Variation of Normal Anisotropy Ratio "r" during Plastic Forming

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1 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, Pape eceived: UDC Pape accepted: Vaiation of Nomal Aniotopy Ratio "" duing Platic Foming Silav Alekandovi * - Milentije Stefanovi - Dagan Adamovi - Vuki Lazi Univeity of Kagujevac, Faculty of Mechanical Engineeing, Seia Cold olled thin heet metal ae typical aniotopic mateial a a conequence of the poduction poce of olling. Aniotopy i uually decied fom two apect: a plane aniotopy and a a nomal one. Mot fequently ued aniotopy paamete i the nomal aniotopy atio o the value, which epeent tain atio in heet metal plane and along it thickne. It i detemined expeimentally, uually a mean contant numeic valu, without teting the poile vaiation in dependence on ealized platic tain. Accuate defining of the value ha geat ignificanc, ince it i not only the fomaility paamete, ut alo the cucial aniotopy paamete in oftwae fo imulation of the platic foming poce. The pape peent the eult of expeimental invetigation of thee typical mateial: low caon Al killed teel DC04 heet metal, alloy AlMg4.5Mn0.7 heet metal and tainle teel X5CNi18-10 heet metal. Paticula attention i given to defining the dependence of the value on platic tain duing the foming poce. The expeiment equie ophiticated device and accuate calculation. In the actual cae, the computeized meauing ytem Zwick/Roell Z 100 wa ued. In addition, the pape contain the popoal on how to take into account vaiation of the value duing the platic foming poce Jounal of Mechanical Engineeing. All ight eeved. Keywod: heet metal, aniotopy, value 0 INTRODUCTION Cold olled heet metal ae vey ignificant in moden induty. Regiteed expot of cold olled teel heet metal (including coated one) in 2006 wa 71.9 million ton on the gloal level [1]. Total poduction of pimay aluminum in the wold in 2007 wa 38.7 million ton [2]. Appoximately one quate of that quantity i poceed into thin heet, foil excluded [2]. Due to complex metallugical poce of olling and it tuctual pecific, thin heet metal have pominent aniotopy, i.e., inequality of diffeent chaacteitic depending on the conideed diection in volume. Since heet metal ha a pecific geomety, two dimenion in plane which ae ignificantly lage than the thid dimenion thickne, aniotopy i conideed fom two apect: in heet metal plane and pependicula to that plane, along thickne. In the fit cae, one efeent diection, mot often the olling diection and two othe coeponding diection ae defined with epect to the olling diection. Thoe mot often ae at 45 and 90 o with epect to the olling diection. Fo each of thee diection, the neceay mateial chaacteitic ae detemined, like the elaticity modulu, yield tength, tenile tength, tain at factue, the mean value, tain hadening exponent, etc. The majo diffeence in thei diffeence along diffeent diection indicate the ignificant influence of plane aniotopy. The econd cae i elated to the o-called nomal aniotopy, i.e., the diffeence in heet metal tain in plane and along it thickne. The quantitative indicato of that diffeence i the nomal aniotopy atio o the value, which i vey impotant fo heet metal. In aniotopic platicity theoy, tating with the Hill appoach and including all the othe [3] and [4], it i ued in almot all impotant elation. In pactice, it i an oligatoy paamete of the heet metal fomaility y deep dawing. Apat fom theoy, the value i vey impotant fo the functioning of all the oftwae fo compute imulation of platic foming poce. It i detemined only expeimentally, y uniaxial tenion poce, accoding to pope tandad pocedue, like ASTM E 517, EN B etc. Uually, the eult i a contant numeic value, which epeent the mean value duing the meauement o the value that coepond to elation at the end of the foming poce. The following quetion i eaonale: what hould e done if thee ae mateial fo which the change of the value duing the 392 * Co. Autho' Adde: Univeity of Kagujevac, Faculty of Mechanical Engineeing, S. Janji 6, Kagujevac, Seia, a@kg.ac.

