extruson temperature) 67954 Ln Z T 1: 199 (correlaton 0:998) : : : : : : (17) and for materal that has been presoluton soaked (SS, heat to soak temperature and cool to extruson
1182 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 temperature) 97955 Ln Z T 1 (correlaton 0:999) : : : : : : (18) :223 It can be seen from the above equatons that n these emprcal equatons, only the ntal temperature and the average stran rate are consdered. Wth the FE method, the evoluton of the nstantaneous Zener Hollomon parameter, n whch the real-tme stran rate and the real-tme temperature are used, can be convenently obtaned from the output program. In ths paper, the nstantaneous Zener Hollomon parameter s ntegrated nto the FEM program to observe ts evoluton durng extruson, and the ntal LnZ and real-tme Ln(Z r ) values are compared. The real-tme Zener Hollomon parameter s defned by Z r ~_e exp (Q=RT) : : : : : : : : : : : (19) where ė s the real-tme stran rate and T s the real-tme temperature. Wth the combnaton of the ntal Z value and the nstantaneous Z hstory, the surface crackng s studed agan by the use of the emprcal equatons. FEM smulaton settng The man smulaton toolng used n ths study s shown n Table 2. The bllet length was 95 mm and the extruson rato 30. Expermental results defnng process condtons nducng an unacceptable surface are taken from Refs. 16 19. The FEM program, FORGE2 1 was used n ths study. It s a process smulaton tool based on the fnte element method. The hyperbolc sne functon was ntegrated nto the FEM to descrbe materal behavour. The consttutve equaton can then be wrtten as 2 s~ 1 " 3 #1 1 a Ln Z nz 2 Z nz1 2 4 5 : : : : : (20) A A where a, A, n are temperature ndependent constants,s6 s the flow stress, and Z s the Zener Hollomon parameter. For alumnum alloy AA 2014, DH~144. 408 kj mol 21, a~0. 0152 m 2 MN 21, n~5. 27, ln A~24. 41. 16 Three frcton laws are avalable n FORGE2 1 : Tresca, vscoplastc, and Coulomb. These three frcton laws have been studed by Fltta, 18 who dscovered that smulatons usng the Tresca crteron gave the best result. As a result, only the Tresca law s adopted n ths paper. The Tresca frcton law s wrtten n the followng form t~{m p s ffff : : : : : : : : : : : : : (21) 3 where s6 represents the flow stress, m s the frcton coeffcent, whch s n effect a percentage of that whch would represent stckng condtons. Temperature evoluton s represented by the followng heat equaton assocated wth a certan number of boundary 3 Predcted tme load curves condtons rc dt dt ~dv(k grad(t))z _W : : : : : : : (22) where r s the materal densty, c s the heat capacty, and k s the conductvty. W. s the heat power dsspated by plastc deformaton, whch s wrtten as _W~gs_ee : : : : : : : : : : : : : : (23) The term g represents here the effcency of the deformaton. s6 s the flow stress and e6. the mean equvalent stran rate. Dscusson of smulaton results concernng load tme hstory and temperature evoluton Before we consder the factors affectng surface crackng, the smulaton results of load hstory and temperature evoluton must be dscussed. Because the stran, the stran rate, and the stress, whch are key parameters n the crackng crtera, are closely related to the load and the temperature, t s of prmary mportance to check the FEM predcton concernng these varables. Expermental and FEM predcted values of extruson load are shown n Tables 3 and 4 respectvely. The ntegral fle predcted and FEM predcted values of temperature are also shown. Sheppard 19 ndcated that there s reasonable agreement between these two calculatons, and Dashwood 20 demonstrated that FEM calculatons yeld results that descrbe the metallurgcal features accurately. Duan and Sheppard 21 demonstrated that the FORGE2 program accurately predcts the temperature throughout rollng pass schedules. The predcted tme load curves of all the extruson processes are shown n Fgs. 3 5. Table 2 Toolng of FEM model Run Code Extruson mode Intal bllet temperature, uc Contaner temperature, uc Ram speed, mm s 21 Surface condton 1 Drect 298 275 7. 9 A 2 Drect 396 350 7. 0 B 3 Drect 470 375 7. 3 C 4 Drect 474 430 3. 3 B 5 Indrect 464 375 3. 4 A A Surface condton good throughout extruson. B Surface crackng occurs from the mddle stage of extruson to the end. C Surface crackng occurs from the start of extruson.
Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1183 4 Predcted tme load curve of extruson run 5 6 Postons of area analysed 5 Predcted tme load curve of extruson run 4 In ths paper, the data are extracted from two ponts (sde pont and centre pont) and two lnes (AB and CD) at the de land area, as shown n Fg. 6. The temperature evoluton at the sde pont and centre pont of the entre drect extruson runs are shown n Fg. 7. For the ndrect extruson RUN 5, the postons of the two ponts were changng throughout the extruson because they were movng wth the de. It s therefore dffcult to extract the data contnuously as performed for drect extrusons. The temperatures n ths case are extracted from lne AB at dfferent stages of extruson, as shown n Fg. 8. It can be seen clearly that there s a dfference between the temperatures at the two ponts throughout all the extruson processes. However, at the end of extruson, the temperature at the centre pont rses more quckly than that of the sde pont and the temperature dfference s very small at the end of extruson. Ths phenomenon has been reported prevously. 22 The dfference between the temperature of the extrudate face and centre n ths work was close to 30 K, whle n Venas s work, the dfference was found to be 60 K. Because the bllet sze used n ths study s qute dfferent to that used n Venas s work, t s not strange that there s some dscrepancy. The very sharp temperature gradent near the surface s of great sgnfcance snce t s the surface temperature, and not the average ext temperature, that s crtcal for surface falure such as crackng. Table 3 shows that the predcted loads correlate well wth the expermental results. The predcted temperatures, as shown n Table 4, are also n good agreement wth the expermental measurements. It s necessary to pont out that the cut technology was adopted n ths study. When the materal s extruded out of the de to a certan dstance, the program deletes the element automatcally, as shown n Fg. 9. Fgure 9a shows an extruson settng wthout the cut method, n whch all of the elements reman throughout the calculaton. It therefore takes an extremely long tme to fnsh a smulaton usng ths approach. However, when the cut technology s used, only a certan length of extrudate remans and the calculaton tme wll be sgnfcantly saved, as can be seen from Fg. 9b, c and d. Usng ths method, all fve extruson processes used n ths study were completed wthn a short tme. It should be noted that n the experments, f surface crackng occurs t would appear mmedately on the surface Table 3 Load data Extruson code Expermental max load, tons FEM predcted max load, tons Expermental mn load, tons FEM predcted mn load, tons 1 439. 2 445. 9 285. 8 280. 1 2 295. 6 286. 1 208. 6 195. 7 3 243. 8 240. 2 204. 6 192. 2 4 193. 0 190. 2 179. 3 160. 2 5 197. 4 203. 2 209. 7 205. 8 Table 4 Temperature Extruson code Peak temp.,* uc FEM predcted peak temp., uc Fnal temp.,* uc FEM predcted fnal temp., uc 1 309. 1 315. 2 470. 8 465. 7 2 403. 5 408. 9 501. 2 498. 2 3 476. 1 479. 2 546. 3 539. 6 4 478. 0 482. 1 529. 0 520. 4 5 471. 3 478. 3 488. 8 493. 2 *Peak temp. s the temperature of the extrudate when the peak load occurs. Both peak temp. and fnal temp. here are obtaned from the ntegral profle model.
