Ansoropc Behavors and Is Applcaon on Shee Meal Sampng Processes Welong Hu ETA-Engneerng Technology Assocaes, Inc. 33 E. Maple oad, Sue 00 Troy, MI 48083 USA 48-79-300 whu@ea.com Jeanne He ETA-Engneerng Technology Assocaes, Inc. 33 E. Maple oad, Sue 00 Troy, MI 48083 USA 48-79-300 qhe@ea.com Keywords: Ansoropc, Type of Deformaon, Shee Meal -9
Ansoropc Behavors and Is Applcaon on Shee Meal Sampng Processes ABSTACT Basc behavors of ansoropc properes of maerals, relang o shee meal forg processes, are dscussed. The -value s used o descrbe some forg problems ncludng wrnkles and hnnng falures. Accordng o he analyss resuls, o pon ou ha he ansoropc behavors of maerals affec he formably of blanks n some cases s very serous. Fnally, a numercal example s presened o dscuss hs propery furher. INTODUCTION Durng shee meal forg, ansoropc properes of a maeral usually exhb wo dfferen forms. One s concerned wh he hardenng behavor when measured along wo dfferen drecons on he plane of he shee, meanng he relaonshp of he sress and sran s dfferen n dfferen drecons due o he ansoropc properes of he maeral. Anoher ansoropc propery s he dfferen hnnng values when measured along he plane of he shee nsead of hrough he hckness drecon. These dreconal properes are all named as ansoropc properes of maerals. Because he properes are defned as he ables of maerals o keep a hgh locaon of a forg lm dagram (FLD), o ress hckness change and o decrease wrnkle falures, ha means dfferen ansoropc properes wll lead no dfferen forg resuls and formably. In hs paper, we only dscuss dfferen hnnng behavors depended on he ansoropc properes and he -values of maerals n a requred drecon commonly used o descrbe hese problems durng shee meal forg. As a maer of fac, shape of yeldng spaces, hnnng of formed blanks and wrnkles are all bascally depended on he -values when he ansoropc properes of a maeral are presen. So we descrbe he ansoropc problems jus around he -values. APPOACH Because of he ansoropc properes presen, many characerscs based on he plasc deformaon wll be changed, such as he yeldng curve, sran space, hnnng and ec. These basc behavors mus be undersood frs, f users wan o apply he ansoropc properes o enhance forg processes. Sress and sran spaces depended on dfferen -values In order o smplfy analyses, suppose ha he ansoropc properes of he maeral are he same n he plane of he shee, bu dfferen from he hrough hckness. Hlls (948) yeld creron s used o dscuss he ansoropc properes of maeral, whch s expressed by he followng: ù û é + F( σ ) = σ = σ + σ σ σ + σ () ê + + ë If we selec σ, σ, σ33 as he prncpal sresses, Eq. () can be rewren by: -30
ù û é F( σ ) = σ = σ ê + σ σ σ () + ë Fgure shows several changng yeld curves due o he selecon of dfferen -values under he complex sress componens wh he same effecve sress. smple enson sae σ σ = 5 = = 0 σ Fgure. Sress space wh dfferen -values If he deformaon heory of he sress and sran s seleced o descrbe a sran space wh wo prncpal srans of shee plan, he sran equaon can be gven by he followng: é ù F( ) = = ê + + (3) ë û Ths s a plane prncpal sran ellpse. Wh he same effecve sran and several dfferen - values, several correspondng sran loc are shown n Fgure. smple enson locus = 0 = = 5 Fgure. Sran space wh dfferen -values From pons on Fgure and, we can classfy some conclusons as follows: -3