2 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, poce ae pominent? Thee vaiation can have the geatet ignificance in oftwae fo compute imulation. Accoding to [3], not a ingle moden commecial oftwae contain implemented value that vay with tain, fo diffeent mateial. The aim of thi pape i to point to the natue of thoe vaiation of the value in typical cold-olled heet metal and to popoe how thoe vaiation hould e taken into account. 1 PROCEDURE FOR DEFINING THE VALUE The value i defined a the atio of tue platic tain of width ( ) and tue platic tain of thickne ( ) of pecimen at uniaxial tenile tet: 0 d d ln ln 0 ln log 0 0 ln log, (1) whee 0 and 0 ae the initial value of pecimen width and thickne, epectively, and and ae tue value of width and thickne, epectively, which contain only platic tain. Due to high enitivity of the value to mall meauement eo and mall meauement ae of heet metal thickne, utitution of the / 0 atio i uually pefomed accoding to the well-known potulate of platicity theoy on volume invaiaility: l0 0 0 l cont., (2) whee l 0 i the initial value of the pecimen gauge length, and l i the tue value of gauge length, which contain only the platic tain. Finally, the expeion fo calculating the value ha the following fom: ln ln. (3) l0 l ln ln l l In the claic pocedue fo detemining the value, the pecimen i defomed up to maximally allowed tain, and afte that unloading i pefomed, followed y the emoval of pecimen off the teting device and accuate meauement of length and width accoding to 0 0 tandad ecommendation. Theefoe, the otained value i elated to the end of the foming poce, and it coepond to the maximal tain. The ituation i moe complex when thee i a need to meaue platic tain of length and width imultaneouly duing the pecimen foming poce 5. Since the pecimen i contantly unde load, the meauing ytem mut contantly pefom coection in the ene of eliminating the elatic potion of tain. One method fo olving that polem i given in [6]. The following expeion epeent a imple poiility fo coecting the width and length of gauge pat of the pecimen due to influence of elatic tain. Due to that influence, the width i deceaed and it need to e inceaed, while the length i inceaed and it need to e deceaed., (4) pl tot pl tot P, (5) E whee tot i the total width (it contain oth platic and elatic pat); el epeent elatic change of width which i lot duing unloading; tot i the total change of width, which i uually meaued duing the expeiment; P i Poion atio, i the nominal te, and E i the elaticity modulu. el l l pl ltot lel, (6) l pl l0 ltot l ; E (7) l 0 whee l tot i the total gauge length, which contain oth platic and elatic pat; l el epeent the elatic change of gauge length, which i lot duing unloading; l tot i total change of gauge length, which i uually meaued duing the expeiment. 2 THE EXPERIMENT The main chaacteitic of thi expeiment the eult of which ae peented in thi pape, i an attempt to define, a accuately a poile, the dependence of the value on ealized platic tain duing uniaxial tenion poce fo thee cold olled heet metal intended fo deep dawing. The neceay condition fo uch an expeiment i a ophiticated equipment Alekandovi, S. - Stefanovi, M. - Adamovi, D. - Lazi, V. 393