1184 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 a Run 1; b Run 2; c Run 3; d Run 4 7 Temperature evoluton of the extrudate when t s extruded out of the de. It s therefore evdent that more attenton should be pad to the de land area whle gnorng the stress and stran feld at the extrudate far from the de land. When studyng surface crackng, the cut technology wll not nfluence any aspect of the smulaton, whch wll appear just as a smulaton performed wthout ths technology. The prncpal stress dstrbutons at dfferent extruson stages along the lne AB (as shown n Fg. 6) are shown n Fg. 10. Compared wth the longtudnal stress n paste extruson, whch s shown n Fg. 11, the dstrbuton of the longtudnal stress n hot alumnum extruson s dfferent. As can be seen from Fg. 11, the stress s lnear along the transverse drecton when the extruson rato s hgh n paste extruson, whle t s totally dfferent n the hot alumnum extruson. It can also be seen from Fg. 10 that the maxmum stress at the surface of the RUN 1 extruson s hgher than that of RUN 3, although the surface qualty s much better n RUN 1. Dscusson of crackng crtera If a crteron can explan the followng four phenomena, then t can be regarded as effectve n predctng the surface crackng whch occurs n hot extruson of alumnum alloy AA 2014. 1. Phenomenon 1 (P1): crackng occurs on the extrudate surface and s not seen at other locatons. 2. Phenomenon 2 (P2): the extruson suffers serous surface crackng durng extruson at hgh ntal temperatures, such as n RUN 3. It s not a serous problem for extruson at low ntal temperatures. 3. Phenomenon 3 (P3): n some cases, for nstance the RUN 2 extruson used n ths study, surface crackng occurs durng the mddle perod of the process and becomes more serous as the process contnues. 4. Phenomenon 4 (P4): the severty of crackng s less n the ndrect mode than n the drect mode. 8 Temperature evoluton of lne A B n extruson run 5
Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1185 a before cut; b drect extruson; c ndrect extruson; d end of drect extruson 9 Cut technology It should be recalled that a hgher value of damage parameter,.e. the C1 C6 mentoned above, ndcates a greater chance of crackng. If the assumed crtcal value does exst, then surface crackng wll occur f the predcted value s hgher than the crtcal value. PHENOMENON 1 As can be seen from Fg. 12a f, all smulatons, operatng wth dfferent crtera, gve the maxmum predcted value on the extrudate surface, and the predcted value decreases smoothly from the surface to the centre of the extrudate. The 10 Prncpal stress dstrbuton along lne A B at dfferent stages of hot extruson 11 Prncpal stress dstrbuton n transverse drecton n paste extruson at dfferent levels of extruson rato R (Ref. 14)
1186 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 a Oyane; b C L1; c C L2; d Ayada; e GW; f nstant Z; g surface crackng after crack functon trggered 12 Predcted values of crackng crtera maxmum predcted values also begn to appear near the reentrant de corner, whch can be seen n Fg. 12f. Itfollows that f there s a crtcal value for the crackng crteron, then ths value would be reached frst on the surface, accordng to all of the crtera adopted n ths study. Ths was llustrated after the crack functon of the software was trggered, as can be seen n Fg. 12g. Hence we may conclude that all of the crtera are effectve n predctng the frst phenomenon. PHENOMENON 2 However, as can be seen n Fgs. 13 17, these crtera, except the temperature crteron, do not permt predcton of the second phenomenon. Accordng to the crtera mentoned above, whch all assume there s a crtcal value for surface crackng, the crtcal value should be reached frst n the extruson of RUN 3, whch suffers the most surface crackng n the experments. However, as can be
Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1187 a Oyane; b C L1; c C L2; d Ayada; e GW; f nstant Z; g surface crackng after crack functon trggered 12 Predcted values of crackng crtera (cont.) seen n Fgs. 13 17, n whch the Oyane, C L, Ayada, and GW crtera are employed, the predcted value of RUN 3 s not the maxmum among all the predcted values. The predcted curves of the dfferent RUNs are convoluted and cannot be used to draw the concluson that RUN 3 suffers most from surface crackng. Meanwhle, for the crtera of Ayada and GW, as can be seen n Fg. 13, the predcted curve of the RUN 1 extruson has the hghest poston whle ths extruson has the best surface qualty n the experments. In Fg. 17, the curve of RUN 3 s a lttle lower than the curve of RUN 2, whle n experments the surface crackng whch happened n RUN 2 s less serous than that n RUN 3. The data shown n Fgs 13 15 were extracted from lne CD, as shown n Fg. 5, after the ram travelled the same dstance. The data shown n Fgs. 16 and 17 are extracted from the pont D, as shown n Fg. 5. PHENOMENON 3 It can be seen from Fgs. 18 20 that the frst three crtera,.e. Oyane, C L1, and C L2 crtera, are vald. The predcted peak values at the mddle of extruson are hgher than the maxmum value at the begnnng of extruson. It can also be seen from Fgs. 21 and 22, that the Ayada and GW crtera are obvously effectve. The predcted values of these two crtera are contnuously rsng through out the extruson, and ths corresponds wth the concept that f surface crackng occurs, t wll become more and more severe as the process proceeds. PHENOMENON 4 For the fourth phenomenon, t can be seen from Fgs. 16 and 17 that the Ayada and GW crtera are vald. For the
1188 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 15 Smulaton results usng C L1 crteron a Oyane; b C L1; c C L2; d Ayada; e GW; f nstant Z; g surface crackng after crack functon trggered 12 Predcted values of crackng crtera (cont.) 13 Smulaton results usng Oyane crteron 16 Smulaton results usng Ayada crteron 17 Smulaton results usng GW (Freudenthal) crteron 14 Smulaton results usng C L2 crteron smulaton results of RUN 5, these two crtera gve the predcted curve occupyng the lowest poston n the dagram. The temperature crteron s also vald n explanng the fourth phenomenon, as can be seen from Fg. 7. It has been dscussed prevously that the temperature rse durng extruson results n ncpent meltng of the second phase partcles, whch form an ntergranular network when rapdly quenched, resultng n a brttle product havng poor mechancal propertes. 16 18 Predcted value of Oyane crteron at dfferent stages
Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 1189 19 Predcted value of C L1 crteron at dfferent stages 22 Predcted value of GW crteron at dfferent stages 20 Predcted value of C L2 crteron at dfferent stages 23 Predcted value of Ln(Z r ) n Run 1 21 Predcted value of Ayada crteron at dfferent stages The other crtera are not effectve n predctng the fourth phenomenon. Dscusson of the emprcal crteron Because the emprcal method s regressed from all of the experments, t s evdent that t s effectve n predctng the 24 Predcted value of Ln(Z r ) n Run 2 phenomena 1, 2, 4, and 5 mentoned above. Meanwhle, f only judged from the Ln(Z ) value, t s dffcult to predct f surface crackng wll occur at the start of extruson or part way through extruson. However, wth the FEM predcted value of Ln(Z r ), ths problem can be solved, as dscussed below. It can be seen from Fgs. 23 26 that the predcted Ln(Z r ) value rses sharply at the begnnng of extruson, and then Table 5 Comparson of Ln(Z) values Extruson code Predcted peak value of Ln(Z r ) Predcted mnmum value of Ln(Z r ) Intal value of Ln(Z ) Crtcal value accordng to equaton (17) 1 32. 14 27. 19 31. 83 33. 65 2 27. 92 24. 74 27. 25 27. 83 3 25. 95 24. 68 24. 71 24. 54 4 24. 28 23. 02 23. 55 24. 38 5 18. 23 17. 52 24. 78