a. essan forces of plasc deformaon are ncreased wh he bgger -values when he sresses are dsrbued around wo-srech sae. b. Plasc deformaons are easy o exrac due o he bgger -values n he sress sae wh one srech sress and one compresson sress. c. The -value s changed o be bgger, he deformaon area combned a enson sress wh a compresson sress s smaller. Srans behavors relang o he wrnkle and hnnng falures If we wan o use he ansoropc properes of maerals o mprove he formably of pars, we mus know how he propery behavors are concerned wh forg falures. Forg falures caused by he ansoropc properes usually are wrnkles and hckness hnnng. Wrnkles. Wrnkles are one ype of forg falures. From a mechancs pon of vew, he wrnkles are caused by he compresson nsably, bu no all he compresson nsably condons resul n he wrnkle falures durng shee meal forg. In fac, he wrnkle falures wh many cases are mosly depended on he geomery of pars and maeral properes of blanks. If he geomery of pars and maeral properes of blanks are mached well, he wrnkle problems can be reduced fully. Now we dscuss he wrnkle problems jus around a deformaon area n shee plane wh one elongaon and compresson. When a deformaon pon on a blank s sreched no a de cavy durng a sampng process, a srechng sran and a planar sran n s vercal drecon wll be generaed. Supposng d(geo) s a geomery changng values a he same pon and has he same drecon as. If he wrnkles are no be caused durng he forg process, he sran sae mus sasfy he relaonshp shown below: = d( geo) (4) From Fgure, we know ha he value depends on he -value wh he same sran and he same effecve sran. Accordng o Eq. (3) and he ncompressble assumpon of volume, he sran can be gven as: = ( ) (5) When he deformaon s a smple enson ype, he effecve sran s equal o he or sran. The or sran s: = and gα = =, (6) + (smple enson ype of deformaon) From Fgure 3 and Eq. (6), we see ha he all deformaon areas wh one enson and one compresson sress wll approach a pon and become o he plane sran sae when he - value s close o zero or o nfny. Tha s: -3
hckness, hckness, 0, ( ) 0, ( 0) (7) plane sran sae α = α 0 α 5 α = ( smple enson sae) plane sran sae Fgure 3. Srans varyng wh dfferen -values The bgges changng area of he values s beween he plane sran sae and he smple enson sae. In order o avod he wrnkles caused durng he sampng processes, he bgges -value should be se up vercally around he bgges d(geo) value drecon as far as possble. If an opmal sae can be se up on some cases, you should oban an unexpeced resul. I s a very valuable work o use he ansoropc properes for mprovng he sampng processes, n parcular for some specal pars. Thnnng. In erms of he ncompressble assumpon of volume, we have: ( hckness 33 ) = ( ) ( ) (8) Subsung Eq. (8) no Eq. (3), an equaon relaed wh he or sran and hckness sran s shown as: é = ê + 33 + ë ù 33 û (9) Ths s an ellpse equaon also, whch we named as a hnnng ellpse. Is half long-axs A and half shor-axs B are gven respecvely as: é ù ê ( ) A = ê ê( ) ç æ 3 + ( ) 4 ö ë è + øû (0) é ù ê ( ) B = ê ê( ) ç æ 3 + + ( ) 4 ö ë è + øû -33
Fgure 4 dsplays he shapes of wo ellpses ( several dfferen -values. ellpse and ellpse) wh ellpse ellpses overlap ellpse ellpse = ellpse β hck =0 = 0 β hnnng = 30 Fgure 4. Thnnng Behavor Based on Ansoropc Propery oaon angles of he hnnng ellpse compared wh he prncpal sran ellpse n he shee plane can be descrbed by an equaon below: gβ = () When he angle β s beween he long axs of he ellpse wh he ordnae, whch s hckened angle β hck assocaed wh and beween he long axs of he ellpse wh he abscssa, whch means hnned angle β hn assocaed wh, hey are shown n Fgure 4 a, b and c. Accordng o he dsplay n Fgure 4, some rules concerned abou srans varyng can be concluded as follows: ellpse roaes clockwse when he -value s bgger han. The - a. The value s bgger, he roaon angle s smaller and he value s smaller. b. The ellpse and ellpse overlap wh =, whch means he ellpse equaon wh one ordnae value vs. wo abscssa values and ; ellpse roaes couner-clockwse when he -value s smaller han. c. The The hnnng values ncrease faser wh smaller -values. The hnnng value s bgges when =0. Numercal examples FEA smulaon for shee meal forg can be used o easly calculae he forg resuls o repea he se up o dfferen maeral properes. Usng he ansoropc properes of he maerals, commonly relaes o ha wo man works o be done successfully, meanng: frs, esmae he remanng capacy of he formed blank; second, selec an opmal croppng shape based on he shee rollng drecon. The numercal example descrbed n he followng pages wll dscuss he ansoropc effecs for calculang resuls dependng on he se up of a blank wh dfferen posons based on he rollng drecon. -34