3 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, of high accuacy and eliaility. Hee, thi i the meauing ytem fo teting mateial - Zwick/Roell Z 100 with pneumatic jaw. Fo detemining the value, two tanduce ae ued: extenomete fo meauing elongation type TC- EXMACRO.H01, Zwick/Roell, with gauge length 10 to 100 mm, accuacy aove 1 m, accoding to EN gade 1 and extenomete fo meauing the change of width type TC-EXICLWD.001, Zwick/Roell, meauement ange 1.5 to 11.5 mm with accuacy aove 1m, accoding to EN gade 0.5 [7]. The pecimen wee pepaed accoding to the tandad fo uniaxial tenile tet EN with initial gauge length L 0 = l 0 = 80 mm, paallel ide length L c = 120 mm and initial width 0 = 20 mm. The tet wa pefomed in line with ecommendation of tandad EN and EN B, whoe egulation ae implemented in oftwae TetXpet ve. 10, which ait the pecified meauing ytem. Fig. 1 how the wok pace of teting machine with the pecimen and oth extenomete in woking poition. Fo detemining the value, the mot impotant condition i to have the poce to occu within the limit of homogenou foming. Fo low caon teel heet metal it wa accepted that homogenou foming limit would e the tain of 20%. Fo the Al alloy and tainle heet metal that can e diffeent, o it i neceay to cay out additional teting. The value i vey enitive to meauement accuacy. Small eo in the meaued tain caue a lage eo in the detemined value. Accoding to [8], if the coefficient of width meauement vaiation i aout 0.1% the etimated coefficient of vaiation of i 40 to 70 time lage, i.e., 4 to 7%! Thi i the main eaon fo uing the highly accuate, ophiticated and eliale teting device. Pio to meauement of the value dependence on the value of tain, it wa neceay to detemine all the impotant mechanical popetie of heet metal: elaticity modulu, yield tength (R p ), tenile tength (R M ), tain at maximal foce (A g ), tain at factue (A) and tain hadening exponent (n). The influence of plane aniotopy wa oeved y defining the thee diection in heet metal plane: the olling diection, 0 o, and diection at 45 and 90 o with epect to the olling diection. Specimen wee pepaed and pope chaacteitic wee detemined fo each diection. Fig. 1. Wok pace of teting machine with the pecimen and oth extenomete 3 RESULTS AND DISCUSSION Baic mechanical popetie of all the teted mateial ae given in Tale 1, 2 and 3. The fit mateial i low caon aluminum killed teel heet DC04, thickne 0 = 0.8 mm, the econd i aluminum alloy heet eie 5000 AlMg4.5 Mn0.7 in annealed tempeed tate, thickne 0 = 1.0 mm and the thid i the tainle autenitic teel heet X5CNi 18-10, thickne 0 = 0.7 mm. The influence of plane aniotopy on the value hould e pointed out. In claic low-caon heet metal, uch a invetigated DC04, the mallet value i fo diection, which i at 45 o with epect to the olling diection. The influence thi on fomaility y deep dawing i well known, paticulaly in ectangula geometie. If the poition of non-defomed heet metal, i.e., lank, i adjuted o that the pecified diection of 45 o goe along the middle of lateal ide, and much moe favoale diection of 0 and 90 o with highe value ove the cone zone, ette eult ae achieved: lage dawing atio, fewe defect, etc. 394 Vaiation of Nomal Aniotopy Ratio duing Platic Foming