1190 Peng and Sheppard Surface crackng durng extruson of alumnum alloy AA 2014 25 Predcted value of Ln(Z r ) n Run 3 26 Predcted value of Ln(Z r ) n Run 4 decreases slowly throughout the remander of the process. It s worth pontng out that the Ln(Z r ) tme curve s smlar to the load tme curve, n whch the peak value appears at the start of extruson. As shown n Table 5, for RUNS 1 and 4, the predcted nstantaneous Ln(Z r ) value s lower than the crtcal value throughout extruson. For RUN 2, as can be seen from Fg. 25, the predcted peak value s hgher than the crtcal value at the start of extruson but decreases to values lower than the crtcal value at later stages of extruson. Fgure 26 ndcates that for RUN 3, the predcted value s hgher than the crtcal value throughout extruson. These experments correspond to real stuatons: the surface qualty remaned good throughout the whole process for runs 1 and 4, whle surface crackng occurred part way through extruson n RUN 2, and at the start of extruson n RUN 3. It can be seen from these dscussons that the combnaton of Ln(Z ) and Ln(Z r ) enables surface crackng to be predcted. If Ln(Z ) s hgher than the crtcal value gven by equaton (19), then surface crackng wll occur, and f Ln(Z r ) s hgher than the crtcal value throughout extruson, then the extrudate wll suffer from surface crackng throughout extruson. Conclusons The results are summarsed n Table 6. 1. Surface crackng s closely related to the temperature rse durng extruson. If the heat generated near the de land area ncreases the local temperature above the soldus pont, localsed meltng can occur, whch can cause severe crackng of the surface. Ths concluson s supported by many prevous studes. 1,15,16 2. Gven a so called crtcal value that depends on the ntal condton but not assumed unversal, the emprcal crteron can also predct all fve phenomena. Table 6 Valdty of crackng crtera Phenomenon Crteron 1 2 3 4 Oyane d X d X C L1 d X d X C L2 d X d X Ayada d X d d Freudenthal d X d d Temperature d d d d Emprcal d d d d d effectve; X nvald. 3. The other crtera (Oyane, C L, Ayada, etc.) cannot successfully predct all four crackng mechansms occurrng n hot alumnum extruson. Although they are capable of predctng some phenomena, all crtera except temperature and the emprcal formula faled to predct phenomenon 2. Recommendaton for further work In ths study, all work was performed usng axsymmetrcal extruson, however, the danger of crackng ncreases n shaped extruson near the re-entrant corners. In sectons contanng rbs, for example, whch s an extreme case, there s a danger of the rb dsntegratng. If the shape factor l, whch s used n equatons (13) and (14), s consdered n surface crackng phenomenon then further smulaton work s requred to establsh the ntal crackng condtons. In ths study, the FEM smulaton toolng s fxed and ths s obvously not the case n actual processes. More experments and smulatons wth deformable des are requred f further conclusons are to be drawn. References 1. t. sheppard: Extruson of alumnum alloys, Vol. 5, 205 245; 1999, Dordrecht, Kluwer Academc. 2. l. f. mondolfo, j. g. barlock and a. p. tomeo: Energes: J. Solar Energ. Soc. Am., 1976, 2, 365 386. 3. t. sheppard: Mater. Sc. Technol., 1993, 9, 430 440. 4. r. hambl and m. reszka: Int. J. Mech. Sc., 2002, 44, 1349 1361. 5. s. e. clft, c. e. hartley, n. sturgess and g. w. rowe: Int. J. Mech. Sc., 1990, 32, 1 17. 6. f. a. mcclntock, s. m. kaplan and c. a. berg: Int. J. Mech. Sc., 1996, 2, 614 628. 7. m. oyane, t. sato, k. okmoto and s. shma: J. Mech. Work. Technol., 1980, 4, 65 79. 8. m. g. cockcroft and d. j. latham: J. Inst. Met., 1968, 96, 2444 2477. 9. f. a. mcclntock, s. m. kaplan and c. a. berg: Int. J. Mech. Sc., 1966, 2, 614 630. 10. t. sheppard: Mater. Sc. Technol., 1999, 15, 459 463. 11. j. r. rce and d. m. tracey: J. Mech. Phys. Solds, 1969, 17, 201 218. 12. d. ko, b. km and j. cho: J. Mater. Process. Technol., 1996, 62, 166 174. 13. a. t. domant, d. j. horrobn and j. brdgeater: J. Mech. Sc., 2002, 44, 1381 1410. 14. m. g. tutcher and t. sheppard: Met. Technol., 1980, 7, 488 493. 15. s. j. paterson: The drect and ndrect extruson of alumnum alloys, Vol. 4, 262 280; 1981, London, London Unversty. 16. t. sheppard and r. p. verod: Mater. Sc. Technol., 1985, 1, 321 324.
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