Blanks, de and calculang resuls. Fgure 5 shows forg ools and wo blanks wh a dfferen rollng drecon. The Y-coordnae s he rollng drecon. Blank dameer s φ 50 mm. Thckness s 0.5mm. Parameers of he ansoropc propery are 0 =.87, 45 =.7 and 90 =0.7. The blank s formed by a square cup de wce, each me wh a dfferen holdng force 5KN or 0KN. Fnal forg deph s 60mm. Fgures 6 hrough dsplay some calculang resuls wh dfferen holdng forces and drawng dsances. (a) Sample (b) Sample Fg.5 Blank shape wh a dfferen rollng drecon se up Fg.6 Forg resuls wh a small drawng dsance and small holdng force Fg.7 Forg resuls wh a small drawng dsance and bg holdng force -35
Fg.8 Forg resuls of he fnal sep wh a small holdng force Fg.9 Forg resuls of fnal sep wh large holdng force Fg.0 FLD wh a small drawng dsance and large holdng force Fg. FLD of a fnal forg sep wh large holdng force -36
DISCUSSION From Fgures 6 hrough, we noce a good formably can be obaned when seng up he larges -value drecon along he larges drawng force drecon, ha s along four urnng corners (Sample ). Ths s an area ha plasc flowng of shee meal s more dffcul o deere. Wh hs poson, he hnnng rae of he forg blank s smaller han anoher one, as well as he forg load. Due o s well formably, s nsensve for some processng parameers, such as holdng force, hs blank also receved sasfacory fnal resuls wh wo dfferen holdng forces. Ths propery s very valuable for engneerng producon. If he blank s se up n a dfferen poson based on he rollng drecon, we receved compleely dfferen forg resuls, see pcure (b) n Fgures 6 o. For hs case, he larger -values are se up on fla sdes. Is formably s unsasfacory. The plasc flow propery becomes bad and he hnnng rae of he blank ncreases. Accordng o a resul shown n Fgure 0 (b), he punch moved a small dsance and he par sared o be spl. CONCLUSIONS Almos all he shee seels seleced as he formed blank exhb he ansoropc properes. The -value can be used o descrbe her behavors durng forg processes, ncludng yeldng space, wrnkles and hnnng falures. Some resuls are concluded as follows: a. essan forces of plasc deformaon are ncreased wh he larger -values when he sresses are dsrbued around wo-srech sress sae. b. Plasc deformaons are easy o exrac due o he larger -values n he sress sae wh one srech sress and one compresson sress. c. When he -value s changed o be larger, he deformaon area, combned a enson sress wh a compresson sress, s smaller. d. If he wrnkles are no caused durng he forg process, he changng rae of he blank geomery mus sasfy he sran rae n he same drecon a he same area. e. The ellpse can be used o descrbe he hnnng behavors. When roaes n clockwse ha means he -value s larger han. The -value s larger, he roaon angle s smaller and he hnnng value s smaller. The ellpse roaes n couner-clockwse ha means he -value s smaller han. The hnnng values ncrease faser wh smaller -values. When =0, he hnnng value s bgges. The ellpse overlap wh =, whch ellpse and means he ellpse equaon wh one ordnae value and. EFEENCES vs. wo abscssa values Johnson, W. and P. B. Mellor (973), Engneerng Plascy, Grea Bran. Wang, Z.. (989), Fundamenal of Plasc Workng Mechancs, Naonal Defense Press, Bejng. -37
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