4 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, Tale 1. Popetie of DC04 heet metal DC04 (Mat. N o , DIN EN 10130) 0 = 0.8 mm Angle L 0 0 S 0 E R P0,2 R m A g A n [] [mm] [mm] [mm 2 ] [GPa] [MPa] [MPa] [%] [%] Mean value Tale 2. Popetie of AlMg4.5Mn0.7 heet metal EN AW-5083 (AlMg4.5Mn0.7-0 ; Mat. N o , DIN EN 573-3) 0 = 1.0 mm Angle L 0 0 S 0 E R P0,2 R m A g A n [] [mm] [mm] [mm 2 ] [GPa] [MPa] [MPa] [%] [%] Mean value Tale 3. Popetie of X5CNi heet metal X5CNi18-10 (Mat. N o , DIN EN 10088) 0 = 0.7 mm Angle L 0 0 S 0 E R P0,2 R m A g A n [] [mm] [mm) [mm 2 ] [GPa] [MPa] [MPa] [%] [%] , Mean value Fo Al alloy, a well a fo tainle teel, in the diection of 45 o with epect to the olling diection the value i maximal. Fo Al alloy fom eie 5000, to which the alloy ued hee elong, value ae mall: 0.62 to 1. In uch condition, heet metal i vey pone to thinning, which i unfavoale fo foming y deep dawing fom the technological apect [9]. The teted tainle autenite teel heet metal ha omewhat highe value: 0.82 to 1.15, ut it fomaility i elatively ad a well, epecially when compaed to low-caon teel heet metal [10]. In cetain cae, like the deep dawing of the axially ymmetic piece, it i convenient to ue the mean value accoding to fomula X=(X 0 +2X 45 +X 90 )/4, whee X efe to the value of the coeponding chaacteitic in diection at 0, 45 and 90 o with epect to the olling diection. In that way, one take into account the plana aniotopy 11, ut the effect of the fictituou iotopy ae alo otained. The mean value defined in thi way, hould e applied cautiouly, afte an analyi of each concete foming poce. Fo intance, in deep dawing of the ectangula hape, it i moe adequate to ue value of chaacteitic coeponding to each diection. The mean value ae peented in the lat ow in Tale 1 to 3. The Fig. 2 to 10, how the main expeimental eult. Dependencie of the value and natual, tue, width platic tain on tue platic length tain duing the pecimen foming poce ae given. Fig. 2 to 4 how vey good lineaity of natual width tain, and elatively mall change of value duing the poce. Impotant divegence occu only in the zone of vey mall tain, up to 2% appoximately. It hould e emphaized that accoding to the definition of the value, expeion (3), it value i unknown at the eginning of the poce (= 0 and l=l 0, theefoe =0/0). Conequently, at low-caon teel heet metal, adoption of the mean value a contant duing the entie poce doe not lead to majo eo. Vaiation of Nomal Aniotopy Ratio duing Platic Foming 395

5 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, DC04 0 =0.8 mm ; 0 o AlMg4.5Mn0.7 0 =1 mm ; 0 o ,10 0,15 0,20 Fig. 2. Dependence of the value and tue width tain on tue tain fo heet metal DC04, 0 o with epect to the olling diection (RD) 5 0,10 0,15 0,20 Fig. 5. Dependence of the value and tue width tain on tue tain fo heet AlMg4.5 Mn0.7, 0 o to the olling diection DC04 0 =0.8 mm ; 45 o AlMg4.5Mn0.7 0 =1 mm ; 45 o ,10 0,15 0,20 Fig. 3. Dependence of the value and tue width tain on tue tain fo heet DC04, 45 o to RD 5 0,10 0,15 0,20 Fig. 6. Dependence of the value and tue width tain on tue tain fo heet AlMg4.5 Mn0.7, 45 o to the olling diection DC04 0 =0.8 mm ; 90 o AlMg4.5Mn0.7 0 =1 mm ; 90 o ,10 0,15 0,20 Fig. 4. Dependence of the value and tue width tain on tue tain fo heet DC04, 90 o to RD Fig. 5 to 7 how the pominent ocillatoy vaiation of value which i in line with width change and well-known ocillatoy chaacte of tenion cuve, which ae not hown hee. It i completely clea that the utitution of uch 5 0,10 0,15 0,20 Fig. 7. Dependence of the value and tue width tain on tue tain fo heet AlMg4.5 Mn0.7, 90 o to the olling diection dependence with contant value lead to ignificant eo and neglect of the tue mateial ehavio. Appoximation of the expeimentally otained dependence can e done y inuoidal peiodic function, in the following fom: 396 Alekandovi, S. - Stefanovi, M. - Adamovi, D. - Lazi, V.

6 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, av a in k 2 (8) max min av 2 (9) max min a, 2 (10) whee av, a ae the aveage and amplitude value of, epectively; k the empiic contant which define nume of peiod; max, min maximal and minimal value of ; = l tue platic tain. Fo dependence in Fig. 6 appoximation (8) ha the fom: = in(320). In thi cae, k = 160, which mean that function fo ha 16 peiod within 0 to 0.1 ange of tue tain, Fig. 8. AlMg4.5Mn0.7 0 =1 mm ; 45 o = *in(320) -9 whee B and a ae contant which can e appoximately detemined in the following way: m a m ; B, (12) a a whee the ucipt m denote the elected value of and in the diagam. 5 0,10 0,15 0,20 Fig. 9. Dependence of the value and tue width tain on tue tain fo heet X5CNi 18-10, 0 o to the olling diection X5CNi =0.7 mm ; 0 o X5CNi =0.7 mm ; 45 o ,10 0,15 0,20-9 Fig. 8. Sinuoidal appoximation of the value dependence fo heet AlMg4.5Mn0.7, 45 o to the olling diection Fig. 9 to 11 how the dependencie of heet metal X5CNi18-10, which coepond to peviou diagam. Fo 0 o with epect to the olling diection, the dependence cuve of value inceae monotonouly, Fig. 9. Fig. 10 how mall vaiation of the value, o it i acceptale to adopt the mean contant value. The cuve of the value vaiation in Fig. 11 ha a lightly deceaing chaacte with tain inceae on acia axi. Adoption of the mean contant value lead to a mino eo, which i acceptale. Dependence of the in Fig. 9 can e appoximated y the function of the following fom: a B, (11) 5 0,10 0,15 0,20 Fig. 10. Dependence of the value and tue width tain on tue tain fo heet X5CNi 18-10, 45 o to the olling diection Fo the actual cae in Fig. 9, the following function ae otained: = ; m = 0.1 and m = 0.799, = ; m = max = and m = max = 0.833, = ; m = 0.15 and m = All the thee function ae imila in natue, ut the fit one i moe convenient accoding to expeimental cuve, Fig. 12. Vaiation of Nomal Aniotopy Ratio duing Platic Foming 397

7 Stojniški vetnik - Jounal of Mechanical Engineeing 55(2009)6, Fig. 11. Dependence of the value and tue width tain on tue tain fo heet X5CNi 18-10, 90 o to the olling diection 5 0,10 0,15 0,20 Fig. 12. Appoximation of the value dependence fo heet X5CNi 18-10, 0 o to the olling diection X5CNi =0.7 mm ; 90 o X5CNi =0.7 mm ; 0 o =1.006* 0.1 X5CNi =0.7 mm ; 0 o = *ln -9 Fig. 13. Appoximation of value dependence fo heet X5CNi 18-10, 0 o towad olling diection Since all the expeimental cuve of the value dependence ae otained in digital fom like numeic eie, duing meauing, fo vey accuate defining of appoximation function it i ,10 0,15 0, ,10 0,15 0,20 poile to ue appopiate mathematical method, like the leat quae method. Fo the dependence of the value fom Fig. 9, the logaithmic appoximation in oftwae Statitica give the following function: = log = ln, ee Fig. 13. Log i the ign fo the common logaithm, while ln i the ign fo the natual logaithm. 4 CONCLUSION The nomal aniotopy atio, the value, epeent a vey impotant chaacteitic of cold olled thin heet metal. So fa, it ha een geneally accepted that it i a contant numeic value and a uch, it ha een ued a an indicato of fomaility of heet metal y deep dawing and popety of mateial in oftwae fo a numeic imulation of a platic foming poce. Thi pape ha hown, aed on a ophiticated expeiment, that paticula mateial, like the Al alloy heet metal and tainle autenite heet metal, how ignificant vaiation of the value duing the foming poce. That impoe the need to ue adequate appoximation function, ome of which wee popoed in thi pape. Thu, it i neceay to ue a vey accuate expeiment in ode to detemine dependency of the value on platic tain duing the foming poce, and then to ue pope method in ode to define the convenient appoximation function, which tuly expee aniotopic ehavio of mateial. 5 REFERENCES [1] Januay [2] Januay [3] Roll, K., Wiegand K. Poiilitie of the imulation of foming pocee in the heet metal foming, Poc. of Intenational Confeence on New Development in Sheet Metal Foming, Stuttgat, 2008, p [4] Gome, C., Onipede, O., Lovell, M. Invetigation of pingack in high tength aniotopic teel, Jounal of Mat. Poc. Technology, 2005, 159, p [5] Štok, B. Vh, M. Halilovi, M. Impact of young modulu degadation on pingack 398 Alekandovi, S. - Stefanovi, M. - Adamovi, D. - Lazi, V.

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